Assessing Uncertainties for Lognormal Kriging Estimates

Jorge Kazuo Yamamoto +
 Department of Environmental and Sedimentary Geology, Institute of Geosciences, University of Sao Paulo, Brazil.

Abstract.  Lognormal data calls for lognormal kriging in which the original data are transformed into logarithms. Then ordinary lognormal kriging estimates are backtransformed into original scale of measurement by taking their inverse logarithms. Evidently, we must add some non-bias to the estimates before backtransforming them. After that we have lognormal kriging estimates backtransformed into original scale of data. However, we do not have any idea about errors, because they remain in the logarithmic scale. This paper presents a very simple way to get back errors in the logarithmic domain into original data domain. Three data sets presenting different coefficients of variation are used to show how reliable is the proposed procedure. Furthermore, the non bias term can also be backtransformed giving the estimated smoothing error. This estimated smoothing error presents a reasonable correlation with the true smoothing error. In other words, when the backtransformed estimate presents  high correlation with the actual unknown value, then estimated and true smoothing errors will also present positive correlation.
 

Keywords: uncertainty, interpolation variance, smoothing error, lognormal kriging

In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press).

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