Water Resources Management Problems Research Articles

Fundamental Problems of Water Resources Management in the Helmand River Basin, Afghanistan

The closed hydrology and the geopolitical nature of the Helmand River basin in terms of leadership, management, and use of water resources have created serious threats to its integrity, environmental health, and human security in this river basin. The Helmand River basin, where about 8 million people live, includes about 49 percent of the soil and 11 percent of the water flow of this country. Agricultural sectors and related industries are the main drivers of the economy in this basin and due to the increasing need for food in the country and the region, the population shift towards cities, industrialization, and most importantly climate change and water shortage, competition between major water consumers in this basin is increasing. Despite the increasing number of studies on the water management of the Helmand River basin, no practical research carried out to strengthen and summarize the common conclusions and findings related to the fundamental problems facing the water resources management of this river basin. Therefore, in this article, to fill the aforementioned gap, all related documents, studies, and topics have been comprehensively reviewed and analyzed. To achieve this goal, the qualitative-analytical research method was used to analyze and find the key issues raised, and as a result, the basic problems facing the water resources management of this basin were investigated as much as possible. In the following, the necessary suggestions are also presented so that by implementing it, this country would be able to solve the existing problems by using its hydro political capacities and opportunities and it would also be placed at the center of the water interactions in the river basin, to provide a sustainable and all-round development of the country.

Spatio-Temporal Evolution of Olive Tree Water Status Using Land Surface Temperature and Vegetation Indices Derived from Landsat 5 and 8 Satellite Imagery in Southern Peru

Land surface temperature (LST) and its relationship with vegetation indices (VIs) have proven to be effective for monitoring water stress in large-scale crops. Therefore, the objective of this study is to find an appropriate VI to analyse the spatio-temporal evolution of olive water stress using LST images and VIs derived from Landsat 5 and 8 satellites in the semi-arid region of southern Peru. For this purpose, VIs (Normalised Difference Vegetation Index (NDVI), Enhanced Vegetation Index 2 (EVI2) and Soil Adjusted Vegetation Index (SAVI)) and LST were calculated. The information was processed in Google Earth Engine (GEE) for the period 1985 to 2024, with an interval of every five years for the summer season. The triangle method was applied based on the LST-VIs scatterplot analysis, a tool that establishes wet and dry boundary conditions for the Temperature Vegetation Dryness Index (TVDI). The results indicated a better appreciation of olive orchard water stress over time, with an average of 39% drought (TVDINDVI and TVDISAVI), 24% severe drought (TVDINDVI) and 25% (TVDISAVI) of the total area, compared to TVDIEVI2, which showed 37% drought and 16% severe drought. It is concluded that TVDINDVI and TVDISAVI provide a better visualisation of the water stress map of the olive crop and offer a range of options to address current and future problems in water resource management in the olive sector in semi-arid areas of southern Peru.

Implications of the Mississippi v. Tennessee Supreme Court Decision for Interstate Groundwater Management.

Groundwater allocation is rapidly becoming a contentious water resource management problem around the world. It is anticipated that the effects of climate change would further aggravate this problem. Conflicts over the distribution of freshwater are expected to increase as stakeholders want to access more groundwater to meet their growing demands. In the United States, water conflicts are settled through a litigation process. Water litigations can be expensive, protracted, and fraught with complex legal and technical difficulties. A landmark groundwater case involving Tennessee (TN) and Mississippi (MS) was recently litigated in the Supreme Court of the United States (SCOTUS). In this case, MS sued TN for stealing their groundwater and SCOTUS unanimously ruled that the water contained in the aquifer that naturally crosses the border between TN and MS is subject to equitable apportionment. This decision has significant ramifications for groundwater management as it established a precedent for resolving future interstate groundwater litigations. Although the Court has previously applied the legal doctrine of equitable apportionment to settle disputes involving surface water use, this is the first instance in which the doctrine has been applied to resolve an interstate groundwater dispute. Therefore, currently, there are little or no guidelines available for equitably distributing groundwater resources between two states. The objective of this article is to examine this historic legal dispute to fully understand the scientific justification for the judicial stances taken by the plaintiff and defendants, and the legal reasoning for the final verdict. We also discuss the challenges this ruling presents for managing interstate groundwater resources.

