# Estimation of Monthly Water Table Depth Anomalies Based on the Integration of GRACE and ERA5-Land with Large-Scale Simulations Using Random Forest and LSTM Networks

Leandro Avila, Alban de Lavenne, Maria-Helena Ramos, Stefan Kollet

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Leandro Avila, Alban de Lavenne, Maria-Helena Ramos, Stefan Kollet. Estimation of Monthly Water Table Depth Anomalies Based on the Integration of GRACE and ERA5-Land with Large-Scale Simulations Using Random Forest and LSTM Networks. Water Resources Management, 2025, 39 (6), pp.2899-2918. 10.1007/s11269-025-04097-7. hal-05162915

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# Estimation of Monthly Water Table Depth Anomalies Based on the Integration of GRACE and ERA5-Land with Large-Scale Simulations Using Random Forest and LSTM Networks

Leandro Avila¹,² · Alban de Lavenne³ · Maria-Helena Ramos³ · Stefan Kollet¹,²

Received: 8 October 2024 / Accepted: 5 January 2025 / Published online: 16 January 2025
© The Author(s) 2025

## Abstract

Increasing pressure on groundwater resources, exacerbated by climate change, highlights the need to develop advanced methods for monitoring groundwater storage and levels. While numerical and physics-based models are widely used to analyze the spatial and temporal dynamics of groundwater levels, they require extensive input data and can be computationally expensive for high-resolution and large-scale simulations. In contrast, remote sensing products such as the Gravity Recovery and Climate Experiment (GRACE) provide global-scale information on total water storage anomalies. However, due to its coarse spatial resolution (0.25°), GRACE data cannot be used directly to assess groundwater conditions at local and regional scales. In order to obtain local groundwater levels that can be quickly accessed by stakeholders to monitor and define appropriate groundwater management, this study implements a methodology based on data-driven models to estimate monthly water table depth anomalies (wtda), integrating simulations from the Terrestrial Systems Modeling Platform (TSMP) with GRACE and reanalysis ERA5-Land datasets. Considering the spatial resolution of current TSMP simulations (TSMP-G2A - 0.11 degrees), we tested and compared multiple Random Forest (RF) and LSTM networks at the pixel scale over the Seine River Basin, combining different hydrological and climatological variables with GRACE as input features. For each data-driven approach, we selected the model that best represents the temporal pattern of the wtda during the test period and compared the results with the original TSMP simulation, as well as in-situ groundwater observations. The results indicate that both RF and LSTM networks can well reproduce the temporal patterns of groundwater levels across the Seine Basin obtained by the TSMP simulations, with average Pearson correlations of 0.65 and average KGE of 0.6, respectively. A comparison with multiple groundwater wells allowed us to identify the regions where the applied models are more reliable for representing wtda over the Seine River Basin. In general, the proposed models show good agreement with in-situ observations, independent of the groundwater well depth. However, we found significant differences between observed and simulated water table depths in the downstream regions of the Seine River Basin, where coastal systems and the presence of karst in the chalk might influence groundwater levels and the performance of the adopted models, respectively. The proposed methods provide end users with an extremely lightweight reconstruction and

<figure><img src="image_3.png" /></figure>

<footnote>Extended author information available on the last page of the article</footnote>
prediction tool for wtda at the pixel level, including reliability estimates, which is easy to implement in an ad hoc fashion in any evaluation and groundwater management workflow.

**Keywords** GRACE · Downscaling · Groundwater · TSMP · Machine learning · Deep learning · Water resources management

# 1 Introduction

Groundwater represents nearly one-third of the world's total freshwater resources and is a critical component for sustaining ecosystems, supporting many economic activities, and enabling human adaptation to climate change (Taylor et al. 2013; Saito et al. 2021; Villholth 2006). Increasing pressure on groundwater levels, mainly driven by population growth, has led to a significant decline in groundwater storage and is often accompanied by deterioration in water quality (Khorrami et al. 2021). In addition, the effects of climate change have affected groundwater storage through changes in precipitation and evapotranspiration patterns (Agarwal et al. 2023). Rising groundwater levels are also challenging groundwater management in some arid and semi-arid regions, causing problems such as waterlogging of fields, soil salinization, and increased flooding. (Singh et al. 2010, 2023). Some of the factors that contribute to the rise in groundwater levels are the continuous expansion of irrigation systems, lack of natural and artificial drainage, seepage from unlined canal networks and percolation from irrigated fields (Singh 2014). Therefore, the definition of reliable tools that can effectively monitor and simulate groundwater storage (GWS) and levels is a key task to improve groundwater management and ensure the long-term sustainability of this resource (Gleeson et al. 2012).

