# RECHARGE, a model of potential recharge of aquifers applied to mainland France

Olivier Robelin, Sandra Lanini, Yvan Caballero, Eric Sauquet

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Olivier Robelin, Sandra Lanini, Yvan Caballero, Eric Sauquet. RECHARGE, a model of potential recharge of aquifers applied to mainland France. Journal of Hydrology, 2026, 664, pp.134631. 10.1016/j.jhydrol.2025.134631. hal-05379569

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# RECHARGE, a model of potential recharge of aquifers applied to mainland France

Olivier Robelin<sup>a,b</sup>, Sandra Lanini<sup>b,c,*</sup>, Yvan Caballero<sup>b,c</sup>, Eric Sauquet<sup>a</sup>

## ARTICLE INFO

This manuscript was handled by Renato Mor-
bidelli, Editor-in-Chief, with the assistance of
Nick Engdahl, Associate Editor

Keywords:

Groundwater

Recharge

Effective precipitation

BFI

Infiltration

SURFEX

France

## ABSTRACT

Calculating aquifer recharge provides a means of estimating the renewable fraction of groundwater resources, which is often difficult to quantify. This paper introduces the RECHARGE method, developed to calculate potential groundwater recharge from precipitation infiltration, and its application across mainland France over an extended historical period.

The method relies on a simple soil water budget approach to estimate effective precipitation, using meteorological data and a spatial parameter that accounts for land cover and allows the seasonal variability of evapotranspiration to be reflected. An effective precipitation infiltration ratio (EPIR) is then derived for catchments with homogeneous geological lithology, based on linear regressions involving the baseflow index and a GIS-derived parameter. Given the low interannual variability of the baseflow index, the EPIR is assumed to remain constant over time and is subsequently used to convert effective precipitation into potential recharge at the scale of all groundwater bodies in mainland France.

To validate this approach, annual effective precipitation estimates were compared for 556 selected catchments, both with observed annual river flows and with outputs from the physically based SURFEX model. The calculated potential recharge was also evaluated at both annual and seasonal scales for the entire French territory, using SURFEX as a reference. Results demonstrate that the RECHARGE model can effectively estimate annual and seasonal potential aquifer recharge. It is suitable for large-scale applications without requiring detailed knowledge of aquifer properties. Future improvements are envisioned, particularly to enhance monthly-scale accuracy in mountainous regions.

## 1. Introduction

Groundwater resource stored into aquifers is an essential component of the water flowing into the critical zone (Fan, 2015). Understanding groundwater dynamics and storage characteristics requires a correct description of aquifer properties and of certain complex processes, such as recharge, flow dynamics in the saturated zone, aquifer drainage and hydraulic responses to water abstraction by pumping (Alley et al., 2002). Quantifying the total groundwater resource is often complicated due to the uneasy observation of the underground and the general lack of aquifer geometry knowledge. An alternative method for estimating at least its naturally renewable fraction, is to assess aquifer recharge. This information can be supplied at both local and regional scales, including territories with multiple aquifers (Martinsen et al., 2022).

Moreover, in the context of global change and even under a business-as-usual exploitation scenario, aquifer recharge will be affected by the future climate evolution, potentially impacting the availability of groundwater resources (Al Atawneh et al., 2021; Meixner et al., 2016; Pulido et al., 2018; Reinecke et al., 2021; Smerdon, 2017). Therefore, to develop effective adaptation strategies, water managers need to assess the impact of climate change on future groundwater recharge within their territory (Crosbie et al., 2013).

Groundwater recharge is generally defined as the downward flow of water through the unsaturated zone to the water table, increasing the quantity of water stored in an aquifer formation (de Vries and Simmers, 2002; Scanlon et al., 2002). Strongly dependent on the climate context, groundwater recharge also depends on geomorphological characteristics (slope, hydraulic roughness, etc.), the soil properties (soil type,

<footnote><sup>a</sup> INRAE - RiverLy, Centre Lyon-Grenoble Auvergne-Rhône-Alpes, France</footnote>

<footnote><sup>b</sup> BRGM, Montpellier, France</footnote>

<footnote><sup>c</sup> UMR 183 G-Eau, Univ Montpellier, AgroParisTech, BRGM, CIRAD, INRAE, Institut Agro, IRD, Montpellier, France</footnote>

<footnote>* Corresponding author at: BRGM, Montpellier, France.</footnote>

<footnote>E-mail address: s.lanini@brgm.fr (S. Lanini).</footnote>
available water capacity), the vegetation and the hydrodynamic properties of the subsurface formations (Healy, 2010). Applying a multi-model inference approach to a worldwide recharge dataset, Mohan et al. (2018) found that precipitation, potential evapotranspiration and vegetation cover were the most predictive factors for groundwater recharge.

Recharge can be diffuse over large areas when it results from precipitation or irrigation. It can also be concentrated at specific locations such as tectonic fractures or preferential infiltration landforms (e.g. sinkholes in karstic systems) or surface water bodies such as rivers or lakes. Recharge generally follows downward fluxes, but it can also result in lateral or upward fluxes when supplied by neighbouring aquifers or by surface water bodies such as rivers or lakes (de Vries and Simmers, 2002; Scanlon et al., 2002). In such cases, the flow direction can vary depending on the season or location, as it is primarily controlled by the water head gradient, which is the difference in altitude between the aquifer's water table and the river or lake (Sophocleous, 2002).

Several methods exist to characterize the recharge of an aquifer and comprehensive reviews summarize them (de Vries and Simmers, 2002; Kinzelbach et al., 2003; Scanlon et al., 2002; Singh et al., 2019; Xu and Beekman, 2018). However, not all methods are capable of quantifying groundwater recharge on a regional scale in areas encompassing several aquifers with varying characteristics, while taking into account the impact of climate and land cover/land use change.

Direct observation of groundwater recharge is possible using point measurements taken with lysimeters (Heppner et al., 2007). However, the uncertainties arising from spatial and temporal variability in measured recharge rates make this method impractical at catchment or larger scales (Gong et al., 2021; Moeck et al., 2020; Seneviratne et al., 2012).

Various empirical relationships between climate variables and estimated recharge have been proposed (Andreo et al., 2008; Kessler, 1965; Sobaga et al., 2023; Turc, 1954; Weiss and Gvirtzman, 2007). These empirical equations are generally region specific and provide results with limited temporal resolution (usually annual).

Tracer methods (mainly chloride and environmental isotopes, see Jasechko, 2018; Marei et al., 2010 for a review) can be used to estimate the recharge across a specific area (Alcalá and Custodio, 2014). These methods typically do not integrate climate variables into the assessment and temporal variability is hardly characterized.

Conceptual modelling methods based on the analysis of hydrological variables such as groundwater level or river discharge, have been developed to simulate the temporal evolution of groundwater recharge. The Water Table Fluctuation (WTF) method estimates recharge based on observed groundwater level rises in unconfined aquifers (Cuthbert, 2010; Delin et al., 2007; Healy and Cook, 2002; Maréchal et al., 2006). While this method is easy to apply, it requires the estimation of the specific yield, which can be challenging and is aquifer-specific (Crosbie et al., 2019; Delottier et al., 2018). Additionally, the proximity of a river to the borehole where water levels are monitored can result in underestimation of recharge (Maréchal et al., 2023) and the relationship with climate depends on the downward transit time of recharge water.

