# Large-scale climate drivers of groundwater level variations in northern France over the last century

Lisa Baulon, Nicolas Massei, Bastien Dieppois, Manuel Fossa, Delphine Allier,

Hélène Bessière, Matthieu Fournier

► To cite this version:

Lisa Baulon, Nicolas Massei, Bastien Dieppois, Manuel Fossa, Delphine Allier, et al.. Large-scale climate drivers of groundwater level variations in northern France over the last century. Journal of Hydrology, 2025, 102, pp.132937. 10.1016/j.jhydrol.2025.132937. hal-04978045

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Submitted on 4 Apr 2025

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Research papers

# Large-scale climate drivers of groundwater level variations in northern France over the last century

Lisa Baulon<sup>a,b,*</sup> <small>(D)</small>, Nicolas Massei<sup>b</sup>, Bastien Dieppeis<sup>c</sup>, Manuel Fossa<sup>b</sup>, Delphine Allier<sup>a</sup>, Hélène Bessière<sup>a</sup>, Matthieu Fournier<sup>b</sup>

## ARTICLE INFO

This manuscript was handled by Andras Bar-dossy, Editor-in-Chief, with the assistance of Claus Philip Haslauer, Associate Editor

**Keywords:**

- Groundwater levels

- Low-frequency variability

- Large-scale climate drivers

- Northern France

## ABSTRACT

Groundwater levels (GWL) are often affected by low-frequency variations, i.e., on timescales greater than a year. In northern France, this low-frequency variability (LFV) generally explains more than half of total GWL variability. Such LFV in GWL is thus often responsible for the emergence of groundwater droughts and floods. It is, therefore, essential to explore the large-scale climate drivers of such LFV to improve GWL prediction system and better forecast and manage groundwater droughts and floods. In this study, we investigate the large-scale climate drivers of the LFV of northern France GWL. We use a century long timeseries of GWL and precipitation, and examine their links to different large-scale ocean-atmospheric patterns, using sea-surface temperature [SST] and geopotential heights at 500mb [Z500]. We first assessed the multi-timescale variability of GWL and precipitation using continuous and discrete wavelet transforms. Besides annual variability, interannual (IV: ~7-yr) and decadal (DV: ~14-yr) variability better explain GWLs' total variance. Then, we identify atmospheric and oceanic patterns, which are associated with each timescale of LFV using composite analyses. IV is associated with a "wave train" pattern over the Euro-Atlantic sector with a low (high) pressure system over northern-western Europe favoring wet (dry) conditions over northern France during interannual high (low) GWL. Such pattern seems quite similar to a ridge regime (during high GWL) and Scandinavia blocking regime (during low GWL). IV is also associated with a SST pattern in North Atlantic that is typical of an Atlantic ridge regime. DV seems to be associated with a low (high) pressure system covering Great Britain and extending through the Gulfstream front favoring wet (dry) conditions and leading to decadal high (low) GWL in northern France. The SST in North Atlantic display a very similar pattern than atmospheric circulation. Z500 pattern associated to IV is close to the Scandinavian Pattern (SCAND) index, whereas that associated to DV diverges quite significantly from a standard climate index. Using a multiresolution Empirical Statistical Downscaling model, we show that low-frequency variations of GWL can be correctly simulated using the large-scale low-frequency information in atmospheric fields (Z500), which enhance the simulation of total GWL too. This result highlights the potential of large-scale atmospheric patterns found by composite analysis to be used as predictors in statistical models for reconstructing or predicting GWL.

## 1. Introduction

In a context of climate and environmental changes, the uncertainty concerning future trends and variations in water resources is one of the most significant issues from the end of the last century (IPCC, 2007, 2014, IPCC, 2021). Aquifers are particularly affected by anthropogenic pressure, as, in some countries like France, they can account for more

than half of water supplies (Maréchal and Rouillard, 2020). Groundwater levels (GWL) have therefore been monitored for few decades in France, and the existence of trends has recently been discussed. Trend estimates may help to assess the quantitative evolution of groundwater resource and help to the resource management. The European Union's Water Framework Directive is based on this philosophy for instance (European Commission, 2009), and the detection of negative trends in

<footnote><sup>a</sup> BRGM, 3 av. C. Guillemin, 45060 Orléans Cedex 02, France</footnote>

<footnote><sup>b</sup> Normandie Univ, UNIROUEN, UNICAEN, CNRS, M2C, 76000 Rouen, France</footnote>

<footnote><sup>c</sup> Centre for Agroecology, Water and Resilience (CAWR), Coventry University, UK</footnote>

<footnote>* Corresponding author at: BRGM, 3 av. C. Guillemin, 45060 Orléans Cedex 02, France.</footnote>

<footnote>E-mail address: l.baulon@brgm.fr (L. Baulon).</footnote>
water resources (streamflow, GWL) can lead to some restrictions in order to protect them.

