Riverbank Erosion Hazards and Channel Morphodynamics: A Perspective of Fluvial Geomorphology 9781032010496, 9781032233079, 9781003276685

Table of contents :
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of figures
List of plates
List of tables
Abbreviations
Foreword
Preface
Acknowledgements
Chapter 1 Introduction to fluvial geomorphology: A review
Chapter 2 River basin morphometry: A quantitative study
Chapter 3 Channel geometry and channel bed configuration
Chapter 4 Hydraulic geometry of a channel
Chapter 5 Modelling riverbank erosion hazards
Chapter 6 Channel stability and instability
Chapter 7 Riverbank erosion hazards and human vulnerability
Chapter 8 Channel migration zones identification and suitable site selection: A scientific approach for suitable site selection for human habitation
Index

Citation preview

Riverbank Erosion Hazards and Channel Morphodynamics

This book explores fluvial processes and their consequences on river dynamics in India. It discusses the integration of geomorphic, hydrologic, and socio-economic data with various policies and decisions regarding sustainable river basin management. The volume looks at the origin and development of streams, chronology of fluvial geomorphology, fluvial system concept, process–form interaction, river dynamics, channel migration, flow regime, channel types, and hydraulic and morphometric parameters; and explains how changing hydro-geomorphological dynamics have influenced land use patterns, nature of fluids, behaviour of floods, etc. It examines channel migration vulnerability and bank erosion hazard vulnerability of the Torsa River in the eastern region of India as a case study using channel migration zone and Bank Erosion Hazard Index models. The book presents a new research framework based on field surveys, scientific investigations, and analytical techniques and methods to interpret key geoinformatics data. With its extensive illustrations, this book will be useful to students, teachers, and researchers of geography, earth sciences, environmental geology, and environment and disaster management. It will also interest geographers, civil engineers, hydrologists, geomorphologists, planners, and other individuals and organizations working on fluvial processes and riverbank erosion problems globally. Sourav Dey is Assistant Professor, Department of Geography, Darjeeling Government College, Darjeeling, West Bengal, India. He has served as a guest lecturer at Dewanhat Mahavidyalaya, and Thakur Panchanan Mahila Mahavidyalaya, Cooch Behar, West Bengal. He completed his PhD at the University of Gour Banga, Malda, West Bengal, and was awarded the Junior Research Fellowship by the University Grants Commission. He specializes in fluvial geomorphology and has published several research articles in journals and book chapters in edited volumes. He is a life member of the Indian Institute of Geomorphologists, Allahabad, India. Sujit Mandal is Professor of Geography and Dean, Faculty of Science, Diamond Harbour Women’s University, West Bengal, India. He was formerly a professor at the University of Gour Banga, West Bengal. He completed his PhD at Vidyasagar University, and specializes in applied geomorphology, soil geography, environmental hazards and disasters, and geospatial technology. He is the author of more than 70 research articles published in journals, and three internationally published books. He is the principal investigator of a Minor Research Project sponsored by the University Grants Commission and a Major Research Project sponsored by the Indian Council of Social Science Research. He has been associated with several academic and administrative bodies.

Riverbank Erosion Hazards and Channel Morphodynamics A Perspective of Fluvial Geomorphology

Sourav Dey and Sujit Mandal

First published 2022 by Routledge 4 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 605 Third Avenue, New York, NY 10158 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2022 Sujit Mandal The right of Sujit Mandal to be identified as author of this work has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Disclaimer: The international boundaries, coastlines, denominations, and other information shown in any map in this work do not necessarily imply any judgement concerning the legal status of any territory or the endorsement or acceptance of such information. For current boundaries, readers may refer to the Survey of India maps. Every effort has been made to contact owners of copyright regarding the text and images reproduced in this book. Perceived omissions if brought to notice will be rectified in future printing. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record has been requested for this book ISBN: 978-1-032-01049-6 (hbk) ISBN: 978-1-032-23307-9 (pbk) ISBN: 978-1-003-27668-5 (ebk) DOI: 10.4324/9781003276685 Typeset in Times New Roman by Deanta Global Publishing Services, Chennai, India

Dedicated to all well-wishers

Contents

List of figures List of plates List of tables Abbreviations Foreword Preface Acknowledgements

viii xiv xvi xviii xix xx xxii

1

Introduction to fluvial geomorphology: A review

1

2

River basin morphometry: A quantitative study

32

3

Channel geometry and channel bed configuration

83

4

Hydraulic geometry of a channel

111

5

Modelling riverbank erosion hazards

130

6

Channel stability and instability

157

7

Riverbank erosion hazards and human vulnerability

178

8

Channel migration zones identification and suitable site selection: A scientific approach for suitable site selection for human habitation

228

Index

271

Figures

1.1 1.2 1.3 1.4 1.5 1.6 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16

A complex hydrologic model system An idealized fluvial system A process-based channel classification scheme Process of lateral migration of an alluvial channel Rivers of India Location of Torsa River basin, India (A) Stream ordering map of the Torsa River basin. (B) Sub-basins of the Torsa catchment Relationship between stream order and number of streams in the Torsa River basin Relationship between stream order and stream length in the Torsa River basin Relationship between stream order and mean stream length in the Torsa River basin Relationship between stream order and cumulative mean stream length in the Torsa River basin (A) Stream frequency map of the Torsa River basin. (B) Drainage density map of the Torsa River basin Drainage texture map of the Torsa River basin (A) Constant of channel maintenance map of the Torsa River basin. (B) Length of overland flow of the Torsa River basin (A) Drainage intensity map of the Torsa River basin. (B) Infiltration number map of the Torsa River basin (A) Elevation zone map of the Torsa River basin. (B) Absolute relief map of the Torsa River basin (A) Average slope map of the Torsa River basin. (B) Relative relief map of the Torsa River basin (A) Dissection index map of the Torsa River basin. (B) Ruggedness index map of the Torsa River basin Roughness index map of the Torsa River basin Percentage hypsometric curve of the Torsa River basin Cross-section lines across the Torsa basin Cross profiles of the Torsa River basin

7 8 12 15 19 23 35 38 39 39 40 52 54 55 57 60 61 63 65 66 67 68

Figures 2.17 Longitudinal profile of the Torsa River basin 2.18 Correlation matrix showing the relationship between selected morphometric parameters 2.19 Scree plot 2.20 Prioritized rank map of the Torsa River basin using (A) morphometric parameters and (B) principal component analysis 2.21 Scree plot 2.22 Landscape diversity map of the Torsa River basin based on (A) weighted composite analysis and (B) principal component analysis 3.1 Location of the field sites along the Torsa River in the study area 3.2 Channel cross-sections at (A) Jaigaon, (B) Hasimara, and (C) Chilapata along the Torsa River in a downstream direction 3.3 Channel cross-sections at (A) Silbarihat, (B) Patlakhawa Protected Forest, and (C) Putimari Baksibas along the Torsa River in a downstream direction 3.4 Channel cross-sections at (A) Basdaha Natibari and (B, C) Sajherpar along the Torsa River in a downstream direction 3.5 Channel cross-sections at (A) Sajherpar Ghoramara and (B, C) Salmara 3 along the Torsa River in a downstream direction 3.6 Channel cross-sections at (A) Hokakura, (B) Haripur, and (C) Madhupur along the Torsa River in a downstream direction 3.7 Seasonal and temporal changes of cross-sections of the Torsa River at Basdaha Natibari (site 7) during (A) 2016, (B) 2017, and (C) 2018 3.8 Seasonal and temporal changes of cross-sections of the Torsa River at the confluence of Mora Torsa (site 8) during (A) 2016, (B) 2017, and (C) 2018 3.9 Seasonal and temporal changes of cross-sections of the Torsa River at downstream NH-31 bridge (site 9) during (A) 2016, (B) 2017, and (C) 2018 3.10 Superimposed profiles of the Torsa River along the crosssections of (A–C) site 6, (D–F) site 9, and (G–I) site 31 in three consecutive seasons from 2016 to 2018 3.11 Long profile along the Torsa River from Silbarihat to Balarampur 3.12 Long profile along the thalweg in the Torsa River 3.13 Seasonal channel width variations in the Torsa River and their statistical inference with downstream progress 3.14 Downstream seasonal pattern of channel depth of the Torsa River 3.15 Thalweg orientation of the Torsa River channel (2017) in the downstream 3.16 Downstream seasonal pattern of wetted perimeter of the Torsa River 3.17 Downstream distribution of the channel slope in the Torsa River 3.18 Seasonal patterns of cross-sectional area of the Torsa River 3.19 Seasonal patterns of hydraulic radius of the Torsa River 3.20 Downstream width–depth ratio along the Torsa River

ix 69 70 74 75 78 78 85 86 87 88 88 89 90 91 92 93 94 94 95 95 97 98 98 98 99 100

x

Figures

3.21 3.22 3.23 3.24 3.25 3.26 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 5.1 5.2 5.3 5.4 5.5 5.6

Grain size distribution of the Torsa River bed from sites 1 to 6 Grain size distribution of the Torsa River bed from sites 25 to 30 Bathymetric characteristics of the Torsa River, 2016 Bathymetric characteristics of the Torsa River, 2017 Bathymetric characteristics of the Torsa River, 2018 Changes of channel bathymetry from (A) 2016 to 2017 and (B) 2017 to 2018 Downstream seasonal variations of mean surface flow velocity (2017) of the Torsa River Spatio-temporal variation of flow velocity along the different transects of the Torsa River Seasonal variation of (A) velocity and (B) discharge Statistical correlation between the (A) channel slope and mean velocity of low surface flow velocity and (B) channel slope and mean bankfull surface flow velocity of the Torsa River Seasonal patterns of discharge of the Torsa River Spatio-temporal variation of discharge along the different transects of the Torsa River Downstream unit stream power along the Torsa River Downstream bed shear stress along the Torsa River Relation between (A) Reynolds number and riverbank erosion and (B) Froude number and riverbank erosion Relation between discharge and suspended load (A) Surface velocity distribution and (B) near-bed velocity distribution of the Torsa River, 2016 (A) Surface velocity distribution and (B) near-bed velocity distribution of the Torsa River, 2017 (A) Surface velocity distribution and (B) near-bed velocity distribution of the Torsa River, 2018 Vertical velocity profile in the Torsa River (A) at pool and (B) riffle sections Cross channel distribution of the flow velocity in the Torsa River at (A) Basdaha Natibari, (B) Sajherpar, and (C) Salmara during the pre-monsoon, 2017 Location of the BEHI and NBS bank sample segments Measurement procedure of Bank Erosion Hazard Index parameters Various BEHI parameters: (A) bank height/bankfull height, (B) root depth/bank height, (C) root density, (D) bank angle, and (E) surface protection Reach-wise BEHI scores for individual bank sample segments along the Torsa River: (A) reach 8, (B) reach 9, (C) reach 10, and (D) reach 11 Reach-wise BEHI scores for individual bank sample segments along the Torsa River: (E) reach 12, (F) reach 13, and (G) reach 14 Bank erosion hazard vulnerability zone map through BEHI

102 103 104 105 106 108 112 112 113 114 115 115 116 116 120 122 125 126 127 127 128 132 138 141 143 144 145

Figures 5.7 Bank erosion hazard vulnerability zone map through NBS 5.8 Number of sample segments under different (A) BEHI and (B) NBS ratings 5.9 The bank-wise BEHI and NBS ratings are separately synchronized for each sample segment: (A) left bank and (B) right bank 5.10 Relation of riverbank erodibility (BEHI) and total erosion rate of the Torsa River 5.11 Relation of NBS and total erosion rate of the Torsa River 5.12 Model validates using ROC for (A) bank erosion hazard zone (BEHI) and (B) near-bank stress (NBS) 6.1 Incision ratio 6.2 Lateral stability characteristics of different locations of the Torsa River 6.3 Overall lateral stability characteristics of different locations of the Torsa River 6.4 Model validation using ROC curve for (A) lateral stability and (B) overall lateral stability 6.5 Vertical stability characteristics of different locations of the Torsa River 6.6 Overall vertical stability characteristics of different locations of the Torsa River 6.7 Model validation using ROC curve for the (A) vertical stability model and (B) overall vertical stability model 6.8 Overall reach stability characteristics of the Torsa River 7.1 Ternary diagram determining the soil texture of the bank material 7.2 Riverbank stratigraphy at Basdaha Natibari (left bank) 7.3 Riverbank stratigraphy at Basdaha Natibari (right bank) 7.4 Riverbank stratigraphy at Jatrapur (right bank) 7.5 Near-bed velocity distribution and bank erosion in the Torsa River in (A) 2016, (B) 2017, and (C) 2018 7.6 Surface velocity distribution and bank erosion in the Torsa River in (A) 2016, (B) 2017, and (C) 2018 7.7 Relation between near-bank bed velocity and riverbank erosion in (A) 2016, (B) 2017, and (C) 2018 7.8 Relation between near-bank surface velocity and riverbank erosion in (A) 2016, (B) 2017, and (C) 2018 7.9 Vertical bank profiles of the left bank and right bank show the magnitude of bank erosion in the Torsa River near the upstream of Mora Torsa 1 confluence (at reach 9) 7.10 Bank erosion has been detected in reaches 1 to 14 of the Torsa River from 2017 to 2019 7.11 Erosion along the right and left bank of the Torsa River at (A) reach 1, (B) reach 2, and (C) reach 3 from 2017 to 2019

xi 146 146 150 151 151 153 159 165 166 167 170 171 172 176 192 193 194 195 199 200 201 202 205 206 207

xii

Figures

7.12 Erosion along the right and left bank of the Torsa River at (A) reach 4, (B) reach 5, and (C) reach 6 from 2017 to 2019 7.13 Erosion along the right and left bank of the Torsa River at (A) reach 7, (B) reach 8, (C) reach 9, and (D) reach 10 from 2017 to 2019 7.14 Erosion along the right and left bank of the Torsa River at (A) reach 11, (B) reach 12, (C) reach 13, and (D) reach 14 from 2017 to 2019 7.15 The percentage of erosion along the left and right bank of the Torsa River from reach 1 to 14 in (A) 2017, (B) 2018, and (C) 2019 7.16 The rate of bank erosion from reaches 1 to 14 along the Torsa River 7.17 The area affected by bank erosion and avulsion in the Aratguri mouza in (A) 2001, (B) 2001–2010, (C) 2010–2013, (D) 2013– 2017, and (E) 2018. (F) Glimpse of the Aratguri mouza 7.18 The area affected by bank erosion and avulsion in the Deutibari mouza in (A) 2001, (B) 2001–2010, (C) 2010–2013, (D) 2013– 2017, and (E) 2018. (F) Glimpse of the Deutibari mouza 7.19 The area affected by bank erosion and avulsion in the Hokakura mouza in (A) 2001, (B) 2001–2010, (C) 2010–2013, (D) 2013– 2017, and (E) 2018. (F) Glimpse of the Hokakura mouza 7.20 The area affected by bank erosion and avulsion in the Haripur mouza in (A) 2001, (B) 2001–2010, (C) 2010–2013, (D) 2013– 2017, and (E) 2018. (F) Glimpse of the Haripur mouza 7.21 The area affected by bank erosion and avulsion in the Damodarpur mouza in (A) 2013, (B) 2013–2017, and (C) 2018. (D) Glimpse of the Aratguri mouza 7.22 Number of plots that have been recently eroded due to bank erosion in the (A) Damodarpur and (B) Haripur mouzas from 2017 to 2019 7.23 Vulnerability spider diagram showing the Overall Livelihood Vulnerability Index (LVI) for eight mouzas and three municipal wards (Cooch Behar) of the study area 7.24 Vulnerability spider diagram showing the Livelihood Vulnerability Index-Intergovernmental Panel on Climate Change (LVI-IPCC) for eight mouzas and three municipal wards (Cooch Behar) of the study area 8.1 (A) The ES is determined through estimating the riverbank erosion rate. (B) The GS is intended to account for a riverbank composed of erodible material that will adjust to a more stable configuration from bank erosion processes, such as slumping and collapsing 8.2 Spatial allocation of the Torsa River course: (A) 1913, (B) 1943, (C) 1955, and (D) 1972 8.3 Spatial allocation of the Torsa River course: (A) 1977, (B) 1990, (C) 2001, and (D) 2010 8.4 Spatial allocation of the Torsa River course: (A) 2013 and (B) 2018

208 210 211 212 213 216 217 218 219 220 221 224

225

234 238 239 240

Figures 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 8.15 8.16 8.17 8.18 8.19

8.20 8.21

Changing course of the Torsa River from 1913 to 2018 The historical migration zone map during the period 1913 to 2018 The historical migration zone map during the period 1913–1955 The historical migration zone map during the period 1972–2018 Avulsion hazard zone map Estimation of erosion hazard area by cross-sectional study Erosion hazard area map based from (A) 1913 to 2018 and (B) 1972 to 2018 Expected bank line of the Torsa River from (A) 1913 to 2018, and (B) 1972 to 2018 Disconnected migration area of the Torsa River Channel migration zone map from (A) 1913 to 2018 and (B) 1972 to 2018 Vulnerability of the mouzas to channel migration of the Torsa River based on HMZ: (A) 1913 to 2018 and (B) 1972 to 2018 Vulnerability of the mouzas to channel migration of the Torsa River based on CMZ: (A) 1913 to 2018 and (B) 1972 to 2018 The human habitat suitability factors of the Torsa River floodplain: (A) slope, (B) altitude, (C) geology, and (D) soil The human habitat suitability factors of the Torsa River floodplain: (A) distance from the fault line, (B) drainage density, (C) distance from river, and (D) distance from road The human habitat suitability factors of the Torsa River floodplain: (A) land use/land cover, (B) distance from CMZ, (C) bank erosion vulnerability sites based on BEHI, and (D) bank erosion vulnerability sites based on NBS Flow chart of methodology Suitability map for human habitation in the lower course of the Torsa River basin

xiii 241 242 243 244 246 247 248 250 251 252 253 254 255 256

258 259 260

Plates

3.1 3.2 4.1 5.1 5.2

5.3 5.4 6.1 6.2

7.1 7.2 7.3 7.4

Measurement of (A) channel depth, (B) flow velocity during the non-monsoon and (C) monsoon, and (D) near-bed flow velocity Bed material at field sites (A) 3, (B) 14, and (C) 22 Flow diversion in the Torsa River at reach 10 (A) Collection of primary data through cross-sectional study and (B) GPS survey. (C) Measurements of near-bank slope by clinometer and (D) levelling instrument (A) Construction of embankment along the left bank. (B) Collection of primary data of different parameters. (C) Meeting of important tributary (Kaljani River) with the Torsa River. (D) Formation of turbulent flow during monsoon (A) Primary and secondary flows. (B) Mechanism of bank toe erosion due to formation of secondary flow during bankfull conditions in the Torsa River at Damodarpur mouza (A) Riverbank protected by boulder netting and (B) non-cohesive bank material (A) Measurement of bank height, (B) measurement of bank angle by clinometer, and (C) glimpse of deep-rooted vegetation at Patlakhawa Protected Forest (A) Formation of ripple marks near the confluence of the Kaljani River, (B) formation of helical flow beneath the bridges to accelerate vertical degradation at Sajherpar, and (C) riparian vegetation with embankment near Basdaha Natibari Removal of material from the base of the bank by hydraulic action during high discharge Slab-type bank failure along the Torsa River during the bankfull stage at Kamrangaguri Stages (1 to 3) of bank material removal and toppling process in the Torsa River at the Damodarpur mouza Rotational-type bank failure in the Torsa River during the bankfull stage at Cooch Behar municipal ward 16

86 101 124 133

134 135 136 164

165 180 181 182 183

Plates 7.5 7.6

7.7 7.8 7.9

7.10 7.11

7.12 7.13 7.14

8.1 8.2 8.3 8.4

(A) Slip of bank material over bank foot and (B) slip of slab due to parallel flow attacks after removal of basal support along the Torsa River (A) Failure of non-cohesive bank material underlying cohesive material at Salmara, and (B) undercutting of non-cohesive bank material along the Torsa River at Balabhut near the IndoBangladesh border Cantilever-type bank failure along the Torsa River during the bankfull stage at Balabhut Formation of several tension cracks on the top of the bank before cantilever failure (A) Sheet and rill erosion in the less vegetated exposed surface at Cooch Behar municipal ward 16. (B) Sheet erosion occurred during flooding in 2017 in the less vegetated exposed surface at Harinchawra Rill formation along the Torsa River at (A) Cooch Behar municipal ward 18 and (B) Harinchawra mouza (A) Block failure at Hokakura. (B) Crab-hole erosion through subsurface flow. (C) Removal of the underlying non-cohesive material has led to collapse of the embankment at Deocharai. (D) Gravity collapse due to removal of subsurface support along the Torsa River (A) Wet earth flow of the Torsa River at Deotibari. (B) Dry sands sweeping away at high velocity of wind under fluvial environment at Deocharai (A) Soil sample collected from the riverbank. (B) Sieves used for grain size analysis. (C) Measurement of bank profiles Glimpses of the study area show (A, B) loss of houses and lands due to riverbank erosion, (C) households that are affected by flooding, (D) char land households that are affected by river erosion, and (E, F) structures of the houses in the riparian areas (A) Avulsion at Hokakura during 2017 flood, (B) construction of embankment along the left bank of the Torsa River at Karisal, and (C) 2017 flooding Reach scale channel avulsion during the (A) 2010 flood and (B) 2017 flood Bank stratigraphy of the Torsa River at Harinchawra Loss of lands and houses due to bank erosion of the Torsa River (A) during flooding in 2017 in municipal ward 18 and (B) during flooding in 2018 in the Damodarpur mouza

xv

184

185 185 186

186 187

187 188 192

223 236 245 249 257

Tables

1.1 1.2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20

Scale, source, and examples of stressors that may affect fluvial processes and geomorphology Channel patterns and their characteristics Stream order-wise number of streams of the Torsa River basin and its tributary sub-basins Bifurcation ratio of the Torsa basin and its tributary sub-basins Weighted mean bifurcation ratio of the Torsa River basin Log of some linear parameters of the Torsa River basin Weighted mean stream length ratio of the Torsa River basin Channel sinuosity of the Torsa River and its tributaries based on the Schumm model Channel sinuosity and stage of basin development of the Torsa River and its tributaries based on the Muller model Rho coefficient and hydrologic storage capacity of the Torsa River and its tributaries Form factor and ellipticity index of the Torsa River basin and its tributary sub-basins Values of circularity and elongation ratios for the Torsa River and its tributaries Lemniscate ratio and shape index for the Torsa River and its tributaries Compactness coefficient for the Torsa River and its tributaries Basin relief, gradient ratio, relief ratio, and Melton ruggedness number for the Torsa River and its tributaries Average dissection index and stage of cycle of erosion in the Torsa basin and its tributary sub-basins Average values of morphometric parameters of the Torsa River basin and its tributary sub-basins Prioritization of sub-basins and their ranks using morphometric parameters Total variance explained of the Torsa sub-basins Pattern matrix Prioritization of sub-basins and their ranks using PCA Total variance explained

9 13 35 36 37 40 41 43 44 45 46 47 48 49 58 63 64 72 73 74 75 77

Tables xvii 2.21 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 6.4 6.5 7.1 7.2 7.3 7.4 7.5 7.6 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

Component matrix Froude numbers and Reynolds numbers Flow character of the Torsa River between field sites 7 and 9 Correlation between hydraulic parameters Variation of stream energy in the downstream direction (2016–2018) Seasonal and temporal variation of the nature and pattern of the stream flow (2016–2018) Temporal variation of discharge and suspended load Temporal variation of discharge and bed load Different models of riverbank erosion estimation Allocated index values for the individual parameters to develop Bank Erosion Hazard Index (BEHI) Converted values to develop near-bank stress (NBS) ratings Annual riverbank erosion measured through BEHI and NBS Estimation of area under the curve (AUC) for BEHI and NBS Lateral stability characteristics of different locations in the Torsa River Measurement of stability ratings based on the degree of incision Vertical stability characteristics of different locations in the Torsa River Reach stability characteristics of different cross-section segments in the Torsa River Overall reach stability characteristics of the Torsa River Factors influencing riverbank erosion Statistics of grain size of bank material in the Torsa River Statistics of grain size of bed material in the Torsa River Eroded area in the different reaches of the Torsa River (2017–2019) Statistics on the loss of houses at short time intervals Statistics of bank erosion at short time intervals Status of channel migration along different cross-sections (1913–2018) Status of channel migration along different cross-sections (1972–2018) Saaty’s pairwise comparison scale Criteria pairwise comparison matrix Normalized matrix Weight of each criterion Calculations of weighted columns Random index (RI) Confusion matrix table of site suitability classes for human habitation

77 113 117 117 119 121 122 123 131 137 139 147 153 160 168 169 173 174 189 191 196 209 214 215 232 233 260 262 263 264 265 266 267

Abbreviations

AHP AHZ AUC BEHI CMVZ CMZ DMA EHA ES GIS GPS GS GSI HMZ IPCC LULC LVI NBS PCA PF ROC RPFA SB SOI USGS WCA

analytical hierarchical process avulsion hazard zone area under curve Bank Erosion Hazard Index channel migration vulnerability zone channel migration zone disconnected migration area erosion hazard area erosion setback geographic information system Global Positioning System geotechnical setback Geological Survey of India historical migration zone Intergovernmental Panel on Climate Change land use and land cover Livelihood Vulnerability Index near-bank stress principal component analysis protected forest receiver operating characteristic river presence frequency approach sub-basin Survey of India United States Geological Survey weighted composite analysis

Foreword

I am extremely pleased to introduce this impressive book, Riverbank Erosion Hazards and Channel Morphodynamics: A Perspective of Fluvial Geomorphology, by Sourav Dey and Sujit Mandal. This volume is a collection of rigorous research outputs organized into eight chapters. The authors have generated a huge data set by intensive research work through efforts over a long time and have analyzed their findings with state-of-the-art techniques. All chapters are academically rich and technically sound. The authors emphasize understanding the process–form relationship in bank erosion and predicting potential bank erosion zones. The volume is well structured and rationally presented, and the text is concise and clearly written. Geomorphologists are interested in understanding the process–form relationship to explain the working of rivers under different boundary conditions. Flux boundary conditions and their imprint on seasonal as well as temporal channel geometry are scrutinized in detail. The patterns of channel dynamics observed from imageries and prepared maps are explained through contemporary as well as historical fluvial and anthropogenic processes with high proficiency. Mapping of channel migration zones and identifying the vulnerable areas are important policy inputs for local administrations and engineers as well as policymakers who are working to manage this problem. The authors associate the problem of river shifting and bank erosion to the life and livelihood of the community. They also identify some suitable sites for rehabilitation. From this perspective, their research findings are socially relevant. Thus, the present volume is an exceptional and brilliant instance of academic endeavour of the writers in fostering the quest for understanding the process– form relationship in geomorphic study, promoting rigorous research pursuits, advancing geomorphic understanding, and applying this understanding for societal benefit. Ramkrishna Maiti Professor, Department of Geography, Vidyasagar University Midnapore, West Bengal, India

Preface

Riverbank erosion is a widespread phenomenon in the fluvial environment of a river basin, especially in the Himalayan foothills. The channel morphology of the river frequently changes as a result of channel migration, channel avulsion, and riverbank erosion. The aim of this work is to evaluate and understand channel morphodynamics, and the process and extent of riverbank erosion and its vulnerability analysis in the Eastern Himalayan foothills. Soil erosion prioritization and landscape diversity of a river basin, cross-sectional analysis and channel morphodynamics, hydraulic geometry and fluid dynamics, the process and factors of riverbank erosion, causes and effect of channel avulsion, riverbank stability, near-bank stress, segment- or reach-wise channel stability and instability, channel migration and bank erosion vulnerability, livelihood vulnerability, and suitable site selection for human habitation have been studied and estimated in detail using the following suitable techniques or models. Chapter 1 offers a brief history of geomorphology, the concept of a fluvial system, and an introduction to the fluvial process and bank erosion hazards. Chapter 2 includes river basin morphometric analyses, such as linear, areal, and relief aspects; prioritization of the sub-basin; and landscape diversity of the river basin. Chapter 3 contains cross-sectional analysis and channel morphodynamics, channel geometry, grain-size analysis, and changes of channel bathymetry. Chapter 4 deals with the hydraulic geometry of a channel, stream energy, the nature and pattern of channel flow, load transportation, and fluid dynamics of a river. Next, Chapter 5 discusses riverbank erosion hazards, near-bank stress, bank erosion hazard vulnerability, and the rate of bank erosion. Chapter 6 covers the lateral stability and vertical stability of a river, and the overall reach stability of a river. Chapter 7 examines the types and processes of riverbank erosion, different factors of bank erosion, analysis of bank stratigraphy, temporal study of riverbank erosion, channel avulsion, riverbank erosion hazard, and livelihood vulnerability. Finally, in Chapter 8, the assessment of channel migration, causes of change of channel course, channel migration vulnerability, and suitable site selection for human habitation are elaborated. Morphometric parameters and principal component analysis (PCA) have been applied for prioritization of sub-basins. Weighted composite analysis and principal component analysis have been applied to create a landscape diversity

Preface xxi model. To assess the channel migration zone (CMZ), several methods have been used, including construction of the historical migration zone (HMZ), avulsion hazard zone (AHZ), erosion hazard area (EHA), and disconnected migration area (DMA). Two methods, the Bank Erosion Hazard Index (BEHI) and near-bank stress (NBS), have been used to determine the riverbank instability as well as the bank erosion vulnerability of the Torsa River. Channel stability was assessed using the lateral stability, vertical stability, and overall reach stability models. The Livelihood Vulnerability Index (LVI) and Livelihood Vulnerability IndexIntergovernmental Panel on Climate Change (LVI-IPCC) have been used to determine the livelihood vulnerability of riparian and island households. The analytical hierarchical process (AHP) was applied as a decision-making tool for the identification of suitable human habitation sites. The Torsa River basin is highly elongated, which indicates a low flatter peak flow for longer duration, low erosion, and low capacities of sediment transport. The landform of the Torsa basin is approaching towards the equilibrium stage of basin development and 70% of the basin area has been eroded by the different agents of denudation. The cross-sections of the foothills river are asymmetrical in shape and tend to create a wide V-shape valley, and there has been no specific trend of change within the channel. The channel flow is mostly turbulent in nature during the monsoon in the study area. The riparian areas are vulnerable to channel migration and riverbank erosion hazards. The common bank erosion types in the study are cantilever failure, rotational failure, and slab failure. Extreme nearbank bed velocity increases the scouring process near the bank, which leads to increased cantilever failure, toppling, and undercutting processes. The applied models can be performed and adopted by researchers for further channel morphodynamics and riverbank erosion assessment in the fluvial environment of the Himalayan foothills. This study finds that expansion of human settlement should be considered beyond the channel migration zone and bank erosion hazard vulnerability zone. A detailed understanding of geomorphological processes is significant to address riverbank erosion processes and it also helps to identify suitable sites for human settlement and human development activities in the river basin. The result of this work will be extremely helpful to researchers, geomorphologists, hydrologists, engineers, policymakers, planners, and other concerned authorities working on the aspects of channel morphodynamics and riverbank erosion and their associated problems in the fluvial environment.

