Author for Correspondence:
Alicia Palacios-Orueta
Department of Land Air and Water Resources
One Shields Avenue
University of California
Davis, CA 95616
Phone: (530) 752-5092
e-mail: alicia@vache.ucdavis.edu
Organic matter is generally positively related to the fertility of soils. When erosion increases, portions of the surface horizon are removed and organic matter is lost. Because iron content is related to weathering as well as erosion levels of soils, iron content tends to be higher in highly weathered soils, and in eroded soils when the B horizon is exposed at the surface after the A horizon is eroded. These problems are often manifest at large landscape or regional scales making them suitable for observation with remote sensing satellites. In the absence of anthropogenic disturbance, soil quality is mostly related to long term patterns of climate, parent material, landform and vegetation. Because these factors create a spatial mosaic, variability is also a critical issue that needs to be handled with techniques appropriate at large scales.
Remote sensing and aerial photography techniques have been utilized in soil science for many years as tools to help soil surveyors reduce the time and expense of sampling. Imaging spectroscopy is a newer tool that can be applied to the reflectance/emittance spectroscopy of every pixel in a spatial image (Clark http//speclab.cr.usgs.gov/). With the appearance of these new sensors the possibilities for soil science applications are much greater. This is due to the inclusion of the shortwave-infrared region of the reflected spectrum combined with high spectral resolution and contiguous placement of bands, while keeping an acceptable spatial resolution (Goetz, 1992; Roberts et al., 1993; Palacios-Orueta and Ustin, 1996). Thus, the spectral properties of the soil in the context of the relevant landscape features where the soils are located can be analyzed to assist in determinations of soil quality that can be evaluated at larger regional scales and temporal changes through repeated observations over time.
Spectroscopy has been extensively utilized to detect mineral composition not only at the laboratory scale, but also from remote sensors in earth science investigations as well as in planetary studies (Crowley, 1991; Hook et al., 1991; Jaumann, 1991; Britt et al., 1992). Actual mineralogical detection is dependent on the spectral coverage, spectral resolution, and signal-to-noise of the spectrometer, the abundance of the material and the strength of absorption features for that material in the wavelength region measured (Clark http//speclab.cr.usgs.gov). Although there is extensive information about soil reflectance (Krishnan et al., 1980; Stoner et al., 1980; Irons et al., 1989; Henderson et al., 1992; Csillag et al., 1993) research is still needed to better understand changes in absorption features under different conditions. Some techniques of analysis are based on the correlation between certain properties of the absorption bands and the physicochemical properties of the material (Clark and Roush, 1984). Fisher and Pieters (1994) applied band depth analysis to determine the extent of weathering of lunar soils. They found that band depth at 1000 nm could be used to determine concentration of ferrous iron in mature Lunar soils. Mixing models allow the information contained in the entire spectrum to be used, not only features in narrow spectral bands but also the overall shape of the spectrum. A number of linear and non-linear mixing models have been developed for mapping soil characteristics and their fractional composition in mixed pixel spectra (Johnson et al., 1983; Smith et al., 1985; Shipman and Adams, 1987; Huete and Escadafal, 1991). The Principal Component Approach (PCA) is predicated on the assumption that the spectral variability contained in the data set is due fundamentally to mixing between a small numbers of discrete compositional endmembers with unique spectral properties (Mustard and Sunshine, in press). Huete and Escadafal (1991) utilized PCA to extract soil biophysical properties and their fractional composition in pixel spectra. Britt et al. (1992) applied PCA to compare asteroid and meteorite spectra and Jaumann (1991) identified and quantified correlations between reflectance spectra and properties of lunar materials.
Because soils result from weathering of the parent material, soil composition is a complex mixture of different minerals at many different grain sizes. On the earth, organic matter plays an important role in soil composition as well, therefore, the resultant spectra will depend not only on the mineralogical features of the parent material but also on the degree of weathering and on the content of organic matter. Absorption features in soils are therefore the result of overlapping bands from different mineral components and organic matter. Organic matter affects the spectra by decreasing the overall reflectance and thereby decreasing the spectral contrast, and making the relationship between spectral and physicochemical properties more difficult to detect.