However, while studies of recent trends in GWL remain useful for stakeholders, their interpretations can be strongly misleading in the presence of significant low-frequency variability (LFV; Baulon et al., 2022a). The presence of LFV is common to all hydroclimate variables affecting a catchment (e.g., precipitation, temperature, streamflow), since it originates from large-scale climate variability (Coulibaly and Burn, 2004; Labat, 2006; Massei et al., 2007, 2010; Dieppois et al., 2013, 2016b; Boé and Habets, 2014; Sidibe et al., 2019; Kingston et al., 2020). In addition, the proportion of variance explained by such LFV depends on the catchment characteristics (Gudmundsson et al., 2011; Velasco et al., 2017; Sidibe et al., 2019). Several studies highlighted that morphometric and physical properties of aquifers (e.g., thickness of vadose zone and superficial formations, permeability of vadose zone, transmissivity and storage coefficients, aquifer geometry, connection with neighbouring aquifers and rivers) acted as a low-pass filter on climatic variations (e.g., rainfall and evapotranspiration) (Slimani et al., 2009; El Janyani et al., 2012; Velasco et al., 2017; Rust et al., 2018; Schuite et al., 2019).

In particular, across France, several studies have already highlighted the existence of ~2-4 years, ~5-8 years and ~15 years modes of variability in hydroclimate variables (Massei et al., 2007, 2010, 2017; Fritier et al., 2012; Massei and Fournier, 2012; Dieppois et al., 2013; Fossa et al., 2021). Multidecadal variability (50-80 years) has also been identified in streamflow, precipitation and temperature (Boé and Habets, 2014; Dieppois et al., 2016b). Similar LFV (interannual to multidecadal) with varying magnitudes were found in GWL through France (Slimani et al., 2009; El Janyani et al., 2012; Baulon et al., 2022a, Baulon et al., 2022b), but also in neighbouring countries (Holman et al., 2011; Rust et al., 2019; Liesch and Wunsch, 2019; Neves et al., 2019). However, ~5-8 years and ~15 years variabilities often explain much more of the GWL variability than ~2-4 years variability (Baulon et al., 2022a).

For the last decades, numerous studies have investigated relationships between hydrological variations and large-scale climate variability (Kingston et al., 2007; Lavers et al., 2015; Dieppois et al., 2016b). Most studies previously investigated and identified links between regional hydrological variations and large-scale climate variations using various climate indices, such as the North Atlantic Oscillation (NAO), Scandinavia pattern (SCAND), East Atlantic pattern (EAP), El Niño Southern Oscillation (ENSO), Atlantic Multidecadal Variability (AMV) (Giuntoli et al., 2013; Luppichini et al., 2021). Using more sophisticated techniques, some studies relatively recently illustrated that those linkages between regional hydrological variations and large-scale climate modes of variability were strongly dependent on the timescale and time-period considered (Massei et al., 2007, 2010; Holman et al., 2011; Fritier et al., 2012; Boé and Habets, 2014; Kuss and Gurdak, 2014; Dieppois et al., 2013, 2016b; Neves et al., 2019; Liesch and Wunsch, 2019). In addition, some authors demonstrated that the atmospheric dynamics associated with the different timescales are not systematically consistent with the dynamics associated with the NAO, SCAND and other pre-established climate modes of variability (Massei et al., 2017; Sidibe et al., 2019; Fossa, 2020).

Looking at atmospheric patterns responsible for LFV in GWL then appears more relevant when one seek to better understand the linkages between large-scale climate variability and local-scale hydrological variables. Consequently, in this study, we aim at exploring the links between large-scale climate variability and groundwater low-frequency variations by directly using atmospheric and oceanic fields instead of standard climate indices. This approach consisting of unraveling climate drivers directly from the target data had also been recommended lately by Kingston et al. (2020).

Focusing on groundwater resources appears crucial, since i) in many aquifers, GWL are mostly, if not only, controlled by LFV which then explain water stock changes (Velasco et al., 2017; Rust et al., 2019;

Baulon et al., 2022a); ii) because, for this same reason, the LFV plays a significant role on groundwater droughts and floods occurrence (Rust et al., 2019; Bonnet et al., 2020; Baulon et al., 2022b). The identification of large-scale atmospheric patterns associated with the LFV in GWL would be also useful for predictive purposes. LFV is indeed aperiodic and, consequently, no deterministic prediction of future GWL can be done. However, provided some consistent relationship is found between the large-scale circulation and local-scale variable, the identification of most relevant climate drivers of LFV may allow for a better assessment of future GWL and extreme. For these reasons, we attempt to identify the large-scale climate drivers of groundwater LFV in order to inform and improve predictions of GWL in future studies.

To that aim, we first explore the multi-timescale variability of one-century long precipitation and GWL time series in the chalk of northern France to identify the main components characterizing the low-frequency variability (Section 3.1). We then use a composite analysis to explore the link between large-scale atmospheric-oceanic dynamics and GWL, and identify large-scale climate patterns associated with each of the LFV previously identified (Section 3.2). We then assess whether GWL and associated extreme can be better simulated using a multi-resolution empirical statistical downscaling (ESD) model tracking the driving atmospheric variations at multiple timescales (Section 3.3).

## 2. Data and methods

### 2.1. Data

This study focuses on GWL within the chalk aquifers in France (Fig. 1), where the longest GWL time series are available. We primarily focus on a time series (Tincques) covering the entire 20th century (1903–2022) to explore the long-term variability of GWL and relationships with large-scale climate variability. The Tincques borehole is located in the most northern part of Paris Basin chalk aquifers. There are no reference databases gathering groundwater abstraction data since 1903 in the area. It is therefore not possible to determine the impact of withdrawals on the groundwater level variability. Withdrawals data has only been available since 2008: values have always been less than 180,000 m3/year over 2008–2015 in this area (BNPE: https://bnpe.eaufrance.fr/). In addition, 53 shorter time series (1976–2022) were also used to display the low-frequency behaviour of GWL across chalk aquifers of Paris Basin (France). These time series were selected from a database gathering boreholes where GWL are not (or only sparsely) affected by pumping (Baulon et al., 2020). Moreover, they contain a relatively small number and length of consecutive gaps (<3 years). Missing values were filled using linear interpolation, except for the Tincques time series that was filled using data of neighboring boreholes. GWL data were initially provided by the ADES (Accès aux Données sur les Eaux Souterraines) database (https://ades.eaufrance.fr/; Winckel et al., 2022).

