Groundwater Level Forecasting Research Articles

Deep learning framework with Bayesian data imputation for modelling and forecasting groundwater levels

Although traditional physical models have been used to analyse groundwater systems, the emergence of novel machine learning models can improve the accuracy of the predictions. Deep learning has been prominent in environmental and climate change problems. In this paper, we present a framework for utilising deep learning models to predict groundwater levels based on nearby streamflow and rainfall data. We address the missing data problem using a Bayesian linear regression model within the deep learning framework. Our deep learning framework utilises models such as long-short term memory (LSTM) networks and convolutional neural networks (CNN) for multi-step ahead time series prediction. We examine the fluctuations in groundwater levels at various boreholes located near Middle Creek in New South Wales, Australia. We use the National Collaborative Research Infrastructure Strategy (NCRIS) groundwater database and utilise Bayesian linear regression to impute missing data. We investigate the accuracy of the selected models for individual and regional basins and univariate and multivariate strategies. Our results show that our LSTM-based regional model with multivariate strategy using rainfall data provided the best accuracy.

Evaluating seawater intrusion forecast uncertainty under climate change in the Pajaro Valley, California

Climate change and climate variability impacts such as rising sea levels have the potential to exacerbate seawater intrusion and the strain on coastal freshwater resources in already stressed groundwater basins such as those in the Pajaro Valley groundwater basin, California. Regional hydrologic models are often coupled with climate projections to forecast future hydrologic conditions and inform adaptive resources management strategies. However, there is high uncertainty in the future projections of water resources due to uncertainties from downscaling global general circulation models (GCMs) to local scale climate change projections, future land use changes, and the inherent uncertainty of developed hydrologic models. Future climate projections and the magnitude of their influence on modeled hydrologic drivers are highly variable. Therefore, to develop a forecast model, an ensemble of different projections can be used to capture a wider range of basin responses and the associated uncertainties in the modeled forecasts. Understanding the reliability and uncertainty of forecasts is important for developing climate adaptation strategies such as developing protective thresholds, particularly at the basin scale where the impacts are felt, and adaptation is implemented. To demonstrate this, an uncertainty analysis of groundwater level and seawater intrusion forecasts for the Pajaro Valley groundwater basin was performed using an ensemble of three future climate projections with the Pajaro Valley Integrated Hydrologic Model (PVIHM) and the first-order second moment (FOSM) method. FOSM uncertainty analysis of hydrologic forecasts across a multi-GCM climate ensemble provides an upper and lower bound of potential impacts of climate change on sustainability targets related to mitigating seawater intrusion. The groundwater level forecasts’ narrow range of variability can help policymakers in adaptation planning by constraining possible outcomes to a focused range for risk-management decisions. However, less than one-third of groundwater level forecasts met the current protection thresholds to prevent chronic lowering of groundwater. Therefore, sustainability targets may need to be reassessed. Relative to groundwater level changes, the seawater intrusion forecasts had larger uncertainty due to the GCM climate projections and the simulated hydrologic response that were compounded by the propagation of scaling and bias from the GCMs and model simplifications in simulating the coastal boundary.

A maximal overlap discrete wavelet packet transform coupled with an LSTM deep learning model for improving multilevel groundwater level forecasts

Developing precise groundwater level (GWL) forecast models is essential for the optimal usage of limited groundwater resources and sustainable planning and management of water resources. In this study, an improved forecasting accuracy for up to 3 weeks ahead of GWLs in Bangladesh was achieved by employing a coupled Long Short Term Memory (LSTM) network-based deep learning algorithm and Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) data preprocessing. The coupled LSTM-MODWPT model’s performance was compared with that of the LSTM model. For both standalone LSTM and LSTM-MODWPT models, the Random Forest feature selection approach was employed to select the ideal inputs from the candidate GWL lags. In the LSTM-MODWPT model, input GWL time series were decomposed using MODWPT. The ‘Fejér-Korovkin’ mother wavelet with a filter length of 18 was used to obtain a collection of scaling coefficients and wavelets for every single input time series. Model performance was assessed using five performance indices: Root Mean Squared Error; Scatter Index; Maximum Absolute Error; Median Absolute Deviation; and an a-20 index. The LSTM-MODWPT model outperformed standalone LSTM models for all time horizons in GWL forecasting. The percentage improvements in the forecasting accuracies were 36.28%, 32.97%, and 30.77%, respectively, for 1-, 2-, and 3-weeks ahead forecasts at the observation well GT3330001. Accordingly, the coupled LSTM-MODWPT model could potentially be used to enhance multiscale GWL forecasts. This research demonstrates that the coupled LSTM-MODWPT model could generate more precise GWL forecasts at the Bangladesh study site, with potential applications in other geographic locations globally.

