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Abstract
Change in directional (biconical) spectral reflectance was monitored for three soil samples under air dry and saturated conditions in the laboratory. The illumination angle was set consecutively at = −10°, −40°, and −70° (left side of the sample on the principal plane), while the observation angle ranged from = −60° to + 60° (both sides of the sample in the principal plane) in 5° increments. The soil samples were chosen to represent a variety of soil properties. Emphasis is on observations that illustrate the changes in the directional and spectral distribution of soil reflectance when the soil is dry or saturated.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
5 September 2018: A typographical correction was made to title.
1. Introduction
Soil moisture is a key factor for many fields of study, ranging from hydrology and agronomy to meteorology [1]. The most commonly used methods for soil water content measurements are ground-based techniques (time domain reflectometry, frequency domain sensors, etc.) and microwave remote sensing. Passive, optical remote sensing has also been used to study soil moisture content even though reflectance is derived from the first several millimeters of soil at most [2–5]. In spite of the shallow penetration, changes in reflectance are commonly related to volumetric changes in soil water content [6–10]. The presence of moisture greatly influences spectral reflectance in both the Visible-Near Infrared (VNIR) and shortwave infrared (SWIR). Broadly speaking, reflectance decreases with increasing water content with the effect being more pronounced at longer wavelengths especially in the major water absorption bands [11].
Many researchers have observed the change in the spectral reflectance of soils due to moisture, and some have found empirical, predictive relationships with spectral reflectance values; but these relationships are generally influenced by soil type, and are biased by the reflectance of the dry sample [12]. Some generalization appears to be possible. For example, Sadeghi et al. [9] were able to find general relationships for three broad groups of soil types. However, the physical link connecting soil type, water content and spectral reflectance remains an unsolved problem.
In addition to soil moisture, optical remote sensing has also been used to extract soil physical properties [13,14]. Directional reflective properties of surfaces, e.g., the bi-directional reflectance distribution function (BRDF), or its measurable counterpart, the biconical reflectance factor or conical-conical reflectance factor (CCRF) [15] give additional information about some properties of the observed surfaces, such as their smoothness, density, geometry, and other properties [16–19]. Compared to unidirectional measurements, CCRF is more responsive to structural details of the soil surface. In recent research, relationships between CCRF and soil properties have been documented in laboratory experiments, field studies, and satellite remote sensing observations [17,20–24].
Because soil physical properties and soil moisture content are intermingled in most soil reflectance studies, we focus here on how soil moisture content influences the directional reflectance of soil. Yang et al. [25], indicated that the Hapke model can be extended to soil moisture content study with three selected bands. In other work, an H-function has been used to characterize saturated particulate layers, but only in the visible domain [26]. However, there is limited work focusing on how soil moisture influences directional reflectance over the whole optical domain. In this paper, we measure the directional spectral reflectance (CCRF) of soil samples under both dry and saturated conditions in the principal plane. We focus on how the directional spectral reflectance of soil changes with added water. The saturated soil samples we used are inner-saturated, i.e., subsurface pore spaces filled, but with only an adsorbed water layer on the surface. Although water was adsorbed to the surface of the particles, there was no free water on the sample surface, and no obvious specular reflectance. Thus, we expected that directional reflectance of the saturated soil would still be sensitive to the angle of illumination and observation.
2. Experimental design
The work described here was designed to observe the change in directional (biconical) reflectance in the principal plane, of both air-dried and inner-saturated soil samples when the incidence angle of the light source was fixed at −10°, −40°, and −70° sequentially, while the observation angle ranged from −60° to + 60°, with an interval of 5°. Three soil samples were observed; these varied in particle size distribution, color, and organic matter content. All experiments considered light over the spectral range 350-2500 nm.
2.1 Sample descriptions
Three soil samples (Table 1) were observed in the experiments: a white quartz sand, masonry sand, and a typical Ithaca-area soil (Fig. 1). The quartz sand, acquired from a golf course in Ithaca, NY, consisted of rough, quartz particles, and had a slightly yellowish color. The masonry sand, the darkest sample, consisted of finer particles than the quartz sample, with a sider particle size distribution. The Ithaca soil, acquired from a local orchard, had a higher organic matter content and finer particle size. Water was added slowly at the sample surface at the edge of the sample holder, taking care not to disturb the sample surface near the detector field of view. Water was added until the sand surface was uniformly dark, i.e., the sample was near saturation internally, with a surface water film on the particles, but without water filling the surface pore spaces and no free liquid water at the surface.
