Published online 29 September 2005
Published in Soil Sci Soc Am J 69:1782-1788 (2005)
DOI: 10.2136/sssaj2004.0362
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
Pedology
Soil Property Analysis using Principal Components Analysis, Soil Line, and Regression Models
Garey A. Fox* and
Roopa Metla
Dep. of Civil Engineering, Univ. of Mississippi, University, MS 38677-1848
* Corresponding author (gafox{at}olemiss.edu)
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ABSTRACT
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Past research has attempted to relate surface characteristics of soils to reflectance from remotely sensed images to provide a means for quantifying spatial heterogeneity. Existing procedures have proven valuable, but no research has been performed to compare these techniques. The objective of this research was to compare existing methodologies, that is, principal components analysis (PCA), Chen et al.'s regression model, and the soil line Euclidean distance (SLED) technique, for quantifying spatial heterogeneity in soil surface organic matter (OM) and cation exchange capacity (CEC). The three existing techniques were compared using five bare soil images from three different silt loam to loam fields in the Midwest USA. At the same time as image acquisition, surface (upper 2.54 cm [1 in]) soil properties were measured in situ. Organic matter and CEC were highly correlated (R2 > 0.70) to the first principal component (PC1) for three bare soil images, moderately correlated (R2 > 0.40) for one image, and only slightly correlated (R2 < 0.25) for the final image. The lower correlations were hypothesized to be because of the range in the soil OM and CEC and image exposure. Principal Component 1 accounted for approximately 95% of the total variance in all the fields; therefore, no correlation was observed between the upper 2.54 cm (1-in) surface soil properties and the second, third, or fourth principal components (PC2, PC3, and PC4, respectively). All three techniques equivalently predicted OM and CEC. However, PCA does not require field-specific regression or soil lines parameters. It is also suggested that PC1 can replace the soil line in a technique for identifying soil-sampling locations.
Abbreviations: B, blue • CEC, cation exchange capacity • DCL, data collection location • G, green • NIR, near infrared • OM, organic matter • PC1, first principal component • PC2, second principal component • PC3, third principal component • PC4, fourth principal component • PCA, principal component analysis • R, red • SLED, soil line Euclidean distance • SOC, soil organic carbon
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INTRODUCTION
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THE RELATIONSHIP between soil OM and remotely sensed measurements has been the subject of considerable research (Baumgardner et al., 1970; Al-Abbas et al., 1972; Vinogradov, 1982; Shonk et al., 1991; Chen et al., 2000; Fox and Sabbagh, 2002; Fox et al., 2004; Hong et al., 2004). Numerous researchers have attempted to relate surface characteristics of soils to reflectance from remotely sensed images thus providing a means for quantifying spatial heterogeneity without the collection of a large number of in situ soil samples.
Baumgardner et al. (1970) and Al-Abbas et al. (1972) performed the first airborne experiments to study the relationship between OM and reflectance in the visible and near-infrared (NIR) wavelengths. More recently, Chen et al. (2000) proposed a technique which relates surface organic C (SOC) content in the upper 15 cm of the soil profile to image intensities in the red (R), green (G), and blue (B) bands of the visible spectrum:
 | [1] |
where SOC is the surface organic content; R, G, and B are image intensity values in the red, blue and green bands, respectively; and a, b, c and d are curve-fit parameters. The Chen et al. (2000) regression technique has a drawback in that this technique requires field specific regression parameters that change significantly depending on parent material. Chen et al. (2000) reported that the relationship between soil OM and reflectance was poor when measurements were taken across large geographical areas, suggesting that the difficulties may be the result of different types of parent materials (Fernandez et al., 1988; Henderson et al., 1992; Schulze et al., 1993).