Acknowledgements

This is our opportunity to acknowledge the inspiration of all the well-wishers and critics who have propelled us to be continually motivated for excellence in the activities that we have undertaken. We are grateful to all those persons who encouraged us directly or indirectly. We extend our deepest sense of gratitude to Professor Sunando Bandyopadhyay of the University of Calcutta, India; Professor Ramkrishna Maiti of Vidyasagar University, India; and Professor Veena Joshi, Department of Geography, S.P. Pune University, India, for their continuous motivation, inspiration, and valuable suggestions in our study of fluvial geomorphology. We are grateful to the Survey of India (SOI) for providing us topographical maps corresponding to the study area. We must pay our sincere thanks to the Geological Survey of India for contributing geological settings of the study area. We are grateful to the National Bureau of Soil Survey and Land Use Planning Department for supplying soil maps and land use maps. We extend our thanks to the National Atlas and Thematic Mapping Organization (NATMO) for providing geomorphological maps of the Torsa River basin. We express our deepest sense of gratitude to the United States Geological Survey (USGS) for providing us the scope to access digital elevation model (DEM) data and other satellite data all along the study. Our thanks also go to the Indian Meteorological Department (IMD) for contributing rainfall data, which has helped in understanding the climatic condition as well as channel discharge of the Torsa River. Sourav Dey and Sujit Mandal

1

Introduction to fluvial geomorphology A review

Fluvial geomorphology is the study of various topographic features due to erosion, transportation, and deposition of sediments by a river. There is a close interaction between water, sediments, and catchment boundaries which make distinct features, such as bed forms, cross-sectional geometries, and planforms, in a channel. Continuous changes in the processes and forms in a river basin take place. In any river basin, the geomorphological evolution is a usual and natural process. Streams are dynamic and increasingly important part of the physical environment. Their behaviour is of interest to a broad diversity of concerns, ranging from flood control, navigation, and development of water resources to recreation. Streams represent a potential risk to human beings and property through floods and bank erosion. Rivers are dynamic units whose characteristics differ over time and space with changes in the environmental controls. The character and behaviour of a fluvial system at any particular location reflect the integrated effect of a set of upstream controls, notably climate, geology, land use, and basin physiography, which together determine the hydrologic regime and the quantity and type of sediment supplied (Knighton, 1984). The physical background of a river basin is a part of the geographical elements which play very significant roles in controlling the geomorphological and hydrological phenomena in the river basin. In the watershed area, stream anatomy and interactions are the reflection of the relief, geology, tectonic characteristics, structural geology, geomorphology, climatic condition, nature of soil texture and structure, and riparian vegetation. Tectonic characteristics generate the relief that drives the erosional mechanisms which provide a gargantuan amount of sediment on a river, causing channel avulsion and change of channel gradient (Schumm, 2005). Geology and climate control the discharge and sediment load, which influence the channel geometry (Knighton, 1984). The overall geometry of a stream channel is controlled by the climate and geology of a river basin. Climate is a controlling factor in determining the stream type and hydraulic geometry (Schumm, 2005). Morphometric and hydraulic characteristics as well as the behaviour of discharge of any river channel are largely dependent on monthly and annual patterns of rainfall. Variation of the discharge character of a stream is influenced by climatic factors and physical characteristics of a basin (Knighton, 1984). The bank erosion rate and its spatio-temporal distribution mostly depend on geology, DOI: 10.4324/9781003276685-1

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Introduction to fluvial geomorphology

soil (e.g. size, gradation, cohesivity, and stratification of bank sediments), climate (e.g. amount, intensity, and duration of rainfall), and vegetation (e.g. type, density, and root system) (Knighton, 1984; Maiti, 2016). Bank erosion affects the socio-economic status of the human population in the fluvial environment. At present, the integration between physical and social parameters has become much more significant in the field of geographical research and can help regional planning and development. Alluvial streams are very dynamic landforms subject to rapid change in channel configuration and flow pattern. Higher stream energy channels and less consolidated riverbank and bed materials are most dynamic and susceptible. Stream channels interact with many geographical factors, like climate, topography, lithology, vegetation, land use, and area of catchment. The river basin is a set of morphological attributes, for example, divides, valley side slopes, stream gradients, channel spacing, and floodplains. In a morphological system, the river basin at different parts is considered as the meaningful arrangements of these morphological attributes (Maiti, 2016). The elements of the morphological structures are statistically related one to other, e.g. valley side slopes and stream gradients are directly related to the abundance and spacing of channels (Schumm, 1977). Changes in fluvial morphology may be due to land use changes and human interventions, for example, engineering constructions, cultivation, deforestation, and flooding. Destructive floods can modify stream-channel morphology nearly instantly.

A brief history of geomorphology and fluvial geomorphology Geomorphology deals with the study of the earth’s surface, i.e. landforms, and their origin, evolution, and the processes that shape them. The history of geological and geomorphological investigations can serve to illustrate both the progress and pitfalls involved in the scientific understanding of the earth’s surface and recent geological history (Oldroyd and Grapes, 2008). Giovanni Targioni-Tarzetti (1712–1783) in Italy, Jean-Etienne Guettard (1715–1786) in France, Mikhail Lomonosov (1711–1765) in Russia, and James Hutton (1726–1797) in Scotland established the link between geomorphology and geology. Fluvial geomorphology is the geomorphology of rivers and a significant branch of geomorphology. The history of mankind is closely connected with the history of fluvial geomorphology. The history of fluvial geomorphology started to develop in ancient times with the history of river development. In ancient times, the content of fluvial geomorphology was the normal geomorphologic phenomena of rivers, but at present fluvial geomorphology has developed as the mathematical and engineering geomorphology of rivers. A primary objective of fluvial geomorphology is to explain the relationship among the physical properties of flow in mobile-bed channels, the mechanics of sediment transport driven by the flow, and the alluvial channel forms created by spatially differentiated sediment transport. Graf (1988) opined that geomorphology is the study of earth surface forms and processes and fluvial phenomena related to running water. The science seeks to investigate the complexity of behaviour of river channels as a range of scales from

Introduction to fluvial geomorphology 3 cross-sections to catchments; it seeks to investigate the range of processes and responses over a very long time scale but usually within the most recent climate cycle (Newson and Sear, 1998). Geomorphology is the main branch of physical geography. It is a spatial science dealing with time and space. It is also deals with the origin of the earth’s topographic features caused by various geomorphic processes, e.g. fluvial, glacial, coastal, aeolian, and periglacial. Fluvial geomorphology is concerned with the creation of landforms by river processes through the removal and transfer of materials on the earth’s surface. Process studies are rooted in a number of disciplines, the earliest identifying ‘processes’ as evolutionary time sequences in landforms. Fluvial systems exist over a range of scales, from centimetre-wide intertidal channels and other drainage networks on a sandy beach to the more than 6 million km2 drainage basin of the Amazon. All such systems are complex, self-organizing, and hierarchical in structure. Modelling complex behaviour in hierarchical systems does commonly incorporate lower level ‘process rules’, and this underlies the need in fluvial geomorphology for improved understanding of process mechanisms at all levels. Catchment factors (varying the gradient, sediment, and discharge at individual sites) affect local processes, which in turn may operate to change the character and extent of catchments. Since the 4th century BC, many people have studied the formation of the earth. Ancient Greeks and Romans, such as Aristotle, Strabo, Herodotus, Xenophanes, and many others, demonstrated the origin of valleys, formation of deltas, presence of seashells on mountains, etc. based on their field observations. Traditionally, the history of the development of landscapes was carried out by mapping the sedimentary and morphological features. For understanding the evolution of landscapes, the golden rule ‘the present is the key to the past’, which was propounded by Scottish geologist James Hutton in 1785, has been followed. This rule assumes that the processes that are visible in action today must have occurred in the past also and can be used to infer the reasons for formation of the landscape in the past. Hutton in 1785 provided a meaningful thought in regard to earth surface processes whereby soil and rock are eroded from the land to the sea. Later on, John Playfair (1748–1810) not only rescued Hutton’s ideas from relative obscurity but also contributed to the original ideas of Hutton on the nature and behaviour of river systems. Charles Lyell (1797–1875), in his influential three volume treatise Principles of Geology (1830–1833), emphasized the differential erosive powers of rivers and discussed cases where river systems did not divide simply like the branches of a tree, but cut through higher ground or occupied the eroded axes of anticlines. The word geomorphology was first coined and used between the 1870s and 1880s. It became popular when William Morris Davis propounded the concept ‘geographical cycle of erosion’ in 1889, also known as the ‘Davis cycle of erosion’ or ‘complete cycle of river life’. A lot of work has been accomplished in the field of functional and historical geomorphology. In the present day, many other fields of geomorphology have emerged, including tectonic geomorphology, submarine geomorphology, planetary geomorphology, climatic geomorphology,

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Introduction to fluvial geomorphology

and modelling geomorphology. Powel in 1875 explored a genetic classification of river valleys and consequently classified them into antecedent, superimposed, and consequent valleys, and propounded the significant concept of ‘limit of maximum vertical erosion’ by streams and proposed the term ‘base level’. Following the concepts of Powel, Mallot in 1928 opined three types of base levels: ultimate, local, and temporary. Gilbert (1877, p. 112) wrote: Let us suppose that a stream endowed with a constant volume of water is at some point continuously supplied with as great a load as it is capable of carrying. For so great a distance as its velocity remains the same, it will neither corrode (downward) nor deposit, but will leave the grade of its bed unchanged. But if in its progress it reaches a place where a less declivity of bed gives a diminished velocity, its capacity for transportation will become less than the load and part of the load will be deposited. Or if in its progress it reaches a place where a greater declivity of bed gives an increased velocity, the capacity for transportation will become greater than the load and there will be corrosion of the bed. In this way a stream which has a supply of debris equal to its capacity, tends to build up the gentler slopes of its bed and cut away the steeper. It tends to establish a single uniform grade. Gilbert was the first geoscientist who opined the concept of the ‘graded profile of a river’ and found the relationship between stream load, velocity, and gradient based on quantitative measurements. Clarence Edward Dutton (1841–1912) and Grove Karl Gilbert (1843–1918) incorporated the cycle erosion theory of a river of W.M. Davis (1889, 1899). Davis’s work was appreciated by Chorley et al. (1973) who treated the work as a comprehensive historical study of geomorphology. According to Davis, for a ‘mature’ river ‘a balanced condition is brought about by changes in the capacity of a river to do work, and in the quantity of work that the river has to do’ (1902, p. 86). King (1953) interpreted the development of landscape primarily in terms of scarp recession or parallel retreat of hillslope, and opined that steep slopes are shaped by gravity and turbulent water flow (e.g. in gullying), whereas pediments, the typical landform of erosional plains, are the result of surface water flow (sheet wash), capable of transporting sediment and ‘smoothing’ the bedrock. Geomorphology was started to study the various processes and landforms with a solid quantitative footing in the middle of the 20th century. Following the concept of Gilbert’s uniform grade, several researchers (e.g. William Walden Rubey, Ralph Alger Bagnold, Hans Albert Einstein, Frank Ahnert, John Hack, Luna Leopold, A. Shields, Thomas Maddock, Arthur Strahler, Stanley Schumm, and Ronald Shreve) around the world in the 20th century started to study landform elements considering systematic, direct, and quantitative measurements of various aspects of rivers and hillslopes (Ritter et al., 1995). Quantitative fluvial geomorphology involves fluid dynamics and solid mechanics, geomorphometry, laboratory studies, field measurement, and landscape

Introduction to fluvial geomorphology 5 evolution through time. Horton (1945) and Strahler (1952) introduced the quantitative study of streams and estimated the relative power of different waterways in a drainage basin. Schumm (1956) measured and analyzed both the surface and subsurface processes involved in slope development in order to provide a theoretical analysis of fluvial erosion. Significant contributions to the field of river basin studies have been made by Horton (1932, 1945), Strahler (1950, 1952, 1969), Melton (1957), Anderson (1957), Maxwell (1960), Coates (1958), Morisawa (1959), Leopold and Langbein (1962), Schidegger (1965), Gregory and Walling (1968, 1976), Haggett and Chorley (1969), Wolman (1967), and Richards (1993). Quantitative fluvial geomorphology discusses water technology; water quality treatment; stream discharge; the changing nature of rivers; and quantitative analysis of river depth, width, and length. Leopold and Maddok (1953) discussed the average velocity of river water, and the depth, width, volume, and centricity of sediments to assess the origin and mass movements of various rivers in the United States. Schumm (1977) assessed various rivers and their nature. He analyzed fluvial landforms, depositional landforms of old rivers, and a number of German rivers and explained many numerical analyses to demonstrate process–form interactions in fluvial systems. Modern fluvial geomorphology explores, for example, river channels and drainage basins, river management systems, channel types, floodplains and terraces, bankfull flow, and types of rivers. A river channel system in the landscape is a system that produces and transports runoff and sediments. A channel network is like the veins of the landscape; channels collect sediment produced on hillslopes and transport it to basin outlets. Channels are influenced by sediment production, transportation, routing, and storage processes. In recent years, geomorphology has put more emphasis on quantitative data, experimentation, predictive modelling, tectonic geomorphology (e.g. Burbank and Anderson, 2001), and the understanding of links between process and form. Much recent work is driven by the need for hazard prediction and landscape management in a world that is becoming ever more crowded. Today, the field of geomorphology encompasses a very wide range of different approaches and interests. Modern researchers aim to draw out quantitative ‘laws’ that govern earth surface processes, but equally recognize the uniqueness of each landscape and environment in which these processes operate. Fluvial geomorphologists can give more attention to the potential methods available for sustainable restoration and rehabilitation of urban fluvial systems, and especially the choices between hard and soft engineering. Successful stream rehabilitation likely requires a shift from narrow analysis and management to an integrated understanding of the links between human actions and changing river health.

Concept of a fluvial system Geomorphic systems can be defined as a set of interconnected components, which may be objects (e.g., landforms, mass or energy storage compartments), processes or process bundles or

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Introduction to fluvial geomorphology regimes (e.g., weathering, fluvial erosion, and alluvial deposition), or phenomena or events (e.g., overbank flows, tropical cyclones, and earthquakes). These components are connected by fluxes of matter and energy, feedbacks, spatial or temporal sequencing or connectivity, and process-response relationships. (Phillips, 2012)

Running water is the most important agent of erosion on the continents, and stream valleys are the most common landforms. Rivers flowing to the oceans drain about 68% of the earth’s land surface. The remainder of the land is either covered by ice or drains to closed basins. Rivers gradually mould the land by eroding away the material in some place and depositing it in other. In a geographical area, the drainage systems develop in such a way as to efficiently move water off the land. Each stream in a drainage system drains a certain area, called a drainage basin. Drainage basin system variables are time, initial relief, geology, climate, vegetation, volume of mass, hydrology (runoff and sediment yield), drainage network morphology, hillslope morphology, discharge of water and sediments, channel and valley morphology, depositional system morphology, and sediment characterization. The continuous changes of drainage basin variables happen through time as a result of complex interactions between components. The drainage basin is the basic unit of the fluvial system. This is an open system where energy and materials are exchanged with the surrounding environment (Charlton, 2008). The main inputs in the fluvial system are water and sediments. In fluvial system atmospheric processes, rainfall and channelized flow of water provide energy to regulate the system. The flow of water in accordance with the topography introduces kinetic energy which is expended for moving water and sediments in a drainage basin. The water and sediments which are being moved through the system to the drainage basin outlet, i.e. discharge of water and sediments to the ocean, are termed as outputs. The water and sediments which are being stored in the drainage basin are termed as storage. So, in the fluvial system or in a drainage basin, inputs, outputs, and storage are closely linked with one another, which helps in changing the morphology and system variables through time. There is a complex interaction in a hydrological model system or drainage basin system. All the system components (system inputs, system storage, system transferor movement, and system outflows) of a drainage basin and their complex interaction leads to stable and unstable conditions for achieving geomorphic equilibrium (Figure 1.1). Such interactions promote movement of energy from one component to another component as well as regulate movement of water and sediments from one location to another location of a drainage basin. The complex interactions in a drainage basin or in a fluvial system give birth to three important systems: morphological system, cascading system, and processresponse system. Landforms, such as hillslopes and floodplains, form a morphological system. The forms of hillslopes and floodplains are the outcome of the linkage between components in the fluvial system. Cascading system refers to the

Introduction to fluvial geomorphology 7

Figure 1.1 A complex hydrologic model system. Source: The COMET Program, runoff overview PowerPoint presentation; produced by The COMET® Program, copyright 2006, University Corporation for Atmospheric Research. All rights reserved.

flow of water and sediments from the hillslopes and floodplains. This system is created due to movement of water and sediments through the channel network. In a drainage basin, the existing forms influence the processes and the processes create a form. So, there is two-way feedback in a fluvial system. The development of the forms in a drainage basin is the response of fluvial processes, termed as the process-response system. Schumm (1977) divided a river basin into three process zones: sediment production, sediment transfer, and sediment deposition (Figure 1.2). Each zone is represented by a dominant process (erosion, transportation, deposition). Any segment of a river must be recognized as being a part of an integrated system, and the characteristics and dynamics of a segment of interest will be significantly affected by circumstances prevailing in the drainage basin upstream of the reach, and may also be affected by processes and events occurring downstream (Schumm, 1977). The upper segment of a drainage basin supplies sediments and water to the channel, which promote significant changes in the hydrology and sedimentology. The sediment and water supplies from the drainage basin have the potential to change the equilibrium conditions in the channel. The instability situation that develops in the downstream sections of a fluvial system has the potential to change or alter the system as well as destabilize a section of the channel (Schumm, 1977). So, it is very important to consider each and every segment of a river within the framework of a fluvial system (Schumm, 1977).

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Introduction to fluvial geomorphology

Figure 1.2 An idealized fluvial system. Source: After Schumm (1977).

Fluvial system stressors: A response to hydrology, sediment budget, and channel morphology There are many natural and anthropogenic stressors in fluvial systems. Stressors force mechanisms that can induce change in a fluvial system. Simply, stressors cause change in the fluvial systems, which cause instability in terms of flooding, avulsion, bank erosion, etc. Stream systems are inherently and directly interconnected to vegetation, soils, water quality, hydrology, and humans. Streams are nature’s pipes adjusted to the most efficient condition to transport water and sediment within a watershed (Ritter et al., 2002). Anything that changes the magnitude or spatial or temporal patterns of water and sediment inputs will cause the stream to adjust to those new conditions. In some cases, adjustments in the fluvial system may cause a threshold to be crossed and the stream will change to a new condition, for example, from a meandering to braided pattern in response to an increase in sediment load (Lord et al., 2009). The intricacies of possible responses in a fluvial system to stressors are often complex and unpredictable; this characteristic is termed complexity or complex response (Schumm, 1991). Additional traits of the complexity of fluvial systems important to establishing and understanding cause–effect relationships are singularity, divergence, and convergence (Schumm, 1991). Change in a fluvial system is common and is a result of changes in stressors. The alteration of hydrology in a basin and watershed scale happens due to changes in land use and land cover and land development (Table 1.1). Land development decreases infiltration capacity in a stream system. Land development causes changes in hydrologic patterns, disturbance in stream geomorphology, degradation of water quality, and deterioration of stream habitat (US Environmental

Introduction to fluvial geomorphology 9 Table 1.1 Scale, source, and examples of stressors that may affect fluvial processes and geomorphology Scale

Stressor source Stressor category area

Basin

Outside watershed Inside watershed

Channel Inside watershed

Specific stressor examples

Altered hydrology Climate change and altered Air pollution sediment budget Altered hydrology Urbanization Roads and parking lots Storm drains Vegetation changes Forestry practices Use of groundwater Altered sediment Construction budget Forestry practices Water impoundments Mining Agriculture Vegetation changes Altered topography Landslides Volcanism Construction Altered hydrology Water impoundments (dam) Water diversion Consumptive use of surface water Altered sediment Dredging budget Road and rail crossings Altered channel Channelization Dredging Bridges Bank stabilization structure Grazing Removal or change in riparian vegetation Landslides

Source: Gregory and Wallings (1987).

Protection Agency, 2002a, 2002b 2002c, 2002d, 2002e; Cottingham et al., 2003). Basin development generally leads to an increase in the frequency and magnitude of storm discharges. The increase in storm flow discharges can lead to over a sixfold increase in channel-cross-sectional area over that of a natural stream (Knighton, 1998). Gregory and Walling (1987, p. 295) state that an increase in peak discharges due to the effects of urbanization could, for example, lead to an increase of channel cross-section size, an alteration of channel shape, and increase in the size of meanders and metamorphosis of planform along selected reaches from single thread to multithread as sedimentary bars accumulated.

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Introduction to fluvial geomorphology

The sediment budget in a fluvial system changes with changing hydrology. Changes in hydrology change the driving force for erosion and transportation of sediments. Changes in the availability of sediment or the ability to transport sediment will immediately affect stream sediment transport rates and may affect all three channel vital signs: cross-section, planform, and longitudinal profile (Lord et al., 2009). Due to an increase in overland flow, an increase in the amount of erosion and sediment input in the channel happens, which affects the channel planform, cross-sections, and longitudinal profile. In the same way the sediment budget is simultaneously affected by natural anthropogenic changes in land cover in the watershed, which changes the resistance of soils and other materials over the earth surface. Changes in the sediment budget are caused by natural stressors, such as climatic change, landslides, or fires, and clearly affect the sediment dynamics. But in many cases, anthropogenic stressors can have an even more pronounced effect (Lord et al., 2009). Urbanization and general land development cause significant increases in soil erosion and sediment transport. Changes in a watershed or stream sediment budget not only affect sediment transport rates, but can affect water quality (e.g. turbidity), quality of streambed habitats, and channel cross-section (Cooke and Doornkamp, 1990; US Environmental Protection Agency, 2002a, 2002b 2002c, 2002d, 2002e; Allan, 2004). The channel pattern is monitored by the amounts and types of sediment load, and thus may change in the sediment budget of a stream. The alteration of hydrology causes changes in sediment dynamics, depending on the distance from the site of the stressor and the energy necessary for the reaction. Alteration of stream channels by humans dates back thousands of years caused by natural and anthropogenic stressors. In Denmark, up to 98% of streams may have been directly altered from their natural condition (Brookes, 1995). The alteration is less in the United States. Alteration of stream channels happens to control flood situations, for straightening the channel to facilitate transport, and for bank stabilization. There is an increasing amount of direct channel alteration to restore and rehabilitate streams at present. Stream restoration attempts to return a channel to its natural, pre-disturbance condition (Lord et al., 2009). The processes in one part of the drainage basin cannot be separated from those in another part; thus, measurable change at one site often results in measurable change in others. In this sense, rivers and the valleys they drain are closely linked, and they must be treated as parts of a single, dynamic system. (Osterkamp and Schumm, 1996) Natural and anthropogenic processes in a fluvial system give birth to some significant signs, i.e. watershed landscape characteristics, variation in stream hydrology, nature of sediment transport, channel cross-sections, channel planform, and channel longitudinal profile. So, stressors in fluvial system is a common phenomenon which leads to channel morphodynamics and riverbank erosion hazards in the river basin.

Introduction to fluvial geomorphology 11

Channel morphology and channel classifications Channel morphology (the cross-sectional, plan view, and longitudinal configuration of a channel) develops a form that is adjusted to the regional topographic gradient, long-term average hydrologic regime, and sediment load of the drainage basin. In turn, invertebrates, fish, riparian vegetation (vegetation growing along the banks or on the floodplain), and wildlife adjust to the channel form and hydrologic and sediment transport regimes. The entire system, physical and biological, develops an equilibrium condition in response to external controlling factors such as tectonics, geology, soils, climate, and land use (Schumm, 1977). Channel morphology is the complex interactions between regional geology, climate, topographic gradient, river history, drainage basin hydrology, and sediment load. Although the interactions among these variables can be complex, most data suggest that drainage basin hydrology and channel discharge primarily determine the size of the channel, whereas the calibre and quantity of the sediment load determine channel pattern and cross-sectional morphology (Church, 1992). It is significant to segregate small headwater streams from large streams and rivers and to segregate bedrock channels from alluvial channels to evaluate channel pattern and channel morphology. In the case of small channels, the bed is covered with cobbles (>64 mm) and boulders (>256 mm), and the steep channel gradient ranges from 2° to 20° (Church, 1992). Grant et al. (1990) found that small streams flow downslope and are floored by coarser materials having a step-pool morphology where the steps are formed of clusters of cobbles or boulders, large woody debris (Keller and Swanson, 1979), or even bedrock (Wohl and Grodek, 1994). In sand and gravel bed channels of this scale, the channel morphology is dominated by pool–riffle sequences, where pool–pool or riffle–riffle spacings are typically five to seven times the channel width (Keller and Melhorn, 1978). Sand and gravel bed channels are mostly dynamic where lateral shifting and redevelopment of pool–riffle locations represent normal equilibrium conditions. Incised channels (significant downcutting with steep banks and low width– depth ratios) range from small gullies metres wide and metres deep, to entrenched channels and arroyos of tens of metres. These channels are dominated by clay and silt-sized particles, although sand and gravel may also be present in significant quantities. In humid climates with perennial and intermittent streams, incised channels are typically produced by episodes of rapid incision and channel instability (Schumm et al., 1984). Large streams and rivers exhibit a wide range of morphologies, and a variety of classification schemes have been developed to describe channel patterns. Schumm’s (1981) channel patterns, later modified by Church (1992), are well defined and widely accepted. Leopold and Wolman (1957) classified channels into three categories: straight, meander, and braided pattern. The channel pattern can be of singlechannel and multiple-channel forms. The single-channel pattern includes straight channel with or without bed forms. The straight channel with alternating bars and meandering thalweg grades into sinuous channels and various forms of meandering. Kellerhals et al. (1976) recognized three types of meander channels based on degree

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Introduction to fluvial geomorphology

of regularity: irregular meanders (vaguely repeated pattern); regular meanders with a clearly repeated pattern and maximum deviation angle of 90°. Multi-channel patterns are grouped into the single category of braided channels as propounded by Leopold and Wolman (1957). Braided reaches are multi-channel forms where the channels are separated by bars or islands. The characteristic features of the braided pattern are repeated division and joining of channels, and divergence and convergence of flow, which introduces a high rate of fluvial activity in comparison to other river types (Knighton, 1998). Braiding of the channels can be initiated by deposition and erosion where the erosion depends to some extent on the preceding deposition. Ashmore (1991) in his flume experimental studies identified two depositional (i.e. central bar deposition and transverse bar conversion) and two erosional (i.e. chute cutoff and multiple-bar dissection) mechanisms for braiding. Basically, individual channels in a braided river are seldom in equilibrium and may be very unstable (Hoey and Sutherland, 1991; Ferguson, 1993). High stream power, large fluctuations in bed-load transport rate with successive divergence and convergence, and variation of discharge between channels have made the braided reach more unstable. For this reason, the braided channel pattern has been regarded as disequilibrium. Schumm (1981, 1985) identified 14 channel patterns. Schumm (1981) classified channels into three types: (1) suspended load dominated, (2) mixed load dominated, and (3) bed load dominated, based on the load moved through the channels (Figure 1.3). Suspended load-dominated channels range from straight single channels having low width–depth ratios and low stream power to highly sinuous single channels having low width–depth ratios and low stream power.

Figure 1.3 A process-based channel classification scheme. Source: After Schumm (1981).

Introduction to fluvial geomorphology 13 Highly sinuous, suspended load-dominated channels are stable in form. These channels migrate laterally and meander cutoffs may develop. Mixed load channels range from straight channels with alternate coarse-grained bars to sinuous channels with coarse-grained point bars. Mixed load channels have higher stream power and higher width–depth ratios. This channel transports larger quantities of coarse-grained sediment than suspended load-dominated channels. Sinuous mixed load channels show extensive lateral migration rates compared to highly sinuous suspended load channels. These channels are characterized by well-defined pool– riffle sequences with spacing five to seven times the channel width (Keller and Melhorn, 1978). Mixed load channels are also characterized by steeper gradients, higher stream power, and higher sediment transport rates than suspended load channels. Bed load-dominated channels range from low sinuosity channels with point bars and a small number of mid-channel bars to fully braided multi-channel rivers with many mid-channel bars. Bed load-dominated channels are characterized by high stream power, steep gradients, high width–depth ratios, and high sediment transport rates. These channels are highly dynamic with well-developed mid-channel bars and significant bank erosion. Anastomosing channels represent a branching network of channels that divide and recombine around large segments of the floodplain. Individual channels in an anastomosing pattern are characterized by low width–depth ratios, and the channels tend to be much more stable than multi-channel braided channels. Inter-channel areas are larger, heavily vegetated, have large woody vegetation, and exhibit channel stability. The channel patterns represent equilibrium morphologies which are adjusted to the prevailing sediment load and hydrology in a fluvial system (Table 1.2). All the channel patterns may reveal a distinct kind of morphology with an episode of channel instability. Braided channels are overloaded with sediment with the implication that the braided pattern is a non-equilibrium morphology. However, braided patterns could represent equilibrium, aggrading, or degrading conditions (Germanoski and Schumm, 1993).

Channel instability and bank erosion Most channels are dynamic in which the channel migrates laterally, and channel avulsion is a common phenomenon. But lateral migration and avulsion are

Table 1.2 Channel patterns and their characteristics Characteristic

Anastomosing Meandering Braided

Gradient Sinuosity Width–depth ratio Percentage silt–clay in banks Lateral migration

Low Variable Low High Rare

Source: After Smith and Putnam (1980).

