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The development of groundwater levels (GWL) simulations, based on deep learning (DL) models, is gaining traction due to their success in a wide range of hydrological applications. GWL Simulations allow generating reconstructions to be used for exploring past temporal variability of groundwater resources or provide means to generate projections under climate change on decadal scales. Owing to the diversity of large-scale and local scale forcing factors involved in explaining GWL variability, machine learning or even deep learning approaches reveal relevant tools to simulate GWL. In addition, such methods do not require too much-extended knowledge of physical variables in the links between climate variables and GWL. In this paper, we investigated the capacities of three deep learning models (Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU) and Bidirectional LSTM (BLSTM)) to reproduce GWL variations over time. Among the three deep learning models, GRU performed relatively better in most cases. Another aspect was to evaluate the input data’s impact and usefulness of wavelet pre-processing considering its limitations and best practices. Two different input datasets are compared to each other, one considering Effective Precipitation only, the other considering Precipitation and Temperature. Maximum Overlap Discrete Wavelet Transform (MODWT) preprocessing was used to decompose the input variables to explore the impact of wavelet transform in improving the simulations on several types of GWL time series by unravelling “hidden” though useful information in input data. Results show that the preprocessing (MODWT) helps the models generate better simulations. This improvement is higher with raw climate data (precipitation & temperature) as compared to when effective precipitation was used as input. Finally, the Shapley Additive exPlanations (SHAP) approach was used to interpret the impact of input variables on the model simulations. Analysis of SHAP values indicated that the sources of the information content preferentially learned by the models to achieve best simulations. For instance, it was clear that simulation of inertial and mixed GWL required the models to learn from low-frequency variability presented in the input data.

Groundwater levels (GWLs) very often fluctuate over a wide range of timescales (intra-annual, annual, multi-annual, and decadal). In many instances, aquifers act as low-pass filters, dampening the high-frequency variability and amplifying low-frequency variations (from multi-annual to decadal timescales) which basically originate from large-scale climate variability. Within the aim of better understanding and ultimately anticipating groundwater droughts and floods, it appears crucial to evaluate whether (and how much) the very high or very low GWLs are resulting from such low-frequency variability (LFV), which was the main objective of the study presented here. As an example, we focused on exceedance and non-exceedance of the 80 % and 20 % GWL percentiles respectively, in the Paris Basin aquifers over the 1976–2019 period. GWL time series were extracted from a database consisting of relatively undisturbed GWL time series regarding anthropogenic influence (water abstraction by either continuous or periodic pumping) over metropolitan France. Based on this dataset, our approach consisted in exploring the effect of GWL low-frequency components on threshold exceedance and non-exceedance by successively filtering out low-frequency components of GWL signals using maximum overlap discrete wavelet transform (MODWT). Multi-annual (∼7-year) and decadal (∼17-year) variabilities were found to be the predominant LFVs in GWL signals, in accordance with previous studies in the northern France area. By filtering out these components (either independently or jointly), it is possible to (i) examine the proportion of high-level (HL) and low-level (LL) occurrences generated by these variabilities and (ii) estimate the contribution of each of these variabilities in explaining the occurrence of major historical events associated with well-recognized societal impacts. A typology of GWL variations in Paris Basin aquifers was first determined by quantifying the variance distribution across timescales. Four GWL variation types could be found according to the predominance of annual, multi-annual, or/and decadal variabilities in these signals: decadal-dominant (type iD), multi-annual- and decadal-dominant (type iMD), annual-dominant (type cA), and annual- and multi-annual-dominant (type cAM). We observed a clear dependence of high and low GWL on LFV for aquifers exhibiting these four GWL variation types. In addition, the respective contribution of multi-annual and decadal variabilities in the threshold exceedance varied according to the event. In numerous aquifers, it also appeared that the sensitivity to LFV was higher for LLs than HLs. A similar analysis was conducted on the only available long-term GWL time series which covered a hundred years. This allowed us to highlight the potential influence of multidecadal variability on HLs and LLs too. This study underlined the key role of LFV in the occurrence of HLs and LLs. Since LFV originates from large-scale stochastic climate variability as demonstrated in many previous studies in the Paris Basin or nearby regions, our results point out that (i) poor representation of LFV in general circulation model (GCM) outputs used afterwards for developing hydrological projections can result in strong uncertainty in the assessment of future groundwater extremes (GWEs), and (ii) potential changes in the amplitude of LFV, be they natural or induced by global climate change, may lead to substantial changes in the occurrence and severity of GWEs for the next decades. Finally, this study also stresses the fact that due to the stochastic nature of LFV, no deterministic prediction of future GWEs for the mid- or long-term horizons can be achieved, even though LFV may look periodic.