Another technique, called SLED, was proposed and evaluated by Fox and Sabbagh (2002). This technique estimated soil OM from R and NIR image intensity values by using the soil line concept. The soil line is a widely researched linear relationship between reflectance or image intensity in the R and NIR wavelengths (Campbell, 1996; Baret et al., 1993; Richardson and Wiegand, 1977):
 | [2] |
where NIR and R are near-infrared and red reflectance values, 
is the soil line slope, and ß is the soil line intercept. The soil line extends from a lower region representing darker soils to an upper region having high R and NIR values representing the brighter soils within the field. Pixels with reflectance values to the left of the soil line correspond to the vegetation (Curran, 1983).
The SLED technique requires the identification of the minimum point along the calculated soil line. The minimum point refers to the pixel with the lowest R and NIR intensity values, corresponding to the left-most extreme point on the soil line and representing the darkest soils within the field. The routine then calculates the distance (D) of each pixel's intensity values away from the soil line's minimum point. The SLED technique relates back to the properties that influence the soil line (i.e., soil texture, soil moisture, soil roughness, etc.), and therefore, overcomes the difficulties associated with the Chen et al. (2000) regression technique. The SLED technique also lends itself to a methodology for less intense soil sampling.
Evaluation of the SLED technique included in situ soil samples of OM from the upper 2.54-cm (inch) of the soil profile and digital, aerial, bare-soil images of two fields in the Midwest, USA. Fox and Sabbagh (2002) used an exponential function to characterize the relationship between a pixel's distance along the soil line with OM measured in the upper 2.54 cm (1 inch) of the soil profile:
 | [3] |
where OM is the surface organic matter content, D is the Euclidean distance along the soil line, and a and b are regression parameters with units of percentage OM and inverse image intensity value, respectively.
However, there are difficulties with the SLED technique. Fox and Sabbagh (2002) indicated that significant correlation exists between surface OM and image intensity in the B (400–500 nm) and G (500–600 nm) wavelengths, but failed to use these bands in their analysis. The SLED technique becomes cumbersome with higher dimensional soil planes that attempt to utilize multiple wavelengths (B, G, R, and NIR). The generation of bare soil lines and minimum soil line pixels in two-dimensional space can be difficult even with automated programs (Fox et al., 2004).
An additional body of literature exists on the use of a statistical technique called PCA (Dwivedi, 2001; Suk et al., 2002; Ray et al., 2002; Hong et al., 2004). Principal component analysis is a scene-dependent contrast enhancement and data compression technique (Kirby, 2001) typically associated with multiband imagery that reduces the redundancy contained within the data by creating a new series of images (components) in which the axes of the new coordinate systems point in the direction of decreasing variance (Singh and Harrison, 1985; Crist and Cicone, 1984). The original axes are rotated along the soil line in bare soil images to obtain new data sets called principal component images. The generated PCA images are uncorrelated and ordered by decreasing variance (Singh and Harrison, 1985). The transformed data points are linear combinations of their original data values weighted by their eigenvectors.
The longest axis of the principal components image refers to the brightness image and it has the maximum signal to noise ratio and largest percentage of the total variance (Lillisand et al., 2004). This is the PC1. In a pure bare soil image, the PC1 theoretically corresponds to the soil line. Each subsequent component contains the maximum variance for any axes orthogonal to the previous component. The second principal component (PC2) is perpendicular to the PC1, and generally refers to the greenness image (Crist and Cicone, 1984). Principal component 2 describes the largest amount of variance in the data that is not described by the PC1. The third principal component (PC3) is perpendicular to both PC1 and PC2. In a bare soil image, this component generally describes the moisture content in the plane of soils (Jensen, 1996). Principal component analysis has been shown to reduce the volume of hyperspectral data and be potentially useful for developing soil property variability relationships (Hong et al., 2004).
Existing procedures have proven valuable (Hong et al., 2004; Fox and Sabbagh, 2002; Chen et al., 2000), but no research exists that compares these techniques. Therefore, the objective of this research was to compare existing techniques for relating surface soil properties to remotely sensed images under a number of different imaging conditions. Also, this research attempted to expand relationships between remotely sensed bare soil images and surface properties (i.e., for soil properties intricately linked to OM such as CEC). Theoretically, since CEC is correlated to the percentage of OM for certain soil conditions, techniques for quantifying heterogeneity in surface OM should also prove valuable for CEC. The research investigated relationships between principal components with surface OM and CEC; compared the strengths of the relationships for the Chen et al. (2000) regression, SLED, and PCA techniques; and further investigated the performance of the techniques relative to soil and environmental conditions.
