Radiometry of wet surfaces: When Water Matters 9782759829316

Table of contents :
Preface
Contents
Chapter 1 Visual Effects of Surface Tension on the Appearance of Wet Surfaces
Chapter 2 Reflectance of Wet Natural Soils in the Solar Domain: Contributions and Limitations of Physical Models
Chapter 3 Can the Interpretation of Wet Sand Spectral Responses be Considered a Solved Problem?
Chapter 4 Spectro-Photometric Signatures of Water in Planetary Regoliths
Chapter 5 Measure of Optical Properties of Paper when Wetting Using Monte-Carlo Inversion
Chapter 6 Wet Road Surfaces, a Challenge for Road Users… and for Measurement
Chapter 7 A Virtual Goniophotometer for Modeling the Light Scattered by Rough Surfaces Covered with a Water Layer
Chapter 8 Determination of Water Layer Thickness from Laser Halo
Chapter 9 Impact of a Transparent Layer on the Color of a Non-Homogeneous Colored Support
Contributors

Citation preview

Institut d’Optique Graduate School Advanced Textbook

Directed by Lionel SIMONOT

Radiometry of Wet Surfaces When Water Matters

Institut d’Optique Graduate School Textbook Series: The IOGS Textbook series is a collection of books based on the training provided to the school’s engineering students. Focusing on the main field of modern photonics, these books present in a comprehensive manner the knowledge essential to the professions of engineers and researchers in this discipline. Written in a clear and pedagogical manner, in English or in French, these books are intended to support experts, during their training at the school, but also in their daily professional life. Institut d’Optique Graduate School Advanced Textbook Series: Based on seminars, conferences or the long-standing experience of the school’s researchers or collaborators, these books aim at presenting recent developments in one of the many fields of this discipline.

Cover Illustration: Beach in Sardinia 2012, Ó G. Baranoski. Printed in France

EDP Sciences – ISBN(print): 978-2-7598-2930-9 – ISBN(ebook): 978-2-7598-2931-6 DOI: 10.1051/978-2-7598-2930-9

All rights relative to translation, adaptation and reproduction by any means whatsoever are reserved, worldwide. In accordance with the terms of paragraphs 2 and 3 of Article 41 of the French Act dated March 11, 1957, “copies or reproductions reserved strictly for private use and not intended for collective use” and, on the other hand, analyses and short quotations for example or illustrative purposes, are allowed. Otherwise, “any representation or reproduction – whether in full or in part – without the consent of the author or of his successors or assigns, is unlawful” (Article 40, paragraph 1). Any representation or reproduction, by any means whatsoever, will therefore be deemed an infringement of copyright punishable under Articles 425 and following of the French Penal Code. Ó Science Press, EDP Sciences, 2023

Preface

GDR Appamat is a grouping of research focused on material appearance created in 2019 by the French national center for scientific research (CNRS). GDR Appamat covers broad disciplinary fields. In terms of applications, it concerns remote sensing, physics and chemistry of materials, cosmetics and dermatology, analysis and restoration of works of art, classical and 3D printing, lighting, image synthesis, etc. The approaches of the researchers involved in the GDR Appamat are also very diverse: optical measurements, sensory metrology, radiometric or electromagnetic modeling, simulations, and visual rendering. The question we ask and attempt to answer in this book is: how is the appearance of an object changed when it is wet? In general, as can be observed every day, the object becomes darker and more translucent. However, these are only qualitative observations. To try to investigate the optical effects underlying these changes in appearance, and if possible to model, quantify and predict them, a workshop was organized by GDR Appamat in June 2021. The presentations in this workshop showed that light scattering mechanisms affected by the presence of water depend a lot on the material structure: The optical response is not the same for a moistened porous or powdery material, or for an impermeable diffusing medium covered with a film of water. Moreover, even though appearance is related to human vision, thereby to the visible spectrum of light, the problem can be extended to a wider spectral range, in particular for satellite imaging applications that use the infrared spectral domain and for which the absorption bands of water are important to consider. The cross-view of researchers from these various disciplines and approaches seemed particularly stimulating to us and made us want to share its temporary conclusions through this book. The contributors have respected the multidisciplinary spirit of the workshop by privileging a didactic presentation of their work. The detailed developments can be found in the bibliographic references. More than answers, this book opens up avenues for investigation. It is up to the reader to take advantage of it, either from a DOI: 10.1051/978-2-7598-2930-9.c901 Ó Science Press, EDP Sciences, 2023

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Preface

fundamental research stand point or simply to try to explain effects such as morning dew, a spilt glass of water, wet earth or sand… Material appearance sciences are indeed also a matter of observation and visual poetry.

Detail of a Roman mosaic in Villa Romana del Casale, Sicily, Italy. The colors of the mosaic are faded due to the alteration of the surface over time, but it is enough to wet it (see the right part of the flower pattern) to retrieve dark and saturated colors close to the original ones.

Mathieu Hébert and Lionel Simonot Director and deputy director of GDR Appamat

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 1 Visual Effects of Surface Tension on the Appearance of Wet Surfaces . . . . . . Pascal Barla, Loїc Lachiver and Gaёl Guennebaud

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1.1 Different Types of Surfaces . . . . . 1.2 Surface Tension at Various Scales 1.3 A Phenomenological Model . . . . . 1.4 Discussion . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . .

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2 4 5 8 8

Reflectance of Wet Natural Soils in the Solar Domain: Contributions and Limitations of Physical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alice Dupiau, Stéphane Jacquemoud and Xavier Briottet

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2.1 Layered Models . . . . . . . . . . 2.2 Particulate Models . . . . . . . 2.3 BRF Models . . . . . . . . . . . . 2.4 Conclusion and Perspectives References . . . . . . . . . . . . . . . . . .

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13 16 19 21 23

Can the Interpretation of Wet Sand Spectral Responses be Considered a Solved Problem? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gladimir V. G. Baranoski and Mark Iwanchyshyn

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3.1 Case Study: Expected and Unexpected Predictions . . . . . . . . . . . . . . . 3.2 Practical Implications and Future Perspectives . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 2

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CHAPTER 3

Contents

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CHAPTER 4 Spectro-Photometric Signatures of Water in Planetary Regoliths . . . . . . . . . Antoine Pommerol, Marion Massé and Bernard Schmitt

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4.1 Experimenting with Analogues . . . . . . . . . . . . . . . . . . . 4.2 Reflectance Measurements . . . . . . . . . . . . . . . . . . . . . . . 4.3 BRDF of Wet JSC Mars-1 and Basalt Samples . . . . . . . 4.4 Spectral Evolution of Drying Salt-Basalt Mixtures . . . . 4.5 Reflectance of Intimate Mixtures of Water Ice and Dust 4.6 Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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39 40 40 42 45 47 47

Measure of Optical Properties of Paper when Wetting Using Monte-Carlo Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laurent Brunel

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5.1 Radiative Transfer Properties . . . . . . . . . . . . . . . . 5.2 Measurement of Radiative Transfer Properties . . . 5.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Comparison Between Rendering and Photography 5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Wet Road Surfaces, a Challenge for Road Users… and for Measurement . . . Enoch Saint-Jacques and Roland Brémond

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CHAPTER 5

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CHAPTER 6

The BRDF of Road Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . Wet Road Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BRDF Measurement of Road Surfaces and Wetness Monitoring Measurements of the “Wetness” with UGE’s In-Lab Gonioreflectometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Contents

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CHAPTER 7 A Virtual Goniophotometer for Modeling the Light Scattered by Rough Surfaces Covered with a Water Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mickaël Ribardière, Benjamin Bringier, Arthur Cavalier, Léo Jourdy, Lionel Simonot, Mathieu Hébert and Daniel Meneveaux 7.1 Virtual Goniophotometer 7.2 Results and Discussion . . 7.3 Conclusion . . . . . . . . . . . References . . . . . . . . . . . . . . . .

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75 79 83 84

Determination of the Water Layer Thickness from the Laser Halo . . . . . . . . Lev Dolin, Fanny Dailliez and Lionel Simonot

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CHAPTER 8

8.1 Laser Halo Theory: Formulation of the Problem . . . . . . . . . . 8.2 Halo Formed by Light Within Non-Scattering Water . . . . . . . 8.3 Influence of Light Scattering in Water on the Halo Visibility . 8.4 The Water IOP Determination Algorithms . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 9 Impact of a Transparent Layer on the Color of a Non-Homogeneous Colored Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Fanny Dailliez, Mathieu Hébert, Lionel Simonot, Lionel Chagas, Anne Blayo and Thierry Fournel 9.1 Halo Effect and Darkening Phenomenon 9.2 Reflectance Modelling . . . . . . . . . . . . . . 9.3 Application to Halftone Colors . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Chapter 1 Visual Effects of Surface Tension on the Appearance of Wet Surfaces Pascal Barla, Loїc Lachiver and Gaёl Guennebaud

Some of the most interesting visual aspects of our environment often go unnoticed because of their familiarity. We are so much accustomed to them that we hardly pay attention to their intricacies, even less to our ability to rely on them in everyday behaviors. A convincing example is how water affects the appearance of surfaces, through both microscopic and macroscopic effects. Virtually everything changes: colors, shadows, gloss, geometry, etc., in ways that depend on the type of surface that is wet. Why is that so?

In this article, we take on a quick tour of the appearance of wet surfaces, with the goal to raise new questions that should be addressed with a more rigorous approach. Some effects that we are focusing on are depicted in figure 1.1. They are due to different volumes of water on top or inside a material. We first present in section 1.1 major appearance effects that can be observed depending on the type of surface that is wet. We then focus in section 1.2 on potential effects on appearance of surface tension at various scales, which have not received much attention in the past. In order to motivate further research, we present in section 1.3 a phenomenological approach aimed at mimicking some of the main observed effects through a predefined material model. We finally argue in section 1.4 that the development of wet surface appearance models should be led at the intersection of three research domains: physics, computer graphics and visual perception.

DOI: 10.1051/978-2-7598-2930-9.c001 © Science Press, EDP Sciences, 2023

Radiometry of Wet Surfaces

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FIG. 1.1 – Photographs of wet surfaces. From left to right: asphalt road, metallic plate, and muddy path.

1.1

Different Types of Surfaces

An important surface property that affects the appearance of a wet surface is its porosity. We thus begin by describing different effects that water can have on surfaces depending on their porosity. Adding a layer of water on a non-porous material does not affect the physical properties of that base material: water simply sits on top. However, the propagation of light inside the now-layered material is affected, as summarized visually in figure 1.2a and b, modified from the article from Sawayama et al. [1]. Some light

FIG. 1.2 – Diagrams of non-porous (a, b) and porous (c, d) materials, before (top) and after (bottom) wetting. Different types of light paths get affected in different ways (see text for details). Redrawn with modifications from authors [1]. (e) Surface tension effects may occur at different scales, pointed by arrows. At a macroscopic scale (top), surface tension yields menisci. At a mesoscopic scale (middle), it produces slightly concave puddles. At a microscopic scale (bottom) in porous materials, water conforms to the shape of grains except in capillary channels held by surface tension.

