A Comparative Study of Interpolation Methods for Mapping Soil Properties

and Salas (1985) compared kriging with several other interpolation techniques, including inverse distance, for The choice of an optimal interpolation technique for estimating annual precipitation distributions and found kriging to soil properties at unsampled locations is an important issue in sitebe superior to inverse distance weighting. Warrick et specific management. The objective of this study was to evaluate inverse distance (InvD) weighting, ordinary kriging (KO), and lognoral. (1988) also reported kriging to be better than inverse mal ordinary kriging (KOlog) to determine the optimal interpolation distance weighting for mapping potato (Solanum tumethod for mapping soil properties. Relationships between statistical berosum L.) yield and soil properties, such as percent properties of the data and performance of the methods were analyzed of sand, Ca content, and infiltration rate. Laslett et al. using soil test P and K data from 30 agricultural fields. For InvD (1987) obtained more accurate pH predictions by using weighting, we used powers of 1, 2, 3, and 4. The numbers of the closest kriging than by using inverse distance weighting. Leeneighboring points ranged from 5 to 30 for the three methods. The naers et al. (1990) found kriging to be superior to inverse results suggest that KOlog can improve estimation precision compared distance weighting for the majority of their soil Zn conwith KO for lognormally distributed data. The criteria helpful in tent data sets. Criteria for comparing the methods were deciding whether KOlog is applicable for the given data set were the mean squared error (Warrick et al., 1988), sum of Kolmogorov–Smirnov goodness-of-fit statistic, coefficient of variation, skewness, kurtosis, and the size of the data set. Careful choice squared errors (Laslett et al., 1987), and correlation of the exponent value for InvD weighting and of the number of the coefficients between observed and estimated values closest neighbors for both InvD weighting and kriging (KO or KOlog) (Leenaers et al., 1990). significantly improved the estimation accuracy (P # 0.05). However, Several other studies, however, found inverse disno a priori decision could be made about the optimal exponent and tance weighting to be more accurate than kriging. Weber the number of the closest neighbors based on the statistical properties and Englund (1992) found that squared inverse distance of the data. For the majority of the data sets, kriging with the optimal weighting produced better interpolation results than any number of the neighboring points, a carefully selected variogram other method, including kriging. Wollenhaupt et al. model, and appropriate log-transformation of the data performed (1994) compared inverse distance weighting and kriging better than InvD weighting. Correlation coefficients between experifor mapping soil P and K levels and found inverse dismental data and estimated results of kriging were higher than those of InvD for 57 out of a total of 60 data sets, kriging mean absolute tance to be relatively more accurate. Gotway et al. errors were lower for 44 data sets, and kriging mean errors were lower (1996) observed the best results in mapping soil organic than those of InvD weighting for 31 data sets. matter contents and soil NO 3 levels for several fields when inverse distance was used as an interpolation technique. The studies used mean squared error as a main P agriculture applies principles of farming criterion for comparison (Weber and Englund, 1992; according to the field variability, which creates new Gotway et al., 1996). requirements for estimating and mapping spatial variKriging performance can be significantly affected by ability of soil properties. Improvement in estimation variability and spatial structure of the data (Leenaers quality depends, first, on reliable interpolation methods et al., 1990), and by the choice of variogram model, for obtaining soil property values at unsampled locasearch radius, and the number of the closest neighboring tions and, second, on appropriate application of the points used for estimation. The above-mentioned studmethods with respect to data characteristics. ies by Weber and Englund (1992), Wollenhaupt et al. The interpolation techniques commonly used in agri(1994), and Gotway et al. (1996) used a number of culture include inverse distance weighting and kriging simplified assumptions in kriging applications. For ex(Franzen and Peck, 1995; Weisz et al., 1995). Both methample, the choice of the variogram model was limited ods estimate values at unsampled locations based on to a spherical model, and a fixed number of the closest the measurements from the surrounding locations with neighboring points was used for all the data sets. In a certain weights assigned to each of the measurements. subsequent study, Weber and Englund (1994) noted that Inverse distance weighting is easier to implement, while judicious selection of the variogram model and of the kriging is more time-consuming and cumbersome; hownumber of the closest neighbors used for the estimation ever, kriging provides a more accurate description of led to significantly better estimation precision. the data spatial structure, and produces valuable inforIt has been observed that many of soil properties are mation about estimation error distributions. The acculognormally rather than normally distributed. Numerracy of these two procedures has been compared in a ous examples were reviewed by Parkin and Robinson number of studies. Creutin and Obled (1982) and Tabios (1992), including aggregate size, soil water flux, hydraulic conductivity, content of soil N, and concentration of Dep. of Crop Sciences, 1102 S. Goodwin Ave., Univ. of Illinois, Abbreviations: D, Kolmogorov–Smirnov goodness-of-fit statistic; G, Urbana, IL 61801. Received 30 Dec. 1997. *Corresponding author goodness-of-prediction statistic; InvD, inverse distance; KO, ordinary ([email protected]). kriging; KOlog, lognormal ordinary kriging; MAE, mean absolute error; ME, mean error; RI, relative improvement. Published in Agron. J. 91:393–400 (1999).