Multi-agent system simulation and centralized optimal model for groundwater management considering evaluating the economic and environmental effects of varied policy instruments implemented

Abbreviation

Explanation

AAB

average annual benefit

ABM

agent-based modeling

CDF

cumulative distribution function

COM

centralized optimal model

CPR

common pool resource

HRU

hydrologic response unit

IWRM

integrated water resources management

km

kilometer

MASS

multi-agent system simulation

PSO

particle swarm optimization

SES

social-ecological system

VSF

violation of streamflow

The excessive use of groundwater is often believed to be caused by the failure of the common pool resource (CPR) and can lead to a variety of negative impacts, the decrease in the groundwater level, depletion of streamflow, escalated expenses related to pumping, deterioration of quality of water, damage to water-based ecosystems, and irreversible subsidence of land (Bartolino & Cunningham 2003). The excessive use of CPR and the resulting social and environmental effects can be attributed to the ascent in the global population, escalating levels of consumption, and the widespread use of sophisticated technologies (Grimble 1999; Dietz et al. 2003).

To enhance groundwater management, it is necessary to explicitly model water management systems including humans to uncover not intended and unforeseen feedback (Khan et al. 2017; Pande & Sivapalan 2017; di Baldassarre et al. 2019; Alam et al. 2022). Tools have been developed by integrating human activities with hydrological processes in models that aim to provide solutions for integrated water resources management (IWRM) (Mariño & Simonović 2001; Harou et al. 2009; Pulido-Velazquez et al. 2016) and analyzing water policies (Mulligan et al. 2014; Wu et al. 2015). When stakeholders' behavior is the focus, the approach of an agent-based modeling (ABM) is commonly used to model the consumption of domestic water within intricate water systems (Galán et al. 2009; Ma et al. 2012; Zhang et al. 2023a, 2023b), management of groundwater (Mulligan et al. 2014; Castilla-Rho et al. 2015; Ohab-Yazdi & Ahmadi 2018; Jabbari et al. 2022; Nouri et al. 2022; Aghazadeh et al. 2024; Canales et al. 2024), management of the allocation of water (Yang et al. 2009, 2012), incidents of water pollution (Zechman 2011; Shafiee & Zechman 2013), and urban flood management (Zhang et al. 2023a, 2023b; Nazemi et al. 2024). ABM is favored for its ability to explicitly depict the influencing components in the process of decision-making (Soman et al. 2008). In general, ABM is a modeling technique that simulates the behavior of autonomous and heterogeneous agents and their interactions and comprises four components: (1) agents, which are individual water users; (2) the environment, like a river basin or underground water reservoir, alongside the engineered infrastructure where in agents are situated; (3) management strategies or regulations; and (4) system-level performance metrics, encompassing economic impacts likewise environmental impacts (Zhao et al. 2013). ABMs are becoming more and more popular as a supplement to traditional analytical methods for studying environmental issues. They enable modeling the results at a systemic level that arise from the actions of individual existences. ABMs are particularly useful for studying social-ecological systems (SESs) because they provide a bottom-up perspective. SESs exhibit complex adaptive systems motivated by social and biophysical subsystems that interact with each other but are relatively distinct from each other (Ostrom 2009). ABM first emerged in fields other than water resources management (Schelling 1971; Holland & Sigmund 1995; Axelrod 1997). After that it was adopted for use in water resources management (Yang et al. 2009, 2012; Reeves & Zellner 2010; Holtz & Pahl-Wostl 2012).

To prevent the economic and social impacts that result from excessive use of groundwater, it is desirable to implement strategies for managing that promote the shift toward a more economically efficient utilization of groundwater. To tackle the issue, some of the approaches that can be adopted include implementing quotas, pricing groundwater, and establishing markets to attain effective allocation of groundwater based on economic considerations (Koundouri 2004). Every one of the mentioned policy instruments compels the water user to identify each element of the external consequences related to groundwater extraction. Although numerous research works have explored the effectiveness of varied policy instruments, only a limited number have undertaken this endeavor employing a physically heterogeneous illustration of a basin alongside a spatially disaggregated model (not a single-cell aquifer model) depicting farmers' water utilization behavior (Brozović et al. 2010). Models that consider spatial heterogeneity in groundwater extraction offer a more thorough comprehension of the economic aspects related to groundwater utilization (Mulligan et al. 2014). Quota and tax on water use policy instruments are widely employed to mitigate the poor allocation and excessive utilization of groundwater as a CPR (Koundouri 2004).

