A Copula based observation network design approach
In this paper, a method for environmental observation network design using the framework of spatial modeling with copulas is proposed. The methodology is developed to enlarge or redesign an existing monitoring network by taking the configuration which would increase the expected gain defined in a utility function. The utility function takes the estimation uncertainty, critical threshold value and gain-loss of a certain decision into account. In this approach, the studied spatial variable is considered as a random field in where variations in time is neglected and the variable of interest is static in nature. The uniqueness of this approach lies in the fact that the uncertainty estimation at the unsampled location is based on the full conditional distribution calculated as conditional copula in this study. Unlike the traditional Kriging variance which is a function of mere measurements density and spatial configuration of data points, the conditional copula account for the influence from data values. This is important specially if we are interested in purpose oriented network design (pond) as for example the detection of noncompliance with water quality standards, the detection of higher quantiles in the marginal probability distributions at ungauged locations, the presence or absence of a geophysical variable as soil contaminants, hydrocarbons, golds and so on. An application of the methodology to the groundwater quality parameters in the South-West region of Germany shows its potential.
copulas observation network design utility estimation uncertainty geostatistics spatial dependence