Watershed groundwater level multistep ahead forecasts by fusing convolutional-based autoencoder and LSTM models

The development of deep learning-based groundwater level forecast models can tackle the challenge of high dimensional groundwater dynamics, predict groundwater variation trends accurately, and manage groundwater resources effectively, thereby contributing to sustainable water resources management. This study proposed a novel ConvAE-LSTM model, which fused a Convolutional-based Autoencoder model (ConvAE) and a Long Short-Term Memory Neural Network model (LSTM), to provide accurate spatiotemporal groundwater level forecasts over the next three months. The HBV-light and LSTM models are chosen as benchmarks. An ensemble of point data and the corresponding derived images concerning the past (observations) and the future (forecasts from a conceptual model) of groundwater levels at 33 groundwater wells in Jhuoshuei River basin of Taiwan between 2000 and 2019 constituted the case study. The findings showcase the effectiveness of the ConvAE-LSTM model in extracting crucial features from both point and imagery datasets. This model successfully establishes spatiotemporal dependencies between regional images and groundwater level data over diverse time frames, leading to accurate multi-step-ahead forecasts of groundwater levels. Notably, the ConvAE-LSTM model exhibits a substantial improvement, with the R-squared values showing an increase of more than 18%, 22%, and 49% for the R1, R2, and R3 regions, respectively, compared to the HBV-light model. Additionally, it outperforms the LSTM model in this regard. This study represents a noteworthy milestone in environmental modeling, offering key insights for designing sustainable groundwater management strategies to ensure the long-term availability of this vital resource.

Enhancing Accuracy of Groundwater Level Forecasting with Minimal Computational Complexity Using Temporal Convolutional Network

Multiscale forecasting of groundwater levels (GWLs) is essential for ensuring the sustainable management of groundwater resources, particularly considering the potential impacts of climate change. Such forecasting requires a model that is not only accurate in predicting GWLs but also computationally efficient, ensuring its suitability for practical applications. In this study, a temporal convolutional network (TCN) is implemented to forecast GWLs for 17 monitoring wells possessing diverse hydrogeological characteristics, located across South Korea. Using deep learning, the influence of meteorological variables (i.e., temperature, precipitation) on the forecasted GWLs was investigated by dividing the input features into three categories. Additionally, the models were developed for three forecast intervals (at 1-, 3-, and 6-month lead times) using each category input. When compared with state-of-the-art models, that is, long short-term memory (LSTM) and artificial neural network (ANN), the TCN model showed superior performance and required much less computational complexity. On average, the TCN model outperformed the LSTM model by 24%, 21%, and 25%, and the ANN model by 24%, 37%, and 47%, respectively, for 1-, 3-, and 6-month lead times. Based on these results, the proposed TCN model can be used for real-time GWL forecasting in hydrological applications.

Multi-step ahead groundwater level forecasting in Grand Est, France: Comparison between stacked machine learning model and radial basis function neural network

