Applications of the local estimation of the probability distribution function in environmental sciences by kriging methods

In environmental sciences it is relatively common to encounter certain problems that require specific experimental data treatment by means of spatial estimation methods, for example mapping the spatial distribution of a contaminant concentration exceeding a limit level, an 'alarm problem'. In such situations the real problem is not directly related to the estimation of the variable at any particular point of the study area, but to other functions of the variable itself. This goal requires the selection of an operative model for the spatial estimation of the conditional distribution function. This paper presents a short theoretical description of two nonlinear geostatistical methods, disjunctive kriging and indicator kriging, widely used for the local estimation of the conditional distribution function involving environmental variables. Although their theoretical bases are different, corresponding to parametric and nonparametric approaches, respectively, both lead to the Local function estimation of spatial random variables. Both methods can be applied successfully in many cases regarding environmental studies in which nonlinear estimators are required. Several case studies related to environmental data analysis of the contamination effect on groundwater quality are shown, in which conditional isoprobability maps are used to interpret the degree of contamination and establish the necessary correction measures.