Traditional approaches to groundwater level assessment rely on the use of monitoring wells that provide observations for specific locations. However, measurements from individual wells may not accurately reflect conditions over large regions, and maintaining such networks requires significant resources (Bierkens and Wada 2019). In addition, in most cases the location of monitoring wells is determined by logistical factors, such as the presence of pre-existing pumping wells, rather than scientific and engineering best practices (Condon et al. 2021).

Since in-situ measurements are not sufficient to assess continuous groundwater conditions, the use of numerical models has become an important tool for understanding groundwater dynamics over large areas (Lall et al. 2020). In recent decades, significant progress has been made in groundwater modelling, which plays an important role in the development and management of groundwater resources (Gaur et al. 2011; Akter and Ahmed 2021). As the physical properties and processes governing groundwater flow are highly heterogeneous, many groundwater management problems require complex and fully distributed models that can well represent hydraulic properties with multiple boundary conditions. In addition, Kollet and Maxwell (2006) and Rahman et al. (2019) argue that surface-groundwater interactions should be incorporated into groundwater modelling to provide more reliable predictions. Thus, there has been a common interest to include more physically based models with higher spatial resolution up to continental domains (Condon et al. 2021).

Recent studies have successfully applied integrated hydrological models at large scales to assess and predict groundwater conditions (Maxwell et al. 2015; Yang et al. 2023; Keune

<figure><img src="image_4.png" /></figure>
et al. 2016). Among multiple studies, Furusho-Percot et al. (2019) provided a first simulated long-term terrestrial system climatology over Europe, including variables from groundwater over land surface to the top of the atmosphere (G2A), using the Terrestrial Systems Modeling Platform (TSMP), which is a fully integrated atmosphere-land-surface-subsurface modeling system that closes the water and energy balance from groundwater over land surface to the top of the atmosphere. While the aforementioned studies can well represent the groundwater state over large areas and the interactions with the surface and atmosphere, it is important to note that greater conceptual model complexity translates into a larger number of parameters and longer model run times, preventing the use of this type of model by stakeholders (Pandi et al. 2021; Raudkivi 2013).

Remote sensing products are also useful tools for measuring hydrological variables at large scales. In particular, the Gravity Recovery and Climate Experiment (GRACE) satellite mission provides monthly total water storage anomalies (TWSA) worldwide (Chen et al. 2016), allowing to also evaluate groundwater storage anomalies (GWSA) by removing the contributions from other surface and subsurface components (Frappart and Ramillien 2018; Khorrami et al. 2023b). Although GRACE provides reliable measurements to assess TWS for global and large-scale studies, its application at local and regional scales is limited due to its coarse resolution, requiring in most of cases the use of downscaling techniques. While dynamical downscaling includes the assimilation of GRACE data into physical and land surface models which higher spatial resolution, the statistical methods consider the definition of transfer functions to represent the statistical relationship between large-scale variable and small scale variables (Vishwakarma et al. 2021). With the advancement of machine learning (ML) and deep learning (DL) techniques, the use of data-driven models have become more feasible to downscale many climatological and hydrological variables including precipitation (Gemitzi et al. 2021), evaporation (Yin et al. 2018) or temperature Chen et al. (2021). Other studies take advantage of assimilated physical or land surface models, such as the Global Land Data Assimilation System (GLDAS), to correlate groundwater outputs with GRACE and produce GWS maps at higher resolution without requiring the intense computational costs associated with new simulations (Banerjee, Kumar 2018; Moghim 2020).

In order to bridge the scale gaps between coarse resolution observations and high resolution simulations needed to effectively monitor groundwater levels over large areas, this study explores the integration between GRACE, reanalysis ERA5-Land datasets, and large-scale simulations derived from the Terrestrial Systems Modeling Platform (TSMP) to estimate monthly water table depth anomalies (wtda) over the Seine River basin. We compared the performance of two common data-driven models such as Random Forest (RF) and LSTM networks with the aim of monitoring wtda, considering a spatial resolution similar to that of the TSMP simulations (TSMP-G2A - 0.11 degrees). In this way, we defined two main objectives for this study: (i) emulate TSMP wtda outputs using satellite and global reanalysis datasets, and (ii) downscaling GRACE data to obtain groundwater level maps that can be used for local and regional groundwater management. The adopted methodology consists of constructing independently RF and LSTM network at pixel scale in order to simulate different monthly water table depth time series using readily available atmospheric variables and remote sensing observations. The remainder of this paper is organized as follows: Section 2 provides a description of the study area, research framework, the different datasets and the
adopted methods. Section 3 presents and discusses the main results followed by conclusions in Section 4.

