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SOIL FERTILITY MAP QUALITY: CASE STUDIES IN KENTUCKY T.G. Mueller, K.L. Wells, G.W. Thomas, R.I. Barnhisel, N.J. Hartsock Department of Agronomy University of Kentucky Lexington, Kentucky S.A. Shearer, Department of Biosystems and Agricultural Engineering University of Kentucky Lexington, Kentucky A. Kumar Department of Computer Science University of Kentucky Lexington, Kentucky C.R. Dillon Department of Agricultural Economics University of Kentucky Lexington, Kentucky ABSTRACT The adequacy of soil fertility maps created for variable rate fertilization depends on the variability of the soil properties, sampling design and intensity, interpolation techniques, and mapping protocols. The objectives of this study were to examine the impact of grid sampling intensity and interpolation techniques on the accuracy of soil fertility maps for several fields in Kentucky. The fields were sampled on a 30-m grid and the samples were analyzed for pH, BpH, P, and K. From this data set, 61 and 91-m grids were created. The data were interpolated with kriging (30-m grid) and inverse distance squared (30, 61, and 91-m grids). The root mean squared errors (rmse) were calculated using an independent check data set. Although the data were spatially structured, most predictions were poor at the 30-m grid scale. Soil P at the Shelby Co location was an exception. It performed well at the 30-m grid scale (rmse=6.8), fair at the 61-m grid (rmse=8.9), and marginal at the 91-m grid (rmse=10.7). Generally the differences in rmse for kriging and inverse distance weighted interpolation with a distance exponent of 2 were not large. Keywords: site-specific fertility management, kriging, inverse distance INTRODUCTION Site-specific fertility management (SSFM) is based on the premise that the quantity of fertilizer and lime that produces the maximum economic crop response varies spatially in a way that can be adequately predicted and managed (Sawyer, 1994; Pierce and Nowak, 1997; Mueller, 1998). While many factors influence economic crop responses (e.g. soil fertility levels, other factors that limit yield, crop rotation, commodity values, and costs associated with crop production), traditional lime, P, and K recommendations are sensitive primarily to soil test values. Because most SSFM recommendations are based primarily on whole-field traditional fertility recommendations, the quality of soil fertility maps is fundamental to SSFM. Map quality is defined as the sum of a maps precision and accuracy and is quantified as the mean square error of the residuals (predicted – measured) obtained with a validation data set. A number of factors affect map quality including the nature of the soil variability (Flatman and Yfantis, 1996; Sadler et al., 1998), intensity of sampling, and method of interpolation. In some studies, inverse distance weighted (IDW) interpolation has performed superior to kriging (Weber and Englund, 1992; Wollenhaupt et al., 1994; Gotway et al., 1996) while in other studies, kriging performed superior to IDW (Creutin and Obled 1992; Tabios and Salas, 1995; Laslett et al., 1997; Kravchenko and Bullock, 1999). Kriging requires the preliminary step of modeling a variance-distance relationship. The IDW procedure does not require this step and is very simply and quick. For a field in south central Michigan, map quality was adequate for soil P (range of spatial correlation of 125-m and 81% of the variability was spatially structured) measured at 30.5-m or greater but was substantially poorer for other soil variables (pH, K, Mg, Ca, and Mg). In addition, map quality decreased rapidly for all variables as the intensity of sampling decreased to 61.5 and 100-m grids, and was not greatly impacted by the method of interpolation (i.e. inverse distance weighted and ordinary kriging; Mueller, 1998) The objective of this study was to assess the impact of spatial structure, sampling intensity, and interpolation method on map quality for Kentucky