LIGHT ABSORPTION MODEL FOR WATER CONTENT TO IMPROVE SOIL MINERAL ESTIMATES IN HYPERSPECTRAL IMAGERY

Michael L. Whiting, Postdoctoral Researcher Susan L. Ustin, Professor California Space Institute Center of Excellence, One Shields Ave. The Barn University of California, Davis, CA 95616-8527, United States. [email protected]; [email protected]

Alicia Palacios Orueta, Professor Titular Escuela Tecnica Superior de Ingenieros de Montes, Universidad Politecnica de Madrid, Madrid, Spain. [email protected]

Lin Li, Assistant Professor Department of Geology, Indiana University - Purdue University, Indianapolis, IN, United States. [email protected]

ABSTRACT High spectral resolution of hyperspectral images promise mineral identification and abundance estimates of bare soils for advancing precision farming and carbon cycle modeling. Under desiccated conditions, investigators have shown that band parameter measurements (position, depth, width, and derivatives) can be used as reliable estimators of mineral type and contents. With moisture, even air-dried soil, the water absorption fundamental and combination absorptions reduce accuracy of mineral estimates as soil albedo declines and mineral absorption band-depths diminish. The effects of water on soil albedo were accurately modeled by extrapolating the shortwave infrared (SWIR, 1.0 to 2.4 m) continuum to the water fundamental center at 2.8 m using an inverted Gaussian function, that is located beyond the range of common airborne and field hyperspectral instruments. This improves accuracy of water estimates over modeling the water content using specific water bands (principally, 1.4 and 1.9 m) since these bands are susceptible to saturation by atmospheric water vapor beneath airborne and satellite platforms. In contrast, our soil moisture Gaussian model (SMGM) provides an accurate measure of soil moisture for use with other band metrics in spectral mixture analysis or classification and regression classification models for mapping mineral abundance of surface soils. The improvement contributed by the SMGM parameter to estimates of clay and carbonate mineral contents is demonstrated through a simple linear regression analysis of Airborne Visible/InfraRed Imaging Spectrometer (AVIRIS) and HyMap images from Kings County, California, United States, and La Mancha, Spain, respectively.

INTRODUCTION

Soil classification, soil health inventories, reduction of erosion and desertification are all examples where increased resolution in soil surface mapping will improve our understanding of the implications of soil variability. Greater spatial resolution in mapping clay minerals and organic matter contents will contribute to improved modeling of plant and soil responses to various resource management and global changes. With anticipated changes in rainfall, soil acidification and greenhouse gas exchange, the accuracy of soil carbon sequestration modeling will benefit from greater spatial resolution of clay mineral content due to the close relationship between organic matter and clay. Advances in precision farming require greater detail in the mineral components in developing prescriptions for water, nutrient, herbicide and pesticide applications. Accurate mapping of the mineral and organic matter contents will improve farm management of nitrate and irrigation applications to reduce ground water pollution. In the right circumstances, multi-spectral photography and satellite imagery has been useful in differentiating organic matter and clay contents (Curran, 1979; Sudduth and Hummel, 1991). Research on soil classifications (Horvath et al., 1984; Palacios-Orueta and Ustin, 1996) and soil salinity (Csillag et al., 1993; Metternicht and Zinck, 2003) described spectral characteristics of different soils. In alluvium and lacustrine soils

