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DIVISION S-6 - SOIL & WATER MANAGEMENT & CONSERVATION

Soil Water Retention as Related to Topographic Variables

^a USDA-ARS Hydrology and Remote Sensing Lab., Bldg. 007, Rm. 104, BARC-WEST, Beltsville, MD 20705
^b USDA-ARS Alternate Crops and Systems Lab., Bldg. 007, Rm. 116, BARC-WEST, Beltsville, MD 20705

* Corresponding author (ypachep{at}hydrolab.arsusda.gov)

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS NOTES DISCUSSION REFERENCES

 
Digital elevation models were proposed and used as a data source to estimate soil properties. This study evaluated variability of texture and water retention of soils for a gently sloping 3.7-ha field located in the long-term precision farming research site at the Beltsville Agricultural Research Center, MD. The specific objectives of this research were (i) to characterize variability of water retention across the hillslope, and (ii) determine and describe any correlations of soil water retention with soil texture and surface topography. Soil was sampled along four 30-m transects and in 39 points within the study area. Textural fraction contents, bulk density, and water retention at 0, 2.5, 5.0, 10, 33, 100, 500, and 1500 kPa were measured in samples taken from 4- to 10-cm depth. A 30-m digital elevation model (DEM) was constructed from aerial photography data. Slopes, profile curvatures, and tangential curvatures were computed in grid nodes and interpolated to the sampling locations. Regressions with spatially correlated errors were used to relate water retention and texture to computed topographic variables. Sand, silt, and clay contents depended on slope and curvatures. Soil water retention at 10 and 33 kPa correlated with sand and silt contents. The regression model relating water retention to the topographic variables explained more than 60% of variation in soil water content at 10 and 33 kPa, and only 20% of variation at 100 kPa. Increases in slope values and decreases in tangential curvature values, i.e., less concavity or more convexity across the slope, led to the decreases in water retention at 10 and 33 kPa. Results of this work show a potential for topographic variables to be used in interpretation of field-scale variability of soil properties and, possibly, yield maps in precision agriculture.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS NOTES DISCUSSION REFERENCES

 
AGRICULTURAL and environmental modeling and assessment have many uses for soil hydraulic properties. These properties are notorious for difficulties and high labor costs involved in measuring them. Therefore, there is a trend to estimate soil hydraulic properties from other readily available data (Bouma, 1989; Rawls et al., 1991). Until recently, estimation of soil hydraulic properties was done exclusively from other soil properties available from soil survey (Pachepsky et al., 1999). However, the level of detail given by soil surveys is not sufficient in some applications, in particular, applications related to site-specific agriculture (Schepers and Francis, 1998).

Soil properties are known to be related to landscape position (Ruhe, 1956). Geomorphic information has long been routinely used in soil mapping (Northcote, 1954). Geomorphometry was proposed as a data source to predict soil properties (Moore et al., 1993; McKenzie and Austin, 1993; McSweeney et al., 1994).

Two basic approaches to relate soil properties to landscape position have been suggested to date. The first is based on separating hillslopes into distinct sections, i.e., summit, upper and lower interfluve, shoulder, backslope, upper and lower linear, footslope, toeslope, etc. It has been shown that soil properties within a section vary much less than between sections, so that distinct values of soil properties can be assigned to each section (Ovalles and Collins, 1986). Section-specific regression equations can also be developed to correlate soil properties (Brubaker et al., 1994).

The second approach to relate soil properties to landscape positions is to use topographic variables, or terrain attributes, i.e., mathematical characteristics of the land surface shape, such as slope, profile, plan and tangential curvatures, and aspect (Evans, 1980; Mitásova and Hofierka, 1993; Shary, 1995). These variables can be computed directly at the nodes of a grid and used for statistical correlation with soil properties at these nodes (Walker et al., 1968; Kingbiel et al., 1987; Odeh et al., 1991; Moore et al., 1993). Topographic variables can be used to subdivide the terrain into areas having distinctly different shapes, and average values of soil properties can be defined for these areas (Kreznor et al., 1989; Pennock and de Jong, 1987; Lark, 1999). The topographic variables are also employed to generate secondary terrain attributes, like wetness index or sediment transport index, that in turn can be used in soil-landscape correlations (McSweeney et al., 1994; Thompson et al., 1998, McKenzie and Ryan, 1999).

The readily available information on relationships between soil hydraulic properties and topographic variables is surprisingly scarce, although published results demonstrate some strong correlations (Halvorson and Doll, 1991; Mapa and Pathmarajah, 1995). Much more is known about dependencies of soil hydraulic properties on soil texture, organic matter content, and bulk density (Pachepsky et al., 1999). Soil texture, organic matter, and bulk density are known to reflect landscape position (Van den Broek et al., 1981; Kreznor et al., 1989). Therefore, one can hypothesize that soil hydraulic properties should have some relationship to landscape position. However, different basic soil parameters may have different dependencies on landscape position, and this may weaken dependencies of soil hydraulic properties on topographic variables.