Some methods estimate groundwater recharge by analyzing the recession periods of streamflow time series, considering base flow as a contribution of aquifers drainage to the river flow. Some recession analysis methods compute recharge for each peak of discharge considering the contribution of groundwater drainage to the river flow by event (Rutledge, 2007; Tallaksen, 1995). Other methods are built on conceptual models or digital filters for baseflow separation of streamflow time series considering linear or non-linear groundwater storage – discharge relationships (Chapman and Maxwell, 1996; Eckhardt, 2005; Gustard et al., 1992; Halford and Mayer, 2000; Lyne and Hollick, 1979; Partington et al., 2012).

Wittenberg and Sivapalan (1999) cautions against relying solely on methods that estimate groundwater contributions from streamflow records, as other sources like bank storage, wetlands, and the unsaturated

zone may also contribute to baseflow. Additionally, the choice of model structure (whether linear or not) should be specific to the type of aquifer being studied (Stoelzle et al., 2020). Thus, applying multiple complementary methods (Scanlon et al., 2006), which can be facilitated with dedicated numerical tools (e.g. ESPERE, Lanini et al., 2016; Lanini and Caballero, 2021), is recommended to obtain a realistic estimation of groundwater recharge on a case study. Most of the aforementioned methods, which are widely used because they are easy to apply, have limitations when it comes to describing the recharge of a specific area. They are challenged by different issues (data, representativeness, spatial and temporal variability...): direct measurements are localized, water table fluctuations represent a variable portion of an aquifer and catchment areas contributing to baseflow may be uncertain and vary over time.

Soil water balance methods enable the simulation of diffuse recharge from precipitation across a defined area, which may potentially encompass several catchments and/or aquifers. These methods vary widely in complexity, from simple formulations like those proposed by Thornthwaite (1948) or Dingman (2002), which calculate water balance using few parameters, to complex, physically-based numerical distributed models such as land surface schemes (e.g., SURFEX, Le Moigne et al., 2020; Masson et al., 2013). Sophisticated distributed hydrological models like ORCHIDEE (Cheruy et al., 2020) include a soil-vegetation-atmosphere exchanges module that computes the energy, water and carbon fluxes between the different reservoirs. 1D numerical models such as Hydrus (Simúnek and Van Genuchten, 2008), SWB (Westenbroek et al., 2010), SWAT (Arnold et al., 2012), or Waves (Barron et al., 2012) simulating vertical flow processes in the unsaturated zone accounting for soil cover, can also be used to estimate recharge.

For many of these recharge modelling approaches, one difficulty is to evaluate the infiltration ratio, i.e. to distribute the water from precipitation between surface runoff and infiltration, likely to ultimately reach the water table. This is often done using a calibrated parameter. It can be defined at the catchment scale, like the Runoff Curve Number (Ponce and Hawkins, 1996) or semi-distributed when produced using GIS analysis and combination of geomorphological, soil and lithology variables (Allocca et al., 2014; Andreo et al., 2008; Mardhel and Normand, 2006). Several teams have published results regarding global scale groundwater recharge (Berghuijs et al., 2024; Nazari et al., 2025). The groundwater recharge global map produced by Döll and Fiedler (2008) resulted from the WaterGAP2 model and did not account for land use and land cover. A recent update of the model included a static, satellite-based map of land cover classes (Müller Schmied et al., 2024). More recently, worldwide groundwater recharge projections were provided using a multi-hydrological model ensemble (Reinecke et al., 2021). Less than half of the models integrated a dynamic vegetation module.

In this paper, we present a method allowing to provide an estimation of the groundwater potential recharge at different scales, from catchments to countries, taking into account the climate and land cover variability. The originality of our work lies in the use of the IDPR (French acronym for Network Development and Persistence Index) a qualitative cartographic index of infiltration potentiality, to derive the effective precipitation infiltration ratio. This method, named RECHARGE, uses climate time series as input and can be applied whether with historical data to evaluate past and current potential recharge, or with climate projections to predict potential groundwater recharge future trends. The partition of water flows between runoff and infiltration is ensured by the EPIR (Effective Precipitation Infiltration Ratio) semi-distributed coefficient whose construction relies on a relationship between the IDPR cartographic index and the BaseFlow Index (BFI). The RECHARGE model results are evaluated against observed annual river discharges of selected gauged basins and the SURFEX physically-based numerical distributed model results, at the French national scale. Finally, the map of average annual potential groundwater recharge in mainland France, calculated using this model for the present
period (1959–2020) is presented.

## 2. Data and methods

### 2.1. The RECHARGE model

The methodology adopted to develop the RECHARGE model is based on a soil water balance to calculate effective precipitation and to simulate its infiltration into the subsurface for each unit of a partition of mainland France. The main assumption is that the distribution of effective precipitation between runoff and infiltration is mainly controlled by the local soil and subsurface properties through an infiltration coefficient to be calibrated and considered to be independent of climatic conditions.

The spatial scale for the calculation of effective precipitation is determined by the availability of meteorological data – here the French SAFRAN near-surface reanalysis available at a spatial resolution of 8 km (Vidal et al., 2010). The groundwater recharge, defined as the

part of effective precipitation that infiltrates, is a function of the infiltration coefficient. The latter is calibrated on the hydrogeological units of the BDLisa v3 (Brugeron et al., 2018), which describes homogeneous aquifer systems for mainland France. Calculations are performed using a daily time step, with results subsequently aggregated to monthly or annual time steps for analysis and mapping purposes.

#### 2.1.1. Effective precipitation computation

Effective precipitation (named P\_eff in the following) is computed through a soil water balance applied in each SAFRAN grid cell. In order to take into account the uncertainty associated with the choice of the water balance model, three different formulas are used for the calculations (Edijatno and Michel, 1989; Thornthwaite, 1948; Dingman, 2002). These models differ in the way they compute actual evapotranspiration from potential evapotranspiration (see Appendix A for details).

In order to integrate model uncertainties in the result, like in ensemble simulations, the result provided by the RECHARGE model is the average of the three P\_eff time series obtained with these formulae.