A Unified Spatial-Pressure Sensitivity Partitioning and Leakage Detection Method within a Deep Learning Framework

This study introduces an innovative approach for leak detection in water distribution systems (WDSs), integrating three-order embedding, k-means clustering, and long short-term memory (LSTM) networks, with pressure-sensitive analysis techniques. This comprehensive methodology segments the network into distinct partitions, utilizes simulated leak events to train the deep learning networks, and establishes a sophisticated model for accurately identifying leak partitions. This approach generates a leak dataset by adjusting water demands, which could effectively pinpoint the leaks in a specific partition by leveraging both the pressure sensitivity and spatial coordinates of nodes, allowing for the elimination of the need for manual work and precise identification of leaks in targeted areas. Through the analysis of two case studies, the model demonstrates its ability to effectively pinpoint potential leak partitions, significantly enhancing operational efficiency and reliability in managing the complex problems of urban water resource management. This approach not only optimizes leak detection but also paves the way for advanced, data-driven strategies in WDSs, ensuring sustainable and secure water distribution in urban settings.

Legal bases of the Water Code of the Republic of Kazakhstan

The relevance of the research topic is due to the fact that water security in recent years has been included in the list of global risks of modernity, which requires effective water resources management. In particular, in the Republic of Kazakhstan, this issue has been one of the most acute recently. To date, there are a number of unresolved issues at the inter-national level of water resources management in the republic, as almost all freshwater resources of the country are transboundary in nature, and almost half of them are formed on the territory of neighbouring states. The purpose of this study is to analyse the existing problems in transnational water resources management in the Republic of Kazakhstan and to develop directions for their solution. The research methods include normative-legal method, expert, factual method, content analysis, comparison, generalisation, classification, synthesis and analysis. The article presents the state of water resources of the Republic of Kazakhstan at the present stage of development, including those of transboundary nature. The management of water resources of the republic, including at the inter-national level, is characterised, and problems in this area are revealed. Thus, the main problems to date have been attributed to: dependence on transboundary flows from the territories of neighbouring countries, primarily China and Russia, in recent years increasingly polluting rivers and increasing the volume of water withdrawal, significant wear and tear of infrastructure, low level of automation and digitalisation of management, low efficiency of control over the implementation of measures for the rational use of water resources. To solve the problems, recommendations have been proposed and promising directions for the development of transnational water resources management have been considered, which will contribute to improving the efficiency of transboundary water resources use.

Assessment of the Spatiotemporal Changes in the Extreme Precipitation Climate Indices over the Chungcheong Region of South Korea during 1973–2020

This study analyzed the changes and trends in twelve extreme precipitation-based climate indices obtained using daily data from 10 synoptic stations in the Chungcheong region of South Korea during the 1973–2020 period. The climate indices were used to assess the trends in the extreme precipitation characteristics of duration, frequency, and intensity using the innovative trend analysis (ITA) method. The results of the ITA were further compared with two other non-parametric test methods such as Mann–Kendall (MK) and Spearman’s rho (SR). The results showed that most stations exhibited significant increasing trends in all the investigated climate indices at a 95% confidence level as indicated by the ITA method, with only a few stations indicating significant decreasing trends in R95p, R99p, Rx3day, and Rx5day. The sub-trend analysis further revealed the dominance of neutral behavior around the low-value cluster, especially for the extreme precipitation duration. At the same time, increasing trends dominate the high-value cluster at most stations. Meanwhile, only R10mm, R99p, and R95p exhibited monotonic trends in the Boeun and Seosan stations, respectively. Further, the ITA exhibited superior performance over the MK and SR methods by indicating the presence of more significant trends in the climate indices at most stations. The distribution of the extreme precipitation indices for duration, frequency, and intensity indicate the pronounced risk of flood conditions around the north–central and some parts of southern regions, while the western region indicates a potential drought risk, which could greatly impact the water resources and consequently agricultural activities in the study area. The results of this study provide essential information for addressing the climate-related problems of water resource management and agriculture in the study area and other related climatic regions.

