Abel Henriot

In this study, we use deep learning models with advanced variants of recurrent neural networks, specifically long short-term memory (LSTM), gated recurrent unit (GRU), and bidirectional LSTM (BiLSTM), to simulate large-scale groundwater level (GWL) fluctuations in northern France. We develop multi-station collective training for GWL simulations, using dynamic variables (i.e. climatic) and static basin characteristics. This large-scale approach can incorporate dynamic and static features to cover more reservoir heterogeneities in the study area. Further, we investigated the performance of relevant feature extraction techniques such as clustering and wavelet transform decomposition to simplify network learning using regionalised information. Several modelling performance tests were conducted. Models specifically trained on different types of GWL, clustered based on the spectral properties, performed significantly better than models trained on the whole dataset. Clustering-based modelling reduces complexity in the training data and targets relevant information more efficiently. Applying multi-station models without prior clustering can lead the models to preferentially learn the dominant behaviour, ignoring unique local variations. In this respect, wavelet pre-processing was found to partially compensate for clustering, bringing out common temporal and spectral characteristics shared by all available GWL time series even when these characteristics are “hidden” (e.g. if their amplitude is too small). When employed along with prior clustering, using wavelet decomposition as a pre-processing technique significantly improves model performances, particularly for GWLs dominated by low-frequency interannual to decadal variations. This study advances our understanding of GWL simulation using deep learning, highlighting the importance of different model training approaches, the potential of wavelet pre-processing, and the value of incorporating static attributes.

Assessing long-term changes in groundwater is crucial for understanding the impacts of climate change on aquifers and for managing water resources. However, long-term groundwater level (GWL) records are often scarce, limiting understanding of historical trends and variability. In this study, we present a deep learning approach to reconstruct GWLs up to several decades back in time using recurrent-based neural networks with wavelet pre-processing and climate reanalysis data as inputs. GWLs are reconstructed using two different reanalysis datasets with distinct spatial resolutions (ERA5: 0.25◦ x 0.25◦ & ERA20C: 1◦ x 1◦) and monthly time resolution, and the performance of the simulations was evaluated. Long term GWL timeseries are now available for northern France, corresponding to extended versions of observational timeseries back to the early 20th century. All three types of piezometric behaviors could be reconstructed reliably and consistently capture the multidecadal variability even at coarser resolutions, which is crucial for understanding long-term hydroclimatic trends and cycles. GWLs’multidecadal variability was consistent with the Atlantic multidecadal oscillation. From a synthetic experiment involving a modified long-term observational time series, we highlighted the need for longer training datasets for some low frequency signals. Nevertheless, our study demonstrated the potential of using DL models together with reanalysis data to extend GWL observations and improve our understanding of groundwater variability and climate interactions.

Reliable predictions of groundwater levels are crucial for a sustainable groundwater resource management, which needs to balance diverse water needs and to address potential ecological consequences of groundwater depletion. Machine Learning (ML) approaches for time series prediction, in particular, have shown promising predictive accuracy for groundwater level prediction and have scalability advantages over traditional numerical methods when sufficient data is available. Global ML architectures enable predictions across numerous monitoring wells concurrently using a single model, allowing predictions for monitoring wells over a broad range of hydrogeological and meteorological conditions and simplifying model management. In this contribution, groundwater levels were predicted up to 12 weeks for 5,288 monitoring wells across Germany using two state-of-the-art ML approaches, the Temporal Fusion Transformer (TFT) and the Neural Hierarchical Forecasting for Time Series (N-HiTS) algorithm. The models were provided with historical groundwater levels, meteorological features and a wide range of static features describing hydrogeological and soil properties at the wells. To determine the conditions under which the model achieves good performance and whether it aligns with hydrogeological system understanding, the model’s performance was evaluated spatially and correlations with both static input features and time-series features from hydrograph data were examined. The N-HiTS model outperformed the TFT model, achieving a median NSE of 0.5 for the 12-week prediction over all 5,288 monitoring wells. Performance varied widely: 25 % of wells achieved an NSE > 0.68, while 15 % had an NSE < 0 with the best N-HiTS model. A tendency for better predictions in areas with high data density was observed. Moreover, the models achieved higher performance in lowland areas with distinct seasonal groundwater dynamics, in monitoring wells located in porous aquifers, and at sites with moderate permeabilities, which aligns with theoretical expectations. Overall, the findings highlight that global ML models can facilitate accurate seasonal groundwater predictions over large, hydrogeological diverse areas, potentially informing future groundwater management practices at a national scale.

