CONCEPTUAL DETERMINISTIC ANALYSIS OF THE KRIGING TECHNIQUE IN HYDROLOGY

A stochastic approach to interpolating sparse observation records in hydrology referred to as the ‘kriging technique’ has recently been developed by Matheron (1969, 1970) and systematically used in the field by the Ecole des Mines de Paris. Distinct primary features of this method are supposed to be its predictive reliability and its ability to provide an estimation error. In the present paper a deterministic analysis for the kriging technique is given without resorting to a statistical framework. It turns out that a close relationship with the most traditional interpolation schemes may easily be found. The formulation shows that in relation to other commonly used methods, any claim to produce more accurate estimates fails to be proven, since an arbitrary component is necessarily introduced by the decision process of selecting an operative model. It is recognized that a distinct and unique advantage of the kriging technique is its ability to provide an assessment of the interpolation error. An attempt is also made to give a deterministic interpretation for the main trend. The results show that the use of this concept involves an additional component of arbitrariness whose impact upon the final outcome can hardly be predicted a priori. The conclusions of the present analysis suggest that in practical applications the interpretation model is not improved by the use of a main trend, unless its expression reflects some additional information related to the general hydrologic context but not included in the available observations. Copyright 1979 by the American Geophysical Union.