IntroductionIntegrated water resources management (IWRM), as defined by the Global Water Partnership (GWP 2004), recognizes the interconnection between people, ecosystems, and hydrology, and seeks to promote a coordinated management of natural resources (water, land, and others) that maximizes economic and social welfare in an equitable manner without compromising the sustainability of ecosystems. Adopted as a guideline by most governments in developed countries, IWRM policies have been reported to be difficult to implement. This is true particularly in countries under development (Merrey 2008).In these countries, there is an increasing pressure on often scarce water supplies, exacerbated by the combined effects of climate change, population growth, and increasing urbanization. Cities in developing countries must meet the food, energy, and water demands of 70 million more people each year for the next 20 years (UNDESA, UNCTAD, and UNEP 2011). Increasing global demand for agricultural products, driven by a growing population in addition to the need for renewable sources of energy, will require global agriculture land expansion, particularly in Sub-Saharan Africa and Latin America and the Caribbean (LAC) (Wild et al. 2021). There is already evidence of the effects of climate change on the availability and demand for food, energy, and water, especially in fast-growing countries (Perrone and Hornberger 2014; Schornagel et al. 2012; Shah et al. 2009; Voinov and Cardwell 2009; WWAP 2012).The objectives of food-energy-water (FEW) nexus studies mirror the aims of IWRM. Many of these aims, such as efficient resource management, synergistic thinking, and equitable efforts, within the scope of FEW, are expected to be more tenable to a wider set of stakeholders, particularly those whose primary interests lie in the agriculture and energy sectors. This nexus adds new dimensions to classic hydrologic challenges, causing some additional problems for water scientists, problems that will become even more complex in the context of FEW. In particular, quantification and management of hydroclimatic uncertainty, especially related to extreme events, must be taken seriously and implemented through all sectors relying on water as a resource (Cai et al. 2018).The water allocation challenge among uses, especially in a context of uncertainty and water scarcity, is so important that some authors have suggested that the acronym of IWRM should be changed to IWRAM, which means Integrated Water Resources Allocation and Management (Allan 2003), to highlight the need for allocation studies.As allocation studies are conducted at the level of river basins and subbasins, where the users and sectors compete for limited water resources, the acronym is sometimes defined as integrated river basin management (IRBM). The practical results of IRBM have been described as disappointing due implementation problems. A framework which includes a scientific, integrated, sustainable development assessment and decision-making models is suggested by Ge et al. (2018) as a platform able to help decision makers in their management decisions.The viability of economic growth as well as desirable future environmental conditions depend both on an adequate allocation of water among economic sectors and on the preservation of water quality at the level of river basins (subnationally), which collectively determine national results. In particular, when the economy, the competition for water, and the value of water are all growing at the same time, the benefits of public policies and water allocation decisions to accompany these growths are significant (Rosegrant and Binswanger 1994).Demand management is one of the basic principles of IWRM. As a complementary approach to infrastructure investments (supply management), it focuses on solutions that promote flexibility and adaptability of public policies in the light of increasing water stress, uncertainty about water availability, and the need for increasing water transfers between basins.The demand management main instruments are regulatory and economic mechanisms that implement a rational, economically efficient, and environmentally sustainable use of water resources. Currently, command-and-control regulatory mechanisms are those most commonly used in environmental policies worldwide (Callan and Thomas 2013). This is also true of water resources policies, where regulations regarding water rights and emission standards are the most frequent mechanisms. Despite the increasing number of countries that apply economic instruments, such as charging, these instruments are used inappropriately since the prices charged do not encourage efficient use (Griffin 2016).From an economic perspective, for instance, there are trade-offs in the efficient use of water resources and its quality. The command-control approach regulates polluters by directly applying norms or standards. This is the most conventional and dominant approach to environmental policy in most countries. The market approach uses the polluter pays principle, seeking to internalize the cost of environmental damage within the market for goods whose production results in pollution (Alcoforado de Moraes and Souza da Silva 2019). Conventional solutions are not proving effective, probably because they are based on inefficient environmental objectives and standards. More recently, economic solutions have begun to be used, notably with the application of fines for pollution (Callan and Thomas 2013).Economic solutions have advantages over conventional ones because they use price or other economic variables to encourage the correction of a market failure (inefficient allocation or pollution). However, due to the complexity and dynamism of environmental challenges and markets, those solutions require more complex studies and models.Decision makers often remain ill-informed about water allocation trade-offs and are ill-equipped to deal with a range of plausible outcomes. Public policies and instruments to implement IWRAM need to take into account the FEW nexus, which considers the existing (evident and quantifiable) interactions and dependencies between sectors. Tools and integrative skills extending from basin to regional and national levels across multiple disciplines are needed to address these FEW nexus challenges, adapting as these challenges evolve.These tools must be able to deal with all this complexity and able to determine the effectiveness of alternative allocation mechanisms related to the different aspects considered in the GWP’s definition, namely: economic efficiency, social equality, ecological sustainability, social welfare, and quantity and quality management.By supporting the definition and evaluation of allocation mechanisms considering all these aspects, these tools need to simplify certain complexities of the operating rules of real systems. For example, water quality issues, when considered within these integrated models, are not represented with the same level of detail as in traditional water quality simulation models; that is, they do not include all the processes and constituents. This is because water allocation management support models need to be as prescriptive as possible, requiring abstraction from various specific technical and operational issues. Furthermore, when integrating all IWRM aspects, the areas where they are related is what is truly important for water policy decisions.This article reviews existing basin-level models and decision support systems (DSSs) for water allocation and their main characteristics related to IWRM. The initial search for publications was carried out on the Web of Science database of scientific journals, with works published between 2000 and 2021 and using specific keywords. This extensive literature review organizes the concepts and tools covered in each selected publication, aiming to identify gaps and strong and/or weak links among the concepts to guide future research. Special attention is given to studies that have incorporated water quantity-quality integrated modeling together with socioeconomic aspects in decisions about allocations, a particularly important aim of IWRM that mirrors FEW nexus objectives, given that water use in all the economic sectors affects both water quantity and quality.Allocation Models and Decision Support Systems for IWRMConcepts of IWRMIntegrated Water Resource Management, as defined by the GWP, introduces concepts that need to be considered together with analytical tools (allocation models and DSSs) that can effectively support the design and evaluation of demand management instruments. In this section, these concepts are described in the context of IWRM and then the theoretical foundation of the allocation models and systems is presented.Economic optimization (EC) is the allocation of water resources among all uses/users, maximizing the net benefits (or minimizing scarcity costs) obtained from these uses. An optimal economic allocation effects the transfer of water until the net marginal benefits