This paper investigates the different policy instruments employing a grounded hydrology numerical model that is completely distributed, linked to a distributed model of farmers' water usage behavior influenced by economic factors within an agent-based framework. The study takes into account the heterogeneity related to the productivity of farmers and the physical characteristics of the aquifer in its framework, which is a distinct advantage over the frequently utilized single-cell models in studies of this nature. This work is unique in that it employs a quasi-distributed SWAT watershed model and a numerical model of groundwater flow processes in conjunction with a model representing the dispersed behavior of farmers (agents) in utilizing water that is coupled with Python. These models, when used together, provide a more extensive and authentic illustration of groundwater utilization in a basin, allowing us to evaluate the efficacy of various policies for managing groundwater. This study evaluates three policy instruments: (1) free access with unrestricted behavior of farmers, (2) a consistent tax on water usage, which operates on incentive-based principles, and (3) a consistent quota on water usage, which lacks incentives unless trading is permitted. Every one of these policy instruments is incorporated into an ABM, that is a decentralized model of farmer water utilization behavior. In this paper, the agent-based model will be referred to as multi-agent system simulation (MASS) as it provides a better designation. MASS is used to model the potential behavior of farmers based on their financial factors and the groundwater conditions specific to the local area, as well as the interaction between them. Within MASS, every agent strives to maximize their profits without considering the impacts on profits of other agents, the watercourses, and the underground aquifer. This serves as a typical illustration of market failure in the realm of groundwater CPR, where users prioritize their individual profits over potential anticipated individual and external financial burdens, encompassing the effects on another agent and natural resources depletion. In this paper, an innovative framework utilizing MASS is presented. This framework employs Python-based scripts to integrate the NETLOGO ABM platform with a calibrated MODFLOW groundwater model, which incorporates the SWAT watershed model. One of the other unique aspects of this paper is that it considers the uncertainty associated with farmers' productivity.

The effectiveness of the policy instruments is assessed by comparing them to an ideal strategy for utilizing groundwater referred to as the centralized optimal model (COM) in this paper. The COM is a groundwater use strategy that employs a centralized planner's top-down method to maximize the total agents' profits (or net societal advantages) while adhering to the constraints of streamflow. This is in contrast to the MASS models, which do not have streamflow constraints. The COM is an illustration of potential possibilities accomplished by a central planner possessing complete foresight, allocating groundwater usage across both time and space in a manner that maximizes economic benefits and consistently adheres to streamflow constraints. It functions as a benchmark and ideal against which other measures (free access, tax, and quota MASS) can be evaluated. It represents the upper limit for groundwater management policies intended to sustain streamflow.

This paper is structured in five sections. The methodology is described in Section two, which includes the hydrologic model, the COM and the MASS that is a model of farmers' water usage behavior. Section three provides a detailed presentation of the results. A discussion on these findings is presented in Section four. Finally, Section five provides a summary of the entire study and its significance in the context of groundwater management.

To create COM, a coupled of two models (MODFLOW-MATLAB) is used (Figure 2; Kamali & Niksokhan 2017a, 2017b). The COM is solved using the PSO algorithm in MATLAB. The COM is designed to maximize the total profits of agents across the basin while adhering to streamflow constraints and higher limits on extraction during the period of simulation. A unified objective function encompasses decision variables for every agent. The COM's pumping decisions are made with the consideration of every conceivable situation and choose the most advantageous (optimal) pumping allocation. The management periods of the optimization model are 1 year, yielding a total of 810 (27 agents, 3 crops, and 10 years) decision variables for this model. The formulation is presented in the following equation.