Table 1. Soil sample properties
2.2 Experimental setup
Figure 2 shows a sketch of the experimental setup. Illumination was provided by an ASD Pro Lamp, a 50-Watt halogen-based light source designed to provide stable illumination over the 350 to 2500 nm range. The lamp was mounted on a rotating arm at a fixed 1.12 m distance from the sample surface. The arm was positioned to provide illumination at specific angles.
The spectrometer, an ASD FieldSpec 4, has a spectral range of 350–2500 nm. The spectral resolution of the spectrometer ranges from 3 nm in the visible to 12 nm at 2100 nm, with a sampling interval of 1 nm. A fiber optic probe, fitted with a 3° field of view (FOV) fore optic was mounted on a separate rotating arm, and viewed the sample surface at a fixed distance of 20 cm for all viewing angles. All observations were made in the principal plane, with illumination angle, , and observation angle, . All angles in the illumination quadrant are designated as negative (backward direction), and all angles in the other quadrant are designated as positive (forward direction). The phase angle, the angle between the observation and illumination directions, is then .
The sample holder was a 0.8 cm deep black Delrin cylinder with a 10.2 cm inner diameter. The volume of the sample holder was then 65.4 cm3. Reflectance was determined by measuring the radiance from the sample relative to a calibrated, white (99% reflectance) Spectralon standard panel.
In each case, the sample surface was positioned at the common axis of the motorized rotary stage and viewing mount. The sample holder was initially filled with a dry sample, and the surface was leveled with a metal straight edge providing a uniform surface. The fore optic viewed the center of the sample holder.
2.3 Experimental procedure
To achieve accurate spectral reflectance of each sample and simplify the experimental operation, two calibrations were conducted: 1) panel calibration for each illumination angle, and 2) reflectance calculation for each observation angle.
For the illumination calibration, the 99% reflectance standard, a calibrated Spectralon panel, was illuminated from , , , and , and the radiance was observed at nadir with a 3° FOV fore optic. The illumination angle radiance was used as the primary standard, corresponding to the manufacturer-provided calibration reflectance [6]. Calibration at the other three illumination angle was determined relative to the observations at . Based on the Beer-Lambert cosine law, with an illumination angle of , and an observation angle of 0°, the standard panel calibration, , is calculated as:
where is the standard panel calibration provided by Labsphere [27]. and are radiances measured at nadir () and illumination angle, respectively.Since the standard panel was not a perfect Lambertian surface, it was also necessary to correct for the observation angle. To remove the directional dependence of the observation angle, the radiance observed at angle, , was collected for both the standard panel and the soil samples at three illumination angles (i.e. -10°, −40°, and −70°). The soil sample reflectance, , was then calculated as:
where is the radiance from soil sample with illumination angle, , and observation angle, . is the radiance from the standard panel with illumination angle, , and observation angle, .3. Results
3.1 Soil sample reflectance under dry and saturated conditions
As a point of departure, consider a set of reflectance spectra, viewed at nadir, for the three soil samples under both dry and saturated conditions as shown in Fig. 3. Since most satellite and aircraft observations are made at, or near nadir, this is a useful reference point. When the soil samples were dry, the nadir reflectance was not very sensitive to the changing illumination angle for any of the three samples. For Ithaca soil, reflectance of the dry sample was slightly lower when , but there was no change in the spectral shape. For the saturated samples' reflectance curves, there are two general differences: 1) the change in reflectance relative to the dry samples is more pronounced at longer wavelengths, and is more dramatic at the 1440 nm and 1930 nm water absorption bands than at other wavelengths, 2) the reflectance is always higher when , but the spectral shape is essentially unchanged. Thus, for these three samples, the nadir viewing observations are not very sensitive to changes in the illumination angle.
Fig. 3 Nadir reflectance of three soil samples, a) Quartz sand, b) Masonry sand, and c) Ithaca soil, at dry and saturated conditions with illumination angle at −10°, −40°, and −70°, respectively.