<figure><img src="image_2.png" /></figure>

<table><thead><tr><th>Kc_ini</th><th>Kc_mid</th><th>Kc_end</th><th>Kc_cold</th></tr></thead><tbody><tr><td><strong>0.78</strong> [0.42 – 1.02]</td><td><strong>1.09</strong> [0.78 – 1.29]</td><td><strong>1.00</strong> [0.73 – 1.19]</td><td><strong>0.85</strong> [0.43 – 1.09]</td></tr></tbody></table>

Mean values and range [q05 – q95]

<caption>Fig. 1. Maps of seasonal Kc at the SAFRAN grid spatial resolution.</caption>
All the models used the same meteorological data input at daily time step: precipitation (P), temperature (T) and reference evapotranspiration (ET0). Temperature records are used to estimate snowmelt at each time step through a melt factor varying linearly from 0 to 1 between 0 °C and 6 °C is by definition the maximum quantity of water that can be evaporated by a soil covered by a hypothetical grass reference crop. To take into account the actual vegetation cover or land use, we generalize the methodology proposed by the FAO (Allen et al., 1998) for calculating actual evapotranspiration from ET0, by introducing a crop coefficient (Kc) which varies over the year according to the phases of plant development and which is extended to bare or urbanized soils. Thus, the evapotranspiration used in soil water balance computation is $PET = Kc \times ET0$. To define Kc based on actual land use, we rely on Nistor et al. (2018), who proposed a correspondence table between the category codes of the Corine Land Cover (CLC) map (2018 version) and seasonal values of crop coefficients for main vegetation classes. The 2018 CLC 250 m resolution map includes 44 distinct land cover types, split into five categories: developed land, agricultural land, forests and semi-natural environments, wetlands, water surfaces. We adapted the Nistor table to impose Kc values during the cold season (November-February) equal to those of the spring season (March-May), thereby allowing for the simulation of a consistent annual cycle. Additionally, the coefficients for deciduous and mixed forests were re-evaluated based on formulae provided by Allen et al. (1998), which relate Kc to the leaf area index (LAI) and mean maximum height. Mean annual values of LAI for each biome were obtained from a review paper (Asner et al., 2003). Resulting Kc values vary from 0.9 at the initial stage to 1.2 at mid-season for deciduous forests and from 0.9 to 1 for mixed forest. The resulting seasonal Kc for each cell of the SAFRAN mesh are illustrated on Fig. 1. As expected, the lower Kc values are obtained in urban sectors and high mountains, and the higher seasonal values are obtained during summer. The Seine River basin (north of France) and the Britany region (north-west of France) exhibit the higher values whatever the season, whereas the Isère River basin (south-east) which includes bare rocks and glaciers has the lowest values.

The only (and common) parameter of the three soil water balance formulae is the Soil water Storage Capacity (SSC). Its spatialized values were obtained by adding the surface and the sub-surface total available water capacity (TAWC) given by the European soil map at its soil unit resolution (Hiederer, 2013) and then averaging over each SAFRAN grid cell.

### 2.1.2. Infiltration ratio evaluation

The annual baseflow ($Q_b$) of a river is considered here to be equal to the annual groundwater recharge by precipitation infiltration (annual RECH) of the linked aquifer, under the following assumptions: (i) river flows are not influenced by human actions, (ii) there are no underground exchanges with other catchments or underlying aquifers and (iii) the variation in water storage within the aquifer is negligible at the annual time step. It is thus implicitly assumed that the baseflow, which corresponds to low-frequency variations of the river flow, is solely supplied by the aquifer drainage. In reality, this low-frequency contribution may have other sources such as canal return flows, exchanges with other surface water bodies (such as lakes or wetlands) or glacier melt. Under the same assumptions, annual $P_{eff}$ can be assumed equal to the annual flow (QA) and, as a result, the infiltration coefficient RECH/P_{eff}, named thereafter Effective Rainfall Infiltration Ratio (EPIR), is equal to $Q_b/QA$, which is the definition of the baseflow index (BFI):

$$EPIR = \frac{RECH}{P_{eff}} = \frac{Qb}{QA} = BFI$$

As BFI is only available for gauged basins, a proxy has to be found to estimate the EPIR values for all the basins of a given territory. In that purpose, we established empirical relationships between BFI values computed on a set of selected gauged catchments and a GIS built parameter called IDPR, available over mainland France with a 50 m

spatial resolution (Mardhel et al., 2021). The IDPR index is related to the drainage density and hydrological connectivity. It describes the difference between the theoretical and observed drainage networks. Varying between 0 (no runoff) and 2000 (no infiltration), IDPR provides a qualitative estimation of the infiltration potential of a soil. Several studies have examined the relation between IDPR values and aquifer recharge, considering the geological context and hydrogeological parameters of the underground (e.g. Gay et al. (2016), Seguin and Vernoux (2016), Mardhel et al. (2021)). They all highlighted the integrative nature of IDPR.

We study the relationship between the BFI value at the outlet of a given river basin and the IDPR value averaged over its surface over 611 selected gauged catchments (see Data section). Catchment lithology as described in the French hydrogeological database BDLisa v3 (Brugeron et al., 2018) can be alluvial, sedimentary, karst, hard rock, highly folded or volcanic type (Fig. 3). We added karst systems to this classification as they are likely to present high infiltration capacity. When at least 66 % of the area is identified with a given lithology type, this lithology is associated to the catchment. Catchments with no preponderant lithology are considered as mixed type. We then excluded from our set catchments with more than 50 % of the area identified as impermeable (then considered as non-aquifer) in the BDLisa v3 database. The remaining 556 catchments were used to establish the BFI-IDPR relationships. Based on these relationships, EPIR values were assigned to each of the BDLisa v3 aquifer units according to the average IDPR value calculated on their surface and lithology type.

### 2.1.3. Potential groundwater recharge computation

After calculating the $P_{eff}$ time series for each cell of the SAFRAN regular grid, the RECHARGE model aggregates these series (by spatial averaging) to provide a unique time series for each BDLisa v3 aquifer unit (which is the spatial resolution for EPIR). The model output, i.e. the RECH at a daily time step for each hydrogeological unit, is provided by multiplying the simulated $P_{eff}$ by EPIR. For reporting issues as required in the Water Framework Directive (EC 2000), the calculated potential groundwater recharge is also produced at the spatial scale of the 621 national groundwater bodies (hereinafter referred to as MESO, Mardhel and Normand, 2006).

## 2.2. Data

### 2.2.1. Meteorological reanalysis data

Meteorological input data for models are provided at daily time step by the SAFRAN re-analysis dataset (Vidal et al., 2010) between 1958 and 2020, on the regular grid 8 × 8 km² which covers mainland France. The reference evapotranspiration (ET0) is based on a Penman-Monteith approach using the internationally recommended FAO formula (Allen et al., 1998) with the Hargreaves extrapolation for the radiation variable (coefficient H of 0.175).

### 2.2.2. Hydrological data

Hydrological data are daily river discharge time series from a set of reference gauging stations (Strohmenger et al., 2023) selected for assessing the performance of the hydrological models involved in the production of a large transient ensemble of future streamflow in France within the Explore2 project (Sauquet et al., 2025). Selection criteria were as follows: low alteration of the river flow regime due to human activity, proven data quality, minimum surface catchment of 64 km² and at least 27 years of dataset between 1976 and 2019, leading to a set of 611 gauged basins distributed over mainland France (see Fig. 2 for location) with streamflow measurements at the outlet of the catchment. 556 of those catchments were used for the IDPR - EPIR relationship assessment (see EPIR calibration section).
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** (Left) Map of lithology of mainland France and catchment delineation of gauged basins used for comparison. (Right) Plot of annual river flow log(QA) (x-axis) and log(P\_eff) (y-axis) for both models. One dot per each of the 556 selected catchments over the 1976–2019 period. Lines are linear regressions.</figcaption></figure>

## 2.3. Baseflow index (BFI) calculation

The BFI values can be computed from streamflow time series using different approaches or numerical filters (e.g. Boughton, 1993; Chapman and Maxwell, 1996; Eckhardt, 2005; Gustard et al., 1992; Ladson et al., 2013; Lyne and Hollick, 1979; Pozdniakov et al., 2022). In accordance with Bloomfield et al. (2021) we applied and compared the results provided by two widely used methods: Wallingford (Gustard et al., 1992) and Lyne & Holick (Ladson et al., 2013; Lyne and Hollick, 1979) (see Appendix B for details). They were applied with the parameter values recommended in the literature (Table 1) to derive BFI from the discharge time series of the 556 selected catchments. For each method, the final set comprises 21,575 values of annual BFI (556 multiplied by at least 27 years).