are equal across all uses (principle of microeconomic equimarginality). Uses with benefits that are difficult to measure, such as for recreational or leisure purposes, can also be considered, as there are methodologies for associating their economic benefits (Bekchanov et al. 2015; IWA 2019; Wang et al. 2019; Ward and Pulido-Velázquez 2008). Besides the economic issues, there are institutional restrictions that guarantee, for example, compliance with certain priorities or minimum values such as ecological flows, issues of equality, and sustainability.When considering the economic objective as the criterion to be maximized, an economically efficient allocation is identified, which contributes to maximum benefit or well-being of all users of the available water resources. This allocation is considered optimal from an economic point of view, since aggregate gains offset losses, which means that the distributive aspects are not considered, that is, the issue of equality is not incorporated. Thus, a fair economic optimum implies the need for compensation from those who win to those who lose. Both equality (EQ) and sustainability (SU) can be incorporated into the optimization model through restrictions, which results in the so-called second-best economic optimum.Equality concerns social justice or ensuring access for all users (mainly marginalized and poorer groups) to the quantity and quality of water needed to ensure dignity, human rights, and quality of life. We use the definition of equality of Peña (2011) as that policy environment which provides citizens with a sufficiently equal start in terms of goods, services, and conditions of life, and subsequently fair access to relevant resources that allow them to make use of their individual capacities. Equality can be measured through the Gini coefficient, for example (Hu et al. 2016). Sustainability requires that aquatic ecosystems be also recognized as users and that an appropriate allocation be made to sustain their natural functioning. Meeting this restriction also requires limitation or avoidance of land uses that can negatively impact these ecosystems (IWA 2019). Understanding the interactions between these factors is essential, especially regarding the negative impacts of human activities on the ecosystem. Thus, we consider the integration of quantity and environmental quality separately, with sustainability in this study associated with limits and allocations of the amount of water needed to maintain the natural functions of ecosystems rather than to water quantity-quality issues.Another important socioeconomic aspect included in the concept of IWRM, in addition to economic optimization, is the maximization of social welfare (SOC). The social issue considered in the concept of equality, in general, is incorporated through restrictions on economic optimization. In practice, basic social needs in many countries are often met through institutional protection, which can also be modeled through constraints on optimization problems. The issue of maximizing social welfare involves elements that can be measured through impacts on the main social indicators, such as the number of jobs, income generation in different social strata, and by life expectancy, while equality is related to the distribution of resources that ensures that everyone’s basic needs are met (Peña 2011).This assessment requires integration of network-based models with economy-wide models such as computable general equilibrium (CGE) models and input-output models (IOM). The integration of these two types of models expands the capacity for measuring the effects of different allocation policies, supporting their design and evaluation by considering important social welfare indicators.Throughout the development of this review, it was found that some of the studies reviewed, although they did not consider economic optimization as such, presented measures of economic evaluation, including calculations of benefits and costs. Given the cohesion between economic and social well-being, we included works that presented economic measures but did not consider optimization. Any market context that does not include the criterion of allocative efficiency has a negative effect on the well-being of society (Callan and Thomas 2013).Many authors have sought to insert environmental aspects in their water management models, whether by applying restrictions on maintaining the ecological flow (Chakroun et al. 2015); by exploitation sustainability constraints (Martinsen et al. 2019a); by simulating negative externalities due to water quality (Abbaspour et al. 2015); by assessing the costs of capturing, transporting, and treating water from available sources (Kahil et al. 2018); and by comparing scenarios of water scarcity and abundance, whether or not caused by climate change (Kahil et al. 2015, 2016a). These concepts are more related to sustainability and do not properly model quality aspects.Inserted in the challenges of constructing an IWRM that implements sustainable economic development that ensures natural resources for future generations, water quality management integrated with quantity, or water quantity-quality (QQ), represents an important issue, given its complexity.Network-based economic models, for example, hydro-economic models, use spatial representation to simulate demands from the various economic sectors and to represent offers in a hydrographic basin. This spatial representation of nodes is optimal for representing water quantity aspects; in general, however, these models consider only the quantitative balance (Souza da Silva and Alcoforado de Moraes 2021).The incorporation of quality is required, however, because it affects water availability and can modify the optimal economic allocation.The integration of quality into allocation models increases the number of equations and parameters that require calibration, demands sophisticated computational capacity, generally involves high degrees of nonlinearity, and consequently makes it difficult to present a solution. Nonetheless, this is not the most important issue, as mentioned in the Introduction section, because water quality equations incorporated into integrated models are not represented with the same level of detail that is common in traditional water quality simulation models. Distributed sewage return flow, for example, is usually spatially placed in the node closest to the user, which is not optimal for water quality modeling (Alcoforado de Moraes et al. 2010).Theoretical Foundation of Water Allocation ModelsThere are two main approaches used in modeling to support decision making in the allocation of water resources: (1) descriptive models, which show what will happen if a given strategy is adopted, and (2) prescriptive models, which determine the strategy that must be adopted to satisfy a given objective or decision criteria. It is desirable for water allocation support models to be as prescriptive as possible, but the complexities of operating rules for real systems often direct them toward a more descriptive direction.Optimization models are inherently prescriptive because they determine values of decision variables that optimize an objective function. In fact, mathematical programming (optimization) techniques inevitably engender the development of more prescriptive models. Despite this, simulation and optimization models need not be rigidly categorized as either descriptive or prescriptive (Wurbs 2005).Economic optimization modeling makes it possible to identify not only the economically optimum water allocations but also theassociated marginal values such as shadow prices and opportunity costs.Optimization models also enable delimitation of a Pareto front through different objective functions. For example, in the case of two objective functions (OF1 and OF2), each of the points on the Pareto front represents the maximum OF1, given a certain level of OF2 and vice versa, which means that solutions on the curve form a set of nondominated solutions. Points under the curve, on the other hand, can improve both objectives. Even though these solutions on the Pareto front are nondominated, there are trade-offs among them (Alcoforado de Moraes et al. 2021). This gives policy makers the opportunity to select optimal solutions according to policy priorities.Ideally, water allocation policy decisions should be based on results from both descriptive and prescriptive models. Table 1 summarizes the main characteristics of decision support models, categorized according to the proposed classification together with examples of applications found in the literature. The initials adopted in the column “types” will be the same as that adopted for the analysis that follows in this paper.Table 1. Models for water resources management: approaches and main characteristicsTable 1. Models for water resources management: approaches and main characteristicsMain characteristicsTypesAdvantagesDisadvantagesExamples/references1.Sequentially simulate flows, allocations and volumes