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DIVISION S-6—SOIL & WATER MANAGEMENT & CONSERVATION

Soil Carbon Maps

Enhancing Spatial Estimates with Simple Terrain Attributes at Multiple Scales

^a Dep. of Agronomy, Univ. of Kentucky N-122 Ag. Science North, Lexington, KY 40546-0091
^b Center for Precision Agricultural Systems, Washington State Univ., Irrigated Agricultural Research and Extension Center, 24106 N. Bunn Road, Prosser, WA 99350-8694

* Corresponding author (mueller{at}uky.edu)

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
The quality of soil property maps may be improved and spatial sampling intensities reduced by incorporating secondary data to enhance spatial estimates. The purpose of this study was to evaluate how scale of sampling and secondary spatial information (terrain attributes) affected the quality of spatial estimates of soil C. A field in Central Michigan was sampled using 30.5- and 100-m regular grids and the samples were analyzed for total C. Extracting a 61-m grid from the 30.5-m regular grid (G₃₀) data set created an additional data set. Total C maps were created at each scale using ordinary kriging, kriging with a trend model, cokriging, kriging with an external drift, and multiple regression. Each resulting map was compared with an independent validation data set (n = 24) to evaluate map quality. At the 30-m grid scale, there were modest differences between maps created with ordinary kriging (root mean squared error [RMSE] = 2.9 g kg^-1, isotropic model; RMSE = 3.0 g kg^-1, anisotropic model), kriging with a trend model (RMSE= 2.8 g kg^-1), cokriging (RMSE = 2.9 g kg^-1), kriging with an external drift (RMSE = 2.6 g kg^-1), and multivariate stepwise regression (RMSE = 3.2 g kg^-1). Prediction errors were generally larger at the 61-m grid scale and procedures that utilized secondary the terrain data (cokriging, RMSE = 3.8 g kg^-1; kriging with an external drift, RMSE = 3.8 g kg^-1; stepwise multiple regression, RMSE = 3.0 g kg^-1) outperformed procedures that did not (isotropic ordinary kriging, RMSE = 4.3 g kg^-1; kriging with a trend model, RMSE = 4.3 g kg^-1). At the 100-m grid (G₁₀₀) scale, geostatistical procedures were not appropriate because of the small sample size (n = 12) yet multiple regression performed well (RMSE = 3.8 g kg^-1). Maps of soil C created with regression most resembled the soil color patterns evident in an aerial photograph of the field.

Abbreviations: ATV, all terrain vehicle • DEM, digital elevation model • G₃₀, 30.5-m regular grid • G₁₀₀, 100-m regular grid, G_VAL, validation data set • G₁₀₀₀, 1000 randomly selected points • GPS, global positioning system • IAVIF, intercept adjusted variance inflation factors • MSE, mean squared error • RMSE, root mean square error • RSV, relative structural variability

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
DETAILED MAPS of soil properties needed for soil use and management decisions are usually created with traditional survey methods or interpolation of grid soil sampling data. Often, these maps do not meet desired quality (Moore et al., 1993; Robert, 1993; Bell et al., 1995; Pierce and Nowak, 1999; Mueller et al., 2000; Mueller et al., 2001). Improved estimation and enhanced map quality can be achieved by incorporating secondary spatial information into predictions, with specific methods ranging in complexity from simple linear regression to geostatistical techniques. Terrain attributes (e.g., elevation, slope aspect, curvature) may aid spatial estimation of soil properties because relief has great influence on soil formation (Jenny, 1941). Recent advances in global positioning systems (GPS; Clark and Yoo, 2000) have made it possible to obtain high-resolution digital elevation models (DEM) from which terrain attributes are readily derived. Further, high-resolution digital elevation data are available from the U.S. Geological Survey. While useful in predicting soil properties, there is little consensus regarding which terrain attributes are most important and how analytical techniques and scales of soil measurements influence map quality.