# 2 Methods and Materials

## 2.1 Study Area

The Seine River Basin (SRB) located in the northern region of France covers about 76,000 km² and is mainly located in the sedimentary Paris basin, a major European groundwater reservoir (Fig. 1). The SRB has a pluvial oceanic climate with an average annual precipitation of 666 mm and mean annual discharge at the outlet of the basin approximately of 600 m³/s. The SRB includes a wide variety of interconnected aquifers developed in different geological formations, with groundwater contributing significant to river flow (Rousset et al. 2004). Land use is predominately agricultural (51%), followed by woodland (25%) and grassland (18%) (Mignolet et al. 2007). The total water resource demand in the basin is about 1.8 billion m³ per year corresponding to 23 mm/year per unit watershed area, of which 55% comes from groundwater, mainly for drinking, industry and irrigation (Tavakoly et al. 2019). In terms of groundwater storage, France has not yet faced extreme cases of aquifer depletion as in other countries, however, major challenges to the long-term sustain-

<figure><img src="image_5.png" /><figcaption>**Fig. 1** The Seine River Basin (a) Location and distribution of groundwater observation wells; b Digital Elevation Model (DEM); c Land cover; d Aquifer types</figcaption></figure>

<figure><img src="image_6.png" /></figure>
ability arise from diminished recharge caused by climate change, coastal sea level rise, and future alterations in groundwater usage (Maréchal and Rouillard 2020; Habets et al. 2013).

## 2.2 General Approach

This study tackles the challenge of bridging the gap between coarse-resolution observations, large-scale models at different resolutions, and in-situ data needed for local-scale ground-water level monitoring. We propose a data-driven tool to estimate monthly water table depth anomalies, using open-access, coarse-resolution remote sensing products as input features. These features help reproduce the complex groundwater interactions represented by physics-based models at finer resolutions. This approach enables local estimation of groundwater information, reducing the computational costs of running new simulations of physics-based models. The datasets used include the GRACE satellite mission, which provides monthly global total water storage observations, the ERA5-Land reanalysis, which integrates various land variable evolutions, and the TSMP-G2A dataset, which includes daily aggregated simulation results of hydrological and climatological variables across Europe. Further details on each dataset are provided in the following subsections.

The approach applied in this study (Fig. 2) compares multiple Random Forest (RF) and LSTM networks to estimate water table depth anomalies over the SRB (0.11° × 0.11°). The target variable is the spatio-temporally continuous wtd derived from the integrated hydrological simulation results of the Terrestrial Systems Modelling Platform (TSMP) over Europe (TSMP-G2A). Input features include GRACE TWSA and various hydrological and climatological variables from the ERA5-Land dataset. For each pixel and model, we tested over 15 different models based on the input features and maximum lookback periods (months) (Eqs. 1 - 5). The models are as follows: Model 1 correlates only the monthly wtd time series with TWSA. Models 2–4 include TWSA with different variables from ERA5-Land, such as pre-

<figure><img src="image_7.png" /><figcaption>**Fig. 2** Flow chart of the monthly water table depth anomalies estimation based on GRACE downscaling procedure</figcaption></figure>
cipitation (pr), maximum temperature (tmax) and evaporation (evap), respectively. Finally, Model 5 includes all the input variables considered in the previous models. The model that best fit the wtda derived from TSMP, based on the KGE, was selected for each pixel. For the LSTM networks, the Adam optimization method was used to estimate the parameters of each network. It is worth to notice that similar approaches, such as the Recursive Feature Elimination (RFE) procedures, could also be used to select the best model for each pixel. However, RFE cannot employ because it relies on optimization techniques like gradient descent, which require a differentiable loss function. Notably, this approach implicitly represents the spatial correlation between adjacent pixels, as TSMP incorporates topography and soil properties to simulate 3D spatially correlated WTD time series. Therefore, no static inputs or time series from adjacent pixels are required.

In the first step, we remapped the ERA5-Land datasets to the target resolution of the TSMP-G2A dataset using the conservative spatial aggregation method (Schulzweida et al. 2019). For each pixel, we organized the time series of the input variables and the target variable into a training set (2011–2022), a validation set (2009–2010), and a test set (2004–2008). As shown in Fig. 2, GRACE data from a single pixel are used as input to simulate wtda for the corresponding TSMP pixels. This enables training multiple data-driven models using the same input but different outputs. The performance analysis compares the simulated wtda from both RF and LSTM with the reference TSMP-G2A dataset using metrics such as KGE, RMSE, and Pearson correlation. In addition, we validated the proposed approach by comparing the results with in-situ groundwater depth anomalies obtained for various groundwater wells distributed across the river basin, including the application of the Levene test to assess the variance between the simulated and observed data at each well. The following subsections provide detailed descriptions of the datasets and machine learning models used.

