Introduction

The world’s population has grown four times in the past century, exceeding seven billion now, which has increased global food demands exponentially1. This increase, in turn, has increased irrigated areas in many regions, and water resources are in danger of overuse and pollutant contamination2,3. As consumption rates increase every day, considering just the physical process of a hydrological system is not sufficient for effective water resources management. Efficient planning requires not only forecasting the hydrological situation4 but also understanding the cultural and social factors impacting the system5.

To investigate the interaction of hydrological system components when human behavior heavily influences it, socio-hydrological theories and frameworks have been introduced6. The different characteristics of humans lead to different responses within a water system, and various studies have focused on different aspects. Srinivasan7 developed a model that simulates the dynamic interplay between human activities and water systems. Their research emphasized the role of socio-economic factors, such as population growth, urban expansion, and governance, in shaping water demand and usage patterns. Du et al.8 investigated how collective behaviors, such as coordinated irrigation practices among farmers, can influence water resource sustainability. Additionally, Gonzales and Ajami9 applied social memory theories to understand how historical experiences with water scarcity impact water management strategies.

These studies underscore the importance of considering both the direct and indirect effects of human behavior on water systems. Roby et al.10 examined the cause-and-effect relationships between media coverage and public awareness of environmental issues, illustrating how societal perceptions can feed back into water management decisions.

As more than two-thirds of water consumption is in the agriculture sector, they are more susceptible to scarcities and prone to water struggles11. Agriculture is affected by both human and hydrological system responses, so using socio-hydrological concepts is necessary to better understand its dynamics. Farmers may behave based on their characteristics, such as age, financial dependency, education, and size of their farming land12. Each farmer, based on their social characteristics, assesses the water availability situation, different policies, and usage regulations differently and seeks different routes to maximize profits13, so the decisions they make have the power to impact the entire system, whether in the short or long term. This influence can vary greatly, making it crucial to carefully consider each decision’s potential effects.

The complexity of human-hydrological interactions in agricultural settings necessitates the use of advanced modeling approaches for effective water management. System dynamics and agent-based models (ABMs) have been used widely as socio-hydrological models to simulate the interactions between humans and water resources14. System dynamics, as a top-down approach, focuses on capturing the overall behavior and feedback loops within the entire socio-hydrological framework. This method requires a comprehensive understanding of the broader system, including the interconnections between human actions and water resources15. ABM is a bottom-up approach that models at a singular entity level. Each autonomous entity or agent tries to achieve its goals and adapt to situations based on its character heterogeneity16. These features enable ABMs to explore the behaviors of the system through interactions between agents. While ABMs face challenges in formulating agent behaviors and validating models due to limited real-world data15, recent studies have employed calibration techniques and sensitivity analyses to improve model reliability. Despite these challenges, ABMs have proven valuable in agricultural systems, capturing complex interactions that traditional models struggle to represent17.

Various studies have focused on optimizing water resource systems and maximizing benefits18,19, using simplified heuristics20, or survey-based approaches21. However, these methods often fail to capture the complexity of human decision-making, as noted by Levine et al.22, who argue that such simplified rules may not reflect the realities of real-world behavior. For instance, Di Baldassarre et al.23 demonstrated how societal responses to flood events create feedback loops, while Pataki et al.24 introduced a framework that integrates economic, governance, and decision-making factors in water system management. Jenkins et al.25 presented their research findings concerning a novel ABM designed to assess the complex interactions between various factors in the context of flooding. In a similar vein, Srinivasan7 proposed a model that simulated the dynamic interplay between human activities and water systems in India. The outcomes of this study indicated that urban households, when confronted with water shortages, tend to seek alternative water sources such as privately-owned wells. Consequently, this behavior renders them more vulnerable to water insecurities.