We also analyzed a monthly precipitation time series covering the 20th century (1901–2019) from the Climatic Research Unit (CRU) dataset (CRU TS.v4.04), which is produced on a 0.5°x0.5°grid and is derived from about 4000 weather stations distributed around the world over the last century (Harris et al., 2020). Here, we extracted a regional average for an area corresponding to 2.0E-3.5E in longitude, 49.5 N-50.5 N in latitude, i.e., encompassing the Tincques borehole.

To examine the large-scale atmospheric patterns associated with local precipitation and GWL variability, we used the NOAA Twentieth Century Reanalysis version 3 (20CR v3; Slivinski et al., 2019), an 80-member ensemble global reanalysis (from 1836 to 2015) dataset at a 2°x2° resolution. This reanalysis product assimilates only surface pressure with monthly SST and sea-ice distributions as boundary conditions. This modelling and data assimilation strategies remain constant over the entire period to allow more robust spectral decomposition in analyses of atmospheric circulation across different timescales with reduced sensitivity to artificial shifts induced by assimilation of new
<figure><img src="image_2.png" /><figcaption>Fig. 1. Location of boreholes.</figcaption></figure>

datasets, as is the case for NCEP/NCAR-1 reanalysis as shown in Poccard et al. (2000). In the present study, we extracted geopotential height at 500mb (Z500), zonal and meridional wind at 500mb (U500 and V500) at a monthly time step over a region covering 0–360°E and –20–80°N zone for the composite analysis. These fields are suitable to describe atmospheric circulation, sufficiently high in altitude so as to avoid surface roughness effects (like mountain ranges). However, for the multi-resolution Empirical Statistical Downscaling, the area was restricted to the Euro-Atlantic sector (–110–60°E 35–80°N). In addition, analyses were also performed with the geopotential height at 200mb (Z200), corresponding to the tropopause height and the jet-stream altitude, and sea level pressure (SLP), which provided similar results to Z500 (not shown).

Finally, for investigating teleconnections with precipitation and GWL variability, we used a monthly gridded SST dataset, the Extended Reconstructed SST version 5 (ERSST v5; Huang et al., 2017). ERSST.v5 is derived from the International Comprehensive Ocean-Atmosphere Dataset (ICOADS) Release 3.0, and provides data from January 1854 to the present at a 2°x2° resolution. More importantly, unlike other SST datasets, this dataset is not affected by cold SST biases resulting from satellite data assimilation at the end of the 20th century, which can sometimes induce a modest decrease in the global warming trend, and possibly for decadal signals (Reynolds et al., 2002).

## 2.2. Methodological approach

### 2.2.1. Multi-timescale variability of precipitation and groundwater levels

We identified the dominant timescales of variability in precipitation and GWL at Tincques using the Continuous Wavelet Transform (CWT). The CWT has been extensively used in the past decades for data analysis in hydrology and more generally in environmental sciences (Torrence and Compo, 1998; Labat, 2005; Massei et al., 2010; Turki et al., 2020; Zamrane et al., 2021). The mathematical basis and practical use of the CWT can be found in Torrence and Compo (1998). It consists in breaking down the precipitation or GWL time series into the time-frequency domain allowing us to examine the variance evolution over time and for each timescale. It produces a timescale contour diagram on which the x-axis indicates time, the y-axis the period, and the z-axis the spectral power (i.e., variance or energy). We also derived time-averaged wavelet spectra from CWT to identify what periods (i.e., timescales) display peaks of energy (Torrence and Compo, 1998; Labat, 2010; Abdelkader and Yerdelen, 2022).

Then, the dominant timescales of variability were extracted using a Multi-Resolution Analysis (MRA) based on Maximum Overlap Discrete Wavelet Transform (MODWT; Percival and Walden, 2000). The MODWT-MRA is iterative filtering of the time series using a series of low- and high-pass filters. It performs a scale-by-scale decomposition of the time series (or signal) using a dyadic filter bank. This filter bank is composed of one high-pass filter and one low-pass filter, which compute coefficients associated with high frequencies, called the “detail coefficients”, and low frequencies, called the “approximation coefficients”, by convolution with the signal analyzed. The first lower-frequency signal (or “approximation”) released is then convolved again by the high- and low-pass filters and the same process is repeated iteratively until either the desired or the maximum number of components is reached. The original signal is then separated into a relatively small number of wavelet components from high to low frequencies, which together explain the total variability of the signal. The original signal can be reconstructed by summing up all wavelet details and the last approximation.

Unlike discrete wavelet transform (DWT), MODWT was designed to prevent phase shifts in the transform coefficients at all scales by avoiding downsampling – reducing by a factor of two the number of coefficients – the signal with increasing scales. MODWT then preserves the alignment of the decomposed transform coefficients at each level with the original time series; that is, the variance explained by these coefficients is located where it truly lies in the time series analyzed (Percival and Walden, 2000; Cornish et al., 2003, 2006). For physical interpretation of the wavelet details, this property is fundamental and MODWT has been largely used for that purpose in several studies (Massei et al., 2017; Pérez Ciria et al., 2019; Sidibe et al., 2019).