To create MASS, coupled of two models MODFLOW-NETLOGO are used (Figure 2). NETLOGO is a programming language designed for multi-agent systems for designing, implementing, and analyzing ABMs that has evolved into a popular choice for this goal because of its engaged user community and ease of use. It was authored by Uri Wilensky in 1999 and is open-source. This platform is ideal for modeling complex systems that evolve across the duration. It allows modelers to guide hundreds or thousands of autonomous ‘agents’ carrying out simultaneously. This feature enables investigating the links between the individual behaviors at the micro-level and the overall patterns that arise from their interactions at the macro-level. The tool is mainly coded in Scala and Java, and it provides a variety of methods and functions that facilitate the quick creation of ABMs with spatially clear features.

Various investigations have concentrated on integrating models of ecological (environmental) systems with MASS (e.g. Bithell & Brasington 2009; Reeves & Zellner 2010; Kelly et al. 2013). The coupling of MASS and physical simulations is particularly pertinent in the context of groundwater resources. Given their widespread exploitation, limited availability, and the intricate interactions among heterogeneous users involved in their management, MASS emerges as a suitable modeling choice. Moreover, monitoring groundwater resources in the subsurface is frequently challenging. Hence, numerical modeling can offer valuable insights for effective resource management.

However, the integration of MASS and models of groundwater might pose specific dilemmas attributed to the extended temporal scales and typically lengthy duration of model execution. Castilla-Rho et al. (2015) outline four considerations associated with traditional methods for modeling interconnected groundwater systems: constraints posed by basic aggregated models, technological intricacies arising from the utilization of interconnected software applications and libraries for data exchange, a deficiency in scenario development flexibility, and the lack of practicality analyzing the sensitivity of various models. To overcome the mentioned constraints, they present an engaging environment that straightly incorporates equations of groundwater flow into the widely used NETLOGO agent-based platform. Considering the continuing pattern toward more intricate human–environmental systems, ABMs (Sun et al. 2016), that consequently pose greater challenges in design, this approach offers the benefit of creating an environment designed for user convenience for the development and application of ABMs of groundwater management. However, the use of NETLOGO has constraints in the context of groundwater management issues in cases where existing geohydrological models are accessible for direct reuse or where detailed geohydrological modeling is necessary.

In the MASS and COM, the agents are presented with a selection of three crops: wheat, barley, and potato. These three crops account for a significant portion of agricultural output in the Ardabil Plain, although alfalfa and similar crops are widely favored in that particular area. The financial information regarding costs and revenues is extracted from the local investigation. The operational cost of the farm, denoted as f_c, corresponds to the cost of a particular crop, expressed in million rials per acre for every season of cultivation. For wheat, barley, and potato, f_c is 150,000,000, 80,000,000, and 1,000,000,000 rials per acre. p_c is the crop selling price in rials per kilogram. Regarding wheat, barley, and potato, p_c is 125,000, 120,000, and 150,000 rials per kilogram in 1401. The operational expenses and selling price remain consistent throughout the simulated modeling duration. This data is obtained from local investigation from local farmers.

Two parameters that impact the productivity of the agents encompass crop yield (y_a,c) and crop irrigation requirements (w_a,c). To prevent the uncertainty associated with the productivity parameters from unduly affecting the model results, a total of 10 groups of parameter measurements have been established. Ten runs are conducted for the MASS and COM model types using varied groups of agent productivity parameters. In order to create a basin setting that is more realistic and captures a spectrum of productivity of agent productivity, spanning from highly efficient agents to less efficient ones, the parameters for each agent within every set are subjected to randomization. The aim is to depict in a simplified manner the common variability among agents resulting from experience, embracing technology, and other skills or environmental circumstances. The value of each parameter remains unchanged over the period of the simulation. Due to the prolonged computational processing time and significant storage needs, the decision was made to create only 10 sets of productivity parameters. An overview of the agent parameters within each set is presented in Table 2.