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MATERIALS AND METHODS
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Site Description and Images
This research utilized five bare soil images of three different silt loam to loam fields: Field 1 (1997, 1998), Field 2 (1997, 1998), and Field 3 (1997). Surface measurements were made from the top 2.54 cm (1 in) of the soil surface at each data collection location (DCL) following procedures outlined by Page et al. (1982) for OM and CEC.
Field 1 was a 42.9-ha and located in Buchanan County, IA. This field is generally under a corn (Zea mays L.) and soybean (Glycine max L.) crop rotation. Eight soil series were located within this field: Burkhardt silty loam (sandy, mixed, mesic Typic Hapludolls), 2 to 5% slopes; Flagler sandy loam (coarse-loamy, mixed, superactive, mesic Typic Hapludolls), 0 to 2% slopes; Clyde clay loam (fine-loamy, mixed, superactive, mesic Typic Endoaquolls), 1 to 4% slopes; Readlyn loam (fine-loamy, mixed, superactive, mesic Aquic Hapludolls), 1 to 3% slopes; Olin fine sandy loam (coarse-loamy, mixed, superactive, mesic Typic Hapludolls), 2 to 5% slopes; Sparta loam in sand (sandy, mixed, mesic Entic Hapludolls), 2 to 5% slopes; Schley variant sandy loam (fine-loamy, mixed, superactive, mesic Udollic Endoaqualfs), 1 to 4% slopes; and Kenyon loam (fine-loamy, mixed, superactive, mesic Typic Hapludolls), 2 to 5% slopes. Ranges of soil properties in the upper 2.54 cm (inch) of the soil profile were 1.4 to 8.9% (w/w basis) for surface OM and 5.4 to 29.3 cmol kg–1 for CEC. Bare soil images of Field 1 were acquired on 21 May 1997 and 10 May 1998. Data collection locations (DCLs) are shown in Fig. 1 for 1997 (80 DCLs) and 1998 (123 DCLs). Soil moisture variations were deemed insignificant based on twelve time domain reflectrometry (TDR) measurements located randomly throughout the field. Coefficient of variation (i.e., mean divided by the standard deviation) in soil moisture for this field at the time of image acquisition was <10%.
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Fig. 1. Field boundary and data collection locations for a 42.9-ha field (Field 1) in Buchanan County, IA in (A) 1997 and (B) 1998.
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Field 2, located in Fremont County, IA, was also managed under a corn and soybean crop rotation, and bare soil images were acquired on 22 May 1997 and 16 May 1998. Figure 2
shows the 105 DCLs and 81 DCLs for the 1997 and 1998 bare soil images, respectively. This field was 32.4-ha with two prevalent soil series: McPaul silty loam (coarse-silty, mixed, superactive, calcareous, mesic Mollic Udifluvents), 0 to 2% slopes; and Moville silty loam (coarse-silty over clayey, mixed, superactive, calcareous, mesic Aquic Udifluvents), 0 to 2% slopes. Ranges for the top 2.54 cm (inch) soil properties were 1.2 to 2.9% (w/w) for surface OM and 11.0 to 22.0 cmol kg–1 for CEC. Soil moisture variations were deemed insignificant based on twelve TDR measurements. The coefficient of variation was <10% for moisture content at image capture.
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Fig. 2. Field boundary and data collection locations for a 32.4-ha field (Field 2) in Fremont County, IA in (A) 1997 and (B) 1998.
