Derivado del comportamiento del gasto observado por las unidades administrativas y órganos desconcentrados a cargo de los Programas de Acción Específicos, en lo sucesivo

The role of macroscopic roughness in the directional reflectance of a particulate medium is sensitive to scales ranging from the size of an individual particle to the field-of-view of an airborne sensor [34]. Consequently, macroscopic surface roughness is an important pa- rameter to consider when using ground-based measurements to calibrate imagery obtained

from space-based satellites and airborne sensors. When attempting to retrieve geophys- ical parameters from remotely sensed imagery, failing to account for surface roughness ignores important reflectance phenomena such as multiple scattering within surface cavi- ties and shadowing caused by extreme slope angles. For example, Wang et al employed an image-based bidirectional distribution function (BRDF) approach to analyze the effect of illumination zenith angle on both rough and smooth soil surfaces. They found that BRDF images of clay loam surfaces consisting of large clods were largely made up of shaded pixels, whereas BRDF images of smooth soil surfaces were dominated by illuminated pixels. [25] In another study, Shepard et al found that as surface cavities of sediment surfaces were gradually diminished by compression, reflectance became more isotropic and eventually exhibited stronger forward scattering. [29] Other more recent studies comparing rough and smooth areas of beach sediments on the Queensland coast of Australia have similar results. [66]

We sought to investigate these trends further in a more controlled setting. In this lab- oratory study, we performed radiometric measurements of two sediment samples that were collected during a summer field campaign in Nevada. Both of these samples were collected from a lakebed region and had a high percentage of silt and clay grains making up their grain size distributions. Initially, these samples had significant soil moisture content, but were completely dried in order to create dried soil clods. Both samples then underwent a process in which the materials were incrementally pulverized into their final powderized forms. Bidirectional reflectance measurements and digital elevation measurements were obtained at each roughness level in order to study the effects of macroscopic surface rough- ness on the reflectance of the sediment. Measurements were obtained using two different fore-optic configurations (5 degree and 8 degree) and two different light source positions (25 degree and 45 degree).

Results of this study showed that the photometric effect of macroscopic surface rough- ness is sensitive to the choice of sensor field of view. A method of continuum removal over the spectral region of 350 nm to 2500 nm for each respective sensor orientation angle of the BRDF scan was performed for each roughness level of the sediment. The result of this procedure showed that there was a discernible qualitative trend that measurements obtained with the 5 degree fore-optic attachment had considerably more variance in spec- tral shape than measurements obtained using the 8 degree fore-optic attachment. This suggests that a smaller sensor solid-angle is considerably more sensitive to the effects of macroscopic surface roughness than larger sensor footprints. Future investigations should try to determine how these effects translate to airborne and satellite imagery.

In the future, our laboratory will attempt to determine if this trend is applicable both to larger sensor solid angles and to the sampling extent of hyperspectral imagery. A separate analysis of the data using spectral derivatives was performed as a method of investigating the appearance of a spectral absorption feature centered around 600 nm. It was qualitatively observed that as the surface was made rougher and more surface

additionally observed that there was a clear dependence of these effects on sensor fore- optic. These results suggest that sensors possessing a larger footprint are less sensitive to the effects of macroscopic surface roughness in the spectral domain.

Another goal of this study was to investigate the effect of macroscopic surface roughness when varying the zenith angle in the principal plane of the illumination source. Illumi- nation zenith angles close to nadir (25 degrees) and at more oblique scattering angles (45 degrees) were used in this study. Continuum removal analysis showed that there was a strong dependence of spectral variance on the illumination source orientation. In par- ticular, this result most evident when performing continuum removal within a spectral absorption band located in the region of 1900 nm. Qualitative analysis showed that the variance in band shape for rough samples within this spectral region was greater for mea- surements obtained while the light source was at a 45 degree zenith angle. Illuminating a rough surface from more oblique angles result in single scattering conditions in which light can be reflected randomly by microfacets and may not be directed towards the sensor. In addition, more oblique illumination conditions lead to greater shadowing onto the sample in the forward scattering region of the sample surface. On the other hand, nadir illumi- nation conditions result in increased multiple scattering of light and fewer shadows, and consequently more time spent within the material before being reflected back to the sensor. This phenomena could result in a more determinate band shape and band center. This is supported by many studies that demonstrate how the relative orientations of the viewing geometry and light source can also have drastic effects on the appearance of absorption features. In particular, Hapke notes that the band depth is highly dependent on the sen- sor and illumination geometry. If the BRDF of a material is measured with the sensor and illumination sources close to nadir, then multiple scattering will significantly increase the wings of absorption bands. However, if the reflectance is measured while either the illumination source or the sensor is oriented at oblique angles, then the surface reflectance is dominated by single scattering which results in a shallower absorption depth. [5] This is supported by Huguenin and Jones, who note that the observed scattering of a sample displays significant dependency on phase angle. Varying the phase angle can result in changes in the extent of shadowing due to macroscopic surface roughness, which produces significant shifts in the apparent centers, widths and strengths of absorption bands. [36]

