This chapter introduces the subject of joint analysis of multiple spatial functions such as log-transmissivity and hydraulic head. Cokriging is the equivalent of kriging in the case of multiple variables. The general approach is introduced with a few comments on how to develop geostatistical models using only data. Additional information is given in references.

Joint analysis

Some of the most interesting estimation problems involve two or more spatial functions. For example, in regional groundwater flow studies we deal with piezometric head (or pressure), transmissivity, and net recharge. Each of these quantities is variable in space. We have already seen how one may use logtransmissivity data to obtain a variogram or generalized covariance function and then linear minimum-variance unbiased estimates of log-transmissivity. The same procedure can be followed for the recharge and the head data. The relevant methods were described in Chapters 3 through 7.

However, what about the way each of these variables is correlated with the others? And how about using measurements of one type to estimate values of another type? For example, from groundwater mechanics we know that under certain conditions low values of transmissivity in a certain area tend to increase the slope of the piezometric head in the same area; an above-average elevation and curvature of the head surface correlates with increased rates of recharge in the same area; and so on.