soils. Three fields were chosen to represent several of the agriculturally important soilphysiographic regions of Kentucky. Grid and validation soil samples were collected and analyzed. The gridded fertility values at various scales were interpolated with inverse distance and ordinary kriging. The validation data sets were used to assess map quality. Propagation of Errors Map quality must be considered in the context of the errors associated with SSFM (Shearer et al, 2000). There are three basic sources: errors associated with map production, the generation of fertilizer recommendations maps, and variable rate application. If the soil property of interest is not spatially structured (i.e. large nugget variance or small range of spatial correlation), then the property cannot be accurately predicted spatially. For spatially structured variables, errors may be introduced by the soil sampling procedure (i.e. sampling depth, core diameter, number and orientation of sub-samples in each composite sample), method of sampling (grid sampling or directed/zone sampling), and intensity of sampling (i.e. grid size, zone size). Errors associated with uncertainty of position (i.e. GPS errors), sample preparation, and laboratory analyses may be small compared to errors associated with prediction. The method used to generate spatial predictions at unsampled locations (e.g. nearest neighbor, inverse distance, and kriging) introduces error. Methods used to summarize spatial predictions with contours or application grids cells further degrade map quality. Errors are introduced when fertilizer recommendations are used to transform soil property maps into application map. This may occur because not all of the factors that contribute to an economic crop response are included in recommendation and because recommendations were based on the hybrids, soils, and cropping practiced used in their development. Hergert et al. (1997) provide additional explanations: the economic environment of crop production has changed substantially since the development of recommendations, soil variability has increased over time with management, and spatial variability is already compensated for in many whole field recommendations. Variable rate technologies errors include GPS errors, errors due to heterogeneity of fertilizer composition, errors due to application overlaps and gaps (Fulton et al., 1999), errors due to topographic relief, and errors associated with the response lags when changing application rates. The errors associated with map production, the generation of recommendation maps, and variable rate application are not independent. Errors associated with map production will be magnified by application errors. Further, these errors may propagate non-additively. A model that explains how each source of error affects the economics of SSFM will allow research to be targeted at the most significant factors. Further, SSFM methods can be adjusted by practitioners to minimize theses errors. Approaching SSM research in this way will require an interdisciplinary effort because of the complex nature of the problem. METHODS Site Description This study was conducted on three fields in Kentucky: a 15.0 ha field in Calloway Co., 9.6 ha field in Hardin Co. and a 53.0 ha field in Shelby Co. (Fig. 1). The Calloway field is located in the Purchase region of Kentucky where soils are derived from loess. The principal soils in this field are the Grenada (moderately-well drained; Fine-silty, mixed active, thermic Glossic Fragiudalfs), Calloway (somewhat poorly drained; Fine-silty, mixed active, thermic Glossaquic Fragiudalfs) and Henry (poorly drained; Coarse-silty, mixed, active, thermic Typic Fragiaqualfs) series which differ in both drainage and depth of fragipan. The Hardin field is located in the karstic Pennyroyal region, where the soils are derived from Mississippian-age limestone residuum and a loessial cap with variable thickness. Principal soils in this field are the Crider (Fine-silty, mixed, active, mesic