Traditionally, soil variability has been studied and summarized in soil surveys. These studies delineate soil boundaries, by partitioning continuous soil variability into discrete soil units described by taxonomic variability. For soil processes such as biogeochemical cycling and erosion, other soil properties can be more important than taxonomic criteria. In this study our interest lies more in the description of soil surface properties that can be detected with remote sensing methods rather than on traditional soil taxonomy. Several hyperspectral airborne sensors and one satellite, the Lewis sensor, are available for investigating soil processes. NASA’s Advanced Visible/Infrared Imaging Spectrometer (AVIRIS) sensor has been flown over many geologic sites in the western United States of America, and has been shown to be useful for detection and quantification of clays, iron oxides, and other minerals (Clark et al., 1990; Boardman and Goetz, 1991; Farrand and Singer, 1991; Crowley, 1993; Kruse et al., 1993; King et al., 1995). Palacios-Orueta and Ustin (1996) have shown that AVIRIS could be used to differentiate subtle variation in soil surface properties at the level of soil phases in the same soil series. The 10 nm nominal spectral resolution of AVIRIS makes it suitable for detecting sharp absorption features that are important in soil spectra such as those from clays. The AVIRIS spectral range is excellent for the study of the chemistry of specific organic or inorganic compounds through the determination of electronic transitions and vibrational absorptions in minerals and vegetation. Examples of applications have included identification of iron oxides, and Fe2+ bearing minerals, (King et al., 1995), OH-bearing minerals (Van der Meer, 1994), carbonates and sulfates (Crowley, 1993; Kruse et al., 1993), and vegetation components (Elvidge et al., 1993; Gamon et al., 1993; Roberts et al., 1993; Clak et al., 1995). Lastly, it’s high spatial resolution contributes significantly to the potential for coping with fine scale soil variability, an important issue in terms of possible management and remediation actions.
The aim of this work is to investigate whether AVIRIS wavelengths can be used to study soil properties, specifically iron and organic matter contents in two watersheds in the Santa Monica Mountains Recreation Area, California. Soil development in many areas is limited due to the xeric soil moisture regime typical of Mediterranean climates, as well as the steep terrain, making the region highly susceptible to erosion. Since this type of climate system predisposes wildfires during or at the end of the dry summer season, the lack of vegetation combined with the steep terrain maximizes erosion potential at the start of the winter rain season. The combination of all these factors markedly increases heterogeneity in the distribution of soil properties. This heterogeneity requires synoptic analysis over the larger region but at sufficient spatial resolution to understand soil pattern differences. AVIRIS satisfies these two requirements.
AVIRIS wavelengths were simulated from laboratory spectral data acquired
at higher spectral resolution. Multivariate methods such as Principal Component
Analysis and Canonical Discriminant Analysis were applied for spectral
data exploration and classification, and band depth analysis to examine
specific absorption features. The soil analyses were done both including
and excluding the noisy bands and the water vapor absorption bands.
The locations of the soil samples were identified using a Global Positioning
System unit (Trimble Navigation PROXL) with +/- 1meter accuracy after differential
correction. Out of the 83 samples only 74 could be differentially
corrected therefore, only these samples were used in the analysis.
Statistical analyses showed that the mean surface soil iron content
in Serrano Valley was significantly higher than in La Jolla Valley. In
contrast, surface horizon soil organic matter content was significantly
higher in La Jolla Valley. Variances were similar in both valleys. There
was not significant difference in texture (sand, silt and clay percentages)
between either valley. Table 1 shows the means and standard deviations
for the chemical variables for each valley. Table 2 shows the means, medians,
and second and third quantiles for the complete data set. Between the two
valleys, where iron is high, organic matter tended to be low and where
organic matter was high, iron content was low (Fig.
1).