In recent years, the increasing influence of climate change on the water cycle has emphasized the significance of analyzing and forecasting groundwater level (GWL) for effective water resource planning and management. This study proposes a comparative analysis of multi-step ahead daily GWL prediction by means of two different models. The former is an ensemble model, based on the stacking of two Machine Learning algorithms, Multilayer Perceptron (MLP) and Random Forest (RF). The second model is represented by a Radial Basis Function Neural Network (RBF-NN). For the modelling, a mid-term forecast horizon of up to 30 days was considered, while the precipitation and evapotranspiration were included as exogenous inputs. Three different wells located on the chalk aquifers of the northeastern region of France referred to as PZ, S1, and LS4, were selected for this study. The RBF-NN model demonstrated superior performance compared to the stacked MLP-RF model for wells PZ and S1. Conversely, for well LS4, both models displayed similar performance, albeit with a marginally higher accuracy observed in the stacked MLP-RF model. However, both models yielded accurate predictions of the GWL across all three wells, with R2 values exceeding 0.87 for all the wells and forecasting horizons. Furthermore, the RBF-NN model showed fewer reductions in performance as the forecasting horizon increased compared to the stacked MLP-RF model, leading to more reliable predictions even for a 30-day forecast horizon. An evident trend of decreasing Mean Absolute Percentage Error (MAPE) was observed from the 1st quartile to the 4th quartile of forecasted values. This highlights the models’ improved ability to provide accurate forecasts for deeper GWL values. The future developments of this research will be aimed at overcoming some limitations of the study, including lagged values of the exogenous variables precipitation and evaporation among the predictors, and considering aquifers with different hydrogeological characteristics.

Forecasting groundwater levels using machine learning methods: The case of California’s Central Valley

Groundwater, the second largest stock of freshwater on the planet, is an important water source used for municipal water supply, irrigation, or industrial needs. For instance, California’s arid Central Valley relies on groundwater resources to produce a quarter of the United States’ food demand as farmers rely on this precious resource when surface water is scarce. Despite its importance, the nexus between groundwater dynamics and climate drivers remains difficult to quantify, model, and predict because of the lack of a comprehensive observation network. In this study, machine learning techniques were used to predict groundwater levels with a 3-month forecasting horizon for the Sacramento River Basin. For this, publicly available meteorological and hydrological datasets and in-situ well-level measurements were used. Time series, ensemble-based, and deep-learning models including transformers were all tested, with an ensemble-based, XGBoost model, producing the best mean standard deviation percent error (MSPE) of 32.23% and a root mean squared error (RMSE) of 1.05 m (m) when using a 3- month forecasting horizon and when tested using a monthly rolling window over the years 2017–2020. The model proved to be better at predicting into wet months than the dry summer months and was found to be better at extracting seasonality than explaining well-level residuals, with well-specific features, as opposed to exogenous meteorological features specific to the hydrological unit of the well, ranking as the most important features to the model. Though other forecasting horizons were tested, a 3-month look-ahead window resulted in the best balance of precision and accuracy, where smaller forecasting horizons resulted in smaller RMSE but larger MSPE scores and vice-versa for larger forecasting horizons.

A new real-time groundwater level forecasting strategy: Coupling hybrid data-driven models with remote sensing data

Groundwater level forecasting is significantly crucial for the sustainable management of water resources, especially for arid and semi-arid regions where groundwater resources are highly dependent on. However, the complex groundwater dynamic systems in these regions are strongly influenced by climate change and human activities, which poses severe challenges to the development of accurate groundwater level forecasting models. This study first explored the selection and processing scheme of remote sensing products. Based on this, a new strategy to support real-time groundwater level forecasting with the hybrid data-driven model as the core algorithm is proposed. We applied a Deep Learning algorithm and two Ensemble Machine Learning algorithms, combined with the corrected Wavelet Transformation (WT) to develop hybrid models (WT-LSTM, WT-RF and WT-XGB) valid for real-world applications. The SHapley Additive exPlanations (SHAP) method was used to enhance the interpretability of the forecasting strategy. Real-world applications in the Xi’an and Yinchuan regions of Northwest China have shown that WT-LSTM is the hybrid model with the best overall performance with 0.843, 0.749 and 0.712 mean NSE at 1-, 2- and 3-month forecasting lead time, followed by WT-XGB with 0.763, 0.642 and 0.590 mean NSE, respectively. The accuracy of the WT-based hybrid models is significantly improved compared to the standalone model. Further analysis demonstrates that the performance of the standalone models is influenced by the local climate, especially human activities, while the corrected WT method can overcome such drawbacks. The LSTM-based models have a stronger capability than RF-based model to capture the hydrological signal affecting the local groundwater level from dataset based on remote sensing products. The SHAP method also validates the above findings and the reliability of the forecasting models. We conclude that the groundwater level forecasting strategy proposed in this study improves accuracy, interpretability and generalizability, and provides new insights and a reliable scientific basic for real-time groundwater level forecasting.

