Multivariate Geostatistics for Mapping of Transmissivity and Uncertainty in Karst Aquifers

Abstract

Due to their complex morphology, karst terrains are particularly more fragile and vulnerable to environmental damage compared to most natural systems. Their hydraulic properties, such as their transmissivity (T) and spatial variability, can be relevant for understanding groundwater flow and, consequently, for the sustainable management of water resources. The application of geostatistical methods allows for spatial interpolation and mapping based on observations combined with uncertainty quantification. Direct measurements of T are typically scarce, while those of the specific capacity (Sc) are more frequent. We established a linear and spatial relationship between the logarithms of T and Sc measured in 174 wells in a semi-arid karst region in northeastern Brazil. These relationships were used to construct a cross-variogram, whose Linear Model of Coregionalization proved valid. The values and the cross-variogram of logT and logSc were used to generate interpolations over 2554 values of logSc, which did not spatially coincide with logT. We used ordinary co-kriging (CO-OK) and conditional sequential Gaussian co-simulation (CO-SGS) to generate the interpolations. The cross-variogram of logT and logSc, when considering 174 wells, was isotropic with an exponential structure, a nugget effect of approximately 20% of the sill, and a range of 5 km. Cross-validation indicated an optimal number of 10 neighboring wells used in CO-OK, and we used 500 stochastic realizations in CO-SGS, which were then used to generate maps of logT estimates, deviations derived from the interpolations, and probabilistic scenarios. The resulting transmissivity maps are relevant for the design of groundwater management strategies, including stochastic approaches where the transmissivity realizations can be used to parameterize multiple executions of numerical flow models.