Visual Effects of Surface Tension on the Appearance of Wet Surfaces

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paths are reflected by the water layer instead of being reflected by the base surface (1), inducing distinct reflections of the environment. Light transmitted inside the water impinges on the base layer with different angles due to Snell’s law of refraction and meets a reduced refractive index contrast at the water/base layer’s interface (2), which has the effect of increasing transmission inside the base surface, hence increasing absorption. Some paths get “trapped” inside the water layer (3) due to total internal reflection (TIR), which increases path length and thus chances of absorption, leading to color darkening depending on viewing and lighting directions. Instead, when a porous material (e.g., cloth, sand, limestone, etc.) gets wet, it becomes darker, no matter from which direction it is observed. We are all accustomed to this phenomenon, and we may even rely on it, but how can it be explained? At a microscopic scale, water fills in the pores of the material and affects its light scattering properties. We can consider that the base material is then changed by the addition of water. This is again well summarized in figure 1.2c and d. Some light paths get reflected at the air–water interface as before (4). In contrast, light paths that propagate inside the porous material (5) get scattered more in the forward direction [2]. Moreover, light paths that would result in (weak) retro-reflection due to grain configurations (6) also tend to get scattered forward down the material. On average, light paths that enter the wet material from one side and exit to the same side will have thus travelled a longer distance inside the material until they can “turn back”; not only will they have a lower probability of getting retro-reflected, but they will also have more opportunities for absorption compared to transport in the same dry material. Wet patches will thus not only appear darker, but will also exhibit more saturated colors, since absorption is spectrally dependent. This explains why shells and stones brought back from a day at the beach invariably look duller once at home: the material has less vivid and less deep colors since absorption is much less prominent in a dried state. Water also affects transparency [3]: for thin porous surfaces such as a cloth or a paper, light paths are scattered forward and in this case quickly exit to the other side (i.e., they are transmitted through the surface). The material thus looks more transparent, as familiar examples show, such as oily paper bags, wet t-shirts, glued stickers, etc. We have thus seen that one predominant visual characteristic of wet (opaque) materials is that their colors are darker and more saturated. Such effects directly depend on the refractive index of the liquid: compared to water, a liquid with a higher refractive index, such as oil or varnish, will not only increase the intensity of reflections off the liquid surface, but it will also affect the direction of refraction, the TIR, and the refractive index contrast with the base material, all contributing to an increased absorption compared to water. However, a darkened and more saturated color might occur due to causes other than an addition of liquid: some surfaces may absorb more simply due to higher pigment concentrations. Sawayama et al. [1] argue that our ability to visually assess wetness should also rely on comparisons between multiple image regions. Intuitively, the change in color must be redundant enough to appear to be caused by a common denominator: the presence of water inside the material.

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Radiometry of Wet Surfaces

However, color and reflections are not the only important criteria for perceiving whether a surface is covered by water: very similar optical effects can be achieved by coating a material with varnish or lacquer. Yet, we are usually able to distinguish those coatings from (still) water. What visual information can we rely on, and to which extent it is related to physical properties of the liquid? One potential suspect is surface tension.

1.2

Surface Tension at Various Scales

An added layer of water interacts with a base porous surface in complex ways due to surface tension. Depending on whether we look at macroscopic, mesoscopic or microscopic scales, different visual effects might be observed. These are summarized in figure 1.2e, and discussed in the following. At macroscopic scales, we might distinguish surface zones that are immersed in water, from those that are instead soaked or moist. In immersed zones (like a pond or puddle), and in the absence of wind, the water surface is nearly everywhere perfectly flat due to the action of gravity. However, the liquid behaves differently at the boundaries of immersed zones. The surface tension of water is sufficient to bend the water surface in a convex or concave shape called a meniscus. Here, we focus on the concave case which is most common with water; the convex case is discussed at the end of the section. Such boundary regions take the form of troughs, with a high curvature in the direction across the boundary, and a comparatively low curvature in the orthogonal direction. They have the effect to “trap” specular reflections [4]: they get compressed and stick to the meniscus during motion of the viewpoint, a likely noticeable visual cue even in still images (as seen in the photographs of figure 1.1). Outside of the immersed zones, the water layer stands above the base surface, but is not completely uncorrelated from it. Let us call these locations the soaked zones. If we zoom on mesoscopic scales (still visible at the naked eye), we will observe that water tends to comply to convex regions, while it forms small puddles in concave regions. Surface tension still tends to act on the concave regions so that the water surface shape is not completely flat. This is because we are at scales comparable to the capillary length, which is roughly 2 mm for water [5], where surface tension and gravity act as roughly equal forces to deform the water surface in concavities. The highlights reflected off the water surface thus follow only partially the underlying shape. Appearance would differ with a more viscous fluid, since highlights would tend to comply more exactly to the base shape, in both convex and concave regions. Water eventually penetrates in the material due to its porosity. When this occurs, we may say that the material is moist, a configuration that we have already described in the previous section. However, what happens at the transition between soaked and moist zones? At microscopic scales, the water will temporarily comply to the top layer of “grains” as it sinks into the material due to capillary draining. The result is a perturbed water surface, rougher at microscopic scales compared to the

Visual Effects of Surface Tension on the Appearance of Wet Surfaces

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soaked zones. Reflections will thus look blurrier in this transition region, until they disappear altogether in the moist zones (also visible in the photographs of figure 1.1). Different types of base materials might produce other visual effects. In the case of non-porous materials, there are no moist zones. Instead, the soaked zone boundaries show yet another effect of surface tension: convex profiles commonly found in water drops on hard surfaces. The profile mainly depends on the wettability of the base surface, changing the contact angle of water. In the extreme cases of highly hydrophobic surfaces (e.g., hairy leaves), the water layer will separate into water drops that seem to sit on the surface. Light that enters such a water drop can be reflected off the interior interface, hence getting out of the water drop without penetrating the underlying surface (e.g., without ever interacting with the leaf). This creates a silvery retro-reflective appearance (e.g., dew-drops in the early morning [6]). In the opposite case of an extremely smooth surface, the water layer may become thin enough to act as an optical thin film, or to break in myriads of microscopic droplets. This may happen for instance in a kitchen when water has dried on a tiled floor or a metallic appliance: the water layer gets thinner and thinner, showing subtle colors likely due to interference effects. Even more complex (and rarer) effects can occur with exotic materials exhibiting structural colors, such as on the iridescent feathers of birds that change colors when hydrated [7], or the golden elytra of scarabs that turn transparent with decreased humidity [8].

1.3

A Phenomenological Model

How important are surface tension effects compared to color darkening or additional reflections when it comes to visual appearance? In order to get a first idea of the answer, we have designed a rather simple phenomenological model for wet porous surfaces. It relies on a commonly available material model, based on the microfacet theory [9]: the material is made of a diffuse component (controlled by its colored albedo), and of a specular component (controlled by its roughness). Both the albedo and roughness can be varied spatially via texture maps. Additional geometric properties may also be varied such as mesoscopic surface normals, or ambient occlusion. In practice, we have implemented our model in the Substance Designer, software1 starting from the existing waterLevel node for comparison purposes. We have first decided to segment a surface into four nested zones, as previously discussed (see the top row of figure 1.3): immersed, soaked, moist and dry. In practice, this is done by first locating the immersed zones through a thresholding of the height map (red pixels in figure 1.3), from which the soaked and moist zones are determined in succession using distance and height thresholds. All thresholds are manually determined. The dry zones are simply composed of the remaining pixels (in black in figure 1.3).

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https://www.adobe.com/products/substance3d-designer.html.

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Radiometry of Wet Surfaces

The resulting zone map is then used to alter material parameters. The material color (albedo) of all but the dry zones is darkened and saturated (see figure 1.3a), as was done in the waterLevel node. What is new in our approach is that we include effects due to surface tension at different scales. First, meniscus is added at the transitions between immersed and soaked zones, by affecting the shape of the water surface in these regions. Then small puddles are reproduced in the soaked zones by partially flattening the water surface in locally concave regions. Both effects are achieved by locally blurring the normal map (see figure 1.3b), at the interface of immersed and soaked zones, and in concavities. Second, the roughness of reflections is varied from soaked to moist zones. As in the waterLevel node, roughness is set to zero in immersed zones and reduced in soaked zones. In addition, we increase roughness at the transitions between the soaked and moist zones to mimic the liquid conforming to the shape of microscopic grains (see figure 1.3c). We also reduce the contrast of the ambient occlusion map in immersed zones (see figure 1.3d), as discussed in more detail below.

FIG. 1.3 – Top row: A wet surface is segmented into four zones (left): the immersed zone (inside the red boundary), the soaked zone (inside the yellow boundary), the moist zone (inside the blue boundaries), and the dry zone (elsewhere). A zone map is computed from an input height map (right), starting from the immersed zone obtained by thresholding (red pixels). Bottom row: the texture maps used in our phenomenological model, in the dry (top left halves) and wet (bottom right halves) configurations. The albedo map (a) is darker and more saturated in the immersed, soaked and moist zones. The normal map (b) is flattened in immersed zones and smoothed in concavities of the soaked zone. The roughness map (c) is set to zero in the immersed zones, reduced in the soaked zones and increased in the soaked-moist transitions. The ambient occlusion (AO) map (d) has a reduced contrast in the immersed zones.

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Obviously, a more rigorous approach would be required to connect these experiments to actual physical properties of wet surfaces. Nonetheless, this already gives a first preview of the expected effects of surface tension on visual appearance, as shown in figure 1.4. The meniscus gives rise to typical elongated reflections as expected, the puddles give a convincing look to soaked zones, and the increased roughness indicates transitions to the moist zones as reflections get blurred. out.2

FIG. 1.4 – Starting from a description of zones using the color code of figure 1.3 (left), we show the result obtained with the waterLevel node shipped with Substance Designer (middle), and the result obtained with our modified version taking surface tension and other effects into account (right).

Mimicking viscosity. Another important property of a liquid is its viscosity, which characterizes its resistance to deformations. We have found that it seems possible to mimic effects of viscous liquids via a simple modification of the water surface in soaked zones. In figure 1.5, we uniformly smooth out the water surface at two increasing scales. This simple operator does not behave properly in concave regions to mimic water. Instead, the resulting coated materials look more viscous (sticky or glazed), even though their optical properties are left unchanged.

FIG. 1.5 – Slight modifications of the geometry of the liquid surface in soaked zones can affect perceived viscosity and transform appearance from wet (left) to sticky (middle) to glazed (right). Appearance in immersed zones. One aspect that we barely touched upon is the distribution of light in immersed zones. When the surface is completely immersed in water, the light rays transmitted in the water volume follow Snell’s rule of refraction. 2

A video of our modified version is available at https://youtu.be/OyhYx21MmlM.

Radiometry of Wet Surfaces

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When looking at the sky from below the water, the hemisphere of directions gets shrunk to the so-called Snell window. This strongly affects the appearance of mesoscopic shape features, since both view and light directions are affected. First, the immersed surface is never seen at grazing angles, which tends to flatten relief and to reduce perspective. Second, light paths reach the surface with small angles, which shortens cast shadows for collimated lighting, and attenuates smooth shadows for ambient lighting. A simple solution that we took in our model was to reduce the contrast of ambient occlusion (see figure 1.3d). However, once again this is a totally ad-hoc solution, and a more thorough analysis of light transport in immersed zones would be necessary to better understand the visual cues conveyed in such situations.

