Groundwater level prediction using a multiple objective genetic algorithm-grey relational analysis based weighted ensemble of anfis models

Predicting groundwater levels is critical for ensuring sustainable use of an aquifer’s limited groundwater reserves and developing a useful groundwater abstraction management strategy. The purpose of this study was to assess the predictive accuracy and estimation capability of various models based on the Adaptive Neuro Fuzzy Inference System (ANFIS). These models included Differential Evolution-ANFIS (DE-ANFIS), Particle Swarm Optimization-ANFIS (PSO-ANFIS), and traditional Hybrid Algorithm tuned ANFIS (HA-ANFIS) for the one-and multi-week forward forecast of groundwater levels at three observation wells. Model-independent partial autocorrelation functions followed by frequentist lasso regression-based feature selection approaches were used to recognize appropriate input variables for the prediction models. The performances of the ANFIS models were evaluated using various statistical performance evaluation indexes. The results revealed that the optimized ANFIS models performed equally well in predicting one-week-ahead groundwater levels at the observation wells when a set of various performance evaluation indexes were used. For improving prediction accuracy, a weighted-average ensemble of ANFIS models was proposed, in which weights for the individual ANFIS models were calculated using a Multiple Objective Genetic Algorithm (MOGA). The MOGA accounts for a set of benefits (higher values indicate better model performance) and cost (smaller values indicate better model performance) performance indexes calculated on the test dataset. Grey relational analysis was used to select the best solution from a set of feasible solutions produced by a MOGA. A MOGA-based individual model ranking revealed the superiority of DE-ANFIS (weight = 0.827), HA-ANFIS (weight = 0.524), and HAANFIS (weight = 0.697) at observation wells GT8194046, GT8194048, and GT8194049, respectively. Shannon’s entropy-based decision theory was utilized to rank the ensemble and individual ANFIS models using a set of performance indexes. The ranking result indicated that the ensemble model outperformed all individual models at all observation wells (ranking value = 0.987, 0.985, and 0.995 at observation wells GT8194046, GT8194048, and GT8194049, respectively). The worst performers were PSO-ANFIS (ranking value = 0.845), PSO-ANFIS (ranking value = 0.819), and DE-ANFIS (ranking value = 0.900) at observation wells GT8194046, GT8194048, and GT8194049, respectively. The generalization capability of the proposed ensemble modelling approach was evaluated for forecasting 2-, 4-, 6-, and 8-weeks ahead groundwater levels using data from GT8194046. The evaluation results confirmed the useability of the ensemble modelling for forecasting groundwater levels at higher forecasting horizons. The study demonstrated that the ensemble approach may be successfully used to predict multi-week-ahead groundwater levels, utilizing previous lagged groundwater levels as inputs

Genetic Programming: Efficient Modeling Tool in Hydrology and Groundwater Management

[Extract] With the advent of computers a wide range of mathematical and numerical models have been developed with the intent of predicting or approximating parts of hyrdrologic cycle. Prior to the advent of conceptual process based models, physical hydraulic models, which are reduced scale representations of large hydraulic systems, were used commonly in water resources engineering. Fast development in the computational systems and numerical solutions of complex differential equations enabled development of conceptual models to represent physical systems. Thus, in the last two decades large number of mathematical models was developed to represent different processes in hydrological cycle

Development of a sustainable groundwater management strategy and sequential compliance monitoring to control saltwater intrusion in coastal aquifers