* Model1: $wtd_t = f(TWS_{t,lookback})$; maximum lookback = 4, 6, 8 months (1)

* Model2: $wtd_t = f(TWS_{t,lookback}, pr_{t,lookback})$; maximum lookback = 4, 6, 8 months (2)

* Model3: $wtd_t = f(TWS_{t,lookback}, tmax_{t,lookback})$; maximum lookback = 4, 6, 8 months (3)

* Model4: $wtd_t = f(TWS_{t,lookback}, evap_{t,lookback})$; maximum lookback = 4, 6, 8 months (4)

* Model5: $wtd_t = f(TWS_{t,lookback}, pr_{t,lookback}, tmax_{t,lookback}, evap_{t,lookback})$; maximum lookback = 4, 6, 8 months (5)

## 2.3 Datasets

### 2.3.1 GRACE/GRACE-FO Data

The Gravity Recovery and Climate Experiment (GRACE) satellite mission consists of two identical satellites flying in tandem approximately 220 kilometers apart in a polar orbit at an altitude of about 500 kilometers. Based on the distance between them, small variations in the Earth gravity field that are related to changes in Terrestrial or Total Water Storage (TWS) can be measured (Khorrami et al. 2023a; Tapley et al. 2004). Anomalies in TWS include a vertically integrated measure of water storage changes in groundwater (GW), soil

<figure><img src="image_8.png" /></figure>
moisture (SM), surface water, snow water (SWE), and biomass (Yin et al. 2018). In this study we considered the global monthly anomalies TWS based on the CSR RL06 Mascon grid (CSR-RL06.2) with a spatial resolution of 0.25°x0.25°. The data are available on the website https://www2.csr.utexas.edu/grace/RL06 mascons.html. This grid product does not require any post-processing or application of empirical scaling factors and covers a total period of 221 months, from January 2003 to January 2024. We used cubic spline method to interpolate months with missing data (Long et al. 2016).

### 2.3.2 TSMP-G2A

The TSMP-G2A dataset comprises daily aggregated simulations of several hydrological and climatological variables over Europe (0.11° × 0.11°), considering the TSMP system over the Coordinated Regional Downscaling Experiment (CORDEX) framework (EUR11) (Furusho-Percot et al. 2019). TSMP is a fully integrated atmosphere-land-surface-subsurface modeling system composed by the numerical weather prediction model of Consortium for Small-scale MOdelign (COSMO) (Baldauf et al. 2011), the Common Land Model (CLM) (Dai et al. 2003), and the 3D surface-subsurface hydrologic model ParFlow (Kollet and Maxwell 2006; Maxwell 2013). The integration of these three models allows TSMP to close the water and energy balance from the groundwater over the land surface to the top of the atmosphere. Since TSMP considers a spin-up to set the initial conditions and states up to a dynamic equilibrium, no calibration is required. Furusho-Percot et al. (2019) reported good agreement of multiple hydrometeorological variables between TSMP-G2A and observed data at the regional scale over Europe. Hartick et al. (2021) also compared total water storage anomalies between the TSMP-G2A dataset and GRACE, obtaining Pearson correlation coefficients from 0.69 to 0.89 in the different PRUDENCE regions. Figure 3 shows the long-term average of the water table depth simulated by TSMP for Europe and the SRB as well as the long term average of total water storage derived from GRACE over the SRB.

<figure><img src="image_9.png" /><figcaption>**Fig. 3** Long-term average water table depth over (a) Europe and the (b) Seine river basin derived by TSMP-G2A; and (c) Long term average of total water storage anomalies derived from GRACE</figcaption></figure>
### 2.3.3 Reanalysis Data - ERA5-Land

The ERA5-Land reanalysis dataset provides consistent images of the evolution of land variables over several decades (Munoz-Sabater et al. 2019). The ERA5-Land is produced through global high-resolution numerical integrations of the ECMWF land surface model, using downscaled meteorological forcing from the ERA5 climate reanalysis, and including an elevation correction for near-surface thermodynamic conditions. This results in a finer horizontal resolution of 9 km, compared to the 31 km resolution of ERA5. The increased spatial detail of ERA5-Land enhances its suitability for applications in water resource management, land use, and environmental monitoring, providing researchers and practitioners with more accurate and detailed data for their analyses and decision-making processes (Xie et al. 2022). The ERA5-Land dataset is available for the period from 1950 to 5 days before the current date on the website https://cds.climate.copernicus.eu. For this study we employed the air temperature at 2 m above the surface of land, daily precipitation and evaporation. Hourly data were obtained for the period 2002–2022, and we estimated the corresponding monthly maximum and minimum temperature, as well as the total monthly precipitation and evaporation.