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Field 3, located in Mclean County, IL, was also managed under a corn and soybean crop rotation. The bare soil image used in this research was acquired on 10 June 1997. Figure 3
illustrates the 59 DCLs within this 1997 bare soil image. This field was 27.1 ha and due to production losses in the past, the field had been tiled to improve drainage. Although six distinguishable soil types can be found within this field, most of the land area was classified as Chenoa silt loam (fine, illitic, mesic Aquic Argiudolls) or Ashkum silt loam (fine, mixed, superactive, mesic Typic Endoaquolls), with <2% slopes. Ranges for the top inch soil properties were 3.4 to 5.6% (w/w) for surface OM and 20.1 to 38.8 cmol kg–1 for CEC. Soil moisture variations were deemed insignificant based on six surface TDR measurements. The coefficient of variation was <5% for moisture content at image capture during the 1997-growing season.
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Fig. 3. Field boundary and data collection locations for a 27.1-ha field (Field 3) in Mclean County, IL (1997).
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The images of all the fields were acquired using a digital aerial photography system, which is a part of the Airborne Data Acquisition and Registration (ADAR), manufactured and marketed by Positive Systems (Positive Systems, Inc., Whitefish, MT). The system provides four bands of data corresponding to B (400–500 nm), G (500–600 nm), R (600–700 nm), and NIR (700–1000 nm) wavelengths, with a spatial resolution of 0.5 m. All images were acquired before crop emergence.
Application of Remote Sensing Techniques
The SLED technique was applied using the R and NIR bands of all pixels within the field boundaries of each image. The soil lines were calculated and the minimum point on the soil line was identified. Relationships were derived between the Euclidean distance (D) of the DCL's intensity values from the minimum point and the surface OM measurements. Even though the soil line technique was developed for OM, SLED was also applied for CEC. Regression coefficients were then calculated through nonlinear regression for the Chen et al. (2000) technique by assuming OM equals 1.72 times SOC (Fox and Sabbagh, 2002). The relationships were again used to predict OM at each DCL for all pixels within the field.
Principal component analysis was applied to all pixels' four bands (B, G, R, and NIR) within the bare soil images of all fields. Since PCA is scene dependent, it should be emphasized that pixels utilized with the technique were only within the sampled fields. Steps in PCA included calculating univariate statistics, a covariance matrix, a correlation matrix, the eigenvalues and eigenvectors, the degree of correlation, and new brightness values (principal components). Transformation coefficients were obtained to reproject the original data onto the principal component axes. The linear transformation was derived from the covariance matrix of the original data set. The covariance was calculated by computing the corrected sum of products (SP). Covariance between brightness values were calculated by dividing the sum of products (SP) by (n –1), just as the variance was calculated by dividing the corrected sums of squares (SS) by (n –1).
The correlation coefficient, r, was used to estimate the degree of interrelation between variables. Using the covariance matrix, the eigenvalues and eigenvectors were obtained from MATLAB (The MathWorks Inc., Natick, MA). The eigenvalues are equal to the variance of each corresponding components image. The eigenvectors define the axes of the components. New brightness values based on the principal components were calculated from brightness values and the eigenvector matrix:
 | [4] |
where akp are the eigenvectors in Band k for Component p, BVi,j,k are the brightness values in Band k for the pixel at Row i and Column j, and n is the number of bands.
To further evaluate the predictive capability of the techniques, DCLs within each field were then randomly divided into two groups: one group to derive the predictive relationships for each technique and the other group to evaluate the predictive capability of the derived equations. Derived relationships for PCA, regression, and SLED techniques based on the first group of DCLs were used to predict the OM at each pixel within the evaluation group. Linear regression was performed between predicted and observed OM and CEC within the evaluation group of DCLs.