Bibliometric Analysis of Research Trends in Water Management Aimed at Increasing the Sustainability of the Socio-Economic Development of a Region

The growing negative anthropogenic impact on the environment causes scientific interest in the problems of water management. The increasing number of publications in this scientific field requires their intellectual systematization. The purpose of this study is to conduct a bibliometric review of scientific publications related to water management issues in the context of solving the problems of increasing the sustainability of the socio-economic development of a region for better understanding of current research trends. To achieve this goal, bibliometric analysis using the VOSviewer software product (Manual for VOSviewer version 1.6.17) was used. The international database Scopus was taken as the source of information. This study examined 10,208 articles on water management issues from 2012 to 2022. The basic criterion for including a publication in the selection was that the topic of the work belongs to the subject areas of economics, econometrics and finance and business, management and accounting. As a result of the analysis, it was determined that the problems of water resources management have not lost their popularity in the global research community and the research methodology is evolving towards the concept of “water–energy–food”. The centers of knowledge forming the vector of scientific research are the USA and the Netherlands; however, in recent years, the research of Chinese scientists has become increasingly important. It is concluded that the potential for the development of research in the field of water resources management in the context of solving the problems of the sustainable development of regions is associated with the search for opportunities for revealing the synergy of intersectoral interactions while taking into account their sectoral and regional specifics.

Systems engineering and water resources management: A closer relationship is needed

AbstractSystems engineering can be applied in a broad spectrum of sectors, but only its analysis tool has been applied in the field of water resources management. Because systems engineering has a separate community of practice from water resources, there is little crosstalk between the two fields. As a result, the systems engineering functions that support planning, design, production, procurement, and customer support are not being applied to water systems. Meanwhile, water systems exhibit complexities that have generated a separate field named Integrated Water Resources Management that continues to confuse its followers after several decades. Its methods are applied to a broad spectrum of water issues that affect multiple stakeholders with conflicting interests and involve distinct subsystems, such as water supply or hydropower, as well as combinations of them. Use of systems analysis for such water issues began six decades ago, but it is still a work in progress. Evolving methods of systems engineering offer new possibilities to address problems of water resources management, but they must extend beyond systems analysis, which belongs to multiple disciplines. Examples show possibilities to apply systems engineering methods when water issues exhibit attributes of engineered systems and do not involve social and environmental complexities that cannot be included in system boundaries. Collaboration among systems engineering and water resources management would offer a fertile test bed to advance both fields.

PRINCIPLES OF WATER INFRASTRUCTURE MANAGEMENT IN ENSURING SUSTAINABLE WATER USE IN UKRAINE

The military actions in Ukraine significantly aggravate the problems of sustainable water resources management. Even in the pre-war period, the main funds of the drinking water supply and sanitation systems were characterized by an unsatisfactory technical condition, an extremely high percentage of wear and tear and required large capital investments. During the wartime, the water management infrastructure of Ukraine became the object of massive attacks by the Russian Federation, which led to catastrophic consequences, such as the destruction of critical infrastructure facilities, lack of population access to drinking water supply, contamination of drinking water sources, complications of the sanitary and epidemiological situation, which poses a significant threat to the health of the nation.The purpose of the article is to determine the current state, trends in the restoration and development of the water management infrastructure in Ukraine and the formation of the basic principles of its management to ensure sustainable water use in Ukraine. The methodological tools of the study were such approaches and methods as a systematic approach, methods of system-structural analysis and synthesis, comparison and generalization, economic and statistical methods.