Within the realm of agricultural water management, several studies have endeavored to simulate farmer behaviors in response to different water supply systems. For instance, Elsawah et al.26 presented a methodology for integrating stakeholder knowledge into decision-making on complex socio-ecological systems. Their approach combines cognitive mapping with ABM, applied to viticulture irrigation in South Australia, to elicit, represent, and analyze stakeholder perceptions and decisions, highlighting the importance of understanding and incorporating stakeholder knowledge into formal simulation models for better water resource management. Farhadi et al.27 demonstrated how farmers modify their behaviors when utilizing groundwater supplies, particularly in light of government restrictions and regulations. Du et al.28 focused on exploring diverse irrigation strategies employed by farmers when facing water scarcity issues. Ohab-Yazdi and Ahmadi29 used an agent-based model in their research to demonstrate the effects of enhanced collaboration between the Regional Water Authority and other organizations, coupled with strengthened patrol teams. They concluded that these interactions can dramatically reduce illegal water extractions and help restore aquifer balance. Marvuglia et al.30 discuss the coupling of ABM with environmental Life Cycle Assessment (LCA) to simulate farming activities in Luxembourg, factoring in farmers’ risk tendencies and their social network interactions, which influence long-term agricultural decisions and environmental impacts​.

A noteworthy study by Javan Salehi and Shourian31 integrates the Soil and Water Assessment Tool (SWAT) and MODFLOW to assess the socio-hydrological systems surrounding Lake Urmia in Iran. In this study, they utilized the Value-Belief-Norm Theory to identify factors that influence farmers’ water use behaviors under the pressures of climate change. Their findings reveal that climate change may push financially disadvantaged farmers towards cultivating more water-intensive crops, further diminishing Lake Urmia’s already critical water levels. This shift in farming practices among low-income farmers is a direct response to economic pressures, as these crops tend to offer higher financial returns despite their water demands. The study emphasizes the need for adaptive policy measures that address these economic drivers while also considering the psychological and social factors influencing farmers’ decisions. Such policies can mitigate adverse environmental impacts while simultaneously supporting local farmers’ livelihoods.

Most studies on agent-based modeling focus on interactions among consumer agents (households, farmers), with fewer integrating government or policymaker agents. The involvement of government agents in these models is predominantly centered around financial transactions with consumer agents, such as insurance policies, subsidies, loans, and related matters. However, in regions characterized by arid climates and recurrent water shortages, water allocation policies (e.g., reservoir operation policy) might assume greater significance than purely financial considerations15,32. Bithell and Brasington33 developed a coupled modeling system that integrates an agent-based model of subsistence farming, an individual-based model of forest dynamics, and a spatially explicit hydrological model. This system is designed to explore the effects of demographic changes, deforestation, and their combined impact on water availability and forest ecology. Berger and Troost34 explored the implications of different policies, such as the construction of new reservoirs to expand irrigation areas and the adoption of advanced irrigation technologies, on farmers using an Agent-Based model. Their study revealed that employing a multi-agent system in conjunction with simulations enhances our comprehension of the outcomes associated with various policies. In contrast, Berbel and Mateos35 investigated the impact of introducing modern irrigation systems without taking into account other policy measures, such as water pricing and limitations on land expansion. Their findings highlighted the potential occurrence of a rebound effect15 when farmers are not subject to complementary policies. The rebound effect happens when farmers incorporate various water-saving measures to reduce agricultural water demand; however, they get motivated to expand their farming and thus increase water demand.

Some studies have highlighted the crucial role of operational policies implemented by decision-makers, such as reservoir operators. Sakomoto and Salewicz36 demonstrated how the implementation of different operational policies by a reservoir operator can significantly influence farmers’ behavior. Notably, their study assumed that both stakeholders, namely the reservoir operator and the farmers, may misrepresent their respective situations, including available water resources and water demands. Nouri et al.37 propose an ABM framework for optimal cropping patterns to aid groundwater recovery, incorporating fuzzy inference systems for agents’ behavioral simulation and evaluating the effects of government policies on aquifer levels and farmers’ incomes. Their study showed that policy interventions can effectively influence farmers’ behaviors towards more sustainable water use practices, and carefully designed cropping patterns and policy measures can stabilize farmers’ incomes even under various hydrological scenarios. Dziubanski et al.38 examined the influence of urban agents on farmers, particularly in relation to land conversion decisions. The results indicated that farmers’ choices are primarily driven by crop prices rather than the subsidies offered by urban agents to encourage land conversion.

