Optimal interpolation and isarithmic mapping of soil properties

Abstract

SummaryThe principle of optimal estimation using regionalized variable theory is extended from that of a single soil property to situations where there are two or more spatially interdependent ones. Auto and cross semi‐variograms express the spatial relations among the properties concerned. They can be estimated from data and can then be used to interpolate the values of a variable by co‐kriging from measurements of it plus data on one or more other properties that have been more intensively sampled. The technique of co‐kriging is described and illustrated by a case study of the particle size distribution at Woburn experimental farm. There was a strong co‐regionalization with common anisotropy between topsoil silt, subsoil silt and subsoil sand. This allowed topsoil silt to be estimated and mapped by co‐kriging more precisely than by kriging from data on topsoil silt alone.When the auto and cross semi‐variograms for a set of variables are known in advance or estimated from reconnaissance they can be used to plan an optimal sampling scheme. The main variable is sampled on a rectangular grid with finer grids for subsidiary variables. The maximum kriging variances are calculated for a range of sample spacings and relative sampling intensities. Those that match the maximum tolerable variance are potentially useful. The optimum scheme is the one that achieves the desired precision for least cost. For Woburn it is shown that measuring a main variable would need to cost at least 5 times that of a subsidiary variable to make a design for co‐kriging economically sound. Such differences are unlikely for particle size fractions. Nevertheless there are many other instances in soil research where there are large differences in cost. If there is also a strong co‐regionalization then savings should be possible by designing a sampling scheme that takes advantage of co‐kriging.