3.2 Reflectance changes with illumination and observation angle
The left columns of Fig. 4-6 show the soil sample reflectance measured at observation angles ranging from −60° to + 60°, at 5° intervals. Four wavelengths were selected to represent the angular reflectance changes for a representative demonstration over the whole optical domain. These wavelengths are located in the visible (650 nm), NIR (1000 nm), and two in the SWIR, one (1440 nm) centered on a strong water absorption band, and the other (1680 nm) away from extreme water absorption features. The graphs (a), (b), and (c) present , , and illumination angles, respectively. Due to occultation of the lamp by the fore optic, there are no observations of reflectance within ± 5° of the illumination angle. When illumination is near normal (), shadowing is minimal and the reflectance does not vary greatly with observation angle (Fig. 4(a), Fig. 5(a), and Fig. 6(a)). Approaching the retroreflection point, at , reflectance decreases for quartz sand, while it increases slightly for masonry sand and Ithaca soil; however, the overall change is not obvious. At larger illumination angles, the directional reflectance difference becomes more apparent. At and , the backward reflectance is strengthened, and the forward reflectance is weakened, an effect that is more obvious with an illumination angle of . The directional reflectance feature of dry soil can be explained as a phenomenon caused by surface roughness; the convex soil particle causes shadow on the opposite side of illumination, an effect which is more pronounced as the illumination zenith angle increases. This is apparent in Fig. 4(a)-4(c), Fig. 5(a)-5(c), and Fig. 6(a)-6(c), where the difference in reflectance between forward and backward directions is larger with a −70° illumination angle. There are some theoretical models focusing on BRDF research on particulate surfaces, i.e. the shadow hiding opposition effect (SHOE) [28], the coherent backscattering opposition effect (CBOE) [29], and the H-Function [30]. These models were primarily focused on the “hot spot”, i.e. the high enhanced reflectance very near the opposition point, the region in which there are no observations in the experiment described here. Other researchers have also indicated that backward reflectance is strong over a broad angular range [24], [31,32]. Although these experimental data do not include reflectance measurements near the 0° phase angle, , as in the theoretical models, strong reflectance in backward lobe is verified.
Fig. 4 Quartz sand directional reflectance with at 650 nm, 1000 nm, 1440 nm, and 1680 nm, when , and . The left column is for the dry quartz sand sample, and the right column is for the saturated quartz sand sample.
Fig. 5 Masonry sand directional reflectance with at 650 nm, 1000 nm, 1440 nm, and 1680 nm, when , and . The left column is for the dry masonry sand sample, and the right column is for the saturated masonry sand sample.
Fig. 6 Ithaca soil directional reflectance with at 650 nm, 1000 nm, 1440 nm, and 1680 nm, when , and . The left column is for the dry Ithaca soil sample, and the right column is for the saturated Ithaca soil sample.
3.3 Water influence on soil reflectance
As seen in Fig. 3, the spectral reflectance at nadir decreased at all wavelengths when water was added, but most noticeably in the SWIR region, especially at the two strong water absorption bands, centered at 1440 nm and 1930 nm. Directional reflectance from the wet soil, shown in the right column of Fig. 4-6, also presents a striking contrast to dry soil sample reflectance. Forward reflectance, i.e. observations in the quadrant opposite the illumination, at all four selected wavelengths increases toward . This is especially apparent with . With an illumination angle, , added water reduced the reflectance, but did not alter the angular distribution obviously; however, with increasing illumination angle, the saturated soil sample reflected more radiance to the forward direction. This effect is consistent over all three soil samples. Also, the larger the illumination angle, the higher the forward reflectance is relative to a dry soil sample. For the Ithaca soil sample, the forward reflectance of the saturated sample, Fig. 6(f), is equal to, or even stronger than forward reflectance of the dry sample Fig. 6(c). Observing the directional change over the full range of observation angles, it is particularly remarkable that the addition of water has flattened the directional reflectance, reducing, or even eliminating the enhanced reflectance in the backward direction. The saturated soil samples appear to be diffuse reflectors, with a symmetric reflectance over the range of observation angles, and a magnitude that is nearly independent of the incidence angle. The data indicate that water is controlling both the magnitude and the directional character of soil reflectance. Being a diffuse reflector, it is unlikely that soil structural characteristics (i.e. particle size distribution, porosity) can be extracted from directional reflectance data for saturated soils since it is the directional character of the reflectance that is associated with the structural properties.
Soil water not only darkens the soil reflectance overall, but also redistributes directional reflectance as shown in Figs. 4-6. A strong contrast between forward and backward reflectance exists for dry soil, however, when soil is saturated, the directional reflectance is flattened. Macro photos resolving individual particles (Fig. 7) provide an indication of the way the light distribution differs between the dry and wet samples. The dry sample (Fig. 7(a)) is brighter overall with a broader brightness range and only a few particle facets exhibiting obviously specular reflectance. Although the color is essentially the same, the wet sample (Fig. 7(b)) is darker overall and, except for an increase in the number of bright, specular points, also has a more uniform tone.
Fig. 7 Quartz sand under (a) air-dry, and (b) saturated conditions. Both images were collected under identical lighting using Canon Powershot ELPH 340 HS with identical settings (f/4.5, exposure 1/50 sec.). The width of the red box denotes 1 mm.
