Stochastic Imaging of Environmental Data

Abstract

Interpretation of environmental data is currently confronted with the problem of estimating the spatial variation of a parameter from a limited number of sample points irregularly distributed in space. The challenge is to extract the relevant information for a given problem from the individual observations at control points. For example, in risk analysis (water resource monitoring, overflow forecasting, pollution monitoring), the emphasis is on detecting the maximum value or the anomalies of the appropriate parameter.Within this framework, classical numerical mapping techniques such as spline interpolation, multivariate regression or kriging, are of little use, because they provide an estimation of the mean local value while the expected distribution of the parameter would be more relevant.In this paper, a stochastic simulation technique based on indicator functions is presented. It provides at each unknown point an estimation of the conditional probability function which can be further used to produce a “Stochastic image” or a realistic simulation map of the unknown parameter. This technique is also used to build various non-parametric estimators of an expected value (such as minimum, maximum, median, inter quartile range) which can be used in risk analysis. A case study in environmental monitoring is presented to illustrate the procedure.KeywordsCumulative Distribution FunctionEnvironmental DataStochastic SimulationSequential SimulationExperimental VariogramThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.