at the different network nodes and links for each period.a2.Evaluate performance of the water system over a long period of time.3.Provide realism and flexibility in representing reservoirs’ operational rules as well as water demands and priorities of use.DBRS (descriptive based on rules simulation): Without optimization algorithms (simulation based on Rules of Ad Hoc Models).1.Use of structured programming language to develop interactive procedures that represent all the connections between water requirements and management rules for different network stretches, typically from upstream to downstream, identifying water flows and volumes throughout the network.2.Potential to reproduce water management systems and mechanisms with high precision.Ad Hoc algorithms (specifically developed to simulate real system conditions) are not easily built, since they realistically represent all the system’s operational rules.IRAS (Loucks et al. 1995)DODS: With optimization algorithms.1.Solve distinct optimization problems for each time period to direct water flow, control reservoir volume and allocate water through the network of nodes and links.2.Relatively user friendly and flexible.1.Often requires simplification of math formulation which limits the representation of complex rules of reservoir operation and the entire system, institutional limits, and existing infrastructure.2.Complex operational rules may be difficult to represent, thus hindering replication results.OASIS (Randall et al. 1997)1.Maximize or minimize a specific function-goal to supply values for decision variables simultaneously throughout all time periods, considering all inflows relative to full time horizon under analysis.2.Usually deal with limited time analysis.3.Include simulation components, even if rudimentary, to calculate hydrological flows and levels of quality constituents.PHDC (prescriptive hydrological decision criteria): Decision criterion for hydrological optimization.Identify levels of releases and optimum allocations among the uses that maximize or minimize hydrological indicators, thus reflecting a specific management goal.Fewer details concerning hydrological interactions among the main sources of water and their uses are described, given data complexity and volume as well as specificity of the required analysis to support water policy decisions.HEC-PRM (Ferreira and Lund 1994)PEDC (prescriptive economic decision criteria): Decision criteria for economic optimization.1.Can incorporate social and economic values in water resources allocation.2.Can identify economically optimum water allocations as well as associated marginal values such as: shade-prices and opportunity costs.3.Can incorporate other criteria such as equality into the optimization models through restrictions.Hydrological interactions are described with fewer details given data complexity and volume. Economic analysis is less specific.MITSIM (Strzepek 1981)AQUARIUS (Diaz and Brown 1997)Regarding the model structure, prescriptive or descriptive models that use optimization algorithms can use linear programming where all the mathematical equations are either linear, nonlinear, or able to cope with some nonlinearities. Gradient-based nonlinear programming (NLP) algorithms are widely available and implementations such as CONOPT2 and MINOS have been used to solve complex problems. These are available in the general algebraic modeling system (GAMS), a modeling platform for programming mathematical problems which is especially useful for solving large, complex problems such as those involving a large number of variables and constraints or a high degree of nonlinearity. However, both speed and reliability of these problem-solvers decrease as problem size and complexity increase. Due to this limitation, other methods, such as evolutionary algorithms, have been applied to solve large nonlinear reservoir management models (Cai et al. 2001).Even descriptive models that do not use any optimization algorithm are able to simulate relations among variables and parameters using linear or nonlinear functions. This is the meaning of linearity used in this review to classify the models in Table 3 (column 6). A model can also have deterministic or stochastic characteristics. In deterministic models, the output of the model is fully determined by the parameter values and the initial conditions with “perfect foresight.” Since water management evolves uncertainties, however, the consideration of stochastic models is important. These models possess some inherent randomness; thus, the same set of parameter values and initial conditions may lead to different outputs.Theoretical Foundation of DSS Used for IWRMTraditional DSSs aim to provide partial or complete support to unstructured decision-making activities using analytical models and techniques combined with traditional data access and recovery functions, all through a friendly interface (Paredes-Arquiola et al. 2010; Rousseau et al. 2000). While structured decisions are logical with well-defined factors and results, which are, therefore, programmable, unstructured ones involve a trial-and-error approach, heuristics, intuition, and common sense.A DSS needs to have three sets of technical capabilities: a database management system (DBMS), a model base management system (MBMS), and a system that manages the interface between the user and the system, which has been named the Dialogue Management and Generation System (DGMS) [Sprague (1980) in Alcoforado de Moraes (1997)]. In the context of water resource management and planning, these systems have been used extensively in conjunction with a geographic information system (GIS) and given the name spatial decision support systems (SDSSs). Integration of a GIS with a DSS provides unique advantages for water management: representation of real world spatial relationships in a visual and analytical form; integration of socioeconomic, environmental, and physical components within a broad database; and the potential for modeling simulation and optimization techniques to support problem solving (McKinney et al. 1999). The possibility of connecting these models with geographic databases managed through a GIS is the main advantage of SDSSs in supporting the management of water resources in cases where both the spatial representation of the managing unit, or part of it, and the application of models for problem solving are required.There are a number of strategies for coupling models with GIS (Watkins and McKinney 1997), ranging from loose coupling to tight coupling. A coupling is considered loose when the data are merely transferred between the models and the GIS based on separate systems and, generally, with individual data management. A tight coupling is characterized by integrated data management, where GIS and models share the same database. The strength of the coupling lies in the fact that the data and modeling share the same platform (McKinney et al. 1993; Watkins and McKinney 1997).Making allocation models available and understandable to decision makers involves manipulating data entry and output as well as some graphical interfaces, thus making the input and output interface, or DGMS, in a DSS so important.The ease and flexibility of defining, modifying, and visualizing any basin or section of it in a GIS interface also influences the modeling and analysis of results. Thus, it is possible to create a platform where specific applications (for example, optimization models with different criteria and restrictions) can be developed and modified to the direct specifications of the decision maker with little time and effort. At the same time, responses to changes (generating results from different models) required by the user are made available through the platform and can be easily analyzed and compared.In addition to these technical characteristics, the interface of an SDSS must be able to include the participation of all the stakeholders involved. This interface promotes negotiation and cooperation through the provision of a common framework for modelers and decision makers, making economic decision tools and results available through, for example, participatory modeling. Participatory modeling can encompass the development and use of various computer-based models and analytical tools, communication and visualization tools, in addition to mental and cultural models (Mayer et al. 2017).Another important aspect in the analysis of the results for decision making, in addition to the results of the modeling itself, are the exogenous variables or parameters and the functional forms adopted in the models.As mathematical modeling makes an abstraction of the real world, it requires some exogenous variables (or parameters) to reduce its complexity. Equations can represent, through certain functional forms, the relationships between variables that constitute functions to be met or optimized, whether as restrictions or objective functions. When these parameters and equations are changed, the results will change, making it possible