Moderate High Moderate Moderate Common

High Low High Low Common

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not significant indicators of channel instability. Instability deals with changes in channel bed elevation, cross-sectional morphology (width–depth ratio or crosssectional area) and channel pattern change. An unstable channel may change its planform view, bed elevation, and cross-sectional size systematically. A balance exists between the sediment load and stream power in an alluvial channel, which is related to discharge and channel slope. If the sediment supply is reduced to the channel, it will start to incise or degrade. On the other hand, if sediment supply is increased, the channel will start to aggrade. Such degradation and aggradation may be accompanied by channel morphology. Simultaneously, as a result of an increase or decrease in stream power, the channel may degrade or aggrade and may change its morphology. Rivers are systems in dynamic equilibrium, balancing water flow and sediment transport. When river channels are altered under naturally dynamic hydrologic conditions, the river readjusts itself with respect to dimension, profile, and pattern to reach its former balance or equilibrium. Graf (1983) stated that the stream power in the downstream direction does not systematically increase because of the conflicting influences of channel slope, width, and depth. According to him, the total stream power decreased in the downstream direction during the accretion period earlier than 1896 and increased during the erosion period thereafter. Knighton (1999) explored that the stream power might vary in the downstream direction and the longitudinal profile of the river has an exponential form. The stream power affects sediment transport capacity and influences several aspects of the channel form. Maiti (2016) made an experimental study in a selected part of the Kangsabati River. He identified the pool–riffle location in relation to the meander section and found the relationship between the width–depth ratio and percentage of silt–clay, measured channel form across the river, and prepared a channel bed bathymetry map of the Kangsabati River. He said that sand mining is an important factor in development of the channel form and pattern. Hadadin (2016a, 2016b) investigated the effects of basin hydrology on the hydraulic geometry of channel variability for an incised stream using field data and watershed hydrology model and channel hydraulics for the Yazoo River basin in the United States. He presented the hydraulic geometry relations of bankfull discharge, channel width, mean depth, cross-sectional area, longitudinal slope, unit stream power, and mean velocity at bankfull discharge as a function of drainage area using simple linear regression. He concluded that the channel width is much more responsive to change in the drainage area and bankfull discharge than the mean channel depth or mean velocity. Maity and Maiti (2017) explained the causes and mechanism of sedimentation and seasonal fluctuation of shear stress. They measured textural analysis of sediments, the density of water and sediments, available shear stress, critical shear stress, areas of shoaling and scouring, sand–mud ratio, depth of water, water velocity, and riverbed slope to understand the dynamic behaviour of the channel. The sedimentation at the lower reach of the Rupnarayan River depends on the seasonal fluctuation of available shear stress (Maity and Maiti, 2017). Salmela et al. (2020) determined morphological changes and riffle–pool maintenance in

Introduction to fluvial geomorphology 15 relation to flow conditions in a meandering river channel. They revealed that the variations of discharge and near-bed flow velocity exert important influences on the morphological change and, thus, riffle–pool dynamics in meandering sand-bed rivers. Moreover, the riffle–pool sequences are maintained by the effective hydrological events (Figure 1.4). The lateral migration of an alluvial river channel of the floodplains is the geomorphological process. This lateral migration is accomplished due to bank erosion or cut bank and formation of a point bar through time (Figure 1.4). The meandering streams and braided streams exhibit channel changes over time which is driven by sediment transport. Bierman and David (2014) opined that as flow enters the bank of an alluvial river, the centrifugal force created by the bend instigates helicoidal flow, a corkscrew-like pattern of flow, which drives the hydraulic action acting on the opposing bank and where the primary process in river channel migration of bank erosion happens. The formation of helicoidal flow undercut the bank, resulting in cut banks. The factors which influence the rate of bank erosion along the cut banks are the rate of deposition of the point bar, stream power, and the critical shear stress of the stream bed. Knighton (1998) found that storm frequency, flow properties, variability of stream discharge, bank material compositions, bank geometry, bank moisture condition, channel geometry, vegetation type, and man-induced factors are the major causative factors of riverbank erosion of an alluvial channel. So, bank erosion processes change the course of an alluvial channel and make the floodplain environment more dynamic by altering hydrological and sedimentological regimes in a spatio-temporal scale. The point bar deposition along the convex part of the meander bend helps in the channel migration process. The deposition of sediments and formation of

Figure 1.4 Process of lateral migration of an alluvial channel. Source: https://www .ausableriver.org.

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point bars are compensated by the erosion rate of the cut banks. In most cases, the rate of erosion of the cut bank is equal to the rate of deposition of point bars. The sediment taken from the bank during the process of bank erosion is deposited on the opposing side of the channel fuelling the process called point bar deposition. The helicoidal flow also plays a role in this process by acting as a cross channel component that moves the sediment to the other side (Bierman and David, 2014). The development of point bars acts as a topographic obstruction which further drives flow into the opposite bank and leads to bank erosion. The fluvial processes of rivers are the result of the interaction of stream flow, sediment, and riverbed. The riverbed controls the flow and sediment transport, which in turn enhance changes in the riverbed. Meandering rivers migrate gradually, and hence sinuosity tends to increase. The channel forms almost a closed loop and the meander often gets cut off during a flood. Meandering is therefore the result of streambed instability; in particular, when instability acts on the banks. In floodplains, no channel can be straight enough, as the channel bed is subjected to deposition of sediments. The deposition of sediments over the channel bed changes flow direction and flow velocity, which subsequently promote bank erosion and channel migration. There is an alternate sequence of pools and riffles in a meandering channel where pools are found towards the concave side of the meander bend and riffles are found in the middle in the straight course of the channel. Both pools and riffles are caused by deposition of sediments (Figure 1.4).

Large river system and bank erosion hazards across the world The larger the drainage area of a meandering river, the faster its channel migration. There is a positive relationship between the river channel migration rate and the drainage area of a river (Hudson and Kesel, 2000). In America, both the Mississippi and the Missouri Rivers have been attributed with channel migration where water flow erodes soil on one bank and deposits it on the opposite bank, and finally shifting of the bank line happens through time (Briaud et al., 2007). The large-scale impact of riverbank erosion and channel migration have been observed over the last 200 years (Maynord and Martin, 1996). In the early decades of 18th century, the lower Missouri River was subjected to river modifications by US Army Corps of Engineers (USACE), such as channel straightening and dike construction, to promote river navigation (Alexander et al., 2012). Such humaninduced channel modification caused severe riverbank erosion. Modification of the Mississippi River is still happening, which is causing devastating damage to human infrastructures, lives, and properties. To cope with the situation, the US Congress authorized the Mississippi River Restoration Ecosystem Management Program in 1986 (Prairie Rivers Network, 2012). The Illinois River has been changing its course due to bank erosion since 1939 because of the construction of locks and dams (Bhowmik, 2008). In Europe, the shortening of the Danube River to prevent flooding and encourage navigation has invited destructive riverbank erosion in the middle of the Danube where more than ten settlements are at risk and a large amount of

Introduction to fluvial geomorphology 17 municipal and industrial infrastructure has already been damaged (Szalai et al., 2013). The Danube River is gravel dominated, and has both braided and meandering channel types with active lateral erosion. The Danube River is the border line between Serbia and Croatia. Serbian farmers lost their arable lands, which they occupied on the left riverbanks in Serbia 50 years ago, because of very intensive lateral erosion and vice versa for Croatian farmers (Dragićević et al., 2013). Now most of the countries in Europe realize the need for restoration of rivers to their natural course and application of bioengineering techniques for riverbank erosion control (Donat, 1995). The rivers Danube, Tisza, and Drava have been modified and shortened in Europe, and the actual length of the rivers reduced remarkably. Such modifications have disrupted natural processes of the rivers, changed channel morphology, and caused riverbank erosion problems. The Nile of Africa (6650 km) passes through 11 countries: Ethiopia, Eritrea, Sudan, Uganda, Tanzania, Kenya, Rwanda, Burundi, Egypt, Democratic Republic of the Congo, and South Sudan. The Nile meanders through a watershed that is to more than 30% arid (Wong et al., 2007). The lateral erosion and associated bank erosion problems on the Nile River bank in Egypt was caused by large-scale anthropogenic pressure. Bank erosion has caused a decrease in agricultural lands, which in turn has reduced agricultural production. In Asia, the Mekong River flows over 4800 km through six countries, namely China, Myanmar, Laos, Thailand, Cambodia, and Vietnam (cf. MRC, 2010). The channel pattern of the Mekong is meandering with low sinuosity (Wood et al., 2008). The riverbank zone in the basin provides places for human settlement and also consumption of goods and inputs to production. Thus, bank erosion in the Mekong River not only displaces populations but also brings about loss of household income sources. It was reported that about 600 families in the Tonpheung district of the Bokeo province in Vietnam were forced to migrate from their homes because of riverbank erosion over the past three years. Apart from socioeconomic problems, there are also political problems. The political border line between Laos and Thailand (about 1100 km long) is the deepest line (thalweg) of the Mekong River channel. But this political border line has shifted due to severe bank erosion of the Laos riverbank. Moreover, the altered flow channel made an island that was once part of Laos but is now part of Thailand (Brown, 1999). The Yellow River (or Huang He) is the second largest river in China after the Yangtze River. The river was called ‘China’s Sorrow’ because of frequent occurrences of flooding and suffering of millions of people. In August 1931, a destructive flooding event killed around 3.7 million people, which is recorded as the worst flood disaster in world history. Several dams were constructed in China to prevent flooding, provide water for irrigation, and generate hydroelectric power. The construction of large dams, such as the Sanmenxia Dam on the Yellow River in 1960, the Liujiaxia Dam in 1968, and the Xiaolangdi Dam in 1997, invited riverbank erosion hazards (Ma et al., 2012). Bangladesh has suffered heavily from riverbank erosion for a very long time. Thousands of people have been forced to migrate from their place of origin due to bank erosion in Bangladesh. The major rivers of Bangladesh are the Padma

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Introduction to fluvial geomorphology

River, Jamuna River, and Meghna River. Severe riverbank erosion has eroded several thousand hectares of floodplains, and several kilometres of roads and railways have displaced people. The Ganges-Padma River in Bangladesh is becoming a braided river because of high sediment transportation by the Jamuna and deposition in the Ganges-Padma riverbed (Yeasmin and Islam, 2011). During 1970–2000, the Padma and the Jamuna eroded 180,000 hectares of land and about 200,000 people were displaced (Islam and Rashid, 2011). Displaced people experienced substantial socio-economic impoverishment and marginalization because of forced migration and inequitable access to land and other resources (Mutton and Haque, 2004). Another bank erosion–affected country in Asia is Myanmar. The Irrawaddy and Chindwin Rivers in Magwe Division, central Myanmar, has severe bank erosion problems (Mann, 2013). India is also a land of rivers like other Asian countries. Floods, which are recurring phenomena in India, cause severe bank erosion. Two rivers that are subject to severe bank erosion are the Ganges River and Brahmaputra River, a braided river (Sarma, 2013; Mili et al., 2013; Phukan et al., 2012). The states of Assam, Bihar, and West Bengal (India-WRIS) are severely affected by bank erosion problems and dominated by large river systems. The Indian subcontinent is widely traversed by a large number of rivers. Most of the rivers are located in the Ganga region (Ganga), Brahmaputra region (Brahmaputra and Barak), north-west region (Sutlej, Beas, Ravi, Chenab, and Jhelum tributaries of Indus), and central and Deccan region (Narmada, Tapi, Mahanadi, Godavari, Krishna, and Cauvery) (Figure 1.5). Large-scale riverbank erosion has been recorded in the Ganga and Brahmaputra regions. The lower reach of the east coast rivers experience flood and bank erosion problems. In India, among all eastern and north-eastern states, Assam, and the northern part of West Bengal face bank erosion problems. The Raidak, Jaldhaka, Teesta, and Torsa Rivers of the northern part of West Bengal are dominated by bank erosion problems. In Assam, riverbank erosion wiped out 2500 villages and 18 towns, and affected the lives and livelihoods of nearly 500,000 people from 1992 to 2008 (Phukan et al., 2012). The lower Gangetic Plain consists a major river system in India. The Gangetic Plain covers a large part of India. The Ganga River emerges from the Gangotri glacier, about 4500 m above mean sea level in the Uttarakhand Himalayas, and flows down to the Bay of Bengal covering a distance of 2525 km. The Ganga River carries a large volume of sediment and deposits in the plains areas. These transporting sediment loads are the source of major water resource in the river catchment. Large-scale deposition of sediment over the riverbed creates many hydro-geomorphological problems like decreases in river depth, and changes in flow velocity, flow direction, and discharge. When the flow velocity becomes low, the river puts pressure on both riverbed walls and as a result lateral erosion starts, which causes flooding and riverbank erosion (Thakur et al., 2011). The commissioning of the Farakka Barrage started in 1962 and was completed in 1971. The whole project was completed in 1975. The barrage was constructed to divert about 40,000 cusecs (or 1133 cumecs) of Ganga water towards the Bhagirathi River with a view to wash out the sediment load into a deeper part of

Introduction to fluvial geomorphology 19

Figure 1.5 Rivers of India. Source: https://www.ausableriver.org.

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Introduction to fluvial geomorphology

the estuary and save the navigational status of the Kolkata port (Rudra, 2004). This barrier seems to lead the river to make its own way, mainly in upstream of the Farakka Barrage. Mainly two districts, Malda and Murshidabad of West Bengal, India, are suffer from this obstruction (Banerjee and Chakroborty, 1983). The barrage has caused serious interception in the dynamic equilibrium of the river, hindering the natural oscillation of the river within its meandering belt. The river, which flowed in a southeasterly course between Rajmahal and Farakka during the early decades of the 20th century, has now formed a mighty meander loop concentration to accommodate the additional discharge accumulated due to the barrage leading to massive erosion of the left bank (Rudra, 1996). Due to the obstruction caused by the barrage, each year nearly 64 crore tonnes of silt accumulates over the riverbed. In the last three decades, this has resulted in the accumulation of nearly 1856 crore tonnes of silt. In Malda, the river looks like a closed marshland with aquatic plants flowing in it. Each year in Malda the riverbed rises at the rate of 50 cm, resulting in a declining slope in the opposite direction between Farakka and Rajmahal. The change in the Ganga River course and associated riverbank failure is a long-term natural disaster in West Bengal, India, especially in the upstream of the Farakka Barrage. The rate of riverbank erosion is very rapid and frequent, which results in population displacement from the riverside villages every year (Iqbal, 2010).

Riverbank erosion and human vulnerability across the world Landscape degradation, and environmental and socio-economic impacts are observed in different countries at different scales due to riverbank erosion. But quantitative information on socio-economic consequences of riverbank erosion (total human displacement, loss of occupation, loss of property, impact on health and education, etc.) for all the cases, however small it may be, is not available unlike for other natural disasters. Recently, a few attempts have been made to collect and analyze data at the household and community levels. Such attempts are highly needed to quantify human vulnerability due to riverbank erosion and in turn to formulate appropriate public policy. One such study was the analysis of socio-economic consequences of the Kolubara River bank erosion in Serbia (Dragićević et al., 2013). The analysis was in terms of land loss, land use changes, and economic loss. The study area in this analysis had economic importance, and there was significant density of the agricultural population and settlements. Because of bank erosion in the study area, the farmers who had arable land on the riverbank lost their land assets by the river. The loss of corn production was 3255 tonnes and of wheat production was 1271 tonnes till the year 2010. The level of production losses steadily increased over time. It was estimated that the total value of permanent losses of arable land was 80,560 USD, and the total loss in agricultural production was 634,240 USD till 2010. Erosion of the reservoir of the Three Gorges Dam and downstream Yangtze River banks is a threat to human settlement and to one of the world’s biggest fisheries in the East China Sea. It is expected that more than 4 million people have been displaced due to construction

Introduction to fluvial geomorphology 21 of dams, downstream bank erosion, and other environmental impacts (French, 2007). There is increasing concern that the people displaced due to construction projects and erosion face long-term risks of becoming poorer and are also threatened with landlessness, food insecurity, joblessness, and social marginalization (Gleick, 2009). The socio-economic impact becomes more severe when people are more vulnerable to natural disaster. This is what happens in Asia. High population density and poor economic conditions make consequences of natural disasters more devastating. A large section of the population is bound to stay in high-risk zones like the banks of meandering rivers. This is a common scenario in almost all countries in Asia. In Bangladesh, the poor, small landowners who live near riverbanks are the most affected victims of bank erosion. Bank erosion affects their well-being in terms of safety and shelter, as well as their sources of livelihood (Brouwer et al., 2007). Riverbank erosion is bringing about unemployment, landlessness, and poverty every year, increasingly over time. Riverbank erosion has been supposed to be responsible for the unstable conditions in the country (Rahman, 2013). In Indonesia, those who suffer most during floods and are most vulnerable to rising tides and increasing water levels are the low-income, poor, and informal settlers living along riverbanks and low-lying coastal areas.

Fluvial morphodynamics: Experiences from the Torsa River, India All alluvial rivers are dynamic in nature. In the Torsa River basin, changing hydrogeomorphological dynamics have highly influenced the changing land use patterns, nature of fluids, the behaviour of floods, bottom topography of the channel bed, etc. The changing of hydro-geomorphic dynamics of streams at faster rates brings about the problem of riverbank erosion. Severe bank failures during floods can lead to major channel avulsion or changes. Active tectonics and the influence of tributaries on progressive aggradation changes the character of the sediment load and channel gradient of the foothills of Himalayan streams, which can be reflected on the channel form from straight to sinuous, meandering, and braided. During the rainy season, riverbank dwellers are often not ready to face the changing situation of the hydraulic behaviour of the waters. Human interventions on river basins in terms of short-length bridge construction across rivers, embankment construction along rivers, modification of river flow, lifting of sands and rocks from the riverbed, etc. influence channel changes of the Torsa River. The construction of shortlength bridges across the Torsa River obstruct the water discharge, which controls the normal pattern of the river channel and land use pattern of the river basin. In the Torsa River basin, the geomorphological evolution is a very usual and natural process. The Torsa River is a dynamic geomorphic unit where morphometric characteristics differ seasonally and locationally with changes in the hydraulic controls. In the Duars and Tal region, this alluvial stream has very dynamic landforms subject to rapid change in channel configuration and flow pattern. A higher stream energy channel and less consolidated riverbank and bed materials are most

22 Introduction to fluvial geomorphology dynamic and vulnerable. Stream bank erosion is considered as a potential threat to riparian areas, because the resources, properties, and lives associated with the land on either side of the river are devoured. The river channel adjustment and floodplain development depend on the stream bank erosion, which also threatens man-made structures and destroys valuable agricultural land. Stream bank erosion is an intricate natural process occurring in a river valley. Stream bank erosion is one of the principal means of sediment supply to streams. Two predominant processes are involved in stream bank erosion: (1) hydraulic action and (2) mass failure. The Torsa River basin is a lower catchment tributary of the Brahmaputra River covering the countries of Tibet, Bhutan, India, and Bangladesh, and it is a wellknown name in the river scenario of Duars and Tal region of West Bengal, India. The catchment of the Torsa River is one of the largest river systems in the Eastern Himalayas and its foothills region. The Torsa River basin covers a geographical area of 7486.31 km2 and it is located between 27° 56′ 42.5″ N to 25° 54′ 16.5″ N latitude and 88° 44′ 22.5″ E to 89° 50′ 35.5″ E longitude (Figure 1.6). The catchment area is a part of the Eastern Himalayas (Tibet and Bhutan), and Duars (India) and Tal (India and Bangladesh) region, and lies between the catchments of Jaldhaka on the west and the Sankosh River on the east. The basin is deeply dissected by the Torsa River and its tributaries, including the Kaljani, Raidak-1, and Pa Chu to the east. The Bhutan Himalaya is the primary source of the tributaries. A few of the tributaries originate from the piedmont and northern plains regions of the Himalayan foothills. The Torsa River originates from the Chumbi Valley in southern Tibet at the height of 6996 m above mean sea level. The Torsa is known as Proma Chhu in Tibet, Amo Chu in Bhutan, Torsa River in India, and Dudhkumar River in Bangladesh. The north-south elongated river basin is 295 km, of which 99 km lies in West Bengal, India. This river is also known as Toyrosa (meaning ‘sorrow of river’) in Tibet. The Torsa River is fed by the melting water of glaciers near the Chumbi Valley and a large portion of its course is also fed by rainwater. The entire course of the Torsa River flows from GreaterLesser Shiwalik Himalayas through the steep mountain gorges to the alluvial plains region, and this course ultimately meets as an important right bank tributary of Brahmaputra in the Rangpur district of Bangladesh. The upper course of the Torsa River is linked with many perennial lakes; consequently, the water level of this river is retained during the non-monsoon. The Torsa River basin includes of eight major sub-basins. The Torsa River and its tributaries contain the Brahmaputra River system. The Torsa River basin has been divided into five tectonostratigraphic zones, including four Himalayan tectonostratigraphic zones and one quaternary sediment zone. These five tectonostratigraphic zones have also been divided into 29 subdivisions. The most important stratigraphic features of this basin are the main frontal thrust, main boundary thrust, main central thrust, and lower south Tibetan detachment. The slope direction of the Torsa River basin is mostly southeast, south, and south-west facing. The largest part of the Torsa River basin has southerly facing slopes accounting for about 14.40% of the total basin area.

Figure 1.6 Location of Torsa River basin, India.

Introduction to fluvial geomorphology 23

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Introduction to fluvial geomorphology

The northern part of Torsa River basin covers hills and mountains which belong to the Himalayan range marked by the above 300 m contour and consists of a number of landforms like ridges, gorges, low hills, steep V-shaped valleys, toe cutting of hillslopes, uplifted terraces, and scarps. The northern mountain region covers about 4070.16 km2, or 54.37% of the total area. The Duars region is demarcated by a 60 metre contour line from the northern plains, and this region covers an area of about 1330.18 km2 in the Torsa River basin. The piedmont surface or Duars region has experienced young tectonic activity and the deposition of alluvium. This region is composed of several large and micro alluvial fans at a distance of 30 km from the mountains. In the south, the northern plains region is homogeneous and featureless, and spreads up to the Jamuna (Brahmaputra) River in Bangladesh. This region has led to the formation of numerous wetlands (bills), oxbow lakes, marshy tracts, cutoffs, abandoned river tracks, and wide valley floors. Innumerable tributaries of the Torsa River branch out in many channels giving birth to river meandering and leading to the formation of bills, swamps, and oxbow lakes in the southern part of the northern plains. This lowland region, also known as Tal (Tal means ‘wetland’ or ‘a bill or lake’), covers an area of about 319.84 km2 (Figure 1.1). The Torsa River basin is characterized by high intensity rainfall. The upper catchment of the Torsa River basin covers mountainous yellow and red soils, hill soils, and high altitude meadow soils, coarse with high gravel content, and sandy to sandy loam mixed with pebbles and gravel. The middle catchment is covered with very deep, poorly drained, fine silty soils, whereas the lower catchment is characterized by recent alluvium, mainly very deep, moderately well-drained, and coarse loamy soils. The Torsa River is highly vulnerable to bank erosion and the intensity of bank failure has been great over periods, which damaged or destroyed thousands of acres of agricultural land and habitats in the recent past. This situation impacts the physical and socio-economic landscapes. Also, the lower reach of the Torsa River has changed its course several times in the last few decades. The channel migration and the morphological modification of the Torsa River are frequently occurring. Consequently, the hydro-morphological changes are highly impacted by the channel migration and the development of shoal and palaeochannels, which influence the socio-economic aspects of human life. This situation inspired the selection of the Torsa River as a study area. In addition, every year large areas of riparian households are being inundated during flood events. The avulsion and bank erosion hazards happen due to devastating floods that destroy or damage lots of homesteads, houses, and agricultural land in the riparian area. Consequently, river dwellers take shelter above the embankments, increasing interest in the study area. The occurrences of bank erosion problems in the lower segment of Torsa River are controlled by the amount of sediment and water discharge of the upper segment. The problem of riverbank erosion is a common phenomenon in the lower segment of the Torsa River, which causes great damage to human lives and properties. Riverbank erosion happens due to changing variables of all geomorphological

Introduction to fluvial geomorphology 25 properties. The scientific assessment of geomorphological properties of the Torsa River basin will help to take proper measures to mitigate frequent riverbank erosion problems. Study of the hydraulic geometry in the upper and lower segments will reveal the amount of water released from the upper segment of the basin that is responsible for bank erosion problems, and accordingly suggestions may be put forward to the respective government of India. The morphometric parameters, such as the areal aspects, relief aspects, and shape aspects, of the river basin are to be analyzed with suitable methods and techniques for river basin management. The parameters of channel geometry and hydraulic geometry, including depth, width, velocity, width–depth ratio, hydraulic radius, wetted perimeter, channel bathymetry, discharge, distribution of channel bed materials, stream energy, and flow properties, are to be scientifically assessed to identify channel migration zones and bank erosion-prone areas on both sides of the Torsa River. The quantitative measurement and assessment of morphometric, geomorphic, hydrologic, and sedimentological parameters is of utmost importance for introducing developmental plans in the floodplain environment in the Eastern Himalayan foothills of India. Various quantitative techniques will help planners and policymakers with land and water resource management of the riverine environment. As the Himalayan foothills is characterized by frequent channel course changes, floods, and riverbank erosion which continuously retard the normal regional growth and development, the analysis of fluvial processes and the response to riverbank erosion may provide scientific knowledge and direction for the management of flooding situations and riverbank erosion of the Torsa River in India, the rationale for this study.

Fluvial processes and bank erosion hazards: Experiences from Torsa River, India The channel morphology of the Torsa River frequently changes as a result of channel migration, channel avulsion, and riverbank erosion, which increase the vulnerability of nearby populations. The riparian settlements are greatly affected by the processes of bank erosion and channel migration. In the Torsa River basin, the lateral migration or channel migration has caused a serious problem because of bank erosion and land use change. Every year huge amounts of land are wiped out from the bank due to riverbank erosion. Excessive sedimentation has continued due to the bank erosion process as well as the lateral migration of the channel. As a result, the riverbed is continuously rising and inviting the possibilities of flooding events. Along with physical changes, erosion adversely affects human life in the Torsa River basin. The Torsa is well-known as a worrying river, shifting its course on a regular basis; consequently, a large number of homesteads, houses, many crops, farming land, and construction are destroyed or damaged within the basin. Enormous bank erosion has been observed in several reaches of the Torsa River, causing damage to agricultural land and devastation to human settlements. In the study area, riverbank erosion associated with losses of agricultural land and settlements is a vital problem related to excessive sedimentation and formation of sandbars on the bed of the Torsa River. Shoals are formed over the channel bed

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Introduction to fluvial geomorphology

due to the deposition of sediments. Shoals generally obstruct the channel flow and pass huge volumes of water during the peak season through the narrow channel causing an asymmetry of erosion on the opposite bank. Consequently, the main course as well as thalweg of the Torsa River is being shifted towards the opposite bank. The accumulation of more water along with the generation of enormous flow velocity in the main course or channel thalweg creates immense pressure on the riverbank, which accelerates riverbank erosion. This problem becomes more vulnerable and unavoidable during monsoon season, when huge volumes of river water increase the discharge and the flow velocity. In recent times, massive bank erosion has been occurring near the Cooch Behar municipal wards 18, 16, and 15, and Cooch Behar II block, causing great loss of agricultural land and settlements. Notable bank erosion took place at Salmara, Hokakura, Haripur, Damodarpur, Basdaha Natibari, Deutibari, Aratguri, Petbhata Chandanchaura, Kachuban mouzas, and Cooch Behar municipal wards 18, 16, and 15. The massive bank erosion was caused by seepage erosion and toe erosion of the bank through parallel flow and secondary flow. Hence, the liquefaction and flowage of bank materials and shear failure are the principle mechanisms of bank erosion processes. In the years 2010 to 2017, several places experienced loss of properties due to the occurrences of avulsion and riverbank erosion in the Torsa River basin. Since then, the bank erosion has been concentrated towards the concave left bank in the Torsa River channel. The bend has been changed into a cutoff due to avulsion of the main course of Torsa River during the 2017 flood. The settlements of the riparian area are under threat and suffering from extensive riverbank erosion in the lower course of the Torsa in the Duars and Tal region. Many riparian households have been constructed along the vulnerable banks, which are more vulnerable to bank erosion. Moreover, such construction puts enormous pressure over the bank slope and make the riverbank most vulnerable. The problem of bank erosion in Torsa River is extremely unstable in nature. Since 2015, the char land of the Cooch Behar municipal area has eroded more rapidly than before. During the period 2010–2020, hundreds of acres of agricultural land, houses, and homesteads were destroyed or damaged. The Torsa River is characterized by variable discharge in different seasons. Every year during the peak season, high discharge along with excessive sedimentation and expansion of shoal areas over the bed level of the Torsa River or near the junction of tributaries (confluences of the Mora Torsa-1, Kaljani River, and Raidak River) obstruct the free flow of the Torsa River. This phenomenon causes an adverse impact in the lower catchment of the study area by causing water logging and increasing the intensity of floods. The Cooch Behar and Alipurduar districts are severely affected by the flooding of the Torsa River in the northern plains and Tal regions and its tributaries due to the heavy rainfall during the rainy season. So, a detailed examination of the morphodynamic characteristics of the Torsa River basin is critical for combating flood events as well as riverbank erosion hazards. This study will contribute greatly to planners, policymakers, and developers for implementing micro-level planning programmes at the basin scale which will improve the livelihood status of the common people living in the riparian environment.