### 2.3.4 In Situ Observations

The measured data from 486 groundwater wells were extracted from the ADES database (openly accessible from https://ades.eaufrance.fr) to verify the simulated water table depth time series results after downscaling. Figure 1 shows the location and the depth of the groundwater wells. The water table depths time series were obtained by subtracting the piezometric level from the ground elevation.

## 2.4 Machine Learning Models

### 2.4.1 Long-Short Term Memory - LSTM

LSTM is a special type of recurrent neural network (RNN) used in the field of deep learning and are suitable for processing sequential data (Hochreiter and Schmidhuber 1997). LSTM networks are designed to avoid the issue of vanishing gradients by incorporating a memory cell in which the information is selectively accumulated. In the context of groundwater modeling, LSTM networks have been used for different purposes including donwscaling and time series forecasting. For instance, Vu et al. (2021) implemented LSTM networks to reconstruct groundwater levels observed at different monitoring piezometers located in the Northern region of France. Ma et al. (2021b, 2021a) employed LSTM networks to predict water table depth anomalies over the eight PRUDENCE regions in Europe Christensen and Christensen (2007), based on the TSMP-G2A dataset. Similar to the approach presented in this study, the authors tested multiple LSTM networks at pixel scale considering as input monthly precipitation, evapotranspiration and soil moisture anomalies derived from the TSMP-G2A dataset.

<figure><img src="image_10.png" /></figure>
## 2.4.2 Random Forests

Random Forest (RF) is a supervised machine learning algorithm used for various classification and regression tasks (Hastie et al. 2015). RF operates by constructing multiple decision trees during the training process and outputting the mode of the classes (classification) or mean prediction (regression) of the individual trees. This method improves predictive accuracy and controls overfitting by averaging multiple decision trees, which individually tend to have high variance (Liaw et al. 2002). RF can effectively handle high-dimensional data and nonlinear relations between features. Several studies have applied RF for downscaling purposes including land surface temperature (Hutengs and Vohland 2016; Tang et al. 2021), precipitation (He et al. 2016), soil moisture (Zhao et al. 2018) and total water storage derived from GRACE (Chen et al. 2019; Rahaman et al. 2019; Zhang et al. 2021). RF is typically implemented for downscaling processes by first relating the input features at a coarse resolution, establishing a statistical relationship with the target variable, which can then be used at a high-resolution level (Hutengs and Vohland 2016).

## 2.4.3 Evaluation Index

The selection of each model is based on the comparison of the Kling-Gupta Efficiency (KGE) metric for the test period. The KGE is calculated following Eq. 6, where r is the correlation component (Eq. 7), α is the variability ratio component (Eq. 8) and β is the bias ratio component (Eq. 9). In this case, o denotes the observations and s denotes the simulations. We employed the correlation and root mean square error (RMSE) (Eq. 10) to compare the results of both RF and LSTM networks with the reference TSMP-2GA dataset as well as with the in-situ observations.

$$KGE = 1 - \sqrt{(r - 1)^2 + (\alpha - 1)^2 + (\beta - 1)^2} \quad (6)$$

$$r = \frac{cov(o, s)}{\sigma_o \sigma_s} \quad (7)$$

$$\alpha = \frac{\sigma_s}{\sigma_o} \quad (8)$$

$$\beta = \frac{\mu_s}{\mu_o} \quad (9)$$

$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (o_i - s_i)^2} \quad (10)$$

We also evaluated the heteroscedasticity of the time series based on the non-parametric Levene test to check variance between the simulated and observed time series. For a given k subgroups, where Nᵢ is the sample size of the ith subgroup, the Levene test statistic W is estimated as following:
$$W = \frac{(N - 1) \sum_{i=1}^{K} N_i (Z_i - Z_{i..})^2}{(K - 1) \sum_{i=1}^{K} \sum_{j=1}^{N_i} (Z_{ij} - Z_i)^2} \quad (11)$$

where N is the total number of values in all subgroups; $Y_{ij}$ is the $j_{th}$ value of the $i_{th}$ sub-group; $Z_{ij} = |Y_{ij} - \bar{Y}_y|$; $\bar{Y}_y$ is the mean of the $i_{th}$ subgroup; Z is the mean of all $Z_{ij}$; $Z_i$ is the mean of the $Z_{ji}$ subgroup. Based on the significance level $\alpha$ null hypothesis of the Levene test is rejected if $W > F_{\alpha,k-1,N-k}$, where $F_{\alpha,k-1,N-k}$ is the upper critical value of the F distribution with $k-1$ and $N-k$ degrees of freedom.