The coastal areas of the world are characterized by high population densities, an abundance of food, and increased economic activities. These increasing human settlements, subsequent increases in agricultural developments and economic activities demand an increasing amount quantity of freshwater supplies to different sectors. Groundwater in coastal aquifers is one of the most important sources of freshwater supplies. Over exploitation of this coastal groundwater resource results in seawater intrusion and subsequent deterioration of groundwater quality in coastal aquifers. In addition, climate change induced sea level rise, in combination with the effect of excessive groundwater extraction, can accelerate the seawater intrusion. Adequate supply of good quality water to different sectors in coastal areas can be ensured by adoption of a proper management strategy for groundwater extraction. Optimal use of the coastal groundwater resource is one of the best management options, which can be achieved by employing a properly developed optimal groundwater extraction strategy. Coupled simulation-optimization (S-O) approaches are essential tools to obtain the optimal groundwater extraction patterns. This study proposes approaches for developing multiple objective management of coastal aquifers with the aid of barrier extraction wells as hydraulic control measure of saltwater intrusion in multilayered coastal aquifer systems. Therefore, two conflicting objectives of management policy are considered in this research, i.e. maximizing total groundwater extraction for advantageous purposes, and minimizing the total amount of water abstraction from barrier extraction wells. The study also proposes an adaptive management strategy for coastal aquifers by developing a three-dimensional (3-D) monitoring network design. The performance of the proposed methodologies is evaluated by using both an illustrative multilayered coastal aquifer system and a real life coastal aquifer study area. Coupled S-O approach is used as the basic tool to develop a saltwater intrusion management model to obtain the optimal groundwater extraction rates from a combination of feasible solutions on the Pareto optimal front. Simulation of saltwater intrusion processes requires solution of density dependent coupled flow and solute transport numerical simulation models that are computationally intensive. Therefore, computational efficiency in the coupled S-O approach is achieved by using an approximate emulator of the accompanying physical processes of coastal aquifers. These emulators, often known as surrogate models or meta-models, can replace the computationally intensive numerical simulation model in a coupled S-O approach for achieving computational efficiency. A number of meta-models have been developed and compared in this study for integration with the optimization algorithm in order to develop saltwater intrusion management model. Fuzzy Inference System (FIS), Adaptive Neuro Fuzzy Inference System (ANFIS), Multivariate Adaptive Regression Spline (MARS), and Gaussian Process Regression (GPR) based meta-models are developed in the present study for approximating coastal aquifer responses to groundwater extraction. Properly trained and tested meta-models are integrated with a Controlled Elitist Multiple Objective Genetic Algorithm (CEMOGA) within a coupled S-O approach. In each iteration of the optimization algorithm, the meta-models are used to compute the corresponding salinity concentrations for a set of candidate pumping patterns generated by the optimization algorithm. Upon convergence, the non-dominated global optimal solutions are obtained as the Pareto optimal front, which represents a trade-off between the two conflicting objectives of the pumping management problem. It is observed from the solutions of the meta-model based coupled S-O approach that the considered meta-models are capable of producing a Pareto optimal set of solutions quite accurately. However, each meta-modelling approach has distinct advantages over the others when utilized within the integrated S-O approach. Uncertainties in estimating complex flow and solute transport processes in coastal aquifers demand incorporation of the uncertainties related to some of the model parameters. Multidimensional heterogeneity of aquifer properties such as hydraulic conductivity, compressibility, and bulk density are considered as major sources of uncertainty in groundwater modelling system. Other sources of uncertainty are associated with spatial and temporal variability of hydrologic as well as human interventions, e.g. aquifer recharge and transient groundwater extraction patterns. Different realizations of these uncertain model parameters are obtained from different statistical distributions. FIS based meta-models are advanced to a Genetic Algorithm (GA) tuned hybrid FIS model (GA-FIS), to emulate physical processes of coastal aquifers and to evaluate responses of the coastal aquifers to groundwater extraction under groundwater parameter uncertainty. GA is used to tune the FIS parameters in order to obtain the optimal FIS structure. The GA-FIS models thus obtained are linked externally to the CEMOGA in order to derive an optimal pumping management strategy using the coupled S-O approach. The evaluation results show that the proposed saltwater intrusion management model is able to derive reliable optimal groundwater extraction strategies to control saltwater intrusion for the illustrative multilayered coastal aquifer system. The optimal management strategies obtained as solutions of GA-FIS based management models are shown to be reliable and accurate within the specified ranges of values for different realizations of uncertain groundwater parameters. One of the major concerns of the meta-model based integrated S-O approach is the uncertainty associated with the meta-model predictions. These prediction uncertainties, if not addressed properly, may propagate to the optimization procedures, and may deteriorate the optimality of the solutions. A standalone meta-model, when used within an optimal management model, may result in the optimization routine producing actually suboptimal solutions that may undermine the optimality of the groundwater extraction strategies. Therefore, this study proposes an ensemble approach to address the prediction uncertainties of meta-models. Ensemble is an approach