In this study, we used Daubechies least asymmetric wavelet with 8 coefficients (“s8”) as a filter. First, this wavelet filter is well-suited for the decomposition of turbulent signals (Cornish et al., 2006), such as atmospheric/oceanic variables or precipitation. Although an “s16” or “s20” wavelet filter would be more suitable for the decomposition of GWL since the signal is much smoother, we kept the “s8” that allows us to discriminate the ~14-yr variability as an independent component from the last approximation while setting the maximum decomposition level to details that are not subject to edge effects (i.e., to internal coefficients). We compared the wavelet details of GWL obtained with “s8” and “s20” wavelet filters. The extracted details were rather similar and confirmed the choice to use an “s8” to break down GWL. However, even with the “s8” filter, discriminating the ~14-yr variability from the last
approximation by keeping only internal coefficients is only possible for the one-century GWL time series of Tincques. For the shorter GWL time series in chalk aquifers of the Paris Basin, the maximum level decomposition is therefore set to $log_2(N)$, where N is the length of the time series.

### 2.2.2. Linking large-scale climate patterns with local variability of precipitation and groundwater levels

The investigation of teleconnections between precipitation or GWL at Tincques and the large-scale climate variability for the dominant low-frequency modes is conducted with a composite analysis. Similarly to local variables (precipitation and GWL), the large-scale climate variables (Z500, U500 and V500) are previously decomposed using MODWT-MRA analysis. We then generate a composite map for each dominant low-frequency timescale. First, for each timescale, the values of the Z500, U500 or V500 wavelet detail during periods of high amplitude (i.e., below or above 0.5 standard deviations (SD)) of precipitation or GWL at the same timescale are extracted. For each timescale, it results in two sets of large-scale data: one corresponding to large-scale values when the local variable (precipitation or GWL) values were higher than +0.5SD (wet anomalies), one corresponding to large-scale values when the local variable values were lower than -0.5SD (dry anomalies). The composite maps then represent the difference in large-scale variables between wet and dry conditions. In this study, we display Z500 composite maps with associated wind vectors calculated with U500 and V500 composites.

For the composite large-scale climate anomalies associated with GWL variations, we use a time lag of ~7 months between the large-scale variable and GWL. We assumed that the response of precipitation to large-scale variables is immediate, while that of GWL to precipitation is delayed. We estimated the lag between GWL and precipitation using a cross-correlation function (CCF).

### 2.2.3. Added-value for predictions or reconstructions of groundwater levels

In order to assess the potential of large-scale atmospheric fields, and more specifically of patterns found with the composite analysis, to be used as predictor of GWL in future statistical models, we used an empirical statistical downscaling (ESD) model to determine their capability to correctly simulate the groundwater LFV and total GWL at Tincques.

Briefly, the first step consists of calculating the EOFs of the atmospheric field (Z500): atmospheric fields are decomposed with orthogonal functions determined from the data. The approach is close to a principal component analysis, except that the EOFs allow us to obtain both temporal and spatial patterns. The second step consists in calibrating an ESD model. This ESD modelling is based on multiple linear regression of the local variable (GWL) on empirical orthogonal functions (EOFs) of atmospheric fields (Z500) on an annual basis (Benestad et al., 2015). This regression analysis is used to estimate the best-fit weights (regression coefficients) whose products with the time variations of the different Z500's EOF give the closest representation of the local time series y. It follows the following expression:

$$ \hat{y}(t) = \beta_0 + \sum_{i=1}^{n} \beta_i V_i(t) $$

with $\hat{y}(t)$ the temporal variations of the local variable (GWL), $\beta_i$ the regression coefficients, $V_i(t)$ the temporal variations of the Z500's EOF$_i$.

Two approaches were tested in this study: simple ESD and multi-resolution ESD. For the simple ESD, GWL are directly simulated using the EOFs of the atmospheric field (Z500) without any decomposition of GWL and atmospheric field. For the multiresolution ESD, we use the multi-timescale approach developed by Massei et al. (2017) and used by Sidibe et al. (2020). The approach consists to derive one ESD model for each decomposition level (i.e., for each wavelet detail/component) of GWL and atmospheric field resulting in a simulation of each GWL

component. Then, all simulated GWL components can be summed up to reconstruct total GWL given the use of MODWT-MRA and the orthogonality of the decomposition.

Optimally, the number of EOFs used in the ESD model must be high enough to consider all the main large-scale patterns accounting for the GWL variability, but at the same time not too important to not consider “atmospheric” noise in the modelling process. In this paper, only the first 6 EOFs were used since all higher-order components would explain less than 5 % of total variance.

The ESD model was calibrated over the 1903–2015 period.

For each simulated GWL component and the reconstructed GWL, we calculated the Nash-Sutcliffe model efficiency coefficient (NSE; Nash and Sutcliffe, 1970) and the coefficient of determination ($R^2$) for assessing the quality of simulations. The $R^2$ values range between 0 and 1; a value of 0 indicates no statistical correlation between the data and the line drawn through them, while a value of 1 indicates a perfect relationship. The NSE range between -∞ and 1; a value of 1 indicates a perfect match of forecasted/simulated data to the observed data, while a value less than 0 occurs when the observed mean is a better predictor than the model.