## 3 Results and Discussion

An exploratory analysis was conducted to identify the spatial correlation between wtd and the input variables considered in this study. Figure 4 shows the spatial correlation presented in the SRB, as well as the monthly time series at each pixel (grey lines) and the mean (blue line). The corresponding wtda was calculated using standardised values, using the long-term mean and standard deviation for each pixel. TWSA, tmax and evap exhibit a well-defined seasonal behaviour with low variance across pixels. Monthly precipitation, on the other hand, exhibits more variability and lack a consistent seasonal pattern for the selected dataset between 2002 and 2022. For wtd, significant differences can be observed between the monthly time series for different regions (pixels), indicating that the magnitude of wtd

<figure><img src="image_11.png" /><figcaption>Fig. 4 Spatial correlations and monthly time series for selected variables from GRACE and ERA5-Land with water table depth (wtd) anomalies obtained from TSMP</figcaption></figure>

<figure><img src="image_12.png" /></figure>
is influenced not only by meteorological forcing but also by local characteristics such as topography, soil types and water use. Since TSMP provides continuous spatial information of wtd, we can exclude the use of static information as possible input features.

Figure 4 shows that the monthly TWSA derived from GRACE is strongly negatively correlated with the wtd values from TSMP, with a mean Pearson correlation coefficient of −0.58 and a median of −0.68, indicating that wtd increases as storage decreases. These results indicate that TSMP can effectively represent the groundwater conditions over the Seine basin using GRACE satellite data, even without calibration or data assimilation procedures. Thus, GRACE and TSMP can be directly correlated using machine learning models to estimate wtd anomalies. Low correlation areas, where wtd exceeds 10 metres, indicate regions where wtd dynamics are less tightly coupled to surface exchange processes. Among the ERA5-land variables, the temperature shows the strongest positive correlation with wtd, followed by the evaporation, while precipitation exhibits a weaker, mostly negative correlation. Changes in the sign of the correlation coefficient are also observed in areas with relatively high wtd values.

Figure 5 shows the distribution of LSTM and RF models (Eqs. 1 to 5) that best fit wtd at each pixel, based on the KGE. The selected region includes a total of 714 pixels. For both approaches, Model 1, which uses only GRACE data as input feature, provides the higher KGE for most pixels during the test period, with 30% for the RF models and 38% for the LSTM models. In contrast, Model 2, which incorporates GRACE and precipitation data, provides the best fit for only 5% of the pixels for both approaches. Notable, Model 5, which includes all input variables offers the best fit for only 12% of the pixels for both models. The figure also shows clustering of different types of models in certain regions, particularly when comparing the RF models and the maximum lookback period. For LSTM networks, models based only on GRACE data (Model 1) are primarily found in the upper Seine basin, where groundwater conditions are mainly influenced by hydrological processes, as opposed to the lower part of the basin, where coastal processes and sea level may influence groundwater levels. Additionally, the selection of model type may be influenced by the maximum lookback periods considered in this study. For instance, De Lavenne et al. (2022) identified multi-year memory between river discharge and annual precipitation for some sub-catchments of the Seine. Therefore, increasing the maximum lookback periods can redefine the distribution of the fitted model, including in more cases the precipitation as a feature.

Figure 6 shows the performance of RF and LSTM models, comparing their results with TSMP data. The performance analysis is based on the KGE, the Pearson correlation coefficient and the RMSE obtained during the test period. Additionally, the monthly wtd time series for six randomly selected pixels were compared. The results indicate that, on average, the RF models achieve a KGE of 0.52 while the LSTM models yield a KGE of 0.54. For RSMSE, the RF models have an average value of 0.1, while the LSTM networks have 0.23 m. The average Pearson correlation coefficient is 0.61 for the RF models and 0.60 for the LSTM networks. The results also show that lower KGE values occur in regions where GRACE and TSMP are poorly correlated. Based on the RMSE, lower errors are generally found in regions with shallower wtd (closer to the surface). The time series in Fig. 6 demonstrate how TSMP simulates different groundwater conditions across the SRB. For instance, points (a), (c), and (d), located in regions with shallow wtd near surface and the main river, show a clear seasonal pattern over the years. In contrast, points (b), (d) and (e), exhibit more

<figure><img src="image_13.png" /></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 5** Spatial distribution of selected RF models and LSTM networks based on the input features and maximum lack time over the SRB</figcaption></figure>

stable and less pronounced seasonal variation, likely due to their deeper water table depths, which buffer high-frequency land surface fluctuations.