The instrument was tested for reflectance and wavelength calibration
using a 50% reflectance sample and the rare Earth’s, Erbium Oxide and Prisposium
Oxide. Prior to each day’s set of measurements a 100% Spectralon reflectance
standard was used to normalize possible changes in the spectrometer. The
signal-to-noise ratio was set at 1250. The dry soils were set in sample
holders at a thickness of 1 cm. The measurements were obtained at 1, 2
and 4 nm intervals. Since we were interested in evaluating the potential
of AVIRIS bands for soil discrimination, the data were treated to simulate
AVIRIS bands. The AVIRIS sensor acquires 224 spectral bands with 9.6 nm
nominal spectral resolution, between 400 nm and 2500 nm. The transformation
was done by averaging the spectrometer bands to AVIRIS wavelengths using
a linear weighting function. The value of this function ranged between
0 and 1 across the wavelength interval over each AVIRIS band. The linear
function corresponds to a triangular bandpass with a full-width half-max
specified by the spectral characteristic file that was supplied with the
AVIRIS image. This way, higher weights are assigned to the Cary bands closer
to the center of AVIRIS bands than those at the margins.
The second approach used was statistical, based on multivariate techniques using Principal Components Analysis (PCA) and Canonical Discriminant Analysis (CDA). These statistical models incorporate both narrow absorption bands and the overall shape of the spectrum. PCA was applied to define the shape and the contribution of each eigenvector to the overall reflectance spectra. PCA is applied on the standardized data. Since soil samples were obtained from two separate valleys having statistically different physicochemical characteristics, CDA was applied to determine whether the two valleys could be discriminated spectrally. The application of these statistical methods to reflectance spectra have been discussed in the literature (Smith et al., 1985; Huete and Escadafal, 1991; Britt et al., 1992). Ideally each eigenvector represents a unique soil spectral property. While the weightings of the eigenvectors make it is possible to infer some relationships to chemical and physical properties, we used regression analysis to explore these connections with more confidence. Regression analysis was applied to band depth results, and the derivative of the inflection points. To explore the physical bases of each PC in more depth, the original spectral data was reconstructed using a limited number of eigenvectors. This reconstruction was done first by reconstructing the spectra using different combinations of the principal component eigenvectors, adding them sequentially, and second, by reconstructing the spectra using individual eigenvectors to observe the contribution of each of them. The accuracy of the reconstruction was evaluated by calculating the difference between the original spectral data and the reconstructed data and the standardized mean squared error per site was calculated.
Because we were interested in the potential performance of AVIRIS or
other satellite or airborne hyperspectral sensors to discriminate soil
properties, the same analyses were repeated to investigate the effect of
eliminating water vapor bands and noisy bands on the discrimination. The
bands eliminated were the first five bands of the spectrum, nine around
1400 nm, nineteen around 1900 nm and the last two bands at 2400 nm, resulting
in a 189 band subset of 224. To investigate the significance of these bands
on the variability of the data, we calculated PCA’s in three ways. First,
the eigenvectors were computed using the whole spectrum. In the second
and third way the new variables were calculated by using eigenvectors that
did not contained the described bands. The eigenvectors used in the latter
cases were calculated in two ways: first, by deleting the water vapor bands
from the eigenvectors already calculated, and second, recalculating the
eigenvectors after deleting these bands from the spectra. When the eigenvectors
are calculated with 224 bands, the amount of information that can be extracted
is optimized, and some will be lost when deleting bands (i.e. the second
case). In the third method, the water vapor bands were eliminated from
the spectra prior to recalculating the eigenvectors, this allows bands
that would not receive high weights to become more important. All analyses
were performed using the mathematical software Matlab (1994), and the Statistical
Analysis System, SAS (1993). The statistical analyses were run in SAS,
and the band depth analysis and the reconstruction of the original spectra
were done in Matlab.
Both, the overall shape of the spectrum and absorption bands are important in explaining the spectral properties of soils. The shape of a spectrum can be characterize by the albedo, the continuum slope and the intensity distribution (Jaumann, 1991). Although albedo is the primary source of variability, absorption features play a significant role in relation to specific chemical characteristics.