Typic Hapludalfs), Vertrees (Fine, mixed, mesic mesicTypic Paleudalfs) and Nolin (Fine-silty, mixed, mesic Dystric Fluventic Eutrochrepts) series, with Crider making up most of the field and the Nolin representing all the sinkhole depressional. The Shelby field is located in the Outer Bluegrass region, where the soils are formed in Ordovician-age limestone-shale residuum capped with loess of variable depth. Principal soil series are Lowell (Fine, mixed, active, mesic Typic Hapludalfs) and Nicholson (Fine-silty, mixed, semiactive, mesic Oxyaquic Fragiudalfs). The Nicholson series has a deeper loess cap than the Lowell and also has a fragipan. Soil Sampling and Laboratory Analysis Soil samples were obtained from the fields using a 30.5-m regular grid (G30; Fig. 1.; Calloway, n = 163; Hardin, n = 104; Shelby, n = 588). An additional validation data set (GVAL) was obtained with a two-staged sampling design (GVAL). Samples were chosen randomly with in each grid cell of a regular grid (Fig. 1.; Calloway, n = 60; Hardin, n = 58; Shelby, n = 70). At each grid point, 5 soil sub-samples (1 at the grid point and 4 within a 7-m radius) were obtained using a 2.1-cm diameter core to a depth of 20-cm and these samples were combined to form a composite. Soils were air dried at 25º C and ground to pass a 2-mm sieve. Standard soil analyses were conducted by the Department of Regulatory Services at the University of Kentucky. Analyses included pH (1:1 soil:water mixture), BpH (SMP buffer), P (Mehlich III extractable P), and K (Mehlich III extractable K). Additional data sets were derived from the original sampled data sets including four 61-m grids (G61) and four 91-m grids (G91). The FULL data set consisted of the G61 and the VAL data sets. Data Analysis Normal probability plots were used to assess normality. Contour maps of semivariogram surfaces were used to assess the direction and severity of anisotropy. For the FULL and G30 data sets semivariograms were modeled with Variowin (Pannatier, 1996) and omnidirectional and directional (for soil P) semivariograms were fit to the empirical semivariograms. Grids (4 by 4-m) were calculated with ordinary kriging (Surfer®, Golden Software, Golden, CO) for each of the G30 data sets. Bilinear interpolation was used to calculate the kriged estimate at each VAL data point. The G30, four G61 and G91 data sets were used to calculate an interpolated value at each VAL data point with inverse distance squared (Surfer®). Cross-validation with an independent data set, i.e., jackknife analysis in the sense of Deutsch and Journel (1998), were applied to the interpolations and the mean squared error (MSE) was used as a measure of map quality. The MSE is the sum of accuracy (bias2) and precision, being defined as 1 nv 2 MSE Bias precision vi n v 1 i 1 2 where vi is the difference between the predicted value and observed value at each validation data point si, i = 1, …, nv, and nv is the number of values in the check data sets. The root mean squared error (rmse) is the square root of the MSE and is considered a scaled measure of precision and accuracy. RESULTS AND DISCUSSION Several variables were clearly normally distributed (pH at the Hardin and Shelby fields; BpH at the Calloway and Shelby fields) according to the normal probability plots (data not shown). Others were nearly normal but most were clearly neither normally nor log-normally distributed. This has implications for kriging which is guaranteed to be the best linear unbiased estimator when the data are Gaussian (Cressie, 1993). Non parametric kriging approaches (Deutsch and Journel, 1998; Gooovaerts, 1997) were not considered in this analysis. Based on the field average pH and BpH values (Table 1), the Calloway field would not require lime and the Hardin and Shelby fields would each require (2.24 Mg ha-1) of lime to raise the pH to 6.4 according to the University of Kentucky Cooperative Extension Service Lime and Fertilizer Recommendations (2000). Average soil P and K values were below critical