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RESULTS AND DISCUSSION
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Using all pixels within the bare soil images, a comparison of the strength of relationships between SLED and PCA for OM and CEC are shown in Fig. 4 and 5
for the 1998-bare soil image of Field 1. This same bare soil image was utilized by Fox and Sabbagh (2002) to evaluate the Chen et al. (2000) regression and SLED techniques for OM. For this image, both the Chen et al. (2000) regression and SLED techniques resulted in regression coefficients (R2) of 0.68 for OM when assuming OM to be 1.72 times SOC (Fox and Sabbagh, 2002). For PCA, the percentages of total variance by the PC1 and the PC2 were approximately 95 and 3%, respectively, in each bare soil image. The relationship between PC1 and surface OM and CEC was strong (R2 > 0.70) in three of the five images, moderately strong (R2 > 0.40) in the 1997 bare soil image in Field 2, and weakly correlated (R2 < 0.25) in the 1997 bare soil image of Field 3.
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Fig. 4. Relationship between percentage of surface organic matter (OM) and (A) first principal component (PC1) and (B) distance along the soil line (D) in SLED technique for all pixels within Field 1 (1998).
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Fig. 5. Relationship between surface cation exchange capacity (CEC) and (A) first principal component (PC1) and (B) distance along the soil line (D) in SLED technique for all pixels within Field 1 (1998).
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Similar results were observed between OM and CEC because of their correlation in silt loam and loam soil types. The population correlation between measured OM and CEC, calculated as the covariance of two data sets divided by the product of their standard deviations, were 0.94 and 0.91 for the 1997 and 1998 soil samples in Field 1, 0.62 and 0.78 for the 1997 and 1998 soil samples in Field 2, and 0.66 for the 1997 soil samples in Field 3. Larger correlation generally predicted improved performance when extending the OM techniques into quantifying CEC surface heterogeneity. Extensions of such OM techniques to CEC were most suited in fields with considerable surface organic matter content (i.e., OM > 3% as a first approximation) and silt and loam soils. The second, as well as third and fourth, principal components did not correlate to surface soil properties within any of the five bare soil images.
The DCLs in each field were then randomly divided into two groups: one group to develop the predictive equations and the other group to evaluate the ability of the techniques to predict OM and CEC. Results of the linear regression between observed and predicted OM and CEC for each technique is shown in Tables 1 and 2, respectively. The regression coefficients in PC1, SLED, and the Chen et al. (2000) regression techniques were similar with no one technique outperforming the other techniques. Therefore, PCA appeared to provide equivalent regression coefficients for surface OM and CEC content without requiring automated programs to extract soil line parameters and/or nonlinear regression to quantify regression parameters for the fields.
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Table 1. Results of linear regression ( = slope, ß = intercept, and R2 = regression coefficient) between predicted and observed soil surface organic matter (OM) for half of the data collection locations using Principal Components Analysis (PCA), Soil Line Euclidean Distance (SLED), and Chen et al. (2000) regression techniques. PC1 and PC2 refer to the first and second principal components within PCA.
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Table 2. Results of linear regression ( = slope, ß = intercept, and R2 = regression coefficient) between predicted and observed soil surface cation exchange capacity (CEC) for half of the data collection locations using Principal Components Analysis (PCA) and Soil Line Euclidean Distance (SLED) technique. PC1 and PC2 refer to the first and second principal components within PCA.
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As mentioned previously, correlations between PC1 and OM and CEC were not as strong in the 1997-bare soil image of Field 2 and the 1997-bare soil image of Field 3. Hypotheses included a possible relationship between the performance of the PCA technique, and correspondingly the SLED and Chen et al. (2000) techniques, with the range of values in OM or CEC measured in the field and/or the range of image intensity values in each wavelength band. Clustering of pixels due to less than optimal image conditions (i.e., overexposure, clouds, or shadows) could restrict the ability of the techniques to detect reflectance differences between soil properties.
There appears to be only a slight correlation between the performance of the techniques and the range of OM or CEC in the fields (Table 3). Furthermore, the techniques performed adequately in subsequent year bare soil images, suggesting that the differences were not solely due to the range of soil property values but were also associated with imaging or other field conditions. There was no dependency on the strength of the relationship and the range of image intensity values in a specific wavelength band. Linear regression between the range of image intensity in the R and NIR bands versus regression coefficient resulted in slopes < 0.01, intercepts > 0.6 and R2 < 0.01 for all three techniques.