Figure 8 presents the red, green and blue histograms of the Fig. 7 photos. The brightness distributions for the dry sample (solid lines) are broad and plateau in all three channels. In contrast, the histograms for saturated sample (dotted lines) are more peaked, with a darker mean. The shape of histogram changes from flat-topped for the dry sample, to unimodal for the wet sample, i.e., light is much more evenly distributed over the wet sample image; there is much less contrast between direct illumination and shadows. (Note that the shadows in the dry sample are darker than those in the wet sample.)
3.4 Radiative transfer implication for directional reflectance influenced by soil water
A simple descriptive model of the reflectance from dry soil is illustrated in Fig. 9(a). The incident irradiance, , undergoes Fresnel reflectance at the soil surface (gray arrows in Fig. 9(a)). Assuming that the surface is rough, the reflectance is effectively diffuse but will often include a distinct directional component [28]. Fresnel reflectance depends on the relative index of refraction at the air-particle interface, which typically varies slowly, from 400 to 2500 nm [33], meaning that the reflected radiation will be spectrally flat, i.e., similar to the illumination (note the bright spots in Fig. 7(a)). The reflected radiation that is representative of the soil color is a result of incident radiation that has been transmitted into the soil particle where it is absorbed, scattered, and partially returned through the particle surface (colored arrows in Fig. 9(a)). The far side of the particle is in shadow, illuminated only by scattered light from adjacent particles. This is consistent with the wide dynamic range and deep shadow areas seen in the dry sand image in Fig. 7(a).
Soil is darker when wet, and the overall decrease in reflectance of the soil with increasing water content has been described in a number of papers [7], [34,35]. Less commonly noted is that the spectral character of the reflectance in the VNIR (400-900 nm) is stable, i.e., the brightness decreases, but the relative reflectance (color) remains nearly constant [36]. The implication is that water does not absorb appreciably, but only enhances absorption by the soil. A process that might account for both the darkening and the redistribution of illumination is outlined in Fig. 9(b). Here, the incident radiation first interacts with the water film where, since the water is assumed to be optically smooth, it undergoes Fresnel reflection, producing the bright points seen in Fig. 7(b). The bulk of the radiation penetrates through the water film and interacts with the particle, where the reduced relative index of refraction at the water-soil interface enhances transmission into the soil, leading to increased absorption and an overall reduction in reflectance. This, however, does not account for the redistribution of the illumination apparent in Fig. 7(a) and 7(b). Ångström [34] and Lekner & Dorf [35] argue that the reduction in reflectance can be explained by multiple internal reflections within the water layer at the soil surface, providing a mechanism for the redistribution of light. As illustrated in Fig. 9(b), a significant portion of the light diffusely reflected from the particle surface will be internally reflected at the air-water interface, a process that is repeated multiple times. A portion of that light will be directed to the areas previously in shadow, both within the water film (at point (a) in Fig. 9(b) and beyond (at point (b)). In addition, the area on the particle surface that is directly illuminated (after refraction) will be extended slightly (point (c)).
Given the range of directional reflectance seen in Figs. 4-6, and the large brightness difference between the wet and dry samples (Fig. 8), it is striking how little the color changes in the VNIR. This is illustrated in Fig. 10, in which all spectra have been normalized to the reflectance at 900 nm in order to compare the shape of the curves (i.e., the VNIR “color” of the soil). Spectra of dry samples are shown in orange; spectra of wet samples are shown in blue.
Fig. 10 Spectral reflectance, normalized at 900 nm, from the quartz sand and Ithaca soil samples, for the full range of illumination and viewing angles. Orange curves represent the dry samples, blue curves represent the wet samples. Thin, black lines in the legend indicate missing data where the incidence and observation angles coincide.
If the VNIR color were constant, we would expect to see the same curve for all viewing and illumination angles. This is very nearly the case for the dry quartz sand (orange curves in Fig. 10(a)-10(c)); the normalized reflectance of the dry sample is largely independent of viewing angle and observation angle. The lines overlap, spanning the same range and maintaining the same shape with a spread that is probably related to experimental uncertainty. (The reflectance does not change progressively with the viewing angle, but appears to be random.)
The normalized reflectance of the wet quartz samples are similar to the dry samples from 600 to 900 nm, but are distinctly darker between 400 and 600nm. Given that water absorption is negligible at wavelengths below 900 nm [37] water must be enhancing absorption by the soil. The dip in the “wet” spectra beyond 900 nm is due to a weak water absorption band that is only visible in the quartz spectra, presumably because the quartz particles are semi-transparent, extending the optical path through water that is long enough to produce the absorption feature. While the basic trend is similar for larger illumination angles, the pattern breaks down with higher reflection at larger phase angles, possibly due to specular reflection from the water-coated particle surfaces.
