KRIGRADI: A cokriging program for estimating the gradient of spatial variables from sparse data

KRIGRADI is a universal cokriging program for estimating the directional derivatives of a spatial variable from sparse measurements of the variable and gradient measurements (if available). Then, the gradient vector field can be estimated because the components of the gradient vector are the directional derivatives along the main axis of coordinates. A typical example is the estimation of the hydraulic gradient from head data in groundwater hydrology. The only inferential requirement is the covariance (or semi-variogram) from the measurements of the variable and any other necessary covariance or cross-covariance is obtained by linear systems theory. There is, then, the possibility of including direct measurements of the gradient (if available, and no matter how few) in the estimation of a directional derivative or in the estimation of the gradient field. This is therefore an application of kriging for estimating a vector field from scalars and where experimental vector values could be used in the estimation. The program implements a number of possibilities for estimating the gradient as described in the appropriate section. The program, written in Fortran, can be easily modified for particular needs if desired. A case study is provided to illustrate the performance and implementation of the program.