This paper presents the results of the 2022 Groundwater Time Series Modelling Challenge, where 15 teams from different institutes applied various data-driven models to simulate hydraulic-head time series at four monitoring wells. Three of the wells were located in Europe and one was located in the USA in different hydrogeological settings in temperate, continental, or subarctic climates. Participants were provided with approximately 15 years of measured heads at (almost) regular time intervals and daily measurements of weather data starting some 10 years prior to the first head measurements and extending around 5 years after the last head measurement. The participants were asked to simulate the measured heads (the calibration period), to provide a prediction for around 5 years after the last measurement (the validation period for which weather data were provided but not head measurements), and to include an uncertainty estimate. Three different groups of models were identified among the submissions: lumped-parameter models (three teams), machine learning models (four teams), and deep learning models (eight teams). Lumped-parameter models apply relatively simple response functions with few parameters, while the artificial intelligence models used models of varying complexity, generally with more parameters and more input, including input engineered from the provided data (e.g. multi-day averages). The models were evaluated on their performance in simulating the heads in the calibration period and in predicting the heads in the validation period. Different metrics were used to assess performance, including metrics for average relative fit, average absolute fit, fit of extreme (high or low) heads, and the coverage of the uncertainty interval. For all wells, reasonable performance was obtained by at least one team from each of the three groups. However, the performance was not consistent across submissions within each group, which implies that the application of each method to individual sites requires significant effort and experience. In particular, estimates of the uncertainty interval varied widely between teams, although some teams submitted confidence intervals rather than prediction intervals. There was not one team, let alone one method, that performed best for all wells and all performance metrics. Four of the main takeaways from the model comparison are as follows: (1) lumped-parameter models generally performed as well as artificial intelligence models, which means they capture the fundamental behaviour of the system with only a few parameters. (2) Artificial intelligence models were able to simulate extremes beyond the observed conditions, which is contrary to some persistent beliefs about these methods. (3) No overfitting was observed in any of the models, including in the models with many parameters, as performance in the validation period was generally only a bit lower than in the calibration period, which is evidence of appropriate application of the different models. (4) The presented simulations are the combined results of the applied method and the choices made by the modeller(s), which was especially visible in the performance range of the deep learning methods; underperformance does not necessarily reflect deficiencies of any of the models. In conclusion, the challenge was a successful initiative to compare different models and learn from each other. Future challenges are needed to investigate, for example, the performance of models in more variable climatic settings to simulate head series with significant gaps or to estimate the effect of drought periods.

In this study, we used deep learning models with recurrent structure neural networks to simulate large-scale groundwater level (GWL) fluctuations in northern France. We developed a multi-station collective training for GWL simulations, using both “dynamic” variables (i.e. climatic) and static aquifer characteristics. This large-scale approach offers the possibility of incorporating dynamic and static features to cover more reservoir heterogeneities in the study area. Further, we investigated the performance of relevant feature extraction techniques such as clustering and wavelet transform decomposition, intending to simplify network learning using regionalised information. Several modelling performance tests were conducted. Models specifically trained on different types of GWL, clustered based on the spectral properties of the data, performed significantly better than models trained on the whole dataset. Clustering-based modelling reduces complexity in the training data and targets relevant information more efficiently. Applying multi-station models without prior clustering can lead the models to learn the dominant station behavior preferentially, ignoring unique local variations. In this respect, wavelet pre-processing was found to partially compensate clustering, bringing out common temporal and spectral characteristics shared by all available time series even when these characteristics are “hidden” because of too small amplitude. When employed along with prior clustering, thanks to its capability of capturing essential features across all time scales (high and low), wavelet decomposition used as a pre-processing technique provided significant improvement in model performance, particularly for GWLs dominated by low-frequency variations. This study advances our understanding of GWL simulation using deep learning, highlighting the importance of different model training approaches, the potential of wavelet preprocessing, and the value of incorporating static attributes.

In this study, we used deep learning models with recurrent structure neural networks to simulate large-scale groundwater level (GWL) fluctuations in northern France. We developed a multi-station collective training for GWL simulations, using both “dynamic” variables (i.e. climatic) and static aquifer characteristics. This large-scale approach offers the possibility of incorporating dynamic and static features to cover more reservoir heterogeneities in the study area. Further, we investigated the performance of relevant feature extraction techniques such as clustering and wavelet transform decomposition, intending to simplify network learning using regionalised information. Several modelling performance tests were conducted. Models specifically trained on different types of GWL, clustered based on the spectral properties of the data, performed significantly better than models trained on the whole dataset. Clustering-based modelling reduces complexity in the training data and targets relevant information more efficiently. Applying multi-station models without prior clustering can lead the models to learn the dominant station behavior preferentially, ignoring unique local variations. In this respect, wavelet pre-processing was found to partially compensate clustering, bringing out common temporal and spectral characteristics shared by all available time series even when these characteristics are “hidden” because of too small amplitude. When employed along with prior clustering, thanks to its capability of capturing essential features across all time scales (high and low), wavelet decomposition used as a pre-processing technique provided significant improvement in model performance, particularly for GWLs dominated by low-frequency variations. This study advances our understanding of GWL simulation using deep learning, highlighting the importance of different model training approaches, the potential of wavelet preprocessing, and the value of incorporating static attributes.