Machine learning models combined with wavelet transform and phase space reconstruction for groundwater level forecasting

Reliable forecasting of groundwater levels plays an important role in water resource management and the prevention of environmental problems. This study aims to introduce a novel hybrid model combining machine learning with wavelet transform (WT) and phase space reconstruction (PSR) for groundwater level forecasting. The development of the proposed hybrid model consists of two levels. Firstly, a popular data-driven nonlinear artificial neural network (ANN) model was selected as the base model. Thereafter, the WT is used to decompose the groundwater level time series. In addition, the PSR method is further adopted to select the suitable sub-series components resulting from the WT decomposition processes. At the first level, the hybrid model only combines the WT with ANN (WT-ANN). At the second level, a two-step preprocessing process, WT coupled with PSR, is implemented before the ANN, namely WT-PSR-ANN. Meanwhile, three mother wavelets (Daubechies, Symlets, and Dmeyer) are selected to further investigate the effect of wavelet type. Finally, the model's performance is evaluated using visual analysis and statistical metrics (root means square error, correlation coefficient, and the Nash-Sutcliffe efficiency coefficient). The results show that the WT-ANN model outperformed the vanilla ANN model. Furthermore, the WT-PSR-ANN model achieved the best accuracy for all selected mother wavelets. The most suitable mother wavelet is specific to each well, and there is no one-size-fits-all answer. This study highlights the effectiveness of PSR combined with WT as a data preprocessing step when the ANN model is applied for groundwater level forecasting.

A parsimonious methodological framework for short-term forecasting of groundwater levels

Groundwater plays a significant role as a strategic resource in reducing the impact of droughts. In spite of its importance, there are still many groundwater bodies in which there is not enough monitoring data to define classic distributed mathematical models to forecast future potential levels. The main aim of this study is to propose and evaluate a novel parsimonious integrated method for the short-term forecasting of groundwater levels. It has low requirements in term of data, and it is operational and relatively easy to apply. It uses geostatistics, optimal meteorological exogenous variables and artificial neural networks. We have illustrated our method in the aquifer “Campo de Montiel” (Spain). The analysis of optimal exogenous variables revealed that, in general, the wells with stronger correlations with precipitation are located closer to the central part of the aquifer. NAR, which does not consider secondary information, is the best approach for 25.5 % of the cases and is associated with well locations with lower R2 between groundwater levels and precipitation. Amongst the approaches with exogenous variables, the ones that use effective precipitation have been selected more times as the best experiments. NARX and Elman using effective precipitation had the best approaches with 21.6 % and 29.4 % of the cases respectively. For the selected approaches, we obtained a mean RMSE of 1.14 m in the test and 0.76, 0.92, 0.92, 0.87, 0.90, and 1.05 m for the forecasting test for months 1 to 6 respectively for the 51 wells, but the accuracy of the results can vary depending on the well. The interquartile range of the RMSE is around 2 m for the test and forecasting test. The uncertainty of the forecasting is also considered by generating multiple groundwater level series.

Deep Ensemble-Based Approach Using Randomized Low-Rank Approximation for Sustainable Groundwater Level Prediction

Groundwater is the most abundant freshwater resource. Agriculture, industrialization, and domestic water supplies rely on it. The depletion of groundwater leads to drought. Topographic elevation, aquifer properties, and geomorphology influence groundwater quality. As the groundwater level data (GWL) are time series in nature, it is challenging to determine appropriate metrics and to evaluate groundwater levels accurately with less information loss. An effort has been made to forecast groundwater levels in India by developing a deep ensemble learning approach using a double-edge bi-directed long-short-term-memory (DEBi-LSTM) model approximated with a randomized low-ranked approximation algorithm (RLRA) and the variance inflation factor (VIF) to reduce information loss and to preserve data consistency. With minimal computation time, the model outperformed existing state-of-the-art models with 96.1% accuracy. To ensure sustainable groundwater development, the proposed work is discussed in terms of its managerial implications. By applying the model, we can identify safe, critical, and semi-critical groundwater levels in Indian states so that strategic plans can be developed.

