Upscaling and regionalizing hydraulic conductivity and effective porosity at watershed scale in deeply weathered crystalline aquifers

Abstract

Two innovative approaches for upscaling and regionalizing hydraulic conductivity and effective porosity at watershed scale are proposed. They are based on the concept that large-scale variations in hydraulic head may characterize large-scale properties and were tested on an unconfined granitic aquifer exposed to deep weathering, located in South India (Maheshwaram watershed, 53 km2). Both methods are based on field data such as water levels, discharge rates of irrigation wells, geological observations and the results of small-scale hydraulic tests. The resulting hydraulic-conductivity map uses the statistical empirical relationship between log-normal distributions of hydraulic conductivity from small-scale tests and linear discharge rates from exploited wells, i.e. the ratio between discharge rate and the saturated aquifer thickness. The empirical relationship agrees with Thiem–Dupuit’s assumption for unconfined aquifers. The performance of the method was compared to the values of local hydraulic-conductivity estimates deduced from small-scale tests (not used for drawing the map). About 90% of simulated values varies less than 20% from local measurements (Log K ± 0.4 on average), which is reasonable considering the complexity of the studied fractured aquifer. The regionalization of the effective porosity was based on a method that combines both water-table fluctuation and groundwater-budget techniques in the absence of recharge from rainfall. However, the use of these techniques at cell scale requires a good knowledge of groundwater flux to and from the cells, which here is unknown. To avoid this difficulty a coarse-graining method was used, assuming that increasing the cell size for such computations leads to a negligible contribution of these flux compared to net groundwater abstraction from the cell. Our results show that cell sizes over 520 × 520 m achieve a negligible balance. In addition, porosity maps provide average values of around 1.5% that are almost identical to the ones previously found at watershed scale. The proposed methods for regionalizing hydraulic conductivity and porosity fields provide access not only to the average large-scale values, but also to their spatial distribution, which is of prime interest in terms of flux and contaminant transport in a hard-rock environment. The uncertainty introduced by field data, the choice of the computation scale as the impact of cell size on the calculated effective porosity value and the possible meaning of their spatial variations are also discussed.