SOCIEDAD DE GESTION COLECTIVA ASAMBLEA GENERAL ORDINARIA

Continuum removal can be performed within spectral absorption features by selecting two predetermined wavelengths on the wings of a known diagnostic absorption feature, and calculating the convex hull between these wavelengths. The two samples examined in this study, WA02-03 and WA04-02, were collected at field sites that were relatively close geographically. The samples, therefore, had similar material properties and absorption features. Two absorption features that are characteristic of silty/clay soils were examined in this study, centered at wavelengths of approximately 900 nm and 1920 nm. These re- gions were chosen due to the fact that both materials exhibited absorption features in these spectral regions. For the continuum removal procedure, the wavelength ranges chosen for convex hull calculations were 850 nm to 950 nm, and 1870 nm to 2050 nm, respectively. We examined the depth and shapes of these absorption features across varying sensor viewing orientations to determine how macroscopic surface roughness correlated with a tendency towards higher variance in these properties. Identifying this trend could provide evidence that determining roughness parameters within photometric models can be improved by examining the spectral of directional reflectance measurements. These diagnostic features will be discussed individually in the following subsections.

1920 nanometer Absorption Feature

Both samples examined in this study had high concentrations of silt and clay, and exhibited a strong absorption feature in the region of approximately 1910 nm that indicated the presence of hydroxyl that has been adsorbed onto the grains of the soil. [68] Continuum removal across this diagnostic absorption feature was performed by using wavelengths located at 1870 nm and 2050 nm. It is evident that there is significant variation in both the band depth and shape by qualitatively examining the spectral library renderings of the directional reflectance scans. An example of this can be seen in Figure 4.8, which details the reflectance scans of sample WA04-02 while using a 5 degree fore-optic attachment and illuminating the sample at a 45 degree zenith angle. A color bar is included, showing the azimuth orientation of the fore-optic sensor for each respective view angle orientation of the hemispherical scan.

By examining the spectral feature located in the region of approximately 1900 nm in Figure 4.8, it is clear that there is a trend towards decreasing variance of the band shape as the sample is progressively smoothed. The left wing of the absorption band gradually becomes less pronounced and eventually becomes symmetric with the right wing of the absorption band for the smoothest state of the material. In order to capture this trend quantitatively, we performed continuum removal on the absorption band for each sensor orientation of the BRDF scan. The result of performing this procedure is shown in Figure 4.9.

Figure 4.8: Spectral library renderings of sample WA04-02 at decreasing macroscopic roughness levels from left to right. For these scans, a 5 degree fore-optic was used and the light was positioned at a 45 degree zenith angle. Spectral bands that were corrupted due to low signal-to-noise were removed.

magnitude of the right wing of the absorption feature exhibit higher variance as the surface becomes progressively rougher. The variance of the left shoulder also increases but not as dramatically. In order to capture this trend, the wavelength dependent variance of the band-depth was calculated for each roughness state of a given sample, as can be seen in Figure 4.9(d). It is evident that there is an increase in variance of the band depth as the macroscopic roughness of the surface increases.

It is evident from these results that there is a clear correlation between the roughness level of a given sample and the variance in wavelength dependent band depth. In particu- lar, for the curves shown in Figure 4.9 there is a broad spectral range along the right wing of the absorption feature from approximately 1930 nm to 2000 nm where the relationship is strongest. However, it should be noted that this trend holds across both samples for all combinations of fore-optic and light zenith angles. The total variance within the ab- sorption feature was captured in a metric by performing numerical integration over the entire spectral range of the band-depth variance curves. This metric, denoted as the total integrated variance, was then regressed against the roughness metrics obtained using our elevation measurement system in this study. In Figure 4.10, this procedure is shown for the band-depth variance curves illustrated in Figure 4.9 (d).

This procedure was carried out for both samples that were used in this series of exper- iments (WA04-02 and WA02-03), and for all combinations of fore-optics (5 degree and 8 degree), and light zenith angles (25 degree and 45 degree). The fitted R2 values obtained as a result of following this procedure for each measurement configuration are detailed below in Table 4.4.