The ESD modelling was undertaken with R package “esd” (Benestad et al., 2020).

## 3. Results

### 3.1. Precipitation and groundwater level variability in chalk over the 20th century

Precipitation and GWL variability at Tincques are first explored using CWT (Fig. 2). For precipitation, the CWT highlights significant seasonal and annual variabilities. The low-frequency is expressed at timescales of about 2–4 years (interannual ~4-yr), 5–8 years (interannual ~7-yr) and 12–23 years (decadal ~14-yr). These variabilities are also displayed by the time-averaged global wavelet spectrum of precipitation (Fig. 3). The decadal variability seems attenuated between ~1930 and ~1970, while the annual variability seems amplified during this period (Fig. 2).

For GWL, annual (~1-yr), interannual (~7-yr, IV) and decadal (~14-yr, DV) variabilities are particularly significant, while the seasonal variability is much less expressed (Figs. 2 and 3). For that reason, in the following sections, we primarily focus on ~7-yr and ~14-yr variabilities. However, unlike precipitation, the DV in GWL does not seem reduced between 1930 and 1970 (Fig. 2).

The interannual (~7-yr, IV) and decadal (~14-yr, DV) variability of precipitation and GWL at Tincques are extracted by MODWT-MRA (Fig. 4a and 4b). Such low-frequency timescales of variability represent only a small part of precipitation variability accounting only for 4 % of total monthly variability, while they are strongly amplified in GWL accounting for 44 % of total variability. This is related to the low-pass filter effect of catchment and aquifers (filtering out high-frequency variabilities and amplifying low-frequency variabilities), which is already significantly documented in the literature (Slimani et al., 2009; Gudmundsson et al., 2011; Fossa et al., 2021).

The same LFV can be also identified and extracted from the shorter GWL time series of chalk aquifers (Fig. 4c). It shows that GWL low-frequency variability is spatially coherent over a much broader region, with higher (lower) levels than normal almost observed over the same time-period. In precipitation and GWL time series of Tincques, the low-frequency components exhibit numerous amplitude changes over the 20th century indicating the aperiodic behavior of such variability (Fig. 4a and 4b). These amplitude changes in LFV are also identified in other boreholes with shorter GWL time series, particularly for the IV (Fig. 4c). A decreased amplitude of DV is found between 1945 and 1965 in GWL, which did not really appear in the CWT (Figs. 2 and 4b).

Such timescales of variability (~7-yr, ~14-yr) in GWL are also identified in other aquifers (chalk, limestones, sands) across France and
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** One-century precipitation and groundwater levels time series at Tincques (top) and continuous wavelet transform (CWT; bottom). On CWT, the greater the spectral power (red), the greater the signal amplitude at that timescale and time-period is. Black lines surround regions of the spectrum that are statistically significant at the 95% confidence limit (Monte-Carlo test). White dashed lines correspond to the cone of influence, where edge effects are important and may lead to underestimated variance.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Time-averaged global wavelet spectra of precipitation (left) and groundwater levels (right) at Tincques.</figcaption></figure>

neighboring countries (Liesch and Wunsch, 2019; Neves et al., 2019; Rust et al., 2019; Baulon et al., 2022a-b). However, their significance in total GWL variability changes between aquifers, depending on their physical and morphometric properties (Slimani et al., 2009; El Janyani et al., 2012; Velasco et al., 2017; Schuite et al., 2019). For many aquifers, including the southern part of the Artois-Picardy chalk aquifer here studied with Tincques time series, the LFV explains more than half of GWL variability. Hence, LFV significantly supports the extremely high and low GWL leading to the emergence of groundwater droughts and floodings (Baulon et al., 2022b). For that reason, the identification of large-scale climate patterns associated with such IV and DV remains fundamental, particularly for predictive purposes of groundwater droughts and floodings. This topic is investigated in the next section.

## 3.2. Climate drivers of interannual and decadal variabilities in precipitation and groundwater levels

To deepen our understanding of the link between large-scale ocean-atmospheric circulation and regional hydrological variability, we study the spatial patterns of climate dynamics by computing composite anomalies associated with IV (~7-yr) and DV (~14-yr) (Fig. 5). Hereafter, only results with SST, Z500 and winds at 500 mb are presented (Fig. 5). Other pressure levels have however been tested, and they provided similar results (not shown).

Z500 pattern associated with IV in precipitation and GWL is a wave

train pattern extended through the northern hemisphere that also seems to be connected to a zonal pattern in the subtropical Pacific ocean (Fig. 5a). The Z500 pattern exhibits four centers of action over the Euro-Atlantic area, which are arranged longitudinally with alternating low- and high-pressure systems. This pattern may lead to alternating ridge (leading to wet conditions and high interannual GWL) and blocking (leading to dry conditions and low interannual GWL) weather types over northern France. In other words, during drier conditions and lower GWL periods, high-pressure systems are locked over the British Isles, preventing moisture advection from the North Atlantic and surrounded areas. Conversely, during wetter conditions and high GWL periods, low-pressure systems are locked over the British Isles, enhancing moisture advection from the North Atlantic and surrounded areas. The SST pattern in the North Atlantic ocean associated with IV in precipitation and GWL is consistent with the atmospheric circulation (Fig. 5b). This pattern is reminiscent of SST patterns associated with Atlantic ridge and Scandinavia blocking regimes (Cassou et al., 2004). Indeed, during blocking weather regimes that lead to drier conditions and low GWL periods, colder water than normal is observed off the Canadian coast, and warmer water than normal off the U.S. coast. Conversely, during ridge weather regimes that lead to wetter conditions and high GWL periods, warmer water than normal is observed off the Canadian coast, and colder water than normal is observed off the European and U.S. coasts.