1.4

Discussion

Wet surfaces are conveyed by a variety of visual cues, the ones coming first to attention being darker and more saturated colors caused either by scattering being pushed forward inside volumes, or by TIR at the water/air interface. Distinguishing among different types of liquids might require to take into consideration the visual cues brought about by surface tension and viscosity at various scales, in addition to darkening changing with the refractive index of the liquid. This does not exhaust the variety of interesting effects due to the addition of water, including retro-reflection by water drops on hydrophobic surfaces and modified light fields in immersed zones. A more rigorous approach to the modelling of wet surface appearance would require to explicitly take into account physical properties. This first includes the optical properties of wet surfaces that govern diffusion in volumes with and without water, as well as scattering at layered interfaces. This further includes mechanical properties such as surface tension and viscosity that affect the shape of the liquid layer. However, an overly accurate physical characterization of wet surfaces might also raise several issues: some physical parameters are hard to measure or set by hand, and might have limited impact on the final visual appearance. This is where computer graphics’ solutions can be relevant: finding reasonable approximations or equivalent models that achieve physically plausible results, while being controlled by a few intuitive parameters. Ultimately, visual perception should also be taken into account, since it will help assess the relevance of model approximations, but also weigh the impact of different visual cues.

References [1] Sawayama M., Adelson E. H., Nishida S. (2017) Visual wetness perception based on image color statistics, J. Vis. 17. [2] Twomey S. A., Bohren C. F., Mergenthaler J. L. (1986) Reflectance and albedo differences between wet and dry surfaces, Appl. Opt. 25, 431. [3] Jensen H. W., Legakis J., Dorsey J. (1999) Rendering of wet materials, in Proceedings of the 10th Eurographics Conference on Rendering, EGWR’99 (Goslar, DEU). Eurographics Association, pp. 273–282.

Visual Effects of Surface Tension on the Appearance of Wet Surfaces

9

[4] Dövencioğlu D., Shahar O., Barla P., Doerschner K. (2017) Specular motion and 3D shape estimation, J. Vis. 17. [5] de Gennes P., Brochard-Wyart F., Quere D. (2003) Capillarity and wetting phenomena: Drops, bubbles, pearls, waves. Springer New York. [6] Seymour L., Minnaert M. (1995) Light and color in the outdoors. Light and color in the outdoors series. Springer New York. [7] Rashid I., Hassan M. U., Nazim M., Elsherif M., Dou Q., Hu D., Kamran M., Dai Q., Butt H. (2020) Structural colouration in the Himalayan monal, hydrophobicity and refractive index modulated sensing, Nanoscale 12, 21409. [8] Vigneron J.-P., Pasteels J., Windsor D., Vertesy Z., Rassart M., Seldrum T., Dumont J., Deparis O., Lousse V., Biro L., Ertz D., Welch V. (2007) Switchable reflector in the Panamanian tortoise beetle Charidotella egregia (Chrysomelidae: Cassidinae), Phys. Rev. E – Stat. Nonlinear Soft Matter Phys. 76, 1. [9] Torrance K. E., Sparrow E. M. (1967) Theory for off-specular reflection from roughened surfaces, J. Opt. Soc. Am. 57, 1105.

Chapter 2 Reflectance of Wet Natural Soils in the Solar Domain: Contributions and Limitations of Physical Models Alice Dupiau, Stéphane Jacquemoud and Xavier Briottet

On a rainy day or during a tide on the beach, one can observe that wet soil is darker than dry soil; this is the case for most rough surfaces. The presence of water on the surface of the soil affects its reflectance not only in the visible range, but also in the near-infrared and shortwave infrared ranges, where water strongly absorbs light. By studying the light reflected from a wet soil, it is possible to predict its water content remotely.

Soil moisture was recognized as an Essential Climate Variable in 2010 by the Global Climate Observing System. Water resource management is under unprecedented pressure worldwide, and according to the IPCC WGII Sixth Assessment Report 2022, “on-farm water management, water storage, soil moisture conservation and irrigation are some of the most common adaptation responses [to water-related risks] and provide economic, institutional or ecological benefits and reduce vulnerability”. Therefore, monitoring soil moisture content (SMC) is essential not only for many applications such as agriculture, hydrology, and climate, but also in defense and planetary science. This parameter is highly variable in time and space, so field measurements are not well suited to map it over large areas. Since the 1970s and along with the improvement of imaging technologies, remote sensing has emerged as a useful tool to make continuous monitoring of SMC in the solar (0.4–2.5 µm), thermal infrared (3–12 µm), and microwave (0.5–100 cm) domains. Each spectral domain allows for a different soil depth to be probed: the longer the wavelength, the deeper the soil moisture can be estimated. This chapter will focus on the solar DOI: 10.1051/978-2-7598-2930-9.c002 © Science Press, EDP Sciences, 2023

12

Radiometry of Wet Surfaces

domain where light penetrates very little into the medium, being absorbed or scattered by the first millimeters of soil. The effect of soil moisture on spectral reflectance is observable on the whole solar domain. In the visible range (0.4–0.7 µm), the wetter the soil, the lower the reflectance. From the near-infrared (0.7–1.4 µm) to the shortwave infrared ranges (1.4–2.5 µm), in addition to the overall decrease in the reflectance continuum amplitude, spectral deformations are also observed due to the absorption of light by liquid water, in particular in the strong absorption bands around 1.4 µm and 1.9 µm. Figure 2.1 shows reflectance spectra of a soil sample at different moisture levels, measured under a 15° illumination and a viewing at nadir. For high moisture levels, a film of water forms on the soil surface, resulting in an increase in reflectance in the specular direction. This effect is however rarely taken into account in models.

FIG. 2.1 – Measured (solid lines) and modeled (dashed lines) reflectance spectra of a silty soil at different SMCs (%). Estimated MARMIT-2 parameters are shown in the legend as ðLðcmÞ;
; dÞ. Estimating SMC from the spectral reflectance remains a challenge. The first option is to use empirical methods. Some studies directly link soil reflectance to SMC using exponential [1–3] or polynomial [4, 5] functions. Other ones isolate the absorption features due to water from those due to other soil constituents by normalizing the reflectance spectrum of wet soil by the one of dry soil or by the continuum removal method [5–10]. Spectral indices, such as those widely used for vegetation stress monitoring, have also been designed to estimate SMC from a combination of reflectance values at strategically chosen wavelengths. Examples include WISOIL [11, 12], NSMI [13], NINSOL & NINSON [5], and SASI [14]. Finally, a matrix decomposition method has been implemented to express wet soil reflectance as a linear combination of spectral vectors determined for a specific database of dry and wet soil reflectance spectra [15].

Reflectance of Wet Natural Soils in the Solar Domain

13

The limitation of these empirical methods is that they are often highly dependent on the type of soil being studied and do not allow to model the reflectance of wet soils on the whole solar domain. Researchers have been working to develop more physical models to better understand the optical phenomena involved in modeling light scattering and absorption by wet soils. In order for these models to be operational for remote sensing, a tradeoff must be found between the realism of the soil representation and its simplicity: the number of input parameters must be as small as possible to avoid a strong dependence on in situ data. We will first present the simplest models that represent wet soils as two superimposed horizontal layers and then those that take into account the granularity of soils. Surface roughness is another key parameter that controls soil reflectance; therefore, we will show how BRF (Bidirectional Reflectance Factor) models can be adapted to changes in soil moisture.

2.1

Layered Models

As soils are porous media made of particles with complex chemical composition and geometry, the interaction of light with soils is difficult to model. Two-layer models describe a wet soil as a rough surface topped with a thin layer of water. Ångström was the first to introduce this representation in 1925 [16]. When a light ray hits the interface between air and water, it is partly reflected and partly refracted. The refracted ray that enters the water layer is reflected or absorbed by the underlying soil surface. The reflected ray returns to the water–air interface, which reflects or refracts the light again. According to Ångström, the darkening of the soil when watered is due to the total reflection in the water layer, which acts as a light trap. The reflectance of the wet soil, Rmod , is expressed as a function of the reflectance of the dry soil, Rd , and the refractive index of water, nw : Rmod ¼

nw2 ð1

Rd  Rd Þ þ Rd

ð2:1Þ

Equation (2.1) is obtained by considering the rays exiting the water layer after multiple reflections within it. The Ångström model was later improved by Lekner and Dorf [17, 18] who calculated the reflection probabilities at the air–water and water-soil interfaces more accurately. These authors predicted the reflectance of a water-saturated soil from the reflectance of a dry soil, knowing the refractive indices of water and soil particles, but could not predict the reflectance of a partially wet soil. Moreover, this model was limited to the visible range because it ignores the absorption of water in the shortwave infrared range. Bach and Mauser [19] extended the model of Lekner and Dorf by accounting for water absorption and introducing a parameter that quantifies the moisture content. MARMIT (multilayer radiative transfer model of soil reflectance) is based on the same principle [20]. It can estimate SMC with good accuracy, but not correctly predict the reflectance of wet soils in the solar domain: the visible reflectance is overestimated and the reflectance in the water absorption bands centered around 1.4 µm and 1.9 µm is poorly modeled.

14

Radiometry of Wet Surfaces

The change in the refractive index of water upon dissolution of soil particles and the alteration of the appearance of the soil surface when wet [21] are the main causes of inaccuracy in two-layer models. In order to improve the modeling, it is necessary to consider that the water layer is not pure liquid water, but a mixture of water and organic and mineral matter. For instance, Bach and Mauser [19] modified the specific absorption coefficient of the water layer (figure 2.2).

FIG. 2.2 – Specific absorption coefficients of water used in several soil reflectance models: Bach and Mauser [19]; MARMIT [20]; and MARMIT-2 [22] for two values of the volume fraction of soil particles d (adapted from [22]). MARMIT-2 [22] represents a wet soil as a dry soil topped with a thin layer of a mixture of water and soil particles that occupy a volume fraction d in the water layer such that 0  d  0:25 (figure 2.3). This is the main change in MARMIT-2 compared to MARMIT. An effective complex refractive index of the water layer is calculated from d and the indices of water and soil particles. This alters the specific absorption coefficient of the water layer as shown in figure 2.2. We also took into account the light scattering around the water spots; this phenomenon is known in the printing domain as the optical dot gain and usually modeled with the Yule–Nielsen equation [23]. In MARMIT-2, the spectral reflectance of the wet soil, Rmod , is written as:
1 m 1 ð2:2Þ Rmod ¼
Rwm þ ð1 
ÞRdm with m  1 an empirical parameter related to the scattering power of the soil,
the coverage fraction of the water layer such that 0 
 1 (the dry soil may be fully or partially covered by water), Rw the reflectance of a completely wet soil, and Rd the reflectance of the dry soil in the background. Rw is calculated as the sum of the light rays exiting the water layer after undergoing multiple reflections:

Reflectance of Wet Natural Soils in the Solar Domain

Rw ¼

t12 t21 Rd Tw2 1  r21 Rd Tw2

15

ð2:3Þ

with t12 the Fresnel amplitude coefficient for transmittance at the air–water interface and t21 and r21 the Fresnel amplitude coefficients for transmittance and reflectance at the water–air interface, respectively. These coefficients depend only on the refractive index of the mixture of water and soil particles and are calculated for diffuse light. Tw is the transmittance of the water layer, calculated using the Beer–Lambert–Bouguer law, also extended to diffuse light by integration over a hemisphere. It depends on the thickness of the layer of water and soil particles and on its specific absorption coefficient, which is calculated from the complex refractive indices of both constituents using a mixing function.