Techniques to optimize spatial estimates of soil properties include complex methods, such as kriging with an external drift and cokriging; however, simpler methods like regression (Moore et al., 1993; Bell et al., 1995; Gessler et al., 1995; Thompson and Robert, 1995) may be as robust depending on the situation. The regression approach is relatively easy but makes no attempt to account for spatial dependence in the data since it relies solely upon the relationship between the soil property of interest and the selected terrain attributes. Kriging with an external drift (Goovaerts, 1997; Deutch and Journel, 1998) has been used to enhance estimates of soil properties (horizon thickness, residual nitrates, heavy metals) using a number of drift variables (terrain attributes, corn grain yield, and kriged Zn concentration) (Bourennane et al., 1996; Gotway and Hartford, 1996; Goovaerts, 1997). Cokriging incorporates secondary information into spatial estimates in a way that accounts for the spatial cross-correlation between primary and secondary variables (Goovaerts, 1997). Despite the complexity of this procedure, cokriging has been a popular technique for enhancing spatial estimates of soil properties (Zhang et al., 1992; Vaughan et al., 1995; Rosenbaum and Söderström, 1996; Gotway and Harford, 1996; Zhang et al., 1997; Goovaerts, 1997; Juang and Lee, 1998).

Previous comparisons have generally found that methods using secondary spatial information were superior to methods that do not (Zhang et al., 1992; Gessler et al., 1995; Vaughan et al., 1995; Bourennane et al., 1996; Gotway and Harford, 1996; Rosenbaum and Söderström, 1996; Goovaerts, 1997; Zhang et al., 1997; Juang and Lee, 1998; Triantafilis et al., 2001). However, comparison studies are limited in number and have usually been conducted at one scale of measurement. This study evaluates how different analytical techniques and different scales of spatial data affect the spatial prediction of soil C using several terrain attributes (elevation, slope, aspect, and various curvature measures) as secondary spatial variables.

	MATERIALS AND METHODS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Site Description
This study was conducted in a 12.5-ha field (47° 47' 30'' N lat., 83° 52' 30 W long.) located 6 km south of Durand, MI in the Shiawassee River watershed (Fig. 1) . The field had been cropped in a corn (Zea mays L.)–soybean (Glycine max L. [Merr.]) rotation for more than 10 yr. Soil color differences in an aerial photograph (Fig. 1a) were related primarily to differences in soil organic matter content and drainage; however, soil color did not match well with the second-order soil survey map unit boundaries (Fig. 1b). Soils in this field were mapped (Fig. 1b) as somewhat poorly drained Alfisols with the exception of the Breckenridge (Bt), a poorly drained Inceptisol (Soil Conservation Service–USDA, 1974). Most of the field had slopes of <2% except for the Metamora map unit (MsB), with slopes ranging from 2 to 6%.

View larger version (134K): [in this window] [in a new window]   Fig. 1. Study location: (a) areal photograph and (b) soil and kinematic GPS measurement locations overlain by soil type boundaries. The scanned and enlarged aerial photograph (original scale = 1:7920; not georectified) taken 23 June 1988 was purchased from the USDA-AFS Aerial Photography Field Office in Salt Lake City, UT. The locations of sample points for the three soil sampling strategies (G30 = ; G100 = ð; validation points = +) and the location of the elevation measurements (o) are overlain by NRCS soil map unit boundaries (Bt = Breckenridge sandy loam; CtA = Conover loam with 0 to 2% slope; MaA = Macomb loam with 0 to 2% slope; MsA = Metamora sandy loam with 0 to 2% slopes; MsB = Metamora sandy loam with 2 to 6% slopes; WeA = Wasepi sandy loam with 0 to 2% slopes; Soil Conservation Service–USDA, 1974).

