Universal cokriging of hydraulic heads accounting for boundary conditions

Abstract

When contouring scalar potentials from point observations the process can often benefit from including the known effects of boundary curves with specified potential or gradient. Here we consider the hydraulic head in an aquifer and both no-flow and constant-head boundary conditions. We present a new approach to enforcing that equipotential contours be normal to no-flow boundaries. A constant-head boundary, with unknown head, can be included through the same process by rotating the boundary vector by 90°. Collocated observations of heads and boundaries can specify a constant-head boundary of known value. We estimate head given both head and boundary condition observations, cokriging with both types of information. Our new approach uses gradient vectors in contrast with previous approximate finite-difference methods that include boundary conditions in kriging . Either the approach given here or the finite-difference method must be implemented with smooth covariance models, e.g., Gaussian, generalized Cauchy, and Matérn.