FIG. 2.3 – Schematic representation of MARMIT-2 (adapted from [22]).

In brief, MARMIT-2 simulates the spectral reflectance of wet soils as a function of three parameters: the thickness of the water layer L, the coverage fraction of the water layer
, and the soil particle volume fraction d. Figure 2.1 shows a very good agreement between the measured and modeled reflectance spectra of a silty soil taken at different moisture contents. Verhoef et al. [24] and Yang et al. [25] proposed a model based on the Lekner and Dorf model which is different from MARMIT. This is still a two-layer model, but here the thickness of the water layer is a discrete value that varies statistically according to a Poisson distribution whose variance is empirically related to SMC. Philpot [26] published a simplified reflectance model of wet soils in which the decrease in the visible reflectance continuum amplitude and the spectral deformations of the near-infrared water absorption bands are treated separately. As in Bach and Mauser [19], the specific absorption coefficient of water is empirically altered to account for dissolved organic matter and the presence of soil particles in the water layer.

Radiometry of Wet Surfaces

16

The approach of Ciani et al. [27], Sadeghi et al. [28, 29] and Yuan et al. [30] is somewhat different: they adapted the Kubelka–Munk theory [31] originally developed to predict the reflectance of paint layers and prints. The soil is considered as a layer of uniformly distributed absorbing and scattering particles whose size is much smaller than the thickness of the layer. It is characterized by two parameters: the absorption coefficient K and the scattering coefficient S, which are both wavelength dependent. In the case of a soil layer of infinite thickness, reflectance R is expressed as: s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  K K 2 2K ð2:4Þ R ¼ 1þ  þ S S S Equation (2.4) can be rearranged using the so-called transformed reflectance r ¼ K =S [28]: r¼

ð1  RÞ2 2R

ð2:5Þ

The soil moisture is then related to r through the following expression: SMC ¼ SMCsat

rðr  rd Þ rs  r þ rðr  rd Þ

ð2:6Þ

where SMCsat is the moisture content of a saturated soil, rd and rs are the transformed reflectances for dry and saturated soil, respectively, and r is a parameter ranging between 0 and 1 whose physical meaning is related to the relative strength of scattering in dry and saturated soil.

2.2

Particulate Models

While representing wet surfaces as horizontal layers may be realistic for impermeable surfaces such as asphalt or concrete, this is less the case for agricultural soils that are porous media. More sophisticated models consider light scattering by a set of spherical soil particles. They have mainly been used on dry soils, their applications to wet soils is rare. The Melamed model [32, 33] is a geometrical model predicting the reflectance of a granular medium composed of spherical particles whose diameter is large compared to the wavelength. These particles are assumed to be arranged in a hexagonal compact pattern and to have a Lambertian surface. For clarity, a single layer of identical particles is shown above a Lambertian substrate in figure 2.4. Considering the multiple reflections within the particles, on the substrate and on the surface of the particles, the total reflectance of the soil is expressed as a function of the diameter of particle D, their complex refractive index np , and a parameter accounting for their spatial arrangement xu . The calculation of the reflectance is complex and will not be detailed here, which leads to the following expression:

Reflectance of Wet Natural Soils in the Solar Domain

Rd ¼

1 þ me ðA þ B Þ þ AC 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 þ me ðA þ B Þ þ AC Þ2 4ðme þ C ÞðA þ B Þ 2ð m e þ C Þ

17

ð2:7Þ

A, B, and C are auxiliary terms for the calculation expressed as: A ¼ 2xme B ¼ x ð1  2xme ÞT C ¼ ð1  x Þð1  me ÞT

ð2:8Þ

with me the external reflection coefficient of the air–soil interface, x the probability that a ray from the center of a particle exits upwards, and T the fraction of light transmitted by a particle after multiple reflections.

FIG. 2.4 – Schematic representation of the Melamed model. The particles are separated from the bulk medium for clarity (adapted from [32]). Garay et al. [34] adapted the Melamed model to wet soils for four stages of the drying process: (1) the soil is saturated, all particles are surrounded by water (figure 2.5a); (2) the water evaporates, the soil begins to dry at the surface (figure 2.5b); (3) the water between the particles is partly replaced by air, leaving only a thin film of water around the particles (figure 2.5c); and (4) the soil is completely dry, the pores are filled with air (figure 2.5d). The Melamed model corresponds to this last step. In step (1), the refractive index of air is replaced by that of water and specular reflections at the water–air interface are considered. Step (2) is similar to step (1), except that on the top surface of the particles, the reflection coefficients are calculated for an air-particle interface. Step (3) is the most difficult to derive from the Melamed model. The water coating is assumed to be uniform around the particles and T is recalculated by considering multiple reflections within it. This work was limited to the visible region where water does not absorb light, so it cannot be easily extended to the near-infrared and shortwave-infrared regions.

18

Radiometry of Wet Surfaces

FIG. 2.5 – Schematic representation of a soil at different moisture levels (adapted from [34]). Sadeghi et al. [35] introduced an additional level of complexity to these particulate models by assuming that the reflectance of a dry soil is the sum of a surface component and a volume component. The surface reflectance Rsurface is calculated by considering an infinite number of reflections in a thin layer of particles. The volume reflectance Rvolume is the reflectance of a set of soil particles supposed to be under the surface layer. The contribution of Rsurface to the total reflectance is much higher than that of Rvolume . This model allows to study the effect of the particle size on the soil reflectance which is commonly observed: the smaller the particles, the higher the reflectance. However, the reflectance of infinitely fine particles reaches a maximum value Rmax \1. In other words, a very fine powder of black particles will never be white [36]. An adaptation of this model to wet soils by surrounding soil particles with a film of water of varying thickness could be the subject of future work. In addition, Bänninger et al. [37, 38] showed that the spatial distribution of water in the soil pores altered the reflectance of the soil. They used a beam tracing model considering four distributions of soil particles, water, and air. They also differentiated water bound to soil particles by molecular forces from free water that can easily evaporate. They attributed different optical properties to the two water phases, but showed that considering bound water did not have much effect on reflectance. Finally, Kimmel and Baranoski [39–41] developed a ray tracing model called SPLITS (SPectral LIght Transport model for Sand) that calculates photon transport in sand. Sand is represented as randomly distributed particles, which can be

Reflectance of Wet Natural Soils in the Solar Domain

19

mineral or composed of organic matter, and are surrounded by water and air. The mineral particles can be either quartz, hematite, goethite, or magnetite; they can be pure or coated with another mineral. The interfaces between the particle, its coating and the surrounding medium are simulated by a model of randomly oriented microfacets. The propagation of the visible light in this medium is described with the laws of geometrical optics. SPLITS can be used to simulate synthetic images of sand beaches.

2.3

BRF Models

As discussed in sections 2.1 and 2.2, wet soils can be represented with different levels of accuracy. The relatively simple two-layer models can satisfactorily predict the spectral reflectance of flat wet soils. Natural soils are much more complex. To study the reflectance of rough wet soils, we can use BRDF (Bidirectional Reflectance Distribution Function) models that describe the angular distribution of light scattered by a surface. The BRDF is the ratio of the radiance measured in the direction of observation to the irradiance received by the surface in the direction of illumination [42]. Although the BRDF has been studied extensively, it has no simple expression. The quantity usually measured in remote sensing is the BRF (Bidirectional Reflectance Factor) which is the ratio of the BRDF of a surface to that of a perfect Lambertian white diffuser and is expressed as: BRFðhi ; ho Þ ¼ pBRDFðhi ; ho Þ

ð2:9Þ

The Hapke model is a radiative transfer model commonly used in planetary science. It predicts the BRF of a semi-infinite medium composed of randomly oriented, irregular particles whose size is large relative to the wavelength. The BRF is expressed as the sum of a single scattering component that depends on the phase function of the soil particles and a multiple scattering component that is assumed to be isotropic (equation 2.10). There are several versions of this model that differ according to the approximations made. In the original version [43], the BRF of a soil illuminated by a collimated light beam with a zenith angle hi and observed with a zenith emergence angle ho is written: BRFðhi ; ho Þ ¼

x 1 ½ð1 þ B ðhÞÞP ðhÞ þ H ðl0 ÞH ðlÞ  1 4 l0 þ l

ð2:10Þ

l0 ¼ cosðhi Þ;

ð2:11Þ

l ¼ cosðho Þ;

ð2:12Þ

H ðx Þ ¼

1 þ 2x pffiffiffiffiffiffiffiffiffiffiffiffi ; 1 þ 2x 1  x

ð2:13Þ

Radiometry of Wet Surfaces

20

with x the single scattering albedo, P ðhÞ the phase function which depends on the phase angle h, and B ðhÞ the backscattering function which describes the opposition effect. It is expressed as a function of h and a parameter related to soil porosity. Twomey et al. [44] and Ishida et al. [45] predicted soil reflectance from the single scattering albedo using only the isotropic component of the Hapke model. Moreover, they explained the darkening of wet soils by the decrease in the relative refractive index of the medium surrounding the soil particles, which increases forward scattering. In a wet soil, a light ray has to undergo more scattering events to be reflected and will thus be absorbed with a higher probability. Jacquemoud et al. [46] extended the Hapke model to the solar domain and, to account for the specular reflectance of smooth, wet soils, they introduced a phase function P ðh; h0 Þ that describes scattering both in the backward and forward directions. They showed that, to a first approximation, only the single scattering albedo x varied with wavelength, but it did not relate it to SMC. Pommerol et al. [47] also inverted the Hapke model to estimate the parameters that best fit BRF measurements of Mars soil analog samples in dry and wet conditions. Verhoef and Bach [48] first linked x to the wet soil reflectance Rw by:
2 w 1  11R þ Rw x¼ ð2:14Þ
2 w 1 þ b4 11R þ Rw where b is a parameter of the phase function. The wet soil reflectance is written as a function of the dry soil reflectance Rd using the Beer–Lambert–Bouguer law [49–51]: Rw ¼ Rd ean

ð2:15Þ

where n is the equivalent water thickness of the soil and a the specific absorption coefficient of water. Linking the single scattering albedo retrieved from BRF measurements of soil samples to SMC has been the subject of a few studies: Yang et al. [49] and Gao et al. [52] established a linear regression between n and SMC; Zhang et al. [53] proposed a physics-based normalized difference soil moisture index. The RPV (Rahman–Pinty–Verstraete) model [54] is a semiempirical model that expresses the BRF of natural surfaces (e.g., soils, vegetation) as a function of three parameters: an arbitrary parameter characterizing the surface reflectance intensity q0 , the Minnaert parameter k indicative of the level of surface anisotropy, and the intensity of forward (g [ 0) and backward (g\0) scattering. A fourth parameter h was introduced in [55] to consider the hotspot effect, i.e., the increase in reflectance in the illumination direction due to the absence of shadow. The BRF is given by:  k1  cos hi cosk1 ho BRFðhi ; ho Þ ¼ q0 F ðhÞRðhÞ ð2:16Þ ðcos hi þ cos ho Þ1k F ðhÞ is the Henyey–Greenstein phase function that depends on the asymmetry parameter g and on the phase angle h:

Reflectance of Wet Natural Soils in the Solar Domain

F ð hÞ ¼

21

1  g2 3

½1 þ g 2  2g cosðp  hÞ2

ð2:17Þ

RðHÞ is the hotspot function expressed as a function of a geometrical factor Hðhi ; ho Þ and the hotspot parameter h: R ðH Þ ¼ 1 þ

1h 1þH

ð2:18Þ

Roosjen et al. [55] measured the BRF of five soil samples at various SMC levels. They then inversed the RPV model to fit the data in the principal plane. Both Pommerol et al. [47] and Roosjen et al. [55] have shown that soil wetting affects not only the reflectance level but also the angular distribution of scattered light. An increase in SMC leads to a decrease in backward scattering and hotspot effect in favor of the apparition of a forward scattering peak whose intensity increases with the amount of water. Roosjen et al. [55] found a strong correlation between the asymmetry parameter g of the RPV model and SMC. However, neither the Hapke model nor the RPV model is able to well reproduce the specular reflection peak that is observed with water-saturated soils. The modeling of rough and wet soil BRF remains a topic of study in the literature and no comprehensive model encompassing all physical effects exists to date. The models presented in section 2.3 are related to macroscopic surface properties. It is likely that the parameters estimated from laboratory measurements made on a few square centimeters and from airborne or satellite images with a spatial resolution of a few meters or tens of meters will differ. To understand these changes in scale, 3-D ray-tracing models could be useful. DART [56], Raytran [57] and more recently Eradiate [58] are very powerful ray-tracing models that could simulate the BRF of rough soils. They take as input parameters the digital terrain model (DTM) of a soil cut into micro-facets and the optical properties of those facets. In DART-Lux, the latest version of DART, the facets can be Lambertian or their BRF modeled by the RPV model. The MARMIT-2 model is being integrated into DART-Lux to represent Lambertian facets at different moisture levels. A remaining challenge is to describe the spatial distribution of moisture as a function of soil roughness at the field scale.

2.4

Conclusion and Perspectives

We have presented different models of the soil spectral reflectance as a function of moisture content (table 2.1). Soils are complex media characterized by many physical and chemical parameters, but satisfying estimations of SMC can be obtained even with simple representations based on a limited number of variables. Ray-tracing models have been identified as a useful tool to investigate the effect of soil roughness at various spatial scales by simulating the BRF of rough, wet soils.

Radiometry of Wet Surfaces

22

TAB. 2.1 – Summary of the main models presented in this article and their parameters. Parameters used to fit the wet soil reflectance or BRF measurements are in bold type. Parameters that vary with wavelength are underlined. Reference Bach and Mauser (1994) [19] MARMIT (Bablet et al., 2018) [20]

MARMIT-2 (Dupiau et al., 2022) [22]

Parameters Dry soil reflectance Rd Complex refractive index of water nw

Comments Empirical calibration linking L:
to SMC

Thickness of the water layer L Surface coverage of water  Dry soil reflectance Rd Complex refractive index of water nw

Empirical calibration linking L:
to SMC

Incidence zenithal angle of light hi Thickness of the water layer L Surface coverage of water  Dry soil reflectance Rd Complex refractive index of water nw

Empirical calibration linking L:
to SMC

Complex refractive index of soil particles np Yule–Nielsen parameter m Thickness of the water layer L Surface coverage of water  Volume fraction of soil particles in the water layer d Sadeghi et al. Dry soil reflectance Rd (2015) [28, 29] Water-saturated soil reflectance Rs Relative strength of scattering in dry and water-saturated soils r Soil moisture content at saturation SMCs Soil moisture content SMC Garay et al. Dry soil reflectance Rd (2016) [34] Refractive index of water nw Complex refractive index of soil particles n*p Mean diameter of soil particles D Parameter of spatial arrangement of particles xu

SOILSPECT (Jacquemoud et al., 1992) [46]

Incidence zenithal angle hi Viewing zenithal angle ho Phase function Pðh; h0 Þ Single scattering albedo x

RPV (Rahman et al., 1993) [54]

Incidence zenithal angle hi Viewing zenithal angle ho Surface reflectance intensity q0 Minnaert parameter k Asymmetry parameter g Hotspot parameter h

Explicit relation between soil reflectance and SMC

Water absorption not accounted for Reflectance is estimated at different drying stages and matched with measurements at 620 nm Empirical calibration linking x to SMC

q0 can be linked to SMC through a reflectance model of wet soil (e.g., MARMIT-2)

Reflectance of Wet Natural Soils in the Solar Domain

23

The challenge for future research is the validation of physical models of the wet soil reflectance on airborne or satellite multispectral (Sentinel-2) and hyperspectral (PRISMA, EnMAP) images. A recent study [59] used the MARMIT model to map SMC from drone images. This topic paves the way to the study of soil darkening by other liquids with different refractive indices, with applications such as the detection of soil contamination by hydrocarbons or the remote sensing of methane on Titan, Saturn’s largest moon.

Acknowledgements This study was supported by the LabEx UnivEarthS, ANR-10-LABX-0023 and ANR-18-IDEX-0001.

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[15] Jiang C., Fang H. (2019) GSV: A general model for hyperspectral soil reflectance simulation, Int. J. Appl. Earth Obs. Geoinf. 83, 101932. [16] Ångström A. (1925) The albedo of various surfaces of ground, Geogr. Ann. 7, 323. [17] Lekner J., Dorf M. C. (1988) Why some things are darker when wet, Appl. Opt. 27(7), 1278. [18] Mall H. B., da Vitoria Lobo N. (1995) Determining wet surfaces from dry, in Proc. IEEE International Conference on Computer Vision, pp. 963–968. [19] Bach H., Mauser W. (1994) Modeling and model verification of the spectral reflectance of soils under varying moisture conditions, in Proc. 14th International Geoscience and Remote Sensing Symposium (IGARSS’94), Vol. 4, pp. 2354–2356. [20] Bablet A., Vu P. V. H., Jacquemoud S., Viallefont-Robinet F., Fabre S., Briottet X., Sadeghi M., Whiting M. L., Baret F., Tian J. (2018) MARMIT: A multilayer radiative transfer model of soil reflectance to estimate surface soil moisture content in the solar domain (400–2500 nm), Remote Sens. Environ. 217, 1. [21] Planet W. G. (1970) Some comments on reflectance measurements of wet soils, Remote Sens. Environ. 1(2), 127. [22] Dupiau A., Jacquemoud S., Briottet X., Fabre S., Viallefont-Robinet F., Philpot W., Di Biagio C., Hébert M., Formenti P. (2022) MARMIT-2: An improved version of the MARMIT model to predict soil reflectance as a function of surface water content in the solar domain, Remote Sens. Environ. 272, 112951. [23] Hébert M. (2014) Yule-Nielsen effect in halftone prints: graphical analysis method and improvement of the Yule-Nielsen transform, in Proc. SPIE Color Imaging XIX: Displaying, Processing, Hardcopy, and Applications, pp. 9015–9027. [24] Verhoef W., van der Tol C., Middleton E. M. (2018) Hyperspectral radiative transfer modeling to explore the combined retrieval of biophysical parameters and canopy fluorescence from FLEX–Sentinel-3 tandem mission multi-sensor data, Remote Sens. Environ. 204, 942. [25] Yang P., van der Tol C., Yin T., Verhoef W. (2020) The SPART model: A soil-plant-atmosphere radiative transfer model for satellite measurements in the solar spectrum, Remote Sens. Environ. 247, 111870. [26] Philpot W. (2010) Spectral reflectance of wetted soils, in Proc. IEEE Art, Science and Applications of Reflectance Spectroscopy Symposium, Vol. II, 12 pp. [27] Ciani A., Goss K. U., Schwarzenbach R. P. (2005) Light penetration in soil and particulate minerals, Eur. J. Soil Sci. 56(5), 561. [28] Sadeghi M., Jones S. B., Philpot W. D. (2015) A linear physically-based model for remote sensing of soil moisture using short wave infrared bands, Remote Sens. Environ. 164, 66. [29] Sadeghi M., Sheng W., Babaeian E., Tuller M., Jones S. B. (2017) High-resolution shortwave infrared imaging of water infiltration into dry soil, Vadose Zone J. 16(13), 1. [30] Yuan J., Wang X., Yan C., Wang S., Ju X., Li Y. (2019) Soil moisture retrieval model for remote sensing using reflected hyperspectral information, Remote Sens. 11, 366. [31] Kubelka P., Munk F. (1931) Ein Beitrag zur Optik der Farbanstriche, Zeit. Tech. Physik 12, 593. [32] Melamed M. T. (1963) Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders, J. Appl. Phys. 34(3), 560. [33] Mandelis A., Boroumand F., vanden Bergh H. (1990) Quantitative diffuse reflectance spectroscopy of large powders: The Melamed model revisited, Appl. Opt. 29(19), 2853. [34] Garay H., Monnard A., Lafon-Pham D. (2016) Influence of moisture content on reflectance of granular materials. Part II: Optical measurements and modelling, Granul. Matter 18, 39. [35] Sadeghi M., Babaeian E., Tuller M., Jones S. B. (2018) Particle size effects on soil reflectance explained by an analytical radiative transfer model, Remote Sens. Environ. 210, 375. [36] Callet P. (2004) Couleur et apparence visuelle, le transparent et l’opaque, Techniques de l’Ingénieur, AF3252. [37] Bänninger D., Flühler H. (2004) Modeling light scattering at soil surfaces, IEEE Trans. Geosci. Remote Sens. 42(7), 1462. [38] Bänninger D., Lehmann P., Flühler H., Tölke J. (2005) Effect of water saturation on radiative transfer, Vadose Zone J. 4(4), 1152.