This study evaluated variability of texture and water retention of soils across a gently sloping field located in the long-term precision farming research site at the Beltsville Agricultural Research Center, MD. We hypothesized that differences in water retention might account for observed variability in yields. The specific objectives of this research were (i) to characterize variability of water retention across the hillslope and (ii) to determine and describe any correlations of soil water retention with soil texture and surface topography.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS NOTES DISCUSSION REFERENCES

 
Study Area and Data Collection
The 3.7-ha study area, located at the USDA Beltsville Agricultural Research Center, MD, (76°50'25'' W, 39°01'15'' N), is a long-term site for studying crop and soil management used in precision farming research in nonirrigated conditions. Soil cover of the site is defined as Cedartown-Galestown-Matawan soil association (NRCS, 1995). Cedartown and Galestown are siliceous, mesic Psammentic Hapludults, whereas Matawan is fine loamy, siliceous, semiactive, mesic Aquic Hapludult. Slope gradients range from 0 to 5%, and the predominant topsoil texture has been defined as a loamy sand for this soil association by the soil survey. Table 1 presents some characteristics of these soils from the soil survey report (NCRS, 1995).

View larger version (26K): [in this window] [in a new window]   Fig. 1. Location of sampling sites and topography of the site; symbols , •, , and show location of 30-m long Transects A, B, C, and D, respectively, grid sampling locations are shown with symbol .

Topographic Variables
Elevation values were obtained from a digital elevation model constructed by interpolation of the photogrammetric mass points data to nodes of a 30- by 30-m grid. The 30-m spacing was selected as the spacing at which the USGS made available DEMs for the USA (7.5-Minute DEM 30- by 30-m data spacing at http://rockyweb.cr.usgs.gov/elevation/dpi_dem.html; verified July 9, 2001). This resolution was assumed to be sufficient to capture the spatial variability of gently sloping terrain in the study area. Because there is no unanimous opinion regarding the best method to interpolate topography (Wise, 1998), we built five different DEMs using inverse square distance interpolation, kriging, minimum curvature interpolation, radial basis function method, and triangulation with linear interpolation. Those were selected on the basis of common methods reported in the literature. All DEMs were built by the SURFER software version 7.00 (Golden Software, Inc., 1999).

Values of maximum slope, profile curvature and tangential curvature were used as topographic variables for the study area. Profile curvature is defined as curvature of the surface cross-section made in the direction of maximum slope. This is the uphill rate of change in slope. Negative (positive) values of profile curvature indicate convex (concave) flow paths where a surface flow accelerates (slows down). Tangential curvature is defined as curvature of the vertical surface cross-section made perpendicular to the direction of maximum slope. Negative (positive) values of tangential curvature represent areas of divergent (convergent) flow (Mitásova and Hofierka, 1993). Maximum slope (s), the profile curvature (v), and the tangential curvature (h) can be expressed by derivatives of the dependence of the elevation z = f on horizontal coordinates x and y (Evans, 1980):

[1]

Here f_x, f_y, f_xx, f_xy, f_yy are partial derivatives of the function f(x,y):

[2]

The partial derivatives were estimated from a grid-based digital elevation model by the moving three-by-three grid network described by Moore et al. (1993). The second order polynomial

[3]

was fitted to the nine points of three-by-three networks and values of p, q, r, s, u and t were computed as suggested by Shary (1995):

[4]

Here the first and the second subscripts denote the grid lines parallel to the y and x axes, respectively, w is the grid spacing. These coefficients were used in Eq. [2] as approximations of the derivatives

[5]

Values of slopes and curvatures were computed at all but boundary nodes of the elevation grids by means of Eq. [1] to [5]. Values of slopes and curvatures at the points of water retention and texture measurements were computed from the nodal values of those variables by bilinear interpolation (Press et al., 1992). Slopes are unitless, curvatures have the dimension per meter in this study.

Statistical Analysis
A linear regression was used to express the dependencies of water retention on topographic variables and to estimate the proportion of variation in water retention that could be explained by topographic variables. The data had spatial structure, and for this reason we used the least square model with correlated errors (Thisted, 1988).

The linear regression model

[6]

relates the vector of observed water retention values to the matrix of values of topographic variables T. The vector has m elements, _i, i = 1,2,3, ... m, m is the number of measurements. The matrix T has elements t_ij which are values of the jth topographic variable in the ith measurement point; j = 1,2, ... N, and N is the total number of topographic variables taken into regression. The vector ß contains regression coefficients ß_j, j = 1,2, ... N. Vector ₀ and matrix T₀ contain average values of observed water retention and topographic variables, respectively. The vector contains the regression errors _i, i = 1,2,3, ... M.