Z500 pattern associated with DV in precipitation and GWL exhibits
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** (a) Interannual (~7-yr; IV) and decadal variability (~14-yr; DV) in precipitation at Tincques (blue) extracted by MODWT, which are superimposed to the original time series (grey). Red numbers in top-right corner of each panel indicate the energy percentage of the corresponding component (i.e., the relative importance of each component in total precipitation variability). (b) Same as (a), but for groundwater levels at Tincques. (c) Interannual and decadal variability in groundwater levels at Tincques (blue), which are superimposed to those of other boreholes, with shorter time series, in the chalk aquifers of Paris basin (grey).</figcaption></figure>

four centers of action over the Euro-Atlantic area (Fig. 5a). During wetter (drier) conditions and high (low) GWL periods, there are higher (lower) pressure than normal in the tropics/sub-tropics and high latitudes, and lower (higher) pressure than normal in the mid-latitudes between NW Europe and the U.S. Consequently, during high GWL periods on decadal timescales, a low-pressure system persists roughly over British Isles attracting moisture, while during low GWL periods a high-pressure system persists, blocking incoming moisture fluxes. The signal is particularly stronger over two centers of actions, one to the South of Greenland and one on the British Isles. The roughly similar pattern as Z500 can be observed into SST fields with a tripolar SST pattern, with cold SSTs located on the trajectories of the westerlies during high GWL periods, probably due to latent heat fluxes (Fig. 5b). Furthermore, the SSTs in the eastern equatorial Pacific ocean display an El Niño - Southern Oscillation (ENSO) pattern. During wetter (drier) conditions and high (low) GWL periods, El Niño (La Niña) events can be identified in the equatorial Pacific ocean with warmer (colder) water over eastern Pacific.

Fig. 5 highlights that large-scale atmospheric and oceanic patterns are not the same across timescales. In addition, centers of action of Z500 patterns associated with IV and DV in precipitation and GWL (Fig. 5a) do not exactly correspond to those of well-known climate indices, such as North Atlantic Oscillation (NAO), Scandinavian Pattern (SCAND), East Atlantic Pattern (EAP) (Barnston and Livezey, 1987; Comas-Bru and McDermott, 2014). Fig. 6 shows the first three eigenvectors of the gridded winter (December-February) Z500 anomalies for the North Atlantic area calculated using the NOAA 20CR dataset. The first three eigenvectors correspond to the spatial pattern of NAO (Fig. 6 – Left), EAP (Fig. 6 – Middle), and SCAND (Fig. 6 – Right), respectively. The

centers of action of these three well-known climate indices are indeed not really the same than those found using the Z500 composite analysis for precipitation and GWL, especially the DV. The Z500 pattern of IV remains however fairly close to the SCAND pattern (Figs. 5 and 6). Such a result indicates that for predictive purposes of GWL, it would be more appropriate to use directly large-scale atmospheric fields rather than pre-defined indices, such as NAO, because we are specifically tracking a driving atmospheric circulation. In addition, NAO-type circulation, or more generally westerlies circulation, is here only found for DV. Consequently, running a prediction system using just the NAO index or EAP index would not predict well one part of the GWL signal (i.e., the IV). In the next subsection and in the first instance, we aim at assessing the possibility to simulate historical GWL in Tincques using the large-scale atmospheric information (Z500 field).

### 3.3. Capability of large-scale atmospheric fields to simulate groundwater levels

In this subsection, we aim at assessing whether the large-scale atmospheric fields, and patterns previously identified in the last subsection, are able to correctly simulate and reproduce GWL (i.e., the GWL low-frequency variability and total GWL) in order to determine their capability to be used as predictors in future prediction models of GWL. For the simulation of GWL at Tincques, we used Z500 as large-scale variable. First, we compared the simulated GWL obtained with a simple approach using ESD model and a multi-component approach using multiresolution ESD model developed by Massei et al. (2017) (Fig. 7).

Fig. 7a shows the observed GWL (blue) compared to simulated GWL (green) obtained using a simple ESD approach (top), and the CWT of
<caption>(a)</caption>

Precipitation

<figure><img src="image_6.png" /></figure>

Groundwater levels

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>(b)</figcaption></figure>

Precipitation

<figure><img src="image_10.png" /></figure>

Groundwater levels

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 5. (a) Composite anomalies of Z500 (m) associated with precipitation and GWL variations exceeding +/-0.5 standard-deviation (i.e., wet minus dry anomalies) on interannual (~7-yr; IV) and decadal (~14-yr; DV) timescales. The maps are used to visualize areas where Z500 is low when precipitation or groundwater levels are high (blue) and conversely where Z500 is high when precipitation or groundwater levels are high (red). Arrows represent wind vectors anomalies at 500mb. (b) Same with SST (°C).</figcaption></figure>

simulated GWL (bottom). With the simple approach, the simulated GWL
display a very weak LFV compared to observed GWL. This is particularly
striking on the CWT with annual and seasonal variability explaining
much more variability of simulated GWL than LFV. On the contrary, the
multi-component ESD approach allows us to account for the large
amplitude of LFV in GWL (Fig. 7b). Indeed, the CWT displays strong IV
and DV and weak seasonal variability, similarly to observed GWL. These
results significate that a multi-component ESD approach is performing
better than a simple ESD approach in simulating GWL, and especially its
LFV, take as it allows to track potential atmospheric predictors at

multiple timescales.