Soil Sampling Design and Laboratory Analysis
Soil samples were obtained from the field in May of 1997 using a 30.5-m regular grid (G₃₀; n = 134; 10.7 samples ha^-1), a 100-m regular grid (G₁₀₀; n = 12; 1 sample ha^-1), and a set of validation points (n = 26; 2.1 samples ha^-1) (Fig. 1b). Two of the validation points were in the middle of the region where the elevation data was removed and these were not used in any analyses. Therefore the validation (G_VAL) data set consist of 24 points. All sample point locations were georeferenced using a DGPS system. At each sample location, five subsamples (one at the grid point and four within a 1.5-m radius) were obtained to a depth of 20-cm using a 2.5-cm diam. soil core and composited. Soils were dried under forced air at 35°C for 3 d and ground to pass a 2-mm sieve. A pulverized 0.1-g subsample of soil from each grid location was analyzed for total C using a Carlo Erba NA 1500 Series 2 N/C/S analyzer (CE Instruments Milan, Italy). An additional predication data set was created by extracting one of four possible 61-m grids (G₆₁; n = 38; 2.7 samples ha^-1) from the G₃₀ data set.

Data Analysis
The first step was to assess normality of the data sets and this analysis was performed for the G₃₀ data set with histograms and by using normal probability (Q-Q) plots with 95% confidence intervals (Friendly, 1991). Contour maps of semivariogram surfaces were created for total C and the terrain attributes to determine the direction of the anisotropic axes (Isaaks and Srivastava, 1989; Goovaerts, 1997). Directional (anisotropic) semivariograms were calculated for soil properties and terrain attributes using angular tolerances of ±22.5° for the soil variables (Goovaerts, 1997) and ±15° for terrain attributes (a smaller angle was used because the terrain data was more dense). For total C, nested semivariogram model (combinations of spherical, exponential, and Gaussian models, if warranted) were chosen based on their fit to the empirical variograms. The models were described with three parameters: range of spatial correlation, nugget, and sill. The range of the spatial correlation measures the distance beyond which two observations are spatially uncorrelated. The nugget represents measurement error and unobserved microscale variability. For second-order stationary spatial processes, the sill represents the constant variance of the observations. In models with a nugget effect, the partial sill represents the difference between the sill and the nugget effect. Isaaks and Srivastava (1989), Cressie (1993), and Goovaerts (1997) provide a more thorough discussion of these semivariogram parameters. We have defined the relative structural variability (RSV) as the ratio of the partial sill to the sill (Robertson et al., 1993). The RSV indicates that proportion of the variability that is spatially structured. All semivariogram modeling was performed with Variowin (Pannatier, 1996). Correlations and stepwise multiple regression ( = 0.15) analyses were calculated using SAS (SAS, 1991) for each grid sampling interval.

The G₃₀ and G₆₁ data sets were interpolated (4 by 4 m grids) with regression, ordinary kriging, kriging with a trend model, kriging with an external drift, and standardized ordinary cokriging (Gooverts et al., 1997, Deutch and Journel, 1998). Because there were too few points in the G₁₀₀ data set for the geostatistical analyses (n = 12), only regression analysis was performed. All geostatistical interpolation methods were conducted with GSLib (Deutsch and Journel, 1998). SAS (SAS, 1990) was used for stepwise regression ( = 0.15) analysis with the following regressor variables: Easting (m), Northing (m), elevation (m), slope (%), plan curvature (m^-1), profile curvature (m^-1), and tangential curvature (m^-1).

Cross validation with an independent validation data set, referred to as jackknife by Deutsch and Journel (1998), was applied to interpolations to obtain the estimated mean squared error (MSE) as a measure of map quality. The MSE is the sum of accuracy (bias²) and precision and is defined as

where v_i is the difference between predicted value and observed value at location s_i, i = 1, ..., n_v, and n_v is the number of values in the check data set. For all analyses bilinear interpolation was used to estimate the predicted value at each G_VAL grid location because the validation points did not always coincide with the 4 by 4 m prediction grids.

The RMSE is the square root of the MSE. Prediction efficiency, referred to as goodness-of-prediction by Gotway et al. (1996), was calculated as

Positive prediction efficiencies can be interpreted as the percentage of reduction in MSE compared with the field average approach. A kriging prediction efficiency of 15%, for example, indicates that compared with the field average approach, kriging reduced the MSE by 15%. The RMSE and prediction efficiencies are scaled measures of map quality. We used the RMSE and prediction efficiency to compare map quality for the interpolations of C across different scales of sampling.