Introduction to fluvial geomorphology 27

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Melton, M.A. (1957). An analysis of the relations among the elements of climate, surface properties and geomorphology. Technical Report 11. New York: Department of Geology, Columbia University. Mili, N., Acharjee, S., & Konwar, M. (2013). Impact of flood and river bank erosion on socioeconomy: A case study of Golaghat revenue circle of Golaghat district, Assam. International Journal of Geology, Earth & Environmental Sciences, 3(3), 180–185. Morisawa, M.E. (1959). Relations of quantitative geomorphology to stream flow in representative watersheds of the Appalachian Plateau Province. Project NR 389–042. Technical Report 20. Columbia University, Office of Naval Research. Mutton, D., & Haque, C.E. (2004). Human vulnerability, dislocation and resettlement: Adaptation processes of river-bank erosion-induced displaces in Bangladesh. Disasters, 28(1), 41–62. Newson, M.D., & Sear, D. (1998). The role of geomorphology in monitoring and managing river sediment systems. Water and Environment Journal, 12(1), 18–24. Oldroyd, D.R., & Grapes, R.H. (2008). Contributions to the history of geomorphology and Quaternary geology: An introduction. In R.H. Grapes, D. Oldroyd & R. A. Grigelis (Eds.), History of geomorphology and quaternary geology (Special Publications, Vol. 301, pp. 1–17). London: Geological Society. Osterkamp, W.R., & Schumm, S.A. (1996). Geoindicators for river and river-valley monitoring. In A.R. Berger & W.J. Iams (Eds.), Geoindicators (pp. 97–114). Rotterdam: Balkema. Phillips, J.D. (2012). Synchronization and scale in geomorphic systems. Geomorphology, 137, 150–158. Phukan, A., Goswami, R., Borah, D., Nath, A., & Mahanta, C. (2012). River bank erosion and restoration in the Brahmaputra River in India. Clarion, 1(1), 1–7. Rahman, M.R. (2013). Impact of Riverbank Erosion Hazard in the Jamuna Floodplain Areas in Bangladesh. Journal of Science Foundation, 8(1–2), 55–65. Richard, K., Chandra, S., & Friend, P. (1993). Avulsive channel system: Characteristics and Examples. In J.L. Best & C.S. Bristo (Eds.), Braided Rivers (Vol. 75, pp. 195–203). Geological Society Publication. Ritter, D.F., Kochel R.C., & Miller J.R. (1995). Process geomorphology. Boston, MA: McGraw-Hill. Ritter, D.F., Kochel, R.C., & Miller, J.R. (2002). Process geomorphology. New York: Mc Graw-Hill. Rudra K (1996) Problems of Bank Erosion in Murshidabad District of West Bengal. Journal of Geography and Environment, Vidyasagar University, West Bengal, 1, 25–32. Rudra, K. (2004). The encroaching Ganga and social conflicts: The case of West Bengal, India (p. 40). Littleton: Independent Broadcasting Associates. Salmela, J., Kasvi, E., Vaaja M.T., Kaartinen, H., Kukko, A., Jaakkola, A., & Alho, p. (2020). Morphological changes and riffle-pool dynamics related to flow in a meandering river channel based on a 5-year monitoring period using close-range remote sensing. Geomorphology, 352, 1–43. Sarma, D. (2013). Rural risk assessment due to flooding and Riverbank Erosion in Majuli, Assam, India. Master’s thesis. University of Twente. Scheidegger, A.E. (1965). The algebra of stream—order numbers. US Geological Survey Professional Paper, 525B, 187–189. Schumm, S.A. (1956). The evaluation of drainage system and slopes in badlands at Perts Amboi, New Jersey. Geological Society of America Bulletin, 67, 597–646. Schumm, S.A. (1977). The fluvial system. New York: Wiley. Schumm, S.A. (1981). Evolution and response to the fluvial system, sedimentologic implications. In F.G. Ethridge & R.M. Flores (Eds.), Recent and Ancient Nonmarine

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2

River basin morphometry A quantitative study

The term morphometry derives from two words: morpho meaning ‘the forms of the earth surface’ and metry meaning ‘the measurement of such forms’ (Sen, 1993). Morphometry is the ‘Measurement of the shape, or geometry, of any natural form – be it plant, animal or relief features’ (Strahler, 1969). But in geomorphology, the morphometry may be defined as the mathematical and geometrical analysis of the configuration of the earth’s surface as well as the shape and dimension of its landforms. Morphometric analyses of drainage basins provide a scrupulous quantitative science from an unpretentious quantitative and deductive approach and present practical results for river geomorphologists (Strahler, 1964). Basin morphometry comprises the quantitative study of the area, elevation, slope, volume, land profiles, and characteristics of the drainage basin in the concerned area (Singh, 1972). River basin morphometry may be defined as the quantitative study and mathematical analysis of the basin geometry; configuration, topological characteristics, and profiles of the drainage basin; and slope of the area concerned. The morphometric analysis of any river basin focuses on the geospatial dimensions, and it provides the specific information about the measurable features of drainage networks, and also helps in understanding of the geologic and geomorphologic characters of the basin (Rai et al., 2017). The systematic study of the river or drainage basin morphometry provides a quantitative description of the river basin geometry and its drainage network. Morphometric analysis is very important to understand the development of topography and landforms, and the erosional characteristics; it also gives useful evidence about the hydrological behaviour of the surface lithology and development of a drainage network within the basin. The analysis of river basin morphometry reveals an idea about the basin dynamics and the earth’s surface geometrical dimensions (Gregory and Walling, 1973; Ali and Khan, 2013). Morphometry of a river basin can be divided into two distinct branches: relief morphometry and fluvial morphometry. Relief morphometry incorporates an analysis of the topographical features through different aspects, such as hypsometric curves, altimetric frequency histograms and curves, area–height curves, clinographic curves, serial profiles, superimposed profiles, projected profiles, and composite profiles, that assist in dealing with various aspects of landform characteristics of any geomorphic unit or river basin. The fluvial morphometry includes DOI: 10.4324/9781003276685-2

River basin morphometry

33

the consideration of various kinds of aspects such as linear or one-dimensional aspects, areal or two-dimensional aspects, and relief or three-dimensional aspects of a river basin. The linear aspect of a river basin incorporates the study of stream order, stream number, bifurcation ratio, stream lengths, stream length ratio, sinuosity indices, and their relationships with the law of stream numbers, law of stream lengths, etc. The areal aspects of a river basin include the study of basin geometry, viz. basin perimeter, basin area, basin shape, and related morphometric laws, such as the laws of basin area and allometric growth; stream frequency; drainage density; drainage texture; drainage intensity; length of overland flow; constant of channel maintenance; and infiltration number. The relief aspects of a river basin incorporate the analysis of basin relief, gradient ratio, average slope, relief ratio, absolute and relative reliefs, dissection index, and profiles of the terrain. Several geomorphologists have focused on the development of quantitative morphometric methods over the last few decades to give details about the evolution and behaviour of drainage networks of basins (Horton, 1945; Leopold and Maddock, 1953; Abrahams, 1984). The remote sensing technique is a very convenient and useful method to analyze drainage basin morphometry because the satellite imageries provide a synoptic view of the basin area (Javed et al., 2011).

Basin morphometry Analysis of the drainage system based on the morphometric parameters is very important for basin or sub-basin planning, because it gives an idea about the characteristics of the drainage basin in terms of topography, slope, condition of soil, runoff characteristics, etc. (Javed et al., 2011). The basin morphometric analysis or investigation can be attained through the measurement of linear, areal, and relief aspects of the basin. Linear aspects The linear aspects of basins are closely related to the channel patterns of the stream network, in which the topographic characteristics of the stream segments are analyzed in terms of open links of the drainage system. The linear aspect deals with stream order, stream number, bifurcation ratio, stream lengths, stream length ratio, sinuosity indices, and their relationships with the law of stream numbers, law of stream lengths, etc. Analysis of these parameters gives details about, for example, the evolution of the drainage basin, hydrological potentialities, behaviour of floods, and channel migration of the river. Stream order (Su) Stream order (Su) is the most important parameter for the analysis of the drainage basin. Hierarchical stream ordering is very important in giving an idea about the hydrodynamic character of a river basin. Stream ordering is the measure of the position of a stream in the hierarchy of streams within a drainage basin (Horton

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1945; Strahler 1957; Leopold et al., 1964; Leopold and Bull, 1979; Kondolf and Herve, 2003).In 1914 Gravelius made the first attempt to determine the stream order. Thereafter, a number of scholars have attempted to determine stream ordering schemes for the analysis of stream hierarchy; such scholars were Horton (1932, 1945), Strahler (1952, 1957), and Gregory and Walling (1973). Most geomorphologists have used Strahler’s stream ordering scheme for the morphometric analysis of stream networks, because it is simple and very easy to apply. Streams of the basin have been numbered on the basis of Strahler’s (1957) scheme of stream ordering to determine the hierarchy of streams within the Torsa River system. According to Strahler (1969), each fingertip channel is designated as a first-order stream segment. Where a first-order stream flows downwards and joins with another first-order stream, it forms a second-order stream. At the junction of any two second-order streams, a third-order stream is created, and so forth. The hierarchical order does not increase if a relatively lower-order stream segment meets with a higher-order stream segment. The hierarchical order increases only when two equal-order stream segments meet with each other and form a stream junction. This stream ordering scheme is popularly known as the ‘stream segment method’. For example, the Torsa River basin is attributed with a dendritic drainage pattern (Figure 2.1A), as well as a tree-like pattern with an irregular branching of tributaries in various directions with different angles. It has been found that the Torsa River basin is designated as a sixth-order basin having 1024 streams with a preponderance of lower-order streams, and sub-basins are fashioned from third to fifth orders (Figure 2.1A; Table 2.1). Only the Raidak 1 sub-basin of the Torsa system is designated as the highest fifth-order stream (Table 2.1). Physiographic and structural conditions can control the stream ordering and their coverage areas. Stream order is directly proportional to the size of the drainage basin, dimension of the channel, and stream discharge (Rai et al., 2017). The size of a stream, area of a stream, and runoff are directly proportional to the size of the drainage basin. A higher stream order carries a huge volume of water and sediment loads with extreme discharge and velocity of stream flow. The Torsa basin is dominated by first-order streams (754) (Table 2.1). Therefore, it is observed that in the Torsa basin the number of streams as well as stream frequency decreases as the stream order increases and vice versa. Towards downstream the Torsa River gradually increases its width with increasing volume of water and discharge because of several lower-order streams. Bifurcation ratio (Rb) Bifurcation ratio (Rb) may be defined as the ratio of the number of the stream segments of a given order (Nu) to the number of streams of the next higher order (Nu+1). It is expressed as follows (Schumm, 1956): Bifurcation ratio ( R b ) =

Nu N u +1

(2.1)

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Figure 2.1 (A) Stream ordering map of the Torsa River basin. (B) Sub-basins of the Torsa catchment. Table 2.1 Stream order-wise number of streams of the Torsa River basin and its tributary sub-basins Basin name Torsa River Kaljani River Raidak-1 River Pa Chu Samchu Khola Tromo Chhu Khangphu Chu Chimkhiphu Chhu Tangka Chhu

Number of streams (Nu) Nu 1

Nu 2

Nu 3

Nu 4

Nu 5

Nu 6

Total Nu

754 107 74 68 55 69 17 26 13

204 31 20 19 13 19 4 6 2

48 10 7 4 4 4 1 1 1

14 1 3 1 1 1

3

1

1024 149 105 92 73 93 22 33 16

1

Source: Data calculated by the author.

The bifurcation ratio is a dimensionless property which varies from 2.0 to 5.0 or more (Table 2.2). This ratio is controlled by the drainage density, basin shape, basin area, entrance angles of the stream, and lithological characteristics of the basin. The Rb varies from 3.00 to 4.67 in the Torsa River basin (Table 2.2).

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Table 2.2 Bifurcation ratio of the Torsa basin and its tributary sub-basins Basin name Torsa River Kaljani River Raidak-1 River Pa Chu Samchu Khola Tromo Chhu Khangphu Chu Chimkhiphu Chhu Tangka Chhu

Bifurcation ratio (Rb) Rb 1 - 2

Rb 2 - 3

Rb 3 - 4

Rb 4 - 5

Rb 5 - 6

Mean Rb

3.70 3.45 3.70 3.58 4.23 3.63 4.25 4.33 6.50

4.25 3.10 2.86 4.75 3.25 4.75 4.00 6.00 2.00

3.43 10.00 2.33 4.00 4.00 4.00

4.67

3.00

3.81 5.52 2.97 4.11 3.83 4.13 4.13 5.17 4.25

3.00

Source: Data calculated by the author.

Values of Rb are not fixed from one order to the next higher order in the Torsa basin due to variation of the basin’s lithology and geology. Rb shows the degree of integration prevailing between streams of various orders in a drainage basin (Rai et al., 2017). A very high Rb indicates an early hydrograph peak with a higher possibility of flash flooding during the monsoon (Howard, 1990; Rai et al., 2017). Very high values of Rb in any river basin indicate a strong structural control on the drainage pattern, whereas low values of Rb are indicate that parts of the basin are not affected by structural instabilities (Strahler, 1952, 1957, 1964; Chopra et al., 2005; Rai et al., 2017). The bifurcation ratios of the Torsa River basin are very high in the mountain (Himalayan) and piedmont regions where there is strong structural control on the drainage pattern, whereas the northern alluvial plains region has a less disturbing drainage pattern. On the other hand, flash flooding occurs during the peak discharge period in the foothills and piedmont regions of the Torsa basin which exhibit high Rb values (Table 2.2). Mean Rb values of the sub-basins Chimkhiphu Chhu, Tangka Chhu, Tromo Chhu, Khangphu Chu, and Pa Chu in the Himalayan region range between 4.11 and 5.17 (Table 2.2), which indicate strong structural control on the drainage pattern. The sub-basins Kaljani and Pa Chu indicate strong structural control on the drainage pattern with flash floods occurring during the monsoon, whereas the drainage pattern of Raidak-1 is not structurally controlled and this sub-basin is less affected by flash floods during peak discharge.

Weighted mean bifurcation ratio (Rbwm) The weighted mean bifurcation ratio (Rbwm) is obtained by multiplying the bifurcation ratio for each consecutive pair of stream orders by the total stream numbers involved in the ratio and taking the average of the sum of these values (Strahler,

River basin morphometry

37

1952; Rai et al., 2018). Schumm (1956) applied the same method to identify the weighted mean bifurcation ratio. This equation is expressed as: R bwm = R b1* N u - r1+ R b 2 * N u - r 2 +¼.R b n * N u - r n / N u - r1+ N u -r 2 +¼.N u -r n

(2.2)

The value of the weighted mean bifurcation ratio for the Torsa River basin is 3.80 (Table 2.3). Law of stream numbers The stream number (Nu) is defined as the total number of streams of each order in a given drainage basin. The number of streams is directly proportional to the extent of a drainage basin and the dimension of the channels (Rai et al., 2017). Horton’s (1945) law of stream numbers connects the clear relationship between stream order and the number of streams in a drainage network. The law of stream numbers states that ‘the number of stream segments of successively lower orders in a given basin tend to form a geometric series beginning with the single segment of the highest order and increasing according to constant bifurcation ratio’ (Horton, 1945). The stream order and stream numbers are plotted on the Cartesian coordinates (Figure 2.2) where stream order is plotted along the abscissa (x-axis) on an arithmetic scale and the stream number is plotted along the ordinate (y-axis) on a logarithmic scale (Rai et al., 2017). The Torsa River basin comprises a total of 1024 streams, including the Torsa River (Table 2.1). Out of the total streams, 73.63% (754) are first-order streams, 19.92% (204) are second-order streams, 4.69% (48) are third-order streams, 1.37% (14) are fourth-order streams, 0.29% (4) are fifth-order streams, and 0.10% (1) are sixth-order streams (Table 2.1). The variation of stream numbers of each order of streams is largely influenced by the structure, lithology, tectonics, and the Table 2.3 Weighted mean bifurcation ratio of the Torsa River basin Su

Nu

1 2 3 4 5 6 Total Mean

754 204 48 14 3 1 1024

Rb

Nu–r

Rb × Nu–r

3.70 4.25 3.43 4.67 3.00 19.04 3.81

958 252 62 17 4 1293

3540.84 1071.00 212.57 79.33 12.00 4915.75

Rbwm

3.80

Source: Data calculated by the author. Notes: Su, stream order; Nu, stream number; Rb, bifurcation ratio; Nu–r, number of streams used in the ratio; Rbwm, weighted mean bifurcation ratio.

Number of streams of given order (Nu)

38

River basin morphometry 1000

y = -125.7x + 610.8 R² = 0.998 r = - 0.795

100 10 1

0

1

2

3

4

5

6

Stream Order (Su)

Figure 2.2 Relationship between stream order and number of streams in the Torsa River basin.

geomorphological situation of the basin (Romshoo et al., 2012; Rai et al., 2017). The present study shows that the stream numbers are decreasing exponentially with increasing stream order (Figure 2.2) at a notable rate (R2 = 0.998). Horton’s law of stream numbers of the Torsa River basin shows a very strong negative correlation between stream order and stream numbers with a r value of –0.795 (Figure 2.2). The result (Figure 2.2) validates Horton’s law of stream numbers. The highest stream numbers are located in the Himalayan region of the Torsa basin, which designates impermeable lithology and less infiltration of water. Law of stream length The stream length (Lu) is designated as the total lengths of a stream network of each of the successive stream order in a drainage basin (Horton, 1945). Lu is a significant hydrologic parameter of any drainage basin. The overall stream length of all order segments is 4179.27 km in the Torsa basin. In the Torsa basin, the total stream length of first-order segments is 2162.23 km, which is about 51.74% percent of the basin area. The stream length of second-order segments is 817.22 km (19.55%), 493.40 km (11.81%) for third-order segments, 390.79 km (9.35%) for fourth-order segments, 109.10 km (2.61%) for fifth-order segments, and 206.53 km (4.94%) for sixth-order segments. Normally, the total stream length decreases with increasing stream order (Figure 2.3). The Torsa River basin shows a negative regression line plotting on the semi-log graph and an established theoretical relationship. The scatter plot shows a strong negative relationship (about 85%) between the stream order and stream length that approximately follows a straight-line relation with an r value of –0.845 (Figure 2.3). Mean stream length (mLu) has been calculated by dividing the total stream length of order u by the total number of stream segments of the same order u. The mean stream length value varies from basin to basin, and is directly proportional to the extent and physiography of the basin (Rai et al., 2017). Mean stream length

39

Stream length (Lu) in Km

River basin morphometry 10000.00

y = -343.0x + 1897 R² = 0.849 r = -0.845

1000.00 100.00 10.00

0

1

2

3

4

5

6

7

Stream Order (Su)

Mean Stream Length in Km (mLu)

Figure 2.3 Relationship between stream order and stream length in the Torsa River basin. 1000.00

y = 32.37x - 65.31 R² = 0.955 r = 0.768

100.00 10.00 1.00

0

1

2

3 Stream Order (Su)

4

5

6

Figure 2.4 Relationship between stream order and mean stream length in the Torsa River basin.

is a distinctive property which is connected to the size of the stream network and its associated topography (Strahler, 1964). The mean stream length is calculated according to the following equation: Mean stream length ( mL u ) =

å Lu Nu

(2.3)

where ∑Lu is the sum of the total stream lengths of a given order, and Nu is the number of total streams of the same order. The mean stream length values vary from 2.87 km to 206.53 km in the Torsa River basin. The scatter plot shows a strong positive relationship (about 95%) between the mean stream length and the stream order that approximately follows a straight-line relation with an r value of 0.768 (Figure 2.4). Horton’s law (1945) of stream length states that ‘the cumulative mean lengths of stream segments of successive higher orders increase in geometrical progression starting with the mean length of the 1st order segments with constant length ratio’. In this connection, it is found that the Torsa basin follows the theoretical relationship of Horton’s law of stream lengths. The scatter plot shows a very good positive relationship (r = 0.82) between stream order and cumulative mean stream length with an R2 value of 0.994 (Figure 2.5; Table 2.4).

Cumulative Mean Stream Length (CmLu) in km

40

River basin morphometry 1000 100 10 1

y = 47.91x - 94.14 R² = 0.994 r = 0.82 0

1

2

3

4

5

6

7

Stream Order (Su)

Figure 2.5 Relationship between stream order and cumulative mean stream length in the Torsa River basin. Table 2.4 Log of some linear parameters of the Torsa River basin Stream Log of Log of stream order (SU) number of length streams (Log Lu) in km (Log Nu)

Log of mean Cumulative mean stream length stream length (Log mLu) (CmLu) in km in km

Log of cumulative mean stream length (Log CmLu) in km

1 2 3 4 5 6

0.46 0.60 1.01 1.45 1.56 2.31

0.46 0.84 1.23 1.65 1.91 2.46

2.88 2.31 1.68 1.15 0.48 0.00

3.33 2.91 2.69 2.59 2.04 2.31

2.87 6.87 17.15 45.07 81.43 287.96

Source: Data calculated by the author.

Stream length ratio (RL) The stream length ratio (RL) may be defined as the proportion of mean stream lengths between two successive stream orders of a basin. The stream length ratio gives an idea about the permeability of the rock developments in a river basin. The stream length ratio is a very important parameter to examine the hydrological characteristics of any river basin (Rai et al., 2017). The stream length ratio is calculated using the following the equation: stream length ratio ( R L ) =

mL u mL u -1

(2.4)

where mLu is the mean length of all stream segments of a given stream order. The RL values vary between 1.30 and 5.68 in the Torsa River basin. The value of the stream length ratio changes in different stream orders of the Torsa basin. This type of change has been occurring because of the variation in slope and topographic characteristics indicating the early mature stage of geomorphic development of the Torsa basin (Singh and Singh, 1997; Rai et al., 2017).

41

River basin morphometry Weighted mean stream length ratio (Lurwm)

The weighted mean stream length ratio (Lurwm) is acquired by multiplying the stream length ratio for each consecutive pair of stream orders by the total stream numbers intricate in the ratio and taking the average of the sum of these values. This equation is expressed as: L urwm = L ur1* L ur -r1+ L ur 2* L ur - r 2 L ur -r n +¼L ur n * L ur -r n / L ur - r1+ L ur -r 2 +¼L

(2.5)

The value of the weighted mean stream length ratio for the Torsa River basin is 2.07 (Table 2.5). Sinuosity indices Stream channel sinuosity (SI) means the degree of deviation of its actual course or path from the expected theoretic straight course or path. Channel sinuosity means the ratio between the observed and expected straight path of a stream. Two models have been applied for the calculation of channel sinuosity of the Torsa River and some of its important tributaries. The channel sinuosity has been assessed to know how far these rivers are controlled by the structural and terrain characteristics of this particular region. Schumm (1963) identified five categories of channel sinuosity on the basis of the following equation: Channel sinuosity (SI ) = O L / E L

(2.6)

where OL is the observed length, and EL is the expected straight length.

Table 2.5 Weighted mean stream length ratio of the Torsa River basin Su 1 2 3 4 5 6 Total Mean

Lu 2162.23 817.22 493.40 390.79 109.10 206.53 4179.27

Nu

Lu/Su

Lur

754 204 48 14 3 1 1024

2.87 4.01 10.28 27.91 36.37 206.53 287.96

1.40 2.57 2.72 1.30 5.68 2.73

Lur–r

Lur × Lur–r

2979.46 1310.62 884.18 499.88 315.63 5989.77

4162.14 3362.95 2401.04 651.24 1792.58 12369.95

Lurwm

2.07

Source: Data calculated by the author. Notes: Su, stream order; Lu, stream length; Nu, stream number; Lur, stream length ratio; Lur–r, stream length used in the ratio; Lurwm, weighted mean stream length ratio.

42

River basin morphometry

Channel sinuosity of the Torsa River is 1.33 (Table 2.6). The channel sinuosity has noticeably increased towards downstream in this basin. The degree of sinuosity of the Torsa River is low in comparison to the Raidak-1, Kaljani, and Pa Chu tributaries. J.E. Muller (1968) presented his models of channel sinuosity index in terms of hydraulic sinuosity and topographic sinuosity, based on the channel length (CL), valley length (VL), and air length (AL) (Equations 2.7–2.11). Air length refers to the shortest distance between the source and the mouth of the river. Channel Index ( CI ) = Valley Index ( VI ) =

CL AL

(2.7)

VL AL

Standard Sinuosity Index (SSI ) =

(2.8) CL VL

Hydraulic Sinuosity Index ( HSI ) =

(2.9)

CI - VI ´ 100% CI -1

Topographic Sinuosity Index ( TSI ) =

VI -1 ´ 100% CI -1

(2.10) (2.11)

On the basis of the Standard Sinuosity index (SSI) value, uniformity of SSI indicates a straight river course, whereas SSI values ranging between 1.0 and 1.5 represent a sinuous course, and an SSI value of more than 1.5 represents a meandering course. The Hydraulic Sinuosity Index (HIS) and Topographic Sinuosity Index (TSI) may be used to learn about the causal factors of sinuosity and determine the stages of the basin development. During the early stage of basin development, the other factors remain constant and the topographic sinuosity (greater than 60%) value dominates over the hydraulic sinuosity value; and in the late mature and old stages, the hydraulic sinuosity (greater than 60%) scores dominate over the topographic sinuosity (Singh, 2007). Hence, sinuosity indices elucidate the topographic and hydraulic characteristics of the river basin. The middle and lower course of the Torsa River and its tributaries, like Kaljani and Raidak-1, pass through the piedmont and alluvial zone with high HSI values and low TSI values. The upper course of the Torsa River flowing over mountain rock surfaces has high HSI values (Table 2.7). Rho coefficient (ρ) The rho coefficient (ρ) is defined as the ratio between the stream length ratio and the bifurcation ratio (Horton, 1945). The rho coefficient is an important parameter relating the drainage density and physiographic development of a drainage basin, which determine the water storage capacity of drainage network (Horton, 1945).

Source: Data calculated by the author.

105.67 106.20 42.59 17.59 39.73 24.67 22.28 18.90

Kaljani Raidak-1 Pa Chu Samchu Khola Tromo Chhu Khangphu Chu Chimkhiphu Chhu Tangka Chhu

67.16 57.52 29.36 16.50 33.94 20.84 21.55 16.21

1.57 1.85 1.45 1.07 1.17 1.18 1.03 1.17

1.33

306.07

Torsa

230.30

Observed Expected Channel length (km) straight sinuosity length (km)

Name of the river

Regular Regular Regular Transitional Transitional Transitional Straight Transitional

Regular

Sinuosity category

Upper and middle catchments thrust-fault controlled and lower catchment terrain controlled Upper catchment thrust-fault controlled Upper catchment thrust-fault controlled Terrain-thrust controlled Terrain-thrust controlled Thrust controlled Fault line controlled Terrain controlled Lower south Tibetan detachment controlled

Control

Table 2.6 Channel sinuosity of the Torsa River and its tributaries based on the Schumm model

River basin morphometry 43

44

River basin morphometry

Table 2.7 Channel sinuosity and stage of basin development of the Torsa River and its tributaries based on the Muller model Name of the river

Standard Hydraulic Topographic River course Stage sinuosity sinuosity sinuosity type of basin index index (%) index (%) development

Torsa Upper course (Torsa) Middle course (Torsa) Lower course (Torsa) Kaljani Raidak-1 Pa Chu Khangphu Chu Tangka Chhu

1.20 1.19 1.18 1.27 1.37 1.66 1.19 1.02 1.03

68.67 70.40 75.95 79.26 74.02 86.44 51.82 11.91 20.69

31.33 29.60 24.05 20.74 25.98 13.56 48.18 88.09 79.31

Sinuous Sinuous Sinuous Sinuous Sinuous Meandering Sinuous Sinuous Sinuous

Late mature Late mature Late mature Late mature Late mature Old Mature Early youth Youth

Source: Data calculated by the author.

The climatological, geological, biological, geomorphological, and anthropogenic factors determine the changes in the rho parameter (Rai et al., 2018). The rho coefficient (ρ) is calculated after Horton’s method (1945): Rho Coefficient (r ) =

RL Rb

(2.12)

where RL is the stream length ratio, and Rb is the bifurcation ratio. Higher values of rho coefficient indicate a higher amount of water storage capacity of drainage networks, whereas the lower values indicate a lower amount of water storage capacity in a drainage basin. The value of the rho coefficient for the Torsa River basin is about 0.72 (Table 2.8), which indicates high hydrologic storage capacity during floods. The values of rho coefficients for the sub-basins of Torsa River system varies from 0.35 to 0.91 (Table 2.8), indicating medium to very high hydrologic storage capacity during floods. Areal aspects The areal aspects of the drainage basin represent the characteristics of the catchment area. They explain the degree of erosion in a catchment area and describe how the drainage basin area controls and adjusts with hydrological behaviour. The areal aspects of the drainage basin include the geometry of the basin shape, stream frequency, drainage density, drainage texture, drainage intensity, length of overland flow, constant of channel maintenance, and infiltration number. Geometry of basin shape The geometry of the basin shape is very important in depicting and comparing different shapes of the drainage basins, which is connected with the functioning of

River basin morphometry

45

Table 2.8 Rho coefficient and hydrologic storage capacity of the Torsa River and its tributaries Basin name

Rho coefficient Hydrologic storage capacity

Torsa River Kaljani River Raidak-1 River Pa Chu Samchu Khola Tromo Chhu Khangphu Chu Chimkhiphu Chhu Tangka Chhu

0.72 0.60 0.91 0.58 0.59 0.58 0.35 0.42 0.58

High storage capacity High storage capacity Very high storage capacity Moderate storage capacity Moderate storage capacity Moderate storage capacity Low storage capacity Moderate storage capacity Moderate storage capacity

Source: Data calculated by the author.

the basin units and its genesis (Singh, 2007). Form factor, ellipticity index, circularity ratio, elongation ratio, lemniscate ratio, and shape index are used to assess shape characteristics of a basin. FORM FACTOR (FF)

The form factor (Ff) is defined as a dimensionless ratio of the basin area to the square of the basin length (Horton, 1932). The form factor indicates the flow characteristics (Horton, 1945), degree of erosion (Meshram and Sharma, 2015), and sediment load transport capacities (Soni, 2016) in a basin of a defined area. The form factor is a quantitative expression of the outline of drainage basin. The form factor is calculated using Horton’s method (1932): Form factor ( Ff ) =

A Lb 2

(2.13)

where A is the basin area, and Lb is the basin length. The value of Ff varies from 0 for highly elongated shapes to 1 for perfect circular shapes. A drainage basin with the higher form factor value is normally circular in shape and experiences higher peak flows of shorter duration, whereas an elongated basin with a low form factor value will have a low, flatter peak flow for longer duration. The Ff value of the Torsa River basin is 0.12 (Table 2.9). The Torsa basin and its most of the tributary sub-basins show a lower value of Ff which indicates a highly elongated basin with low flatter peak flow for longer duration, lower erosion, and lower capacities of sediment transport. The Samchu Khola sub-basin has a high form factor value indicating higher peak flows of shorter duration, more erosion, and higher sediment transport capacities, whereas Raidak-1 has a lower form factor value indicating lower peak flows of longer duration, less erosion, and lower sediment transport capacities (Table 2.9).

46

River basin morphometry

Table 2.9 Form factor and ellipticity index of the Torsa River basin and its tributary sub-basins Basin name

Basin area (km2)

Basin Form Shape of the basin Ellipticity Shape of the length factor index basin (km)

Torsa River 7486.31 248.02 0.12 Kaljani River 1307.59 73.03 0.25 Raidak-1 River 891.92 69.68 0.18 Pa Chu 408.18 36.45 0.31 Samchu Khola 276.88 24.08 0.48 Tromo Chhu 600.04 47.35 0.27 Khangphu Chu 177.40 21.96 0.37 Chimkhiphu Chhu 142.84 24.46 0.24 Tangka Chhu 146.07 19.23 0.40

Highly elongated Highly elongated Highly elongated Elongated Semi-circular Elongated Elongated Highly elongated Semi-circular

6.45 3.20 4.27 2.55 1.64 2.93 2.13 3.29 1.99

Highly elliptic Highly elliptic Highly elliptic Elliptic Semi-circular Elliptic Elliptic Highly elliptic Semi-circular

Source: Data calculated by the author. ELLIPTICITY INDEX (EI)

The ellipticity index (Ei) shows a relationship between the morphometry and hydrology of a drainage basin. The ellipticity index is measured after Stoddart (1965): Elipticity Index ( E i ) =

pL b 2 4A

(2.14)

where A is the basin area, Lb is the length of the basin, and the value of π is 3.14. The value of the ellipticity index varies from 1 to infinity, i.e. 0. The ellipticity index is inversely proportional to the form factor (Ff). A lower value on the ellipticity index indicates that the runoff drains rapidly from the catchment into the stream channel and vice versa. The value of Ei for the Torsa basin is 6.45 and in sub-basins it varies between 1.64 and 4.27 (Table 2.9). The Torsa basin shows the high value of the ellipticity index indicates the runoff draining slowly during floods with slow sediment transport. CIRCULARITY RATIO (C R)

The circularity ratio (CR) is defined as the dimensionless ratio of the basin area to the area of the circle with the same perimeter as the basin (Miller, 1953). The circularity ratio is influenced by the slope, relief, geological structures, length of streams, number of streams, climatic condition, and land use/land cover of the basin. The circularity ratio (CR) is calculated using Miller’s method (1953): Circularity ratio ( CR ) =

4pA rb 2

where rb is the basin perimeter.