A few observations can be made from Table 4.4. There is a high degree of correlation between the Hapke photometric roughness parameter, ¯θ and the total integrated variance across all sensor fore-optic combinations and light zenith angle orientations (R2 ≥ 0.95). There is also a high correlation for the retrieved random-roughness metrics for both sam-

Figure 4.9: Renderings of the band-depths of the absorption feature centered around 1900 nm after performing continuum removal on the spectra shown in Figure 4.8. Roughness levels 1, 2 and 3 are represented by (a), (b) and (c), respectively. The color bar shows the azimuth angle corresponding to each sensor orientation of the BRDF scan. The y- axis indicates the band-depth at the respective wavelength. 8 d) shows the wavelength dependent variance of the band depth plotted for these 3 roughness states.

Figure 4.10: Total integrated variance of the band depth plotted against (a) Hapke mean slope angle parameters, (b) Random Roughness, and (c) Sill Semivariance. Sample shown is WA04-02, with a 5 degree fore-optic attachment and the light oriented at 45 degree zenith angle.

WA02-03 and WA04-02 for the absorption feature centered at 1920 nm. The light orien- tation is shown for value of a 25 degree zenith angle and a 45 degree zenith angle.

Sample Metric R 2 _{- 5} ◦ _FoV, 25 ◦ Zenith R2 - 8◦ FoV, 25 ◦ Zenith R2 - 5◦ FoV, 45 ◦ Zenith R2 - 8◦ FoV, 45◦ Zenith

WA02-03 Mean Slope Angle 0.95 1.00 0.99 0.97

RR 1.00 0.97 0.98 1.00

Sill Variance 0.95 0.85 0.88 0.93

WA04-02 Mean Slope Angle 0.99 0.99 0.98 0.97

RR 0.98 0.99 0.98 0.97

Sill Variance 1.00 1.00 1.00 1.00

ples across all measurement configurations (R2≥ 0.97). The sill variance metric has high correlation values for sample WA04-02 as is seen in Table 4.4 (R2 = 1.0), but lower cor- relation values for sample WA02-03 (R2 ≥ 0.85). This can be explained potentially by examining the process by which the theoretical semivariogram parameters are derived. Chiles and Delfiners state that the first few points of the experimental semivariogram are the most important for theoretical variogram fitting due to the fact that short range points are used to model both the nugget variance and the slope at the origin. [39] In particular, the nugget variance is a combination of factors such as measurement noise, short range trends, and microstructures below the scale of the elevation measurement sampling. The most reliable solution for improving these estimates is to have a tighter sampling grid for estimating the empirical semivariogram at short lag distances. This can be viewed as a critical step for modeling the roughness of grains that vary on a sub-centimeter scale. In the series of laboratory and field experiments, we develop photogrammetric techniques such as structure-from-motion that take advantage of an on-board camera system of our goniometer system-T in order to examine roughness on a sub-centimeter level.

900 nanometer Absorption Feature

The same approach described in the preceding section was applied to an observed spectral absorption feature in the region of 900 nm. The wavelengths chosen for performing convex hull calculations on this absorption feature were from 850 nm to 950 nm. This absorption feature was much shallower than the one present at 1920 nm, which has been noted to cause issues in the examination of band-depths. [36] Continuum removal analysis showed that the shallow nature of the absorption feature resulted in greater noise when measuring both samples WA04-02 and WA02-03. For lighting conditions where the light was oriented at a 45 degree zenith angle, it appeared that there was an ability to discern some relationship between wavelength dependent variance of the band depth and roughness gradient. For

WA02-03 while the light was oriented at a 45 degree zenith angle and a 5 degree fore-optic attachment was used. The total integrated variance of the band depth and the roughness metrics used in this study still exhibit a high degree of correlation, however, as is seen in Figure 4.11 (b), (c), and (d).

The result shown in Figure 4.11 is an example of a case that is not corrupted by signal- to-noise issues, and oftentimes the trend between the total integrated variance and the roughness metrics for the absorption band was either not as obvious or somewhat reduced due to noise. This can potentially be attributed to the shallow depth of the absorption feature in comparison to the noise present at the corresponding spectral range. This is shown in Figure 4.12, which details results shown for several different BRDF measurements performed in this study.