	RESULTS AND DISCUSSION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Our interest was how various analytical approaches to spatial prediction of soil properties using terrain attributes perform over a range of scales of grid sampling. Soil C was selected for analysis because it was known to vary spatially. Further, it had obvious spatial trends as evidenced from the aerial photography (Fig. 1) and visual observations as verified in the data sets reported here.

Elevation and its derivatives (terrain attributes) varied considerably in the 12.5-ha central Michigan field. While the absolute range in elevation was only 4 m, rapid changes in slope and aspect over short distances created considerable microrelief typical of glaciated areas of the upper Midwest of the USA. Total C in the surface 20 cm ranged from 2 to 29 g kg^-1 (Fig. 2) and tended to be higher in depressions and lower on slopes, reflecting drainage, soil erosion, and deposition processes within this field.

View larger version (82K): [in this window] [in a new window]   Fig. 2. Surface maps of (a) elevation and (b) slope, and (c) a contour map of elevation overlain with arrows indicating aspect.

View this table: [in this window] [in a new window]   Table 2. Correlations between total C, terrain attributes, and point coordinates and explained variability (G30 data set).

An important requirement for the application of geostatistical techniques is that the data are spatially structured. Both soil C and elevation were highly structured with range of spatial correlation values >198 m and RSV values >73% (Table 3). Although isotropic models could be used (Table 3), the semivariogram surfaces indicated significant anisotropy for C and elevation (Fig. 3) . Semivariogram surfaces are used to quickly identify the presence of anisotropy and if it exists, to determine the directions of the anisotropic axes. The x and y-axes on a semivariogram surface plot are distance lags and the center of the plot represents the semivariance of points separated by zero distance (approximately the nugget variance). The semivariance in any direction at any lag distance can be determined by examining the plot and using the scale bar (see Isaaks and Srivastava [1989] for a more detailed explanation).

View larger version (51K): [in this window] [in a new window]   Fig. 3. Contour maps of semivariogram surfaces for total C (G30) and elevation.

While geostatistical interpolation with non-Gaussian data is appropriate, the predicted values are not guaranteed to be best linear unbiased estimates (Cressie, 1993). We were primarily concerned with soil C and elevation, variables that were well suited for geostatistical prediction techniques (kriging, kriging with a trend model, cokriging, kriging with an external drift). Soil C was positively skewed and elevation had a bimodal distribution (Fig. 4) . Normalizing soil C with a log-normal transformation markedly improved the normality of the distribution, however, there was minimal impact on the spatial structure (range, RSV, etc.). In another Michigan study, kriged prediction accuracy did not necessarily improve consistently with log-normal transformations of similarly distributed variables (Mueller et al., 2001). Because the deviations from normality for C were not large, the geostatistical analyses were conducted on the raw, untransformed soil C data.

View larger version (35K): [in this window] [in a new window]   Fig. 4. Histograms (bars) and theoretical normal distributions (lines) for total C (G30) and elevation.

Ultimately, through sampling and data analysis, we are after the highest quality maps for practical use such as soil survey or site-specific management. The interpolations obtained using the regression (Table 1) and geostatistical (Table 3) models were used to develop contour maps at the G₃₀, G₆₁, and G₁₀₀ (regression only) grid scale (Fig. 5) . At the G₃₀ scale, there were substantial differences in the interpolations (Fig. 5). Based on quantitative measures of map error, kriging with an external drift was the best and regression was the worst performer (Fig. 6) . Map quality assessments are incomplete without an examination of plots of predicted versus measured (Mueller et al., 2001). Plots of predicted versus measured (Fig. 7) indicated that that many of the differences in map quality between methods were generally small but not substantial at the G₃₀ scale. Clearly, the plots of predicted versus measured were the best for kriging with an external drift. Compared with cokriging, kriging with an external drift is a relatively simple procedure, however, not as simple as the regression approach.

View larger version (63K): [in this window] [in a new window]   Fig. 5. Contour maps of total C (g kg-1). Oki = ordinary kriging with an isotropic model; OKa = ordinary kriging with an anisotropic model; KT = kriging with a trend; COK = cokriging; KED = kriging with an external drift; REG = multiple stepwise regression.