Crop yield (y_a,c) for every agent is extracted from the local investigation from local farmers. The crop data provides the mean yield in each year for every part, specified as the overall production for each crop in tons per acre. The values of y_a,c are given to each agent through an initial development process an empirical CDF (cumulative distribution function) that is divided into linear parts and adjusted to the crop yield data across time and space, establishing a correlation between yield and relative frequency. Each agent is subsequently allocated the relative frequency values by choosing random values within the range of 0–1 of a uniform distribution. The agents' assigned relative frequency values are employed to select the corresponding yield value through the inverse of the empirical CDF.

A summary of each modeling framework, MASS and COM, is presented in Table 4. The overall cost for every cultivation season for every agent is calculated by adding the operational costs, costs associated with pumping, and any applicable taxes. The pumping cost is determined by the groundwater depth, the water weight, the price of electricity, and the quantity of water pumped. The income generated by the calculation of every agent involves multiplying the price (at which a product is sold, p_c) with the total production for the cultivation season. The cumulative output during the cultivation season depends on two parameters of productivity y_a,c and w_a,c and the amount of pumped water. By deducting the overall cost from the overall revenue, the overall profit of each agent is calculated. The tax payment is regarded as a positive contribution to the administration and is manifested in the ultimate analysis by adding up the overall profits of the agent and the overall taxes remitted to assess the monetary outcome in each model iteration, or the overall gains of society.

The function describing the production supposes that the agent will modify the count of cultivated acres with irrigation based on the water pumping decision. To illustrate this point, suppose an agent has 1,000 acres of land area and wheat requires 300 mm of water and because of restrictions the agent reaches a decision to use 150 mm throughout the season of cultivation. The model proceeds under the assumption that the agent will implement reducing the 150 mm of water to half (150/300) for 500 acres so that 500 acres will receive 300 mm of water for wheat irrigation, while the remaining 500 acres will not be irrigated.

MASS aims to maximize the profit of a single agent. The agent's profits are optimized while adhering to pumping upper bounds (dictated by available crop irrigation requirements and land area) and, if applicable, water usage quotas. For this model, an objective function with a decentralized structure is employed for each agent at the beginning of every season of cultivation. At the beginning of each season of growth, the groundwater model computes new groundwater depth values, relying on the previous year's groundwater utilization. Thus, the choices made by the agents regarding water usage encompass their influence on alterations in the groundwater level. The formulation for management, applicable to each agent and each year, is presented in the equation for the water utilization behavior model of the farmer below.

The pumping decision variable is established annually for each season of cultivation. This means that the decision on how much to pump is made once a year, and it applies to the entire cultivation season. The cost of pumping for each year is determined by the initial groundwater depth at the beginning of the cultivation season. It is assumed that the loss of head because of pipe friction is insignificant and the efficiency of pumping is 70%. It is taken for granted that the return flows applicable to both COM and MASS model types constitute 20% of the water volume extracted. After each agent's yearly optimization, the storage capacity is examined to ensure sufficient available water for supplying the flow rate set by the optimization model.

In the event that there exists an inadequate water supply in the proximity of their well, agents refrain from pumping in that particular cultivation season. Equation (4) shows that fixed costs are anticipated to be considerably less than variable costs. Therefore, we did not include any fixed costs in this analysis.

The MASS formulation includes water use quotas and taxes to assess alternative, practical policy instruments. The water usage tax and quota are consistently imposed on all agents. The tax is incorporated into the objective function as a levy on complete water utilization, calculated in million rials per m³, falling within the range of 1–11 million rials per m³. Due to the significant differences in the productivity of agents, some agents are more likely to be affected by a tax increase than others. Agents with lower productivity are anticipated to decrease their rate of pumping or stop pumping at a reduced tax rate compared with agents with higher productivity. The tax rates employed in this examination are elevated and are probably not feasible from a political standpoint. The reason for the high rates of tax applied in this study is that the profits from the crops significantly surpass the total costs in the solution of free-access MASS. Therefore, to encourage agents to irrigate a smaller area and diminish water consumption, a high tax rate is required. This is a fact that needs to be acknowledged if the strategy to curtail water usage and, consequently, influence the streams relies solely on a uniform tax. If the revenue of tax is redistributed among the agents in a quantity that is approximately equivalent to the loss of welfare resulting from the tax, then a consistent tax could become a more feasible alternative.