## 2.4. Diagnostic and validation

In order to evaluate the RECHARGE model, results are compared both to the observed annual runoff QA of the 556 selected catchments and to the results of the deterministic model SURFEX v8.0 applied over mainland France (Le Moigne et al., 2020; Masson et al., 2013). Using river flow data allows to check that the RECHARGE model is able to reproduce catchments water balance (comparing P\_eff to mean annual specific discharge for a set of catchments) as suggested by Hannaford et al. (2023). SURFEX is a surface modelling platform composed of surface-atmosphere coupled models. It computes surface fluxes at the interface atmosphere/ground and solves both energy and water balances over vegetated areas. The main processes in the soil–plant-atmosphere system are represented. Surface evaporation is simulated, runoff occurs over saturated areas and aquifers recharge is linked to deep soil infiltration. Diffusive equations are explicitly solved using Darcy (soil moisture) and Fourier’s (heat profiles) laws for a better characterization of infiltration through the soil (Decharme et al., 2011). Results are provided on the SAFRAN grid cells at an hourly time step over the period 1959–2019. The parametrization of the model when applied to the entire French territory is based on the BDLisa v3 database for aquifers and the ECOCLIMAP2 vegetation map (Faroux et al., 2013) for the land

<caption>**Table 1**</caption>

Parameters of the two BFI computation methods. Lyne and Holick: A is the filter parameter and n the number of passes. Wallingford: d is number of days for minimum discharge research and p the percentage of minimum discharge kept.

<table><thead><tr><th>Method Parameter</th><th>Lyne & Hollick A</th><th>n</th><th>Wallingford d (days)</th><th>p</th></tr></thead><tbody><tr><td>Value</td><td>0.925</td><td>3</td><td>5</td><td>0.9</td></tr></tbody></table>

cover distribution, including 12 distinct land cover types described at a resolution of 1 km. Among the SURFEX output variables at the SAFRAN grid scale, the runoff (RUNOFFC) and infiltration (DRAINC) fluxes are especially of interest for our analysis. SURFEX does not account for the water table depth. However, it can be combined with a groundwater flow module to simulate groundwater level fluctuation as it is in SIM2 (Habets et al., 2008).

The results provided by the RECHARGE model are compared to observed QA and to SURFEX results over mainland France at different time (year, season, and month) and spatial scales:

- For the 556 selected catchments, the P\_eff calculated by RECHARGE is compared to the specific QA values and to the sum of runoff and infiltration (RUNOFFC + DRAINC) computed by SURFEX at the annual scale. A comparison at the seasonal scale is also provided with SURFEX results only.

- P\_eff simulated by RECHARGE and SURFEX models are compared at their computation resolution (i.e. SAFRAN grid cell).

- RECHARGE and SURFEX infiltration (resp. RECH and DRAINC) are compared at the MESO groundwater bodies coarser spatial resolution.

Agreement is assessed with the Mean Bias Error (MBE) for the calculation of which, observed or SURFEX values are considered as the reference:

$$MBE = \frac{1}{n} \sum_{i=1}^{n} (SURFEX_{i} \text{or Observed value}_{i} - \text{RECHARGE value}_{i})$$

## 3. Results

This section starts with the presentation of the RECHARGE P\_eff results and the comparison with QA and SURFEX. Then, the BFI results are presented, its stability assessed and relationships between BFI and IDPR according to subsoil lithology for the EPIR estimation are presented. Finally, the RECHARGE simulated RECH variable is compared to the drainage simulated by SURFEX at the France national scale.

### 3.1. Evaluation of the effective precipitation calculated by the RECHARGE model

#### 3.1.1. Comparison with annual specific discharge at the catchment scale

RECHARGE and SURFEX annual P\_eff were compared to specific QA for the 556 gauged catchments (Fig. 2) over the 1976–2019 period. As shown by the linear regressions, there is no systematic deviation: for both models, for catchments with QA > 800 mm/year, simulated P\_eff is
lower than QA while, for catchments with QA < 400 mm/year, QA is lower than P\_eff. The MBE are respectively of -69.6 mm/year and 12.3 mm/year for RECHARGE and for SURFEX. The river flow temporal variability (Fig. 3) is well reproduced by both models on an annual time scale although RECHARGE appears to overestimate QA. Thus, the RECHARGE model tends to overestimate effective rainfall, but it simulates reasonably well the temporal dynamics of the water balance in the selected catchments.

### 3.1.2. SURFEX versus RECHARGE effective precipitation

We have shown that for a set of studied catchments and at the annual time scale, the RECHARGE P\_eff is slightly higher than that simulated by SURFEX (Fig. 3). In order to analyse consistency between model results on a seasonal scale and for the whole French territory, linear regressions between SURFEX and RECHARGE P\_eff calculated at each SAFRAN grid cell are presented on Fig. 4 (left side). P\_eff estimates are highly correlated (R² > 0.70). However specific seasonal behaviours appear:

- In autumn, the cumulative RECHARGE P\_eff are globally close to or larger than those of SURFEX.

- In winter, a rather good agreement is found between the two models results. However, some large differences can be observed locally (particularly for low values, where cumulative RECHARGE P\_eff values are lower than SURFEX ones).

- In spring and summer, the cumulative RECHARGE P\_eff are lower than that of SURFEX with a quite large spread of differences.

The spatial analysis (Fig. 4, right) helps to understand some of the seasonal differences. In the mountainous areas of the Alps and Pyrenees, the lower value of P\_eff of SURFEX compared to RECHARGE in winter is related to the storage of snow in a simulated snowpack for the SURFEX model. The simulated melting of the latter during spring and summer results in a RECHARGE P\_eff higher than that of SURFEX. The RECHARGE model, which applies a simple snowmelt module, simulates neither the snow storage nor the snowmelt cycle with the same complexity as SURFEX. Nevertheless, the consistency between the simulated P\_eff of the RECHARGE and SURFEX models on a seasonal scale appears acceptable. Moreover, it appears strong in winter, the main groundwater recharge period, which gives confidence in the use of RECHARGE model results on the annual time scale, since differences will be compensated between seasons (autumn and winter for instance) and will have little impact on cumulative annual values.

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Annual P\_eff simulated by the RECHARGE and by the SURFEX models versus observed discharge (means of the 556 selected catchments). The inter-annual mean over the entire period is 477, 546 and 485 mm/years respectively for the observed QA, the RECHARGE and the SURFEX simulated P\_eff.</figcaption></figure>

## 3.2. EPIR calibration

### 3.2.1. Baseflow index distribution and stability

The distributions of the two sets of BFI calculated over a long time period (at least 27 years) for the 556 selected catchments show a longer range for Wallingford method (Wal) [0.24–0.98] than for Lyne & Hollick method (LH) [0.35–0.95] (Fig. 5, bottom panel), as in Bloomfield et al. (2021). The yearly BFI set is also more spread ([0.05–0.99] for Wal than [0.1–0.98] for LH). Looking at each gauging station, standard deviation of yearly BFI is rather low and slightly higher for Wal (mean: 0.06) than for LH (mean: 0.05) (not shown). The absolute deviation of the yearly BFI to the BFI computed over the whole period for all the stations is shown in Fig. 6, demonstrating the stability of BFI over time. Note that the higher the BFI, the more stable it is. The two methods, Wal and LH, converge towards the same value above 0.8.

