Estimation of spatial covariance structures by adjoint state maximum likelihood cross validation: 3. Application to hydrochemical and isotopic data

Paper 3 of this three‐part series presents applications of our adjoint state maximum likelihood cross‐validation (ASMLCV) method to real data from aquifers. The Madrid basin in Spain serves as the source of information about 11 hydrochemical variables (pH, electrical conductivity, silica content, and the concentration of major ions) and two isotopes (oxygen 18 and carbon 14). Due to a lack of sufficient vertical resolution, our analysis is restricted to the horizontal plane. With the exception of oxygen 18 and silica, the variables appear to be free of a horizontal drift. No discernible directional effects are seen. All variables exhibit a large nugget effect which is indicative of background noise. We conclude that more detailed and careful sampling in three dimensions is required if groundwater quality information is to become less prone to such noise and thereby more useful in the context of quantitative hydrogeological analyses. Despite the existing noise, we are able to confirm geostatistically some (though not all) of the hypotheses advanced by others about hydrochemical evolution and isotope changes in the basin. The ability of ASMLCV to filter out spatial variations from part of the measurement noise is illustrated on carbon 14 data. The same data are also used to investigate the utility of model structure identification criteria in selecting the best among a set of alternative semivariogram models.