The utilization of water quota is added to the framework for optimizing water usage in the model as limitations on the amount of water applied, which can range from 100 to 600 mm per season of cultivating. The depth is determined by calculating the entire volume of water pumped throughout the season of cultivation and dividing it (measured in cubic meters) by the area of land that can be irrigated (measured in acres) and then expressing the result to millimeters.

The water usage quota imposes a consistent decrease in water usage for each agent, while considering the quantity of land owned by each agent. The number of irrigated acres owned by each agent stays consistent throughout the planning period.

Various policy instruments were assessed based on their impacts on the economic and environmental consequences, then were contrasted to the COM and the free-access MASS. The environmental and economic impacts of a management plan are measured using two main indicators: the violation of streamflow and the average annual benefit (AAB). The violation of streamflow is the proportion of instances (percentage) where the simulated streamflow falls below the specified streamflow objectives that match the streamflow limitation values implemented in the COM. The AAB is calculated by adding the average annual profit across the entire basin and, if relevant, the average annual tax revenue generated across the entire basin.

According to Figure 7, MASS with free access (green square) yields the highest AAB for agents (around 151 trillion rials). However, it has a significant impact on streamflow, with approximately 90% of the violation of streamflow. This outcome mentions that the approach of free access for self-interested and shortsighted agents lacks sustainability in streamflow. The groundwater depletion reserves have resulted in a considerable rise in the violation of streamflow, and the rising costs associated with pumping over a duration have not prevented this depletion. According to this figure, COM (red square) yields around 120.3 trillion rials the average annual benefit for agents. However, it has no impact on streamflow, with 0% of the violation of streamflow. COM suggests that if there is a complete understanding and centralized management of all pumping activities, the limitation on streamflow can achieve contentment, and comparatively great benefits can be obtained (while not reaching the same level as those observed in the free-access approach). Although it is probably impractical, the optimal solution sets the highest attainable outcome that could be accomplished via a policy related to groundwater customized to mitigate the effects on streamflow.

The consistent tax and consistent quota policy instruments demonstrate that it is challenging to achieve the optimal solution due to the limitations of incomplete foresight and the basin heterogeneity. In both cases, when a tax or quota is put into effect, there are significant reductions in average annual benefit or a high violation of streamflow. Neither policy instrument implemented in the MASS can match the performance of an optimal pumping plan that delivers both high economic feasibility (around 120.3 trillion rials) and low streamflow impacts (0% violation of streamflow). In the case of the MASS with quota and the MASS with tax, almost every agent is required to cease pumping to achieve zero violation of streamflow, resulting in extremely low average annual benefit. As it is challenging to minimize the violation of streamflow without significant economic consequences, it seems that a non-zero violation of streamflow must be accepted. The results suggest that the violation of streamflow 20% can be attained with acceptable economic advantages using the MASS with tax and likewise MASS with quota policy instruments. The yellow and orange lines illustrated the results of MASS with tax outcomes, signifying a spectrum influenced by the extent of tax revenue allocation for the advantage of the agents. The orange line in the figure represents the scenario where all revenue from taxes is utilized to the advantage of the agents, while the yellow line demonstrates the scenario in which none of the agents derive benefits from the utilization of tax revenue. Values on the horizontal axis of the orange line represents the average annual benefit of the agents plus the average annual tax revenue and the yellow line represent the average annual benefit of the agents. If the distribution of tax earnings is not efficient (yellow line), the advantages of the agents are substantially lower than those of the optimal solutions and free access. If the allocation of tax revenue is redistributed (orange line), the agents experience notable benefits even in situations where the violation of streamflow is low. In both scenarios, the agents show a minimal reaction in pumping behavior to reduced rates of tax (points on each line located in the figure's upper-rightmost section).