(2.15)

River basin morphometry

47

The value of CR varies from 0 for the elongated shape to 1 for the circular shape of the basin. Low to high values of CR indicate the young to old stages of the drainage basin life cycle (Wilson et al., 2012). A low value of CR shows a more elongated shape of the basin and highly permeable uniform geologic materials. The Torsa basin shows a low CR value of 0.24 (Table 2.10), which indicates the basin is highly elongated with low discharge of runoff and extremely permeable lithology. The low value of CR shows that the Torsa basin is at an early maturity stage in the topographical life cycle. The CR value of sub-basins ranges between 0.41 and 0.67 (Table 2.10), which indicates an elongated basin shape with permeable homogenous lithology (Miller, 1953). ELONGATION RATIO (E R)

The elongation ratio (ER) is defined as the ratio of the diameter of the circle with the same area as the drainage basin and maximum length of the basin. The elongation ratio is calculated using the following equation after Schumm (1956): Elongation ratio ( E R ) =

2 p

Ff

(2.16)

The value of the elongation ratio varies from 0 for a highly elongated shape to 1 for a circular shape for the basin. A high ER value indicates a more circular basin shape, whereas a low ER value indicates a more elongated shape. The value of the elongation ratio of the Torsa basin is 0.39, which indicates a more elongated basin shape (Table 2.10) having a high infiltration capacity and low runoff. The low elongation ratio of the Torsa basin indicates a low rate of soil loss. The values of ER for the sub-basins vary from 0.48 to 0.78 (Table 2.10), which indicates a less elongated basin shape. Table 2.10 Values of circularity and elongation ratios for the Torsa River and its tributaries Basin name

Basin Circularity Shape of the Elongation Shape of the basin perimeter ratio basin ratio (km)

Torsa River

627.84

0.24

Kaljani River 172.53 Raidak-1 River 164.36 Pa Chu 97.64 Samchu Khola 71.83 Tromo Chhu 130.51 72.42 Khangphu Chu Chimkhiphu Chhu 60.87 Tangka Chhu 56.05

0.55 0.41 0.54 0.67 0.44 0.42 0.48 0.58

Source: Data calculated by the author.

Highly elongated Elongated Elongated Elongated Elongated Elongated Elongated Elongated Elongated

0.39

More elongated

0.56 0.48 0.63 0.78 0.59 0.78 0.78 0.78

Elongated More elongated Elongated Less elongated Elongated Less elongated Less elongated Less elongated

48

River basin morphometry

LEMNISCATE RATIO (K)

The lemniscate ratio (K) is used to determine the gradient or slope of the drainage basin (Chorley et al., 1957). The lemniscate ratio is calculated using the following equation: Lemniscate ratio ( K ) =

Lb 2 4A

(2.17)

where Lb is the basin length, and A is the basin area. The drainage basin with a high value of K indicates an elongated shape of the basin, whereas a circular basin has a low value of K. The Torsa basin shows a high K value, which indicates an elongated basin shape. The K values of the subbasins vary from 0.52 to 1.36, showing a semi-circular to highly elongated basin shape (Table 2.11). The Torsa basin and its sub-basins, like Raidak-1, Kaljani, and Chimkhiphu Chhu, have high K values indicating a very gentle slope in the northern plains and Himalayan regions, whereas the other sub-basins of the Torsa basin in the upstream show low values of K, indicating a steep slope gradient (Table 2.11). SHAPE INDEX (SB)

The shape index (SB) is simply the inverse of the form factor, that is, a reciprocal of the form factor having a dimensionless entity. The shape index is calculated using Horton’s method (1932): Shape index (SB ) =

1 Ff

(2.18)

where Ff is the form factor. Table 2.11 Lemniscate ratio and shape index for the Torsa River and its tributaries Basin name

Lemniscate ratio

Shape of the basin

Shape index

Shape of the basin

Torsa River Kaljani River Raidak-1 River Pa Chu Samchu Khola Tromo Chhu Khangphu Chu Chimkhiphu Chhu Tangka Chhu

2.05 1.02 1.36 0.81 0.52 0.93 0.68 1.05 0.63

Highly elongated Elongated Highly elongated Elongated Semi-circular Elongated Less elongated Elongated Less elongated

8.22 4.08 5.44 3.25 2.09 3.74 2.72 4.19 2.53

Highly elongated Highly elongated Highly elongated Elongated Semi-circular Elongated Elongated Highly elongated Elongated

Source: Data calculated by the author.

River basin morphometry

49

The drainage basin with a higher value of shape index is normally elongated and experiences weak flood discharge for longer duration, whereas a circular basin has a lower value and high flood discharge for short duration. The SB value of the Torsa River basin is 8.22 (Table 2.11), which indicates an elongated basin shape with weak flood discharge and less erosion. The values of the shape index for the sub-basins of the Torsa River system range from 2.09 to 5.44 (Table 2.11), indicating a semi-circular to highly elongated basin. Compactness coefficient (CC) The compactness coefficient (CC), also known as a Gravelius index (Gi), is defined as the ratio of the perimeter of the basin to the circumference of the circular area having an area equal to the basin (Gravelius, 1914). The compactness coefficient is independent of the size of the drainage basin and dependent only on the steepness of the slope (Horton, 1945). The CC is measured using the following formula after Gravelius (1914): Compactness Coefficient ( CC ) = 0.2841* P/A 0.5

(2.19)

High values of the compactness coefficient reveal an elongated drainage basin and low erosion, whereas low values indicate a less elongated drainage basin and more erosion (Meshram and Sharma, 2015). The value of CC for the Torsa basin is about 2.06, whereas the values of CC for the sub-basins vary from 1.23 to 1.56 (Table 2.12). The Torsa basin and the Raidak-1, Khangphu Chu, and Tromo Chhu sub-basins show a higher value of CC, which indicate a more elongated drainage basin with low erosion (Table 2.12). Mean basin width (Wb) The mean basin width (Wb) is defined as the ratio of the basin area to the basin length. The mean basin width is computed after Horton (1932): Table 2.12 Compactness coefficient for the Torsa River and its tributaries Basin name

Compactness coefficient

Shape of the basin

Degree of erosion

Torsa River Kaljani River Raidak-1 River Pa Chu Samchu Khola Tromo Chhu Khangphu Chu Chimkhiphu Chhu Tangka Chhu

2.06 1.36 1.56 1.37 1.23 1.51 1.54 1.45 1.32

Highly elongated Elongated Highly elongated Elongated Less elongated Highly elongated Highly elongated Elongated Elongated

Less erosion Moderate erosion Less erosion Moderate erosion More erosion Less erosion Less erosion Moderate erosion Moderate erosion

Source: Data calculated by the author.

50

River basin morphometry Mean basin width ( Wb ) =

A Lb

(2.20)

where A is the basin area, and Lb is the basin length. The mean basin width of the Torsa River basin is 30.18. Relative perimeter of drainage basin (Pr) The relative perimeter (Pr) of the drainage basin is defined as the ratio of the basin area to the basin perimeter. The relative perimeter is calculated after Schumm (1956): Relative Perimeter ( Pr ) =

A rb

(2.21)

where A is the basin area, and rb is the basin perimeter. The relative perimeter for the Torsa River basin is 11.92. The values of the relative perimeter for the sub-basins of the Torsa River system vary from 2.35 to 7.58. Length area ratio (Lar) For a large number of drainage basins, Hack (1957) identified that the length of the stream and basin area is connected by a simple power function. The length area ratio (Lar) is used to find out the length–basin area relationship. The equation of the length area ratio is as follows: Length area ratio ( Lar ) = 1.4 * A 0.6

(2.22)

where A is the basin area. The length area ratio for the Torsa basin is 295.59. The values of Lar of the subbasins of the Torsa River system vary from 27.48 to 103.76. Fitness ratio (RF) The fitness ratio (RF) is the ratio between the main channel length and the perimeter of the basin. This ratio is measured to know the topographic fitness of the watershed. The fitness ratio is calculated after Melton (1957): Fitness ratio ( R F ) =

CL rb

where CL is the main channel length, and rb is the perimeter of the basin.

(2.23)

River basin morphometry

51

The fitness ratio of the Torsa River basin is 0.49. The values of RF of the subbasins of the Torsa basin vary from 0.24 to 0.65. Wandering ratio (RW) The wandering ratio (RW) is defined as the ratio between the main channel length and the length of the basin. The RW is estimated after Smart and Surkan (1967): Wandering ratio ( R W ) =

CL Lb

(2.24)

where CL is the main channel length, and Lb is the length of the basin. The basin length is defined as the longest dimension of the basin parallel to the main stream line (Schumm, 1956). The wandering ratio of the Torsa River basin is 1.23. The values of RW of different sub-basins range between 0.73 and 1.52. Stream frequency (Sf) Stream frequency (Sf) or drainage frequency is defined as the total number of streams per unit area. It is calculated by the following formula introduced by Horton (1945): Stream frequency (Sf ) =

åN A

(2.25)

where N is the total number of streams, and A is the total basin area or a unit area. The stream frequency data can be classified into different categories depending upon the characteristics of the data. The Torsa basin is classified into five stream frequency zones: very low, low, moderate, high, and very high (Figure 2.6A). Most of the basin exists under low stream frequency (2–5 streams/km2) (Figure 2.6A). Very low to low stream frequency areas are located in the northern plains region of the Torsa basin. High to very high categories of stream frequency are located in the northern, central, and southern parts of the Himalayan mountain region of the Torsa basin (Figure 2.6A). Greater stream frequency in the Himalayan region clearly indicates the maximum drainage development and high drainage texture with steeper slope, greater relief variation, and prominent dissection. The high value of stream frequency designates a greater surface runoff and high relief as well as a steep ground surface (Horton, 1932, 1945). The stream frequency value of the Torsa River basin is very low (0.04) to very high (17.72), indicating a gentle ground slope to steep ground slope associated with permeable to impermeable subsurface material or rocks promoting low to greater surface runoff and infiltration. It mainly depends on the geology and lithology of the drainage basin and texture of the drainage network (Aouragh and Essahlaoui, 2018). The value of the stream frequency for the basin shows positive correlation

52

River basin morphometry

Figure 2.6 (A) Stream frequency map of the Torsa River basin. (B) Drainage density map of the Torsa River basin.

with the drainage density value of the area representing the increase in stream number regarding the increase in drainage density (Rai et al., 2017). The average values of the stream frequency for the sub-basins of the Torsa River system range from 4.07 (SB9) to 8.23 (SB5) streams/km2 (Table 2.15). Drainage density (Dd) Drainage density (Dd) refers to the ratio of the total stream length of all the stream orders in a given basin to the total area of that basin. It is calculated by the following formula introduced by Horton (1945): Drainage Density ( Dd ) =

å Lu A

(2.26)

where Lu is the total length of streams, and A is the total basin area or a unit area. The drainage density data is also classified into different categories depending upon the characteristics of the data. The Torsa basin is classified into five drainage density zones: very low, low, moderate, high, and very high (Figure 2.6B).

River basin morphometry

53

About 41.18% of the total basin area falls in the low drainage density class of 0.40–0.60 km length/km2. A very high drainage density indicates a highly dissected drainage basin with a relatively quick hydrological response during the rainy season, whereas a very low drainage density specifies an inadequately drained basin with a sluggish hydrologic response (Melton, 1957; Rai et al., 2017). Drainage density indicates the dissection of landscape, potentiality of runoff, infiltration capacity, nature of climate, and vegetation cover of the river basin. The drainage density of the Torsa River basin varies from 0.03 to 1.27 (Figure 2.6B). The southern part of the Torsa basin shows a low drainage density covered with highly permeable subsurface material and low relief (Figure 2.6B). On the other hand, the upper and middle catchments of the Torsa basin are registered with high drainage density with the presence of weak and impermeable subsurface topography and high relief area (Figure 2.6B). The low drainage density means a coarse drainage texture, whereas high drainage density means a fine drainage texture, high runoff, and the possibility of erosion in the river basin (Strahler, 1964). The average values of the drainage density of different sub-basins of the Torsa River system range from 0.39 (SB9) to 0.65 (SB5) km/km2 (Table 2.15). Drainage texture (Dt) The drainage texture (Dt) is defined as the total number of stream segments of all orders per the perimeter of the basin (Horton, 1945). It is a valuable concept of geomorphology, which signifies that the relative spacing of stream lines, and it depends on the underlying lithology, capacity of infiltration, relief of the terrain, and the stage of development. The drainage texture is calculated using the following formula from Horton (1945): Drainage textures ( D t ) =

N rb

(2.27)

where N is the number of streams, and rb is the perimeter of the basin. The drainage texture of the Torsa River basin ranges from 4.43 to 0.01(Figure 2.7), whereas the average drainage texture of the basin is 1.30 (Table 2.15). The average drainage texture values of various sub-basins of the Torsa basin range between 1.02 (SB9) and 2.06 (SB5) (Table 2.15). The subbasins of Raidak-1, Khangphu Chu, and Tangka Chhu show coarse drainage textures, whereas the sub-basins of Kaljani, Tromo Chhu, and Chimkhiphu Chhu show moderate drainage textures; and the sub-basins of Pa Chu and Samchu Khola reveal fine drainage textures (Table 2.15). Drainage textures of the Torsa River basin are classified into five zones (Figure 2.7). The drainage textures of very coarse, moderate, and fine categories cover an area of about 1431.68 km2, 1696.44 km2, and 1258.15 km2, respectively (Figure 2.7). Similar to the drainage density and stream frequency, drainage texture is also high (fine texture) in the Himalayan mountain region and low (coarse texture) in the northern plains region of the Torsa basin (Figure 2.7).

54

River basin morphometry

Figure 2.7 Drainage texture map of the Torsa River basin.

Constant of channel maintenance (Ccm) The constant of channel maintenance (Ccm) is the inverse of the drainage density having the length’s dimension as a property (Schumm, 1956). The constant of channel maintenance indicates the units of drainage area which are needed to bear one unit of the channel length. The value of this parameter increases with a decrease of drainage density and vice versa. The constant of channel maintenance can be measured by the following equation: Constant of channel maintenance ( Ccm ) = 1/ D d

(2.28)

where Dd is the drainage density. The Torsa River basin has been categorized into five Ccm zones: very low, low, moderate, high, and very high (Figure 2.8A). The Ccm class of 1.50–2.00 km/km2

River basin morphometry

55

Figure 2.8 (A) Constant of channel maintenance map of the Torsa River basin. (B) Length of overland flow of the Torsa River basin.

covers a large part of the basin. The average value of Ccm is 2.24 km/km2 in the Torsa basin (Table 2.15). The values of Ccm for the sub-basins of the Torsa River system vary between 1.47 and 2.20 (Figure 2.8A). The average values of the Ccm for the sub-basins of the Torsa River system range from 1.58 (SB5) to 2.90 (SB9) km/km2 (Table 2.15). The higher values of constant of channel maintenance are located in the northern alluvial plains and some pockets in the piedmont region, which indicate strong control of lithology with high surface permeability in those areas (Figure 2.8A). The middle course of the Torsa and the upper courses of the Kaljani and Raidak-I Rivers recorded low values of constant of channel maintenance due to the presence of several palaeochannels (Figure 2.8A). Length of overland flow (Lg) The length of overland flow is one of the most important morphometric parameters affecting the hydrologic and physiographic development of drainage basins (Horton, 1932). The length of overland flow (Lg) has been calculated after Horton (1945):

( )

Length of overland flow Lg = 1/ 2Dd

(2.29)

56

River basin morphometry

The values of Lg of the Torsa basin range from 0.39 to 19.35 (Figure 2.8B). The average value of Lg of the Torsa basin is 1.12 (Table 2.15), which indicates a relatively finer stream pattern with a longer course for the peak flow through the low relief area, and it is characterized by the late youth or early mature stages of basin development (Prakash et al., 2017). The average values of Lg of the sub-basins of the Torsa vary between 0.79 (SB5) and 1.45 (SB9) (Table 2.15). The length of overland flow of the Torsa basin has been classified into five categories: very low, low, moderate, high, and very high (Figure 2.8B). Similar to the constant of channel maintenance, it is also high in the northern alluvial plains, some pockets of the piedmont region, and some flat valleys of the northern Himalayan regions, which indicate high permeability with more seepage erosion (Figure 2.8B). Low values of Lg are found in the Himalayan region and foothills region of the Torsa basin indicating low permeability and rapid surface runoff with flash flooding (Figure 2.8B). Drainage intensity (Di) The drainage intensity (Di) is defined as the ratio of the stream frequency to the drainage density of the same area. The drainage intensity is measured using the following equation of Faniran (1968): Drainage intensity ( Di ) =

Sf Dd

(2.30)

where Sf is the stream frequency, and Dd is the drainage density. The values of drainage intensity range from 0.16 to 61.56 (Figure 2.9A), and the average drainage intensity is 9.48 in the Torsa basin (Table 2.15). The average values of the Di of different sub-basins of the Torsa River systems range from 6.37 (SB3) to 13.52 (SB4) (Table 2.15). The drainage intensity of the Torsa River basin has been classified into five categories: very low, low, moderate, high, and very high (Figure 2.9A). The Torsa basin is characterized by high drainage intensities with high drainage frequency and density, which indicates maximum surface runoff in the upper course (Figure 2.9A). The lowest drainage intensity is found in the northern plain regions as well as lower courses of the Raidak-1, Kaljani, and Torsa Rivers (Figure 2.9A). Infiltration number (If) The infiltration number (If) is defined as the product of drainage density and stream frequency. The infiltration number is calculated applying the following formula of Faniran (1968): Infiltration number ( If ) = Sf ´ Dd where Sf is the stream frequency, and Dd is the drainage density.

(2.31)

River basin morphometry

57

Figure 2.9 (A) Drainage intensity map of the Torsa River basin. (B) Infiltration number map of the Torsa River basin.

The infiltration number is inversely proportional to the infiltration capacity of the basin area (Romshoo et al., 2012). If the infiltration number is higher, than the infiltration rate will be lower and, consequently, the runoff will be higher. The values of the infiltration number for the Torsa River basin vary between 0.01 and 19.29 (Figure 2.9B), and the average infiltration number of the Torsa basin is 3.21 (Table 2.15), indicating high infiltration and low surface runoff with less erosion in the basin. The Samchu Khola sub-basin shows a higher infiltration number indicating low infiltration and high runoff, whereas the average infiltration numbers are low for the Tangka Chhu, Khangphu Chu, Raidak-1, and Kaljani sub-basins indicating a higher infiltration rate and low runoff (Table 2.15). The spatial character of the infiltration number has been divided into five categories (Figure 2.9B). Relief aspects The relief aspect of a drainage basin is defined as the study of three-dimensional features of a catchment connecting area, volume, and relief of landforms. The relief aspects of a drainage basin include the basin relief, gradient ratio, average slope, relief ratio, relative relief, dissection index, and profiles of the terrain.

58

River basin morphometry

Basin relief (Bh) The basin relief (Bh) is defined as the maximum vertical distance between the lowest and highest point of a river basin (Schumm, 1956). It is responsible for the gradient of the stream and influences flood patterns and the volume of sediment that can be transported. The basin relief is measured after Schumm (1956): Basin relief ( Bh ) = H - h

(2.32)

where H is the highest elevation of the basin, and h is the lowest elevation of the basin mouth. The highest and lowest elevations of the Torsa basin are 6696 m and 8 m, respectively (Table 2.13). The Bh values for the sub-basins of the Torsa River system range from 1791 m to 3615 m (Table 2.13). Gradient ratio (Rg) The gradient ratio (Rg) is defined as the ratio of the difference between the elevation at the source and the elevation at the mouth of the main stream of the basin to the horizontal equivalent or length of the same main stream. The gradient ratio is calculated using the method of Sreedevi et al. (2009):

( )

Gradient ratio R g =

Es - E m Lb

(2.33)

where Es is the elevation at the source, Em is the elevation at the mouth, and Lb is the horizontal equivalent or stream length. The gradient ratio is an indicator of channel slope from which volume of the runoff can be calculated (Sreedevi et al., 2005). The Torsa basin shows a high

Table 2.13 Basin relief, gradient ratio, relief ratio, and Melton ruggedness number for the Torsa River and its tributaries Basin name

Basin relief

Gradient ratio

Relief ratio

Melton ruggedness number

Torsa River Kaljani River Raidak-1 River Pa Chu Samchu Khola Tromo Chhu Khangphu Chu Chimkhiphu Chhu Tangka Chhu

6688 2398 1791 3523 3615 2674 2425 1968 2404

21.85 15.80 10.92 82.73 205.51 67.30 98.29 88.35 127.21

26.97 32.84 25.70 96.66 150.12 56.47 110.41 80.45 125.02

77.38 66.56 60.20 174.38 217.25 109.16 182.07 164.66 198.91

Source: Data calculated by the author.

River basin morphometry

59

gradient ratio of 21.85 (Table 2.13), which indicates that the Torsa River originates from hilly terrain. The gradient ratios of the sub-basins range from 10.92 to 205.51 (Table 2.13), which reflect moderate to very steep gradients. Relief ratio (Rh) The relief ratio (Rh) is defined as the dimensionless ratio between the basin relief and the longest measurement of the basin length parallel to the principal stream line. The relief ratio is measured applying the following formula from Schumm (1956): Relief ratio ( R h ) =

Bh Lb

(2.34)

where Bh is the basin relief, and Lb is the basin length. The relief ratio is directly related to the relief and the gradient of the channel. The relief ratio of the Torsa basin is 26.97 (Table 2.13). The Torsa basin is characterized by moderate relief ratios. The relief ratios for the sub-basins of the Torsa River system vary from 25.70 to 150.12 (Table 2.13), which indicate moderate to very high relief ratios. Elevation An elevation map has been generated using the digital elevation model (DEM) through a geographic information system (GIS). The elevation of the Torsa basin varies from 6696 m to 8 m. The Torsa basin has been divided into 12 elevation zones (Figure 2.10A). Variations of elevation increase prominently towards the north, i.e. the Himalayan mountain region (Figure 2.10A). Absolute relief (AR) The absolute relief refers to the maximum elevation of a particular area in any drainage basin. The absolute relief map has been developed using the contour map on a GIS platform. The average absolute relief of the Torsa River basin is 2023.62 m (Table 2.15). The absolute relief of the basin varies between 20 m and 6696 m. The Torsa basin has been divided into 12 absolute relief zones (Figure 2.10B). The absolute relief increases towards the north and decreases towards the south, i.e. northern plains region (Figure 2.10B). Average slope (SA) The slope of the topography controls the runoff speed associated with affecting the required time for rainwater to enter the riverbeds and also controls the stream water velocity that changes the river morphology and network of the river basin (Rai et al., 2017). Average slope directly influences the erodibility of a drainage

60

River basin morphometry

Figure 2.10 (A) Elevation zone map of the Torsa River basin. (B) Absolute relief map of the Torsa River basin.

basin. Erosion increases with an increasing slope, if all other factors remain constant. The average slope (SA) is calculated after Wentworth (1930): Average slope (SA ) = tan q =

C´I K

(2.35)

where C is the average number of contours crossing per unit grid, I is the contour interval, and K is the constant (636.6). In the Torsa River basin slope varies from 0°26′ to 61°30′ (Figure 2.11A), and the basin is classified into five slope categories (Figure 2.11A). The average slope of the Torsa basin is 17° (Table 2.15). The Himalayan mountain region is characterized by moderate to very steep slopes (Figure 2.11A). The slope distribution over the piedmont region is quite gentle, but some places of isolated hillocks, uplifted terraces, and river valleys are characterized by moderate slope (Figure 2.11A). Minimum variations of the average slope are found in the northern plains region due to the topographic flatness or monotonous nature of this region (Figure 2.11A). It is observed that the surface runoff and stream water velocity and erosion decrease with decreasing slope towards the lower catchment of the Torsa basin.

River basin morphometry

61

Figure 2.11 (A) Average slope map of the Torsa River basin. (B) Relative relief map of the Torsa River basin.

Relative relief (RR) Relative relief is closely associated with slopes and is an important morphometric parameter for the assessment of morphological characteristics of any topography (Gayen et al., 2013; Rai et al., 2017), although it does not take into account the dynamic potential of the terrain. The relative relief (RR) of the whole drainage basin is calculated after Smith (1935): Relative Relief ( R R ) = H A - L A

(2.36)

where HA is the highest altitude and the LA is the lowest altitude. The relative relief in the Torsa River basin ranges between 10 m and 2037 m (Figure 2.11B), and the average relative relief is 560 m above mean sea level (Table 2.15). The result shows that the Raidak-1 sub-basin having a lower value of RR has a low magnitude of elevation difference with the low intensity of erosion, whereas the Samchu Khola sub-basin, with a higher value of RR, has a high magnitude of elevation difference with high intensity of erosion (Table 2.15).

62

River basin morphometry

Eight categories of relative relief have been identified for the Torsa basin (Figure 2.11B). The relative relief of the Torsa basin increases from the southern plains to the northern Himalayan mountain region except the northernmost tip near the source of the Torsa River (Figure 2.11B). High to extremely high amplitudes of relative relief are found over the Himalayan mountain region, indicating the maximum magnitude of elevation difference and a high degree of slope in the river valley side associated with high intensity of erosion (Figure 2.11B). The lower catchment as well as the northern plains region of the Torsa basin have a low to very low relative relief, which indicates low magnitude of elevation difference, low degree of slope on the river valley side, and flat topography associated with low intensity of erosion over the plains region (Figure 2.11B). Dissection index (DI) The dissection index (DI) is defined as the ratio of relative relief to the absolute relief of any unit area. The dissection index is an important morphometric parameter of the drainage basin in understanding the intensity and vulnerability of vertical erosion and explains the stages of the cycle of erosion attained by the stream in the course of the evolution of the basin concerned (Nir, 1957). It is useful in the study of the nature and magnitude of the terrain and the drainage basin dynamics. The dissection index is calculated applying the following formula after Dov Nir (1957): Dissection Index (D I ) =

RR AR

(2.37)

where RR is the relative relief, and the AR is the absolute relief. The values of dissection vary between 0 and 1. Higher values of DI reflect an early stage in the cycle of erosion with a high degree of dissection. In the Torsa River basin dissection index values range from 0.03 to 0.88 (Figure 2.12 A). The average value of dissection for the Torsa River basin is 0.41, which indicates the presence of vertical erosion in the basin, and this basin is passing through the late youthful stage of the cycle of erosion (Table 2.14). The average values of dissection for the sub-basins vary between 0.12 and 0.53, which indicate that the subbasins of the Torsa are passing through the mature to young stages of the cycle of erosion (Table 2.14). The Torsa basin has been divided into eight categories for the dissection index (Figure 2.12A). A high dissection index is found in the middle catchment of the Torsa basin consisting of the Lesser and Shiwalik Himalayan regions and some pockets of the piedmont region (Figure 2.12A). Ruggedness index (Rg) Ruggedness refers the degree of corrugation of the topography. Ruggedness is defined as the product of the relative relief and the drainage density. Computation

River basin morphometry

63

Figure 2.12 (A) Dissection index map of the Torsa River basin. (B) Ruggedness index map of the Torsa River basin. Table 2.14 Average dissection index and stage of cycle of erosion in the Torsa basin and its tributary sub-basins Basin

Dissection Cycle of Basin index erosion stage

Torsa Kaljani Raidak-1 Pa Chu Samchu Khola

0.41 0.52 0.53 0.51 0.44

Young Young Young Young Young

Tromo Chhu Khangphu Chimkhiphu Tangka Chhu

Dissection Cycle of index erosion stage 0.12 0.13 0.16 0.21

Mature Mature Mature Mature

Source: Data calculated by the author.

of the ruggedness index is done using the following formula on the basis of 1 km2 grids:

( )

Ruggedness Index R g =

R R ´ Dd K

(2.38)

where RR is the relative relief, Dd is the drainage density, and K is a constant (1000).

64

River basin morphometry

The ruggedness index increases with increasing the values of drainage density and relative relief. Very high values of ruggedness index occur when slopes of the basin are steeper and longer. Higher ruggedness values reveal more vulnerability to soil erosion and vice versa. The Rg values of the Torsa basin vary from 0.01 to 1.63 (Figure 2.12B), and the average Rg value of the Torsa basin is 0.32 (Table 2.15). It has been noted that the highest values of ruggedness are found in the Himalayan mountain region followed by the piedmont region, which indicates more proneness to soil erosion (Figure 2.12B). The northern plains region as well as the lower catchment of the Torsa basin show low to very low ruggedness index (Figure 2.12B), indicating less proneness to soil erosion where relative relief and drainage density are low. Melton ruggedness number (MRn) The Melton ruggedness number (MRn) is a slope index that provides specialized depictions of the relief ruggedness within a basin (Melton, 1957). The equation for the Melton ruggedness number is as follows: Melton Ruggedness Number ( MRn ) =

H A 0.5

(2.39)

The value of Melton ruggedness number of the Torsa basin is 77.38 (Table 2.13), indicating a debris flow basin, where bed load sediments are under transport. The sub-basins of the Torsa River system having moderate to high values of Melton ruggedness numbers ranging from 60.20 to 217.25 (Table 2.13), indicating a normal flow in the mainstream with less to more debris flow.

Table 2.15 Average values of morphometric parameters of the Torsa River basin and its tributary sub-basins

Sf Dd Dt Ccm Lg Di If SA AR RR Rg Ri

SB1

SB2

SB3

SB4

SB5

SB6

SB7

SB8

SB9

5.20 0.55 1.30 2.24 1.12 9.48 3.21 17° 2023.62 560 0.32 0.49

4.85 0.62 1.21 1.79 0.90 8.05 3.20 7°45′ 322.89 196.91 0.14 0.49

4.23 0.60 1.06 1.86 0.93 6.37 3.15 6°13.8′ 185.64 126.07 0.11 0.48

7.80 0.58 1.95 1.77 0.88 13.52 4.63 28°28.8′ 2444.76 1185.30 0.68 0.50

8.23 0.65 2.06 1.58 0.79 12.73 5.50 27°50.4′ 2952.53 1250.90 0.83 0.50

6.07 0.54 1.52 2.03 1.01 11.11 3.58 20°13.2′ 4751.31 547.58 0.29 0.49

4.68 0.42 1.17 2.77 1.39 10.64 2.28 22°29.4′ 5177.87 677.88 0.29 0.49

6.91 0.55 1.73 2.11 1.06 11.84 4.57 28°3′ 5099.69 815.04 0.46 0.50

4.07 0.39 1.02 2.90 1.45 10.42 1.73 27°19.8′ 4878.33 1019.06 0.41 0.49

Source: Data calculated by the author.

River basin morphometry

65

Roughness index (Ri) The roughness index is widely used by geomorphologists in connection with the morphometric analysis of terrain. The roughness index leads to better understanding of how the surface configuration evolved under multifaceted geomorphic processes within the basin. Using the DEM in QGIS (version 3.2), roughness all over the Torsa basin has been mapped. The values of roughness vary from 0.16 to 0.79 (Figure 2.13), and the average value of roughness is 0.49 (Table 2.15) in the Torsa basin. The Torsa River basin has been grouped into five roughness index zones (Figure 2.13). The Torsa basin, having moderate to high grades of roughness, is influenced by higher stream power, high stream frequency and drainage density, fine drainage texture, steep

Figure 2.13 Roughness index map of the Torsa River basin.