Groundwater level (GWL) variations can be expressed over a wide range of timescales. As aquifers act as low-pass filters, low-frequency variability (interannual to decadal variability) originating from large-scale climate variability represents a significant part of GWL variance. Anthropogenically-driven climate change may affect, and have maybe already affected, the internal climate variability which explains the low-frequency variability of hydrological processes. Such changes in internal climate variability could therefore affect GWL variations. How GWL, including extremes, may respond to such changes and variations in climate variability however remains an open question. To tackle this issue, we implemented an empirical numerical approach allowing to assess the sensitivity of aquifers to changes in large-scale climate variability, using the whole Seine hydrosystem (76000 km2) as a case study. The approach consisted in: i) identifying and modifying the spectral content of precipitation, originating from large-scale climate variability, using signal processing; ii) injecting perturbed precipitation fields as input in a physically-based hydrological/hydrogeological model (the CaWaQS software) for the Seine river basin for simulating perturbed GWL; iii) comparing the spectral content, trend and extremes of perturbed GWL with the reference GWL. We used the Safran precipitation field over the period 1970-2018, which was initially used for model calibration and validation. GWL data for the Seine basin is a subset of a database of climate-sensitive time series (i.e. low anthropogenic influence) recently set up at the BRGM and University of Rouen Normandy. First, the Safran reanalysis and observed GWL time series were analyzed using continuous wavelet transform to identify the different timescales of variability: interannual (2-4yr and 5-8yr) and decadal (~15yr). Then, the different timescale of precipitation time series were extracted using maximum overlap discrete wavelet transform. For each time series of the precipitation field, the amplitude of each timescale was modified individually, by either increasing or decreasing it by 50%. This led to six scenarios of perturbed low-frequency variability of precipitation, which are subsequently used as input in the CaWaQS model to assess the response of GWL variability and extremes. Preliminary results indicate that perturbations of the amplitude of interannual to decadal precipitation variability result in substantial changes in the variability of GWL, affecting the same timescales, as well as timescales that were not modified in the precipitation field. Implications of these findings on potential trends and the frequency of extremes of GWL is currently being explored.

Groundwater levels (GWL) very often fluctuate over a wide range of timescales (infra-annual, annual, multi-annual, decadal). In many instances, aquifers act as low-pass filters, dampening the high-frequency variability and amplifying low-frequency variations (from multi-annual to decadal timescales) which basically originate from large-scale climate variability. In the aim of better understanding and ultimately anticipating groundwater droughts and floods, it appears crucial to evaluate whether (and how much) the very high or very low GWLs are sensitive to such low-frequency variability (LFV), which was the main objective of the study presented here. As an example, we focused on exceedance and non-exceedance of the 80 % and 20 % GWL percentiles respectively, in the Paris Basin aquifers over the 1976–2019 period. GWL time series were extracted from a database consisting of relatively undisturbed GWL time series regarding anthropogenic influence (water abstraction by either continuous or periodic pumping) over Metropolitan France. Based on this dataset, our approach consisted of exploring the effect of GWL low-frequency components on threshold exceedance and non-exceedance by successively filtering out low-frequency components of GWL signals using maximum overlap discrete wavelet transform (MODWT). Multi-annual (~7-yr) and decadal (~17-yr) variabilities were found to be the predominant LFVs in GWL signals, in accordance with previous studies in the northern France area. Filtering out these components (either independently or jointly) to (i) examine the proportion of high level (HL) and low level (LL) occurrences generated by these variabilities, (ii) estimate the contribution of each of these variabilities in explaining the occurrence of major historical events associated to well-recognized societal impacts. A typology of GWL variations in Paris Basin aquifers was first determined by quantifying the variance distribution across timescales. Four GWL variation types could be found according to the predominance of annual, multi-annual or/and decadal variabilities in these signals: decadal dominant (type iD), multi-annual and decadal dominant (type iMD), annual dominant (type cA), annual and multi-annual dominant (type cAM). We observed a clear dependence of high and low GWL to LFV for aquifers exhibiting these four GWL variation types. In addition, the respective contribution of multi-annual and decadal variabilities in the threshold exceedance varied according to the event. In numerous aquifers, it also appeared that the sensitivity to LFV was higher for LL than HL. A similar analysis was conducted on the only available long-term GWL time series which covered a hundred years. This allowed us to highlight a potential influence of multidecadal variability on HL and LL too. This study underlined the key role of LFV in the occurrence of HL and LL. Since LFV originates from large-scale stochastic climate variability as demonstrated in many previous studies in the Paris Basin or nearby regions, our results point out that i) poor representation of LFV in General Circulation Models (GCM) outputs used afterwards for developing hydrological projections can result in strong uncertainty in the assessment of future groundwater extremes (GWE), ii) potential changes in the amplitude of LFV, be they natural or induced by global climate change, may lead to substantial changes in the occurrence and severity of GWE for the next decades. Finally, this study also stresses the fact that due to the stochastic nature of LFV, no deterministic prediction of future GWE for the mid- or long term horizons can be achieved even though LFV may look periodic.