The red line in the figure represents the MASS with quota solutions, which falls between the yellow and orange lines linked to the tax policy instruments. Therefore, the effectiveness of the tax is heavily reliant on the revenue of tax redistribution policy. The proximity of the line of quota to the orange line suggests that the quota may be more effective than most potential redistribution policies.

Specifically, when agent productivity changes, the violation of streamflow remains relatively stable, while the benefits for the agents undergo alterations, though not to a degree sufficient to significantly impact the instrument's comparative effectiveness. This is because, in all MASS with quota scenarios, every agent pumps to some extent since the quota limits the amount of each user's pumped water. The pumping would cease only when the associated costs of pumping reached an excessively high level. This results in greater fairness in comparison to the tax outcomes. The scenarios involving MASS with tax lead to a shift in water usage toward the agents with higher productivity, since numerous less-productive ones discontinue water usage when the tax reaches excessive levels. The quota policy option is more resilient when considering the heterogeneity of agents.

Table 5 presents the outcomes of model runs of MASS with quota and MASS with tax in comparison to the COM and free-access MASS. This table illustrates the impact of distinct different configurations of parameters for each model type similar to Figure 7. Generally, the distinctions among the models are more significant than the uncertainty span depicted through the sets of parameters, though there is a certain commonality.

The first row enables a comparison of COM and free-access MASS. Two crucial observations can be identified: (1) The free access of self-interested agents is detrimental to the environment and (2) COM can achieve zero the violation of streamflow with only a minor reduction in agent profits. The second row displays the results of MASS with quota. Reducing the quota to mitigate streamflow depletion leads to substantial and probably unaffordable economic consequences. As the quota decreases, there is a minor reduction in the violation of streamflow up to approximately 300 mm, after which a more significant decrease in the violation of streamflow occurs. A quota as low as this one leads to a substantial reduction in the basin's production. One significant difference between quota and tax policies is that the impact of variations in productivity on streamflow violation variability is lessened with a quota policy, which is an anticipated outcome. This is noteworthy because it significantly diminishes the uncertainty linked to the impact of the quota on streamflow. In all runs, a quota of a little more than 100 mm on maximum water usage is necessary to decrease the violation of streamflow to 20% or less. To match the COM's average yearly basin-wide profit of 120.3 trillion rials, a quota of a little more than 200 mm or more is necessary. However, this results in a little more than 39% violation of streamflow. The third row displays the results of MASS with tax (a). Increasing the tax from 1 to 5 million rials per m³ does not result in any advantages for reducing the violation of streamflow and agent profits. The violation of streamflow experiences a significant decline when the tax ranges from 5 to 11 million rials per m³ because many agents stopping pumping. A tax exceeding a little more than 9 million rials per m³ is necessary to decrease the violation of streamflow to below 20%. To achieve the same, average annual benefit as the COM, a tax of a little less than 9 million rials per m³ or less is necessary. However, this results in a minimum violation of streamflow of a little more than 26%. The fourth row displays the results of MASS with tax (b). It is not feasible to maintain low violation of streamflow without decreasing the profits of the agent using this formulation. Increasing the tax from 1 to 5 million rials per m³ does not result in any advantages for reducing the violation of streamflow. Instead, it only leads to a decrease in agent profits. The violation of streamflow experiences a significant decline when the tax ranges from 5 to 11 million rials per m³ due to the presence of numerous agents stop pumping. In this scenario, only the most skilled agents utilize water. A tax exceeding a little more than 9 million rials per m³ is necessary to decrease the violation of streamflow to below 20%. At this tax rate, the average annual benefit is not substantially declined. To achieve the same average annual benefit as the COM, a tax of a little less than 3 million rials per m³ or less is necessary. However, this outcome at a minimum the violation of streamflow of a little more than 88%. The violation of streamflow is most significantly influenced by the variability in farmer productivity.

