Sustainable groundwater use relies on adequate rates of groundwater recharge, which are expected to change with climate change. However, climate impacts on recharge remain uncertain due to a paucity of measurements of recharge trends globally. Here we leverage the relationship between climatic aridity and long-term recharge measurements at 5,237 locations globally to identify regions where recharge is most sensitive to changes in climatic aridity. Recharge is most sensitive to climate changes in regions where potential evapotranspiration slightly exceeds precipitation, meaning even modest aridification can substantially decrease groundwater recharge. Future climate-induced recharge changes are expected to be dominated by precipitation changes, whereby changes in groundwater recharge will be amplified relative to precipitation changes. Recharge is more sensitive to changes in aridity than global hydrological models suggest. Consequently, the effects of climatic changes on groundwater replenishment and their impacts on the sustainability of groundwater use by humans and ecosystems probably exceed previous predictions.

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.

Developing a reliable conceptual model is crucial for analyzing groundwater systems. An essential part of the aquifer conceptualization is the identification of the hydrological stresses that control the hydraulic head fluctuations. By effectively capturing and understanding these stresses, the propagation of potential errors and uncertainties through subsequent modeling steps can be minimized. This study aims to test data-driven models as screening models for conceptualizing a groundwater system. The case study is applied to the Grazer Feld Aquifer in southeast Austria. Time series models are applied to: (1) identify the stresses likely influencing the observed head fluctuations and their spatial variability; (2) identify locations where a lack of understanding of head fluctuations exists; and (3) discuss the limitations and opportunities associated with data-driven models to support system conceptualization. Time series models were created for 144 monitoring wells where sufficient head observations were available during the calibration period (2005–2015). A total of 576 models were developed, incorporating the combinations of stresses: recharge, river level, and a step trend. Following the model selection process, each model was categorized based on its performance and divided into four groups. At 88 sites, recharge and river level variations were identified as the primary controlling stresses influencing head fluctuations. The inclusion of the step trend was found to be necessary at five sites to accurately simulate heads due to dam construction. The application of data-driven models in this study enhanced the identification of key aquifer stresses, facilitating a more informed understanding of the groundwater system.

Predictions of groundwater fluctuations in space and time are important for sustainable water resource management. Infiltration variability on monthly to decadal timescales leads to fluctuations in the water tables and thus groundwater resources. However, connections between global-scale climate variability and infiltration patterns and groundwater are often poorly understood because the relationships between groundwater conditions and infiltration tend to be highly nonlinear. In addition, understanding is further hampered because many groundwater records are incomplete and groundwater tables are often anthropogenically influenced, which makes identifying the effects of infiltration variability difficult. Previous studies that have evaluated how infiltration variability controls groundwater are based on a limited number of point measurements. Here, we present a global assessment of how infiltration variability is expected to affect groundwater tables. We use an analytical solution derived from Richards' equation to model water level responses to idealized periodic infiltration variability with periods that range from months to decades, to approximate both the effects of short-term and long-term climate variability and thus infiltration patterns. Our global-scale assessment reveals why infiltration variability would lead to periodicity in groundwater recharge in particular regions. The vadose zone strongly dampens short-term (seasonal and shorter) variations in infiltration fluxes throughout most of Earth's land surface, while infiltration cycles exceeding 1 year would yield transient recharge, except in more arid regions. Our results may help forecasting long-term groundwater tables and could support improving groundwater resource management.

The performance of time series models is assessed using synthetic head series simulated with a numerical model that solves Richards' equation for variably saturated flow. Heads were simulated in a homogeneous unconfined aquifer between two parallel canals; measured daily precipitation and potential evaporation are specified at the land surface and root water uptake is simulated. The head response to a precipitation event is nonlinear and depends on the saturation degree and rainfall before and after the precipitation event while evaporation reduction occurs during summers. Synthetic series were generated for 27 years and three different soil types; the unsaturated zone thickness varies between 0 and >5 m. The synthetic head series were simulated with a linear and nonlinear time series model. Performance of a linear time series model with four parameters, using a scaled Gamma response, gave R² values ranging from 0.67 to 0.96. The nonlinear time series model with five parameters simulates recharge using a root zone reservoir after which the head response to recharge is simulated with a scaled Gamma response function. The nonlinear time series model was able to simulate all synthetic head series very well with R² values above 0.9 for almost all models. The head response of the nonlinear model to a single precipitation event compares well to the response of the variably saturated groundwater model. The provided scripts may be used to simulate synthetic head series for other climates or for systems with additional complexity to assess the performance of other data-driven models.

