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

Abstract

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.

Geostatistical analysis of tritium, groundwater age and other noble gas derived parameters in California

“…Previous studies have focused on many other features such as contaminants and the risk to human health, rather than gathering information about the hydrological functioning of the groundwater system using travel time tracers. Geochemical and isotopic data and signatures have been the subject of variogram analysis and kriging in the past (Samper and Neuman, 1989;Myers et al, 1982;Subyani and Ş en, 1989). More recent work focused on soil water content (Snepvangers et al, 2003) and contaminants such as nitrate (Mendes and Ribeiro, 2010;Chica-Olmo et al, 2014) and arsenic (Gong et al, 2014;Antunes and Albuquerque, 2013;Goovaerts et al, 2005;Lee et al, 2007;James et al, 2014) The geostatistical analyses in this study were performed on the state-wide data set, which was divided into subsets according to depth in order to address the vertical structure of the data.…”

Approximation of confidence limits on sample semivariograms from single realizations of spatially correlated random fields

“…Chloride concentrations at 120 monitoring well locations were used to develop a kriging standard error against which alternative monitoring well network designs were compared. Samper and Neuman [1989] estimated the spatial covariance structures of certain hydrogeochemical and isotopic data using an adjoint state maximum likelihood cross-validation method. One of their conclusions was that although there have been few applications of geostatistics to hydrogeochemical and isotopic variables, hydrogeochemical data are suitable for geostatistical analysis.…”