Groundwater levels forecasting using machine learning models: A case study of the groundwater region 10 at Karst Belt, South Africa

The crucial role which groundwater resource plays in our environment and the overall well-being of all living things can not be underestimated. Nonetheless, mismanagement of resources, over-exploitation, inadequate supply of surface water and pollution have led to severe drought and an overall drop in groundwater resources’ levels over the past decades. To address this, a groundwater flow model and several mathematical data-driven models have been developed for forecasting groundwater levels. However, there is a problem of unavailability and scarcity of the on-site input data needed by the data-driven models to forecast the groundwater level. Furthermore, as a result of the dynamics and stochastic characteristics of groundwater, there is a need for an appropriate, accurate and reliable forecasting model to solve these challenges. Over the years, the broad application of Machine Learning (ML) and Artificial Intelligence (AI) models are gaining attraction as an alternative solution for forecasting groundwater levels. Against this background, this article provides an overview of forecasting methods for predicting groundwater levels. Also, this article uses ML models such as Regressions Models, Deep Auto-Regressive models, and Nonlinear Autoregressive Neural Networks with External Input (NARX) to forecast groundwater levels using the groundwater region 10 at Karst belt in South Africa as a case study. This was done using Python Mx. Version 1.9.1., and MATLAB R2022a machine learning toolboxes. Moreover, the Coefficient of Determination (R2);, Root Mean Square Error (RMSE), Mutual Information gain, Mean Absolute Percentage Error (MAPE), Mean Squared Error (MSE), Mean Absolute Error (MAE), and the Mean Absolute Scaled Error (MASE)) models were the forecasting statistical performance metrics used to assess the predictive performance of these models. The results obtained showed that NARX and Support Vector Machine (SVM) have higher performance metrics and accuracy compared to other models used in this study.

Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) model for Forecasting Groundwater Level in the Pravara River Basin, India

Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) model for Forecasting Groundwater Level in the Pravara River Basin, India

Groundwater Level Forecasting in the Jakarta Groundwater Basin

Groundwater is an important source of fresh water worldwide. Jakarta, the capital city of the Republic of Indonesia, is a large city with a population of more than 10 million and the center of the country’s economy and urban development. However, Jakarta has many challenges related to groundwater management. Changes in well GWL serve as a direct indicator of the effects of groundwater evolution, and GWL time series usually contain important information about aquifer dynamics. Therefore, water managers and engineers must model and predict GWL, identify and measure groundwater resources, and maintain a balance between supply and demand. Measuring and analyzing the groundwater table (GWL) of an aquifer are an important and valuable activity in the management of groundwater resources, and information on GWL variability can be used to determine groundwater availability. Accurate and reliable groundwater level estimation is very important because it provides important information about the quantitative groundwater status of an aquifer. The main advantage of AI models is their ability to reproduce nonlinear and complex processes without a full understanding of the underlying physics. As a result, the use of AI techniques in GWL modeling continues to grow, attracting the attention of scientists around the world. Using a nonlinear autoregressive network with extrinsic input (NARX) with a timestep of 14 days, this study is aimed at predicting the volatility of Jakarta’s GWL. Based on the research results, both JKT-01 and JKT-03 show a linear downward trend. On the other hand, JKT-02 and JKT-04 show a stable linear trend. GWL increases the linear trend of JKT-05. Variable results are generated by model performance. Model performance ( R ) varied between 0.2 and 0.9 during the training phase and between 0.2 and 0.9 during the validation phase. The overall performance of the model varies from 0.3 to 0.9. The diverse lithology and high pumping capacity in Jakarta are the reasons for the different modeling results. Forecasts for 14 days (14 timesteps) show that GWL remains constant at certain well locations, while GWL decreases at other locations. This is a consideration that stakeholders can consider to reduce the small effect of the daily GWL pattern as a result of NARX modeling.