In this study, we used deep learning models with recurrent structure neural networks to simulate large-scale groundwater level (GWL) fluctuations in northern France. We developed a multi-station collective training for GWL simulations, using both “dynamic” variables (i.e. climatic) and static aquifer characteristics. This large-scale approach offers the possibility of incorporating dynamic and static features to cover more reservoir heterogeneities in the study area. Further, we investigated the performance of relevant feature extraction techniques such as clustering and wavelet transform decomposition, intending to simplify network learning using regionalised information. Several modelling performance tests were conducted. Models specifically trained on different types of GWL, clustered based on the spectral properties of the data, performed significantly better than models trained on the whole dataset. Clustering-based modelling reduces complexity in the training data and targets relevant information more efficiently. Applying multi-station models without prior clustering can lead the models to learn the dominant station behavior preferentially, ignoring unique local variations. In this respect, wavelet pre-processing was found to partially compensate clustering, bringing out common temporal and spectral characteristics shared by all available time series even when these characteristics are “hidden” because of too small amplitude. When employed along with prior clustering, thanks to its capability of capturing essential features across all time scales (high and low), wavelet decomposition used as a pre-processing technique provided significant improvement in model performance, particularly for GWLs dominated by low-frequency variations. This study advances our understanding of GWL simulation using deep learning, highlighting the importance of different model training approaches, the potential of wavelet preprocessing, and the value of incorporating static attributes.

In this study, we used deep learning models with recurrent structure neural networks to simulate large-scale groundwater level (GWL) fluctuations in northern France. We developed a multi-station collective training for GWL simulations, using both “dynamic” variables (i.e. climatic) and static aquifer characteristics. This large-scale approach offers the possibility of incorporating dynamic and static features to cover more reservoir heterogeneities in the study area. Further, we investigated the performance of relevant feature extraction techniques such as clustering and wavelet transform decomposition, intending to simplify network learning using regionalised information. Several modelling performance tests were conducted. Models specifically trained on different types of GWL, clustered based on the spectral properties of the data, performed significantly better than models trained on the whole dataset. Clustering-based modelling reduces complexity in the training data and targets relevant information more efficiently. Applying multi-station models without prior clustering can lead the models to learn the dominant station behavior preferentially, ignoring unique local variations. In this respect, wavelet pre-processing was found to partially compensate clustering, bringing out common temporal and spectral characteristics shared by all available time series even when these characteristics are “hidden” because of too small amplitude. When employed along with prior clustering, thanks to its capability of capturing essential features across all time scales (high and low), wavelet decomposition used as a pre-processing technique provided significant improvement in model performance, particularly for GWLs dominated by low-frequency variations. This study advances our understanding of GWL simulation using deep learning, highlighting the importance of different model training approaches, the potential of wavelet preprocessing, and the value of incorporating static attributes.

This paper presents the results of the 2022 groundwater time series modeling challenge, where 15 teams from different institutes applied various data-driven models to simulate hydraulic head time series at four monitoring wells. Three of the wells were located in Europe and one in the USA, in different hydrogeological settings but all in temperate or continental climates. Participants were provided with approximately 15 years of measured heads at (almost) regular time intervals and daily measurements of weather data starting some 10 years prior to the first head measurements and extending around 5 years after the last head measurement. The participants were asked to simulate the measured heads (the calibration period), provide a forecast for around 5 years after the last measurement (the validation period for which weather data was provided but not head measurements), and to include an uncertainty estimate. Three different groups of models were identified among the submissions: lumped-parameter models (3 teams), machine learning models (4 teams), and deep learning models (8 teams). Lumped-parameter models apply relatively simple response functions with few parameters, while the artificial intelligence models used models of varying complexity, generally with more parameters and more input, including input engineered from the provided data (e.g., multi-day averages). The models were evaluated on their performance to simulate the heads in the calibration period and the validation period. Different metrics were used to assess performance including metrics for average relative fit, average absolute fit, fit of extreme (high or low) heads, and the coverage of the uncertainty interval. For all wells, reasonable performance was obtained by at least one team from each of the three groups. However, the performance was not consistent across submissions within each groups, which implies that application of each method to individual sites requires significant effort and experience. Especially estimates of the uncertainty interval varied widely between teams, although some teams submitted confidence intervals rather than prediction intervals. There was not one team, let alone one method, that performed best for all wells and all performance metrics. Lumped-parameter models generally performed as well as artificial intelligence models, except for the well in the USA, where the lumped-parameter models did not use (or use to the full benefit) the provided river stage data, which was crucial for obtaining a good model. In conclusion, the challenge was a successful initiative to compare different models and learn from each other. Future challenges are needed to investigate, e.g., the performance of models in more variable climatic settings, to simulate head series with significant gaps, or to estimate the effect of drought periods.