In our samples, maximum reflectance ranged from 12% to 60%. There are six regions of the spectrum that exhibit distinct absorption features and high variability among the samples (400-560, and around 1000, 1400, 1900, 2200, 2300 nm). While in the visible region the absorption features are usually broad, the features in the infrared region of the spectrum (e.g., at 2200 or 2300 nm) tend to be narrower and sharper. Figures 2.a and 2.b show the mean and the standard deviation of spectra for samples from the two study locations, Serrano and La Jolla Valleys respectively.
The visible portion of the reflectance spectra shows different curvature among the soils. An inflection point ranged from 509.3 to 558.7 nm in most of the soil samples. Huete and Escadafal, (1991) working in the 300-900 nm range found that 540 nm is one of the key wavelengths to characterize soil spectra. Most samples have a second inflection point between 421.4 nm and 440.8 nm. They also reported 400 nm and 440 nm as key bands. These wavelengths have been reported to be associated with iron in it’s ferric form, the low reflectance in this region is due to a ligand field band near 450 nm and a charge transfer band in the near ultraviolet (Gaffey et al., 1993). No correlation was found between the derivative of the spectrum at these points and any of the physicochemical properties analyzed.
While intact soil crusts may contain cynobacteria which may exhibit spectral features in the blue band ( Karnieli and Sarafis, 1996), in this case the processing of the soil samples prior to spectral analysis effectively minimizes any possible contribution to these results.
Most soils from Serrano Valley distinctly display the 1000 nm Fe2+ absorption band. This absorption is due to electronic transitions in the ferrous ion (Irons et al., 1989), and is stronger that those at shorter wavelengths. Among the samples that do not exhibit this absorption feature, spectra show different degrees of curvature at wavelengths shorter than 1300 nm, ranging from concave to highly convex spectra. The two main water and hydroxyl absorption bands at 1400 and 1900 nm are present in all samples. Both bands are more accentuated in the soils from Serrano Valley, indeed the absorption at 1400 nm almost disappears in some of the soils from La Jolla Valley. Both bands indicate the H-O-H bend and the band at 1400 nm indicates stretching of OH ion as well (Baumgardner et al., 1985; Gaffey et al., 1993). The small size of this band seems to be related to the low reflectance across the whole spectrum because of high organic matter content, which decreases the resolution of the absorption band. Because of the high organic content, this happened primarily in soils from La Jolla Valley. In the region between 1900 and 2500 nm, two bands located at 2200 nm and 2300 nm are observed. The latter appears more frequently in Serrano Valley soils. The hydroxyl ion linked to metals produces a metal-OH bend with band positions typically in the 2200 to 2300 nm region. In soils, it is understood that the band at 2200 nm is produced by AlOH and the band at 2300 is produced by MgOH (Roush et al., 1993).
Some spectra in the data set present such a low reflectance that spectral contrast is too low to display any significant absorption features. Analyses of the soils having low reflectance showed that all of these samples also have a low sand content. The absorption features are observed more strongly when soil samples have higher sand content. A mineral mixture with a given particle size will have a specific reflectance, when particle size changes, reflectance increases or decreases depending on the opacity and transparency of the material. Quartz is usually the main constituent of sand and is translucent in this region of the spectrum, therefore, when sand content increases, light will be more transmitted through the soil particles, and this will tend to enhance the observed band strength of absorbance features in the reflectance spectra of other soil constituents. When sand is low, small opaque material will dominate and the sample will exhibit low reflectance, little dynamic range, and poor resolution of the absorption features.