View larger version (26K): [in this window] [in a new window]   Fig. 6. Prediction efficiencies and RMSEs for estimating total C. Oki = ordinary kriging with an isotropic model; OKa = ordinary kriging with an anisotropic model; KT = kriging with a trend; COK = cokriging; KED = kriging with an external drift; REG = multiple stepwise regression.

View larger version (22K): [in this window] [in a new window]   Fig. 7. Plots of predicted total versus measured total C for the validation data sets. The solid line is a regression fit to the data. The dashed line is the 1:1 line. Oki = ordinary kriging with an isotropic model; OKa = ordinary kriging with an anisotropic model; KT = kriging with a trend; COK = cokriging; KED = kriging with an external drift; REG = multiple stepwise regression.

The differences in the maps (Fig. 5) and map quality (Fig. 6 and 7) at the G₃₀ and G₆₁ scales were small for the regression approach; however, map quality worsened substantially at the G₁₀₀ scale. Nevertheless, regression at the G₁₀₀ scale performed about as well as kriging and kriging with a trend model at the G₆₁ scale (Fig. 6). The data suggest that the use of terrain attributes may allow similar levels of map quality to be achieved with a reduced soil sampling density.

Soil reflectance is strongly related to soil C under many circumstances (Fernandez et al., 1989; Shonk et al., 1991; Chen et al., 2000). The similarities between Fig. 1a and Fig. 6 suggest that the aerial photo in this study provides a good indication of the spatial distribution of soil C across this field. The regression-derived maps (Fig. 6) most closely resemble the spatial patterns of soil color (Fig. 1). In fact, the aerial photo may be a more reliable validation data set than G_VAL, which only contains 24 points. The similarities between the regression map at the G₃₀ scale (Fig. 5) and the aerial photo (Fig. 1a) suggest that regression likely did a very good job of predicting soil C.

Although terrain attributes can be used to enhance estimates of soil C, it may be more practical to use aerial photos, which are less costly. In a Georgia investigation, an aerial photograph of bare-surface soil was used to accurately predict soil C values with regression (r² = 0.97; Chen et al., 2000). Remote sensing approaches should be considered for this Michigan field.

	SUMMARY AND CONCLUSIONS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
This study provided a comparison of techniques with and without secondary spatial information (terrain attributes) at multiple scales. Generally, methods that utilize secondary terrain information produced maps of higher quality than those that did not, however, the extent to which this was true depended on the scale of sampling. At the G₃₀ scale, kriged and cokriged maps were of similar quality, while maps created with the kriging with an external drift procedure were appreciable better than kriged maps. At the G₆₁ scale, the use of secondary spatial data greatly affected map quality, maps created with the regression approach being of the highest quality. At the G₁₀₀ scale, maps created with regression-outperformed maps created with kriging at the G₆₁ scale. Within a single field where soil properties have trends such as soil C in this field, it may not be necessary to use the more sophisticated geostatistical techniques to achieve the highest quality maps. Furthermore, these results support the notion that by using techniques that incorporate terrain attributes, sampling intensity can be substantially reduced, while maintaining high levels of prediction accuracy and precision. Since the cost of grid sampling is inversely related to the square of the grid sampling increment, enhancing spatial estimates with terrain attributes is economically appealing. Other methods that combine regression and geostatistical procedures (regression kriging and random field analysis) should be considered.

	ACKNOWLEDGMENTS

 
The authors gratefully acknowledge John Anibal for allowing us to conduct this research on his farm, Philip Robertson and Pierre Goovaerts for their advice in geostatistical analysis, Jim Walseth from Mid-Tech^® for creating the elevation survey, Paul Cornelius and Oliver Schabenberger for discussions regarding multicolinearity, Brian Long for help in the field, and Bill Bower for help with data collection.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
Contribution No. 01-06-136 from the Kentucky Agricultural Experiment Station, Lexington, KY.

Received for publication September 7, 2001.

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