As the Lyne & Hollick (LH) method provides results with lower absolute deviations of the yearly BFI to the BFI computed over the whole period, it was finally selected for the estimation of EPIR. Fig. 6 presents the relative variation of QA and annual BFI compared to their means over the whole 1976–2019 period for the 556 selected catchments. The [5 %-95 %] relative variations of QA are in the range [−73%; +139 %] while those of BFI are limited to [−26%; +28 %]. The Sen's slope of the median of QA variation is −6% per decade while it is slightly positive (0.67 % per decade) for the median of BFI. There is no evidence of a strong sensitivity of BFI values to climatic variability. This strengthens the confidence in finding relationships at the catchment scale between BFI, a stable hydrological signature and IDPR a physiographic index related to hydrological connectivity.

### 3.2.2. Relationship between BFI and IDPR

The plot of BFI values for the 556 selected catchments versus the average IDPR values calculated on their surface, regardless of their lithology type, show a weak link between these two indexes at the catchment scale (R² = 0.06, not shown). Thus, we applied a multilevel regression approach. Following Beck et al. (2013) that showed that among 18 input parameters, snow is the one that explains the most the variance in BFI, altitude (which is a proxy data for snow) was included together with the main lithology class as explanatory variables in the multilevel regression.

Results of the regression analysis are presented in Fig. 7. Sedimentary and hard rocks lithology types are, by far, the most represented among the 556 catchments (Table 2). There are no catchments with alluvial lithology due to the generally small area covered by this type of geological formation compared to that of the selected catchments. The average proportion of homogeneous lithology per surface area in each of the catchment is 87 % for karst and volcanic whereas it is 95 % for sedimentary, hard rocks and folded.

A significant correlation between the BFI and the mean catchment elevation (coloured dots in the scatter plots) appears for folded catchments, where the higher the elevation, the higher the BFI. This is in agreement with the fact that most of these catchments are located in mountainous regions, where there is a slow and low frequency contribution of the snowmelt to river discharge, as highlighted by Beck et al. (2013). Correlations between BFI and mean elevation are much less significant for the other catchment classes and there is no clear trend of variation of BFI with elevation. Karst basins show a reverse regression slope to that observed for other types of formation. The BFI value of karst catchments appears to decrease with altitude (500 m and 1000 m, mainly in the Jura massif).

To assess the relationship between IDPR and BFI for each type of lithology, we applied an Ordinary Least Square (OLS) and a Weighted Least Square (WLS) regression, the latter to account for the potential influence of the mean elevation on the regressions. The weight chosen for the WLS regression is $w = 1/z$, in order to reduce the contribution of high altitude catchments to the global regression. WLS regressions increase the coefficient of determination R² for sedimentary and, to a
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** (Left column): Seasonal P simulated by SURFEX (x-axis) and RECHARGE (y-axis). Seasonal cumulative P_{eff} at each simulation point is shown in light blue and a linear regression is plotted. (Right column): Spatial distribution of the MBE, red colour means that the RECHARGE model simulates higher values than SURFEX model and the opposite for black colour. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Top panel) Stability analyse of yearly BFI over 556 selected catchments with Wallingford (blue) and Lyne & Hollick (red) methods between 1976 and 2019. Boxplots are plotted for each 0.1 range of BFI and the y-axis shows the absolute deviation of the yearly BFI to the BFI computed over the whole period (dev = ||BFI - BFIyear||). On the top, the histogram shows the number of values contained in each 0.1 range. The box contains the inter-quantile (IQR) range (Q75 - Q25) and the whisker is extended to 1.5 x IQR. Bottom panel) Distribution of BFIs calculated over the whole 1976–2019 period for each method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

lesser extent, karst classes. Catchments of sedimentary and karst lithology type present the higher coefficient of determination R² for their regressions (Table 2). There appears to be no correlation between the BFI and IDPR for hard rocks, folded and volcanic lithology catchments. Compared to the IDPR distribution over the BDLisa aquifer units of France (red boxplots), the IDPR values of the selected catchments can be considered as representative for hard rock, folded and sedimentary lithologies. Those of the volcanic catchments seem to represent the upper part of the distribution values.

Based on these results, the equations presented in Table 3 were proposed to calculate the effective precipitation infiltration ratio (EPIR) from the average value of the IDPR for a given BDLisa unit, using the WLS regression and depending on its lithological class, under the following assumptions:

* The regression obtained for sedimentary lithology catchments is extended to alluvial catchments, as well as folded and volcanic catchments which have a similar range of distribution for both BFI and IDPR. Taken all together, they represent 62 % of mainland France surface area. The resulting values of EPIR range between 0 and 1 for IDPR values ranging between 2000 and 0.

* For the karst catchments (14 % of mainland France surface area), the weighted regression established for this lithological class is applied. Keeping this specific formula for karst catchments is justified by the fact that, unlike for other catchment classes, the regression slope for karst catchments is positive (that would mean that when IDPR increases, infiltration increases);).

* For hard rocks catchments (24 % of mainland France surface area), the BFI variance is not explained by IDPR (R² < 0.1) and the average IDPR values over the selected catchments seem representative of the IDPR values distribution for all the BDLisa units of hard rocks lithology over mainland France. While a low R² is also obtained for catchments of volcanic and folded lithology, the large number of catchments of hard rocks lithology and the low dispersion of their annual BFI prevent them for being included in the sedimentary class. A constant EPIR value was thus preferred, equal to the median value of BFI for hard rock catchments.

The uncertainty associated with the calculation of the EPIR using these equations is about 10 %, as the RMSE between it and the BFI calculated on the 566 selected catchments is equal to 0.1. The resulting map of the EPIR computed for each aquifer unit of the BDLISA v3 for mainland France is presented on Fig. 8.

### 3.3. Potential recharge assessment

The daily effective precipitation calculated by the RECHARGE model combined with the EPIR map allowed the generation of potential recharge time series for each hydrogeological unit of the BDLisa v3 database (Fig. 9). The resulting average potential recharge value over mainland France for the 1991–2020 period is 250 mm/year. This average spatial value is relatively high as it integrates mountainous aquifers. For the plains, the calculated recharge is consistent with the mean value of 163 mm/year for the North-West part of France simulated by the AQUIFR platform over the 1958–2018 period (Vergnes et al.,
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Yearly variations of QA (grey) and BFI (dark blue, computed using L&H method) to the mean value over the 1976–2019 period for the 556 selected stations. The envelope indicates the interquantile range [5% – -95%] of the 556 values. Trends (dashed lines) are plotted using Sens's slope calculated on the medians of the 556 yearly variations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

2020). The lower potential recharge values are observed in the south-west of France (around 90 mm/year), the central part of the Seine basin and along the Mediterranean coast (both around 130 mm/year). These results should be considered as the maximum values of the aquifer recharge. The obtained spatial pattern is consistent with our current knowledge on surface hydrology and groundwater-river exchanges. Potential recharge values for non-aquifer units are provided on the basis that they may still contain small aquifers for which the calculated recharge may be of interest.