The band depths of the main absorption features (Clark and Roush, 1984) were calculated in order to correlate these with physicochemical properties. The bands used for analyses were at 1000, 1400, 1900, 2200, and 2300 nm. The bands that show the strongest correlation with iron and organic matter content were at 1400 nm and at 1900 nm. The absorption band at 1400 nm is deepest when iron content is high, and organic matter is low, except in samples where sand content is also very low. When iron content is intermediate (ie. 3.39<iron<4.17 %) this band is observed only when organic matter is lower than 1.96 %. In summary, the 1400 nm band is well defined in spectra from soils with high iron content or intermediate iron content and low organic matter content. Band depth at 1900 nm is highly correlated (r2=0.94, with Prob >F = 0.0001) with the depth at band 1400 nm. Iron content is correlated with this band (r2=0.5 with prob>F =0.001) when iron is higher than 4.23 %. Although absorption features for iron and organic matter do not occur in these bands, perhaps the interaction of both components together with the particle size distribution makes them more sensitive to changes in composition.
The appearance of the band at 1000 nm is limited to sand contents higher than 40% (Fig. 3.a and 3.b). When sand content is lower, the band does not appear or is almost imperceptible. In terms of this absorption band, it seems that there are three levels of variability present in the soil spectra. In this graph, iron content is indicated by the tone of the symbols and organic matter by their shape. There is a group of samples that have a deep absorption band and a high level of variability. Most of these samples also have low organic matter content and were collected from Serrano Valley. Most of these samples had high iron content except some of them had either high sand or low organic matter. In these latter samples, the band depth overestimated iron content. A second range of variability is observed in samples where the band is present but not as deep (Fig. 3.b). In most of these soils, iron content ranges from intermediate to high, and organic matter content is intermediate. In this case, the presence of organic matter causes the band depth method to underestimate the iron content. The sample group where the band depth is zero or imperceptible were mainly soils with high values of organic matter and low iron content. Most of these samples were collected from La Jolla Valley. Soils with low sand content are also located in the group expressing low variability independently of their chemical composition. Samples with iron content less than 3.18 % are all in the low variability group and did not display the absorption band at 1000 nm. It seems that both variables, iron and organic matter have a significant confounding effect on spectral detection. In many samples, the iron content could not be detected due to the high values of organic matter and vice versa. In samples with low organic matter content and high sand content, the effect of iron is accentuated.
To study these interactions further, a second approach using PCA was performed. PCA was used in order to summarize the information contained in the specific absorption features but also in the overall shape of the spectra. PCA defines the independent sources of variations in the data set. The contribution of each eigenvector needed to reconstruct the original data was related to the content of the chemical in the sample (Huete and Escadafal, 1991). This chemistry is quantified in the new variables. To evaluate how many principal components summarize the information in the data set, we looked at the eigenvalues of the correlation matrix, (Table 3). Another way to retrieve this information was to reconstruct the original spectra using different combinations of PCs and calculating the errors per site at each step.
The first eigenvector (Fig. 4.a) shows the general form of the spectra; it displays a marked sigmoidal shape from 540 to about 900 nm. This PC accounts for brightness variation (Smith et al., 1985); soils with low reflectance have low weights on this first component. Regression analyses (Fig. 5) show that the values of the first PC are well correlated with sand content, when sand is less than 40%. Some of the PC1 values are negative because the spectra was standardized prior to the principal component transformation. Soils with low weights on the first PC show the lowest values in sand content. In these cases, the main absorption bands are barely apparent, it seems that low PC1 scores indicates limited expression of important soil features. When sand content is higher, total reflectance increases and spectral contrast is sufficient to display absorption bands, therefore spectral features are more related to other properties. Analyses showed also that correlations were higher when samples with low sand were eliminated (Table 4). PC1 shows positive correlation with the derivative of the inflection point in the visible area of the spectra (r2=0.48 with prob>F=0.0001). Since PC1 is related to albedo, and due to the overall increase of reflectance from the ultraviolet to the infrared, soils with high overall reflectance have higher derivatives in the inflection point.
