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Division S-8—Nutrient Management & Soil & Plant Analysis

Map Quality for Ordinary Kriging and Inverse Distance Weighted Interpolation

^a University of Kentucky, Dep. of Agronomy, N-122 Ag. Science North, Lexington, KY 40502
^b Dep. of Biosyst. and Agric. Eng., University of Kentucky, 218 C.E. Barnhart, Lexington, KY 40546-0276

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

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 (PE_validation) and with cross-validation (PE_{cross-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, PE_{cross-validation} poorly describes the performance of PE_validation 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.

Abbreviations: FULL, datasets created by combining the validation and 30.5-m grid datasets • IDW, inverse distance weighted • IDW_1.2, IDW interpolation with a distance exponent of 1.2 • MSE, mean squared error • PE, prediction efficiency PE_validation, PE determined using an independent data set • PE_{cross-validation}, PE determined with cross-validation • PE_validation, difference in PE between ordinary kriging and IDW_1.2 as determined using an independent validation dataset • PE_{cross-validation}, difference in PE between ordinary kriging and IDW_1.2 as determined with cross-validation • r²_{semivariogram, F}, the coefficient of determination for the relationship between semivariogram pairs and the semivariogram model values • Range_F, range of spatial correlation as determined with the FULL datasets • Range_S, range of spatial correlation as determined with the sample dataset RSV relative structural variability • RSV_F, RSV as determined with the FULL datasets • RSV_S, RSV as determined with the sample datasets • RSV, RSV_F – RSV_S • SSFM, Site-specific fertility management

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