Quantitative analysis and management of sustainable development of ecological water resources and digital financial system based on an intelligent algorithm

Abstract In the modern day, water is a crucial resource for advancing society and preserving ecological balance. Growth, which lessens poverty and increases equality, is often seen as inextricably linked to the effective use of water resources. Traditional water system management aims to optimize surface water and subsurface aquifers to meet conflicting needs. As a result, the special difficulties in water resource management (WRM) would be exacerbated by the added uncertainty brought on by climatic change. Managing the world's water supplies sustainably is crucial to the planet's continued existence and prosperity. However, ecological planning for sustainable water development is difficult because of complex impacts, random processes, and hydrological restrictions. The study was inspired to address the issues head-on by creating a hybrid AI algorithm for ecological water resource sustainability and digital finance (HAI-EWRS-DF) system for solving complex, multi-scale problems in WRM. Control mechanisms, including social, financial, and sustainability on ground-level and surface-level water resource facilities, are recommended to enhance WRM to increase the applicable revenue, promote community well-being, and pave the way for greater economic development.

Ant-Inspired Metaheuristic Algorithms for Combinatorial Optimization Problems in Water Resources Management

Ant-inspired metaheuristic algorithms known as ant colony optimization (ACO) offer an approach that has the ability to solve complex problems in both discrete and continuous domains. ACOs have gained significant attention in the field of water resources management, since many problems in this domain are non-linear, complex, challenging and also demand reliable solutions. The aim of this study is to critically review the applications of ACO algorithms specifically in the field of hydrology and hydrogeology, which include areas such as reservoir operations, water distribution systems, coastal aquifer management, long-term groundwater monitoring, hydraulic parameter estimation, and urban drainage and storm network design. Research articles, peer-reviewed journal papers and conference papers on ACO were critically analyzed to identify the arguments and research findings to delineate the scope for future research and to identify the drawbacks of ACO. Implementation of ACO variants is also discussed, as hybrid and modified ACO techniques prove to be more efficient over traditional ACO algorithms. These algorithms facilitate formulation of near-optimal solutions, and they also help improve cost efficiency. Although many studies are attempting to overcome the difficulties faced in the application of ACO, some parts of the mathematical analysis remain unsolved. It is also observed that despite its popularity, studies have not been successful in incorporating the uncertainty in ACOs and the problems of dimensionality, convergence and stability are yet to be resolved. Nevertheless, ACO is a potential area for further research as the studies on the applications of these techniques are few.

Hydro-Economic Modeling of Water Resources Management Challenges: Current Applications and Future Directions

Hydro-economic modeling (HEM) addresses research and policy questions from socioeconomic and biophysical perspectives under a broad range of water-related topics. Applications of HEM include economic evaluations of existing and new water projects, alternative water management actions or policies, risk assessments from hydro-climatic uncertainty (e.g., climate change), and the costs and benefits of mitigation and/or adaptation to such events. This paper reviews applications of HEM in five different categories: (1) climate change impacts and adaptation, (2) water–food–energy–ecosystems nexus management, (3) capability to link to other models, (4) innovative water management options, and (5) the ability to address and integrate uncertainty. We find that (i) the increasing complexity and heterogeneity of water resource management problems due to the growing demand and competition for water across economic sectors, (ii) limited availability and high costs of developing additional supplies, and (iii) emerging recognition and consideration of environmental water demands and value, have inspired new integrated hydro-economic problems and models to address issues of water–food–energy nexus sustainability, resilience, reliability through water (re)allocation based on the relative “value” of water uses. In the past decade, the field of HEM has improved the integration of ecosystem needs, but their representation is still insufficient and mostly ineffective. HEM studies address how to sustainably manage water resources, including groundwater which has become an area of particular interest in climate change adaptation. The current most used spatial and temporal resolutions (basin-scale and yearly time-step) are appropriate for planning but not for operational decisions and could be underestimating impacts from extreme events (e.g., flood risk) captured only by sub-monthly time scales. In addition, HEM primarily focuses on biophysical and economic indicators but often overlooks preferences and perspectives of stakeholders. Lastly, HEM has been widely used to analyze transboundary cooperation, showing benefits for increasing water security and economic development, particularly as climate change develops. We conclude that the field of HEM would benefit from developing more operational models and enhancing the integration of commonly neglected variables, such as social equity components, ecosystem requirements, and water quality.

