IDENTIFICATION AND OPTIMAL ESTIMATION OF RANDOM-FIELDS FROM SCATTERED POINT-WISE DATA

A self-contained presentation of the interpolation problem in two-dimensional spatial random fields is given. The authors investigate the case where the random field is not necessarily stationary, where the data are so scarce and so scattered in space that sample covariance function estimates are not meaningful and where, therefore, an analytical parametric 'variogram' model is used in lieu of the covariance. They discuss several variogram parameter estimation techniques (LS, GLS, ML, Interpolation Error Method) and show how to derive estimates of various functionals of the random field from the variogram. The problem of estimating the daily rainfall over a river basin is presented.