Lessening the adverse effect of the semivariogram model selection on an interpolative survey using kriging technique

Many parameters in environmental, scientific and human sciences investigations need to be interpolated. Geostatistics, with its structural analysis step, is widely used for this purpose. This precious step that evaluates data correlation and dependency is performed thanks to semivariogram. However, an incorrect choice of a semivariogram model can skew all the prediction results. The main objectives of this paper are (1) to simply illustrate the influence of the choice of an inappropriate semivariogram model and (2) to show how a best-fitted model can be selected. This may lessen the adverse effect of the semivariogram model selection on an interpolation survey using kriging technique.

The influence of the semivariogram model selection is highlighted and illustrated by thematic maps drawn using four different models (Gaussian, magnetic, spherical and exponential). Then, a guideline to select the most suitable model, using mean error (ME), mean square error (MSE), root mean square error (RMSE), average standard error (ASE), and root mean square standardized error (RMSSE), is proposed.

The choice of a semivariogram model seriously influences the results of a kriging survey at both endpoints and amplitude of the range of the estimated values. However, the direction of variation of the interpolated values is independent of the semivariogram model: different semivariogram models (with the same characteristics) produce different thematic maps but, the areas of minimum and maximum values remain unchanged. Yet, the suitable model can be selected by means of ME, MSE, RMSE, ASE and RMSSE.

The present article illustrates how the use of an inappropriate semivariogram model can seriously distort the results of an evaluation, assessment or prediction survey. To avoid such an inconveniency, a methodical approach based on the computation and analysis of ME, RMSE, ASE, RMSSE and MSE is proposed.