Gaussian process simulation of soil Zn micronutrient spatial heterogeneity and uncertainty – A performance appraisal of three semivariogram models

Abstract

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Geostatistical modelling has proven to be a good tool for decision making in soil nutrient management because it has the ability to map spatial heterogeneity and uncertainty. This study outlines a comparative approach to quantify the uncertainties and correlations in spatial process models as illustrated for the distribution of Zn in top soils of a semi-arid environment. The spatial correlation of Zn uncertainties is investigated by calculating the semi-variance of normalized Zn concentration residuals, for a sufficiently large dataset, as a function of distance between pairs of locations within the Zn field. Three semi-variogram models, namely: Exponential, Gaussian, and Spherical models were tested on the spatial correlation structure of the normalized residuals and further used as default input model for Sequential Gaussian Simulation. The Sequential Gaussian Simulation led to an improved description of spatial heterogeneity and uncertainty. The choice of semivariogram model is therefore critical for robust Sequential Gaussian Simulation and uncertainty analysis. A new criterion is proposed to inform the choice of default input model for sequential Gaussian simulation given by ratio of partial sill to square of major range. With this criterion, Exponential model performed better than both Gaussian and Spherical models. The results indicate spatial correlation in Zn field and it is suggested that the spatial correlation of Zn uncertainties should be considered to exclude inaccurate estimation for spatially distributed systems when performing nutrient distribution studies. Keywords: Botswana, Semi-arid soil, Semivariogram, Sequential Gaussian Simulation, Zn micronutrients