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SPECIAL SECTION: FROM FIELD- TO LANDSCAPE-SCALE VADOSE ZONE PROCESSES

Scale Effects in Estimating the Variogram and Implications for Soil Hydrology

Institute for Hydraulic and Water Resources Engineering, Vienna Univ. of Technology, Karlsplatz 13, A-1040 Vienna, Austria
^* Corresponding author (skoien{at}hydro.tuwien.ac.at)

Received 23 May 2005.

In monitoring and modeling landscape soil processes, the sampling and modeling scales should, ideally, be commensurate with the scales of the soil characteristics of interest. Unfortunately, this is usually not possible, both because the true covariance structure of the variable of interest is unknown a priori and because of logistical constraints. We examine the biases and random errors in variogram parameters that result from the choice of a sample scale triplet (spacing, extent, and support) that is not commensurate with the scales of the underlying "true" soil variability. We generate numerous two-dimensional random fields, from which we sample data sets randomly or on a grid. We use these samples to estimate the variogram parameters with various methods. The results indicate that both biases and random errors may be large and depend on the sampling scale triplet relative to the scale of the underlying soil variability. The maximum likelihood (ML) method of parameter estimation gives the smallest biases for largely spaced random samples, while the weighted least squares (WLS) method gives the smallest biases for largely spaced gridded samples. Nonparametric estimates exhibit smaller random errors but larger biases than estimates from the two parametric methods (ML, WLS).

Abbreviations: ML, maximum likelihood • NLLF, negative log likelihood function • OLS, ordinary least squares • REML, restricted maximum likelihood • TBM, turning bands method • WLS, weighted least squares

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