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota with greater homogeneity, techniques developed in spectroscopy are more useful. In these cases, hyperspectral imagery has been successful in discriminating the secondary clay mineral types that influence the soil shrink-swell potential important for urban development and other engineering structures (Chabrillat et al., 2002). Water is a principal component among the many compositional variables in the soil surface interacting with the incident light. The complex nature of soils in situ, as organic matter and mineral particles and films, results in non- linear light absorptions related to the component proportions. Primary and secondary mineral grains are coated with films of water, clay and iron chelated-organic matter (Clark, 1999). Pore space concentrates light absorbing gases such as CO2 that may be 10 to 100 times greater than the above ground atmosphere (Brady and Weil, 1996), as well as water vapor. Accurately measuring mineral contents from bare soil images is significantly influenced by the presence of water in the pore spac and as particle film (Kruse and Clark, 1986; Liu et al., 2002). For remote sensing, spring or irrigated soil moisture increases water content causing a decline in the albedo and low contrast of absorptions from the spectral continuum (Bowers and Hanks, 1965), inhibiting accurate mineral identification and abundance. Although highly variable spatially, the soil moisture parameter is one that is easily measured. The estimate of clay and carbonate contents are physically based on the combination and overtone bands of Al- OH and CO3 bonds, respectively, in the SWIR (Clark, 1999). Effective measures of mineral abundance include band-depth (Clark and Roush, 1984; Van der Meer, 2004) and shape of the absorption (Ben-Dor and Banin, 1995) in desiccated materials. The depth and width of the mineral absorptions is an indication of the quantity of the electronic transitions and molecular bond stretching and vibrations. In addition, the overlap of adjacent absorptions should be considered at each wavelength as demonstrated in modeling mineral constituents (Mustard, 1992), such as the Modified Gaussian Model (Sunshine et al., 1990) algorithms. The exponential of the sum of all apparent absorptions defines reflectance for optically thick materials (Clark and Roush, 1984), where the apparent absorption is the product of the optical depth and absorption coefficient (Kortum, 1969). This general principle is not mathematically sensitive to accurately decomposing the spectra into endmember content estimates (Hapke, 1993), although understanding the sum of absorptions does lead toward understanding a spectrum by the absorptions of the contributing components. The most commonly used technique for determining absorption depth is continuum removal (Clark and Roush, 1984; Van der Meer, 2004). Continuum removal calculates normalized spectra by dividing the reflectance within an absorption region by an interpolated reflectance straight-line datum between the two local maxima that bound the region. The maximum band-depth is found by subtracting this normalized spectral reflectance from 1.0 (Clark and Roush, 1984). In Figure 1, the transformation is shown from the original spectrum in 1a through the continuum removal process as it appears in 1b. The band center at the minimum normalized-reflectance position and the asymmetry of the absorption shape can be used to determine mineral type (Van der Meer, 2004). After the water bands at 1.4 nd 1.9 m, the next strongest absorptions in the SWIR are assigned to silt and secondary clay minerals near 2.2 m, and carbonate minerals in the 2.3 m region (Clark, 1999). Organic matter in soil introduces cellulose absorption bands near 2.1 and 2.3 Figure 1. (a) Soil spectrum with fitted straight-line continuum to m. These band-depth and convex hull boundary points, and (b) spectrum after normalizing with absorption shapes are influenced by the continuum, or continuum removed (Whiting, 2004). the presence of soil moisture (Liu et al., 2002; Lobell and Asner, 2002; Whiting et al., 2004).

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota Presented here is our method for characterizing the amount of soil water as a step to developing a water content parameter for mineral abundance models. The soil moisture Gaussian model (SMGM) is calculated simultaneously with the continuum removal band-depth. To demonstrate the effectiveness of the SMGM to improve clay and carbonate estimates, we present a simple multiple linear regression analysis using the SMGM and mineral band- depths calculated using spectra extracted from hyperspectral images over Tomelloso, Castilla-La Mancha, Spain, and Lemoore, Kings County, California, United States.

The SMGM and Its Physical Basis The Soil Moisture Gaussian Model (SMGM) fits an inverted Gaussian function to the convex hull boundary points in the SWIR region of a bare soil spectrum (Whiting et al., 2004). The function’s variables with the greatest predictive value are the depth (amplitude) of the function and the area of one side of the Gaussian function, above the spectral continuum. Sunshine et al. (1990) describes a modified Gaussian distribution for modeling the broadening of the range of energy frequencies that are absorbed with increasing mineral abundance. The length and rate of stretching and bending increase randomly and symmetrically with additional shorter and longer wavelength bonds absorbing energy. The nominal bond length can be associated with the central absorption peak. In spectra- moisture trials, Whiting et al. (2004) found fitting the SMGM to the 2.8 µm water absorption center assumed a similar randomness. However, the absorption of energy by water at the fundamental is predictably, asymmetrically greater towards longer wavelengths (Bishop et al., 1994). Over other fitting polynomials, the Gaussian function has an advantage in using only a few functional parameters. Following the Beer- Lambert law, the spectra were transformed to natural log. The convex hull boundary points used to define the continuum were fitted with an Figure 2. The SWIR continuum declines as the 2.8 m water fundamental extends inverted Gaussian its short wavelength tail. This phenomenon was modeled by fitting an inverted distribution function after Gaussian function to the convex hull boundary points (+) from the position of Miller et al. (Miller et al., maximum reflectance ( i) to the assigned water fundament center ( 0), with 1990): Gaussian amplitude (Rd) and distance to inflection (σ). The Gaussian area, above the spectrum, is denoted as A (Whiting et al., 2004).