66

River basin morphometry

slope of the terrain, steeper gradient of streams, high rainfall, and lack of vegetation cover. Hypsometric analysis The hypsometric curve represents the relationship between the drainage basin area and elevation. In the present study, the percentage hypsometric curve (Strahler, 1952) has been used. This curve involves the ratios of relative height (h/H), which is plotted along the ordinate, and relative area (a/A), plotted along the abscissa in terms of percentage. The hypsometric curve is generally used to recognize the stage of the topography as well as the cycle of erosion in a drainage basin (Sen, 1993; Singh, 2007). In the present context, the hypsometric integral (HI) method is essential to know the stages of denudation and stages of basin development. The hypsometric integral refers to the ratio between the area bound by the hypsometric curve and the total area which is bound by the limits of the coordinates (Sen, 1993). The value of HI for the Torsa basin is 0.30 (Figure 2.14), which indicates that the landform is approaching the equilibrium stage of basin development and 70% of the basin area has been eroded by the different agents of denudation. Profile analysis Profile is the visual perception of the topographic elevation or actual nature of the terrain. Generally, profiles are of two types: terrain profiles and river profiles. The terrain profiles of any river basin are divided into four types: (i) serial profiles, (ii) superimposed profiles, (iii) projected profiles, and (iv) composite profiles. River

Figure 2.14 Percentage hypsometric curve of the Torsa River basin.

River basin morphometry

67

profiles are classified into two types, namely (i) transverse or cross profiles, and (ii) longitudinal profiles. CROSS PROFILE ANALYSIS

Cross profiles are drawn across the river basin or across the river. Cross profiles help in determining the change of slope and elevation of the terrain along the section line. Cross profiles have been drawn across the Torsa River basin from the source to the mouth to assess terrain characteristics. Sixteen cross profiles have been plotted to understand the diversity of topography, the nature of the V-shaped valley, variation of slope, etc. (Figures 2.15, 2.16). It is evident from Figure 2.16 (from A-A′ to F-F′) that wide V-shape cross profiles show the late youthful stage

Figure 2.15 Cross-section lines across the Torsa basin.

68

River basin morphometry

Figure 2.16 Cross profiles of the Torsa River basin. Source: ASTER DEM data.

River basin morphometry

69

Figure 2.17 Longitudinal profile of the Torsa River basin. Source: ASTER DEM data.

of basin development. The east–west trending cross-sectional profiles show the reduction of relief diversity from the upper catchment to the lower catchment of the basin (Figure 2.16). The cross profiles (G-G′ to I-I′) between the Himalayas and plains also depict the maximum fluctuation of relief (Figure 2.16). LONGITUDINAL PROFILE

The longitudinal profile of a river means a profile which is drawn from the source to the mouth of the river. This profile gives a vivid picture of the topographic breaks and gradients which help to examine the nature of landform development. The longitudinal profile reveals that the landscape is approaching the state of equilibrium (Figure 2.17).

Intercorrelation among different morphometric attributes Spatial interrelationships among the morphometric parameters have been determined through multivariate analysis using SPSS 17.0 software. A correlation matrix shows the relationship between some selected areal and relief morphometric parameters in the Torsa River basin (Figure 2.18). Spatial relationships among all the parameters reveal that some pairs are strongly correlated (more than 0.9), such as stream frequency (Sf) and drainage texture (Dt), length of overland flow (Lg) and constant of channel maintenance (Ccm), stream frequency (Sf) and infiltration number (If), drainage texture (Dt) and infiltration number (If), and relative relief (RR) and ruggedness number (Rg) (Figure 2.18). Some pairs having good correlation (more than 0.60) between the

Sf

.038**

.798**

-.425**

-.425**

.714**

.941**

.452**

.382**

.576**

-.013

.746**

.040**

Ccm

Lg

Di

If

SA

AR

RR

Di

Rg

Ri

.040**

.746**

-.013

.576**

.382**

.452**

.941**

.714**

-.425**

-.425**

1.000

Dt

-.028*

-.261**

-.098**

-.128**

-.014

-.091**

-.436**

.067**

1.000**

1.000

Ccm

.040**

.608**

-.223**

.656**

.555**

.509**

.497**

1.000

Di

.031**

.651**

.089**

.408**

.225**

.329**

1.000

If

.048**

.675**

-.198**

.735**

.593**

1.000

SA

.030**

.556**

-.751**

.690**

1.000

AR

* Correlation is significant at the 0.05 level (2-tailed).

-.028*

-.261**

-.098**

-.128**

-.014

-.091**

-.436**

.067**

1.000

Lg

.054**

.920**

-.142**

1.000

RR

Figure 2.18 Correlation matrix showing the relationship between selected morphometric parameters.

** Correlation is significant at the 0.01 level (2-tailed).

.030**

.365**

.238**

.103**

-.068**

.078**

-.668**

-.668**

.657**

.657**

1.000**

Dt

1.000

Dd

Dd

1.000

Sf

.006

-.016

1.000

Di

Ri

1.000

Below ± 0.6

±0.6 to ±0.9

Above ±0.9

Index

.045**

1.000

Rg

70 River basin morphometry

River basin morphometry

71

parameters, such as drainage density (Dd) and infiltration number (If), drainage intensity (Di) and absolute relief (AR), average slope (SA) and relative relief (RR), stream frequency (Sf) and ruggedness number (Rg), drainage texture (Dt) and ruggedness number (Rg), stream frequency (Sf) and drainage intensity (Di), drainage texture (Dt) and drainage intensity (Di), stream frequency (Sf) and drainage density (Dd), drainage density (Dd) and drainage texture (Dt), absolute relief (AR) and relative relief (RR), relative relief (RR) and drainage intensity (Di), ruggedness number (Rg) and drainage intensity (Di), ruggedness number (Rg) and infiltration number (If), average slope (SA) and ruggedness number (Rg), drainage density (Dd) and length of overland flow (Lg), and drainage density (Dd) and constant of channel maintenance (Ccm) (Figure 2.18). Such highly correlated parameters affect each other and indicate the possibility of individual variables to appear as dominant variables.

Prioritization of sub-basins The prioritization of sub-basins is defined as the ranking of different sub-basins. The prioritization of watersheds or basins has been done by many researchers and geoscientists in the recent past on the basis of the sediment yield index (Bali and Karale, 1977), morphometric parameters and sediment yield index (Biswas et al., 1999), morphometric parameters and land use/land cover (Javed et al., 2009), different morphometric parameters (Gajbhiye et al., 2013; Meshram and Sharma, 2015; Aouragh and Essahlaoui, 2018), morphometric parameters and weighted score method (Rekha et al., 2011; Tripathi et al., 2013), and morphometric parameters and principal component analysis (Meshram and Sharma, 2015). In the present study, both morphometric parameters and principal component analysis have been effectively applied for prioritization of the sub-basins. Prioritization of sub-basins using morphometric parameters Morphometric analysis is a significant approach for prioritization of sub-basins for natural resource management (Tripathi et al., 2013) because it largely supplies the required information concerning the topographic and hydrologic behaviour of the watershed. In recent times, quantitative studies of basin morphometric parameters have become popular among geoscientists and geomorphologists. Morphometric parameters, such as mean bifurcation ratio (Rbm), form factor (Ff), circularity ratio (CR), elongation ratio (ER), shape index (SB), compactness coefficient (CC), stream frequency (Sf), drainage density (Dd), drainage texture (Dt), length of overland flow (Lg), relief ratio (Rh), average slope (SA), relative relief (RR), and ruggedness index (Rg), are also termed erosion risk assessment parameters (Meshram and Sharma, 2015; Aouragh and Essahlaoui, 2018) and have been used for prioritization of sub-basins for treatment and conservation measures of soil in the Torsa River basin. The ranking of every sub-basin was carried out on the basis of the average values of different morphometric parameters. The morphometric parameters mean

72

River basin morphometry

bifurcation ratio (Rbm), stream frequency (Sf), drainage density (Dd), drainage texture (Dt), length of overland flow (Lg), relief ratio (Rh), average slope (SA), relative relief (RR), and ruggedness index (Rg) have a direct relationship with soil erodibility (Javed et al., 2009; Gajbhiye et al., 2013; Meshram and Sharma, 2015; Aouragh and Essahlaoui, 2018). The highest rating was given a value of 1, the second highest a value of 2, and so on; the lowest value is last in ranking. Some areal or shape parameters, such as form factor (Ff), circularity ratio (CR), elongation ratio (ER), shape index (SB), and compactness coefficient (CC), have an inverse relationship with soil erodibility (Javed et al., 2009; Gajbhiye et al., 2013; Meshram and Sharma, 2015; Aouragh and Essahlaoui, 2018). Thus, the lowest shape parameter value was assigned a rating of 1, the next lowest value was assigned a rating of 2, and so on; the highest value was last in ranking. After that, the compound values of each sub-basin was determined by adding the ranking values of all morphometric parameters for each sub-basin. On the basis of the average values of these parameters, the sub-basin with the lowest value was assigned the highest rating for soil erosion, the second lowest value was given the second highest rating for soil erosion, and so on. Nine sub-basins of the Torsa River basin have been categorized by prioritization, based on the compound parameter values by taking into account 14 morphometric variables (Table 2.16). Sub-basin 5 (SB5) had the lowest compound parameter value of 3.57, indicating the highest priority with greater degree of soil erosion followed by SB4, SB8, SB9, SB1, SB7, and SB6 (Figure 2.20A; Table 2.16). SB3 registered the lowest priority with the highest compound parameter value of 6.43 and low potentiality of soil erosion (Figure 2.20A; Table 2.16). The result shows that SB5 has a greater degree of soil erosion and it can be a potential area for applying the first soil conservation measures, followed by SB4, Table 2.16 Prioritization of sub-basins and their ranks using morphometric parameters Parameter

SB1

SB2

SB3

SB4

SB5

SB6

SB7

SB8

SB9

Mean bifurcation ratio Form factor Circularity index Elongation ratio Shape index Compactness coefficient Drainage frequency Drainage density Drainage texture Length of overland flow Relief ratio Average slope Relative relief Ruggedness index Compound parameter Prioritized rank

7 1 1 1 9 9 5 5 5 3 8 7 6 5 5.14 5

1 4 7 3 6 3 6 2 6 7 7 8 8 7 5.36 6

8 2 2 2 8 8 8 3 8 6 9 9 9 8 6.43 7

5 6 6 5 4 4 2 4 2 8 4 1 2 2 3.93 2

6 9 9 6 1 1 1 1 1 9 1 3 1 1 3.57 1

4 5 4 4 5 6 4 6 4 5 6 6 7 6 5.14 5

4 7 3 6 3 7 7 7 7 2 3 5 5 6 5.14 5

2 3 5 6 7 5 3 5 3 4 5 2 4 3 4.07 3

3 8 8 6 2 2 9 8 9 1 2 4 3 4 4.93 4

Source: Data calculated by the author.

River basin morphometry

73

SB8, SB9, and SB1. It is very difficult to determine the most important morphometric parameter responsible for sub-basin prioritization in the context of soil erosion. Prioritization of sub-basins using principal component analysis Principal component analysis (PCA) is applied to calculate the correlation between the morphometric parameters, and to find out the principal components and most effective parameters for prioritization of sub-basins of the Torsa basin. PCA has been applied to judge the validity of prioritization of the sub-basin for soil erosion. PCA is based on applying the first factor loading matrix and pattern matrix (Tables 2.17, 2.18). The first component of the pattern matrix is strongly correlated with RR, Rg, and SA, and has good correlation with Dt, Sf, and Rh for prioritization, which can be defined as the relief-density component (Table 2.18). The second component of the pattern matrix is strongly correlated with Dd and Lg, and has good correlation with Dt and Sf, which may be termed as the drainage component. The third component of the pattern matrix is strongly correlated with CC and has good correlation with CR, SB, Ff, and ER, which can be defined as a shape-form component for sub-basins of the Torsa basin (Table 2.18). It is observed (Table 2.18) that the most important parameter is RR followed by Rg, SA, Dd, Lg, and CC, and these morphometric parameters were taken into account for the sub-basin prioritization. The scree plot (Figure 2.19) verifies the clarification capability of different components. After considering the PCA on the basis of the six selected principal morphometric parameters, the nine sub-basins of the Torsa River basin were categorized Table 2.17 Total variance explained of the Torsa sub-basins Component

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Initial eigen value

Extraction sum of squared loadings

Total

% of variance

Cumulative %

Total

% of variance

Cumulative %

7.438 3.257 1.833 1.011 0.216 0.147 0.089 0.009 0.000 0.000 0.000 0.000 0.000 0.000

53.130 23.266 13.091 7.222 1.543 1.049 0.637 0.062 0.000 0.000 0.000 0.000 0.000 0.000

53.130 76.396 89.487 96.709 98.253 99.301 99.938 100.000 100.000 100.000 100.000 100.000 100.000 100.000

7.438 3.257 1.833

53.130 23.266 13.091

53.130 76.396 89.487

Source: Data calculated by the author.

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River basin morphometry

Table 2.18 Pattern matrix Parameter Relative relief Ruggedness index Average slope Drainage texture Stream frequency Relief ratio Length of overland flow Drainage density Compactness coefficient Circularity ratio Shape index Form factor Elongation ratio Mean bifurcation ratio

Component 1

2

3

0.957 0.942 0.935 0.764 0.762 0.713 –0.005 –0.072 –0.061 0.190 –0.246 0.462 0.437 –0.213

–0.097 0.228 –0.257 0.601 0.602 –0.295 –0.992 0.985 –0.129 0.190 0.164 –0.213 –0.367 0.054

–0.056 –0.044 –.002 –0.007 –0.007 –0.407 0.096 –0.039 0.953 –0.880 0.838 –0.648 –0.615 –0.482

Source: Data calculated by the author.

Figure 2.19 Scree plot.

again into different priority ratings (Table 2.19). Here SB5 had the lowest compound parameter value of 2.67, indicating the highest priority with a greater degree of soil erosion followed by SB4, SB9, SB8, SB1, and SB2. SB3 had the lowest priority with the highest compound parameter value of 7.17 (Figure 2.20B; Table 2.19). The prioritized map of the Torsa basin (Figure 2.20B) shows that the soil conservation measures and their management can first be applied to SB5 followed by SB4, SB9, SB8, SB1, and SB2 depending upon their priority.

River basin morphometry

75

Table 2.19 Prioritization of sub-basins and their ranks using PCA Parameter

SB1

SB2

SB3

SB4

SB5

SB6

SB7

SB8

SB9

Compactness coefficient Drainage density Length of overland flow Average slope Relative relief Ruggedness index Compound parameter Prioritized rank

9 5 3 7 6 5 5.83 6

3 2 7 8 8 7 5.83 6

8 3 6 9 9 8 7.17 8

4 4 8 1 2 2 3.50 2

1 1 9 3 1 1 2.67 1

6 6 5 6 7 6 6.00 7

7 7 2 5 5 6 5.33 5

5 5 4 2 4 3 3.83 4

2 8 1 4 3 4 3.67 3

Source: Data calculated by the author.

Figure 2.20 Prioritized rank map of the Torsa River basin using (A) morphometric parameters and (B) principal component analysis.

It has been found that the priority ranks do not change for SB5, SB4, SB7, and SB2, whereas SB1, SB2, SB8, and SB9 are closer to the previous result (Figure 2.20A, B; Tables 2.16, 2.19). Only for SB6 did the result not match with the previous model. Finally, it is assumed that both approaches are equally capable of examining the sub-basin prioritization of a drainage basin that originated in

76

River basin morphometry

the Himalayan mountains and its foothills. The PCA-based approach perhaps is better representative of sub-basin prioritization because it reduces the parameters.

Landscape diversity model Both the weighted compositing method and principal component analysis were applied to the landscape diversity model. Landscape diversity of Torsa basin using weighted composite analysis The collective forms of the morphometric parameters have been used by several geomorphologists and geoscientists in the recent past (Rekha et al., 2011; Tripathi et al., 2013). In the present study, the calculation of the weight of each morphometric parameter was made using the correlation matrix (Figure 2.18), which is applied for standardization of the data. The total correlation score was calculated by adding the individual correlation score of the same parameter. The individual weighted score was measured by dividing the individual total correlation score by the maximum total correlation score. The value of each attribute was derived by multiplying the defined weight of each individual attribute. The landscape diversity score was calculated by adding the weighted values of 13 selected morphometric variables. In this case, it is very difficult to get the most significant morphometric parameter responsible for landscape diversity of the Torsa basin. So, principal component analysis is applied to find out the principal component or parameter which largely controls the landscape diversity. Landscape diversity of Torsa basin using principal component analysis PCA was applied to judge the validity of the weighted composite analysis for landscape diversity in the Torsa basin. PCA is based on applying the factor loading matrix and component matrix (Tables 2.20, 2.21). Results of the PCA show that the eigen values of the first four components are more than 1, which explain 85.81% of the morphometric variability of the total components in the Torsa basin (Table 2.20). The scree plot (Figure 2.21) verifies the clarification capability of different components. It is observed that the first component of the component matrix is strongly correlated with Dt and Sf, and has good correlation with Rg, If, RR, Di, SA, and Dd (Table 2.21). The second component has good correlation with Lg, Ccm, and AR for the Torsa basin (Table 2.21). The result depicted that the drainage parameters are more prominent explanatory factors than the relief parameters for landscape diversity (Table 2.21.). In landscape diversity, PCA is able to select only the 11 most important morphometric parameters from components 1 and 2 (Table 2.21). From the landscape diversity mapping through PCA (Figure 2.22B), it can be interpreted that three morphometric parameters – absolute relief, relative relief, and average slope – are equally significant for landscape diversity, as the loading values of these parameters are higher.

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77

Table 2.20 Total variance explained Component

1 2 3 4 5 6 7 8 9 10 11 12 13

Initial eigen value

Extraction sum of squared loadings

Total

% of variance

Cumulative %

Total

% of variance

Cumulative %

5.930 2.898 1.322 1.005 0.915 0.420 0.329 0.090 0.060 0.019 0.014 0.000 0.000

45.615 22.292 10.171 7.732 7.038 3.227 2.528 0.690 0.460 0.143 0.104 0.000 0.000

45.615 67.907 78.077 85.810 92.848 96.075 98.603 99.292 99.753 99.896 100.000 100.000 100.000

5.930 2.898

45.615 22.292

45.615 67.907

Source: Data calculated by the author.

Table 2.21 Component matrix Parameter Drainage texture Stream frequency Ruggedness index Infiltration number Relative relief Drainage intensity Average slope Roughness index Drainage density Length of overland flow Constant of channel maintenance Absolute relief Dissection index

Component 1

2

0.945 0.945 0.875 0.860 0.762 0.695 0.635 0.062 0.607 –0.489 –0.489 0.557 –0.107

–0.115 –0.115 0.209 –0.296 0.449 0.467 0.437 0.006 –0.684 0.678 0.678 0.653 –0.562

Source: Data calculated by the author.

The landscape diversity maps (Figure 2.22A, B) show that both methods provide the same result and the weighted composite analysis (WCA) is perfectly validated by the principal component analysis. The landscape diversity maps (Figure 2.22A, B) show that a high degree of landscape diversity is located in the upper catchment of the Torsa basin because the loading factors are higher in these areas. The Himalayan region is categorized as having moderate to very high degrees of landscape diversity, and these conditions indicate less infiltration of

78

River basin morphometry

Figure 2.21 Scree plot.

Figure 2.22 Landscape diversity map of the Torsa River basin based on (A) weighted composite analysis and (B) principal component analysis.

River basin morphometry

79

water and more surface runoff with greater soil erosion potentiality (Figure 2.22A, B). This region will be scarce of soil nutrients because of more potentiality of soil erosion, and consequently this mountainous region may not be suitable for agricultural practice and settlement construction. Moderately low to moderate degrees of landscape diversity are found mainly in the piedmont region (Figure 2.22A, B). This region is not suitable for agricultural practice due to moderate susceptibility of soil erosion. The lower catchment of the Torsa basin is categorized as having a very low degree of landscape diversity (Figure 2.22A, B), because of high infiltration rates and low surface runoff associated with the higher potentiality of agricultural practice due to lots of moisture and nutrients available in the soil. This region also experiences excessive sedimentation deposition as well as siltation, which are highly effective for high agriculture production.

Conclusion The highly elongated-shape river basin indicates low flatter peak flow for longer duration, low discharge of runoff, and extremely permeable lithology associated with less erosion and lower capacities of sediment transport. The landform of the Torsa basin is approaching the equilibrium stage of basin development. The Himalayan mountain region has high amplitudes of relative relief, indicating the maximum magnitude of elevation difference and high degree of slope as well as high intensity of erosion. The lower catchment of the Himalayan foothills river basin is a low relative relief, indicating a low magnitude of elevation difference and low degree of slope associated with low intensity of erosion over the plains region. The prioritized map of the Torsa basin demonstrated that the soil conservation measures and their management can first be applied to the Samchu Khola sub-basin (SB5) because of its greater degree of soil erosion vulnerability. Sub-basin prioritization and soil erosion vulnerability assessment of the Torsa River basin is considered to be one of the most important methods for basin scale planning and management. The Torsa River basin is an erosion-prone area and the present work will help to provide better understanding to planners for conservation and management of soil.

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Nir, D. (1957). Maps of dissection index of terrain. Proceedings of the Yorkshire Geological Society, 29 p. Prakash, K., Singh, S., Mohanty, T., Chaubey, K., & Singh, C.K. (2017). Morphometric assessment of Gomati river basin, middle Ganga plain, Uttar Pradesh, North India. Spatial Information Research, 25, 449–458. Rai, P.K., Chandel, R.S., Mishra, V.N., & Singh, P. (2018). Hydrological inferences through morphometric analysis of lower Kosi river basin of India for water resource management based on remote sensing data. Applied Water Science, 8(15), 1–16. Rai, P.K., Mishra, V.R., & Mohan, K. (2017). A study of morphometric evaluation of the Son basin, India using geospatial approach. Remote Sensing Applications: Society and Environment, 7(2017), 9–20. Rekha, V.B., George, A.V., & Rita, M. (2011). Morphometric analysis and microwatershed prioritization of Peruvanthanam sub-watershed, the Manimala River Basin, Kerala, South India. Environmental Research, Engineering and Management, 3(57), 6–14. Romshoo, S.A., Bhatand, S.A., & Rashid, I. (2012). Geoinformatics for assessing the morphometric control on hydrological response at watershed scale in the Upper Indus Basin. Journal of Earth System Science, 121(3), 659–686. Schumm, S.A. (1956). Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey. Geological Society of America Bulletin, 67(5), 597–646. Schumm, S.A. (1963). Sinuosity of alluvial rivers on the Great Plains, Bulletin of the Geological Society of America, 74(9), 1089–1100. Sen, P.K. (1993). Geomorphic analysis of drainage basins. Burdwan: The University of Burdwan. Singh, S. (1972). Altimetric analysis: A morphometric technique of landform study. National Geographers, 7, 59–68. Singh, S. (2007). Geomorphology (pp. 358–412). Allahabad: Prayag Pustak Bhawan. Singh, S., & Singh, M.C. (1997). Morphometric analysis of Kanhar river basin. National Geographical Journal of lndia, 43, 31–43. Smart, J.S., & Surkan, A.J. (1967). The relation between mainstream length and area in drainage basins. Water Resources Research, 3(4), 963–973. Smith, G.H. (1935). The relative relief of Ohio. Geographical Review, 25, 272–284. Soni, S. (2016). Assessment of morphometric characteristics of Chakrar watershed in Madhya Pradesh India using geospatial technique. Applied Water Science, 7, 2089–2102. Sreedevi, P.D., Owais, S., Khan, H.H., & Ahmed, S. (2009). Morphometric analysis of a watershed of South India using SRTM data and GIS. Journal of the Geological Society of India, 73(4), 543–552. Sreedevi, P.D., Subrahmanyam, K., & Ahmed, S. (2005). Integrated approach for delineating potential zones to explore for groundwater in the Pageru River basin, Cuddapah District, Andhra Pradesh, India. Hydrogeology Journal, 1, 534–543. Stoddart, D.R. (1965). The shape of atolls. Marine Geology, 3(5), 369–383. Strahler, A.N. (1952). Hypsometric analysis of erosional topography. Bulletin of the Geological Society of America, 63(11), 1117–1142. Strahler, A.N. (1957). Quantitative analysis of watershed geomorphology. Transactions. American Geophysical Union, 38(6), 913–920. Strahler, A.N. (1964). Quantitative geomorphology of drainage basins and channel networks. In V.T. Chow (Ed.), Handbook of applied hydrology (pp. 39–76). New York: McGraw-Hill.

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3

Channel geometry and channel bed configuration

A river channel is a three-dimensional form, which is defined by its slope, crosssection, and pattern (Petts and Foster, 1985), and its water course is confined within the valley walls on both sides (Singh, 2007; Petts and Foster, 1985). The river channel may be bedrock or alluvial in nature depending on the material of the earth crust on which the river has been developed. Morphology of the stream channels is relayed in terms of the relationship between discharge (Q), channel width (w), channel depth (d), velocity (v), and their rate of change (Leopold and Maddock, 1953). The morphology or overall geometry of a river channel is fully controlled by the independent variables of the discharge and load, i.e. the geology and climate of the drainage basin (Morisawa, 1985). The morphology of the river channel is the result of the reciprocal interaction of a few broad categories of variables such as (a) channel fluid dynamics or hydraulics of flow (such as velocity, discharge, roughness, and shear stress), (b) the channel character or channel configuration or channel geometry at the reach (which includes channel width, channel depth, wetted perimeter, shape of the channel and its thalweg, channel slope, and channel pattern), (c) sediment load entering the reach (calibre and amount), and (d) bed and bank material (textural composition of sands and sediments), etc. (Morisawa, 1985; Singh, 2007). Therefore, the channel morphology of a river includes the consideration of channel geometry or cross-sectional characteristics of the channel, channel fluid dynamics, hydraulic geometry, channel types, channel bed topography or configuration, and channel pattern (Singh, 2007). Channel geometry or channel form is defined as the shape and size of the cross-sectional and longitudinal channel form (Singh, 2007) as well as the three-dimensional form of a channel. Channel geometry incorporates channel width, channel depth, wetted perimeter, channel shape, channel bend, channel slope, shape of the channel thalweg, and their interrelationship (Singh, 2007). Adjustment of the channel geometry of exterior controls can be considered in terms of four degrees of freedom: cross-sectional form, bed configuration, planimetric geometry or channel pattern, and channel bed slope (Knighton, 1984). River channel bed topography means the channel bed configuration of the stream in terms of channel bathymetry and positive–negative bed features such as the presence or absence of pools and riffles, sandbars, sand islands, shoals, and ripple marks (Singh, 2007; Mukhopadhyay et al., 2012). The formation of channel DOI: 10.4324/9781003276685-3

84 Channel geometry bed features such as sandbars, ripples, sand dunes, plane beds, and anti-dunes indicates the presence of systematic propensities in the capacity and competency of rivers to sort and transport sediment loads over a wide range of flow and bed material conditions (Knighton, 1984). Usually, streams which are passing through the foothills region achieve more stream energy to change the channel geometry as well as channel bed configuration. The Torsa River frequently changes its channel form and configuration due to high discharge along with more velocity, and the supply of sediments from upstream. This chapter focuses on the spatial and seasonal changes of channel geometry and channel bed configuration of the Torsa River.

Cross-sectional analysis and channel morphodynamics The cross-sections are considered across the channel to recognize the channel forms or channel geometry. Thirty-four cross-sections have been considered along the Torsa River to recognize the channel geometry (Figure 3.1). In this regard, the channel depth was measured using an echo sounder and measuring staff (Plate 3.1A, B). The field sites were selected on the basis of specific criteria, such as the location of pools and riffles, location of the tributary confluence, and location of the bridges. The depth distribution across the channel depends mainly on the width of the channel that also depends on the discharge (Maiti, 2016). In the Torsa River, the channel width and depth fluctuate along the cross-sections, and there are no fixed scale factors (Figures 3.2–3.6). It was observed that almost all the cross-sections in the study reaches are asymmetrical in shape. Basically, the channel form largely depends on the channel width, the geometry of the shoals and bars, flow pattern, spacing of pools and riffles, channel orientation, and human intervention. Human-induced unscientific activities such as the mining of pebble, cobble, gravel, and sand from the riverbed at some selected parts (field sites 1, 3, 10, 15) largely affected the channel forms (Figures 3.2, 3.5, 3.6). Cross profiles show that the Torsa River valley tends to be a wide V-shape. In most cases, the channel has been divided into two or more segments having more than one thalweg (field sites 1, 14) due to formation of mid-channel bars (Figures 3.2, 3.6).

Seasonal variation of cross profiles The shape of the cross-sections of a river channel at any location is a function of the stream flow, the quantity, and character of the sediment, and the textural composition of the bed and bank material making up the bed and bank of the channel (Knighton, 1981; Maiti, 2016). Channel width, channel depth, wetted perimeter, cross-sectional area, hydraulic radius, channel slope, flow pattern, spacing of pools and riffles, width–depth ratio, location of shoals and bars, etc. are important parameters to understand the channel forms. In the study area, all cross-sections of the Torsa River were revealed to be asymmetrical. The channel is also braided and asymmetrical in nature. An asymmetrical channel is formed when the thalweg

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Figure 3.1 Location of the field sites along the Torsa River in the study area.

point lies close to the riverbank (Maiti, 2016). Seasonal and temporal changes of the cross-sections show that the channel is more dynamic and asymmetrical in nature due to generation of turbulent flow near the bridges and stream junctions associated with bed cutting and the rapid rate of sedimentation. The situation leads to shifting of the thalweg position and shifting of the shoal area (Figures 3.7–3.9).

Analysis of superimposed cross profiles The superimposed cross profile of a river channel assists in determining the different levels of the channel bed surface and determining the bank line migration.

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Plate 3.1 Measurement of (A) channel depth, (B) flow velocity during the non-monsoon and (C) monsoon, and (D) near-bed flow velocity.

Figure 3.2 Channel cross-sections at (A) Jaigaon, (B) Hasimara, and (C) Chilapata along the Torsa River in a downstream direction.

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Figure 3.3 Channel cross-sections at (A) Silbarihat, (B) Patlakhawa Protected Forest, and (C) Putimari Baksibas along the Torsa River in a downstream direction.