### 3.4. Comparison with SURFEX results at the groundwater body scale

The soil infiltration flow simulated by the SURFEX model (DRAINC) and the potential recharge (RECH) calculated by the RECHARGE model are compared on Fig. 10 at the MESO groundwater body scale. The annual RECH simulated by the RECHARGE model is lower than DRAINC, linked to a significant underestimation in winter and spring, whereas in autumn they are of a similar range. As already mentioned, the contrary is observed for the annual P, which is higher simulated by the RECHARGE model than by the SURFEX model due to an over-estimation in autumn (Fig. 4).

Fig. 11 presents the spatial differences between SURFEX and RECHARGE model simulations of P\_eff and DRAINC or RECH at inter-annual scale. The simulated P\_eff annual values are compared at the SAFRAN grid resolution and DRAINC and RECH values at the MESO groundwater bodies scale. The two models are, in general, consistent. The DRAINC and RECH RMSE and mean relative deviations are smoothed in comparison to P\_eff, due to the averaging switch from the SAFRAN cell scale to MESO groundwater body scale. The greater differences between both models in terms of DRAINC and RECH are observed in the south-west of France and the Rhône River basin. In those regions, while both models appeared to be consistent in terms of P\_eff, RECHARGE generally simulates RECH values that are lower than those simulated by SURFEX, with the exception of the southern part of the

Rhône River basin, where the reverse is observed. Nevertheless, those large RMSE and deviations generally correspond to the lower EFF-P and RECH (Fig. 9) values at the country scale.

## 4. Discussion

The RECHARGE model has been demonstrated to simulate the P\_eff and the RECH with a reasonable degree of consistency, in comparison with the annual specific river discharge for selected catchments and the results of the physically-based SURFEX model.

### 4.1. BFI estimation

The hydrological data used for BFI computation has undergone a visual inspection campaign which facilitated the identification of anomalies, including linear interpolation, drops, noise, point anomalies, and other such type of phenomena (Strohmenger et al., 2023). This data was used to ensure that, firstly, the annual specific river discharge, to which the annual P\_eff simulated by SURFEX and RECHARGE are compared (Fig. 2) and, secondly, the resulting EPIR estimation based on the computed BFI (Fig. 8), were not influenced by anthropogenic or measurement perturbations. However, it should be noted that other factors, not easily detectable, of river flow perturbation may be considered, such as the extraction of groundwater by pumping in boreholes or inter-basin groundwater flows. These factors can lead to the underestimation of the actual BFI, for the former, and to underestimation/overestimation of the actual size of the hydrogeological catchment in comparison to the catchment size derived from surface topography, for the latter, depending on whether they result in losses or gains. This is particularly the case in the context of karst catchments (Le Mesnil et al., 2020). Furthermore, Fig. 3 shows that substantial discrepancies persist even when employing both low-perturbed river flow data and effective precipitation data simulated using a robust, proven and tested physically-based model such as SURFEX.

### 4.2. Effective precipitation calculation

While simple, the effective precipitation computation approach adopted in the RECHARGE model includes the main soil and vegetation processes (soil water balance, evapotranspiration) involved in the transformation of precipitation into runoff and infiltration, at the catchment scale. The number of parameters required is limited (SSC and Kc) and can be obtained from national or global databases. Examples of such databases include the Soil Geographical Data Base of France (INRA, 1998), the European Soil Data Centre (Panagos et al., 2022) or the Harmonized World Soil Database version 2.0 for SCC, and FAO for Kc.

For whole mainland France, almost 60 % of annual precipitations are lost by evapotranspiration. The application in our water balance calculation of the seasonal crop coefficient extended to all types of land cover (included urban soils) has a significant impact on results. The inter-annual mean (on the 1991–2020 period) of effective precipitation over whole France is increased of 8 % (35 mm/year) compared to the one that would be calculated considering a homogeneous reference grass cover (with a constant Kc = 1). The temporal variation of Kc is also necessary to consider the annual variation of evapotranspiration according to the phenological stages of crops and natural vegetation. Deciduous and evergreen forests impact differently the water balance especially during winter. Their seasonal Kc estimation was improved using physical variables such as the Leaf Area Index (LAI) and mean maximum height. LAI are given by literature but could be retrieved from satellite imagery to include temporal evolution.

### 4.3. Using EPIR for potential recharge computation

The EPIR is used to transform the computed P\_eff into RECH in the RECHARGE model. Its estimation method is based on the strong
<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Relationship between IDPR (x-axis) and BFI LH (y-axis) for the 556 catchments classified by lithology. The catchments are represented by the dots coloured according to altitude. Regressions with Ordinary Least Square (OLS, solid blue line) and Weighted Least Square (WLS, solid green line) are plotted. Corresponding lithology is given with the number of catchments considered. The boxplots represent respectively the distribution of the mean IDPR value for the BDLisa hydro-geological units of each lithology type in whole France (red, not calculated for mixed lithology as there is no mixed lithology type in BDLisa) and the BFI distribution of the selected catchments (blue). Black line represents the median value and black cross the mean value. The box contains the inter-quartile (IQR) range (Q75 – Q25) and the whisker is extended up to 1.5 *IQR*. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>**Table 2**
Summary of lithological regression.</caption><thead><tr><th></th><th></th><th></th><th>Sedimentary</th><th>Alluvial</th><th>Hard rocks</th><th>Folded</th><th>Volcanic</th><th>Karst</th><th>Mixed</th></tr></thead><tbody><tr><td rowspan="2">Number of catchments</td><td></td><td>N</td><td>195</td><td>0</td><td>193</td><td>32</td><td>11</td><td>41</td><td>84</td></tr><tr><td></td><td>%</td><td>35 %</td><td>0</td><td>35 %</td><td>6 %</td><td>2 %</td><td>7 %</td><td>15 %</td></tr><tr><td>OLS</td><td>BFI = f(IDPR)</td><td>R<sup>2</sup></td><td>0.28</td><td></td><td>0.05</td><td>0.04</td><td>0.09</td><td>0.37</td><td>0.01</td></tr><tr><td>OLS</td><td>BFI = f(z)</td><td>R<sup>2</sup></td><td>0.13</td><td></td><td>0.00</td><td>0.52</td><td>0.09</td><td>0.18</td><td>0.06</td></tr><tr><td>WLS</td><td>BFI = f(IDPR, w = 1/z)</td><td>R<sup>2</sup></td><td>0.46</td><td></td><td>0.00</td><td>0.07</td><td>0.08</td><td>0.39</td><td>0.00</td></tr></tbody></table>

assumption that the baseflow is entirely supplied by the groundwater drainage from aquifers connected to the river drainage network. Nonetheless, alternative contributions to baseflow from other delayed

sources (Halford and Mayer, 2000; Tallaksen, 1995) remain challenging to distinguish from the groundwater drainage signal. In mountain catchments, the presence of glaciers or snow covered areas has been
<table><caption>**Table 3**
Effective Precipitation Infiltration Ratio (EPIR) equations for different lithological classes.</caption><thead><tr><td>Catchment lithology class</td><td>EPIR calculation</td></tr></thead><tbody><tr><td>Sedimentary / Aalluvial / Ffolded / Vvolcanic</td><td>EPIR = -0.74 * IDPR/2000 + 1</td></tr><tr><td>Karst</td><td>EPIR = 0.36 * IDPR/2000 + 0.39</td></tr><tr><td>Hard rocks</td><td>EPIR = 0.6</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Effective Precipitation Infiltration Ratio (EPIR) map for mainland France at the scale of the BDLISA v3 aquifer units.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Map of annual potential recharge (mean 1991 – 2020) over French hydrogeological units of the BDLisa V3.</figcaption></figure>

demonstrated to contribute to the slow component of the river discharge, due to the melting of water slow rate (Miller et al., 2014). The EPIR value and the consecutive potential recharge is therefore likely to be overestimated in these areas.