⎛ −− λλ )( 2 ⎞ λ = ⎜ 0 ⎟ (1) Rg d exp)( ⎜ ⎟ ⎝ 2σ 2 ⎠

Because the wavelength of the functional center for the water absorption is beyond the range of our laboratory and field instruments, the iterative fitting algorithm extrapolates the function along the convex hull points to the wavelength of maximum absorption, λ0, in nanometers, defined by the fundamental absorption of water at 2.8 µm. The inverted amplitude for the fundamental absorption is negative normalized reflectance, Rd. The distance from the center to the inflection point, σ, is measured along the wavelength axis. The relationship of the Gaussian function and parameters to normalized spectra is shown in Figure 2, derived from Miller et al. (1990). The area within the Gaussian curve, A, is found by integrating the wavelengths and Gaussian normalized reflectance values between the center and the short wavelength tail of the function:

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota

π ⎛ − λλ ⎞ RA σ ∗= erf ⎜ 0 i ⎟ (2) d 2 ⎝ 2 ∗σ ⎠ where Rd = Rλ0 - Rλi, and erf denotes the Gaussian error function.

In the previous study, the Gaussian function was fitted to 3,441 spectra, of which 2,592 were used for modeling and 849 for validation, from replicate soil samples as moisture increased in 5% intervals (Whiting et al., 2004). The area within the Gaussian curve (A) was the best indicator. Within the range of soil field capacity, less than 32% moisture, the area was highly correlated, and had a coefficient of determination (r2) for both calcareous and clayey soils of 0.94. The error of prediction of the linear regression for the model and validation sets for moisture content were within 0.027 RMSE of water content by weight for these soils. Separately for the calcareous soil r2 was 0.95 and clayey soil r2 was 0.94. Further stratifying the samples by natural divisions in the landscape, i.e., geomorphic position or salinity, improved the r2 to 0.98 and RMSE to within 0.017 for water content for several soil stratifications.

METHOD

In order to demonstrate the effectiveness of water content parameterization, we calculated the SMGM and mineral band-depths to illustrate the importance of the individual absorptions in determining the clay and carbonate contents. Soil spectra were extracted from images of bare soil from two distinctly different Mediterranean regions with substantially different mineral content ranges. The extracted spectra corresponded to ground sample locations and were regressed against mineral contents measured at these locations. The regression models with the best determination coefficients and lowest error rates were then applied to the spectra from the areas of bare soil within the images using band math to portray surface mineral contents. The images and spectral parameters were processed with Interactive Data Language (IDL) scripts and ENVI image software (Research Systems Incorporated, Boulder, Colorado). The statistical linear modeling was processed in S-Plus statistical software (Insightful Corporation, Seattle, Washington).

