Developing a pan-European high-resolution groundwater recharge map - Combining satellite data and national survey data using machine learning.

Groundwater recharge quantification is essential for sustainable groundwater resources management, but typically limited to local and regional scale estimates. A high-resolution (1 km × 1 km) dataset consisting of long-term average actual evapotranspiration, effective precipitation, a groundwater recharge coefficient, and the resulting groundwater recharge map has been created for all of Europe using a variety of pan-European and seven national gridded datasets. As an initial step, the approach developed for continental scale mapping consists of a merged estimate of actual evapotranspiration originating from satellite data and the vegetation controlled Budyko approach to subsequently estimate effective precipitation. Secondly, a machine learning model based on the Random Forest regressor was developed for mapping groundwater recharge coefficients, using a range of covariates related to geology, soil, topography and climate. A common feature of the approach is the validation and training against effective precipitation, recharge coefficients and groundwater recharge from seven national gridded datasets covering the UK, Ireland, Finland, Denmark, the Netherlands, France and Spain, representing a wide range of climatic and hydrogeological conditions across Europe. The groundwater recharge map provides harmonised high-resolution estimates across Europe and locally relevant estimates for areas where this information is otherwise not available, while being consistent with the existing national gridded datasets. The Pan-European groundwater recharge pattern compares well with results from the global hydrological model PCR-GLOBWB 2. At country scale, the results were compared to a German recharge map showing great similarity. The full dataset of long-term average actual evapotranspiration, effective precipitation, recharge coefficients and groundwater recharge is available through the EuroGeoSurveys' open access European Geological Data Infrastructure (EGDI).

A Simple Analytical Formula for the Leakage Flux Through a Perforated Aquitard.

In this methods note, we present a simple analytical formula to quantify the steady-state leakage flux (Q) over a perforated aquitard. The flux depends on the aquitard thickness (D), the radius of the perforation (R), the hydraulic conductivity of the material inside the perforation (kfill ), the conductivities of the overlying and underlying aquifers (k1 and k2 , respectively), and the head difference between the two aquifers (ΔH): [Formula: see text]. This equation assumes an aquitard separating two homogeneous and infinite aquifers (R ≪ aquifer thickness) in which radial flow to and from the perforation occurs, with no other recharge or discharge boundaries near the perforation. The flux through a perforation in a hypothetical case study with D = 10 m, k1 = 10 m/d, k2 = 20 m/d, R = 0.072 m, and ΔH = 1 m ranges between less than 1 mL/d if the hole is backfilled with bentonite (k(fill ) = 10(-4) m/d), to several liters per day if the perforation is backfilled with sand from the overlying aquifer (k(fill) = 10 m/d), to several m(3) /d if the perforation forms an open conduit (k(fill) = 10(5) m/d). The leakage fluxes calculated with this model agree well with those calculated using a numerical model (MODFLOW).

Simulating piecewise-linear surface water and ground water interactions with MODFLOW.

The standard MODFLOW packages offer limited capabilities to model piecewise-linear boundary conditions to describe ground water-surface water interaction. Specifically, MODFLOW is incapable of representing a Cauchy-type boundary with different resistances for discharge or recharge conditions. Such a more sophisticated Cauchy boundary condition is needed to properly represent surface waters alternatively losing water through the bottom (high resistance) or gaining water mostly near the water surface (low resistance). One solution would be to create a new package for MODFLOW to accomplish this. However, it is also possible to combine multiple instances of standard packages in a single cell to the same effect. In this specific example, the general head boundary package is combined with the drain package to arrive at the desired piecewise-linear behavior. In doing so, the standard USGS MODFLOW version can be used without any modifications at the expense of a minor increase in preprocessing and postprocessing and computational effort. The extra preprocessing for creating the input and extra postprocessing to determine the water balance in terms of the physical entities from the MODFLOW cell fluxes per package can be taken care of by a user interface.