For non-snow dominated catchments, there is not yet a consensus on the most appropriate discharge separation method for quantifying the contribution of groundwater to river baseflow. Indeed, different types of conceptual models can be considered for baseflow modelling, depending on the aquifer characteristics (Stoelzle et al., 2015). It is a general

<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Linear regression of SURFEX (x-axis) and RECHARGE (y-axis) results for potential recharge at the MESO groundwater body scale (621 MESO used for the linear regression) at yearly and seasonal time step.</figcaption></figure>

recommendation to use several baseflow separation methods because of uncertainty associated with using only one. The two baseflow separation methods chosen for our study, which are among the most popular in the scientific literature, gave quite similar results and have been validated in some case studies in previous work (Caballero et al., 2021, 2016; Lanini et al., 2021). The use of an alternative method is likely to lead to different EPIR and potential recharge values.

The classification of catchments depending on their main lithology leads to a variable number of catchments by lithology. This justifies that alluvial, sedimentary, folded and volcanic lithology catchments were grouped into the same thematic relationship between IDPR and BFI (Table 3). Moreover, adding the alluvial, folded and volcanic catchments to sedimentary ones do not significantly degrade the statistical regression quality using the WLS method, as $R^2_{sedimentary} = 0.462$ while $R^2_{sedimentary+folded+volcanism} = 0.459$. Conversely, the use of a constant EPIR value regardless of the mean IDPR value for hard rock lithology catchments is supported by the narrow distribution of BFI values obtained with a significant number of catchments of this type of lithology available in the database (Fig. 7).

The threshold value of 66 % of the catchment area used to describe the catchments lithology, although not calibrated, seems to be a good compromise as it is lower than the average area of homogeneous sedimentary, hard rocks and folded surfaces on each catchment (see BFI/IDPR relationship section). Thus, increasing the threshold area ratio for considering a catchment to belong to a lithological class seems has no effect on the regression results between BFI and IDPR. The same value was used to distinguish between karst and sedimentary catchments, and it is considered acceptable as reducing it would lead to an increase or reduction in the coefficient of determination for the respective regressions. The Fig. 8 shows that the BFI of karst catchments, with an average altitude above 500 m (mainly located in the Jura massif), is generally lower than that of catchments at lower altitudes. Interbasin groundwater flow could explain that situation, as the higher the elevation of a karst system, the more it may be subject to losses that could flow to aquifers located outside the catchment area, thereby reducing its contribution to the base flow of the considered catchment. Further analysis is needed before a conclusion can be reached on that aspect (Le Mesnil et al., 2020).

Whatever the equation used for the estimation of EPIR, its value is set constant over time, which is a strong assumption of the modelling method. Nevertheless, a sensitivity analysis of BFI has verified this, particularly when Lyne & Hollick filter is applied (Fig. 6) and the assumed stability is consistent with previous studies (Beck et al., 2013).

In the SURFEX model, the DRAINC simulated flow depends on the physical equations used for the simulation of infiltration in the soil.
## 4.4. Applications of the method

The main advantage of the RECHARGE method lies in the fact that it does not require advanced knowledge of the characteristics of the aquifers present in the study area. The produced potential recharge values can be considered as a maximum estimate of the groundwater resource that can be stored into aquifers annually for a given period. The actual groundwater resource stored may depend on aquifer characteristics such as permeability, storage capacity, depth to and thickness of the saturated zone. The absence of an aquifer does not necessarily mean that subsurface infiltration is impossible. In fact, it can benefit to small structures such as perched aquifers, fractured zones able to store water or springs with small drainage areas, such as those found in mountainous regions, where wide, homogeneous aquifers barely exist. This is the case in France where mountainous regions are generally defined as highly folded type of aquifers (Fig. 2). These aquifers can be small and fractured, feeding springs or they can be impermeable sectors, in which case all the simulated potential recharge returns to the downstream river.

Potential recharge values produced using the RECHARGE model are useful for estimating a groundwater stress index, which is defined as the ratio between the groundwater resource use to its availability. It enables the calculation of indexes based on renewable groundwater resource such as the ratio of withdrawal or consumption to renewable groundwater, among others, as discussed in Tabarmayeh et al. (2022) for example. While the absolute value of the resulting index is likely to be low (due to the potential overestimation of the recharge), its relative variation would indicate to most heavily exploited aquifers or sectors, for example on the national scale for France.

The computed potential recharge can also be used as input to numerical groundwater models, as in Vergnes et al. (2023) where an earlier version of the RECHARGE model was used.

The RECHARGE model can also be used to explore the impacts of future climate projections on effective precipitation in any territory worldwide (Lanini et al., 2021). More generally, it can be used to explore the future evolution of potential recharge in the context of global change, both by applying climate projections and by studying the influence of changes in vegetation cover and its prospective evolution. However, it should be noted that changes in climatic forcing or vegetation cover can only impact the calculated effective rainfall. At the current state of the method's development, changes in EPIR cannot be considered as a function of global change. This is certainly a major limitation of the method.

Further development of the model could be oriented towards the inclusion of other potentially significant processes, such as the influence of precipitation intensity on soil infiltration properties or, though probably less important, vegetation interception. Nonetheless, this additional parameterisation would probably require an increasing number of parameters and is not necessarily preferable to switching to existing more detailed and physically-based 1-D soil infiltration models.

## 5. Conclusion

A simple method for the computation of potential groundwater recharge is presented in this paper and applied at the scale of mainland France. It is based on a soil water balance performed using three different formulations, considering the influence of vegetation cover and plant development for a better simulation of the seasonal variability. The computed values of effective precipitation have been compared with river discharge observations and to similar outputs from the physically based model SURFEX. The potential recharge is estimated

using the effective precipitation and the EPIR infiltration ratio, the value of which is obtained based on linear regressions involving the baseflow index and a GIS-built parameter called the IDPR.

Present and future values and trend analysis of potential groundwater recharge were conducted in the framework of the Explore2 project (Sauquet et al., 2025). At an annual timescale, the RECHARGE model produces results that enable the water balance to be closed at the river basin scale. At the seasonal scale, time lags between the precipitation and the recharge occurrences can be moderately well captured by the method for snow covered mountainous regions. For regions without snow cover, monthly values of effective precipitation and potential recharge are useful. These results should be considered as the maximum values of the aquifer recharge. However, the simplified soil water budget scheme applied in the RECHARGE model limits the usefulness of daily time step outputs even though these can be computed.