Soil Characteristics Reconnaissance surveys were used to gain an overview of the surface characteristics that would impact soil reflectance and quantification of the surface mineral contents. The surface differences of greatest influence on reflectance measurements are moisture, particle size, and roughness. Aspect and slope are not important in the two study areas are generally level or have low slopes. While not evaluated in this trial, stratifying the sites into regions of surface homogeneity is expected to improve the mineral abundance estimates, so the samples here were dispersed over these strata. Tomelloso, Castilla-La Mancha, Spain. Soils from the vineyards and grain lands near the town of Tomelloso are formed on calcareous and alluvial Miocene terraces, which have high albedo due to adsorbed and free amorphous calcium carbonate. Sanchez (Sanchez et al., 1996) described the general types using the FAO soil classification system. Within the sampled area, on the older surfaces are Petric Calcisols, and on the younger alluvium and river wash materials soils are described as Haplic Calcisols. Five landforms were identified on uplifted and alluvial terraces, and sample sites were randomly selected within these positions by overlaying a numbered grid of 40m by 40m cells using GIS. Twelve sites were sampled, as shown in the CIR image, Figure 3. Within each site, nine surface samples, 1-2 cm deep, were collected, 10 m apart on a 3 by 3 grid, for a total of 108 samples.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota Lemoore, Kings County, California, USA. Soils from near the city of Lemoore were formed on the basin and rim of the Tulare Lake playa in the southern San Joaquin Valley. The principal crops are cotton, tomatoes and grain. The USDA Natural Resources Conservation Service described these soils as a mixed mineralogy of illite and montmorillonite clays (USDA, 1978). Using the USDA classification system, the soils include fine-loamy, mixed (calcareous), thermic Typic Torriorthents, and fine, montmorillonitic, thermic Typic Natrargrids. Highly saline-sodic areas were separated from healthy soil regions using a previous year CIR composite image of vigorous and chlorotic plant growth, seen in Figure 4. A Normal Difference Vegetation Index (NDVI at 0.65 Figure 3. HyMap image, 3 June 2002, in false-color infrared (CIR) from m and 0.85 m) threshold value of the Tomelloso project site displaying the landform delineations for 0.855 was identified by matching stratifications and sampling sites cyan points. the low and high sodic samples to pixel NDVI values. The high sodium contents deflocculate the soil structure with repeated rainfall or irrigation, causing the horizontal orientation of mineral grains to influence soil reflectance (Courault et al., 1993). The Sodium Absorption Ratio (SAR) of the stratified soil samples is shown in Table 1. The SAR is the sodium concentration (meq) divided by the square root of the mean of calcium plus magnesium concentrations (meq) (Richards, 1954) extracted from a soil saturation paste, and measured by atomic absorption spectrometry (DANR, 2004). The six sample sites were distributed broadly over 194 ha, in three adjacent 65 ha fields. Within each site, the soils were sampled with the same 3 x 3 sample grid strategy used at Tomelloso, described above, for a total of 54 samples.

Comparison of Soil Regions These two project regions also provided soils with varying dry and moist colors, and dry maximum reflectance as shown in Table 1. Organic carbon contents were similar, less than 2% for both regions. These soils exemplify the strong mineral absorptions in the SWIR assigned to secondary clay minerals and carbonate. The kaolin clay content is low to medium in Tomelloso (11% to 34% by weight, with a mean for the samples of 21.2%), and medium to high smectite clay content in Lemoore (22% to 43%, mean of 32.1%). Clay contents were determined in soil suspension by hydrometer (Gee and Bauder, 1982). This method has a detection limit of 1% sand, silt and clay (dry soil basis) and is generally repeatable within 8% relative error (DANR, 2004). The carbonate content was low in Lemoore (0.2 to 2.4%, mean of 0.75%), and medium to high content in Tomelloso (23 to 66%, mean of 46.8%). The carbonate contents were determined by gravimetric loss after reaction with hydrochloric acid (Staff, 1954), and is generally repeatable within a relative 10% (DANR, 2004). While Tomelloso soils are high in carbonate, Lemoore soils are high in sodium. The SAR in Tomelloso is very low, typically near 0.12 or less. The SAR in Lemoore was nearly continuous through both the low and high strata sites, with an approximate threshold between the photographically determined low and high sodicity sites near SAR 5. The strata ranges were 1.9 to 4.9, and 5.0 to 19.2.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota Table 1. Soil characteristics of study sites (Whiting et al., 2004).

Mean Surface Clay Munsell Soil Color Maximum Roughness Content CaCO3 Reflectance Course Range Range Typical Soil Landform Dry Moist (R%) Fragments (%) (%) SAR Textures Tomelloso, Castilla-La Mancha, Spain Uplifted calcareous 5YR6/4 5YR4/4 59.3 23 - 28 49 - 66 0.12 loam terrace (TU) uplifted terrace surface 5YR6/3 5YR4/4 57.5 22 34 - 65 0.12 loam drains Coarse (TD) sands, and pedogenic loam to first cut- CaCO3 sandy fill terrace 5YR5/4 5YR4/2 48.5 23- 34 31 - 48 0.05 grains clay (UB) loam second cut-fill sandy 5YR5/4 5YR4/4 52.4 11 -16 32 - 57 0.08 terrace loam (MB) flood 5YR5/4 5YR3/4 49.3 13 - 20 23 - 36 0.08 silt loam plain (FB)