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Table 3. Results of linear regression ( = slope, ß = intercept, and R2 = regression coefficient) between the range of organic matter (OM) and the performance of Principal Components Analysis (PCA), Soil Line Euclidean Distance (SLED) and Chen et al. (2000) regression techniques.
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One hypothesis for the reduced performance of all three techniques in the 1997 image of Field 2 involves microshadow prevalence. In the 1997 image of Field 2, the image was bright (Fig. 2) such that vegetation in the image was underexposed. Also, fluvents (Entisols whose development is hindered by frequent flooding and deposition) are easily slaked by raindrop impact (Lado et al., 2004). This process reduces microshadows. As can be observed from visual inspection of the images, Field 2 appeared to be tilled closer to image acquisition in 1998 as compared with tillage in 1997. Because the field was freshly worked, microshadows were still present in this field at the time of image acquisition and exposure was improved. Such hypotheses need to be further verified with other bare soil images acquired collectively with in situ soil samples.
This research highlights the strength of the PCA technique and suggests the continued use of the technique for detecting spatial heterogeneity in surface soil properties. Other soil properties have been related to principal components in the use of PCA with hyperspectral images (Dwivedi, 2001; Ray et al., 2002; Suk et al., 2002; Hong et al., 2004). The Chen et al. (2000) regression technique is limited to the B, G, and R wavelengths. The SLED technique becomes cumbersome for higher-dimensional soil planes when including information from wavelengths other than R and NIR.
A strength of the SLED technique was the ability to use field-specific soil conditions, which correspondingly allows a procedure to guide soil sampling. Fox and Sabbagh (2002) referred to their procedure as the seven-point percentile method in which specific percentile locations along the soil line could be selected to guide in situ soil samples at seven field locations. These seven soil samples were shown to detect the range of OM within the field and provide information to develop predictive equations for characterizing the entire surface OM heterogeneity. The seven-point percentile method can also be used with PC1 simply by computing the range of brightness values or reflectance along PC1 and calculating the suggested seven percentiles.
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CONCLUSIONS
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This research compared existing remote sensing techniques (i.e., Chen et al. (2000) regression model, SLED, and PCA) under a number of different soil and environmental conditions. This research applied all three techniques to image intensity in B, G, R, and NIR bands of digital aerial images of five bare soil images. At equivalent times to aerial image acquisition, upper 2.54-cm (1 in) soil properties (OM and CEC) were measured in situ at DCLs. The strength of relationships derived from the techniques with measured OM and CEC were first determined using all data collection locations within the fields. In general, OM and CEC correlated to the PC1 within PCA for all bare soil images. The strength of the correlation was strong (R2 > 0.70) in three of the five bare soil images. The DCLs were then divided into two groups: one group to develop predictive equations and the other group to evaluate the predictive equations. The first principal component, SLED, and the Chen et al. (2000) regression techniques were similar with no one technique outperforming the others. Relationship strength was found to be slightly correlated to the range of OM and CEC measured in the fields and not correlated to the range of image intensity values in any specific wavelength for all three techniques. In general, PCA provided the most efficient approach for determining relationships that predict OM and CEC from remotely sensed images. The SLED technique uses the soil line, which is defined from the bare soil image, to identify the most appropriate soil sampling locations in the field, whereas PC1 represents the soil line without the need to derive soil line parameters. Principal component analysis can also utilize hyperspectral images (Hong et al., 2004). It is suggested in this research that PC1 can be used in lieu of the soil line in the seven-point percentile method to guide soil sampling.
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ACKNOWLEDGMENTS
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The authors acknowledge the technical guidance of George J. Sabbagh, Environmental Research Division, Bayer Crop-Science, Stilwell, KS; Greg L. Easson, Associate Professor, Department of Geology and Geological Engineering, University of Mississippi, University, MS; and Amanda K. Fox, Consultant, Oxford, MS.
Received for publication November 22, 2004.
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TOP
ABSTRACT
INTRODUCTION