The second eigenvector (Fig. 4.b) shows highly positive weights in the area before 1100 nm and negative values around 1900 nm; 1291.1 nm is the point where the sign changes. It seems that this eigenvector determines the spectral curvature between 500 and 1000 nm. Traditionally this region has been related to both organic matter and ferric iron contents. Our results showed negative correlation between PC2 and organic matter content (Fig. 6). Soils with low PC2 show a concave shape between 500 nm and 1000 nm while it gives positive weights to bands at wavelengths longer than 1400 nm.
The third eigenvector (Fig. 4.c) is important in defining the shape of the absorption band at 1000 nm which is related to iron content. Soils with high PC3 coefficients clearly exhibit this absorption band. Although the total amount of variability accounted for by this eigenvector is smaller, the band is mostly affected by increasing or decreasing the reflectance at 1269 nm, just preceding the water band at 1400 nm. This way, this variable influences not only the band depth at 1000 nm but also at 1400 nm. A highly negative point in this eigenvector is found at 837.9 nm, which is directly related to iron absorption. PC3 is more directly correlated to the band depth at 1400 nm than to band depths at 1000 nm, possibly due to the fact that the latter is highly affected by the weights of the second PC. Our analyses show that PC3 is negatively correlated with iron content (Fig. 7). It seems that PC3 can be a good predictor of iron for soils with sufficiently high reflectance to let absorption bands be observed. Some positive correlation was found also between PC3 and organic matter content.
Although the fourth principal component (Fig. 4.d) did not account for significant amount of variability, analyses of the errors showed that some of the reproduced spectra using the first three PCs differ significantly from the original value. Two examples of this effect are shown by soils from sites 15 and 62 (Fig. 8). Although soils from these two sites show different spectral shapes, their first three PCs are very similar. Therefore it is PC4 that distinguishes them. All these soils are low in organic matter content and have extreme values of PC4.
PC2 and PC3 are the best predictors for iron and organic matter content. Figure 9 shows a scatterplot of PC2 vs. PC3. The spectra shown in the corners are those shown in Figure 10. They show the general shape of the spectra of the samples located on that area of the plot. The symbols are the same used in Figures 3.a and 3.b. Soils with sufficiently high reflectance and low PC3, are located on the left side of the figure. These soils have a high iron content (black symbols) and either low (inverted triangle) or intermediate (closed circle) organic matter. Samples with intermediate iron content (gray color) that are located in this quadrant of the figure show either high sand, minimal organic matter, or a combination of both. In terms of the overall shape of the spectra located in this quadrant, the band at 1000 nm is highly inflected. Samples that have high levels of iron that do not show a low value of PC3 have a low sand content, therefore, the typical iron absorption features were not expressed. These soils can be discriminated from soils having more sand by their low PC1. Soils with low PC2 are those with higher organic matter content (inverted triangles), among them, soils with low iron (open symbols) are observed on the right side of the figure. In these spectra, the curvature in the area at wavelengths less then 1300 nm is related to PC2, therefore to organic matter. Samples with intermediate values of either organic matter or iron (gray circles) are mainly in the central part of the figure. Most of the soils that were not well classified are related to extreme values of reflectance, either too low with no spectral contrast or too high, and over-emphasizing spectral features. This analysis showed that a big portion of the variability was due to differences in organic matter content. There was higher variability among the soils from La Jolla than from Serrano Valley.