Lemoore, California, United States sandy clay Smooth, no loam, basin, low 0.2 – 1.9 - 10YR5/3 10YR4/3 39.4 micropeds, 22 - 43 silty clay sodicity 1.2 4.9 slaked with loam, wetting, clay cracked loam basin, dry 1.6 – 5.0 - clay high 10YR6/3 10YR5/3 38.4 29 - 43 2.4 19.2 loam sodicity

Tomelloso Image Preparation and Spectra Extraction The European Space Agency, the German Aerospace Center, DLR, flew the HyMap sensor over the Tomelloso project site as part of the larger Digital Airborne Experiment (DAISEX1999) campaign on 3 June1999 (Muller and Hausold, 2001). HyMap collects 126 bands in the 0.450 m to 2.480 m range, with 0.016 m full wide half maximum (FWHM) channels (http://www.hyvista.com). The square pixels in this image are nominally 5 m, and were georectified using digitized ground control points (GCP) for image features found in a 1:25,000 scale topographic map with registration accuracy within 3 pixels (Muller and Hausold, 2001), and atmospherically corrected using ATCOR4 (Richter, 2000). Transformations of images using continuum removal were used with spectral math to isolate the vegetated areas from the bare soils by green vegetation and lignin-cellulose absorptions in the VNIR and SWIR regions. Vegetation is strong absorber both at 0.68 m in visible near-infrared region and near 2.1 m in the SWIR. The presence of non- photosynthetic vegetation, e.g., lignin and cellulose, was identified by the flattening of the soil spectral shape and the reduced shoulder on the long wavelength side of the soil organic matter and iron absorptions, beyond 0.50 m. This determination was combined with the lignin and cellulose apparent absorptions around 2.1 m and near 2.3 m to eliminate vegetation cover from the processing mask for bare soil.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota Modeling and validation spectra were extracted from the bare soil image pixels surrounding the GPS ground sample points. To overcome registration and sample location inaccuracies and spectra resampling during geo- rectification, the ground reference data were associated with regions of interest (ROI) created around each sampled pixel using a 3 x 3 window. A weighted average spectrum was generated from the ROIs using weights of 7, 3 and 1, for the center, lateral, and corner pixels, respectively. Thus, nine spectra were extracted from the grouped points (sample blocks in cyan), shown in Figure 3. The influence of the geomorphic positions (strata) was included by selecting an equal number of samples, with two sites within each soil strata.

Lemoore Image Preparation and Spectra Extraction As collaborator in the NASA/USDA AG2020 precision agriculture program, NASA-Jet Propulsion Laboratory collected Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS) data on 28 August 1999 and 5 May2002 over the Lemoore project site. The images contain nominal 10 m pixels in 224 channels between the 0.400 m to 2.500 m, with a nominal 0.010 m FWHM channel (Chrien et al., 1999). These images were atmospherically corrected using ACORN software (AGI, Boulder, Colorado) and georectified with differentially corrected global positioning system (GPS) measured field corners. Figure 4. shows the CIR composite of the unrectified 28 August 1999 AVIRIS image of full canopy cotton and saline-sodic areas used to stratify the sampling regions. The 5 May 2002 AVIRIS image was of bare fields recently planted to cotton and senescent grain and garlic fields. This second image was analyzed after separating the bare fields from roads and vegetated fields using the grower-supplied crop map and the interactive digitizer in the ENVI image processing software. These AVIRIS images were lower resolution than the HyMap image, so the sampling strategy placed one point in each of the adjacent nine pixels, seen in Figure 4. The registration accuracy of these images was within one pixel. The same method used for the Tomelloso images was used to extract weighted average spectra from the ROI surrounding the sampled pixels, and generate the three band bare soil parameters.