Collaborative Watershed Modeling as Stakeholder Engagement Tool for Science-Based Water Policy Assessment in São Paulo, Brazil

This study describes a collaborative modeling process deployed at the Cantareira Water Supply System (CWSS) in São Paulo City Metropolitan Area, Brazil. The CWSS faces challenges for meeting the increasing water demand, while land-use and climate change and their combined effect on its water cycle and balance have created a complex water resources management problem. Through a stakeholder engagement process—involving scientists and policymakers, the water utility company, and state administration—environmental simulation models were developed to elicit and represent multiple environmental, economic, and policy perspectives, developing a mutual language to communicate and establish common goals of water resources management. Study outputs include estimation of biophysical and economic benefits associated with prioritized native vegetation restoration activities in the source watersheds. These outputs are deployed in support of landscape planning and the decision process integrating multiple stakeholder perspectives in São Paulo state administration, the water utility company, and municipalities.

Possibilities of Using the Unitization Model in the Development of Transboundary Groundwater Deposits

Groundwater belongs to the category of strategic minerals, along with hydrocarbon resources, so the supply of drinking water will become one of the urgent problems of modern society. The management of groundwater resources and their protection is a very complicated task, especially in border areas where neighboring states jointly exploit aquifers. The problem of transboundary water resources management, in particular groundwater, has been considered at the international level for more than 30 years. However, despite the adoption of a number of conventions, agreements and programs, both at the global and in the format of interstate relations, an understanding for the approach of a universal solution to the transboundary water issue has not yet been formed. An attempt to study the possibilities of applying the principles of unitization on the example of transboundary oil and gas fields in comparison with groundwater cross-border deposits is made in the paper for the first time. As a successful example, the unitization agreement between Norway and the UK for the development of the Frigg field was chosen. It is established that unitization agreements concluded by states in the joint development of transboundary mineral deposits, actively used in regulating the activities of transboundary oil and gas fields, can be used as one of the possible models of international agreements on the extraction of groundwater in transboundary territories.

Understanding the Climate–Water–Energy–Food Nexus and the Transition Towards a Circular Economy: The Case of Morocco

The world is currently marked by increasing pressure on natural resources and a big demand for energy, water, and food. Energy, Water, and food are strongly interlinked, and the choices made in one area often have consequences on the others. These interconnections intensify and will be more complex as the demand for resources increases with climate change, population growth, changing consumption patterns, and a linear economy model of ‘take-make-dispose’. however, a circular economy (CE) ensures that economic growth must not necessarily lead to more resource consumption. This paper aims to discuss the circular economy transition with a focus on understanding the interdependencies and complexities of system Climate-Water, Energy, and food security in Morocco. This work first outlines the problem of water resources management in Morocco and determined the areas of intersection between the food-energy-water sectors. It also attempts to explain why water circularity is part of the key factors to accelerate the transition from a linear economy to a circular economy to meet the Sustainable Development Goals, and how circularity can be implemented in the water sector. Finally, it studies two circular alternative solutions (water-saving - drip irrigation, and renewable energy) that Morocco uses to face climate change-induced water scarcity.