Figure 10 shows three examples of spectra with different shapes and physicochemical properties. These spectra were reconstructed from the PCs to analyze the contribution of the bands to each of the PC weightings and for each PC to the spectra. Since the PCA was performed on the standardized spectra, some of the figures show results from the standardized spectral data and some from the original spectral data. The purpose of showing standardized results is to emphasize the contribution of each of the eigenvectors in relative terms. When showing the results from original data, the biggest contribution is from the first PC. However, this PC is not the most important for discriminating between soils. The variability accounted by for the other eigenvectors is relatively diminished in this representation of the data. The first PC generates the general shape of the spectrum while adding subsequent PCs emphasizes the characteristics of the absorption features due to their physiochemical differences. Figure 11 shows the contribution of each eigenvector to the reproduction of the standardized spectra from Figure 10. The first eigenvector reproduces the general shape of the spectra, focusing the main differences in albedo (Fig. 11.a). When only PC2 is used (Fig. 11.b) the resultant curve emphasizes differences in the area between 500 nm and 1000 nm. It is observed that site 47 which had high organic matter content showed a highly concave shape over this area. PC3 (Fig. 11.c) emphasizes variability on both sides of the 1000 nm band, hence, soils with high PC3 show higher values in bands centered around 1300 nm. This result agrees with correlation found between PC3 and band depth at 1400 nm. Perhaps this PC would be useful when using airborne data from AVIRIS when analysis of atmospheric water bands can not be used. The variability accounted for by the PC4 (Fig. 11.d) is smaller but gave some weight in the area between 500 nm and 1000 nm and in the area between 1500 nm and 1900 nm. Figure 12 shows the reconstruction of the original data using each eigenvector independently. In this case, the data are not standardized therefore, it can be observed that the range of variability of the third and fourth eigenvectors was much smaller than those of the first and second.
Another way to evaluate the importance of the principal components was to calculate the difference between the original spectral data and the reconstructed data. For this purpose the normalized mean squared error per site was calculated. Results showed that when only the first eigenvector was used, higher errors were concentrated at soils with low and high values of PC2, this corresponded to the extreme values in organic matter as well. When the first two eigenvectors were used the errors followed the same pattern with iron content and the values of the PC3. The errors calculated when using PC1-PC3 could not be correlated with a specific physicochemical variable but they follow the same trends with respect to PC4.
Canonical Discriminant Analysis was applied to investigate whether the two study locations could be spectrally discriminated and to analyze how iron and organic matter were related to this discrimination. The analysis was run using different numbers of PCs. The best discrimination between both valleys was found when the first five PCs were used (Fig. 13). Regression analyses show that the ratio organic matter/iron content was correlated with the first canonical variable (r2=0.51 with prob>F = 0.0001). It is interesting to note that the relationship between this ratio and the first canonical variable was stronger when the discriminant analysis is run only with the first three principal components (r2=0.7 with prob>F = 0.0001), while the discrimination between valleys was not as good (Fig. 14). This fact emphasizes the idea that PC2 and PC3 summarize the variability introduced by organic matter and iron contents. When other PCs are included in the analysis new sources of variability are added that help to discriminate between valleys but decrease the relative weights of iron and organic matter in the discrimination process. The crossvalidation and resubstitution errors are shown in Table 5.
Although band depth analysis could explain some of the variability of the data set, PCA was more explanatory not only in terms of summarizing information but also in finding relationships with physicochemical properties. Out of all the bands chosen only those at 1000 nm 1900 nm and 1400 nm showed some significant correlations with chemical data. When band depth analysis was used, spectra having low variability could not be discriminated while PCA was able to enlarge differences inside of this group. Since in this case soil chemical properties are not independent, it is not surprising that more than one of the PCs are related to the same soil property, such as PC3 that is related primarily to iron but also to organic matter.
Since the ultimate goal is to work with airborne AVIRIS data we were
interested in the impact of eliminating the water bands. PCA was applied
in two ways: by eliminating bands after the eigenvectors were calculated
and by calculating new eigenvectors after eliminating the water bands.
In the first case, the shape of the eigenvectors is the same but the new
variables are different, in the second case both the eigenvectors and the
new variables are different. In the first case, results show that the correlation
between organic matter and PC2 decreased from r2=0.51 to r2=0.43
with prob>F = 0.0001. Correlation between PC3 and iron content was completely
lost. In the second case, the correlation between PC2 and organic matter
content was r2=0.52 and between PC3 and iron content r2=0.39.
It seems that the weights that were initially given to the water bands
were redistributed along the whole spectra, and in this way the same amount
of information related to iron and organic matter was extracted. Figure
15 represent PC2 vs. PC3, it can be observed that the location of the
samples in the plot is very similar to their locations in Figure
9. The discrimination between valleys followed the same pattern.
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