Artificial Neural Network Technique for Groundwater Modelling of Jaspura Block

As a result of economic development and climatic change, arid and semi-arid areas are confronted with significant difficulties in the management of limited freshwater resources. For the most part, groundwater is the most significant water supply in these regions. Groundwater level prediction is a critical component of appropriate sustainable development and must be done correctly. The use of physical-based models is often used in the modelling and prediction of groundwater. However, owing to data shortages in many arid and semi-arid regions, they are not relevant in these areas. The usefulness of data-driven techniques in modelling complicated and nonlinear hydrological processes has been shown in many studies. It is the implementation and comparison of four algorithm-based models for forecasting groundwater levels that is the focal point of this research. This article compares the different Artificial Neural Network method and applies to the Jaspura Block of Banda Districts which is part of the Yamuna River Basin. For the forecast of groundwater levels four distinct algorithms Levenberg Marquardt, Gradient Descent, Scaled Conjugate Gradient and Bayesian regularization are used for optimal design. The ANN training data for input is collected from Recharge and Discharge data while groundwater level data for output layer were being used. The best algorithm comes to the Levenberg Marquardt algorithm in comparison with the other algorithms.

Employing machine learning to quantify long-term climatological and regulatory impacts on groundwater availability in intensively irrigated regions

The steady overexploitation of the Ogallala Aquifer underlying the U.S. High Plains Region has put irrigated crop production at risk, particularly in the Southern and Central High Plains. To manage this issue properly, a data-driven modeling framework is developed and tested that is fast to employ and yet provides reliable long-term groundwater level (GWL) forecasts as a function of climatological and anthropogenic factors. The modeling framework uses the random forests (RF) technique in combination with ordinary kriging, and is tested in Finney County in southwest Kansas. The introduction of groundwater withdrawal potential as a new surrogate for pumping intensity enables the RF model to capture decline in groundwater depletion rate as the system progresses towards aquifer depletion and/or as a result of well retirement policies. The RF model is executed from 2017 to 2099 for 20 different downscaled global climate models (GCMs) for the two representative concentration pathways (RCP) scenarios of 4.5 and 8.5. The results show the aquifer will cease to support irrigated agriculture in most of the county by 2060 under status quo management and average climate conditions. Moreover, climate will likely shift the aquifer’s depletion time frame by 15 years or less in most of the study area. The long-term combined impact of well retirement plans and climate conditions on groundwater depletion trends imply well retirement policies do not lead to sustained groundwater savings. This study demonstrates the capacity of machine learning models to serve as a rapid assessment tool, informing policymakers about future groundwater availability in intensively irrigated regions and under different climate and management conditions.

Mathematical and Machine Learning Models for Groundwater Level Changes: A Systematic Review and Bibliographic Analysis

With the effects of climate change such as increasing heat, higher rainfall, and more recurrent extreme weather events including storms and floods, a unique approach to studying the effects of climatic elements on groundwater level variations is required. These unique approaches will help people make better decisions. Researchers and stakeholders can attain these goals if they become familiar with current machine learning and mathematical model approaches to predicting groundwater level changes. However, descriptions of machine learning and mathematical model approaches for forecasting groundwater level changes are lacking. This study picked 117 papers from the Scopus scholarly database to address this knowledge gap. In a systematic review, the publications were examined using quantitative and qualitative approaches, and the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) was chosen as the reporting format. Machine learning and mathematical model techniques have made significant contributions to predicting groundwater level changes, according to the study. However, the domain is skewed because machine learning has been more popular in recent years, with random forest (RF) methods dominating, followed by the methods of support vector machine (SVM) and artificial neural network (ANN). Machine learning ensembles have also been found to help with aspects of computational complexity, such as performance and training times. Furthermore, compared to mathematical model techniques, machine learning approaches achieve higher accuracies, according to our research. As a result, it is advised that academics employ new machine learning techniques while also considering mathematical model approaches to predicting groundwater level changes.

Improving Results of Existing Groundwater Numerical Models Using Machine Learning Techniques: A Review

This paper presents a review of papers specifically focused on the use of both numerical and machine learning methods for groundwater level modelling. In the reviewed papers, machine learning models (also called data-driven models) are used to improve the prediction or speed process of existing numerical modelling. When long runtimes inhibit the use of numerical models, machine learning models can be a valid alternative, capable of reducing the time for model development and calibration without sacrificing accuracy of detail in groundwater level forecasting. The results of this review highlight that machine learning models do not offer a complete representation of the physical system, such as flux estimates or total water balance and, thus, cannot be used to substitute numerical models in large study areas; however, they are affordable tools to improve predictions at specific observation wells. Numerical and machine learning models can be successfully used as complementary to each other as a powerful groundwater management tool. The machine learning techniques can be used to improve calibration of numerical models, whereas results of numerical models allow us to understand the physical system and select proper input variables for machine learning models. Machine learning models can be integrated in decision-making processes when rapid and effective solutions for groundwater management need to be considered. Finally, machine learning models are computationally efficient tools to correct head error prediction of numerical models.