Figure 4. Unrectified AVIRIS, 28 August 1999, false color infrared Band-depth Measurements image (CIR) of full canopy cotton of Lemoore project site with The extracted spectra from the sample points as black ‘+’ marks. sample sites for all bare soil pixels were processed by 1) determining the convex hull boundary points within the SWIR and calculating the SMGM, and 2) measuring the band-depths by subtracting from unity the absorption minima for clay and carbonate absorption bands of the normalize reflectance created with continuum removal using an IDL script. The continuum removal script constructed straight line datums between sequential convex hull boundary points on each side of the clay or carbonate absorptions. Some investigators have ignored adjacent absorptions and hull points by bounding their absorption of interest at predetermined local maxima. This procedure runs the risk of setting the ends of the datum at weak shoulders affected by other absorptions, which will underestimate the true band-depths. On the other hand, if the continuum is constructed using only end points of across a broad region containing multiple absorptions, ignoring the hull points located on strong shoulders that are between the mineral absorption features, the measured depths will be shallower than their full absorption because the straight line continuum undercuts the local maxima at shared absorption shoulders. Missing hull points between strong absorptions is often due to overlapping tails of strong absorptions for either or both clay and carbonate bands. Overlapping tails occurred in spectra from Tomelloso soils containing both clay content greater than 20% and carbonate content greater than 30%. The datum was initiated at the water-clay shoulder hull point (~2.0 m) and extended to the hull point beyond the carbonate absorption near the end of the SWIR mineral region. If both the water-clay shoulder and the clay-carbonate shoulder were missing, then the continuum is indeterminate and the pixel spectrum was eliminated from further processing. Typically, spectra that lacked the 2.0 m water-clay shoulder hull points were eliminated during the vegetation masking close to the 2.1 m cellulose/lignin absorptions. In Lemoore, the fields were clean till, recently planted cotton fields, and as expected, none of the pixels were eliminated due to vegetation absorptions. A few were masked due to high soil water content because of flooding from a broken irrigation ditch that exceeded the upper measurement limit for soil moisture (field capacity) using the SMGM.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota Defining Parameters and Modeling Single and multiple absorption band-depths were regressed against the concentration determined in the laboratory soil measurements to create a prediction model for each component (Kokaly and Clark, 1999; Martin and Aber, 1997; Van der Meer, 2004). For brevity here, each site is used to demonstrate the model effectiveness for improving the content estimates of the dominant mineral, Tomelloso for carbonate (~2.35 um) and Lemoore for secondary clay minerals (~2.2um). At both sites, three parameters were used as regressors for predicting mineral contents: soil moisture Gaussian model (SMGM), clay and carbonate band-depths. The lab analyses of the soil mineral components were combined with the numerical parameters of SMGM and mineral band-depths in multiple linear regressions to estimate the mineral contents. In equation 3, the complete list of parameters in the multiple regression is shown with the mineral band-depths of clay represented by Xi1 and carbonate by Xi2, and the SMGM is Xi3.:

= β + β + β + β + ε yi i i22110 3XXX 3 ii (3)

The importance of each parameter was evaluated by comparing the t*statistic with the value of the t(0.95; n-1): t* = bi / s (Richards, 1954). The parameter regression coefficient divided by its standard deviation was provided by the coefficient table (Neter et al., 1996). The parameter was deemed unimportant to the model if the probability of t*statistic did not exceed the t table value at the 95% significance level. Each acceptable model’s prediction accuracy was evaluated based on the coefficient of single or multiple determination (r2, R2) and the root mean squared errors (RMSE) (Neter et al., 1996).

RESULTS AND DISCUSSION

Tomelloso Carbonate Estimates From Tomelloso, 65 bare soil spectra were extracted from the initial 108 sample points after the vegetated spectra were eliminated. The carbonate estimates based solely on the band-depth of the carbonate were poorly correlated, and the addition of the clay band-depth was found to be insignificant. The coefficient of single determination (r2) for carbonate was 0.42, with standard errors of 8.0 % for the regression mean of 44.8 % carbonate content, shown in Table 2. The combination of carbonate band-depths and SMGM was significant and slightly improved the multiple variable coefficient of determination (R2) for carbonate content estimates to 0.54 and 7.2 % RMSE carbonate by weight. The difference in RMSE contributed by the moisture in the air-dried soil in the image (at approximately 4% water content) was approximately 0.8 % carbonate RMSE, or a reduction in the error of prediction by 10%. The laboratory variability is included within the spectral regression model for determination of carbonate and thus increases the spectral error estimate. The influence of moisture on these air dried soils is due to the weaker absorption of water by the carbonate mineral, and these coarser soils hold less water at air dry conditions.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota Table 2. Regression model coefficients and coefficient of determination.