The primary goal of this study was to investigate the ability to correlate macroscopic surface roughness with roughness metrics derived from a custom LiDAR system on the GRIT-T goniometer system. Three different roughness metrics were used in this study that are frequently referred to in the literature in studies of the photometric effect of macroscopic surface roughness: the photometric mean slope angle, the sill variance, and random-roughness. All three roughness metrics were correlated with a custom measure of the band shape for a spectral absorption feature located at 1900 nm: the total integrated variance in band depth. Results showed that for both samples and all configurations of

fore-optics and illumination zenith angles, there were relatively high R2 values across all roughness metrics. For the photometric mean slope angle metric, the 5 degree fore-optic had a minimum R2 value of 0.98 and the 8 degree fore-optic had a minimum R2 value of 0.77. For the random roughness metric, the R2 values for 5 degree and 8 degree fore- optics exceeded 0.91 and 0.76, respectively. For the sill variance metric, R2 values for the 5 degree and 8 degree fore-optics achieved minimum values of 0.76 and 0.85, respectively. These correlations indicate that centimeter-scale elevation models can be directly related to variance in band shape.

In addition to studying view-angle dependent variance in band shape for spectral absorption features, we also investigated a spectral region where no spectral absorption feature existed. This spectral region was in the near-infrared spectral region between 600 nm to 840 nm. A continuum removal procedure was performed over this spectral range in order to provide a quantitative metric of the change in spectral shape as the roughness of the sample was mechanically manipulated. Correlation of roughness metrics with the total integrated variance in band depth showed a strong relationship between increasing surface roughness and increasing spectral variance. For the photometric mean slope angle metric, the R2 values for a 5 degree fore-optic and 8 degree fore-optic were at least 0.98 and 0.77, respectively. For the random roughness metric, the R2 values for a 5 degree fore-optic and 8 degree fore-optic were at minimum 0.91 and 0.93, respectively. For the sill variance roughness metric, the R2 values of 5 degree and 8 degree fore-optic attachments exceeded 0.76 and 0.85, respectively. These results indicate that even hyperspectral sensors that are solely capable of measuring the VNIR spectral range can provide insight into the macroscopic roughness of the surface.

In a follow up study to the initial experiment, an additional sample denoted as MC01- 1 was added to this analysis. The results from radiometric measurements sample, along with measurements of samples WA02-03 and WA04-02, were used to study the view-angle dependent variance in band shape across all samples used in the study. Whereas the ini- tial analysis focused on examining isolated samples across different roughness levels, this segment of the analysis focused on examining relationships across all samples. For this portion of the analysis, only measurements made using the 5 degree fore-optic were ana- lyzed due to the fact that this sensor was observed to be most sensitive to the photometric effect of roughness. Only the 1920 nm spectral absorption feature and the NIR spectral region from 600 nm to 850 nm were analyzed. It was observed that the photometric effect of roughness was more evident when the light was at a oblique illumination orientation of 45 degrees than at a nadir-like illumination orientation of 25 degrees. In addition, it was observed that the highest correlations between the roughness metrics and the view-angle dependent variance in band-shape was observed for the NIR spectral region. For example, when the light was oriented at 45 degrees zenith angle and a 5 degree fore-optic attach- ment was used, correlations of R2 ≥ 0.72 were observed across all roughness metrics. For the same illumination and sensor conditions, a R2 ≥ 0.57 was observed when performing

observed effect is not isolated to individual samples, but rather is likely to hold across clay samples obtained from multiple geographic regions.

One of the ultimate goals of our laboratory is to retrieve geophysical surface proper- ties such as density, surface bearing strength and surface roughness from physical model inversion of observed photometric reflectance of sediment surfaces. One of the challenges in using the Hapke photometric model for geophysical parameter retrieval is the large number of free parameters to be considered when modeling the reflectance of sediments such as clays and sand; these parameters typically have been determined through com- putationally expensive multi-dimensional optimization procedures. By constraining the parameters through relevant spectral information, retrieval of physical properties can be both more efficient and more accurate. We will attempt to use the results of this experi- ment to improve our ability to constrain model inversion parameters, such as the Hapke mean slope angle metric.

