The impact of statistical methodologies on studying groundwater has been significant in the last several decades, due to cheaper computational abilities and presence of technologies that enable us to extract and measure more and more data. This paper focuses on the validation of statistical methodologies that are in practice and continue to be at the earliest disposal of the researcher, demonstrating how traditional time-series models and modern neural networks may be a viable option to analyze and make viable forecasts from data commonly available in this domain, and suggesting a copula-based strategy to obtain directional dependencies of groundwater level, spatially. This paper also proposes a sphere of model validation, seldom addressed in this domain: the model longevity or the model shelf-life. Use of such validation techniques not only ensure lower computational cost while maintaining reasonably high accuracy, but also, in some cases, ensure robust predictions or forecasts, and assist in comparing multiple models.

Long-term groundwater level (GWL) measurement is vital for effective policymaking and recharge estimation using annual maxima and minima. However, current methods prioritize short-term predictions and lack multi-year applicability, limiting their utility. Moreover, sparse in-situ measurements lead to reliance on low-resolution satellite data like GLDAS as the ground truth for Machine Learning models, further constraining accuracy. To overcome these challenges, we first develop an ML model to mitigate data gaps, achieving $R^2$ scores of 0.855 and 0.963 for maximum and minimum GWL predictions, respectively. Subsequently, using these predictions and well observations as ground truth, we train an Upsampling Model that uses low-resolution (25 km) GLDAS data as input to produce high-resolution (2 km) GWLs, achieving an excellent $R^2$ score of 0.96. Our approach successfully upscales GLDAS data for 2003-2024, allowing high-resolution recharge estimations and revealing critical trends for proactive resource management. Our method allows upsampling of groundwater storage (GWS) from GLDAS to high-resolution GWLs for any points independently of officially curated piezometer data, making it a valuable tool for decision-making.

Land degradation and air pollution are primarily caused by the salinization of soil and desertification that occurs from the drying of salinity lakes and the release of dust into the atmosphere because of their dried bottom. The complete drying up of a lake has caused a community environmental catastrophe. In this study, we presented an optimization problem to determine the total surface runoff to maintain the level of salinity lake (Urmia Lake). The proposed process has two key stages: identifying the influential factors in determining the lake water level using sensitivity analysis approaches based upon historical data and optimizing the effective variable to stabilize the lake water level under changing design variables. Based upon the Sobol'-Jansen and Morris techniques, the groundwater level and total surface runoff flow are highly effective with nonlinear and interacting impacts of the lake water level. As a result of the sensitivity analysis, we found that it may be possible to effectively manage lake levels by adjusting total surface runoff. We used genetic algorithms, non-linear optimization, and pattern search techniques to solve the optimization problem. Furthermore, the lake level constraint is established based on a pattern as a constant number every month. In order to maintain a consistent pattern of lake levels, it is necessary to increase surface runoff by approximately 8.7 times during filling season. It is necessary to increase this quantity by 33.5 times during the draining season. In the future, the results may serve as a guide for the rehabilitation of the lake.

Modeling groundwater levels continuously across California's Central Valley (CV) hydrological system is challenging due to low-quality well data which is sparsely and noisily sampled across time and space. A novel machine learning method is proposed for modeling groundwater levels by learning from a 3D lithological texture model of the CV aquifer. The proposed formulation performs multivariate regression by combining Gaussian processes (GP) and deep neural networks (DNN). Proposed hierarchical modeling approach constitutes training the DNN to learn a lithologically informed latent space where non-parametric regression with GP is performed. The methodology is applied for modeling groundwater levels across the CV during 2015 - 2020. We demonstrate the efficacy of GP-DNN regression for modeling non-stationary features in the well data with fast and reliable uncertainty quantification. Our results indicate that the 2017 and 2019 wet years in California were largely ineffective in replenishing the groundwater loss caused during previous drought years.

This paper presents a comprehensive comparison of various machine learning models, namely U-Net [12], U-Net integrated with Vision Transformers (ViT) [11], and Fourier Neural Operator (FNO) [4], for time-dependent forward modelling in groundwater systems. Through testing on synthetic datasets, it is demonstrated that U-Net and U-Net + ViT models outperform FNO in accuracy and efficiency, especially in sparse data scenarios. These findings underscore the potential of U-Net-based models for groundwater modelling in real-world applications where data scarcity is prevalent.

Groundwater level prediction is an applied time series forecasting task with important social impacts to optimize water management as well as preventing some natural disasters: for instance, floods or severe droughts. Machine learning methods have been reported in the literature to achieve this task, but they are only focused on the forecast of the groundwater level at a single location. A global forecasting method aims at exploiting the groundwater level time series from a wide range of locations to produce predictions at a single place or at several places at a time. Given the recent success of global forecasting methods in prestigious competitions, it is meaningful to assess them on groundwater level prediction and see how they are compared to local methods. In this work, we created a dataset of 1026 groundwater level time series. Each time series is made of daily measurements of groundwater levels and two exogenous variables, rainfall and evapotranspiration. This dataset is made available to the communities for reproducibility and further evaluation. To identify the best configuration to effectively predict groundwater level for the complete set of time series, we compared different predictors including local and global time series forecasting methods. We assessed the impact of exogenous variables. Our result analysis shows that the best predictions are obtained by training a global method on past groundwater levels and rainfall data.

In the present study, six meta-heuristic schemes are hybridized with artificial neural network (ANN), adaptive neuro-fuzzy interface system (ANFIS), and support vector machine (SVM), to predict monthly groundwater level (GWL), evaluate uncertainty analysis of predictions and spatial variation analysis. The six schemes, including grasshopper optimization algorithm (GOA), cat swarm optimization (CSO), weed algorithm (WA), genetic algorithm (GA), krill algorithm (KA), and particle swarm optimization (PSO), were used to hybridize for improving the performance of ANN, SVM, and ANFIS models. Groundwater level (GWL) data of Ardebil plain (Iran) for a period of 144 months were selected to evaluate the hybrid models. The pre-processing technique of principal component analysis (PCA) was applied to reduce input combinations from monthly time series up to 12-month prediction intervals. The results showed that the ANFIS-GOA was superior to the other hybrid models for predicting GWL in the first piezometer and third piezometer in the testing stage. The performance of hybrid models with optimization algorithms was far better than that of classical ANN, ANFIS, and SVM models without hybridization. The percent of improvements in the ANFIS-GOA versus standalone ANFIS in piezometer 10 were 14.4%, 3%, 17.8%, and 181% for RMSE, MAE, NSE, and PBIAS in the training stage and 40.7%, 55%, 25%, and 132% in testing stage, respectively. The improvements for piezometer 6 in train step were 15%, 4%, 13%, and 208% and in the test step were 33%, 44.6%, 16.3%, and 173%, respectively, that clearly confirm the superiority of developed hybridization schemes in GWL modeling. Uncertainty analysis showed that ANFIS-GOA and SVM had, respectively, the best and worst performances among other models. In general, GOA enhanced the accuracy of the ANFIS, ANN, and SVM models.

Contaminated water might have leaked from the damaged Fukushima nuclear reactors after erroneous settings on water gauges lowered groundwater levels nearby, according to the plant operator. Tokyo Electric Power (TEPCO) said the settings on six of the dozens of wells around the reactors were 70 centimetres (three feet) below the requirement. Groundwater at one well briefly sank below the contaminated water inside in May, possibly causing radioactive water to leak into the soil. An underwater robot has captured images inside Japan's crippled Fukushima nuclear plant. The marine robot, is on a mission to study damage and find resources inside the devastated plant.