to analyze the robustness of a model based on the intensity of these changes. Sensitivity analysis refers to variations in model results due to changes in the parameters. On the other hand, the analysis of scenarios allows comparison of model results when changing equations and restrictions. DSSs are able to analyze scenarios and/or sensitivity to changes that represent specific conditions such as climate change, variation in demands, and different environmental and land use policies.Review of Models and Decision Support Systems for IWRMMethodologyArticles and papers published between 2000 and 2021 were searched. We sought to review models and systems that could support water allocation policies applied to river basin levels using at least one of the concepts discussed in section “Allocation Models and Decision Support Systems for IWRM” (economic optimization; equality; sustainability; social welfare and economic assessment; and quality and quantity integration).The search procedure, resulting in a selection of 68 publications, is described below:Step 1. Search for publications related to models and DSSs to support IWRM at the basin level using the Web of Science database of scientific journals for articles that contained the following keywords with the conditional operator AND. •Water allocation model•Decision support system•Integrated water resources managementThe result of the initial research came up with an almost equal distribution between topics related to Engineering (2,764) and to Economics (2,585), resulting in a total of 4,929 publications. Some of these articles were classified by the system under both topics.Step 2. Filter the selection of articles based on the application of the terms ‘river basin’ AND ‘integrated modeling’ AND ‘planning water resources system’ throughout the text, which reduced the result to 820 publications.Step 3. Analyze the titles and abstracts of the articles found in Step 2, removing those that did not consider any of the IWRM concepts described above, thus establishing the final sample at 68 publications, which we considered adequate for the purposes of the review proposed in this study.Step 4. Analyze articles by reading all those selected in Step 3, tabulating their characteristics based on the IWRM concepts, the theoretical foundations of the models, and the DSSs as described in the section “Allocation Models and Decision Support Systems for IWRM”.Step 5. Elaborate on and analyze the results.Studies TabulationInitially, in Step 4, an article’s main water management issue was identified based on the classification of tools to support the management of water resources presented by Harou et al. (2009), adapted as shown in Table 2.Table 2. Description of major challenges to classify water resources management toolsTable 2. Description of major challenges to classify water resources management toolsMajor challengeDescriptionIn-stream and off-stream intersectoral allocation and useApplications for in-stream uses include hydropower, navigation, and recreation. Off-stream uses are usually related to consumption, e.g., irrigated agriculture or urban supply. To allocate water efficiently, in-stream flow values must be incorporated into the allocation process.Conjunctive use of groundwater and surface waterSupport for integrated groundwater management with surface water.Institutions, water markets, and pricingThese support the design and evaluation of economic instruments, such as water and collection markets, and thus also support the establishment of regulatory frameworks, as well as institutions using economic theory. Regulatory instruments can also be designed and evaluated based on their modeling.Conflict resolution, transboundary management, and sustainabilityThese identify efficient allocations, account for “virtual water” values and interregional exchanges between economic sectors. From these values, conditions can arise for collaboration and adaptability that can help to resolve local, regional, and cross-border conflicts.Managing for climate change and droughtThese consider extreme events such as droughts and floods, as well as climate change. In general, these situations are included as scenarios.Land use management: floods and water qualityThese consider land use management and its impact on water quantity and quality.Many of the studies reviewed here address more than one category of challenges. However, in the present work, only one category was assigned to each article cited.Then, the models presented in the articles were evaluated in relation to their use of IWRM concepts, as discussed in the section “Allocation Models and Decision Support Systems for IWRM”: economic optimization, equality, sustainability, social welfare/economic assessment, and integration between water quality and quantity. The models were also classified according to their structure, as “linear” or “nonlinear” and “deterministic” or “stochastic” (Section “Theoretical Foundation of Water Allocation Models”), and based on their orientation, as being “descriptive” or “prescriptive” (see section “Theoretical Foundation of Water Allocation Models”).The DSSs were classified according to specific aspects related to automated systems such as: coupling intensity (loose or tight), existence of a model or criteria base (availability of more than one model or criterion), analysis of scenarios or sensitivity (functionality present in the DSS), and existence of an interface developed for the user/stakeholder, following the concepts presented in section “Allocation Models and Decision Support Systems for IWRM”.The analysis of the 68 selected articles was tabulated using these aspects, obtaining first a characterization of each allocation model and DSS described in the paper, related to the consideration (presence or not) of each of the IWRM concepts, its orientation, and structure as detailed in Tables 3 and S1. On the Table 3 it is indicated if the allocation models are available in a DSS, whose specific characteristics are presented in Table 4. A description of the main characteristics of the descriptive optimization-driven simulation (DODS) models is given a specific column (DODS APPROACHES MAIN OBJECTIVE in Table 3) since they do not fit into any other evaluation of the IWRM concepts.Table 3. Allocation models and decision support systems, classified according to the major challenge/IWRM conceptsTable 3. Allocation models and decision support systems, classified according to the major challenge/IWRM conceptsQuality modelDSS nameLocationReferenceECEQSUSOCQQORIENT/STRUCDODS approaches main objectiveXXX—XPEDC/L+D—No specific name—Syr Darya River Basin, Central AsiaCai et al. (2002)XX——PEDC/N+D———Dong Nai River Basin, VietnamRingler et al. (2006)————XDODS/N+DSee Table S1 – Supplemental MaterialsQUAL2KMOSDEWGermany, West Africa, and Central Asia basinsGaiser et al. (2008)X———XPEDC/N+D—Streeter–Phelps—Pirapama River Basin, BrazilAlcoforado de Moraes et al. (2010)————XDODS/N+SSee Table S1 – Supplemental MaterialsGESCAL moduleAQUATOOLAraguari River Basin, BrazilSalla et al. (2014)—XXX—DBRS/N+D——SDSSIchkeul Basin, TunisiaChakroun et al. (2015)XX———PEDC/N+S———Santa Cruz River Basin, USA/MexicoGhosh et al. (2017)——X——DBRS/N+S———Neshanic River WatershedGiri et al. (2018)X———XPEDC/N+D—Mike ECO Lab—Kelani River, Sri LankaGunawardena et al. (2018)X—X——PEDC/N+D———Mekong River BasinRingler et al. (2004)XXX——PEDC/L+D———Sefidrud River Basin, IranRoozbahani et al. (2020)——XX—PHDC/N+D———Wei River Basin and Han River Basin, ChinaMa et al. (2021)———X—PHDC/N+D——HEALFour interlinked river basins in Northeast of BrazilAlcoforado de Moraes et al. (2021)————XDODS/N+DSee Table S1 – Supplemental MaterialsQUAL2E—Arkansas River Basin, EUADai and Labadie (2001)——X——DBRS/L+D——Web-based DSS prototypeGanges River, India and BangladeshSalewicz and Nakayama (2004)——X——DODS/L+DSee Table S1 – Supplemental Materials—REALMThe Goulburn and the Melbourne Water Supply System, AustraliaPerera et al. (2005)X——X—PEDC/N+D———São Francisco River Basin, BrazilManeta et al. (2009)X————PEDC/N+D———Semiarid region with a Mediterranean climateZhu et al. (2015)XXX——PEDC/N+S———Jucar Basin, SpainKahil et al. (2016b)——XXXPHDC/N+D—No specific name—Theoretical regionAbdulbaki et al. (2017)—XXX—PHDC/L+D———South FloridaMirchi et al. (2018)——X——DODS/L+DSee Table S1 – Supplemental Materials—WEAP21Urmia Lake basinSprague (1980)——XXXPHDC/L+D—No specific name—Haihe River Basin, ChinaMartinsen et al. (2019a)——X——PHDC/L+D———Zayandehrud River Basin, IranChakraei et al. (2021)X————PEDC/N+D———The Brantas River Basin, IndonesiaRodgers et al. (2003)——X—XDODS/L+DSee Table S1 – Supplemental MaterialsQuality Module WEAP21WEAP21Sacramento RiverYates et al. (2005)——XX—DODS/L+DSee Table S1 – Supplemental Materials——California’s Friant-KernMarques et al. (2006)—XXX—DBRS/L+D———South Africavan Heerden et al. (2008)XXX——PEDC/N+D———Rio GrandeWard and Pulido-Velázquez (2008)——X——DODS/N+DSee Table S1 – Supplemental Materials——Rio GrandeSandoval-Solis and McKinney (2014)——XX—DODS/L+DSee Table S1 – Supplemental