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[39] Kimmel B. W., Baranoski V. G. (2007) A novel approach for simulating light interaction with particulate materials: Application to the modeling of sand spectral properties, Opt. Express 15 (15), 9755. [40] Kimmel B. W., Baranoski V. G. (2009) A compact framework to efficiently represent the reflectance of sand samples, IEEE Trans. Geosci. Remote Sens. 47(11), 3625. [41] Kimmel B. W., Baranoski V. G. (2010) Simulating the appearance of sandy landscapes, Comput. Gr. 34(4), 441. [42] Simonot L., Obein G., Bringier B., Meneveaux D. (2019) Modeling, measuring, and using BRDFs: Significant French contributions, J. Opt. Soc. Am. A 36, C40. [43] Hapke B. (1981) Bidirectional reflectance spectroscopy: 1. Theory, J. Geophys. Res. 86(B4), 3039. [44] Twomey S. A., Bohren C. F., Mergenthaler J. L. (1986) Reflectance and albedo differences between wet and dry surfaces, Appl. Opt. 25(3), 431. [45] Ishida T., Ando H., Fukuhara M. (1991) Estimation of complex refractive index of soil particles and its dependence on soil chemical properties, Remote Sens. Environ. 38, 173. [46] Jacquemoud S., Baret F., Hanocq J. F. (1992) Modeling spectral and bidirectional soil reflectance, Remote Sens. Environ. 41(2–3), 123. [47] Pommerol A., Thomas N., Jost B., Beck P., Okubo C., McEwen A. S. (2013) Photometric properties of Mars soils analogs, J. Geophys. Res. Planets 118, 2045. [48] Verhoef W., Bach H. (2007) Coupled soil – Leaf-canopy and atmosphere radiative transfer modeling to simulate hyperspectral multi-angular surface reflectance and TOA radiance data, Remote Sens. Environ. 109, 166. [49] Yang G. J., Zhao C.J., Huang W., Wang J. H. (2011) Extension of the Hapke bidirectional reflectance model to retrieve soil water content, Hydrol. Earth Syst. Sci. 15, 2317. [50] Yao Y., Liu Y., Gao M., Chen Z. (2018) Hyperspectral inversion of soil moisture content based on SOILSPECT model, in Proc. IEEE 7th International Conference on Agro-Geoinformatics. [51] Ding A., Ma H., Liang S., He T. (2022) Extension of the Hapke model to the spectral domain to characterize soil physical properties, Remote Sens. Environ. 269, 112843. [52] Gao C., Xu M., Xu H., Zhou W. (2021) Retrieving photometric properties and soil moisture content of tidal flats using bidirectional spectral reflectance, Remote Sens. 13, 1402. [53] Zhang Y., Tan K., Wang X., Chen Y. (2020) Retrieval of soil moisture content based on a modified Hapke photometric model: A novel method applied to laboratory hyperspectral and Sentinel-2 MSI data, Remote Sens. 12(14), 2239. [54] Rahman H., Pinty B., Verstraete M. M. (1993) Coupled surface-atmosphere reflectance (CSAR) model: 2. Semiempirical surface model usable with NOAA advanced very high resolution radiometer data, J. Geophys. Res. 98, 20779. [55] Roosjen P. P. J., Bartholomeus H. M., Clevers J. G. P. W. (2015) Effects of soil moisture content on reflectance anisotropy – Laboratory goniometer measurements and RPV model inversions, Remote Sens. Environ. 170, 229. [56] Gastellu-Etchegorry J. P., Grau E., Lauret N. (2012) DART: A 3D model for remote sensing images and radiative budget of Earth surfaces, in Modeling and simulation in engineering (Catalin Alexandru). [57] Govaerts Y. (2015) Sand dune ridge alignment effects on surface BRF over the Libya-4 CEOS calibration site, Sensors 15(2), 3453. [58] Leroy V., Govaerts Y., Misk N., Schunke S., Nollet Y. (2020) Eradiate scientific handbook, Technical Report, Eradiate, https://www.eradiate.eu/site/docs/. [59] Eon R. S., Bachmann C. M. (2021) Mapping barrier island soil moisture using a radiative transfer model of hyperspectral imagery from an unmanned aerial system, Sci. Rep. 11, 3270.

Chapter 3 Can the Interpretation of Wet Sand Spectral Responses be Considered a Solved Problem? Gladimir V. G. Baranoski and Mark Iwanchyshyn

More than one third of the planet’s land surface is covered by sand. Not surprisingly, a broad scope of studies have been carried out on the spectral responses of this ubiquitous granular material. Consequently, one might expect that there are no more open questions about its interactions with light, even considering different environmental conditions. In fact, sometimes, environmentally elicited changes in its appearance may be so obvious that one does not require any specialized equipment to identify and interpret them. Take, for sample, a costal area covered by sand. As a wave breaks into the beach, one can observe sand becoming darker and slowly getting brighter again as the water gently recedes. We all have a good understanding about what is happening, namely the presence of water in the sand’s pore space alters the amount of light reflected by this material. Hence, apparently, no “mysteries” need to be solved for this cause-effect phenomenon. However, if one explores it more deeply, one may encounter some interesting situations that may be worth of future investigations, suggesting that the current knowledge in this area, albeit considerable, may still be far from complete. Here, we employ an exploratory case study to illustrate this aspect and to highlight significant data constraints usually overlooked in this context.

Before addressing the core issues related to the posed question, we find it appropriate to briefly review some of the fundamental characteristics and provenance aspects of sand, notably those relevant for the proposed discussion involving its interactions with light. We note that most of the following background information about sand has been summarized from previous publications (e.g., [1–3]), and it is DOI: 10.1051/978-2-7598-2930-9.c003 © Science Press, EDP Sciences, 2023

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concisely provided here for completeness. The reader interested in more details is referred to those publications. As a type of soil, sand is primarily composed of grains (particles) of weathered rocks immersed in a medium of air and water (the pore space) [4]. The texture of a soil corresponds to the proportion of sand-sized grains (particles with dimensions between 0.05 and 2.0 mm), silt-sized grains (particles with dimensions between 0.002 and 0.05 mm) and clay-sized grains (particles with dimensions smaller than 0.002 mm) forming the sample [5, 6]. The fraction of the total volume of a soil sample not occupied by its constituent grains is defined as its porosity [7]. On average, naturally occurring sand-textured soils, henceforth referred simply as sand, contain at least 85% sand-sized particles [5], and their porosity normally varies between 35% and 50% [4, 8]. The rocks forming the core (parent) material of a sand sample’s constituent grains are typically silicate minerals like quartz [9]. Trace amounts of mineral impurities, notably iron oxides (e.g., hematite, goethite and magnetite), can significantly affect the reflectance (fraction of incidence light reflected by the material [10]) of these soils [11, 12], notably in the spectral region from 400 to 1000 nm. The grains’ core materials may occur as pure particles, as particles mixed with impurities or as coated particles [13–15]. A particle coating is formed by a mineral (e.g., kaolinite) matrix that may embed impurities as a result of the weathering processes responsible for the formation of a sand deposit [14]. We note that iron oxides may also be present in a soil sample as pure particles [15]. These weathering processes can also affect the morphology of the sand grains. For example, the transportation of grains by wind may involve rolling, suspension and saltation stages [16] that can alter their roundness and sphericity [17]. Generally speaking, a high roundness value specifies a grain with a smooth surface, while a high sphericity value indicates a grain with a geometry close to that of a sphere. Sand can be found in a wide range of landscapes, from costal areas to dune fields. As aridification and desertification elicited by climate change and human actives continue to evolve, the areas occupied by sandy landscapes are increasing. Sand is also often transported (e.g., via aeolian events) from these landscapes to arable fields and crops found in nearby and even relatively distant regions. Its presence in terrains used for agricultural purposes highlights the importance of establishing a robust knowledge base about its optical properties. This base would be central to the development of more cost-effective technologies for the monitoring and management of sandy landscapes. It would also allow for a high degree of realism in the reproduction of sand appearance changes using image synthesis techniques. The presence of water in the pore space of a sand sample can be quantified in terms of its degree of water saturation, denoted by S. This quantity corresponds to the probability of light encountering water while traversing the pore space of a given sand sample [1], and it can vary from zero (dry state) to one (water-saturated state). There are also situations in which the sand grains, albeit immersed in a pore space filled with air, may be encapsulated by water films [6, 18]. This may happen, for example, after the bulk of water in the pore space has been either drained via gravity or partially evaporated, leaving only the water films created by surface tension

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between the water and the grains [3, 6]. For illustrative purposes, distinct water saturation states are schematically depicted in figure 3.1. The thickness of a water film depends on the sand sample’s morphological characteristics, its previous water saturation state [6, 19] and other environmental factors such as temperature [20, 21]. Not surprisingly, direct measurements of water film thickness are difficult to be performed with the current technology [21]. In related investigations [18, 19], the values considered for this physical parameter are usually on the order of micrometers. Note that, for practical purposes, the water films can be treated as thin interfaces between the grains and the pore space [6, 9, 22]. Accordingly, the denomination of a dry state (S = 0) with the grains encapsulated by water films is employed here to indicate that, although light is not attenuated while traveling in the pore space (due to the absence of water), it may be attenuated when it interacts with a water film. Significant experimental and computational developments in the last decades have resulted in an unprecedented expansion of our understanding about environmental factors affecting the appearance of natural materials like sand. This might suggest that we reached the end of the road when it comes to the investigation of their interactions with light, at least in the visible and near infrared domains. In this context, issues like data scarcity and simulation predictability may be quickly overlooked. Here, we aim to provide a slightly different perspective on this matter.

FIG. 3.1 – Diagrams (not to scale) illustrating distinct water saturation states (associated with the presence, or absence, of water in the pore space of a sand sample). (a) Dry state. (b) Intermediate water-saturated state. (c) Water-saturated state. (d) Dry state with the grains encapsulated by water films. For clarity, only a relatively small number of grains (particles) are depicted in the diagrams.

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More specifically, we seek to bring to the foreground the fact that, despite all the information about sand spectral responses available in the literature, it may still be too early to consider this avenue of research closed. To demonstrate that, we conducted a case study involving the spectral responses of a typical sand sample subjected to different degrees of water saturation. This was accomplished employing a first-principles in silico (computational) approach supported by measured data available in the literature. Besides addressing the practical implications of the conducted case study, we also elaborate on steps that can be taken to strengthen the current knowledge about the spectral responses of dry and wet sand.

3.1

Case Study: Expected and Unexpected Predictions

For our case study, we used as a reference a typical sand sample whose reflectance spectrum was measured by Rinker et al. [23]. In the absence of a complete morphological and mineralogical description of this sample, which was obtained from a Californian outcrop, the values assigned to its characterization parameters were chosen from physically valid ranges reported in the literature. More precisely, we employed quartz as its core material and kaolinite as its coating matrix. Furthermore, we considered the selected sample to be composed of 92.5% sand-size grains and 7.5% silt-sized grains. These percentages, in turn, were employed to calculate the size of the sample’s grains using a particle size distribution provided by Shirazi et al. [24]. Accordingly, the major axes defining the ellipsoids used to represent the sand-sized and the silt-sized grains were assigned dimensions provided by this distribution, with average values equal to 0.132 mm and 0.022 mm, respectively. As for the grains’ type distribution, we considered the sample to be composed of 50% pure particles, 25% mixed particles and 25% coated particles. Regarding the sample’s iron oxide contents, we took into account its original goethite-rich designation, and assigned to the ratio between the mass fraction of hematite to the total mass fraction of hematite and goethite a value equal to 0.25, with the total mass fraction of hematite and goethite equal to 0.042. Our in silico experiments consisted in the computation of directionalhemispherical reflectance curves [10] for the selected sample under dry and wet conditions. For these computations, we used a virtual spectrophotometer [25, 26] and an enhanced version of the predictive light transport model for particulate materials originally known as SPLITS (Spectral Light Transport Model for Sand) [1, 2]. Its stochastic ray-optics formulation includes parameters describing the morphology and mineralogy of the grains forming a sand sample, as well as the distribution of these grains within its pore space. We employed a sample thickness equal to 1 m, a value that guarantees depth-invariant readings [27] like those obtained in actual measurements [23]. The simulated curves were obtained considering an angle of incidence of 0º, 106 rays per sampled wavelength and a spectral resolution of 5 nm.