To independently validate the proposed LSTM and RF models, a comparison with in-situ observations was conducted, including wtd values derived from TSMP as a benchmark. Standardized values were calculated for each time series using the long-term mean and standard deviation. The comparison was made using 486 WTD wells. To match the resolution of the simulated data, each WTD well was assigned to the nearest pixel. If multiple wells were located in the same pixel, their monthly mean value was calculated, resulting in a total of 236 pixels with observed data. Figure 7 shows the Pearson correlations between the observed data and the different modeling approaches, including TSMP. We also compared the wtda time series at six randomly selected pixels. The size of each point (station) indicates the depth of each WTD well relative to the average depth of the observed time series. For all WTD wells, the average correlation coefficient was 0.3, with a maximum of 0.89. Based on Fig. 7, the performance varied by the location of the WTD wells. Points (d), (e) and (f) show more seasonal behaviour in water depths, which are well captured by the simulated data, with mean correlations between 0.42 and 0.89 and mean RMSE values between 0.99 and 0.28, respectively. These points are located in the upper part of the catchment, where groundwater dynamics are more tightly linked to surface exchange processes.

<figure><img src="image_15.png" /></figure>
<figure><img src="image_16.png" /><figcaption>**Fig. 6** Comparative performance metrics of WTD obtained from TSMP and the downscaled WTD obtained from LSTM and RF models</figcaption></figure>

However, for points (a), (b) and (c), the simulated data do not satisfactorily capture the temporal variations, with poor correlation in the lower Seine basin, regardless of the well depth. In these regions, we argue that groundwater levels are influenced by coastal systems and sea levels, leading to lower wtda variance. Therefore, a limitation of TSMP can be identified in this area, as coastal systems and sea levels are not considered in the modeling process. Additionally, the presence of karst in the chalk and strong interactions with streamflow in the lower part of the Seine river basin can affect the performance of the TSMP simulation over this particular region (Le Mesnil et al. 2020).

Levene's test was performed to statistically evaluate the differences between the simulated and observed wtd time series at each WTD well. Figure 8 shows the p-values obtained from Levene's test for each WTDobs well, considering different significance levels. Red dots indicate a p-value lower than 0.01, orange dots indicate p-values between 0.01 and 0.05 and green dots represent a p-value greater than 0.05. The results show that, on average,
<figure><img src="image_17.png" /><figcaption>Fig. 7 Pearson correlation coefficient between observed monthly water table depth anomaly and (A) the simulated by TSMP (TSPM-G2A) and the downscaled results obtained with (B) LSTM networks and (C) RF for the period 2004–2018. (D) (a)-(f) Time series for six arbitrary selected grid cells marked on the map in (A)</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 8 P-values obtained from the Levene test for each data-driven model and the reference TSMP-G2A dataset at each WTDobs well</figcaption></figure>

38% of the WTDobs wells reject the null hypothesis at $\alpha = 0.01$, while 55% of the WTDobs wells do not reject the null hypothesis at a significance level of $\alpha = 0.05$. In addition, 8% of the WTDobs wells have a p-value between 0.01 and 0.05. Similar to Fig. 7, most of WTD wells where the simulated data do not follow the same variance with the observed data are located in the lower part of the Seine basin, whereas orange dots are mainly located in center of the basin.

Finally, based on the results from Fig. 7, we generated interpolated maps using Pearson correlation and RMSE create confidence maps for monitoring groundwater level anomalies over the SRB (Fig. 9). Overall, both data-driven models show similar spatial patterns, with

<figure><img src="image_19.png" /></figure>
<figure><img src="image_20.png" /><figcaption>Fig. 9 Interpolated Pearson correlation maps between observed and simulated groundwater depth anomalies over the Seine river basin</figcaption></figure>

lower Pearson correlations in the lower part of the basin and correlations up to 0.7 in the upper basin. While the LSTM and RF models show higher correlations in some areas, they do not significantly differ from the original TSMP simulations. The LSTM approach, however, is less reliable and has more areas with Pearson correlations below 0.2 compared to the RF models. Although the LSTM model's performance could be improved with additional parameter tuning, such as adjusting the number of epochs and the batch size, the current results suggest that the RF can better represent the monthly wtda pattern over the Seine basin. Thus RF is a more efficient and parsimonious approach for simulating wtda at the pixel scale. However, given the multi-year memory observed in previous studies between river discharge and precipitation, the maximum lookback period should be increased to fit the adopted models, specially for LSTM.