The literature suggests that the consistent water usage quota and consistent water usage tax possess certain benefits (Pistón et al. 2009; Valle-García et al. 2024). However, the method of modeling used in this study, which combined a groundwater model that considers physical properties and includes heterogeneous agents with varying characteristics, shows that these approaches are more complex than previously thought when applied in practice. The paper suggests that the quota is more resilient and effective than tax. It's worth noting that these findings do not account for precipitation fluctuations, which might be the scenario where the tax operates more effectively. For example, in periods of prolonged aridity, agents could extract water up to the point of economic feasibility, unlike the imposed quota, which would restrict water use regardless of the climate condition. In summary, in the event that variability of climate was to be offered, the tax might become a more attractive alternative. The tax system, when not redistributed, generates a higher return in contrast to the quota, which leads to an equivalent reduction in streamflow. The study indicates that it is crucial to evaluate the appropriate policy prescription for a basin by examining the aquifer's physical depiction and the farmers' heterogeneity.

This paper does not consider numerous other feasible and noteworthy forms of groundwater management approaches such as subsidies for efficient irrigation technologies, a temporary prohibition on new well construction, exchangeable permits, geographically diverse quotas/taxes, adaptable policies, and voluntary limitations. According to most literature, a quota and trade program that provides incentives for managing groundwater use could lead to higher economic returns for irrigation in contrast to the current policy of a quota without trade provisions (Thompson et al. 2009). The text suggests that it would be a logical next step to evaluate each of these alternative policy configurations within the framework established in this paper, considering the outcome of examining data. The text shows that the literature agrees with our findings on two key points regarding the reallocation of tax revenues to the agents (Mulligan et al. 2014). First, the reallocation of a substantial portion of the revenues of tax must be redistributed back to the agents to render the tax choice feasible. Second, the text suggests that the quota system is probably the favored policy choice compared with the tax system. The reason for this is achieving homogeneous tax rates necessary to sufficiently mitigate the impacts on streamflow is likely politically unattainable due to their substantial size. As previously mentioned, introducing a varied tax could be adopted to enhance the feasibility of the tax system.

The study has some limitations that should be taken into account when interpreting the results. These limitations include: (1) presuming that the inputs and parameters of the model remain consistent over time, including productivity parameters, annual climate conditions, operational costs for farmers, and prices at which crops are sold; (2) the precision of numerical solvers for MODFLOW and the optimization algorithms; (3) disregarding the agents fixed costs; (4) employing a function of crop production that is linear; and (5) utilizing streamflow goals that are not connected to the genuine goals within the plain.

This study used a physically based model to evaluate four distinct strategies for the utilization of groundwater in the Ardabil plain aquifer. The COM was employed as a reference point for assessing mechanisms of policy in a world where complete understanding and anticipation are not available. The evaluation of the strategy involved using a behavior model of water utilization of heterogeneous farmers, coupled with a flow process model of heterogeneous groundwater. The policy assessment examined the consistent tax and the consistent quota. The outcomes indicated that these policies were not successful in comparison to the COM in a scenario where agents acted shortsightedly and neglected their impact on streamflow. Each management strategy was evaluated using two key metrics: the average annual benefit, which represents economic benefits, and the violation of streamflow, which represents environmental impact.

A tax of greater than 9 million rials per m³ is needed to decrease the violation of streamflow to fewer than 20%. However, a tax of such size caused the closure of almost all the agents. In evaluating the benefits (sum of the agent profits and tax), this turned into a more feasible choice. A water quota of a little more than 100 mm or less is needed to decrease the violation of streamflow to fewer than 20%. However, this led to a considerable decline in the average annual benefit and significantly decreased the basin's crop production. The study found that the following results were observed: (1) To examine policy instruments implemented in a groundwater plain, an intricate physical model was required. (2) The free-access MASS policy instrument, which assumed shortsighted and self-interested agents, led to notable reductions in streamflow and proved to be unsustainable. (3) The consistent tax policy instrument proved to be somewhat ineffective and necessitated the implementation of a redistribution program for its execution. (4) The consistent quota policy instrument performed more effectively than the tax when not redistributed; however, it needed a quota to such a minimal extent that agents were unable to satisfy their crop requirements for the extent of land dedicated to crops under their ownership. (5) The quota is a stronger and more resilient policy choice for decreasing the violation of streamflow than the tax.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.