ЕКОЛОГІЧНІ ТА СОЦІАЛЬНІ РИЗИКИ В МІЖНАРОДНИХ ТА ВІТЧИЗНЯНИХ СИСТЕМАХ ОЦІНКИ МІНЕРАЛЬНИХ РЕСУРСІВ

It was defined that the ecological and social risks became key in the implementation of mining projects from the stage of geological study through development till mining operation. The main components of these risks are fixed over the past years, which are related to the problems of water resources management, the processes of decarbonization of production, the reduction of the negative impact on climate change, the environmental friendliness of production and the emissions volumes that are directly or indirectly related to mining enterprises, etc. A comparison of domestic and international standards for the assessment of mineral reserves and resources was carried out according to the basic features of classification with the determination of social and environmental assessment factors. The features of the Classification of Mineral Reserves and Resources of the State Subsoil Fund, the UN Framework Classification, the PRMS Petroleum Resources Management System, the International Reporting Standards of the CRIRSCO Mineral Resources Committee are analyzed and compared in order to find features that allow determining the social and environmental risks of mining projects. The presence of these direct features in the classification systems indicates the orientation of the assessment standards to the comprehensive assessment of projects as such meeting the goals of sustainable development. The social and ecological viability of subsurface and natural resource projects is used as a direct feature only in the UN Framework Classification, while its inclusion took place in 2009 in the part of social factors, and in 2019 – in the part of environmental factors. This classification is considered as a tool for the effective management of national resources, necessary for the realization of the goals of sustainable development, which enables all stakeholders to find a common understanding of the development of resources and territories, to compare projects in different types of resources and subsoil use. In other international standards, as well as in the domestic classification of the State Fund of Subsoil, socio-ecological criteria are taken into account indirectly, which is one of the key areas of development of these mineral resource assessment systems. Such development can take place in two directions: the inclusion of social and ecological criteria directly as basic features, while this is possible both in the form of complex parameters and individual classes/subclasses; use and improvement of existing methods of resource and reserves valuation, taking into account the environmental and social risks of the implementation of subsoil use projects.

Evaluation and Optimization of Hydrological Connectivity Based on Graph Theory: A Case Study in Dongliao River Basin, China

Hydrological connectivity affects the material cycling and energy transfer of ecosystems and is an important indicator for assessing the function of aquatic ecosystems. Therefore, clarification of hydrologic connectivity and its optimization methods is essential for basin water resources management and other problems; however, most of the current research is focused on intermittently flooded areas, especially in terms of optimization, and on hydrological regulation within mature water structures, while research on hydrological connectivity in dry, low rainfall plain areas remains scarce. Based on the graph and binary water cycle theories, this study assessed and hierarchically optimized the structural hydrological connectivity of the Dongliao River Basin (DRB), integrating artificial and natural connectivity, and explored the hydrological connectivity optimization method in the arid plain region at the basin scale to increase connectivity pathways. The spatial analysis and evaluation of hydrological connectivity was also carried out based on the results of the hierarchical optimization, and provided three scenarios for the construction of hydrological connectivity projects in the basin. The hierarchical optimization yielded a total of 230 new water connectivity paths, and the overall hydrological connectivity increased from 5.07 to 7.64. Our results suggest a large spatial correlation in hydrological flow obstruction in the DRB. The center of gravity of circulation obstruction shifted to the south after optimization for different levels of connectivity. With the increase in the optimization level of hydrological connectivity, the national Moran index rose and then fell. The magnitude of the increase in hydrological connectivity effects varied at different optimization levels, and there were sudden points’ increase points. From an application point of view, Scenario 1 is necessary and the most cost effective is Scenario 2, which provides a scientific basis for guiding the construction of future ecological projects in the DRB.