Normalized reflectance spectra of the dry Ithaca soil samples with (orange lines in Fig. 10(d)) are essentially independent of viewing angle. At higher illumination angles (Fig. 10(d)-10(f)) a slight (noisy) trend develops in the dry samples with generally lower relative reflectance at higher phase angles, but the shapes of the curves are nearly identical.
The normalized reflectance of the wet Ithaca soil samples lack the water absorption feature in the IR seen in the quartz spectra, suggesting that water is not operating as an absorbing medium over this spectral range. This would be consistent with a much shorter optical path through water. As with the quartz sample, the difference between the saturated and dry samples in the visible suggests that water is functioning to enhance absorption by the soil over the visible and into the infrared, although the difference is much more pronounced for the Ithaca soil. Also similar to the quartz sample, the normalized reflectance increases as the wavelength decreases for reflectance in the forward direction. This is particularly obvious for . In this case the increase is much more pronounced and wavelength dependent, strongly enhancing reflectance toward the blue end of the spectrum. The simplest explanation would be specular reflection from the water surface, but that begs the question of why the effect is so much more pronounced for the Ithaca soil than it is for the quartz sand.
The clear separation of the normalized spectra for the dry and wet Ithaca soil between 400 and 800 nm is more difficult to explain. The difference is most clearly seen in Fig. 10(d), with , but it persists for all illumination angles, whenever the phase angles, . The difference persists for most illumination and viewing angles. The fact that the color difference is insensitive to all but the largest phase angles suggests that it is a function of absorption and scattering within the particles rather than a surface reflection or scattering phenomenon.
4. Summary and conclusion
Changes in directional spectral reflectance over a range of illumination and observation angles were monitored for three soil samples under air dry and saturated conditions. The illumination angle was set sequentially at −10°, −40°, and −70°. In each case, the observing angle ranged from −60° to + 60° in 5° increments. Samples were chosen to represent a range of properties: particle size distribution, texture, color, etc. There were significant differences in the general shape of the spectral reflectance of the three soils when dry.
The initial intent of this study was to examine the possibility of extracting enhanced soil moisture information by considering directional reflectance in the principal plane. With the knowledge that backward reflectance is stronger than forward reflectance for dry soil, and that forward scattering would be enhanced when water was filling the pore spaces, we hypothesized that the difference in directional reflectance from varied observation angles would be reduced when soil was saturated.
For all three soil samples, the nadir reflectance was spectrally stable for all illumination angles, and varied only slightly with illumination angle. When soil samples were dry, the directional reflectance changed obviously with phase angle, with a stronger backward reflectance, while the forward reflectance was generally lower. For saturated soil samples, the directional spectral reflectance was reduced overall, and the strong backward scattering was weakened significantly.
A simple conceptual model was introduced outlining how directional reflectance might change when a soil particle is coated with water. The concept combines surface (specular and diffuse) reflection from the soil and water surfaces, multiple internal reflection within the water layer, and absorption and scattering within the soil particle (volume reflection). The color stability in the VNIR is ascribed to volume reflectance from the particles, while the more uniform illumination is related to the redistribution of light by internal reflectance.
From this study, several conclusions and their implications (indicated by ➔) may be drawn:
- 1. Soil reflectance at nadir was insensitive to illumination angle changes for both dry and saturated conditions. ➔ Soil reflectance observed using nadir-viewing remote systems may be relatively insensitive to sun angle.
- 2. Reflectance magnitude of wet soils is largely insensitive to changes in illumination angle. While reflectance did increases with viewing angle, it was similar for all illumination angles, except for when the viewing angle was large and in the same direction. ➔ The water coating on the soil particle surfaces is redistributing the incident light, minimizing shadowing, reducing the overall range of reflectance, and diffusing the reflected light.
- 3. VNIR soil color (normalized reflectance) (Fig. 10) is stable over a large range of illumination and viewing angles.
- a. air-dry spectra have the same shape, forming a tight cluster for all illumination and viewing angles, with a small but consistent deviation for large phase angles.
- b. saturated spectra maintain the same shape for phase angles less than 60° ➔ This suggests that VNIR soil color may be comparable over a wide range illumination and viewing angles.
- c. water, though not effectively absorbing, alters the spectral reflectance of soils in the VNIR in ways that are specific to the soil type.
- 4. The directional reflectance appears to be controlled by the surface roughness, which is effectively masked by a film of water. ➔ This will complicate retrieval of any useful structural information from the BRDF for soils near saturation, and possibly for soils well below saturation.
Funding
U. S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF-15-1-0071.
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