The superimposed cross profiles (during three consecutive years from 2016 to 2018) show that the right bank at site 6 has moderately migrated towards the right (Figure 3.10A, B, C). At site 9, between 2016 and 2018, a very marginal rate of bank erosion occurred towards the right bank (Figure 3.10D, E, F). At site 31, the superimposed cross profiles show that there is no bank line migration during three consecutive years because of the presence of embankments along both banks (Figure 3.10G, H, I). The cross-sectional study of three different seasons (pre-monsoon, monsoon, and post-monsoon) shows that there is no specific trend of change within the channel during 2016 to 2018. At sites 6 and 9, the noticeable variation of channel depth along the cross-sections was found due to generation of turbulent flow close to the bridges.

Study of long profile and thalweg profile The long profile of the riverbed varies towards the downstream due to variation in the size and shape of the bed material, spacing of pools and riffles, and other variables (Knighton, 1984). The longitudinal profiles are very important for recognizing the trends of down cutting and accretion within the riverbed (Bernhardt et al., 2005). The long profile of the study reach was studied between Silbarihat and Balarampur covering 50.082 km (Figure 3.11). The long profile shows that

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Figure 3.4 Channel cross-sections at (A) Basdaha Natibari and (B, C) Sajherpar along the Torsa River in a downstream direction.

Figure 3.5 Channel cross-sections at (A) Sajherpar Ghoramara and (B, C) Salmara 3 along the Torsa River in a downstream direction.

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Figure 3.6 Channel cross-sections at (A) Hokakura, (B) Haripur, and (C) Madhupur along the Torsa River in a downstream direction.

the channel depth and the channel width vary along the Torsa River, but the channel thalweg is meandering in nature (Figure 3.12). The thalweg slope varies from one reach to another reach due to movement of sediments as well as deposition of sediments. The gradient of the thalweg between Silbarihat and Balarampur is 0.000357. From site 4 to site 13, the gradient of the thalweg is 0.000284.

Channel geometry Channel geometry is defined as the shape and size of the cross-sectional and longitudinal channel form (Singh, 2007) as well as the three-dimensional form of a channel. Channel geometry incorporates channel width, channel depth, wetted perimeter, channel shape, channel bends, channel slope, shape of the channel thalweg, and their interrelationship (Singh, 2007). Adjustment of the channel geometry of exterior controls can be considered in terms of four degrees of freedom: cross-sectional form, bed configuration, planimetric geometry or channel pattern, and channel bed slope (Knighton, 1984).

Seasonal channel width variation The channel width of a river course at any given point represents the straight cross-sectional distance of the channel displaying the level of water (Singh,

Figure 3.7 Seasonal and temporal changes of cross-sections of the Torsa River at Basdaha Natibari (site 7) during (A) 2016, (B) 2017, and (C) 2018.

90 Channel geometry

Figure 3.8 Seasonal and temporal changes of cross-sections of the Torsa River at the confluence of Mora Torsa (site 8) during (A) 2016, (B) 2017, and (C) 2018.

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Figure 3.9 Seasonal and temporal changes of cross-sections of the Torsa River at downstream NH-31 bridge (site 9) during (A) 2016, (B) 2017, and (C) 2018.

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Figure 3.10 Superimposed profiles of the Torsa River along the cross-sections of (A–C) site 6, (D–F) site 9, and (G–I) site 31 in three consecutive seasons from 2016 to 2018.

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Figure 3.11 Long profile along the Torsa River from Silbarihat to Balarampur. Source: Field survey (2017).

Figure 3.12 Long profile along the thalweg in the Torsa River. Source: Field survey (2017).

2007). It is noticeable that the channel width increases with an increasing volume of water and discharge during the bankfull stage. In the Torsa River, the maximum channel width has been found during the bankfull stage of discharge (Figure 3.13). The channel width of the Torsa River varies from 192.4 m to 629.1 m, and 431.1 m to 2121.6 m during the non-monsoon and monsoon periods, respectively (Figure 3.13). The channel width across the Torsa River was also measured by a cross-sectional study along with a GPS survey (Plate 3.1A, B). The result shows the negative correlation between the distance and channel width (Figure 3.13). The channel width varies largely from the pre-monsoon to monsoon season. At site 8, the channel had minimum width due to the construction of short-length bridges. Generally, the channel width increases from upstream to downstream. But, this kind of width change does not happen in the Torsa River. Because human intervention, like construction of short-length

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Figure 3.14 Downstream seasonal pattern of channel depth of the Torsa River. Source: Field survey (2017).

bridges (near the Madarihat, Sajherpar, and Ghughumari bridges), along with embankment construction caused reduction of the channel width of the Torsa River during the monsoon. The channel width of the Torsa River is maximum where the river tends to flow freely.

Seasonal pattern of channel depth The channel depth means the vertical distance from the water surface to the bed of the channel. The channel depth is measured by an echo sounder and levelling staff (Plate 3.1A). The Torsa River is usually wide and shallow, where the depth of water largely fluctuates from 0.6 m to 1.4 m during the non-monsoon (Figure 3.14). But the depth increases up to 6 m near the bridges and the confluences of tributaries due to prevalence of the scouring process. The depth of the Torsa River in the entire foothills and Duars region is shallower than the lower course of the Torsa in the northern plains and Tal regions because of the high rate of sedimentation.

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In the plains, the sedimentation is more, but the volume of water as well as channel depth increases due to the huge influx of water by the tributaries of Torsa, like the Kaljani, Mora Torsa, and Bura Torsa. The maximum depth during the monsoon (5.16 m) and non-monsoon season (3.66 m) have been found at site 33 near Deocharai. The average depth varies from 0.54 m to 3.52 m during the monsoon and varies from 0.43 m to 2.02 m during the non-monsoon period (Figure 3.14). During the monsoon, the channel depth increases with increasing rainfall intensity. The channel depth also increased during the monsoon due to the supply of water from upstream.

Orientation of thalweg The thalweg of the channel denotes the line that connects all the deepest points of water from the source to the confluence along the river channel. The channel behaviour of the Torsa River is unstable because of regular shifting of the channel thalweg. In the study area, it has been found that the thalweg of the Torsa River has been concentrated towards the left bank (21 field sites) than the right bank (13 field sites) in the Duars and northern plains regions (Figure 3.15). It proved that the cross profiles of the Torsa River were asymmetrical in nature. It was found that the channel thalweg frequently changes its position during the high discharge period.

Seasonal pattern of the wetted perimeter The wetted perimeter represents a distance of wetted portion along the cross-section in the valley. The distance of the wetted perimeter increases during the monsoon with the increasing volume of water and discharge. During the monsoon, the wetted perimeter frequently changes in the Torsa River from the foothills to the northern plains. In the study area, the wetted perimeter of Torsa increased about two times (average) in the monsoon than the non-monsoon period (Figure 3.16). It has been found that the seasonal wetted perimeter changes with changing the channel width.

Downstream distribution of channel slope The channel slope, also known as a gradient, means the ratio between the elevation difference in the channel bed along a given length of the channel and the actual length of the reach. The channel morphological behaviour and channel hydraulics are directly influenced by the channel slope. Generally, the channel slope decreases with the increasing downstream distance. In the study area, the elevations of the channel bottom were measured using a measuring staff (6 m) and GPS receiver. The highest channel slope was recorded at reach 2, whereas the lowest channel slope was recorded at reach 13. The result (correlation, r = –0.879; and coefficient of determination, R2 = 0.772) significantly proved that the channel slope of the Torsa River in the Indian territory decreased downstream (Figure 3.17).

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Figure 3.15 Thalweg orientation of the Torsa River channel (2017) in the downstream. Source: Field survey (2017).

Seasonal pattern of cross-sectional area The cross-sectional area of a channel indicates the area occupied by the channel flow, which is measured by multiplying the channel width and the mean flow depth of the channel. The cross-sectional area changes with time in response to the variations in discharge during the monsoon and non-monsoon periods. The maximum cross-sectional area indicates the effluent channel that contributes the

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Figure 3.16 Downstream seasonal pattern of wetted perimeter of the Torsa River. Source: Field survey (2017).

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Figure 3.17 Downstream distribution of the channel slope in the Torsa River. Source: Field survey, 2017.

Figure 3.18 Seasonal patterns of cross-sectional area of the Torsa River. Source: Field survey, 2017.

maximum volume of water during a flood. It was observed that the cross-sectional area largely varies between two seasons from the foothills to the northern plains (Figure 3.18). On average, the cross-sectional area increased for about 4.88 times during the monsoon than the non-monsoon. From 2016 to 2018, the

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Figure 3.19 Seasonal patterns of hydraulic radius of the Torsa River. Source: Field survey, 2017.

cross-sectional area increased about 4 to 9 times during the monsoon than the premonsoon or post-monsoon season.

Seasonal pattern of hydraulic radius The hydraulic radius measures the efficiency of channel flow. It is delineated as the ratio between the cross-sectional area and the wetted perimeter of the channel. The channel is more efficient when the hydraulic radius is high and vice versa. In the study area, site 1 is characterized by the minimum hydraulic radius and site 33 is characterized by the maximum hydraulic radius during the monsoon. It indicates that site 33 is more efficient in channel flow and site 1 is less efficient in channel flow (Figure 3.19). The highest and lowest hydraulic radii were found at sites 6 (1.587) and 9 (1.032) during the monsoon in the year 2016.

Width–depth ratio The width–depth ratio is an important parameter to understand the channel form. More suspended load is being transported through the narrow and deep river channel with a low width–depth ratio. Transportation of suspended load depends largely on the turbulence and velocity of flowing water, which is more in the narrow and deep river (Coleman, 1969; Maiti, 2016). Transport of the bed load is more in the shallow and wider channel with a high width–depth ratio. Bed loads are being transported by shear on the bottom of the stream (Coleman, 1969; Maiti, 2016). In the study reach, the width–depth ratio changes continuously because of the channel adjustment with the water discharge, types of load, and bed slope. The channel width as well as the width–depth ratio largely depends on the discharge, nature of bed and bank material, erosional velocity, types of transporting loads, and uplift rate of bed material (Schumm, 1960). In the study area, the width–depth ratio varies between 179.76 (site 6) and 3928.89 (site 1). Most of the sites have a high width–depth ratio, which indicates a coarser type of bed material (Figure 3.20).

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Figure 3.20 Downstream width–depth ratio along the Torsa River. Source: Field survey, 2017.

Bed material distribution The development of alternating pools and riffles are characteristic of straight and meandering channels with variable size of bed material (Knighton, 1998). Here, D is used to understand the sediment size, using millimetres (mm) for sand and coarser sediments, and microns (μ) for clay and silt (Garcia, 2004). D50 (median size) is derived by the measurement of the middle axis of various particles. (Lawlor, 2004). Based on this median size of the bed armour or substrate particles, a river can simply be classified into either a gravel bed channel or as a sand-bed channel if the D50 value is less than or greater than 2 mm (Garcia, 2004). The particle size of the bed material has been classified on the basis of the median size. In the present study, Bureau of Indian Standards (BIS) standard sieves have been used to classify the bed material for all selected sites. The D50 graph shows the distribution of bed material that help to assess the dominant bed material. In the study area, pools are filled with finer bed material, whereas riffles are aggraded with large-size bed material. Pebble, cobble, and gravel are accumulated in front of the riffles which are immediate downstream of the bridge. The study reach is largely filled with coarse to fine sand and silt. From the D50 graphs, it has been found that the Torsa River course is mainly composed of coarser bed material (Plate 3.2A) in the foothills and Duars regions (sites 1 to 6), whereas the lower part (sites 27 to 30) of the Torsa is mainly composed of finer bed material (Figures 3.21, 3.22; Plate 3.2B, C).

Channel bed configuration Bankfull discharge and inundation of the bars occur mainly in the rainy season or monsoon floods. In the pre-flood and post-flood period, the water level is comparatively low when only the main channel is inundated. The bathymetric surveys were conducted throughout the low-flow stage between 2016 and 2018 (Plate 3.1A, B). The measurements of depth were randomly selected at various locations with minute distance intervals in the study reach (Plate 3.1A, B, C, and D).

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Plate 3.2 Bed material at field sites (A) 3, (B) 14, and (C) 22.

Channel morphology in changing discharge and flow conditions Changes of channel morphology are strongly related to the variations of water discharge and near-bed flow velocities between pools and riffles. High and low discharges of water effects in the channel change during the monsoon and nonmonsoon periods. The scouring and filling process of the channel bed happen at high flows during the monsoon, which tends to fill and scour at the same locations during low flows of the non-monsoon period (Andrews, 1979). In the study reaches, the active scouring process as well as bed erosion and bank toe erosion happen in the pools or concave sides of the channel bends during high discharges (Figures 3.23–3.25) and, alternatively, the deposition or filling process is active during low discharges at the same locations.

Channel bathymetry at the lower reach of the Torsa River The distribution of channel depth varies greatly, which largely depends on channel width, slope, volume of discharge, spacing of pools and riffles, etc. The channel width of a river largely depends on water discharge. An increase in water discharge through a channel increases the channel depth (Leopold and Maddock, 1953). The channel bathymetry map shows that the longitudinal channel depth is

Figure 3.21 Grain size distribution of the Torsa River bed from sites 1 to 6. Source: Field survey, 2017.

102 Channel geometry

Figure 3.22 Grain size distribution of the Torsa River bed from sites 25 to 30. Source: Field survey, 2017.

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Figure 3.23 Bathymetric characteristics of the Torsa River, 2016. Source: Field survey, 2016.

dynamic in nature (Figures 3.23–3.25). The depth is maximum at the pools and minimum in the riffles section. In the lower reach of the Torsa River, the pools are characterized by finer material such as silt, clay, and very fine sand, whereas riffles are dominated by coarser material such as medium to coarse sand, gravel, pebble, and cobble. These types of irregularities have been formed along the river channel to establish the equilibrium conditions in the energy distribution (Maiti,

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Figure 3.24 Bathymetric characteristics of the Torsa River, 2017. Source: Field survey, 2017.

2016). The depth is more near the confluence of tributaries of the Torsa River and below the railway and highway bridges in comparison to other sections.

Seasonal variation of the channel bathymetry The channel depth varies seasonally. During the pre-monsoon and post-monsoon periods, scarcity of water is a very common phenomenon in the foothills of the

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Figure 3.25 Bathymetric characteristics of the Torsa River, 2018. Source: Field survey, 2018.

Himalayas due to lack of rainfall and ice melting water. As a result, the volume of water discharge through the channel is very low and there is decreasing tendency of channel depth. During the monsoon, the high discharge leads to scouring of the riverbed, which increases the depth of the channel. In the study reaches, most of the places have the maximum depth of above 3 m during the monsoon period. During the non-monsoon period, the depth of the river varies from 0.05 m to 6 m.

Channel geometry 107 During this period, the channel depth ranges between 0.05 m and 1.4 m in the riffle section, while the channel depth of the Torsa River varies from 1.2 m to 6 m in the pool section (Figures 3.23–3.25).

Location of pools and riffles Topographically, pools are low areas along the channel, and the bed material of the pools usually have fine material. Whereas riffles are topographically high areas along the channel, and bed material of riffles are formed by a lobate accumulation of coarser material. The riffles are formed in the high points of the channel bed, whereas the pools are formed in the deep reaches. Over the pools, the water surface slope is gentle, depth of flow is deeper, and flow velocity is slower during the low stage. Over the riffles, the water surface steep is gentle, depth of flow is shallower, and flow velocity is more rapid during the low stage (Summerfield, 2013). The spacing of pools and riffles are shown to be regular in a sinuous and meandering reach of the channel; they are typically spaced at about five to seven times the channel width. In the alluvial channel, the spacing between pools and between riffles is observed to be five to seven times that of the channel width (Maiti, 2016). The development of pools and riffles and their arrangement is proposed on the basis of the regularity in the spacing of pools and riffles in an alluvial river (Keller, 1972). The Keller model is not applicable in a braided channel because the spacing of pools and riffles does not tend to form evenly or regularly. The study shows that the distance between pools and riffles is less than seven times the channel width and sometimes it becomes two to three times the channel width, which is intrinsically unstable and dynamic (Figures 3.23–3.25). The spacing of pools and riffles is subsequently increasing and decreasing three to seven the channel width (Leopold et al., 1964; Maiti, 2016). The scouring process accelerates riverbank erosion and riverbed erosion at the toe of the bank and within the channel, respectively. The channel widens when the flows are segmented into two or more channels, and two thalwegs are being formed near the banks (Figures 3.23, 3.24).

Pool–riffle sequences and maintenance At the study reach, the Torsa River is characterized by multiple channels which are categorized as a braided channel pattern. The multiple thalweg lines are formed on the channel, and multiple pools are also developed on the concave side of the channel bends along the cross-section. The developments of pools are located on the concave side of the channel bends, and riffles are developed at the crossovers during peak discharge. The location of pools and riffles are strongly related to the riverbank erosion. During high discharge, the locations of pools are more vulnerable to bank erosion than the riffles (details in Chapter 6). The channel bed morphology is continuously changed due to high discharge with turbulent

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Figure 3.26 Changes of channel bathymetry from (A) 2016 to 2017 and (B) 2017 to 2018. Source: Field survey from 2016 to 2018.

flow, which is linked with the locations of pools and riffles. The pools and riffles developed in 2016, 2017, and 2018 (Figures 3.23–3.25). At Salmara 3, pools developed along the concave side of the channel during high discharge in 2016. These pools transformed into a shallow depth pool in 2017 due to deposition of sediments (Figures 3.23–3.25).

Changes of channel bathymetry During the period of 2016–2017, maximum change occurred at the stream (Mora Torsa 1) junction amounting to –2.27 m (Figure 3.26A). From 2017 to 2018, the highest positive (3.23 m) and negative (–2.65 m) change of the channel depth were found near the Mora Torsa 1 confluence and upstream of the Mora Torsa 1 confluence (Figure 3.26B). In the year 2018, maximum vertical erosion of the riverbed was observed near the Mora Torsa 1 confluence because of development of a narrow channel with more flow velocity. Finally, it can be inferred that the pools have been changed into a shallow depth pool or riffle as a result of active aggradation processes. On the other hand, the riffles have been changed into pools due to active scouring processes with high discharge.

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Conclusion It is observed that almost all the cross-sections are asymmetrical in shape, and the valley tends to be a wide V-shape. The cross-sectional study of three different seasons shows that there is no specific trend of change within the channel during 2016–2018. The long profile shows that the channel depth and the channel width vary from one site to another site, and the channel thalweg is meandering in nature. The Torsa River with a higher width–depth ratio indicates the bed material is coarser in type. The lower course of the Torsa River is hydraulically efficient. Moreover, the sequences of the pools and riffles along with the channel bathymetry of the Torsa River have frequently changed leading to turbulence flow during high discharge. The channel widens when the flow diverts into two or more channels due to the presence of a mid-channel bar. Subsequently, thalwegs are being formed close to the banks, which accelerates bank erosion processes. There are continuous and frequent changes of channel morphology in the Torsa River, which have made the river more dynamic.

References Andrews, E.D. (1979). US Geological Survey Professional paper 1117, United States Government Printing Office, Washington. Bernhardt, E.S., Palmer, M.A., Allan, J.D., Alexander, G., Barnas, K., Brooks, S., Carr, J., Clayton, S., Dahm, C., Follstad-Shah, J., Galat, D., Gloss, S., Goodwin, P., Hart, D., Hassett, B., Jenkinson, R., Katz, S., Kondolf, G.M., Lake, P.S., Lave, R., Meyer, J.L., O'Donnell, T.K., Pagano, L., Powell, B., & Sudduth, E. (2005). Synthesizing U.S. river restoration efforts. Science, 308(5722), 636–637. Coleman, J.M. (1969). Brahmaputra River: Channel process and sedimentation. Sedimentary Geology, 3(2–3), 129–139. Garcia, M.H. (2004). Sedimentation and erosion hydraulics, hydraulic design handbook, chapter 6. New York: McGraw-Hill. Keller, E.A. (1972). Development of alluvial channels: A five stage model. Bulletin of the Geological Society of America, 83, 1531–1536. Knighton, A.D. (1981). Local variations of cross-sectional form in a small gravel bed stream. Journal of Hydrology, 20(2), 131–146. Knighton, D. (1984). Fluvial forms and processes: A new perspective (pp. 44–161). London: Edward Arnold Ltd. Knighton, D. (1998). Fluvial forms and processes: A new perspective (p. 383). London: Arnold. Lawlor, S.M. (2004). Determination of channel-morphology characteristics, bankfull discharge, and various design-peak discharges in Western Montana. U.S. Department of Agriculture-Forest Service. Scientific Investigations Report, 2004-5263. Leopold, L.B., & Maddock, T. (1953). The hydraulic geometry of stream channels and some physiographic implications. USGS Professional Paper, 252, 1–57. Leopold, L.B., Wolman, M.G., & Miler, J.P. (1964). Fluvial processes in geomorphology. San Francisco, CA: W.H. Freeman & Co. Maiti, R. (2016). Modern approaches to fluvial geomorphology (pp. 1–200). Delhi, India: Primus Books.

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Morisawa, M. (1985). Rivers form and process. In K.M. Clayton (Eds.) Rivers: Form and Process (pp. 71–89). London and New York: Longman. Mukhopadhyay, S., Mukhopadhyay, M., & Pal, S. (2012). Advance river geomorphology (pp. 162–184). Kolkata: ACB Publications. Petts, G., & Foster, I. (1985). Rivers and landscape. Edward Arnold. Schumm, S.A. (1960). The shape of alluvial channels in relation to sediment type. U.S. Geological Survey Professional Paper, 352(D). Singh, S. (2007). Geomorphology (pp. 358–412). Allahabad: Prayag Pustak Bhawan. Summerfield, M.A. (2013). Global geomorphology: An introduction to the study of landforms (pp. 217–218). New York: Routledge.

4

Hydraulic geometry of a channel

Understanding the distribution of hydraulic attributes such as water depth, velocity, and shear stress at different points in natural rivers is very important to hydraulic engineers, river geomorphologists, and river ecologists (Chiu and Tung, 2002; Rosenfeld et al., 2011; Grandgirard et al., 2013; Maity and Maiti, 2018). Hydraulic geometry illustrates the system wherein flow velocity, channel width, and channel depth alter in response to these discharge variations (Charlton, 2008). The hydraulic geometry of a river channel is defined as the analysis of the interrelationship among stream discharge (Q), velocity (v), channel shape, channel width, channel depth, channel slope, and sediment load. The term ‘hydraulic geometry’ was used for the first time by Leopold and Maddock (1953), and they considered the channel properties of a river as continuous functions of increasing discharge. Changes in hydraulic geometry at a single cross profile are a result of many processes that happen at different time scales and flows (Schumm and Lichty, 1963; Wolman and Gerson, 1978; Moody et al., 1999; Costigan et al., 2013). The distribution of vertical velocity shows that the velocity decreases from the water surface to the bed (Savini and Bodhaine, 1971). The relationship amongst all hydraulic geometry reveals that the rates of increase in width and velocity is greater towards downstream and depth is lesser than average values for each river in the world (Leopold et al., 1964; Knighton, 1998; Maity and Maiti, 2018). The changes of channel morphology and magnitude of riverbank erosion are influenced by the spatial and seasonal changes in hydraulic geometry of a channel and their interrelationships in the fluvial environment.

Hydraulic geometry The components of a cross-section of channel appearance are termed the hydraulic geometry (Leopold and Maddock, 1953). The hydraulic geometry of a channel is the analysis of stream discharge, flow velocity, channel shape, channel width, channel depth, channel slope, and sediment load, and the interrelationships among these parameters. Two components of hydraulic geometry are required to be measured for the analysis of stream hydraulics. The relationship between the parameters and their resulting adjustments at a specific location, and the downstream changes at a specific time along a stream channel are to be considered. Most rivers DOI: 10.4324/9781003276685-4

112

Hydraulic geometry of a channel

have exhibited quite reliable relationships between the changes in discharge at a specific location and resulting alterations in the channel width, depth, and mean flow velocity (Summerfield, 2013). Seasonal variation of mean flow velocity The flow velocity of a river is measured using a flow meter or digital current meter. The flow velocity varies from one point to another point or along any cross-section in a natural channel. The channel flow velocity changes with the channel width and the cross-sectional area at different sites (Figures 4.2, 4.3A; Table 4.1). The flow velocity decreases in the downstream direction during the monsoon and non-monsoon (Figure 4.1). In an open channel, the flow velocity fluctuates rapidly at a specific point within the channel flow due to the effects of turbulence. The flow velocity varies with changing depth, and it becomes 0 at the channel bed. The intensity of riverbank erosion varies because of the changes in channel flow velocity at different sites. In our study, flow velocities were measured for the pre-monsoon, monsoon, and post-monsoon seasons. In the study reaches, the highest mean flow velocity was observed at site 2 (2.96 m/sec) near the Torsa bridges at Madarihat and site 1 (1.92 m/sec) near the Indo-Bhutan border during the monsoon and non-monsoon,

Figure 4.1 Downstream seasonal variations of mean surface flow velocity (2017) of the Torsa River. Source: Field survey (2017).

Figure 4.2 Spatio-temporal variation of flow velocity along the different transects of the Torsa River. Source: Field survey (2016–2018).

Hydraulic geometry of a channel 113

Figure 4.3 Seasonal variation of (A) velocity and (B) discharge. Source: Field survey (2016–2018). Table 4.1 Froude numbers and Reynolds numbers Field site

Froude number

Reynolds number

Field site

Froude number

Reynolds number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.497 0.369 0.306 0.284 0.254 0.337 0.318 0.192 0.355 0.245 0.197 0.332 0.327 0.183 0.232 0.185 0.323

388.96 681.92 416.92 631.13 405.61 708.24 792.64 442.68 711.14 450.81 448.60 609.90 693.98 347.37 405.25 348.70 791.32

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

0.243 0.163 0.129 0.176 0.181 0.147 0.296 0.154 0.208 0.165 0.218 0.245 0.328 0.160 0.180 0.153 0.179

387.12 399.86 296.78 378.70 402.84 377.68 636.20 594.35 636.29 453.77 667.19 693.66 771.07 463.25 505.17 672.02 587.61

Source: Field survey, 2017.

respectively. Site 2 has a narrow cross-sectional area due to construction of shortlength bridges that pass a huge volume of water in a short time during monsoon; consequently, the flow velocity has been increasing. The monsoon flow velocity is two times greater than the pre-monsoon and post-monsoon. In the study reach, the flow velocity increased with an increasing channel slope during the monsoon and non-monsoon. It is clear that there is positive correlation

114

Hydraulic geometry of a channel

between both mean velocity of low surface flow velocity and channel slope, and mean bankfull surface flow velocity and channel slope (Figure 4.4). Temporal changes of the flow velocity in same study reach were made (Figures 4.2, 4.3A). During the monsoon, the highest (3.678 m/sec) and lowest (1.295 m/sec) flow velocities were estimated at sites 6 and 10 for 2017 and 2016. (Figure 4.2). Seasonal variation of discharge Discharge means the amount of flow passing in a given period through the channel. Water discharge of a river is calculated by multiplying the channel width, channel depth, and the mean velocity of water (Leopold and Maddock, 1953). The discharge of a channel is calculated using the following equation: Q = wdv

(4.1)

where Q is the discharge, w is the channel width, d is channel depth, and v is the mean velocity of water. Discharge also changes with time along a river course. The channel configuration at any point is dependent on the discharge and sediment supply from upstream. Usually, the discharge of a main stream channel increases in the downstream because the drainage basin area increases and tributaries join with the main channel (Charlton, 2008). The discharge of the non-monsoon period is almost the same in the Torsa River between site 1 and site 30. On the other hand, the monsoon discharge changes frequently day after day (Figure 4.5). Sometimes, discharge varies from one site to another site due to the meeting of tributaries and unequal rainfall. During the period 2016–2018, the monsoon discharge increased 10 to 18 times the pre-monsoon and post-monsoon discharge (Figures 4.3B, 4.6). Stream energy Stream energy is defined as the capacity or ability to cause erosion and accretion. Stream power is also defined as the rate of erosion or accretion, and is measured

Figure 4.4 Statistical correlation between the (A) channel slope and mean velocity of low surface flow velocity and (B) channel slope and mean bankfull surface flow velocity of the Torsa River. Source: Field survey (2017).

Hydraulic geometry of a channel 115

Figure 4.5 Seasonal patterns of discharge of the Torsa River. Source: Field survey (2017).

Figure 4.6 Spatio-temporal variation of discharge along the different transects of the Torsa River. Source: Field survey (2016–2018).

in watts per unit length of stream channel, usually W m–1 (Charlton, 2008). Stream power is an important criterion to determine the capacity of the given flow transporting the sediments per unit time (Charlton, 2008) for an open channel. The available stream power (Ω) per unit length of a stream is measured using the following equation: W = rgQs

(4.2)

where ρ (the Greek letter rho) is the mass density of the fluid (1000 kgm3), g is the gravitational constant (9.8 m s–2), Q is the discharge, and s is the slope of the channel. The measured value of the stream power was 812.25 W m–1 at field site 2 and 79.78 W m–1 at field site 3, which indicates a continuous decreasing trend of stream power downstream leading to deposition. In the downstream, the stream power fluctuates at different sites due to changes in channel slopes near bridges and the meeting of the tributaries. The specific stream power (lowercase omega, ω) is computed by dividing the stream power by the channel width: w=

W w

(4.3)

116

Hydraulic geometry of a channel

Specific stream power is useful for comparisons between specific locations. The measured value of the specific stream power was 3.43 W m–2 at field site 2 and 0.09 W m–1 at field site 10, which indicates a narrow channel along with a minimum cross-sectional area characterized by high specific stream power and vice versa (Figure 4.7). The bed shear stress (τ0) is expressed applying the following equation: t0 = rghs

(4.4)

where τ0 is the bed shear stress, h is the flow depth, and s is the channel slope. The bed shear stress (in N m–2) is a force of the riverbed at per unit area that increases with increasing the flow depth and the slope of the channel. The τ0 has also declined likewise to the specific stream power due to decrease in channel slope (Figure 4.8). In the piedmont region, the stream power, specific stream power, and bed shear stress are high, and they declined downstream during low flow. This situation indicates more deposition over the channel bed. During the monsoon, the stream power, specific stream power (Table 4.2), and bed shear stress increase with increasing channel depth. Extreme stream power can transport the maximum volume of sediments and lift heavier bed material that promote scouring processes.

Figure 4.7 Downstream unit stream power along the Torsa River. Source: Field survey (2017).

Figure 4.8 Downstream bed shear stress along the Torsa River. Source: Field survey (2017).

Hydraulic geometry of a channel 117 Table 4.2 Flow character of the Torsa River between field sites 7 and 9 Season

Value

Type of flow pattern

Post-monsoon, 2017 Post-monsoon, 2018

0.000224 0.000081

Non-uniform Non-uniform

Source: Field survey, 2017.

