Proposal of a generalization for Exponential and Gaussian semivariogram models
Keywords:Variographic analysis, Spatial continuity, Range of spatial dependence
The aim of this work was to propose a correction for Exponential and Gaussian models due to the different percentages of explanation of the contribution. The procedure consisted in determining the value of a correction called k, based on the percentage of explanation of the contribution that one wants to reach. Correction k was calculated for 95% and 99.99% of the contribution, showing that it is possible to obtain different mathematical expressions for Exponential and Gaussian models. In addition, generalized expressions for these two models were constructed. For better observation of the behavior of models for different values of k, a scenario of spatial dependence was simulated, and from this scenario, the Exponential and Gaussian models were fitted considering the range obtained at 95% and 99.99% of the contribution. It was possible to perform the correction, and based on the results, a generalization of Exponential and Gaussian models was constructed. Furthermore, it was possible to visualize that it is possible to model different spatial dependences, since different percentages of explanation of the contribution can be considered. However, it is noteworthy that the percentage of 99.99% of explanation of the contribution is the closest to reality, showing that the correction with k = 9 is the ideal situation for a better approximation to the actual behavior of the phenomenon.
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