to assimilate multiple similar or different algorithms or base learners (emulators). The basic idea of ensemble lies in developing a more reliable and robust prediction tool that incorporates each individual emulator's unique characteristic in order to predict future scenarios. Each individual member of the ensemble contains different input -output mapping functions. Based on their own mapping functions, these individual emulators provide varied predictions on the response variable. Therefore, the combined prediction of the ensemble is likely to be less biased and more robust, reliable, and accurate than that of any of the individual members of the ensemble. Performance of the ensemble meta-models is evaluated using an illustrative coastal aquifer study area. The results indicate that the meta-model based ensemble modelling approach is able to provide reliable solutions for a multilayered coastal aquifer management problem. Relative sea level rise, providing an additional saline water head at the seaside, has a significant impact on an increase in the salinization process of the coastal aquifers. Although excessive groundwater withdrawal is considered as the major cause of saltwater intrusion, relative sea level rise, in combination with the effect of excessive groundwater pumping, can exacerbate the already vulnerable coastal aquifers. This study incorporates the effects of relative sea level rise on the optimized groundwater extraction values for the specified management period. Variation of water concentrations in the tidal river and seasonal fluctuation of river water stage are also incorporated. Three meta-models are developed from the solution results of the numerical simulation model that simulates the coupled flow and solute transport processes in a coastal aquifer system. The results reveal that the proposed meta-models are capable of predicting density dependent coupled flow and solute transport patterns quite accurately. Based on the comparison results, the best meta-model is selected as a computationally cheap substitute of the simulation model in the coupled S-O based saltwater intrusion management model. The performance of the proposed methodology is evaluated for an illustrative multilayered coastal aquifer system in which the effect of climate change induced sea level rise is incorporated for the specified management period. The results show that the proposed saltwater intrusion management model provides acceptable, accurate, and reliable solutions while significantly improving computational efficiency in the coupled S-O methodology. The success of the developed management strategy largely depends on how accurately the prescribed management policy is implemented in real life situations. The actual implementation of a prescribed management strategy often differs from the prescribed planned strategy due to various uncertainties in predicting the consequences, as well as practical constraints, including noncompliance with the prescribed strategy. This results in actual consequences of a management strategy differing from the intended results. To bring the management consequences closer to the intended results, adaptive management strategies can be sequentially modified at different stages of the management horizon using feedback measurements from a deigned monitoring network. This feedback information can be the actual spatial and temporal concentrations resulting from the implementation of actual management strategy. Therefore, field-scale compliance of the developed coastal aquifer management strategy is a crucial aspect of an optimally designed groundwater extraction policy. A 3-D compliance monitoring network design methodology is proposed in this study in order to develop an adaptive and sequentially modified management policy, which aims to improve optimal and justifiable use of groundwater resources in coastal aquifers. In the first step, an ensemble meta-model based multiple objective prescriptive model is developed using a coupled S-O approach in order to derive a set of Pareto optimal groundwater extraction strategies. Prediction uncertainty of meta-models is addressed by utilizing a weighted average ensemble using Set Pair Analysis. In the second step, a monitoring network is designed for evaluating the compliance of the implemented strategies with the prescribed management goals due to possible uncertainties associated with field-scale application of the proposed management policy. Optimal monitoring locations are obtained by maximizing Shannon's entropy between the saltwater concentrations at the selected potential locations. Performance of the proposed 3-D sequential compliance monitoring network design is assessed for an illustrative multilayered coastal aquifer study area. The performance evaluations show that sequential improvements of optimal management strategy are possible by utilizing saltwater concentrations measurements at the proposed optimal compliance monitoring locations. The integrated S-O approach is used to develop a saltwater intrusion management model for a real world coastal aquifer system in the Barguna district of southern Bangladesh. The aquifer processes are simulated by using a 3-D finite element based combined flow and solute transport numerical code. The modelling and management of seawater intrusion processes are performed based on very limited hydrogeological data. The model is calibrated with respect to hydraulic heads for a period of five years from April 2010 to April 2014. The calibrated model is validated for the next three-year period from April 2015 to April 2017. The calibrated and partially validated model is then used within the integrated S-O approach to develop optimal groundwater abstraction patterns to control saltwater intrusion in the study area. Computational efficiency of the management model is achieved by using a MARS based meta-model approximately emulating the combined flow and solute transport processes of the study area. This limited evaluation demonstrates that a planned transient groundwater abstraction strategy, acquired as solution results of a meta-model based integrated S-O approach, is a useful management strategy for optimized water abstraction and saltwater intrusion control. This study shows the capability of the MARS meta-model based integrated S-O approach to solve real-life complex management problems in an efficient manner