Fig. 8 (right) details the simulation for each GWL component and confirms that LFV (>1-yr) are better simulated than high-frequency variabilities (≤1-yr). The simulated annual variability (~1-yr) shows however high NSE and R² coefficients with observed component but its amplitude is sometimes clearly overestimated (beginning of the 1960's) or underestimated (around the year 2000). Among LFV, ~7-yr and ~14-yr variabilities are however better simulated than ~2-yr and ~4-yr variabilities. Each simulated component is associated to a large-scale (Z500) predictor that is depicted by the spatial distribution of
<figure><img src="image_14.png" /><figcaption>Fig. 6. First three eigenvectors of the gridded winter (December-February) Z500 anomalies for the North Atlantic area (1903–2015) calculated using the NOAA 20CR dataset: (Left) North Atlantic Oscillation (NAO), (Middle) East Atlantic Pattern (EAP), (Right) Scandinavian Pattern (SCAND). In red is displayed the percentage of the total variance explained by each eigenvector.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 7. (Top) Simulated groundwater levels at Tincques generated with (a) simple ESD and (b) multiresolution ESD. Observed groundwater levels are in blue, simulated groundwater levels are in green (simple ESD) and red (multiresolution ESD). (Bottom) Continuous wavelet transform of simulated groundwater levels with (a) simple ESD and (b) multiresolution ESD.</figcaption></figure>

regression coefficients. It is interesting to note that predictors (i.e., atmospheric patterns) change across timescales. In addition, Z500 predictors of simulated IV (~7-yr) and DV (~14-yr) of GWL are the same as Z500 patterns derived from the composite analysis and introduced in Section 3.2. These Z500 patterns are then able to correctly simulate and reproduce LFV of GWL, particularly the DV.

Since LFV is often responsible for the emergence of extremely high- and low GWL (Baulon et al., 2022b), it is clear that LFV (phase and amplitude) must be properly simulated to correctly simulate groundwater flood and drought periods. However, the Artois-Picardy chalk aquifer here studied with Tincques time series, displays a combined behavior of the water table, with LFV of GWL that is superimposed to significant annual variability (Baulon et al., 2022b). Consequently, the annual variability also explains a significant part of the emergence of groundwater floods and must be also correctly simulated in amplitude to simulate and reach such extremely high levels. Given the regular over (under)estimation of annual variability, the extremely high levels such

as the 2001 flood are rarely reached (Figs. 7 and 8). In addition, during the 2001 flood, the amplitude of IV (~7-yr) is clearly underestimated (Fig. 8), while it is known that IV has been for a great part responsible for the emergence of 2001 flood in many instances (Baulon et al., 2022b). Finally, a correct simulation of groundwater droughts requires a precise simulation of IV and DV since they are more dependent on LFV (Baulon et al., 2022b).

To summarize, the results show a significant improvement of the GWL simulation when the large-scale predictors of each GWL component are used in an ESD model. The simulated GWL then follows the major water table fluctuations observed, whereas an ESD model that does not use predictors of each GWL component does not allow it. However, like many models, the multi-component ESD model fails to simulate the extremely high- and low GWL.
<figure><img src="image_16.png" /><figcaption>**Fig. 8.** (Left) Spatial distribution of regression coefficients of the multiple linear regression model based on 6 EOFs of Z500 as predictor and groundwater levels at Tincques as predictand. Each map represents the Z500 spatial predictor of groundwater levels at each timescale. (Right) Simulated groundwater level component (red) superimposed to the observed component (blue) at each timescale.</figcaption></figure>
# 4. Discussion and conclusion

This paper aimed at determining (i) the main variabilities constituting LFV of GWL in the chalk of northern France using continuous and discrete wavelet transform, (ii) the large-scale climate drivers of such variabilities using multiresolution composite analysis, (iii) the ability of large-scale atmospheric drivers previously found to be used in statistical models in order to improve GWL simulation using a multiresolution empirical statistical downscaling (ESD) model.

GWL variability in chalk is dominated by a significant LFV which comprise of interannual (~7-yr; IV) and decadal (~14-yr; DV) variabilities that are also found in precipitation. Such variabilities are also found in other aquifers in France (Baulon et al., 2022a) and neighboring countries (Holman et al., 2011; Neves et al., 2019; Liesch and Wunsch, 2019; Rust et al., 2019), but also in other hydroclimate variables such as temperature, streamflow, evapotranspiration (Dieppois et al., 2013; Rust et al., 2019; Fossa et al., 2021). They are known to be significantly involved into hydrogeological drought and flood occurrence (Baulon et al., 2022b), hence the importance of finding the climate drivers of these variabilities. Furthermore, this supports the idea that groundwater abstractions have little impact on GWL IV and DV.