Materials——Middle Guadiana Basin, SpainBlanco-Gutiérrez et al. (2013)———X—DBRS/L+D———Haihe River Basin, ChinaWhite et al. (2015)X—X——PEDC/N+S———Nar River Basin, EnglandGarbe and Beevers (2017)XXX——PEDC/N+S———Malian River Basin, ChinaGao et al. (2019)XX——PEDC/L+D———California’s major water supply systemDraper et al. (2003)X————PEDC/L+D———Euphrates river basin in Turkey and SyriaTilmant et al. (2008)——X——DODS/N+DSee Table S1 – Supplemental Materials—NILE DSSAtankwidi catchment, West AfricaGeorgakakos (2007)——XX—DODS/L+DSee Table S1 – Supplemental Materials——Musi River, IndiaGeorge et al. (2011)——X——DBRS/N+D——IRAS-2010Thames basin, EnglandMatrosov et al. (2011)X———XPEDC/L+D—Streeter–Phelps—Ziya River, ChinaDavidsen et al. (2015)—XX——DODS/L+DSee Table S1 – Supplemental Materials——Zayandehrud River Basin, IranSafavi et al. (2015)X—X——PEDC/N+D———Aral Sea Basin, Central AsiaBekchanov et al. (2015)X———XPEDC/L+D—No specific name—Kaidu-Kongque River Basin, ChinaZeng et al. (2016)—X—X—PHDC/N+S———Qujiang River Basin, ChinaHu et al. (2016)———X—PHDC/N+D———Iran’s central desertHabibi Davijani et al. (2016)X—X——PEDC/L+D——SEWEMAral Sea Basin, Central AsiaBekchanov and Lamers (2016)——XX—PHDC/L+D———GenericZhang and Vesselinov (2017)XXX——PEDC/N+D——See note 2São Francisco River Basin, BrazilSouza da Silva and Alcoforado de Moraes (2018)—XXX—DBRS/L+D——BRIMBow River Basin, CanadaWang et al. (2019)——X——PHDC/L+D———Fuhe River basin, ChinaYan et al. (2020)X————PEDC/N+S———São Marcos River Basin, BrazilBof et al. (2021)—XX—XDBRS/N+D—Modified QUAL2E-UNCASModified MODSIM and QUAL2E-UNCASPiracicaba River Basin, Brazilde Azevedo et al. (2000)————XDBRS/L+D—QUAL2EGIBSIChaudière River basin, CanadaRousseau et al. (2000)——XXXDBRS/N+D—MULINO Quality ModuleMULINO DSS – mDSSDyle, Belgium; Caia, Portugal; Vahlui, Romania; Bure and Yare, England; Vela and Cavallino Catchments, ItalyMysiak et al. (2005)——X—XDBRS/N+D—No specific name—Jiaojiang River Basin, ChinaZhang et al. (2010)————XPHDC/N+S—SWAT quality modules (CREAMS, QUAL2E, WASP)—Wenyu River Catchment, ChinaZhang et al. (2011)——X—XDODS/N+DSee Table S1 – Supplemental MaterialsGESCAL moduleAQUATOOLJucar Basin, SpainParedes-Arquiola et al. (2010)X———XPEDC/N+D—0—Maipo River BasinRosegrant et al. (2000)————XDODS/N+DSee Table S1 – Supplemental MaterialsSWAT—EuropeAbbaspour et al. (2015)————XPHDC/N+S—HEQM Module (WQM)—Huai River Basin, ChinaZhang et al. (2016)XX——XPEDC/N+S—No specific name—Sinos River Basin, BrazilDalcin and Fernandes Marques (2020)——X—XDBRS/N+D—DSM2-SJR/QUAL/ APSIDEModular Modeling System/Object User InterfaceSan Joaquin River BasinQuinn et al. (2004)———XXDODS/L+DSee Table S1 – Supplemental MaterialsNo specific name—Galego River Basin, SpainGraveline and de Recherches (2014)XXX—XPEDC/N+S—No specific name—Dongjiang River Basin, ChinaZhou et al. (2015)—XXX—PHDC/N+D———Orb River Basin, FranceGirard et al. (2015)X————PEDC/N+S———Heihe River Basin, ChinaLi et al. (2016)X—X——PEDC/N+S———Karkheh River Basin, IranFereidoon and Koch (2018)—XXX—DBRS/N+D———Zayandehrud River Basin, IranSafaei et al. (2013)Table 4. Decision support systems, classified according to the major challengeTable 4. Decision support systems, classified according to the major challengeDSS nameDatabase loose/tight couplingScenarios/sensitivity analysisUser interface developedConcepts considered (see note 1)ReferenceY/NApplied modelsMOSDEW**LooseYes(1) Downscaling model of climate scenarios output from GCM, (2) agroeconomy: ACRE, (3) discharge groundwater: MODFLOW, LARSIM (HBV), (4) water quality: QUAL 2K, MONERIS, (5) cultivation methods, income, diffuse pollution: EPIC, SLISYS, (6) water supply: WEAP, and (7) fresh water ecology: CASIMIRTwo different official development scenariosYesQQGaiser et al. (2008)AQUATOOLTightNo1.Water balance: SIMGES2.Quality model: GESCAL3.Discharge groundwater: HBV (for rural subbasins). Parameters of HBV calibrated using evolutionary algorithmsAnalysis of the sensitivity of the variables of state to changes in the values of the coefficients of re-aeration, decomposition of carbonaceous organic matter and of organic nitrogen among othersNoQQSalla et al. (2014)SDSSTightYes1.Scenarios generation: MODICHKEUL2.Other models were not namedFour scenarios: current conditions with the water demand projected to 2015, additional 90 million m3 transferred from a dam, construction of one additional dam, construction of two additional damsNoEQ+SU+SOCChakroun et al. (2015)HEALStrongYesCriteria based on water allocation strategiesScenarios regarding water allocation for users and water storageYesSOCAlcoforado de Moraes et al. (2021) (See note 2)Web-based DSS prototypeTightNoThe names of the models are not available in the paperThree scenarios: average, better than average and worse than average monsoon conditionsYesSUSalewicz and Nakayama (2004)REALMLooseYesREALM modelsHydrological scenarios with capacities and penalty functionsYesSUPerera et al. (2005)WEAP21TightYes(1) Surface-hydrologic, groundwater, water temperature, and allocation models developed in WEAP21, and (2) climate change: HadCM3 and LARS-WG to downscale the dataThree future emission scenarios based on the IPCC and five water management scenarios: current situation, crop pattern change, improving the conveyance and distribution efficiency, among othersYesSUSprague (1980)WEAP21TightYesSurface-hydrologic, groundwater, water temperature, and allocation models developed in WEAP21Three scenarios: base, increase in irrigated area of 35%, and 50% reduction in irrigated areaYesSU+QQYates et al. (2005)NILE DSSTightYesIncludes a database, a set of models: 1.River simulation and management2.Agricultural planning: GT-AgroPlan3.Hydrologic modeling: Sacramento type watershed models4.Remote sensing: Georgia Tech rainfall estimation methodTwo development scenarios: current condition and four large hydropower projects built and operated using dynamic inflow forecasts and multi-reservoir control methodsYesSUGeorgakakos (2007)IRAS-2010TightYes1- IRAS-2010 linked to a generic user interface HydroPlatform—YesSUMatrosov et al. (2011)SEWEMLooseNoSEWEM ModelsTwo scenarios: optimal levels of irrigation benefits without and with considering the energy production and consumptionNoEC+SUBekchanov and Lamers (2016)BRIMLooseYesModel structures in the BRIM – the water supply, population, municipal, agricultural environmental, and recreational sectors – are adapted from the Invitational Drought Tournament (IDT) ModelThree water demand scenarios related to four conditions: licensed allocations; four modified common indices; five industrial management policies; and three management gaming scenariosYesEQ+SU+SOCWang et al. (2019)GIBSITightYes(1) Hydrological model: HYDROTEL, (2) Model erosion and sediment transport: USLE + Yalin’s sediment transport equation, (3) Agricultural-chemical transport: based on SWATs algorithms, and (4) Water quality: QUAL2ETwo scenarios: a timber harvest and a municipal clean water programYesQQRousseau et al. (2000)MULINO DSS – mDSSLooseYesThe names of the models are not available in the paper, but the main model is composed of user interface, decision models, hydrologic models, data management and reporting systemNine types of analysis: tornado diagram, pairwise comparison of option and criteria, simple average weighting, among othersNoSU+SOC+QQMysiak et al. (2005)AQUATOOLTightNo1.Water balance: SIMGES2.Quality model: GESCALThree scenarios: current, medium- and long-term scenarios from the River Basin PlanYesSU+QQParedes-Arquiola et al. (2010)Modified MODSIM and QUAL2E-UNCASLooseYesModified MODSIM and QUAL2E-UNCASFive alternatives composed of different levels of urban sewage and industrial wastewater treatments, release and storage in existing reservoirs and flow augmentation from new reservoirsNoEQ+SU+QQde Azevedo et al. (2000)Modular Modeling System/Object User InterfaceTightYes(1) Climate simulations: HadCM and PCM, (2) water allocation and streamflow simulation: CALSIM-II, (3) agricultural production and drainage salinity: APSIDE, and (4) river flow and water quality simulation: extension of DSM2 [DSM2-SJR (HYDRO)], QUAL (based on QUAL2E)Six scenarios: wet and warm climatic trends (Hadley Centre Model) and cool and dry projections (Pacific Climate Model) for 2025, 2065 and 2090YesSU+QQQuinn et al. (2004)The main characteristics of a DSS (see section “Theoretical Foundation of DSS Used for IWRM”) were observed in each of the studies, and then described and tabulated in Table 4. The presence or absence of a developed user interface and tight coupling are important features as these indicate maturity in the DSS structure, facilitating the insertion of data and the manipulation of simulations and results. Another important aspect is the existence of a model base able to use different criteria, allowing the adaptation of the DSS to the user’s purposes. Nonetheless, there are still many limitations on the interchange of models between platforms and systems while achieving the necessary flexibility.Results and DiscussionUsing the models and automated systems described