Revolutionizing Groundwater Management with Hybrid AI Models: A Practical Review

Developing precise soft computing methods for groundwater management, which includes quality and quantity, is crucial for improving water resources planning and management. In the past 20 years, significant progress has been made in groundwater management using hybrid machine learning (ML) models as artificial intelligence (AI). Although various review articles have reported advances in this field, existing literature must cover groundwater management using hybrid ML. This review article aims to understand the current state-of-the-art hybrid ML models used for groundwater management and the achievements made in this domain. It includes the most cited hybrid ML models employed for groundwater management from 2009 to 2022. It summarises the reviewed papers, highlighting their strengths and weaknesses, the performance criteria employed, and the most highly cited models identified. It is worth noting that the accuracy was significantly enhanced, resulting in a substantial improvement and demonstrating a robust outcome. Additionally, this article outlines recommendations for future research directions to enhance the accuracy of groundwater management, including prediction models and enhance related knowledge

Groundwater Level Forecasting Using Wavelet and Kriging

In this research, a hybrid wavelet-artificial neural network (WANN) and a geostatistical method were proposed for spatiotemporal prediction of the groundwater level (GWL) for one month ahead. For this purpose, monthly observed time series of GWL were collected from September 2005 to April 2014 in 10 piezometers around Mashhad City in the Northeast of Iran. In temporal forecasting, an artificial neural network (ANN) and a WANN were trained for each piezometer. Kriging was used in spatial estimations. The comparison of the prediction accuracy of these two models illustrated that the WANN was more efficacious in prediction of GWL for one month ahead. Thereafter, in order to predict GWL in desired points in the study area, the kriging method was used and a Gaussian model was selected as the best variogram model. Ultimately, the WANN with coefficient of determination and root mean square error and mean absolute error, 0.836 and 0.335 and 0.273 respectively, in temporal forecasting and Gaussian model with root mean square, 0.253 as the best fitted model on Kriging method for spatial estimating were suitable choices for spatiotemporal GWL forecasting. The obtained map of groundwater level showed that the groundwater level was higher in the areas of plain located in mountainside areas. This fact can show that outcomes are respectively correct

Groundwater Level Modeling with Machine Learning: A Systematic Review and Meta-Analysis

Groundwater is a vital source of freshwater, supporting the livelihood of over two billion people worldwide. The quantitative assessment of groundwater resources is critical for sustainable management of this strained resource, particularly as climate warming, population growth, and socioeconomic development further press the water resources. Rapid growth in the availability of a plethora of in-situ and remotely sensed data alongside advancements in data-driven methods and machine learning offer immense opportunities for an improved assessment of groundwater resources at the local to global levels. This systematic review documents the advancements in this field and evaluates the accuracy of various models, following the protocol developed by the Center for Evidence-Based Conservation. A total of 197 original peer-reviewed articles from 2010–2020 and from 28 countries that employ regression machine learning algorithms for groundwater monitoring or prediction are analyzed and their results are aggregated through a meta-analysis. Our analysis points to the capability of machine learning models to monitor/predict different characteristics of groundwater resources effectively and efficiently. Modeling the groundwater level is the most popular application of machine learning models, and the groundwater level in previous time steps is the most employed input data. The feed-forward artificial neural network is the most employed and accurate model, although the model performance does not exhibit a striking dependence on the model choice, but rather the information content of the input variables. Around 10–12 years of data are required to develop an acceptable machine learning model with a monthly temporal resolution. Finally, advances in machine and deep learning algorithms and computational advancements to merge them with physics-based models offer unprecedented opportunities to employ new information, e.g., InSAR data, for increased spatiotemporal resolution and accuracy of groundwater monitoring and prediction

Machine Learning with Metaheuristic Algorithms for Sustainable Water Resources Management

The main aim of this book is to present various implementations of ML methods and metaheuristic algorithms to improve modelling and prediction hydrological and water resources phenomena having vital importance in water resource management

Validating the KAGIS black‐box GIS‐based model in a Mediterranean karst aquifer: Case of study of Mela aquifer (SE Spain)

Karst Aquifer GIS‐based model (KAGIS model) is developed and applied to Mela aquifer, a small karst aquifer located in a Mediterranean region (SE Spain). This model considers different variables, such as precipitation, land use, surface slope and lithology, and their geographical heterogeneity to calculate both, the run‐off coefficients and the fraction of precipitation which contributes to fill the soil water reservoir existing above the aquifer. Evapotranspiration uptakes deplete water, exclusively, from this soil water reservoir and aquifer recharge occurs when water in the soil reservoir exceeds the soil field capacity. The proposed model also obtains variations of the effective porosity in a vertical profile, an intrinsic consequence of the karstification processes. A new proposal from the Nash–Sutcliffe efficiency index, adapted to arid environments, is presented and employed to evaluate the model's ability to predict the water table oscillations. The uncertainty in the model parameters is determined by the Generalized Likelihood Uncertainty Estimation method. Afterwards, when KAGIS is calibrated, wavelet analysis is applied to the resulting data in order to evaluate the variability in the aquifer behaviour. Wavelet analysis reveals that the rapid hydrogeological response, typical of a wide variety of karst systems, is the prevailing feature of Mela aquifer. This study proves that KAGIS is a useful tool to quantify recharge and discharge rates of karst aquifers and can be effectively applied to develop a proper management of water resources in Mediterranean areas.This research was funded by the Spanish Ministry of Science and Innovation, Projects CGL2013‐48802‐C3‐3‐R and CGL2015‐69773‐C2‐1‐P; and by the University of Alicante, Projects GRE15‐19 and GRE17‐12