Geostatistical Analysis of Soil Chemical Properties of Large Land Areas. I. Semi‐variograms

Abstract

Soil properties are usually sampled on some grid or pattern which presumes to represent the unsampled neighborhood. Spatial dependence is a measure of the extent a soil sample represents the unsampled neighborhood. Geostatistics provides procedures to measure spatial dependence. Eighty pedons (Andepts) on the Island of Hawaii were sampled and spatial dependence was measured with semi‐variograms. Areas of soil with similar properties (zones of influence) were delineated by the “range” of the semi‐variogram. Areas of similarity were much greater for soil properties of the 0‐ to 15‐cm depth than of the 30‐ to 45‐cm depth. The ranges of the semi‐variograms for soil pH, Ca, Mg, K, Si, and P sorbed at 0.02 mg P/L were 32 to 42 km while the range of the variogram of rainfall had a similar value of 32 km. Semi‐variograms for Ca, Mg, K, and P based on 30 to 45‐cm‐depth samples demonstrated much greater variability and had smaller zones of influence (Ca, Mg, and K) or were extremely variable (P). Silicon in saturation extract, however, had the same zone of influence in the subsoil as in the topsoil. These results suggest that rainfall has imposed a degree of uniformity on the surface soil properties not apparent in the subsoil. Subsoil properties were highly variable, as might be expected, resulting from great variation over short distances in age and weathering of volcanic ash. The results suggest that soil chemical properties may be spatially dependent and that the spatial dependence in this example represents the imprint of soil‐forming processes and perhaps management. Zones of influence as delineated by semi‐variograms of soil properties may suggest groupings for soil management or soil classification.

Spatial scales in CZCS‐chlorophyll imagery of the southeastern U.S. continental shelf1

“…Huijbregts 1975;Journel and Huijbregts 1978;Clark 1979). The basic calculation of the technique is called semivariance and a plot of semivariance vs. lag distance is a semivariogram, sometimes abbreviated to variogram (Huijbregts 1975;Journel and Huijbregts 1978;Jumars 1978;Yost et al 1982). Oceanographers and meteorologists have referred to variograms as structure functions (Dantzler 1976;Deschamps et al 198 1;Mackas 1984;Denman and Freeland 198 5), and variograms are very similar to graphs of Gear-y's c statistic vs. lag distance (e.g.…”

An Overview of Spatial Variability of Soil Microbiological Properties using Geostatistics

“…In many instances spatial variation in these properties is not random but tends to follow a pattern in which variability decreases as distance diminishes between points in space (Youden and Mehlich, 1937;Warrick and Nielsen, 1980). Spatial dependence has been observed for a wide range of soil physical, chemical, and biological properties and processes (Yost et al, 1982;Wollum and Cassel, 1984;Cahn et al, 1994;Cambardella et al, 1994;von Steiger et al, 1996;Amador et al, 1997;Lyons et al, 1998;Go¨rres et al, 1998;Raun et al, 1998). Soil is fundamental and irreplaceable entity; it governs plant productivity of terrestrial ecosystems and it maintains biogeochemical cycles because of microorganisms which possess the ability to degrade all organic compounds including persistent xenobiotics and naturally occurring polyphenolic compounds.…”

Sub-kilometer length scales in coastal waters

“…First developed by mining engineers in their studies of mineral deposits, the empirical variogram or semi-variogram provides a description of how data are correlated with distance (Huijbregts, 1975;Journel and Huijbregts, 1978;Jumars, 1978;Yost et al, 1982). The semi-variogram function, ĝðhÞ, was originally defined by Matheron (1963) as half the average squared distance between points separated by a distance h and is computed as follows:…”