Incorporating models of spatial variation in sampling strategies for soil

D.J. Brus

    Research output: Thesisexternal PhD, WU


    The efficiency of soil sampling strategies can be increased by incorporating a spatial variation model. The model can be used in the random selection of sample points i.e. in the sampling design, or in spatial estimation (prediction). In the first approach inference is based on a sampling design, in the second on a probabilistic model. The advantages and disadvantages of these two approaches, referred to as the design-based and model-based approach, are dealt with from a theoretical and a practical point of view. Estimation by random sampling stratified by soil map unit, and kriging are taken as examples of the two approaches in several case studies.

    The commonly accepted belief in geostatistical literature that the design-based approach is not valid in areas with autocorrelation is incorrect. Furthermore, the claimed optimality of the model-based approach is questionable. The two approaches use different criteria for assesment of the quality of estimates, consequently optimum estimation has a different meaning in each approach.

    In a regional survey with small observation density (1 observation per 25 ha), estimates of values at points were generally not significantly improved by soil map stratification (α=0.10), neither by estimation with variograms as in kriging. Stratified random sample estimates of values at points were as accurate as those provided by kriging.

    In the model-based approach the quality of the estimates depends on the quality of the model. To avoid this, a new approach for spatial estimation is proposed, the model-assisted approach, making use of non-ergodic variograms. This approach incorporates the sampling error of the non-ergodic variogram in the kriging error, making the estimation variance estimates always valid. A set of new methods is presented for unbiased and robust estimation of the non-ergodic variogram and its sampling error.

    Many factors determine the efficiency of an approach that incorporates spatial variation models, making the decision process rather complicated. A simple decision-tree is presented with seven questions related to the aim of the survey (local or global estimation, criteria for assessment of the quality of the estimates), the constraints (available budget and sampling costs) and prior information (soil map).

    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • Bouma, J., Promotor
    • de Gruijter, J.J., Promotor, External person
    Award date19 Nov 1993
    Place of PublicationWageningen
    Print ISBNs9789054851837
    Publication statusPublished - 1993


    • soil analysis
    • sampling
    • models
    • research
    • geostatistics


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