Use of Geostatistics in Designing Sampling Strategies for Soil Survey

Semivariograms are used to quantitatively assess spatial variability of depth to mottles, depth to gravels, and thickness of loamy sand and/or coarser-textured layers, which are definitive criteria for classification of soils derived from alluvium on the Canterbury Plains near Lincoln College, New Zealand. The three properties vary anisotropically with the anisotropy ratio being highest for depth to mottles (k — 5.84), lowest for thickness of loamy sand and/or coarser-textured layers (k = 1.58), and intermediate for depth to gravels (k = 2.43). Directions of maximum variation for depth to mottles and depth to gravels are NE-SW across an abandoned channel hollow. This pattern is reflected in the soil map of the study area and in the smaller-scale soil map of the adjacent region. Such variation reflects the past regional drainage patterns of channels flowing predominantly in a NW-SE direction. The appropriate field configuration of a sampling scheme for future survey of similar adjacent soils would be rectangular with a sample spacing in the direction of least variation k (anisotropy ratio) times that in the direction of maximum variation. Suitable sample numbers and sampling intervals to achieve desired levels of precision in the direction of maximum variation are determined. These are obtained from graphs showing relationships between kriging standard error, sample spacing and sample number. This geostatistical approach is more efficient than conventional statistical methods in designing sampling strategies: less samples are needed for kriging than for the conventional method to achieve the same level of precision. S is A THREE-DIMENSIONAL body whose properties vary spatially as a result of interacting environmental factors. In same cases, there may be only one or two dominant factors that govern formation and distribution of soils in a specific region. Soils derived from alluvium are often highly variable (Karageorgis, 1980; Mausbach et al, 1980; Wilding and Drees, 1983) because of marked vertical and lateral changes of texture within the parent materials. Spatial variation of soil properties in alluvial systems has traditionally been qualitatively assessed and partitioned by field survey and mapping. Application of geostatistical techniques have recently allowed a more quantitative approach to be undertaken (Burgess and Webster, 1980a; Webster, 1985; Trangmar et al., 1985, 1986; Warrick et al., 1986). Soil surveyors are often confronted with the dilemma of how many observations should be made and where they should be located in the field. This is particularly true in flat alluvial systems where the inherent spatial variability of soil properties is not easily predicted from soil-landform relationships. The conventional statistical approach to soil variability assumes that variation of properties within sampling units is random or spatially uncorrelated. It H.J. Di and R.A. Kemp, Dep. of Soil Science, Lincoln College, Canterbury, New Zealand; and B.B. Trangmar, N.Z. Soil Bureau, DSIR, Christchurch, New Zealand. Contribution of the Dep. of Soil Science, Lincoln College, New Zealand and N.Z. Soil Bureau, DSIR, Christchurch, New Zealand. Received 8 Sep. 1988. "Corresponding author. Published in Soil Sci. Soc. Am. J. 53:1163-1167 (1989). also assumes that the sample mean is the best estimate of a soil property at any location within the sampling area, and that estimation precision is characterized by parameters such as variance, standard error and confidence limits. The number of samples needed for estimating the mean values of a soil property within a sampling unit can then be determined from the following formula (Cline, 1944) ; n = tas/(x p.) ' [I] where n is the number of observations needed for the estimation of mean n with a tolerable deviation of x — n, if the variance is s. The quantity to is the student's t at the chosen level of confidence. Studies using geostatistics have shown that soil properties often tend to be spatially correlated (Burgess and Webster, 1980a; Trangmar etal.j 1985, 1986; Webster, 1985; Warrick et al., 1986). The'classical statistical model is suboptimal for determining sampling numbers under such conditions because it takes no account of spatial correlation and relative positions of sampling locations. \ Geostatistics provides a tool for improving sampling design by utilizing the spatial dependence of soil properties within sampling regions. The kriging estimation variance for predicting soil property values at unsampled locations (Burgess and Webster, 1980a,b) depends on the degree of spatial dependence, which is expressed by the semivariogram, and! on the configuration of observation points in relation to the area to be estimated. The minimized estimation variance for block kriging is obtained from the expression