On the use of a main trend for the kriging technique in hydrology

A technique of interpolation based on a stochastic approach and referred to as 'kriging' technique has recently been contributed by the French School. A primary feature of the algorithm is its ability to provide an assessment of the predictive reliability. The accuracy of estimate depends on the evaluation of two stochastic quantities: the variogram gamma and the main trend m of the hydrologic event z to be reconstructed. For an effective use of the method a correct understanding of the actual role played by m is required. With some ad hoc examples it is shown that using a polynomial trend with unspecified coefficients as suggested by the general theory may lead to paradoxical results whose behaviour is hard to predict a priori. It turns out that increasing the degree of m may yield an increase of the estimation error where one would expect to obtain the opposite. An alternative formulation is suggested which assumes m to be fully known in advance. Its expression is supposed to be derived from both the general behaviour of z as is recognizable from the available records and some extra-amount of information related to the general physical knowledge of the hydrological context. If this extra-amount of information is missing, the use of a constant trend should be recommended.