Structural analyses of sodium adsorption ratio (SAR), pH of saturation paste (pHs), CaCO3, and CO3 + HCO3 ions (in saturation extract) were stochastically modeled at different depths. One hundred four (13 x 8) samples were drawn at 12- x 12-m grid nodes in each of four depths of a Fine Loamy Typic/Natric Haplustalf. Each sample was a composite of four samples drawn within 1-m2 area (support) around grid nodes. The coefficient of variation (CV) in different layers varied from 78 to 91 for SAR, 60 to 130 for CaCO3 and 29 to 43% for CO3 + HCO3 ions. Geostatistical analysis of soil heterogeneity revealed that the spatially dependent stochastic component was generally predominant over the nugget effect. Structured variation was modeled into isotropic, positive, and definite spherical functions. In the upper layers, the spatially dependent component (C1) explained most of the variability in SAR and pHs. However, beyond the 60- to 90-cm depth, the unstructured or nugget component also became significant. Distribution of CaCO3 in the 0- to 30-cm depth, however, was almost a random phenomenon. However, below 30-cm depths its distribution was also a spatial stochastic process. For CO3 + HCO3 ions, spatial dependence and nugget variances were almost in equal proportions. Range, i.e., the scale of autorelationship was almost the same in different depths and for most of the properties studied. There was a linear relationship (two-parameter fit) between variance and mean oyer all the depths. Hence, scaled variograms were computed accordingly, and an intrinsic function of variability for the super region of four depths was arrived at. Cross-variability among depths was established by treating them as simultaneous intrinsic random fields.
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