The constant value of the EPIR over time is the main limitation of the modelling method. The drainage to runoff ratio simulated by SURFEX shows a temporal variability that seems to be related to P_eff (the wetter the conditions, the more the soil infiltrates). Gnann et al., 2023 showed a similar behaviour using eight global water models that project higher groundwater recharge rates for higher precipitation in wet-warm climate. However, they also indicate a large disagreement with observation data, which suggest constant or lower recharge when precipitations increase. Previous studies showed that none of the soil and subsoil parameters alone can explain the linear variance in BFI (Beck et al., 2013; Haberlandt et al., 2001; Lacey and Grayson, 1998). Of the tested available parameters (IDPR, surface area, altitude and lithology), lithology was found to be the most significant factor leading to derive relationships between IDPR and BFI by lithological class. Nevertheless, a better understanding of the link between aquifer drainage and river baseflow should provide a way to consider a temporal variation of the EPIR, which could, for example, be linked to P_eff.

## 6. Funding information

Explore2 was funded by the French Ministry of the Environment and the French Biodiversity Agency (OFB). The authors benefitted from the use of the cluster at the Centre de Calcul Scientifique en région Centre-Val de Loire.

## 7. Data availability

Monthly groundwater potential recharge at the MESO scale can be downloaded on the DRIAS-EAU portal (https://www.drias-eau.fr). Other data will be made available on request.

### CRediT authorship contribution statement

**Olivier Robelin:** Writing – original draft, Software, Conceptualization. **Sandra Lanini:** Writing – review & editing, Writing – original draft, Methodology, Conceptualization. **Yvan Caballero:** Writing – review & editing, Writing – original draft, Methodology, Conceptualization. **Eric Sauquet:** Writing – review & editing, Supervision, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
# Appendix A

Detailed description of the three formulae applied to compute the soil water budget (adapted from Edijatno and Michel, 1989; Thornthwaite, 1948; Dingman, 2002)

Three different formulas are used for the soil water balance calculations. These models differ in the way they compute actual evapotranspiration from potential evapotranspiration.

At each time step, the difference between the input from precipitation (rainfall and snowmelt) and the potential evapotranspiration (PET) is calculated. If this difference is negative, the effective precipitation is assumed to be zero, and all available water in the system is mobilized for evapotranspiration. The amount of water (PET – Precipitation) is drawn from the soil water stock:

* until it is depleted (Thornthwaite, 1948),

* according to a decreasing exponential law (Dingman, 2002),

* according to a quadratic law (Edijatno and Michel, 1989).

Conversely, if the difference (Precipitation – PET) is positive, it:

* first fills the soil water reservoir. When this reaches its maximum value (namely the Soil water Storage Capacity), the surplus generates $P_{eff}$ (Thornthwaite and Dingman),

* is distributed between $P_{eff}$ and storage in the soil reservoir (as long as it has not reached its maximum value SSC) according to a quadratic law (Edijatno & Michel).

<table><thead><tr><th></th><th>If P &lt; ETP</th><th>If P &gt; PET</th></tr></thead><tbody><tr><td>Thornthwaite</td><td>SWS<sub>k</sub> = max (0; SWS<sub>k-1</sub> + P<sub>k</sub> - PET<sub>k</sub>)CET<sub>k</sub> = min (PET<sub>k</sub>; SWS<sub>k-1</sub> + P<sub>k</sub>)<br>EffP<sub>k</sub> = 0</td><td>SWS<sub>k</sub> = min (SWS<sub>k</sub>; SWS<sub>k-1</sub> + P<sub>k</sub> - PET<sub>k</sub>)CET<sub>k</sub> = PET<sub>k</sub>EffP<sub>k</sub> = max (0; SWS<sub>k</sub> + P<sub>k</sub> - PET<sub>k</sub> - SWS<sub>k</sub>)</td></tr><tr><td>Dingman</td><td>SWS<sub>k</sub> = SWS<sub>k-1</sub> * exp[-(PET<sub>k</sub> - P<sub>k</sub>)/SWS<sub>k</sub>]CET<sub>k</sub> = P<sub>k</sub> + SWS<sub>k-1</sub> -<br>SWS<sub>k</sub>EffP<sub>k</sub> = 0</td><td>SWS<sub>k</sub> = min (SWS<sub>k</sub>; SWS<sub>k-1</sub> + P<sub>k</sub> - PET<sub>k</sub>)CET<sub>k</sub> = PET<sub>k</sub>EffP<sub>k</sub> = max (0; SWS<sub>k</sub> + P<sub>k</sub> - PET<sub>k</sub> - SWS<sub>k</sub>)</td></tr><tr><td>Edijatno & Michel</td><td>dSWS = [(SWS/SWS<sub>k</sub>)<sup>2</sup> - 2 * SWS/SWS<sub>k</sub>] * dE<sub>n</sub>dETC = -<br>dSWS EffP = 0</td><td>dSWS = [1 - (SWS/SWS<sub>k</sub>)<sup>2</sup>] * dP<sub>n</sub>CET = PETdEffP = (SWS/SWS<sub>k</sub>)<sup>2</sup> * dP<sub>n</sub></td></tr></tbody></table>

with $P$ = total precipitations, $PET$ = potential evapotranspiration, $CET$ = calculated actual evapotranspiration, $SWS$ = soil water storage, $SWSmax$ = maximum soil water storage, $EffP$ = effective precipitations.

# Appendix B

Wallingford and Lyne and Hollick (1979) methods to compute the baseflow

Among the recursive digital filters, Lyne and Hollick (1979) were the first to propose applying a “low-pass” filter to extract the baseflow component (Qb) from a streamflow time series (Q). The filter can be expressed as follows: $Q_b(t) = a \cdot Q_b(t-1) + \frac{(1-a)}{2} \cdot [Q(t) + Q(t-1)]$ where a is the filter coefficient.

The filter is applied several times, alternating the direction of processing (forward in time, then backward, then forward again, and so on). The greater the number of passes ($n$), the smoother and smaller the resulting baseflow becomes. Lyne and Hollick (1979) recommended applying the filter twice with $a$ values between 0.7 and 0.9, noting limited sensitivity to this parameter. Nathan and McMahon (1990) used three passes with $a$ values between 0.9 and 0.95, and their analysis of 186 Australian catchments identified an optimal value of 0.925. Ladson et al. (2013) further reported that the optimal number of passes depends on the data time step, with $n = 3$ commonly adopted for daily data and nine passes recommended for hourly data.

The Wallingford Hydrology Institute developed a procedure in three steps (Gustard et al., 1992):

- Identification of the minimum values of flows over consecutive 5-day periods in the streamflow daily time series;

- Among these minima, identification of the *turning points*, ie those for which 90 % of their value is lower than the minima of the adjacent 5-day periods;

- Construction of a daily baseflow series by linear interpolation between the *turning points*.

The values of the two parameters ($d = 5$ days and $p = 90 \%$) were empirically determined based on the application of the method to a large number of British catchments. Five days reflects the average time during which the runoff generated by a rainfall event reaches the river and influences its discharge.

## Data availability

Data will be made available on request.

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