levels, the value at which a crop response would be expected (30 mg kg-1 Mehlich III extractable P; 150 mg kg-1 Mehlich III extractable K), for P at the Hardin field and K at the Hardin and Shelby fields. Based on field average fertility values and if fertilizing for corn, the Calloway field would not require P2O5 or K2O, the Hardin location would require 78 kg ha-1 of P2O5 and 45 kg ha-1 of K2O, and the Shelby location would require 0 kg ha-1 of P2O5 and 56 kg ha-1 of K2O. If the fertility values were calculated for Table 1. Basic statistics. mean median min max CV (%) —————————————Calloway—————————— 0.21 pH 7.0 7.0 6.2 7.7 3 BpH 7.3 7.3 7.1 7.4 0.072 1 -1 33 P (mg kg ) 82 74 35 216 41 66 K (mg kg-1) 310 316 158 522 21 —————————————Hardin——————————— 0.40 pH 6.1 6.2 5.6 7.0 6 0.21 BpH 6.9 6.8 6.6 7.5 3 9.1 P (mg kg-1) 15 13 7 40 60 30.3 K (mg kg-1) 105 94 82 187 29 —————————————Shelby——————————— 0.36 pH 6.3 6.4 5.2 7.5 6 0.17 BpH 6.7 6.7 6.2 7.4 3 19 P (mg kg-1) 31 28 3 118 61 34 K (mg kg-1) 112 105 21 283 30 each 30-m grid sample, the Calloway field would not require P2O5 or K2O, the Hardin location would require 79 kg ha-1 of P2O5 and 60 kg ha-1 of K2O, and the Shelby location would require 36 kg ha-1 of P2O5 and 57 kg ha-1 of K2O. This data suggests that there would not be savings in fertilizer costs if whole field fertility recommendations were used site specifically. Soil fertility values varied spatially within each field and between locations (Fig. 2.) There were significant areas in the Hardin and Calloway fields that were in the critical ranges for P and K. The Calloway field was above the critical levels for all sample points for P and K. The low P values, especially for the Shelby field, were well clustered. The data were spatially structured (Fig. 3), although the semivariogram parameters varied substantially (Table 2). The ranges of spatial correlation and relative structural variability values (RSV) values were large (i.e. range > 100-m and > 90%) for P at the Hardin and Shelbyville locations and K at the Hardin location. Soil P exhibited intrinsic behavior (i.e. drift) which was handled by nesting two exponential models (Table 2). The large differences in total spatial variation (i.e. semivariance at the plateau of the semivariograms) was due to the large differences in sampling variance (i.e. note the differences in the standard deviations in Table 2). Table 2. Semivariograms model parameters for the FULL data sets. Range is the range of spatial correlation, sill is the partial sill, RSV is the relative structural variability calculated where RSV = sill (sill + nugget)-1, and e indicates an exponential semivariogram model. Min indicates minimum, max indicates maximum, indicates the standard deviation, and CV indicates the coefficient of variation. —————Structure 1———— ———Structure 2——— model range Sill RSV model range Sill m % m ———————————————Calloway—————————————— pH 0.028 E 190 0.015 35 BpH 0.0006 E 62 0.0042 88 P 0 E 34 419 100 E 1000 1075 K 2000 E 90 1920 49 ———————————————Hardin——————————————— pH 0.032 E 133 0.15399 83 BpH 0 E 80 0.0316 100 P 36 E 430 450 93 K 0 E 415 4500 100 ———————————————Shelbyville————————————— pH 0.02 E 67 0.07599 79 E 600 0.046 BpH 0.0057 E 84 0.0153 73 E 600 0.0105 P 0 E 330 345 100 E 800 45 K 334 E 134 541 62 E 600 265 nugget Fig. 2. Posted maps overlain by 1.0-m elevation contours (black contours). 0.24 0.04 BpH 0.18 0.03 0.12 0.02 0.06 0.01 0.00 0.00 P K (mg kg ) 4000 3000 2 -2 800 2 -2 (mg kg ) Semivariance pH 400 2000 1000 0 0 0 100 200 300 400 lag (m) 0 100 200 300 400 Calloway Hardin Shelby Fig. 3. Experimental semivariograms using the FULL data sets for each Fig. 3. Experimental semivariograms using the FULL data sets for each location. location. The plots of predicted versus measured indicated that the kriged prediction for soil P using the 30-m grid was exceptional for the Shelby field (Fig. 4). Predictions at the Hardin field were good for soil BpH, P, and K. The performance of P at the Hardin and