The selection of a spatial interpolation methods will impact the quality of site‐specific soil fertility maps. The objective of this study was to describe and predict the relative performance of inverse distance weighted (IDW) and ordinary kriging. Soil samples were collected on 30.5‐m grids for fields in five Kentucky counties and analyzed for pH, buffer pH, P, K, Ca, and Mg. From these data sets, 61‐m grid subsets were extracted. Data were interpolated with IDW and kriging procedures. Prediction efficiency (PE) was determined using an independent dataset (PEvalidation) and with cross‐validation (PEcross‐validation). Multiple stepwise regression was used to develop models that described the relative performance of ordinary kriging and IDW with statistical properties of the data. At the 30.5‐m grid scale, the performance of ordinary kriging relative to IDW improved as the range of spatial correlation increased and fit of the semivariogram model improved. However, at the 61.0‐m grid scale, the performance of ordinary kriging relative to IDW diminished as the degree of spatial structure increased and the fit of the semivariogram model improved. Alone, PEcross‐validation poorly describes the performance of PEvalidation across locations, soil properties, and sampling intervals (r2 = 0.18). However, in combination with the range of spatial correlation, substantial variability at the 30.5‐m grid scale was described for variables with sample semivariograms that reached plateaus (R2 = 0.61). In some situations, better decisions will be made regarding the use of these methods by considering the range of spatial correlation and cross‐validation statistics.

The performance of site‐specific fertility management (SSFM) systems depends on the quality of soil property maps used to develop variable‐rate fertilizer recommendations. Map quality assessment, however, may be too expensive for routine site‐specific soil sampling. The objectives of this study were (i) to evaluate the quality of soil property maps created with ordinary kriging for five fields in Kentucky, and (ii) to develop a model describing the relationship between map quality and statistical properties of data. Five fields across Kentucky were sampled on 30.5‐m grids and samples were analyzed for pH, buffer pH (bpH), P, K, Ca, and Mg. For each field, four 61.0 and nine 91.5‐m data subsets were extracted from the 30.5‐m grid. Semivariograms could only be adequately modeled for the 30.5‐ and 61.0‐m grid datasets. Therefore, only these data sets were interpolated with ordinary kriging. Map quality was evaluated with an independent data set. Multiple stepwise regression was used to model map quality using data from several Kentucky fields and from a previously published Michigan study. Prediction efficiency (PE) was a function of the relative structural variability, range of spatial correlation, and grid increment (R2 = 0.82). The range of spatial correlation was the major factor controlling map quality within the range of variation studied. This model may potentially be a useful tool for the development of sampling designs for site‐specific management.

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Inverse distance weighted interpolation can be easily optimized with commercially available software by selecting distance exponent values that minimize cross-validation (V CROSS ) errors of prediction. The effectiveness of this approach has not been critically evaluated but is of concern because of known limitations of the V CROSS procedure. To evaluate this optimization procedure, it should be validated with an independent data set (V IDS ). The objectives of this study were (1) to develop and test an optimization procedure based on V CROSS and V IDS analyses, (2) to test the accuracy of optimization of the V CROSS procedure, and (3) to evaluate the quality of maps created with V CROSS . Soil fertility and bulk soil electrical conductivity data from two previously published studies were used for the analyses. These included prediction and validation data sets for multiple locations. Our optimization procedure compared well with those obtained with a commercially available software program. The use of V CROSS resulted in overprediction of optimal distance exponent values and a substantial reduction in map quality. In many cases, the maps produced with V CROSS optimization were blocky and unrealistic. The V CROSS procedure should not be used to optimize distance exponent values for data collected on regular grids or along transects. Instead, distance exponent values between 1.5 and 2.0 should be used. Software developers should consider creating a V IDS optimizing procedure. (Soil Science 2005;170:504-515)