in the papers analyzed (see Tables 3 and S1 for more detailed information), a quantitative analysis was conducted regarding the consideration of the IWRM concepts by the tools provided. Fig. 1 presents a representation of the publications mentioning the individual IWRM concepts.As can be seen in Fig. 1, sustainability is the most used criterion (44). This can be explained by the global concern of countries and institutions about the need for measures to conserve ecosystems. Equality, on the other hand, was given few mentions within an integrated analysis, as were social welfare and economic assessment.Another detail in the quantitative analysis was considered, dealing with the evolution and trend of the number of concepts treated simultaneously, regardless of which ones, and to what extent they have been incorporated over the years into the models/systems described in the publications analyzed. Recent publications show a tendency for more models to incorporate more IWRM concepts. Fig. 2 presents a weighted average and trend line of the number of concepts incorporated into the approaches reported annually, indicating an evolution in the tools available to support the integrated management of water resources.Fig. 3 depicts an analysis of concepts included in the publications reviewed over the years selected for this study. The years are presented on the X axis, while the various combinations of concepts considered in the papers are indicated by their acronyms on the Y axis. The number of publications from a specific year using the combination of concepts specified on the Y axis determines the size of the circle with the number reported in its center. The circles are filled according to the number of concepts considered. For instance, circles that represent one criterion are filled with a light gray color. The year 2022 represents the total number of models and systems integrating each of the possible combinations of concepts, for the period 2000–2021.Sustainability with integration of quality and quantity were presented in 4 publications. Other publications also considered these two concepts integrated with other components [SU+SOC+QQ (3); EC+SU+QQ (1); EQ+SU+QQ (1); EC+EQ+SU+QQ (2)], which means that sustainability and integration of quality and quantity were present in 11 publications out of the 68 analyzed. They were also considered individually, in 9 and 7 publications, respectively. In summary, sustainability and integration of quality and quantity were included in 57 of the publications studied, individually or in addition to other aspects.Section “Models and Decision Support Systems for IWRM Considering Integration of Water Quantity and Quality” will discuss in more detail what was found in the publications reviewed concerning the characteristics of the models and systems that integrated the quantity and quality of water, both those which used this concept in isolation and those which included sustainability (most frequently) and other IWRM concepts.The economic optimization criterion was used as the sole criterion in 5 of the publications studied. Its frequency increases significantly when integrated with other concepts [EC+SU (7) – the most frequent combination of two concepts; EC+EQ (1); EC+SOC (1); EC+QQ (4); EC+EQ+SU (5); EC+SU+QQ (1); EC+EQ+SU+QQ (2)], being referred to in 27 of the analyzed publications.The economic optimization models, in general, incorporated equality and/or sustainability issues through constraints. Identification of the economic optimum helps in establishing incentives that lead to economic efficiency. This enables decision makers to incorporate, measure, and evaluate economic institutional, environmental, and access restriction issues, facilitating the design of instruments based on economic theory, making the benefits and economic costs associated with the different strategies of government regulation and intervention transparent for decision makers and for society. Overall, sustainability in these economic optimization models was represented in the reviewed publications by ecological use, established in terms of minimum flows in allocation, which, in general, did not significantly increase the complexity of the model. For example, the economic optimization models considered ecological flow as a quantitative restriction for incorporating the sustainability criterion (Souza da Silva and Alcoforado de Moraes 2018).Social welfare/economic assessment appeared as the sole criterion in 3 models and combined with others [EC+SOC (1); SOC+QQ (1); SU+SOC (5); EQ+SOC (1); SU+SOC+QQ (3); EQ+SU+SOC (6)] in approximately 30% of the publications studied. Most of the models/systems in this category carried out economic assessment, but only 8 included social welfare direct measures. The economically driven simulation model developed by Marques et al. (2006) is a good example of the use of an IWRM tool with economic assessment. This model provides estimates of economic and operational impacts of alternative policies for the modeled system, represents demands based on users’ willingness to pay for water, and improves economic approaches to water management. Bekchanov et al. (2017) have reported the difficulty of combining network-based economic models with models such as IOM and CGE. This can be associated with the difficulties of incorporating the criterion of social welfare, which is measured through social indicators such as employment and income. Meanwhile, the importance of integrating this aspect is increasingly recognized. Alcoforado de Moraes et al. (2021) integrated a network-based optimization with an input-output model, made available through an SDSS (the HEAL System), to support the design and evaluation of water allocation policies. In a case study using four interlinked hydrographic basins in northeastern (NE) Brazil, they calculated the ratio between the proportionate economic impact, assessed through changes in social (employment) and economic [gross domestic product (GDP)] indicators, in response to the proportionate water impact (changes in the water allocations) for each economic sector. The HEAL System is also able to identify and support water management in another northeastern basin at Brazil (São Francisco river basin–SFRB), as it recently (Souza da Silva and Alcoforado de Moraes 2021) has incorporated the hydro-economic model, which identifies an optimal economic allocation of water resources in that basin (Souza da Silva and Alcoforado de Moraes 2018). Habibi Davijani et al. (2016) presented social welfare as the objective function in the optimal allocation of water resources. Their results showed an increase of 13% in the number of jobs created in the industrial and agricultural sectors when compared to the previous water use situation.Equality was the least incorporated criterion and did not appear individually in any model studied, but was associated with other concepts in 18 publications [EC+EQ (1); EQ+SU (1); EQ+SOC (1); EC+EQ+SU (5); EQ+SU+SOC (6); EQ+SU+QQ (1); EC+EQ+QQ (1); EC+EQ+SU+QQ (2)]. Among the few studies that considered equality, most did this through definitions of priority for human use. In particular, de Azevedo et al. (2000) and Cai et al. (2002) incorporated temporal equality by introducing restrictions to ensure that the benefits of water use would not diminish over the years; they and incorporated spatial equality by ensuring that users in different locations in the basin would have equitable access to water.Four aspects of the IWRM definition [EC+EQ+SU+QQ (2)] were considered by Zhou et al. (2015) and Cai et al. (2002). To address these aspects simultaneously, Zhou et al. (2015) developed an integrated optimal allocation model (IOAM) for a complex system of water resources management combined with adaptive allocation, dynamic allocation, and multi-objective optimization.Another important aspect to consider is the development of integration between concepts categorized as either economic or physical (engineering). To evaluate this integration, a matrix was built (Table 5), recording the frequency with which the paired concepts are present in the analyzed models. The matrix can be analyzed by criterion both along the rows and down the columns. Among the economic concepts, economic optimization is the one that appears most integrated with the engineering concepts (23 times), followed by equality (19) and social welfare/economic assessment (18). Among the economic concepts, the combinations occur less frequently, with the occurrence of the integration of economic optimization and equality (9) and between equality and social welfare/economic assessment (7). Analysis of the engineering concepts shows that environmental sustainability appears integrated with economic concepts more often (44 times) than the criterion of water quantity-quality (16).Table 5. Correlation matrix between economic and physical criteria (engineering criteria)Table 5. Correlation matrix between economic and physical criteria (engineering criteria)SUQQECEQSOCEconomic