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For the reader interested in the reproduction of the radiometric outcomes of this case study, we have made the enhanced implementation of SPLITS, termed SPLITS-2 [22], available for online use [28] through the NPSG (Natural Phenomena Simulation Group) model distribution system [29], along with supporting spectral datasets (e.g., refractive index and extinction coefficient curves) [30]. It is worth noting that the employed light transport model provides directional-directional radiometric outputs as well [1]. Thus, it can also be employed in investigations involving the computation of BSSRDF (bidirectional scattering surface reflectance distribution function [10]) or BRDF (bidirectional reflectance distribution function [10]) quantities for sand samples using virtual goniophotometers [26, 31]. Initially, we computed reflectance curves considering three distinct water saturation states, namely dry (S = 0.0), intermediate (S = 0.5) and saturated (S = 1.0). As it can observed in figure 3.2a, the simulated reflectance curve obtained for the dry state closely agrees with its measured counterpart (root mean square error equal to 0.0076 [32]), indicating that the employed sample characterization provides a plausible baseline for our experimentations. Furthermore, the curves computed for the intermediate and saturated states depict the expected qualitative behaviour, i.e., the increase in the degree of water saturation resulted in a decrease in the sample’s reflectance in the 400–1000 nm spectral domain. As mentioned earlier, the reflectance decrease of a wet sand sample is translated into markedly noticeable changes in its appearance in the visible spectral domain. Such changes are illustrated in the sand swatches presented in figure 3.2b–d. The color attributes of each swatch were computed through the convolution of the relative spectral power distribution of a standard CIE illuminant (D65, average daylight [33, 34]), the corresponding simulated reflectance values (from 400 to 700 nm) and the broad spectral response of the human photoreceptors [34]. This last step was performed by employing a standard CIEXYZ to sRGB color system conversion procedure [35]. The resulting colors were then employed to generate sand swatches in conjunction with the use of an achromatic hue modulation map (raster file). Subsequently, we computed reflectance curves for two intermediate water saturation states (S = 0.40 and S = 0.45) and a dry state (S = 0.0) with the individual grains encapsulated by water films (5 μm thick [19]). As it can be observed in figure 3.3a, the reflectance curve obtained considering the water films practically superimposes the curves computed for the intermediate water saturation states. As one might expect, this close proximity among the reflectance curves leads to nearly indistinguishable chromatic attributes as illustrated by the swatches presented in figure 3.3b–d. Taking into account the physical differences between the intermediate water saturation states and the dry state with grains encapsulated by water films, particularly in terms of water presence in the sample’s pore space, one might expect the respective simulated curves to be less similar, both quantitatively and qualitatively. In the next section, we examine these aspects more closely and discuss their ramifications.

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FIG. 3.2 – Simulated spectral curves and swatches obtained for a sand sample subjected to distinct water saturation states (represented by different degrees of water saturation S). The simulated curves (associated with the dry (S = 0.0), intermediate (S = 0.5) and saturated (S = 1.0) states) are presented in plate (a) along with a measured curve [23] for the dry state, which is included for reference purposes. The corresponding swatches for the dry, intermediate and saturated states are presented in plates (b), (c) and (d), respectively.

FIG. 3.3 – Simulated spectral curves and swatches obtained for a sand sample subjected to water saturation states leading to an apparent overlap of its spectral responses. The curves associated with two intermediate water saturation states (represented by slightly different degrees of water saturation, namely S = 0.40 and S = 0.45) are presented in plate (a) along with a simulated curve associated with a dry state (S = 0.0) in which the individual sample grains are encapsulated by water films. The corresponding swatches for the intermediate state with S = 0.40, dry state with water films and intermediate state with S = 0.45 are presented in plates (b), (c) and (d), respectively.

Interpretation of Wet Sand Spectral Responses

3.2

33

Practical Implications and Future Perspectives

Depending on the morphological characteristics of a soil, an intermediate state of water saturation may correspond to its field capacity, i.e., the amount of water available for plant uptake until the permanent wilting point is reached [6]. This point, in turn, represents the situation in which water is held too firmly by the soil grains (forming the encapsulating films around them) for plants to extract it [6]. Thus, from agricultural and ecological viewpoints, the impacts of these two water saturations states, intermediate and dry with water films, on plant development are quite different. However, from a spectrophotometric viewpoint, the outcomes of the conducted case study suggest that these states may elicit nearly indistinguishable spectral signatures. If confirmed, this spectral similarity might have undesirable consequences. For example, it might induce to incorrect estimations about the presence of water in the pore space of sandy landscapes, which could lead to unreliable assessments about these terrains’ capacity to support vegetation growth. One might suggest that the putative spectral overlap depicted in the conducted case study may be an isolated instance, and the outcomes could be different for other sand samples. It is worth mentioning that we have performed the same simulations for other samples, which are not described here for conciseness, and we have observed similar spectral overlaps. Nonetheless, although it may be possible to find samples for which such a spectral overlap does not take place, our simulations suggest that it may occur for others. Those cases alone would be sufficient to cast shadows in the interpretation of sand spectral responses associated with distinct water saturation states. It is also possible that the observed spectral overlap may result from a flaw in the design of the employed light transport model. After all, it has been noted that “all models are wrong” [36], albeit some may be useful. Therefore, first and foremost, it becomes essential to confirm whether the observed phenomenon really occurs in nature, or it is just an incorrect model prediction. To achieve that, one needs data, which can also be used to verify the usefulness of the models being used in this type of investigation. For instance, a light transport model originally developed for image synthesis purposes can have its scope of applications extended beyond the generation of believable renderings depicting a target material [37]. It can also be instrumental in the formulation of new hypotheses and theories associated with this material. However, these will only be translated to tangible scientific advances upon proper evaluation of the model’s predictive capabilities. To effectively evaluate these, one needs to quantitatively and qualitatively assess the fidelity [38] of its predictions by comparing them with measured datasets (e.g., spectral reflectance curves) obtained from real exemplars of the target material. Despite their importance, however, measured datasets are still scarce. Although one may be led to believe that there is an abundance of data ready to be used, notably for ubiquitous natural materials like sand, our empirical observations in this area tell us that this is rarely the case. Besides being relatively scant, spectral measurements for sand are usually limited to a few viewing and illumination

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geometries and/or to samples with some morphological and/or mineralogical characteristics (e.g., uniform grain size and/or devoid of mineral impurities) markedly distinct from those of naturally occurring sand deposits. Furthermore, the samples’ descriptions are usually sketchy, which makes comparisons between simulated and measured spectral quantities more difficult. Often, the viable alternative to mitigate this sample characterization constraint consists in assigning values to the material parameters (to be used as input into a simulation) taking into account their physical ranges and averages provided in the literature. Ideally, one would like to be able to have access not only to spectral measured data for a wide variety of sand samples, but also to their comprehensive morphological and mineralogical descriptions (characterizations). Such well-integrated datasets would resemble those obtained for plant leaves in the LOPEX (Leaf OPtical EXperiments) project [39]. Although a significant collaborative effort among various research groups would be required to achieve that, the resulting datasets would likely become instrumental for future advancements involving the study and simulation of light and sand interactions. In summary, going back to the posed question, we believe that there is still a long way to go before one can consider the interpretation of wet sand spectral responses a solved problem. To strengthen the current knowledge in this area, it will be necessary to intensify the synergy between simulation and measurement initiatives. The good news is that during such a pursuit, as happens in many fields, one may come across phenomena that have not been identified before, which may lead to even broader scientific discoveries.

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[9] Leu D. J. (1977) Visible and near-infrared reflectance of beach sands: a study on the spectral reflectance/grain size relationship, Remote Sens. Environ. 6(3), 169–182. [10] Nicodemus F. E., Richmond J. C., Hsia J. J., Ginsberg I. W., Limperis T. (1992) Geometrical considerations and nomenclature for reflectance. In L. B. Wolff and S. A. Shafer and G. E. Healey, editors, Physics-based vision principles and practice: Radiometry, Jones and Bartlett Publishers, Boston, pages 94–145. [11] Bullard J. E., White K. (2002) Quantifying iron oxide coatings on dune sands using spectrometric measurements: An example from the Simpson-Strzelecki desert, Australia. J. Geophys. Res. 107(B6), 1–11. [12] Viallefont-Robinet F., Bacour C., Bouvet M., Kheireddine M., Ouhssain M., Idoughi R., Grignon L., Munesa E., Lemaître F., Rivière T. (2019) Contributions to sandy site characterization: Spectro-directional signature, grain size distribution and mineralogy extracted from sand samples, Remote Sens. 11(2446), 1–24. [13] Mottana A., Crespi R., Liborio G. (1978) Simon and schuster’s guide to rocks and minerals. Simon and Schuster Inc., New York, NY, USA. [14] Wopfner H., Twidale C. R. (2001) Australian desert dunes: wind rift or depositional origin?, Aust. J. Earth Sci. 48, 239–244. [15] Baranoski G. V. G., Kimmel B. W., Chen T. F., Miranda E. (2014) Influence of sand-grain morphology and iron-oxide distribution patterns on the reflectance of sand-textured soils, IEEE J-STARS 7(9), 3755–3763. [16] Wadell H. (1932) Volume, shape, and roundness of rock particles, J. Geol. 40(5), 443–451. [17] Wadell H. (1933) Sphericity and roundness of rock particles, J. Geol. 41(3), 310–331. [18] Neema D. L., Shah A., Patel A. N. (1987) A statistical model for light reflection and penetration through sand, Int. J. Remote Sens. 8(8), 1209–1217. [19] Mekonen A., Sharma P., Fagerlund F. (2014) Transport and mobilization of multiwall carbon nanotubes in quartz sand under varying saturation, Environ. Earth Sci. 71, 3751–3760. [20] Li W., Zhang Y., Wei W., Gu Z. (2015) Discussions of some issues for wind blown sand flow simulation, Procedia IUTAM 17, 1190128. [21] Zheng X., Zhang R., Huang H. (2014) Theoretical modeling of relative humidity on contact electrification of sand particles, Sci. Rep. 4, 4399. [22] Iwanchyshyn M. Y., Kimmel B. W., Baranoski G.V.G (2020). Revisiting the SPLITS model: Towards an enhanced implementation. Technical report, CS-2020-01, D.R. Cheriton School of Computer Science, University of Waterloo, Canada. [23] Rinker J. N., Breed C. S., McCauley J. F., Corl P. A. (1991) Remote sensing field guide – desert. Technical report, ETL-0588, U.S. Army Topographic Engineering Center, Fort Belvoir, VA, USA. [24] Shirazi M. A., Boersma L., Hart J. W. (1988) A unifying quantitative analysis of soil texture: Improvement of precision and extension of scale, Soil Sci. Soc. Am. J. 52(1), 181–190. [25] Baranoski G. V. G., Rokne J. G., Xu G. (2001) Virtual spectrophotometric measurements for biologically and physically-based rendering, The Visual Comput. 17(8), 506–518. [26] Baranoski G. V. G., Rokne J. G. (2004) Light interaction with plants: A computer graphics perspective, Horwood Publishing, Chichester, UK. Chapter 3. [27] Ciani A., Goss K. U., Schwarzenbach R. P. (2005) Light penetration in soil and particulate materials. Eur. J. Soil. Sci. 56, 561–574. [28] Natural Phenomena Simulation Group (NPSG). (2020) Run SPLITS-2 online. D.R. Cheriton School of Computer Science, University of Waterloo, Ontario, Canada. http://www.npsg. uwaterloo.ca/models/splits2.php. [29] Baranoski G. V. G., Dimson T., Chen T. F., Kimmel B. W., Yim D., Miranda E. (2012) Rapid dissemination of light transport models on the web, IEEE Comput. Graph. 32(3), 10–15. [30] Natural Phenomena Simulation Group (NPSG). (2012) Sand data. D.R. Cheriton School of Computer Science, University of Waterloo, Ontario, Canada. http://www.npsg.uwaterloo. ca/data/sand.php. [31] Krishnaswamy A., Baranoski G. V. G., Rokne Jon G. (2004) Improving the reliability/cost ratio of goniophotometric comparisons, J. Graphics Tools 9(3), 31–51.