TOMELLOSO CARBONATE REGRESSION MODELS Carbonate = CO.depth n = 65 Corr. of Determ. (R^2) 0.42 Predictive Error (StdErr) 8.0

Carbonate = CO.dep + SMGM Regression Intercept CO.dep R^2 Predictive Error Coefficients: SMGM n = 65 29.18 3905.12 -0.55 0.54 7.2

LEMOORE CLAY REGRESSION MODELS Clay = CL.depth n = 53 Corr. of Determ. (R^2) 0.24 Predictive Error (StdErr) 4.0

Clay = CL.dep + SMGM Regression Intercept CL.dep SMGM R^2 Predictive Error Coefficients: n = 53 22.44 427.05 -0.00490 0.51 3.6

Band math in the ENVI software was used to apply the regression coefficients to the carbonate band-depth and SMGM images, resulting in a third image, shown as a gray scale of carbonate content in Figure 5. For example, the band math function to calculate carbonates for the Tomelloso images used the regression coefficients in Table 2:

= + − B3 B1 B2 )*55.0()*12.3905(18.29 (4)

The band (B3B ) produces in a single band image for carbonate estimates by applying the coefficients from modeling to the carbonate band-depth (B1B ) and SMGM band image (B2B ).

Carbonate Content (%)

65

20 Nodata

Figure 5. HyMap image, 3 June1999, in gray scale of carbonate contents of bare soil areas.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota

Lemoore Clay Estimates In Lemoore, 53 samples were used to model clay content. All spectra were dry enough to have a hull point at the water-clay shoulder, but only a few (4 of the 53) had a true hull point between the clay and carbonate absorptions, probably due to a combination of noise and the weak carbonate absorption in the SWIR. Both clay band-depth and SMGM parameters were significant for generating models. Each parameter was evaluated in modeling clay content estimates, shown in Table 2. The clay band was a poor predictor of clay content with r2 = 0.24 and 4.0 % RMSE clay content. By adding the SMGM to the clay band-depth, the R2 doubled to approximately 0.51, and the RMSE decreased to 3.6 %. The difference in RMSE contributed by residual moisture in these air dried soils (approximately 4 to 8% water content) was approximately 0.4 % clay RMSE, or a reduction in the error of prediction by 10% for a regression mean of 30.0 % for the Lemoore soil clay samples. At air dry status with these dominantly smectite clay soils, the SMGM was equally correlated to clay content as the spectral band-depth. With greater soil moisture, the SMGM would possibly make an even greater correction to the clay band-depth model. As with Tomelloso, band math was applied to the parameters images to produce Figure 6 gray scale image of the clay contents. Changes in vegetative growth and salt contents are commonly associated with patches of high sodicity soils, but

Clay Content (%)

45

22 Nodata

Figure 6. Georectified AVIRIS image, 5 May 2002, in gray scale of clay contents of bare soil fields. are not necessary linked to higher clay contents. No correlation was found between laboratory values for sample clay content and SAR, however, there may be minor regression colinearity between the clay band-depths and salinity due to soil surface aggregate size and particle orientation. The cut and fill used to grade the fields for furrow irrigation may help explain the uniform change in clay estimation at the field boundaries.

CONCLUSION

Measuring soil mineral abundance can be improved by accounting for the effect of soil moisture on the spectra. This simple application showing the impact of adjacent mineral absorptions on mineral abundance demonstrates that estimates from hyperspectral imagery can be improved slightly, even under air-dried conditions, when soil moisture is considered a parameter in the analysis. This parameter can be included in many mineral abundance algorithms by first estimating the strength of the water fundamental using a Gaussian function. Continued research is investigating applying the SMGM as a parameter in Principal Component Analysis, partial least squares and other analyses. After determining the parameter for each pixel, the SMGM can be incorporated as a “soil water fractional image” in other mineral determination techniques, such as cluster and classification and regression trees (CART). However, to derive the water content estimate, SMGM regression requires calibration based on a minimal set of soil samples obtained from the region to be mapped. This is the same sample based calibration procedure needed to quantify organic matter and minerals. Further refinement of the moisture and mineral estimates can be gained by stratifying the landscape through pre-mapping other parameters that influence surface reflectance, then including these regions in the sampling design to obtain calibration data for estimating soil moisture and mineral components.

Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota REFERENCES

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Pecora 16 “Global Priorities in Land Remote Sensing” October 23 – 27, 2005 * Sioux Falls, South Dakota