criteriaEC158—91EQ1549—7SOC14417—Physical/engineering criteriaSU—11151514QQ11—844Even though QQ is a quite common criterion among the revised models, quantity-quality integration appears less frequently combined with economic optimization concepts. This occurs in only 7 models: [EC+QQ (4); EC+SU+QQ (1); EC+EQ+SU+QQ (2)].In fact, economic optimization integrated with quantity-quality confers many important benefits to IWRM, indicating the importance of developing more of these models. Thus, the introduction of water quality restrictions for ecological purposes can be priced out, enabling measurement of the costs of environmental restrictions of different intensities. These expenses can be discussed with society and compared with estimates of prevention and correction costs. Compensation schemes and shadow prices can be used to deal with externalities.Regarding the structure of the models, there was a very balanced division between descriptive (28) and prescriptive (40), with most of the analyzed models being prescriptive. Since both descriptive and prescriptive models generally employ equations and nonlinear functions, this demonstrates the complexity of the mathematical modeling required by IWRM.Fig. 4 details this division in the inner two rings. On the third ring, the studies are divided according to the absence or presence of stochasticity. Finally, the IWRM concepts are shown on the outside ring as they are incorporated into the models and systems. The smallest division shown in the figure represents one unit, that is, one study, which enables visualization of the ratio between shapes on the graph and the number of studies.Stochastic models appear in a much higher proportion among the prescriptive models than in the descriptive ones. As prescriptive models maximize or minimize a specific objective function to identify a plan that can be adopted that satisfies the decision criteria, they need to provide values for decision variables simultaneously, in all time periods, as well as consider inflows related to any future time points and scenarios under analysis. Thus, in general, prescriptive models are associated with stochastic optimization techniques and solvers. These tools are becoming more accessible and are able to deal with more complexity, making them well suited to IWRM and its uncertainties.Most of the prescriptive and stochastic studies include concepts of sustainability or the integration of quality and quantity within economic optimization, reflecting the need to consider the question of uncertainty in this integration. On the other hand, both linear and nonlinear descriptive models are mostly deterministic and usually consider only the ecological aspects, more specifically, questions of sustainability and integration of quantity and quality, whether combined or isolated. The economic aspects of equality and social welfare/economic assessment appear much less frequently, either isolated or combined with only one of the ecological criteria. There is only one occurrence of the aggregation between equality, social welfare/economic assessment, and an ecological criterion (sustainability). This analysis is important to guide future studies, as well as to develop methodologies that will enable effective support for real integration of the various criteria in management decisions.It is possible to verify through Table 4 and Fig. 5 that 11 of the 16 DSSs that have scenarios/sensitivity analyses also have friendly-user interfaces, which means they facilitate the design of scenarios and the comparison of the results obtained. 76.5% presented multicriteria analyses and 64.7% included a tight coupling, offering common geodatabases that allow linkages of model input and output to the associated simulation models.An important observation regarding the DSS found in this review is that few studies provided allocation models that considered any economic criterion. For the most part, these automated systems introduce models that consider only engineering concepts: sustainability and quantity-quality.Models and Decision Support Systems for IWRM Considering Integration of Water Quantity and QualityAs already noted, the integration of quantity and quality combined with sustainability criteria was very frequent in the water allocation models and in those that are made available through a DSS, which increases the potential of applying these tools.To a lesser extent, there were models which considered this combination together with economic optimization [EC+SU+QQ (1); EC+EQ+SU+QQ (2)], or other economic aspects [SU+SOC+QQ (3); EQ+SU+QQ (1)]. Of the latter, with some economic component integrated to the two engineering/sustainability concepts (SU and QQ), almost none were available through a DSS. In isolation, the quantity-quality criterion only appears less frequently than models that consider the aspect of sustainability alone, which does not include water quality.In general, the consideration of the quantity-quality criterion in management models, in isolation or added to other concepts, was frequent in the studies (24) and demonstrated the ability to deal with greater complexity (17 of these studies are nonlinear models). This integration and sophistication of tools thus represents a recognition of the challenges associated with water quality management and water availability. The details of the quality modeling, integrated with the allocation models described in Table 4, are given in Table 6. It is important to highlight the existence of other important papers that present the integration of quantity-quality such as (Xu et al. 2019). This paper addressed reservoir operation by running a quasi-three-dimensional water quality model to simulate reservoir hydrodynamic conditions, nutrient cycles, water-sediment exchanges, and algal dynamics under various water supply schedules.Table 6. Water quality modelingTable 6. Water quality modelingDSSConcepts consideredREFModelParametersHighlightsNo specific nameSalt emissions——EC+EQ+SU+QQCai et al. (2002)QUAL2KpH, temperature, electrical conductivity, SS, N, and forms of PQUAL2K is fed by MONERIS, which collects all pollutant emissions and daily discharge values provided by the hydrological model. Diffuse pollution is supplied through the Soil and Land Resources Information System – SLISYSMOSDEWQQGaiser et al. (2008)Streeter–PhelpsBOD, DO, and PThe self-purification phenomenon makes it possible to use the assimilation capacity and prevent releases above what is endurable by the water body. The model allocated water and effluents in the field guaranteeing the water quality in the watercourse and reservoirs—EC+QQAlcoforado de Moraes et al. (2010)GESCAL moduleDO, BOD, organic nitrogen, ammonia, nitrate, and TP—AQUATOOLQQSalla et al. (2014)Mike ECO LabBOD and DO——EC+QQGunawardena et al. (2018)QUAL2EQuality model of groundwater return flow (calcium and magnesium ions – soil salinity) and 15 water quality constituentsThe integration between the quantity (MODSIM) and the quality model (QUAL2E) was a challenge due to the difference in the representation of the network in each model, which was solved through modifications in the QUAL2E source code—QQDai and Labadie (2001)No specific nameTotal dissolved solids, pH, Hardness and SodiumThe model seeks to minimize the total water cost, including the economic cost of treatment and distribution and the associated environmental costs (carbon footprint)—SU+SOC+QQAbdulbaki et al. (2017)No specific nameSurface water quality classesEach run of the model was optimized according to a single objective, with different constraints on secondary objectives to analyze trade-offs between them—SU+SOC+QQMartinsen et al. (2019b)Quality Module WEAP21TemperatureThe water temperature is impacted by hydropower production, which is important for the maintenance of the region as a suitable habitat for anadromous Chinook salmonWEAP21SU+QQYates et al. (2005)Streeter–PhelpsBOD——EC+QQDavidsen et al. (2015)No specific nameCOD, TN, TP——EC+SU+QQZeng et al. (2016)QUAL2ELoads and dissolved oxygen, chlorophyll a, dissolved P and organic P, forms of N, BOD and pesticides—GIBSIQQRousseau et al. (2000)Modified QUAL2E-UNCASDO, BOD, N, P and fecal coliforms—Modified MODSIM and QUAL2E-UNCASEQ+SU+QQde Azevedo et al. (2000)MULINO Quality ModuleSeveral applications, including nitrate—MULINO DSS – mDSSSU+SOC+QQMysiak et al. (2005)No specific nameCOD, ammonia nitrogen, TN and TP——SU+QQZhang et al. (2010)SWAT quality modules (CREAMS, QUAL2E, WASP)ammonia nitrogen and COD——QQZhang et al. (2011)GESCAL moduleConductivity, SS, CBOD, DO (second level of complexity), ammonium, and nitratesAccording to the authors, AQUATOOL was one of the main instruments used in Spain to analyze water quantity and quality aspects of water resources systems for the compliance with European Water Framework DirectiveAQUATOOLSU+QQParedes-Arquiola et al. (2010)SWATPoint and diffuse sources of N to investigate the nitrate leaching into the groundwaterSWAT can be used to build models to evaluate the effects of alternative management decisions on