In the ordinary least square model, errors _i are assumed to be independent and to belong to the same normal distribution (0, ²) with the zero mean and the variance ². Therefore, the vector belongs to the normal distribution of independent normally identically distributed values (0, ²I) where I is the identity m x m matrix with all diagonal elements equal to one. Because there is correlation between errors, all off-diagonal elements are equal to zero. This model has N+1 parameters, N values of ß_j and value of ² to be found from the data.

In the least square model with correlated errors, errors _i belong to normal distribution (0, ²C), where C is the m x m correlation matrix, so that C_ik is the correlation coefficient between ith and kth error. The semivariogram of errors is used to compute the elements of the correlation matrix as

[7]

Here is the semivariogram, d_ik is the distance between the ith and kth sampling points, ² is the sill of the semivariogram (Pinheiro and Bates, 2000). This regression model has more parameters than the ordinary least square model; the list of parameters includes the range, , and the nugget effect, c₀, of the semivariogram along with N values of ß_j and the value of sill ². Estimates of values of ß_j, ², , and c₀ are computed simultaneously during a nonlinear optimization with the minimum likelihood criterion.

We used Splus software (MathSoft, 1999) to fit the least square model with correlated errors to our dataset. Averages of duplicated measurements were used for this regression. The software required specifying the type of semivariogram equation and initial estimates for the range and nugget. To specify the type of semivariogram equation, we applied the ordinary least square model first, obtained values of errors, and computed their semivariogram with the SURFER software (data not shown). An isotropic semivariogram was used because of the similarity in orientation of transects. The visual inspection of graphs suggested that the Gaussian variogram model with the nugget in the form

[8]

is the most suitable for our data. Initial estimates of the range and the nugget effect were set at 10 m and at 0.2, respectively.

The t-test, F-test, and the Kolmogorov-Smirnov tests were used to test hypotheses about the equality of average values, equality of variances and the difference between distributions of regression residuals and normal distribution, respectively. All statistical comparisons were made at the 0.05 significance level.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS NOTES DISCUSSION REFERENCES

 
The spatial distribution of soil texture is shown in Fig 2 ¹. Sands, loamy sands, and sandy loams are represented in the study area. The range of textures is wider than suggested by the soil survey. A comparison of Fig. 1 and Fig. 2 shows that soils on steeper slopes represented by Transects B and D are richer in sand and poorer in silt than soils in Transects A and C.

View larger version (42K): [in this window] [in a new window]   Fig. 2. Distribution of soil texture. Symbols in the textural triangle are the same as in Fig. 1.

View larger version (18K): [in this window] [in a new window]   Fig. 3. Comparison of elevation interpolation methods used to compute topographic variables in sampling locations; —inverse distance interpolation, —kriging, —radial basis functions, —triangulation with linear interpolation all compared with the minimum curvature method. Lines show one-to-one dependencies.

View larger version (45K): [in this window] [in a new window]   Fig. 4. Relationships between soil textural component contents and topographic variables; symbols , •, , and show data from Transects A, B, C, and D, respectively, grid sampling is shown with symbol . a, b, c, d—minimum curvature, inverse square distance interpolation, kriging, and radial basis functions interpolation methods, respectively.

View this table: [in this window] [in a new window]   Table 2. Soil texture and soil water retention in transects.

View larger version (53K): [in this window] [in a new window]   Fig. 5. Relationships between soil water retention and contents of textural components; symbols , •, , and show data from Transects A, B, C, and D, respectively, grid sampling is shown with symbol .

View larger version (52K): [in this window] [in a new window]   Fig. 6. Relationships between soil water retention and topographic variables; symbols , •, , and show data from Transects A, B, C, and D, respectively, grid sampling is shown with symbol .

[9]

Results of the regression analysis are shown in Table 3. The distributions of residuals did not significantly differ from normal distributions, and residuals did not show any spatial dependence. Slope, profile, and tangential curvatures used as predictors could explain about 67% of the variation in water retention at capillary pressures of 10 and 33 kPa. Topographic variables were not good predictors for the water retention at 100 kPa, being able to explain only about 20% of variation. Regression coefficients for the profile curvature were not significantly different from zero for 10 and 33 kPa capillary pressures. For the 100 kPa capillary pressure, regression coefficients for curvatures had low statistical significance. Ranges and nugget effects of the semivariograms of errors were similar for all three matric potential level. Signs of the coefficients in the regression equation indicated a decrease in water retention with an increase in slope or with the increase in convexity of the land surface shape across the slope. Sites with larger tangential curvature, i.e., with larger convergence of flows, had larger water retention. The interpolation method had only small effect on the accuracy of regressions and variance explained by regression (data not shown).