Simulation of the Water Storage Capacity of Siling Co Lake on the Tibetan Plateau and Its Hydrological Response to Climate Change

Due to their special geographical locations and environments, plateau lakes play a key role in maintaining regional water balance, but lake water storage changes are upsetting this balance. Based on data from lakes on the Tibetan Plateau (TP), this study used the Spatial Processes in Hydrology (SPHY) model to simulate the runoff process in the Siling Co basin from 2000 to 2016 and estimated the changes in water storage of Siling Co and the contribution of each component of runoff into the lake. The results showed that the water storage capacity of Siling Co has increased by 1.2 billion m3/yr, and the lake area continues to expand; declines in precipitation have significantly reduced baseflow (BF), rainfall runoff (RR), and snow runoff (SR), while temperature increases have raised glacier runoff (GR). The simulated average runoff showed that BF, GF, RR, and SR contribute 24%, 22%, 16%, and 38%, respectively, of the flow into Siling Co. Based on hypothetical climate change scenarios and two Shared Socioeconomic Pathways (SSP1-2.6 and SSP3-7.0) from the MRI-ESM2-0 GCMs, this study estimated that a 10% increase in precipitation could lead to a 28% increase in total runoff, while a 1 °C increase in temperature could lead to a 10% decrease in runoff. The average runoff depth of the basin is expected to increase by 30–39 mm, since the temperature and precipitation may increase significantly from 2020 to 2050. The intensification of glacial melting caused by the increase in temperature continues, posing a greater challenge to many water resources management problems caused by the expansion of lakes.

Short-term rainfall forecasting using machine learning-based approaches of PSO-SVR, LSTM and CNN

Short-term rainfall forecasting plays an important role in hydrologic modeling and water resource management problems such as flood warning and real time control of urban drainage systems. This paper compares the performances of three machine and deep learning-based rainfall forecasting approaches including a hybrid optimized-by-PSO support vector regression (PSO-SVR), long-short term memory (LSTM), and convolutional neural network (CNN). The approaches are used to develop both 5-minute and 15–minute ahead forecast models of rainfall depth based on datasets of Niavaran station, Tehran, Iran. Results of applying the models to all data points indicated that PSO-SVR and LSTM approaches performed almost the same and better than CNN. Subsequently, rainfall events were divided into four classes depending on their severity and duration using K-nearest neighbor method, and a separate forecast model was built for each of the classes. Classification of the events improved the forecast models accuracy where PSO-SVR and LSTM were the best approaches for the 15-minute and 5-minute ahead rainfall forecast models, respectively. Investigating the impact of more predictors on the forecast quality, adding differences of rainfall depths to model predictors improved the accuracy of PSO-SVR approach for the 5-minute ahead forecast model up to 13%. Furthermore, depending on the rainfall event, additional input variables considering rainfall depth fluctuations over shorter time periods than the forecast lead time increased the performances of the PSO-SVR and LSTM approaches between 3–15% and 2–10%, respectively.

Stackelberg equilibrium water allocation patterns in shallow groundwater area under uncertainties

• Establishing a multi-level water resource management model applicable in shallow groundwater area. • Considering process-based crops growth model (detailed water and salt movement). • Introducing uncertainties into multi-level programming model. The hierarchical agricultural water resource management problem in shallow groundwater area is expected to be solved through establishing a practical and feasible mathematical model. This study proposes a multi-level programming model with considerations of process-based crops growth model and uncertainties. The model is solved by a fuzzy approach that ensures the decision-making proceeds from top to bottom sequentially and the leader supervises the solution search direction. The leeway given by each level decision maker expands the decision-making space and lets Stackelberg equilibrium solution more satisfactory. The model is applied in Hetao Irrigation District in China. After optimization, the Stackelberg equilibrium water allocation pattern and satisfaction degrees of each level decision makers can be identified. Summarized conclusions are as follows: (1) under uncertainties of available water, the water diversion is allocated in a similar pattern, while the groundwater allocation has larger variabilities; (2) when available water decreases, local farmers can improve crop production through modifying or optimizing irrigation water amount in each growth period; (3) the combined use of water diversion and groundwater is expected to become an effective approach for achieving a win–win situation between government managers and local farmers. The proposed model performs well in generating Stackelberg equilibrium solutions satisfied by multi-level decision makers. It can be extended to provide decision makers a more complete decision support system and also has potential to be applied in other similar areas.