We then examined the potential large-scale climate drivers of GWL IV and DV. While most studies examining links between GWL LFV and the large-scale climate circulation are performed using standard climate indices, such as North Atlantic Oscillation (NAO), East Atlantic Pattern (EAP) or Scandinavian Pattern (SCAND) (Neves et al., 2019; Liesch and Wunsch, 2019; Rust et al., 2022), assuming that these modes of climate variability are spatially stationary, we use a new approach combining multiresolution spectral decomposition and composite analysis to identify the main large-scale climate drivers of IV and DV without any a priori on the spatial position of centers of action.

First, we find that GWL IV is associated with a wave train pattern in Z500, which is reminiscent to a ridge (blocking) weather-type as described by Cassou et al. (2004), leading to wet (dry) conditions and high (low) GWL over northern France. This wave train circulation pattern associated with GWL IV is, however, significantly different from large-scale circulation patterns linked to streamflow and precipitation in the same region in previous studies, highlighting the role of the NAO (Massei et al., 2017; Fossa, 2020). This is probably linked to the study period, which in our case is much longer (all 20th century) than that studied by Massei et al. (2017) or Fossa (2020), which is limited to 1950–2007 and 1968–2008, respectively. This difference raises, mainly for modeling aspects, a question concerning the choice of model calibration period and climate covariates to be used in potential future predictive models. Second, GWL DV is found to be associated with a low (high) pressure system extending from the eastern coast of U.S. to U.K. and high (low) pressure systems over North Africa and Labrador Sea, leading to wet (dry) conditions and high (low) GWL in northern France. In addition, this circulation pattern is consistent with described in previous studies investigating the impact of ENSO on the North Atlantic atmospheric circulation and highlighting a strong relationship between the two (Gouirand et al., 2007; Ivasić et al., 2021). Examining global SST anomalies associated with GWL DV, we could confirm a significant relationship with ENSO variability. In particular, we note that El Niño (La Niña) SST anomalies in the eastern Pacific were associated with higher (lower) GWL on decadal timescales.

Although large-scale climate drivers were identified for a single GWL time series, we have shown that the results are consistent with the results for precipitation. This suggests that the low-frequency GWL signal is little altered by the system (i.e. geological environment, aquifer characteristics, recharge and discharge conditions) compared with precipitation. However, some boreholes display a LFV that may be relatively distorted compared with that of the time series analyzed (Tincques), certainly due to the local geological and morphometric conditions (Fig. 4). For these particular cases, the large-scale climate drivers identified will obviously not be the same as those identified for

Tincques, just like those identified for precipitation. Other large-scale atmospheric mechanisms will be then identified in a composite analysis, but they will not reflect reality, since they will not be consistent with those found for precipitation. Consequently, it is not recommended to produce a simulation-prediction model based on the atmospheric circulation patterns identified for these boreholes.

Overall, we conclude that large-scale climate patterns related to LFV in precipitation and GWL differ according to timescales. This timescale dependence of the connections between regional-scale hydrology and large-scale climate circulation has been already highlighted by Massei et al. (2017) and Fossa (2020) over the Seine River basin, and in other regions, such as Africa (Dieppois et al., 2016a; Sidibe et al., 2019; Ekolu et al., 2024), South America (Arriagada et al., 2019). These results stress out the need for using multi-component approaches, accounting for different predictors at different timescales, when simulating and predicting hydrological variations, and especially for GWL. In addition, we highlight that the use of atmospheric fields in GWL prediction models could enable us to avoid relying on standard climate indices with pre-defined centers of action, which do not necessarily correspond to the circulation patterns that best characterize a given hydrological variability (Massei et al., 2017; Sidibe et al., 2020). For instance, recent studies supported the use of large-scale hidden climate indices derived from the local hydroclimate (oceanic) variability rather than standard climate indices for hydroclimate (oceanic) predictions (Castelle et al., 2017; Renard et Thyer, 2019).

To illustrate the added value of our approach for GWL predictions, we assessed whether the large-scale atmospheric fields (Z500), and more particularly Z500 patterns responsible for GWL IV and DV, would be able to simulate them and ultimately simulate total GWL. The results indicate that GWL simulation is clearly improved when the predictors of each GWL component are used in an ESD model. This analysis highlights the potential of large-scale atmospheric patterns found by composite analysis to be used as predictors in future statistical models for reconstructing or predicting GWL. The insertion of these climate patterns as covariates in GWL prediction models could be tested in future works. Furthermore, although the present analysis focused on a very specific region of Europe, with GWL influenced by large-scale climate drivers that are specific to this part of the planet, it nevertheless shows that: (i) by analyzing and using the local hydrological signal (GWL), it allows for identifying the large-scale climate drivers of GWL variations, (ii) these large-scale climate patterns could be used as predictors in statistical models for reconstructing and predicting GWL.

## CRediT authorship contribution statement

**Lisa Baulon:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Formal analysis, Data curation, Conceptualization.
**Nicolas Massei:** Writing – review & editing, Supervision, Project administration, Methodology, Conceptualization.
**Bastien Dieppois:** Writing – review & editing, Supervision, Methodology, Conceptualization.
**Manuel Fossa:** Writing – review & editing, Supervision, Methodology, Conceptualization.
**Delphine Allier:** Writing – review & editing.
**Hélène Bessière:** Writing – review & editing.
**Matthieu Fournier:** Writing – review & editing.

## 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.

## Acknowledgments

We would like to thank the Agence de l'Éau Seine Normandie, PIREN Seine, BRGM, and Région Normandie for their financial support.
# Data availability

Data will be made available on request.

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