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS NOTES DISCUSSION REFERENCES

The dependence of water retention on clay content was weaker than on other textural components. This seemingly contradicts other studies in which clay content was a leading predictor of water retention (Rawls et al., 1991). However, the range of soil clay contents was much narrower of this study (Fig. 3, 4). The effects of organic matter on water retention might also obscure the effect of clay content on water retention.

A search for the dependencies of water retention on topographic variables is justified only if (i) water retention is significantly different in different parts of the landscape, and (ii) the accuracy of relationships between water retention and topographic variables is comparable with the accuracy of average water retention estimates within a DEM grid cell. Both of these conditions are met in this study. Table 2 shows significant differences in water retention among transects at different landscape positions in the capillary range of soil matric potential. Soil variability within the 30 m DEM cells was represented by the variability within the 30-m transects in this study. Residual mean square errors of the regressions for 10 and 33 kPa (Table 3) were not significantly different from standard deviations of measured water contents across transects in most cases.

The accuracy of the water retention estimation from topographic variables can be limited both by the accuracy of the elevation estimates and by errors in interpolation and differentiation used to obtain the topographic variables from elevations. An increase in the density of elevation data could provide better estimates of curvatures. We did not observe any substantial effect of the interpolation method on the accuracy of the relationships between water retention and topographic variables, probably, because land surface is gently sloping at the site. However, this result cannot be generalized. Arguments for the use of various interpolation methods for elevation data have been made by many authors (see for examples Hutchinson 1989; De Floriani and Puppo, 1995; Wise, 1998). Uncertainty in the interpolation method selection obviously remains unresolved. Yet one more factor affecting the accuracy of the topographic variables is the type of approximations used to compute the same topographic variable. For example, computations of the curvatures and slopes differ in works of Shary (1991), Moore et al. (1993), and Florinsky and Kuryakova (1996). Wise (1998) has demonstrated that the different algorithms used to calculate gradient and aspect in different GIS packages can produce quite different results from the same DEM. A few secondary topographic variables derived from the slopes and curvatures, i.e., catchment area, wetness index, streampower index, flow path length, were listed as potentially useful variables in soil landscape relationships. In summary, there exist various approaches to topographic variable computations, and some experimentation may be necessary to select a procedure that will give the best predictors of soil water retention.

The semivariograms of errors had ranges between 10 and 14 m, which were well within the lengths of transects. That, and a relatively small nugget effect (Table 3), underscored the need for the use of the least square model with correlated errors instead of the ordinary least square model. It was assumed that the variance of errors is the same for observations in all parts of the landscape. We did not have enough data to investigate the heteroscedasticity, i.e., nonequal variances in different parts of the landscape, which also can be handled in least square models with correlated errors (Pinheiro and Bates, 2000).

Substantial differences in soil texture were encountered along the slopes in this study, although slopes were gentle (slope gradients < 5%). The topography-correlated differences in soil texture can be attributed both to the differences in parent material and to erosion processes (Sobecki and Karathanasis, 1992; Tomer and Anderson, 1995). A differentiation in texture with splash and wash was recently observed in controlled experiments. Sutherland et al. (1996) observed in laboratory experiments a preferential removal of fine material with splash and wash that with time was likely to produce a coarser, nutrient depleted interrill soil matrix. Martinez-Mena et al. (1999) found that the texture of the sediment collected for two years from cropped and bare plots was finer than the texture of the matrix soil. The former was on the border between clay loam and silty clay loam, whereas the latter was close to the border between silty clay loam and silt loam. Even gentle slopes have a potential for a substantial texture differentiation.

The strongest relationship between soil water retention and topographic variables was observed at capillary pressures of 10 and 33 kPa, i.e., in the range where the soil reaches its field capacity. As the water content at the wilting point did not vary substantially, the available water capacity depended on landscape position. The strong effect of the landscape position and topographic variables on crop yields and on the impact of the weather pattern on yields in different parts of fields was documented in several studies (i.e., Halvorson and Doll, 1991; Simmons et al., 1989; Timlin et al., 1998). This effect is probably related to the spatial pattern of the available water capacity distribution, since the available water capacity is one of most important soil variables that affect yields of rainfed crops. Results of this work show a potential for the topographic variables to be used as interpretive attributes for yield maps in precision agriculture.

	ACKNOWLEDGMENTS

 
The authors are grateful to Dr. Seth Dabney and Dr. Matthew Kramer for their helpful suggestions. This research was partially supported by the NASA Land Surface Hydrology Program.

	NOTES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS NOTES DISCUSSION REFERENCES

 
¹ The map is obtained by means of the SURFER software using the inverse distance interpolation from sampling points.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS NOTES DISCUSSION REFERENCES

 

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