Shelby fields is encouraging especially considering its agronomic and environmental significance. However, 8 of 12 fertility variables were poor. While in some cases ordinary kriging with isotropic models performed better than IDW (Fig 5.), the improvement in rmse may not have been sufficient to justify the additional time required for kriging (i.e. modeling the semivariogram). It is important to note that we have not exhausted all the possible geostatistical techniques in this analysis (e.g. kriging with different models, kriging with a trend model, kriging with normal score transformations, kriging with an external drift, co-kriging, etc.). Most of the variables in this study did not exhibit anisotropic behavior. However, some variables did exhibit anisotropy. For example P at the Calloway field which was modeled and kriged with an anisotropic semivariogram model. There was a small reduction in the rmse; however, the improvement in the prediction was not substantial enough to make a difference in the appearance of the plot of predicted versus measured (Fig. 6). Calloway Hardin Shelby r2 = 0.50 r2 = 0.21 r2 = 0.31 7.0 pH 6.3 5.6 5.6 6.3 7.0 5.6 r2 = 0.22 6.3 7.0 5.6 r2 = 0.60 6.3 7.0 r2 = 0.10 7.3 BpH Predicted 6.9 6.5 6.5 6.9 7.3 6.5 6.9 7.3 6.5 r2 = 0.55 r2 = 0.11 6.9 7.3 r2 = 0.83 120 P 60 (mg kg-1) 0 0 60 120 0 60 120 0 r2 = 0.66 r2 = 0.02 60 120 r2 = 0.21 300 K 150 (mg kg-1) 0 0 150 300 0 150 300 0 150 300 Measured Fig. 4. Predicted vs measured for ordinary kriging using the G30 data set with the regression line (solid line) and coefficient of determination for the regression (r2). The first bisector is shown as a dashed line. 0.5 Calloway Hardin Shelby 0.4 0.3 pH 0.2 0.1 0.0 0.15 BpH 0.10 Rmse 0.05 0.00 30 20 P (mg kg-1) 10 0 75 50 K (mg kg-1-1) 25 G91 G61 G30 0 1 2 3 4 IDW exponent 1 2 3 4 1 2 3 4 IDW exponent IDW exponent Fig. 5. Performance of IDW (line graphs) at distance exponents of 0.1 to 5.0 for the G30, G61, and G91 data sets and ordinary kriging (bar chart) for the G30 data set. The locations are indicated at the top of the figure and the variables and the units for the rmse values are indicated to the right of the figure. rmse=6.8 G30 35 -1 Predicted (mg P kg ) rmse=6.4 70 G30 IDW OK 0 rmse=8.6 70 G61a rmse=9.3 G61b rmse=8.5 G61c rmse=9.0 G61d 35 IDW 0 rmse=11.1 70 G91a IDW rmse=10.6 G91b IDW rmse=10.6 G91c IDW rmse=10.3 G91d 35 IDW IDW IDW IDW 0 0 35 70 0 35 70 0 35 70 0 35 70 Measured (mg P kg-1) Fig. 6. Predicted vs measured for ordinary kriging (OK) using the G30 data set and for IDW with a distance exponent of 2 using each data set (i.e. G30, G61a-d, and G91a-d). The regression lines are shown as solid lines and the first bisector as a dashed line. The rmse of the prediction of each prediction is given. Map quality for soil P was also examined at the G61 and G91 scales (Fig. 6). Map quality was fair for the G61 data sets and marginal for the G91 data set. Whether map quality was adequate for variable rate P management depends not only on these errors. It also depends on the appropriateness of the fertilizer recommendations for this field and on the errors associated with P application. The relationship between IDW and RMSE appeared to be linear (Fig. 7). -1 RMSE (mg P kg ) 12 11 10 9 8 7 6 20 40 60 80 100 Grid size (m) Fig. 7. The RMSE of IDW interpolations with a distance exponent of 2 vs grid size. CONCLUSIONS The data in each field were spatially structured. Nevertheless, spatial predictions were poor for many of the variables at many of the locations. Spatial predictions for soil P at the Shelby Co. were very good at the 30-m grid scale and fair at the 91-m grid scale. Generally we found that the predictions at the 30-m grid were fair to very good for the variables that were well spatially structured (i.e. range > 100-m and > 90%). Ordinary kriging the G30 data set using exponential models did not yield spatial estimates that were much better than those generated by IDW interpolation. 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