Conjunction of cluster ensemble-model ensemble techniques for spatiotemporal assessment of groundwater depletion in semi-arid plains

• The cluster ensemble technique improved the final cluster structures. • The spatiotemporal ensemble clustering revealed four different patterns of GWL. • LSTM was not appropriate for monthly GWL forecasting compared to ensemble methods. • The neural ensemble has the lowest disorder and a large reduction in uncertainty. • The simultaneous clustering-forecasting ensemble techniques enhanced the outcomes. In this study, first to identify the patterns of groundwater level (GWL) over the Ghorveh-Dehgolan plain (GDP) located in western Iran, as a data pre-processing scheme, three different types of clustering algorithms were applied to monthly GWL data sets of the piezometers. Then, the best structures of all clustering methods were integrated by Combining Multiple Clusterings via Similarity Graph (COMUSA) method to obtain the most homogenous patterns of GWL. The final results of the clustering step indicated that applying COMUSA could enhance the homogeneity of the clusters up to 25%. After dividing the GWL of GDP into four patterns, three single artificial intelligence (AI)-based models were applied to forecast multi-step-ahead GWL of centroid piezometer of each cluster. To benefit from the advantages of the single models, the outcomes were then combined with a neural averaging ensemble (NAE) technique as a post-processing step. Additionally, the assessment of the deep learning (DL) -based long-short-term memory (LSTM) application in multi-step ahead forecasting of GWL showed this method is not an appropriate choice compared to ensemble techniques for modeling the process with limited observed data. The comparison of the proposed GWL forecasting models of this study revealed the superiority of the NAE technique that enhanced the accuracy of the single models up to 23% in the testing phase. It could be concluded that the combination of cluster ensemble and model ensemble techniques could improve the performance of the individual method in reliable forecasting of the future GWL condition and the methodology of this study can be applied to the GWL of other plains.

Forecasting groundwater level of karst aquifer in a large mining area using partial mutual information and NARX hybrid model

Predicting the groundwater level of karst aquifers in North China Coalfield is essential for early warning of mine water hazards and regional water resources management. However, the dynamic changes of strata structure and hydrogeological parameters driven by coal mining activity cause challenges to the process-oriented groundwater model. In order to achieve accurate prediction of groundwater level in large mining areas, this study was the first to use the data-driven Nonlinear Autoregressive with External Input (NARX) model to predict the groundwater level of six karst aquifer observation wells in Pingshuo Mining Area. Three variable input scenarios were set up, solely considering meteorological factors, anthropogenic disturbance factors, and considering both meteorological and anthropogenic disturbance factors. The novel partial mutual information (PMI) screening algorithm was adopted to determine optimized input variables in each scenario. The input and feedback delay coefficients of NARX model were determined by using Seasonal-trend Decomposition Procedure Based on Loess (STL) algorithm and auto- and cross-correlation functions. The results showed that PMI algorithm can effectively screen out the optimal input variables for predicting groundwater level, the NSE coefficients of the PMI-NARX models under the three scenarios were 38.81%, 4.26% and 41.46% higher than those of the corresponding control experiments, respectively. In addition, the prediction performance of the PMI-NARX built on the basis of meteorological factors is poor (NSE <0.63). However, in scenarios which solely use anthropogenic disturbance factors and both use meteorological and anthropogenic disturbance factors, the PMI-NARX coupling models exhibit good prediction performance (NSE and R2 are all greater than 0.8). Especially under solely considering anthropogenic disturbance factors scenario, the model still exhibited good prediction accuracy with a negligible number of input variables. The results can provide technical and theoretical support for the prediction of groundwater level in other mining areas.