Comparison of Methods for Interpolating Soil Properties Using Limited Data

pendence between measurements at different locations. Methods currently in use include kriging, inverse-disSpatial interpolation methods are frequently used to characterize tance weighting, and thin-plate smoothing splines, and patterns in soil properties over various spatial scales provided that the data are abundant and spatially dependent. Establishing these one can use numerous approaches with each of these criteria involved comparisons of abundant data from many fine-scaled (see Journel and Huijbregts, 1978; Cliff and Ord, 1981; (,100 ha) investigations. In this study we investigated whether it was Isaaks and Srivastava, 1989; Watson, 1992; Cressie, appropriate to use spatial interpolation methods with limited (n 5 1993). There is some debate, however, as to which is 46), coarse-scaled (1188 ha) soils data from a Vertisol plain. Methods the best or most appropriate method (Voltz and Webinvestigated included ordinary kriging, inverse-distance weighting, ster, 1990; Laslett, 1994; Hosseini et al., 1994; Wollenand thin-plate smoothing splines with tensions. Comparison was based haupt et al., 1994; Gotway et al., 1996). on accuracy and effectiveness measures, and analyzed using ANOVA Use of any spatial interpolation method is currently and pairwise comparison t-tests. Results indicated that spatial interpobased on a minimum sample size or pairwise comparison lation was appropriate when the data exhibited smooth and consistent criterion and certain characteristics of the data (Journel patterns of spatial dependency within the study area and the selected ranges of estimation and weighting used in this investigation. Nine and Huijbregts, 1978; Isaaks and Srivastava, 1989). The of twelve soil properties we investigated exhibited characteristics other sample size and pairwise comparison criterion are imthan these, however, including independent data, variable and erratic portant because of their effect on results. Specifically, behavior, and extreme values. Our sample design may have been it has been demonstrated that accuracy improves as an important factor as well. Ordinary kriging and inverse-distance sample size or the number of possible pairwise compariweighting were similarly accurate and effective methods; thin-plate sons increases (Journel and Huijbregts, 1978; Uehara smoothing splines with tensions was not. Results illustrate that sample et al., 1985; Isaaks and Srivastava, 1989; Englund et al., size is as important for coarse-scale investigations as it is for fine-scale 1992; Wollenhaupt et al., 1994). Map resolution may investigations with most soils data. However, our ability to predict decline with fewer samples as well (Uehara et al., 1985; successfully with some of our data raises the question as to the exact Gotway et al., 1996). Accuracy also depends on sample nature of the relationship between accuracy, sample size, and sample spacing, and to what extent these factors are related to the property pattern and sample spacing (Voltz and Webster, 1990; under investigation, particularly when data are limited. Englund et al., 1992; Laslett, 1994; Wollenhaupt et al., 1994; Gotway et al., 1996). Data characteristics of importance include the coefficient of variation, skewness, and kurtosis, and whether the data contains outliers or exS interpolation methods offer a means of chartreme values. These are considered important because acterizing a variety of factors or responses over difit is not certain whether data transformation improves ferent spatial scales. Characterization over different spaspatial interpolation (Isaaks and Srivastava, 1989), intial scales has proven invaluable for pest management creases accuracy (Weber and Englund, 1992), or has (Weisz et al., 1995), crop and soil management (Hosseini little effect on results (Cooke et al., 1993). It is also not et al., 1994; Wollenhaupt et al., 1994), and soil properties certain whether highly variable data affects accuracy in mapping (Uehara et al., 1985; Gotway et al., 1996). general (Hosseini et al., 1994; Laslett, 1994) or the extent Under the right circumstances it may also prove invaluto which extreme values exert an influence on results able to elucidating soil–vegetation interrelationships. (Isaaks and Srivastava, 1989; Gotway et al., 1996). Spatial interpolation methods differ from classic modPast research has focused primarily on how soil reeling approaches in that they incorporate information sources vary along a transect (Trangmar, 1984; Voltz about the geographic position of the sample points and Webster, 1990) or at fine scales (,100-ha study (Journel and Huijbregts, 1978; Cliff and Ord, 1981; area) (Burgess and Webster, 1980; Diaz et al., 1992; Isaaks and Srivastava, 1989; Watson, 1992; Cressie, Wollenhaupt et al., 1994; Gotway et al., 1996). Excep1993). Some methods also have the benefit of incorpotions include Uehara et al. (1985) analyses of different rating information about the degree and extent of dedata sets from Africa, and Hosseini et al. (1994) analyses C.A. Schloeder, P.O. Box 445, Fortine, MT 59918-0445; N.E. Zimmerof soils data from southwest Iran. Financial and logistical man, Dept. Landscape Inventories, Swiss Federal Institute of Forest, constraints are often the reasons why there are not more Snow, and Landscape Research, Zuercherstrasse 111, CH-8903 Birmensdorf (ZH), Switzerland; M.J. Jacobs, P.O. Box 445, Fortine, MT Abbreviations: BS, base saturation; CEC, cation-exchange capacity; 59918-0445. Received 29 Nov. 1999. *Corresponding author (mjjcas@ G, goodness-of-prediction (estimate); ID, inverse-distance weighting; libby.org). MAE, mean absolute error; MSE, mean-squared error; OK, ordinary kriging; OM, organic matter; P, total available phosphorus. Published in Soil Sci. Soc. Am. J. 65:470–479 (2001).