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[32] Iwanchyshyn M. Y. (2020) In silico investigation of the light transmission profiles of sand-textured soils. Master’s thesis, D.R. Cheriton School of Computer Science, University of Waterloo, Canada. [33] Ohta N., Robertson A.R. (1982) Colorimetry fundamentals and applications, John Wiley & Sons, New York, NY, USA. [34] Hunt R. W. G. (1991) Measuring colour, 2nd edn. Ellis Horwood Limited, Chichester, England. [35] Baranoski G. V. G., Krishnaswamy A. (2010) Light & skin interactions: Simulations for computer graphics applications, Morgan Kaufmann/Elsevier, Burlington, MA, USA. [36] Box G. E. P. (1976) Science and statistics, J. Am. Stat. Assoc. 71(356), 791–799. [37] Greenberg D. P., Arvo J., Lafortune E., Torrance K. E., Ferwerda J. A., Walter B., Trumbore B., Shirley P., Pattanaik S., Foo S. (1997) A framework for realistic image synthesis, SIGGRAPH, Ann. Conf. Ser. 477–494. [38] Gross D. C. (1999) Report from the fidelity implementation study group. Simulation Interoperability Workshop, Simulation Interoperability and Standards Organization, Orlando, FL, USA, Paper 99S-SIW-167. [39] Hosgood B., Jacquemoud S., Andreoli G., Verdebout J., Pedrini G., Schmuck G. (1995) Leaf Optical Properties Experiment 93 (LOPEX93]. Technical report, EUR 16095 EN, Institute for Remote Sensing Applications, Unit for Advanced Techniques, Ispra, Italy, 1995. Published by the Office for Official Publications of the European Communities, ECSC-EC-EAEC Brussels, Luxembourg.

Chapter 4 Spectro-Photometric Signatures of Water in Planetary Regoliths Antoine Pommerol, Marion Massé and Bernard Schmitt

Water in all its different physical states has played a major role in the formation and evolution of the Solar System and its liquid form is key to the appearance and evolution of life as we know it. Detecting and characterising water at the surface of different classes of astronomical objects is therefore a major objective of the Solar System exploration. While ice, the solid form of water, is abundant throughout the entire Solar System, liquid water is only known to exist at the surface of the Earth and deep within the subsurface of some of the icy moons of the outer Solar System. Mars is an intriguing case, however, as the current surface conditions are compatible with the transient presence of liquid water, especially in the form of very salty brines. While some observations have been interpreted by the presence and action of liquid water, such interpretations remain highly debated. We present here the results of laboratory characterizations of wet and icy analogues that show distinctive radiometric signatures which, depending on the exact circumstances, can help to detect the presence of water/ice or, to the contrary, can keep them hidden from observing instruments.

The surfaces of the large atmosphereless objects of our Solar System consist of a layer of fine particulate material, formed by the constant (micro)meteorites’ bombardment and action of the solar wind on the rocks. The most studied example of such a surface, referred to as planetary “regolith”, is the Moon [1]. In-situ analyses and returned samples have shown that the first few meters below the surface consist of fine particles in the micrometre to millimetre size range, with half of the mass below  100 µm. Similar regoliths have been observed at the DOI: 10.1051/978-2-7598-2930-9.c004 © Science Press, EDP Sciences, 2023

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surface of asteroids and icy regoliths cover the surface of the icy moons in the outer Solar System. Often referred to as a regolith, the Martian soil is essentially particulate, but current Aeolian erosion, ancient aqueous erosion and other geological processes dominate over the interactions with the Solar wind seen on atmosphereless bodies. Liquid water seems rare in the Solar System as it is abundant at the surface of the Earth. The only liquid phase directly observed at a surface is ethane in lakes at the North and South poles of Titan, identified by a strong specular reflection in the infrared spectral range and low diffuse reflectivity at radar wavelengths [2]. Water is very abundant in the form of ice, from deposits in the permanently shadowed craters at the poles of Mercury [3] to the bulk of the icy moons of the giant planets and transneptunian objects (TNOs). Due to internal heating by tidal forces, subsurface liquid oceans are certainly present below the surface of some of the icy moons [4], but water freezes before reaching the surface. The only place beyond the Earth where surface liquid water is known to have played a significant role in the geological history and can still exist today at least in a transient state is Mars. A large fraction of the Martian surface consists of very ancient and heavily cratered highlands dating from the first billions of years (Noachian area) following the formation of the planet [5]. These terrains display abundant signatures of the intense and sustained action of liquid water, in the form of hydrological landforms (riverbeds, delta, basins) and hydrous mineralogy (clay minerals, salts) [6, 7]. The traces of water activity evolve drastically during the Hesperian area, suggesting episodic and violent releases of large volumes of water to the surface from pressurised subsurface aquifers associated with intense volcanic and tectonic activity. Water then disappears from the surface around the transition to the dry and cold climate of the Amazonian area (3Gy – today). The current Martian atmosphere consists mostly of carbon dioxide (96%) with an average surface pressure of 6 mbar, which is coincidentally the pressure of the triple point of water. As the surface temperature can reach 290 K during a summer day, pure liquid water is metastable for short periods of time in regions below the average elevation [8]. Different salts depress the fusion point of water significantly and salty brines can be stable under the current conditions over more extended periods of time and ranges of latitude and altitude. While thermodynamics predict the transient presence of liquid water at the surface, observations of the current or recent presence or action of liquid water at the surface remain inconclusive. Gullies eroded in the steep slopes of impact craters and other topographic features have been interpreted as proofs of recent water flows [9] possibly related to episodic redistribution of ice in the current Amazonian climate in response to periodic variations of the astronomical parameters (obliquity, eccentricity, precession) [10]. Although dark slope streaks are abundant on steep Martian slopes and mostly interpreted as resulting from dry granular processes [11], a special class of small streaks has attracted much attention in the community. Recurring Slope Linae (RSLs) are dark (up to 40% darker than the surrounding areas), appear

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every spring at the same locations, grow in length during spring and summer before fading away in fall and winter [12]. This repetitive behaviour as well as the temperature conditions at which they appear has initially suggested the role of liquid brines. The origin of the water is however unclear and dry processes have then been proposed to explain the observations [13, 14] but with significant challenges to overcome as well. As the Phoenix lander touched the Martian ground at high northern latitudes (68°), its retrorockets interacted with the soil and ice at the surface and some droplets of brines were then observed to stick to the legs of the lander [15]. Dielectric measurements also showed the presence of adsorbed and salty liquid water in the regolith at daytime [16].

4.1

Experimenting with Analogues

Our knowledge of the current state and history of Mars and other objects in the Solar System comes largely from the numerous instruments on board missions sent to fly by, orbit or land at the surface of the studied objects. Physical models and laboratory experiments are then crucial to interpret quantitatively the observations. Here we focus on laboratory experiments done on regolith analogs mixed with the liquid of frozen water. In the case of Mars, natural samples collected from various volcanic provinces of the Earth have been used as Martian regolith analogues for decades. The most used analogue so far is certainly JSC Mars-1, a palagonitic tephra collected on the flank of the Mauna Kea volcano in Hawaii, homogenised and then distributed to the community by a team at NASA’s Johnson Space Center [17]. As the supplies of this particular sample are limited, new approaches are now explored to provide analogues to the community. The team of the Center for Lunar & Asteroid Surface Science (CLASS) at the University of Central Florida has undertaken the production of an artificial analogue by mixing easily procurable individual components to mimic the elemental and mineralogical compositions of the Rocknest soil sample, analysed in-situ by NASA’s Curiosity rover [18]. Terrestrial volcanic rocks such as basalts are also commonly used as the Martian crust is essentially of basaltic composition. Similarly, artificial analogues for asteroids have been designed and produced by the same group based on the measured compositions of different classes of meteorites [19]. Even more challenging than the procurement of relevant geological samples, introducing volatile components in the samples requires elaborated protocols to ensure the reproducibility of the production and stability of the composition and other properties. Further building upon the developments of [20] to produce suitable water ice analogues for cometary nuclei, the Planetary Imaging Group of the University of Bern has built devices to produce in a reproducible way samples that associate water ice and dust of various compositions. The devices are portable and can be moved to different facilities to produce fresh samples in situ and progressively build in this way an extensive library of sample properties using different techniques of investigation [21].

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4.2

Reflectance Measurements

The bidirectional reflectance measurements presented here were obtained using the PHysikalisches Institut Radiometry Experiment, version 2 (PHIRE-2), a radio-goniometer designed to measure dense Bidirectional Reflectance Distribution Function (BRDF) datasets of various analogue samples, including those containing water ice. This instrument, an evolution of the PHIRE device used by [22], consists of two mobile arms rotating around the sample, one holding the tip of a fiber-coupled light source and collimating optics, the other one a silicon detector and light collecting optics. The light source consists of a halogen lamp, a chopper to perform synchronous detection and a filter wheel equipped with 6 broad bandpass filters (FWHM of 70 nm) to probe the visible spectral range regularly between 400 and 1100 nm. The incidence and emission angles can be varied between 0° and  75°, depending on the physical size of the sample and the azimuth angle from 0° to 180° to cover almost an entire half-hemisphere above the sample. The strongest limitation is the difficulty to measure the BRDF at low phase angle (angle between the directions of incidence and emission). While we have obtained data at phase angles as low as 0.5° using a special detector holder equipped with a beamsplitter, the calibration of such data is highly challenging and the resulting signal to noise ratio considerably degraded [23]. We therefore restrict such measurements to very bright samples and generally use a minimum phase angle of 5°. The spectral measurements in this chapter were obtained using the SHINE spectro-gonio radiometer at the Institut de Planétologie et Astrophysique de Grenoble (IPAG). It is a home made bidirectional visible and near-infrared reflectance spectrometer operating over the 0.4–4.8 µm spectral range and covering a wide range of illumination, emergence and azimuth angles (θi = 0–85°, θe = 0–80°, ϕ = 0–180°) [24]. Its illumination beam has high homogeneity and has a very low divergence (0.1°). Correction procedures considering illumination distribution over the observed spot and the non-Lambertian behavior of the Spectralon reference surface allow to reach an absolute photometric accuracy better than 1% under most of the measurement geometries [25].

4.3

BRDF of Wet JSC Mars-1 and Basalt Samples

Figure 4.1 presents optical microscope pictures of a JSC Mars-1 sample, first dry and then with increasing amounts of liquid water (top to bottom) until complete saturation. The sample was wetted by spraying fine droplets of liquid water over the surface and letting them settle and diffuse into the sample. As we need the samples to remain stable for the relatively long periods of time needed for the photometric measurements (tens of minutes), we had to spray significant amounts of water to wet the whole sample from top to bottom and avoid fast drying. We were therefore not able to measure samples with very small amounts of water. The bulk amount of liquid water into the sample was followed by weighting the sample at each wetting step, but these estimates ignore possible vertical gradients which might make the bulk water content different from the one at the surface.

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FIG. 4.1 – Bidirectional measurements of the reflectance factor of dry and wet surfaces of the Mars soil simulant JSC Mars-1. Data are shown here for a fixed incidence angle of 30° and a fixed wavelength of 650 nm. The white spot in the data (on the right of the plots) corresponds to the very low phase angles (