Groundwater level (GWL) simulations allow the generation of reconstructions for exploring the past temporal variability of groundwater resources or provide the means for generating projections under climate change on decadal scales. In this context, analyzing GWLs affected by low-frequency variations is crucial. In this study, we assess the capabilities of three deep learning (DL) models (long short-term memory (LSTM), gated recurrent unit (GRU), and bidirectional LSTM (BiLSTM)) in simulating three types of GWLs affected by varying low-frequency behavior: inertial (dominated by low-frequency), annual (dominated by annual cyclicity) and mixed (in which both annual and low-frequency variations have high amplitude). We also tested if maximal overlap discrete wavelet transform pre-processing (MODWT) of input variables helps to better identify the frequency content most relevant for the models (MODWT-DL models). Only external variables (i.e., precipitation, air temperature as raw data, and effective precipitation (EP)) were used as input. Results indicate that for inertial-type GWLs, MODWT-DL models with raw data were notably more accurate than standalone models. However, DL models performed well for annual-type GWLs, while using EP as input, with MODWT-DL models exhibiting only minor improvements. Using raw data as input improved MODWT-DL models compared to standalone models; nevertheless, all models using EP performed better for annual-type GWLs. For mixed-type GWLs, while using EP as input, MODWT-DL models performed well, with substantial improvements over standalone models. Using raw data as input, improvement of MODWT-DL models is marginal compared to that of standalone models; nevertheless, they perform better than standalone models with EP. The Shapley Additive exPlanations (SHAP) approach used to interpret models highlighted that they preferentially learned from low-frequency in precipitation data to achieve the best simulations for inertial and mixed GWLs. This study showed that MODWT-based input pre-processing is highly suitable to better simulate low-frequency varying GWLs.

Groundwater fluctuations exhibit very often well-pronounced low-frequency variability (multi-annual to decadal timescales), linked to catchment and aquifer ability to smooth out rapid fluctuations from precipitation (low-pass filtering), especially when their characteristic time is long. This low-frequency variability, generated by large-scale climate variability and modulated by the physical properties of hydrosystems, is clearly imprinted in aquifers of northern France. Many recent researches addressed the issue of the capability of global climate models to reproduce low-frequency variability (most of the time multidecadal). For hydrological processes such as groundwater levels, which variance can be dominated by such low-frequency ranges, it may then appear crucial to provide assessment on how very high or very low levels are sensitive to such low-frequency variability. In this study, we investigate how low-frequency variability (from multi-annual to interdecadal timescales) may generate very high or very low groundwater levels (higher or lower than percentiles 80% and 20%, respectively). To test such hypotheses, our approach consists of breaking down groundwater level signals into timescale components using maximum overlap discrete wavelet transform in order to get wavelet details at different timescales. Multi-annual ~7 yr and interdecadal ~17 yr components appeared to be the dominant components of low-frequency variability of the signals. We then substracted these components (either one or both) and simply examined how many values remained over or below the selected threshold.Results highlight that the number of events generated by low-frequency components is consistently closely linked to their contribution to groundwater level variability. Nearly 100% of high and low groundwater levels in inertial aquifers, that exhibit a large predominance of interdecadal variability, are generated by this timescale. At least 50% of high and low groundwater levels in inertial aquifers displaying a combination of interdecadal and multi-annual variabilities are generated by the combination of these two timescales. Finally, less than 50% of high and low groundwater levels in mixed aquifers (i.e. with a well pronounced low-frequency variability superimposed to annual variability) are generated by the multi-annual and interdecadal variabilities. In all studied aquifers with various dynamics, we notice a higher sensitivity of low groundwater levels to low-frequency variability than high groundwater levels.Across aquifers of northern metropolitan France, particularly in the chalk of the Paris Basin, we observe quite a clear dependence of well-known historical high and low groundwater levels to low-frequency variability. In particular, the 2001 high levels and the 1992 low levels are seemingly generated by concomitant multi-annual and interdecadal high levels, and concomitant multi-annual and interdecadal low levels, respectively. On the other hand, the 1995 high levels and 1998 low levels are produced by a multi-annual high level attenuated by an interdecadal low level, and a multi-annual low level attenuated by an interdecadal high level, respectively. These phasings are also observed in precipitation and effective precipitation a few time in advance (ranging from 2 months to 1.5 years). Finally, the contribution of multi-annual and interdecadal variabilities to make the groundwater levels reach or exceed one selected threshold is directly influenced by their prominence in groundwater levels variability.

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