Spatial variability of some nutrient constituents of an Alfisol from loess II. Geostatistical analysis

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Abstract
Spatial variability of NO3, K, Mg and organic C of a loess field was studied by using a geostatistical concept, known as theory of regionalized variables. Fifty measurements were made at the nodes of a 30 m × 30 m grid for each of 0‐30, 30‐60 and 60‐90 cm depths. Semivariograms determined from the data showed that NO3 observations were spatially independent, and hence could be analyzed only by classical methods. Semivariograms of K, Mg and C showed these parameters to be correlated over space for a separating distance between two observations well exceeding 150 m. Their semivariograms were then used in an interpolation method called kriging, which takes into account the correlation between adjacent samples while estimating the interpolated (kriged) value without bias and with minimum variance. Means and estimation variances calculated by punctual kriging were compared to those obtained by classical theory assuming random sampling (i.e., no interdependence between observations). We obtained 1.4 to 3 fold gains in efficiency over that estimated by classical theory. One can, therefore, be sure that the estimation variance of the mean obtained in classical manner will overestimate the real variance unless the sample sites are so far apart that they are spatially independent. The kriged estimates were used to draw contour maps of the properties. Usefulness of such maps and the kriging technique as a whole is discussed to provide better options for management decisions. Finally, a method for determining sample sizes (i. e., number of observations), and hence sample spacing, is developed, taking account of spatial dependence. By this method, sample sizes can be chosen to achieve any desired precision. The sampling effort determined this way in less, and can be very less when based on block or universal kriging, than would have been judged necessary using the classical approach.

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