Expt #2: Study on Directional

Sand Waves

5.1

Introduction and Motivation

An important goal in the field of remote sensing is to mathematically and qualitatively relate the scattering of light to physically derived parameters of the surface being imaged. There are many parametric reflectance models that describe the empirically observed interactions of light with particulate media. Certain models account for the macroscopic roughness of the surface through the use of an explicit roughness parameter. [34, 69] In one such model, Hapke proposes a photometric roughness function that serves as a multiplicative correction for the reflectance from a perfectly smooth surface. Hapke’s model for the photometric reflectance from a rough surface depends not only on incidence, emission, and phase angles, but the effective tilts of surface microfacets. [34]

There have been many reflectance models created to capture the effect of either pe- riodic or random roughness on the reflectance from a sediment surface. Cierniewski and Marlewski propose one such model to predict the reflectance from surfaces composed of soil clods using periodic equally sized ellipsoids on a flat horizontal surface. The results of fitting the parameters of this model to experimental field data showed that the model was able to accurately describe the principal plane reflectance of soil surfaces as a func- tion of ellipsoid shape and a soil-clod spacing interval. [70] In another study, Cierniewski and Verbrugghe used a similar periodic spheroid model to investigate the effect of sur- face roughness on solar principal plane reflectance. The authors found that for high solar zenith angle values, surfaces with greater gaps between spheroids (defined by the authors to be of a lower order of roughness) exhibited lower variance in reflectance along the solar principal plane across different zenith angles. [71] Beckmann developed another model for characterizing the photometric effect of roughness in microwave remote sensing. In this model, Beckmann treats the surface of interest as a stationary process, characterized by

photometric model is a significantly more complex model than the aforementioned models and was originally developed for astronomy applications. Hapke’s model derives a rough- ness correction factor under the assumption that the surface has a random structure with a slope angle distribution that is characterized by Gaussian statistics but independent of azimuth angle. [5]

The previously discussed models propose different corrections for the reflectance from macroscopically rough surfaces under the assumption that the orientations of microfacets are randomly distributed. In other words, all of these previously defined models make the assumption that surface microfacets are distributed with azimuthal independence. While certain sediment surfaces such as agricultural fields or volcanic surfaces exhibit randomly distributed roughness, other surfaces such as sand dunes or coastal beaches are known to exhibit azimuthally dependent roughness in the form of wavelike ripples. [73] It should also be noted that certain agricultural fields that have been recently tilled can also exhibit azimuth preference in their roughness. [74] Geographic regions with azimuthally oriented surface roughness are frequently the focus of remote sensing studies for calibration and validation purposes. For example, Eon et al developed a simulation environment to model the interaction of light in the Algodones Dunes desert. This study was done to assess the feasibility of using the dune system as an intercalibration site for spaceborne instruments, with a focus on compensating for the effects of differing view-angles and temporal offsets between instruments. [75] In another large scale study, Govaerts analyzed the effects of sand dune spatial organization in the Libya-4 desert site on the surface bidirectional reflectance factor using a 3D radiative transfer model. The authors modeled the Libya-4 site’s large scale surface roughness (30 meters in spatial scale) as being characterized by azimuthally oriented sand dunes created by the dominant wind direction. [76] These two studies focus on regions with statistically correlated surface roughness on the order of tens to hundreds of meters. Few studies have paid attention to the photometric effect of directional roughness on the order of millimeters to centimeters, which can significantly impact directional reflectance measurements.

In this study, we sought to analyze the effects of azimuthally oriented roughness using directional reflectance measurements obtained in a laboratory setting. Our motivation was to experimentally assess the photometric effect of the directionality of sand surface waves relative to the incident illumination direction. We also compared these results with directional reflectance measurements of surfaces with randomly distributed roughness of similar spatial frequency. The sediment samples used in our study were prepared in such a manner that the density of the surface was assumed to be constant to within ∼ 1.5%. We utilized a geotechnical technique to ensure that the only parameter being experimentally varied was macroscopic surface roughness. While we did not propose a correction for azimuthally oriented surface roughness, we believe that our results provide experimental evidence that can be used to form a correction factor similar to the one that is used in

correcting for randomly distributed roughness of the Hapke photometric model. [34] It is also important to note that we sought to assess the effect of macroscopic surface roughness on the bidirectional reflectance of sandy surfaces rather than clay surfaces. The samples were collected in a beach environment on Hog Island, Virginia for analysis and manipulation of roughness in this series of laboratory experiments. These samples have a different grain size distribution than the clay soils that were used in the initial laboratory experiment.