Evapotranspiration (ET) is a crucial flux of the hydrological water balance, commonly estimated using (semi-)empirical formulas. The estimated flux may strongly depend on the formula used, adding uncertainty to the outcomes of environmental studies using ET. Climate change may cause additional uncertainty, as the ET estimated by each formula may respond differently to changes in meteorological input data. To include the effects of model uncertainty and climate change and facilitate the use of these formulas in a consistent, tested, and reproducible workflow, we present PyEt. PyEt is an open-source Python package for the estimation of daily potential evapotranspiration (PET) using available meteorological data. It allows the application of 20 different PET methods on both time series and gridded datasets. The majority of the implemented methods are benchmarked against literature values and tested with continuous integration to ensure the correctness of the implementation. This article provides an overview of PyEt's capabilities, including the estimation of PET with 20 PET methods for station and gridded data, a simple procedure for calibrating the empirical coefficients in the alternative PET methods, and estimation of PET under warming and elevated atmospheric CO2 concentration. Further discussion on the advantages of using PyEt estimates as input for hydrological models, sensitivity and uncertainty analyses, and hindcasting and forecasting studies (especially in data-scarce regions) is provided.

Many countries maintain nationwide groundwater networks to monitor the status of their groundwater resources. For effective groundwater resource management, it is fundamental to understand the groundwater dynamics measured in the individual monitoring wells. Nationwide monitoring networks typically cover multiple aquifer systems with different degrees of environmental complexity. The analysis of the data of such networks thus requires flexible modeling approaches. In this study, we assessed the applicability and performance of lumped-parameter models using impulse response functions, as implemented in the Pastas software, to simulate hydraulic head data from the nationwide groundwater monitoring network in Switzerland. The selected 28 monitoring wells in the network are situated in unconsolidated, relatively shallow aquifers across Switzerland. Given the very diverse topography in the study area, snowmelt processes affect some aquifers, while groundwater–surface water interactions are important in the valleys. Different linear and nonlinear models were tested to take precipitation and potential evaporation into account, with a new model developed as part of this study to account for the effect of snow processes on recharge generation. After generally good fits in both the calibration and evaluation were achieved, the models were used to identify and quantify which stresses (e.g., precipitation, river stages) control the groundwater dynamics. The results show that precipitation and evaporation explain large parts of the measured dynamics, and about half of the monitoring wells in the network appear to be influenced by river stages. Explicitly accounting for snow processes in the recharge generating process is found to improve the simulation of the head dynamics across Switzerland, particularly for wells in high-altitude aquifers. This study demonstrates for the first time the applicability of lumped-parameter models using impulse response functions to model heads in Switzerland, and more generally, in climatic settings where snow processes are impacting the head dynamics.

Study region: The Baltic countries (Estonia, Latvia, Lithuania), North Eastern Europe.
Study focus: Time series models are a convenient tool for modeling hydraulic head time series due to their parsimonious parameterization and quick calculation time. However, it is unclear how the model structure and the outcome relate to the respective site characteristics. Time series modeling with impulse response functions was used to model the head time series. The correlations between the model performance and the environmental settings and between the model parameters and the environmental settings were analyzed using Spearman rank correlation and Random Forest regression analyses.
New hydrological insights: From the 460 analyzed head time series, 145 were modeled with satisfactory goodness-of-fit in the calibration period, using only precipitation, potential evaporation, and temperature as model inputs. This number decreased to 68 time series with a satisfactory fit in the validation period. Including additional drivers in wells where a substantial influence is characteristic could improve modeling results. The model results suggest that snow processes are affecting head dynamics in many wells in the Baltic countries. Most correlations between the model performance and the environmental setting were observed with the geological and climatic setting of the site. Models performed best in monitoring wells with shallow groundwater and lower precipitation seasonality.

Karst aquifers are important sources of fresh water on a global scale. The hydrological modelling of karst spring discharge, however, still poses a challenge. In this study we apply a transfer function noise (TFN) model in combination with a bucket-type recharge model to simulate karst spring discharge. The application of the noise model for the residual series has the advantage that it is more consistent with assumptions for optimization such as homoscedasticity and independence. In an earlier hydrological modeling study, named Karst Modeling Challenge (KMC; Jeannin et al., J Hydrol 600:126–508, 2021), several modelling approaches were compared for the Milandre Karst System in Switzerland. This serves as a benchmark and we apply the TFN model to KMC data, subsequently comparing the results to other models. Using different data-model-combinations, the most promising data-model-combination is identified in a three-step least-squares calibration. To quantify uncertainty, the Bayesian approach of Markov-chain Monte Carlo (MCMC) sampling is subsequently used with uniform priors for the previously identified best data-model combination. The MCMC maximum likelihood solution is used to simulate spring discharge for a previously unseen testing period, indicating a superior performance compared to all other models in the KMC. It is found that the model gives a physically feasible representation of the system, which is supported by field measurements. While the TFN model simulated rising limbs and flood recession especially well, medium and baseflow conditions were not represented as accurately. The TFN approach poses a well-performing data-driven alternative to other approaches that should be considered in future studies.