Table 4.3 Correlation between hydraulic parameters Correlation matrix Width Depth Cross- Wetted Hydraulic Velocity Discharge sectional perimeter radius area Width Depth Cross-sectional area Wetted perimeter Hydraulic radius Velocity Discharge

1 0.490 0.900 0.959 0.644 0.464 0.807

0.490 1 0.768 0.598 0.855 0.651 0.828

0.900 0.768 1 0.922 0.877 0.634 0.930

0.959 0.598 0.922 1 0.660 0.463 0.822

0.644 0.855 0.877 0.660 1 0.754 0.890

0.464 0.651 0.634 0.463 0.754 1 0.834

0.807 0.828 0.930 0.822 0.890 0.834 1

Source: Field survey from 2016 to 2018.

Pattern of flow The pattern of flow of a river is identified by the Reynolds number (Reynolds, 1874), which is as follows: Re =

rVH R m

(4.5)

where Re is the Reynolds number, V is the mean velocity of flow, HR is the hydraulic radius, μ is dynamic viscosity, and ρ is the fluid density. If the Reynolds number is less than 500 that indicates laminar flow, 500– 2000 indicates transitional flow, and more than 2000 indicates turbulent flow. The Reynolds numbers were measured for different seasons to recognize the pattern of flow at different sites of the Torsa River. The values of the Reynolds numbers ranged between 296.78 (site 20) and 792.64 (site 7), indicating a laminar to transitional flow pattern (Table 4.3). However, during the monsoon, the Reynolds numbers were more than 2000 at most of the field sites indicating the pattern of flow is turbulent in nature. During the non-monsoon, the pattern of flow is laminar at most of the field sites, but the pattern of flow is transitional where the field sites are located at or close to stream junctions and bridges. The degree of turbulence also controls the rate of sediment (suspended load and bed load) transportation, because the turbulence assists in lifting the heavier material from the riverbed and transporting it downstream. Turbulent flow occurs in the Torsa River during

118

Hydraulic geometry of a channel

a high discharge period or flood (Table 4.3). The channel flow is turbulent near stream junctions and bridges (at field sites 6, 8, and 31) (Table 4.4). The channel of the Torsa River having pool–riffle sequences and consequently the long profile as well as the channel bathymetry of this river change frequently and lead to turbulent flow during high discharge. The relationship between the Reynolds number and riverbank erosion is highly positive (r = 0.797) in the lower reach of the Torsa River close to a bridge (Figure 4.9A). This situation indicates more turbulence with more riverbank erosion. Nature of flow The nature of flow of a river is identified by the Froude number (Knighton, 1998), which is as follows: FR =

V gD

(4.6)

where FR is the Froude number, V is the mean velocity, g is the gravitational constant, and D is the water depth. Froude numbers below 1 indicate sub-critical flow and dominant gravitational forces; more than 1 indicates super critical flow; and equal to 1 indicates the flow is critical or transitional. The influence of gravity on the flow can be determined by the Froude number (Maity and Maiti, 2017). In most cases, the nature of flow is generally sub-critical in the natural stream (Knighton, 1998). The nature of flow was assessed for the Torsa River by measuring the Froude number at different sites (Table 4.3). During the non-monsoon, the values of Froude numbers less than 1 at all sites of the Torsa River indicate the nature of flow is sub-critical with less energy and dominant gravitational forces. It indicates the accretion possibility within the river channel. In the lower reach of the Torsa River, the selected sites are characterized by a tranquil or sub-critical nature of flow (except field site 6 during the pre-monsoon in the year of 2017) in different seasons (2016–2018). The value of the Froude number is estimated to be 1.115 at site 6, which indicates the nature of flow is super critical, because the mean flow velocity has been increased due to the formation of a longitudinal bar (Table 4.4). The Froude numbers vary from one season to another season. Super critical flow leads to scouring processes that invite riverbank erosion as well as changes in the channel configuration. The relationship between the Froude number and riverbank erosion is highly positive (r = 0.672) in the lower reach of the Torsa River close to the bridge (Figure 4.9B). It indicates the bank erosion increases with the increasing Froude number when other factors remain unchanged. Flow characteristics Generally, the flow characteristics of a stream change spatially. The natural flow of a river is usually either non-uniform or unsteady (Hann et al., 1994). The

B

C

A

B

C

Specific stream power (W m–²) A

B

C

Stream power (J)

2017

A

B

C

Specific stream power (W m–²) A

B

C

Stream power (J)

2018

A

B

C

Specific stream power (W m–²)

9.06 160.40 16.03 0.031 0.246 0.040 14.25 182.06 9.35 0.039 0.279 0.026 9.37 167.96 15.68 0.029 0.237 0.031 71.12 1216.85 116.90 0.178 2.029 0.389 107.80 1436.84 77.07 0.174 1.753 0.302 71.57 1299.64 114.35 0.167 1.559 0.286 132.58 2090.74 206.21 0.737 2.144 1.292 188.59 2485.09 151.03 0.872 2.565 0.557 140.68 2241.26 206.15 0.829 2.300 0.664

A

Stream power (J)

2016

Source: Field survey (2016–2018). Notes: A, pre-monsoon; B, monsoon; C, post-monsoon.

7 9 31

Site

Table 4.4 Variation of stream energy in the downstream direction (2016–2018)

Hydraulic geometry of a channel 119

120

Hydraulic geometry of a channel

Figure 4.9 Relation between (A) Reynolds number and riverbank erosion and (B) Froude number and riverbank erosion. Source: Field survey (2017).

flow characteristics of the Torsa River were measured during the post-monsoon between cross-sections (field sites) 7 and 9 using the following equation: æ Dv ö æ Dy ö æ Dy ö Fi = d ç ÷ + v ç Dx ÷ + ç Dt ÷ = 0 Dx è ø è ø è ø

(4.7)

Dv is the rate of flow where d is the channel depth, v is the mean flow velocity, Dx Dy velocity changes with distance, is the rate of channel depth changes with Dx Dy distance, and is the changes of discharge rate with time. Dt The flow characteristics are uniform when the Fi value is 0. The value of Fi indicates that the flow characteristics of the Torsa River are non-uniform in type during the post-monsoon, but they have a tendency to 0 (Table 4.5). The channel bed configuration changes unevenly if the characteristics of the flow are nonuniform in type. Sediment transportation Most river channels can transport sediments either as very small particles (e.g. clay particles) or large particles (e.g. boulders). There are various mechanisms (rolling, sliding, jumping, saltation, etc.) that are involved in sediment transportation within a channel. The sediment transportation process varies with the changing size of sediment. The supply of sediment can control the stream channel form and behaviour (Charlton, 2008). Sediment load may be divided into two types: solid or particulate load, and solution load. The mode of solid load transportation can be divided into two types: suspended load and bed load. Suspended load transportation The suspended load carries finer materials like sand, silt, and clay in the channel flow. These finer materials are carried by the fluid as a suspended load that

0.255 0.161 0.238 0.204 0.216 0.240

A

0.614 0.378 0.740 0.521 0.268 0.513

B

0.454 0.202 0.278 0.286 0.279 0.407

C

Froude number

454.82 391.16 445.69 424.48 373.42 683.39

A

4889.24 3057.18 4648.46 2604.90 1796.43 2618.82

B 546.06 398.18 650.84 811.88 468.64 953.59

C

Reynolds number

2016

Source: Field survey (2016–2018). Notes: A, pre-monsoon; B, monsoon; C, post-monsoon.

6 7 8 9 10 31

Site

1.155 0.935 0.352 0.571 0.327 0.331

A 0.889 0.752 0.606 0.664 0.411 0.615

B 0.426 0.460 0.185 0.323 0.178 0.249

C

Froude number 956.23 1095.18 471.89 741.00 668.52 643.22

A 5642.90 4405.83 3570.97 3235.81 2138.42 3524.61

B 332.13 407.72 300.27 416.70 300.77 594.46

C

Reynolds number

2017

0.549 0.582 0.689 0.660 0.356 0.552

B

0.115 0.381 0.699 0.348 0.320 0.254

C

Froude number 0.324 0.374 0.136 0.341 0.274 0.403

A

Table 4.5 Seasonal and temporal variation of the nature and pattern of the stream flow (2016–2018)

425.24 229.08 309.19 415.89 517.61 691.12

A

3575.44 2721.85 4269.85 2625.23 2418.97 2987.75

B

225.90 330.63 827.28 389.43 498.26 586.14

C

Reynolds number

2018

Hydraulic geometry of a channel 121

122

Hydraulic geometry of a channel

easily floats in the water. The water samples are collected by inserting sampling devices into the river channel at various depths, measuring the concentration of suspended sediment load. The concentration of suspended load increases during the monsoon when the upstream of a river supplies huge amounts of water and sediment in the downstream. The suspended load increases with increasing discharge in the channel. At reach 9, the highest (1.4276 t/m³/sec) and lowest (0.0012 t/m³/sec) diurnal amount of suspended load was estimated for the months of September (monsoon), and November and December (post-monsoon), respectively (Table 4.6). The relationship between suspended sediment load and discharge is highly positive (r = 0.83) in the lower reach of the Torsa River (Figure 4.10). It indicates the suspended load is mostly controlled by the discharge when other parameters remain unchanged. Bed load transportation The bed load consists of coarser materials (fine gravels, coarse to very coarse sand, etc.) that move downstream along the bed of the stream channel. Generally, the bed load of a river is the clastic type that moves through the channel totally supported by the bed of a river channel (Yeh et al., 1995). In the study reaches, the bed loads are sand and gravel, and they easily roll and slide within the channel, Table 4.6 Temporal variation of discharge and suspended load Date

Discharge Suspended Date (m³ s–¹) load (t/m³/sec)

5/1/2018 150.53 12/2/2018 149.56 3/3/2018 203.80 7/4/2018 217.06 11/5/2018 241.57 8/6/2018 1208.36 12/7/2018 2736.33

0.0013 0.0014 0.0043 0.0126 0.0166 0.0196 0.7662

18/8/18 4/9/2018 12/9/2018 13/9/18 29/10/18 1/11/2018 28/12/18

Discharge Suspended load (m³ s–¹) (t/m³/sec) 3308.70 2736.85 2745.38 2581.80 241.06 240.92 240.80

0.4301 0.6295 1.4276 1.0844 0.0024 0.0012 0.0012

Source: Field survey (2018).

Figure 4.10 Relation between discharge and suspended load. Source: Field survey (2018).

Hydraulic geometry of a channel 123 which introduces shear stress in the channel boundary. Consequently, scouring and shoaling processes have been observed over the riverbed. The transport rate of the bed load varies from one point to another point, and it increases with increasing near-bed flow velocity and flow discharge (Table 4.7). It is very difficult to measure the bed load transport during high discharge.

Fluid dynamics The channel fluid dynamics include the flow velocity (surface flow and near-bed flow velocities), discharge, and roughness of a river (Singh, 2007). Roughness of a riverbed depends on the size of bed material, form of the channel bed, and periodic features like pools and riffles. Velocity distribution Velocity is one of the most sensitive and variable properties of any open-channel flow (Knighton, 1998). Velocity distribution and variation in any channel are very important as they influence the process of erosion, transportation, and deposition (Allan and Castillo, 1995). The distribution of velocity along and across a river channel largely depends on the variation of depth, channel shape, slope of the riverbed, boundary conditions, flow resistance, roughness of the bed, channel pattern, volume of discharge, location of bar, sediment transport, pool–riffle sequences, and man-made constructions. Maximum surface flow velocity is observed in the channel thalweg, whereas the minimum velocity is found near the banks because of more friction and resistance force (Dingman, 1989). Separation or diversion of flow also reduces the flow velocity of a river. At reach 10, flow diversion took place due to the presence of a river island at Salmara and Hokakura mouza (Plate 4.1), which reduces the channel flow velocity. In the lower reach of the Torsa River, the spatio-temporal flow velocity is more dynamic in nature (Figures 4.2, 4.3A). The flow velocity during the monsoon is two to three times more than the non-monsoon period. Surface flow velocity, near-bed flow velocity, and flow velocity at different depths are measured by a flow meter or digital current meter (see Chapter 3, Plate 3.1B, C, and D). Velocity distribution across the channel The flow velocity decreases towards the riverbed and bank walls, and increases at or a little below the stream surface due to reduction of frictional effect. The velocity Table 4.7 Temporal variation of discharge and bed load Date

Discharge (m³ s–¹)

Bed load (t/m³/sec)

29/10/18 1/11/2018 28/12/18

241.056 240.916 240.799

0.009 0.1831 0.1830

Source: Field survey (2018).

124

Hydraulic geometry of a channel

Plate 4.1 Flow diversion in the Torsa River at reach 10.

distribution of very wide channel may be nearly uniform throughout the channel. In small rivers and in river curves, the maximum velocity is often observed below the water surface (Leopold et al., 1964; Morisawa, 1985). Channel shape and channel alignment generally changes the symmetrical distribution of flow velocity into typically asymmetrical velocity distribution across the channel. Velocity distribution is highly skewed and may even be separated into numerous cells in the asymmetrical channel (Morisawa, 1985). Discharge regime and flow velocities Heavy rainfall in the middle and lower catchments, and melting of snow in the upper catchment of the Torsa River introduces maximum discharges during the monsoon. The Torsa River recorded maximum discharge during the monsoon, i.e. from June to September, and minimum discharge during the post-monsoon, i.e. from mid-October to February. In the 2016 monsoon, the water discharge exceeded the bankfull discharge (1800 m³/sec) for five days, with the peak water discharge roughly 3000 m³/sec. Water discharge exceeded the bankfull discharge for nine days with the peak discharge around 3600 m³/sec during the monsoon flood in 2017. In 2018, the water discharge remained above the bankfull discharge for six days during the monsoon, with a peak water discharge of roughly 2700 m³/sec. Surface and near-bed flow velocities increase during high discharge in the pool sections (Figures 4.11–4.13). The thalweg (deepest point) is meandering in nature (see

Hydraulic geometry of a channel 125

Figure 4.11 (A) Surface velocity distribution and (B) near-bed velocity distribution of the Torsa River, 2016. Source: Field survey (2016).

Chapter 3, Figures 3.23–3.25). Maximum flow velocities are found in the thalweg position. The strongest near-bed flow velocities were recorded for about 2.173 m/ sec (at a depth of 1.85 m from the water surface) in 2016 between the Northeast Frontier (NEF) Railway bridge and national highway bridge (Figure 4.11B). The near-bed flow velocities were recorded above 2 m/sec when the channel flow was close to the bankfull discharge (2563.43 m³/sec in 2016, 3026.11 m³/sec in 2017, and 2745.38 m³/sec in 2018) (Figure 4.6). The lowest near-bed flow velocity (0.13 m/sec) was also found in the riffles or near mid-channel bars during low discharge. The near-bed flow velocities vary as a result of the generation of turbulent flow, which is generated due to channel bed roughness. The field-generated data shows that the surface and near-bed flow velocities are high near the pools at the bankfull stage and near-bankfull stage (Figures 4.11–4.13). During low discharge or the non-monsoon season, the near-bed flow velocities remain slightly low in the pools. The maximum surface flow velocity is found near the pools or close to the bridges due to the passing of water through a narrow cross-sectional area (Figures 4.11A–4.13A). It is to be concluded that the surface and near-bed flow velocities are fully controlled by discharge, local slope of the channel, and channel width of a specific cross-sectional area.

126

Hydraulic geometry of a channel

Figure 4.12 (A) Surface velocity distribution and (B) near-bed velocity distribution of the Torsa River, 2017. Source: Field survey (2017).

Depth and velocity Channel flow velocity varies over time and space. The flow velocity largely depends on the channel depth. Variations in velocity change with depth, and they can be seen from measurements of time-averaged velocity made at different depths above the channel bed (Charlton, 2008). The flow velocity usually increases from 0 at the bed to the free flow velocity at the edge of the boundary, and flow velocity increases with increasing vertical distance above the bed (Knighton, 1998; Charlton, 2008). In the study reaches, the flow velocity changes seasonally and temporally with changing depth. The flow velocity is much higher in the pool than the riffle area during peak discharge. The vertical velocity profile shows that the surface flow velocity increases with increasing depth but not beyond 1.0 m deep (Figure 4.14). Sometimes the nearbed flow velocity is the same as the surface flow velocity (Figure 4.15) due to turbulence of flow, and hydraulic jump or drop at the riffles, where the channel depth is shallow. However, flow velocities gradually decrease with increasing depth in the pools or thalweg. In the Torsa River, the flow velocity varies from one location to another one due to the generation of secondary flow and riverbed roughness (Figure 4.15).

Hydraulic geometry of a channel 127

Figure 4.13 (A) Surface velocity distribution and (B) near-bed velocity distribution of the Torsa River, 2018. Source: Field survey (2018).

Figure 4.14 Vertical velocity profile in the Torsa River (A) at pool and (B) riffle sections. Source: Field survey (2017).

Conclusion Channels of the Torsa River are more dynamic in nature due to the formation of maximum turbulence during the monsoon along with more sedimentation, and shifting of thalweg and shoals. The bank erosion of a river increases with an increasing Reynolds number, when the pattern of flow is more turbulent in nature

128

Hydraulic geometry of a channel

Figure 4.15 Cross channel distribution of the flow velocity in the Torsa River at (A) Basdaha Natibari, (B) Sajherpar, and (C) Salmara during the pre-monsoon, 2017. Source: Field survey (2017).

and other factors remain unchanged. During the monsoon, higher stream power can transport a huge volume of sediment and lift heavier bed materials that lead to scouring within the channel. Riverbank erosion occurs when the pattern of flow is more turbulent, but bank erosion varies with changing flow velocities. During the monsoon, super critical flow leads to scouring that increases the vertical erosion as well as riverbank erosion.

References Allan, J.D., & Castillo, M. (1995). Stream ecology, the structure and function of running waters. New York: Chapman and Hall.

Hydraulic geometry of a channel 129 Charlton, R. (2008). Fundamentals of fluvial geomorphology. New York: Routledge, Taylor & Francis Group. Chiu, C.L., & Tung, N.C. (2002). Maximum velocity and regularities in open-channel flow. Journal of Hydraulic Engineering, 128(4), 390–398. Costigan, K.H., Daniels, M.D., Perkin, J.S., & Gido, K.B. (2013). Longitudinal variability in hydraulic geometry and substrate characteristics of a Great Plains sand-bed river. Geomorphology, Elsevier, 210, 48–58. Dingman, S.L. (1989). Probability distribution of velocity in natural channel cross-sections. Water Resources Research, 25, 509–528. Grandgirard, V., Legoulven, P., Calvez, R., & Lamouroux, N. (2013). Velocity and depth distributions in stream reaches: Testing European models in Ecuador. Journal of Hydraulic Engineering, 139(7), 794–798. Hann, C.T., Barfield, B.J., & Hayes, J.C. (1994). Design hydrology and sedimentology for small catchments. San Diego, CA: Academic Press. Knighton, D. (1998). Fluvial forms and processes: A new perspective (p. 383). London: Arnold. Leopold, L.B., & Maddock, T. (1953). The hydraulic geometry of stream channels and some physiographic implications. USGS Professional Paper, 252, 1–57. Leopold, L.B., Wolman, M.G., & Miler, J.P. (1964). Fluvial processes in geomorphology. San Francisco, CA: W.H. Freeman & Co. Maity, S.K., & Maiti, R. (2017). Sedimentation under variable shear stress at lower reach of the Rupnarayan River. West Bengal, India. Water Science, 31(1), 67–92. Maity, S.K., & Maiti, R. (2018). Sedimentation in the Rupnarayan River—Volume 1: Hydrodynamic processes under a tidal system. Springer briefs in earth sciences (pp. 1–100). Switzerland: Springer Nature. Moody, J.A., Pizzuto, J.E., & Meade, R.H. (1999). Ontogeny of a flood plain. Geological Society of America Bulletin, 111, 291–303. Morisawa, M. (1985). Rivers form and process. In K.M. Clayton (Eds.) Rivers: Form and Process (pp. 71–89). London and New York: Longman. Reynolds, A.J. (1874). Turbulent flows in engineering. Chichester: Wiley. Rosenfeld, J.S., Campbell, K., Leung, E.S., Bernhardt, J., & Post, J. (2011). Habitat effects on depth and velocity frequency distributions: Implications for modeling hydraulic variation and fish habitat suitability in streams. Geomorphology, 130(3), 127–135. Savini, J., & Bodhaine, G.L. (1971). Analysis of current meter data at Columbia River Gaging Station, Washington and Oregon. U.S. Geological Survey Water Supply-Paper, 1869-F, 59. Schumm, S.A., & Lichty, R.W. (1963). Channel widening and floodplain construction along Cimarron River in south-western Kansas. U.S. Geological Survey Professional Paper, 352-D, 71–88. Singh, S. (2007). Geomorphology (pp. 358–412). Allahabad: Prayag Pustak Bhawan. Summerfield, M.A. (2013). Global geomorphology: An introduction to the study of landforms (pp. 217–218). New York: Routledge. Wolman, M.G., & Gerson, R. (1978). Relative scales of time and effectiveness of climate in watershed geomorphology. Earth Surface Processes and Landforms, 3, 189–208. Yeh, K.C., Li, S.J., & Chen, W.L. (1995). Modeling non-uniform sediment fluvial process by characteristics methods. Journal of Hydraulic Engineering, 121(2), 159–170.

5

Modelling riverbank erosion hazards

The instability of a river is critical to recognize the natural erosion and mechanisms of load transportation in opposition to human influences (Rosgen, 2001b). Riverbank instability is caused due to the extensive sediment load and corresponding record of devastating floods (Rosgen, 2001b). If river channels are unscientifically managed and characterized by non-cohesive or poor bank stratigraphy as well as less riparian vegetation or removing of deep-rooted vegetation, then the banks are subject to accelerated riverbank erosion hazards, and equivalent channel adjustments lead to channel instability (Rosgen, 2001b) and riverbank instability. Most bank segments of alluvial channels are found to be unstable during the monsoon due to generation of helical flow as well as secondary flow. The bars redirect the flow towards the outer banks in a meandering and braided river, causing bank erosion (Ashworth, 1996). The primary flow of the channel directly attacks the outer bend of the bank, whereas the secondary flow directly hits at the base of the bank (Plate 5.3A). As a result, the bank materials are removed from the bank base. After removal of the basal support, the upper part of the bank collapses and the eroded materials are removed by the steady flow (Maiti, 2016). This type of erosion process frequently occurs in the Torsa River in the Duars and Tal region. The mechanics of riverbanks and prediction of riverbank instability analysis have been studied by Thorne (1982, 1999), Simon and Thorne (1996), Darby and Thorne (1996), Simon et al. (1999), Rosgen (2001b), Starr (2009), Ghosh et al. (2016), and Bandyopadhay and De (2017). Numerous methods are used for estimating riverbank erosion (Table 5.1). The Bank Erosion Hazard Index (BEHI) model has been widely applied for estimating the magnitude and amount or rate of riverbank erosion, and predicting riverbank erosion vulnerable zones in different regions of the world. The Torsa River is the lifeline of the Duars and northern plains regions of Eastern India also experiencing severe bank erosion in several parts of its course. Consequently, hectares of land are being eroded on a regular basis within a very short span of time during floods or high discharge periods. Such bank erosion hazards as well as bank instability and vulnerability have been estimated and delineated applying BEHI and near-bank stress (NBS) tools or models. DOI: 10.4324/9781003276685-5

Modelling riverbank erosion hazards 131 Table 5.1 Different models of riverbank erosion estimation Bank erosion model

Method

Photo-Electronic Quasi-continuous data such as magnitude, Erosion Pin (PEEP) frequency, and timing of the riverbank model erosion and deposition is measured at specific sites. Riverbank shifting Superimposing the banks of different (RBS) periods and calculating the gap between two periods. Bank material strength Erosion pins are used for the large-scale studies applying aerial photographs and maps. Experiment Vertical bank profiles make it clear to understand the magnitude of riverbank erosion of any river. Bank Assessment for The BANCS model has been used to Non-point source determine the prediction of riverbank Consequences of erosion rates, and riverbank stability Sediment (BANCS) and instability applying BEHI and NBS tools. BEHI parameters evaluate the properties of riverbanks related to bank stability analysis, whereas NBS evaluates the conditions of channel flow and its impact on riverbank stability. The total erosion rate was measured on the basis of the matrix calibration of BEHI and NBS to demonstrate the annual bank erosion of any river.

References Lawler (1991, 1992a, 1992b, 1993a, 1993b) Gilvear et al. (1994, 1999), Dey and Mandal (2018) Thorne (1981) Imanshoar et al. (2012), Rosgen (2001a) Rosgen (1996, 1999, 2001a, 2001b), Ghosh et al. (2016), Dey and Mandal (2019)

Bank erosion: A process of channel migration Bank erosion is a widespread phenomenon in a fluvial environment that changes the channel morphology. Riverbank erosion leads to channel migration. There is plenty evidence of channel migration through either bank erosion or channel avulsion in the Himalayan foothills and northern plains regions. In the case of the Torsa River in the northern plains, channel migration has occurred due to excessive bank erosion or avulsion. In the Torsa River valley, channel migration is a widespread natural hazard where its intensity has regularly increased due to bank erosion. The migration rate in a channel bend tends to reach a maximum (Knighton, 1998) due to the presence of pools at that location associated with more flow velocity which accelerate the bank erosion process. The rate and pattern of riverbank erosion have an important role in controlling the channel migration of a river, particularly along the meandering reaches, and in determining floodplain development (Knighton, 1998).

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BANCS model The Bank Assessment for Non-point source Consequences of Sediment (BANCS) method predicts the rate of riverbank erosion and estimates riverbank instability and the vulnerability to riverbank erosion hazards. The BANCS method applies bank erodibility estimation tools or models, such BEHI and NBS (Rosgen, 2008). For the Torsa River, 182 cross-sections were selected to derive data from 364 bank sites (Figure 5.1) for determining riverbank instability and predicting the bank erosion rate and bank erosion hazard vulnerability in the Duars and northern plains regions. These kinds of predictions have been assessed on the basis of different parameters of BEHI and NBS (Rosgen, 2001a, 2006; Starr, 2009; Dey and Mandal, 2019). Different kinds of data were derived by field survey for the assessment of BEHI and NBS parameters (Plates 5.1–5.4). Bank Erosion Hazard Index (BEHI) model The BEHI model is used to predict riverbank erosion vulnerability in the different segments of a river based on a combination of numerous physical parameters (Rosgen, 2001a, 2001b; Dey and Mandal, 2019). Assessment of BEHI parameters are assigned a geometric value (Table 5.2) that corresponds to the overall erodibility (very low, low, moderate, high, very high, and extreme) of the riverbank (Rosgen, 2001a). BEHI ratings were assigned considering seven parameters: ratio of bank height and bank full height, ratio of riparian root depth and bank height, root density, bank angle, surface protection, bank material adjustment, and stratification adjustment (Starr, 2009; Ghosh et al., 2016; Dey and Mandal, 2019).

Figure 5.1 Location of the BEHI and NBS bank sample segments. Source: Field survey.

Modelling riverbank erosion hazards 133

Plate 5.1 (A) Collection of primary data through cross-sectional study and (B) GPS survey. (C) Measurements of near-bank slope by clinometer and (D) levelling instrument.

Ratio of bank height and bankfull height Bank height was measured using a levelling staff from the bank toe to the top of the bank in the lean season (Figure 5.2; Plate 5.2B). On the other hand, the bankfull height was measured from the bank toe or thalweg point to water level in the peak season or monsoon (Figure 5.2). The bank height and bankfull height were estimated at different sample segments of the banks of the Torsa River in three successive three years from 2016 to 2018. If the ratio is more than 2.8 (Table 5.2), then the risk of bank erosion is extreme potentiality and vice versa (Rosgen, 2001a, 2006; Starr, 2009; Dey and Mandal, 2019). Ratio of riparian root depth and bank height The riparian root depth and bank height ratio is derived considering the average root depth of riparian plants and the height of the riverbank to estimate the adherence of bank material by the riparian vegetation (Figure 5.2). A very high ratio indicates very low BEHI scores (Rosgen, 2006; Starr, 2009; Dey and Mandal, 2019) associated with very low potentiality of riverbank erosion vulnerability.

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Modelling riverbank erosion hazards

Plate 5.2 (A) Construction of embankment along the left bank. (B) Collection of primary data of different parameters. (C) Meeting of important tributary (Kaljani River) with the Torsa River. (D) Formation of turbulent flow during monsoon.

Root density Root density was estimated by the field observation method and expressed in percentage. It was measured by visual observation, i.e. the proportion of the riverbank segment covered by plant root. A very high value of root density can be indicated with very low BEHI scores and vice versa (Rosgen, 2006; Starr, 2009; Dey and Mandal, 2019). Bank angle The bank angle was measured with the help of a clinometer from the base of the bank at the waterline during base flow to the bank top (Figure 5.2; Plate 5.1C). A steep bank angle is predicted to have an extreme vulnerability to bank failure due to the shear stresses and gravitational force. If the angles of the banks become more than 90 degrees, undercutting processes are dominant. Surface protection Surface protection is defined as the proportion of the riverbank that is covered and protected by deeply rooted plants, woody debris, downed logs, branches of

Modelling riverbank erosion hazards 135

Plate 5.3 (A) Primary and secondary flows. (B) Mechanism of bank toe erosion due to formation of secondary flow during bankfull conditions in the Torsa River at Damodarpur mouza.

roots, revetment, bed rocks, embankments, etc. (Figure 5.2). Surface protection was estimated by the field observation method. These types of surface protection control the mechanism of bank erosion. For example, high surface protection on the riverbanks indicates less bank erosion vulnerability. On the other hand, easily erodible material, such as sand and silt, increases the bank toe erosion that leads

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Modelling riverbank erosion hazards

Plate 5.4 (A) Riverbank protected by boulder netting and (B) non-cohesive bank material.

Modelling riverbank erosion hazards 137 Table 5.2 Allocated index values for the individual parameters to develop Bank Erosion Hazard Index (BEHI) Bank Erosion Hazard Index values Risk rating categories

Bank erosion potential Very low Low

Bank height/ bankfull height Root depth/bank height Root density Bank angle Surface protection Totals

Moderate High

Value 1.0–1.1 Index 1.0–1.9

1.11–1.19 1.2–1.59 2.0–3.9 4.0–5.9

Value Index Value Index Value Index Value Index Index

0.89–0.5 0.49–0.3 0.29–0.15 0.14–0.05 2.0–3.9 4.0–5.9 6.0–7.9 8.0–9.0 79–55 54–30 29–15 14–5.0 2.0–3.9 4.0–5.9 6.0–7.9 8.0–9.0 21–60 61–80 81–90 91–119 2.0–3.9 4.0–5.9 6.0–7.9 8.0–9.0 79–55 54–30 29–15 14–10 2.0–3.9 4.0–5.9 6.0–7.9 8.0–9.0 10–19.5 20–29.5 30–39.5 40–45

1.0–0.9 1.0–1.9 100–80 1.0–1.9 0–20 1.0–1.9 100–80 1.0–1.9 5–9.5

1.6–2.09 6.0–7.9

Very low Extreme 2.1-2.8 8.0–9.0

>2.8 10 64 mm) in the foothills to clay (