# 4 Conclusions

In this study, we investigated the integration of large-scale simulations with remote sensing and global reanalysis datasets to estimate monthly wtda over the Seine basin using RF and LSTM networks. We explored the temporal correlation at the pixel scale between hydrological and climatological variables derived from GRACE and ERA5-Land to generate WTDA anomaly maps originally simulated by TSMP. This allowed us to assess the emulation of TSMP outputs and the downscaling of GRACE total water storage anomalies using data-driven models. Thus, the main innovation of this study is the use of machine learning models to integrate global remote sensing and reanalysis products with large-scale simulations, enabling both the downscaling and emulation of groundwater level anomalies derived from the GRACE and TSMP-G2A datasets, respectively.

<figure><img src="image_21.png" /></figure>
We tested and compared multiple LSTM and RF model structures for each pixel to deter-
mine the best input combination for each case. Unlike implementing a single ML or DL
model for the entire river basin, which requires pooling data for all pixels and using a
uniform set of input variables, the current approach defines the optimal input combina-
tion for the different regions independently, allowing efficient re-training of models with
poor performance. Additionally, the development of lightweight, pixel-scale models enables
independent execution on local computers or in the cloud, which is crucial for stakeholders
and decision-makers.

The comparison between the results from data-driven approaches with TSMP showed
both LSTM and RF models can effectively represent the temporal variations of water
table depth across different regions of the Seine River Basin. This highlights the ability of
machine learning methods to emulate the diagnostic output of complex physical models
using a minimal number of input variables. In this study we did not used static inputs or
data from neighboring pixels to represent the spatial correlation, as these are embedded in
the 3D simulations using TSMP. For the testing phase, the RF models achieved an average
correlation of 0.61, while the LSTM models achieved 0.60. The average KGE values were
0.52 for RF and 0.54 for LSTM, with average RMSE values of 0.18 m for RF and 0.23 m
for LSTM. Given that both approaches showed similar performance, we conclude than RF
models offer a more efficient solution for simulating wtd at the pixel scale, based on compu-
tational cost. However, superior results could be obtained with LSTM models by increasing
the maximum lookback period to include more long-term memory of the selected variables,
given the multi-year memory explored in previous studies.

An independent comparison with in-situ water table depth observations was conducted to validate the proposed models and original TSMP-G2A dataset over the selected area. Gener- ally, higher correlations were found at wtd wells located in the upper part of the river basin, while discrepancies between simulated and observed data increased in the lower part. We hypothesize that these differences are due to the distinct groundwater systems in the Seine basin, particularly in the lower part, where coastal processes may influence water table dynamics, or possibly due to the presence of karst in the chalk. Additionally, the TSMP- G2A dataset does not account for oceanic or coastal processes in the modelling process.

The results from this study can be extended and complemented in future studies by incorporating in situ wtd observation as targets during the training process. For this case, multi-objective functions could be implemented to adjust both the observed data in regions with in-situ information and the simulated values derived from the TSMP-2G dataset. The presented results could also be compared to a single ML or DL model that integrates the information from all pixels. In such a model, static input features should be included in the training process. Additionally, more climate and hydrometeorologic variables, such as soil moisture or runoff volume, could be included to improve the performance of the proposed models at the pixel scale. Finally, we recommend validating the proposed methodology in other regions based on the available data.

**Author Contributions** L.A. and S.K. conducted the research and designed the methodology. L.A. and A.L collected the data. L.A. developed the model code and performed the simulations, with some contributions from S.K., L.A. wrote the paper, S.K., A.L. and M-H.R. helped to revise the paper. All authors read and approved the final manuscript.

<figure><img src="image_22.png" /></figure>
**Funding** Open Access funding enabled and organized by Projekt DEAL. This work is funded by the European Union's HORIZON Research and Innovation Actions Programme under Grant Agreement No. 101059372 (STARS4Water project).

**Data Availability** Materials and data used in the present paper are available under request to the corresponding author.

**Declarations**

**Ethical Approval** Not applicable

**Consent to Participate** Not applicable

**Consent to Publish** Yes

**Competing Interests** The authors have no relevant financial or non-financial interests to disclose.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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**Publisher's Note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Authors and Affiliations

Leandro Avila<fnref n="1" />,<fnref n="2" /> · Alban de Lavenne<fnref n="3" /> · Maria-Helena Ramos<fnref n="3" /> · Stefan Kollet<fnref n="1" />,<fnref n="2" />

<figure><img src="image_25.png" /></figure>

Leandro Avila

l.avila@fz-juelich.de

<figure><img src="image_26.png" /></figure>

<footnote n="1">¹ Institute of Bio and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich, Jülich 52428, Germany</footnote>

<footnote n="2">² Centre for High-Performance Scientific Computing in Terrestrial Systems, Geoverbund ABC/J, 52428 Jülich, Germany</footnote>

<footnote n="3">³ INRAE, UR HYCAR, Université Paris-Saclay, 92160 Antony, France</footnote>
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