Accurate numerical simulation of infiltration in the vadose zone remains a challenge, especially when very sharp fronts are modeled. In this work, we used the mixed hybrid finite element (MHFE) method, which allows a simultaneous approximation of both pressure head and velocity and can handle general irregular grids with highly heterogeneous permeability. For many problems dealing with unsaturated water flow, however, the MHFE solutions exhibit significant unphysical oscillations. To avoid this phenomenon, we developed an efficient mass‐lumping scheme with the MHFE method for solving the mixed form of the Richards equation. In this work, the standard and lumped MHFE formulations were compared and the ability of the lumped formulation to reduce unphysical oscillations was determined for one‐ and two‐dimensional infiltration problems. Theoretical analysis based on the M ‐matrix property, which guarantees the discrete maximum principle, and practical test cases performed in this study underline the advantage of using an acute triangulation to completely remove the unphysical oscillations. Indeed, contrary to the standard approach, the lumped formulation satisfies the M ‐matrix property without any constraint on the time step size to be used.

In hydrogeological modelling, two approaches are commonly used for model calibration: zonation and the pilot-points method. Zonation assumes an abrupt spatial change in parameter values, which could be unrealistic in field applications. The pilot-points method produces smoothly distributed parameters compared to the zonation approach; however, the number and placement of pilot-points can be challenging. The main goal of this paper is to explore the effect of pilot-points number and locations on the calibrated parameters. A 3D groundwater flow model was built for the northern karst aquifer of Qatar. A conceptual model of this aquifer was developed based on MODFLOW software (United States Geological Survey). The model was calibrated using the parameter estimation and uncertainty analysis (PEST) package employing historical data of groundwater levels. The effect of the number and locations of pilot-points was examined by running the model using a variable numbers of points and several perturbations of locations. The calibration errors for all the runs (corresponding to different configurations of pilot-points) were maintained under a certain threshold. A statistical analysis of the calibrated parameters was then performed to evaluate how far these parameters are impacted by the pilot-point locations. Finally, an optimization method was proposed for pilot-points placement using recharge and observed piezometric maps. The results revealed that the pilot-points number, locations, and configurations have a significant effect on the calibrated parameter, especially in the high permeable regions corresponding to the karstic zones. The outcome of this study may help focus on areas of high uncertainty where more field data should be collected to improve model calibration. It also helps the placement of pilot-points for a robust calibration.

Though forming a fundamental component of the water budget, soil evaporation is challenging to quantify in practice. Most water balance and soil moisture studies rely on pan evaporation or empirical relations to calculate evaporation, which is later used for water budget estimation. This study is based on the in situ measurement of soil evaporation in arid regions using smart field lysimeters. These lysimeters calculate the actual evaporation and downward leakage within the soil column using changes in weight, in addition to measuring temperature, soil moisture, soil matric potential, and other ancillary parameters in real time. The study analyses 17 months of data collected from two smart-field lysimeters installed in loamy soil within unirrigated land in Qatar. Lysimeter data were validated using a 1D numerical unsaturated flow model using Hydrus, and utilized laboratory testing results of the water retention. The Hydrus model output shows a good match between numerical and lysimeter results. The volumetric soil moisture of the topsoil in the lysimeters varies between 6% and 36%, with a rapid response to rainfall events. The actual recharge based on data analysis amounts to 5% of the annual rainfall. An analysis of the results reveals a substantial difference between the potential evaporation and the actual evaporation. While the potential values can be adequate for wet countries where rainfall is high, it is irrelevant in arid countries, due to the lack of moisture available for evaporation throughout most of the year. Results also show that while the topsoil responds quickly to rainfall events, it takes a considerable amount of time until such effects are propagated to below the soil’s lower boundary. The findings of this study may help decision makers, researchers, and irrigation engineers plan for the sustainable management and protection of scarce resources.