water resources and non-point source pollution in large river basins—QQAbbaspour et al. (2015)HEQM Module (WQM)Six hydrological, eleven nitrogen, five COD, and six soil carbon parameters were used to model ammonium–nitrogenUsing a multi-objective evolutionary algorithm, the results showed that a Pareto front was formed, providing different satisfactory solutions for users to choose according to their specific objectives—QQZhang et al. (2016)No specific nameBOD and Thermotolerant Coliforms——EC+EQ+QQDalcin and Fernandes Marques (2020)DSM2-SJR/QUAL/APSIDESalinity on the river and the soil and electrical conductivity—Modular Modeling System/Object User InterfaceSU+QQQuinn et al. (2004)No specific nameSalt emissionsSimulated the effects of climatic change, increase in water storage capacity and irrigated land extension, modernization of irrigation technique and two global change scenarios on the water scarcity, salinity, and agricultural profits of the catchment area—SOC+QQGraveline and de Recherches (2014)No specific nameCOD and ammonia nitrogen——EC+EQ+SU+QQZhou et al. (2015)There is a lack of hydro-economic models with water quality modeling associated with water availability limitations. Few models were found (Alcoforado de Moraes et al. 2010; de Azevedo et al. 2000; Cai et al. 2003; Davidsen et al. 2015; Gunawardena et al. 2018; Zeng et al. 2016; Zhou et al. 2015), and progress in the development of these kinds of integrated models remains limited and slow with the need for improvements in the links between water quality (pollution and impacts) and economic benefits (Bekchanov et al. 2017). This is attributed to the complexity underlying the dynamics of water quality (von Braun 2016; Momblanch et al. 2016).Conclusions and RecommendationsThe two environmental sustainability concepts considered in this review (quantity-quality and sustainability) were the most frequently used in the allocation models reviewed, and almost half of them were available in an SDSS. These automated systems presented, in most cases, a well-developed friendly interface enabling the application of more than one model, as well as allowing the use of different decision criteria and restrictions together with the analysis of scenarios/sensitivity, in addition to having a tight coupling and a connection to spatial databases. This greatly facilitates and enhances their use by decision makers and stakeholders, favoring an environmentally sustainable management of water resources.When it comes to effective support for the IWRM recommendations, which combine the requirement of sustainable management maximizing economic well-being together with equity, there are still few allocation models. The good news is that models for this have been developed, especially in recent years (Fig. 3), most of them including three or more concepts taken from both the engineering and the economic categories.Overall, the tools developed between 2010 and 2021 are prescriptive (optimization), nonlinear, and deterministic, configured in sophisticated mathematical models whose viable solutions show an advance in integrated economic-hydrological modeling, which should favor future implementation of an authentic IWRM. These models, however, are not yet available through an SDSS.From the first applications of simulation and optimization models to the management of water resources, economic objectives and constraints have been common (Loucks et al. 1981; Maass et al. 1962). Issues with effective integration of economic and social aspects with physical aspects, especially in studies aimed at evaluating alternatives and policies for water allocation, are not easily solved. They involve a series of difficulties in the exchange of information, touch on different political and administrative restrictions, involve different spatial and time horizons, and depend on complex data availability.Allocation modeling that considers aspects of quantity-quality (including at least one water quality parameter) combined with economic optimization, as shown in this review, has been almost entirely developed in the last decade. The allocation models used simplified quality modeling, representing few constituents. Among these, organic compounds, the main polluters of water sources in developing countries, were represented by biological oxygen demand (BOD) and dissolved oxygen (DO) and simulated using simple formulations, such as the Streeter–Phelps equation. Allocation models that included economic optimization and simulations of phosphorus and nitrogen, components related to the use of fertilizers and pesticides, are rare. For example, one of the studies (Alcoforado de Moraes et al. 2010) estimated the phosphorus concentration as a fraction of the organic matter available, which is not usually taken into consideration in traditional quality modeling.In the works that did integrate quantity-quality with economic optimization, none incorporated other socioeconomic measures. Only the model developed by Zhou et al. (2015) introduced the Gini index in its constraints, a measure that we categorize in this review as related to distributional and equal access issues, but in a comprehensive way may be considered a socioeconomic measure.If just prescriptive economic allocation models (economic optimization) had been considered, no model was identified that integrated measures of welfare and equality.Even using optimization economic models for allocation and measurements of the direct economic impacts of different allocations, these hydro-economic models are not able to obtain broader socioeconomic indicators such as: GDP, employment, government revenues, consumption, investment, exports and imports, income distribution, or comparative advantages between sectors.Water-economy management models are classified into economic models based on a network structure of nodes and links (Brouwer and Hofkes 2008; Harou et al. 2009) and economic models with broader impacts (economy-wide models), which include input-output models (Carneiro et al. 2015; Manzardo et al. 2016; Munoz Castillo et al. 2019) and computable general equilibrium models (Dinar 2012; van Heerden et al. 2008; Sun et al. 2020; López et al. 2019). These economy-wide models can generate socioeconomic indicator values but lack adequate spatial and hydrological representations for supporting water allocation decisions. Links between economic optimization and economy-wide models seem to be a solution but are challenging to construct.These links need to be able to measure broader socioeconomic impacts, aggregating socioeconomic concepts to allocation decisions in the management of water resources, such as water flow, reservoir volume, water quality, and water availability at the river basin level. In this way, allocation model capabilities can be expanded as they become more able to calculate not only the direct economic impacts, but also the indirect impacts and spillover effects of different water allocations through changes in economic and social indicators. Thus, the total economy-wide impact of different water allocation decisions can be measured. These results can produce indicators to support the implementation of river basin sustainable development goals (RiSDGs), as proposed by Ge et al. (2018) and obtained recently (Alcoforado de Moraes et al. 2021). This latter integrated modeling, as it is available through an SDSS (the HEAL System), should allow the development of new optimization models using other criteria, such as the economic one, whose results will be automatically associated with direct and indirect socioeconomic impacts.A recent review stressed the need of integrating these two types of economic models of water management: those of economic optimization (network-based economic models) and the most comprehensive (economy-wide models). Moreover, what still seems challenging and in need of development is the incorporation of the issue of water quality into these economic models (Bekchanov et al. 2017).Finally, it is important to recognize that the inclusion of the economic criterion adds new theoretical concepts and complexities beyond what is common in traditional water management models, which certainly makes it difficult for managers to accept this approach (Harou et al. 2009). The implementation of effective and sustainable IWRM needs a planning and decision process which includes the participation of all the stakeholders involved, and requires support from models and DSSs that are able to promote negotiation and cooperation (Basco-Carrera et al. 2017). There are few SDSS models providing an integration of economy results (Alcoforado de Moraes et al. 2021; Bekchanov and Lamers 2016; Chakroun et al. 2015; Mysiak et al. 2005; Souza da Silva and Alcoforado de Moraes 2021; Wang et al. 2019), and these are mainly prescriptive ones. More than ever, this is an important research study area in the field of IWRM, as these tools can provide common framework for modelers, decision makers, and stakeholders. 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