Most of the studies cited regarding farmer behaviors with agent-based modeling do not consider reservoir operation or have used Standard Operation Policy (SOP) and have not compared the farmer agents’ decision-making changes under different schemes7,20,38,39. While it is reported in practice and found out across previous studies that engaging with farmers and offering them monetary incentives or educating them have resulted in farmers changing their decisions to a more desirable one (from the perspective of water management planers), the effects of different allocation schemes are not explored to this extent15.

Despite the progress in socio-hydrological modeling, a critical gap remains in understanding how different water allocation strategies indirectly influence farmers’ decisions. Additionally, agent-based modeling studies often overlook the comprehensive interactions within a large-scale water allocation framework, particularly those involving multiple competing demands beyond agriculture. This gap is significant because understanding the effects of allocation policy and the responses of heterogeneous agents within an integrated water resources management system is essential for effective and sustainable planning. To address this gap, the present study considers a more indirect form of interaction between policymakers and farmers. In this approach, policymakers influence farmers through reservoir operation policies rather than through direct interaction. By adjusting water allocation strategies, such as implementing the hedging rule, policymakers indirectly affect farmers’ decisions on land use and irrigation technology adoption without direct communication or interventions. This indirect approach is critical in areas experiencing frequent water shortages, where water planners must prioritize demands to conserve water for future essential needs40. Moreover, most studies model agent behaviors and water allocation in isolation and do not consider different priorities and needs not engaged in the agent-based model itself. For instance, Tamburino et al.41 ABM study focused on water management for irrigation and crop yield within a smallholder farming system and didn’t take into account other demands in the area of study besides farming. The present study aims to examine how farmers’ agents act when they are faced with different strategies of a reservoir operation and how their characteristics impact their decisions. To achieve this, two models are constructed and linked to each other. The first model is a network flow-based model to simulate the water allocation to different urban, industrial, and agricultural demands in a large river basin. The network flow model is designed by the MODSIM-DSS software, and it includes a large reservoir to regulate the water supply and several consumption nodes. Developed by Labadie42. MODSIM-DSS uses network flow programming to model the distribution of water within a river basin, taking into account physical, hydrological, and operational constraints. The system incorporates a network of nodes and links, where ‘nodes’ represent key points of water consumption or demand and ‘links’ represent the pathways through which water is conveyed.

The second model is an agent-based model to simulate the farmer agents’ behaviors and decisions. Each farmer agent, modeled as an autonomous entity, decides on land use and irrigation practices based on personal characteristics like age, education, and risk-taking propensity. The farmer agents simulated are among the demand nodes. The reservoir operator agent can also use different strategies. The network flow model would allocate water to farmers simulated in the agent-based model while considering the needs and priorities across the region. The change in reservoir policy affects not only the simulated farmers but also all other demanding nodes.

The application of agent-based modeling within a large-scale water allocation system, such as MODSIM-DSS, is a novel approach presented in this study. In this study, we aim to establish a framework that incorporates social models to represent diverse farmer behaviors and domestic water demands. By simulating these dynamics, we seek to test and predict how different policy scenarios might influence water use and decision-making. Such models are undoubtedly valuable tools for water managers in practice, aiding in the decision-making process and the sustainable management of water resources.

In this research, farmers decide and plan to maximize their benefits based on their socioeconomic heterogeneity. They retain memory and share their experience with each other, and in turn, affect the other farmer agent’s decisions. Through this approach, the designed model tries to mirror real-life relations and dynamics. Throughout the simulation period, farmer agents can decide their land-use area and whether they want to upgrade from traditional irrigation methods to a modern irrigation system.

Methodology

The Zayandehroud basin in Isfahan province in the center of Iran is chosen as the case in the present study. This basin, with an area of 41,500 km2, experiences one of the lowest rainfall values each year in the region. The location of the watershed in the state and country is shown in Fig. 1. The Borkhar Plain, located in the Zayandehroud basin in Isfahan Province, Iran, is a significant agricultural region selected for modeling in this study. The plain experiences an arid to semi-arid climate with average annual temperatures ranging from 16 to 18 degrees Celsius, extreme summer highs exceeding 40 degrees Celsius, and winter lows reaching − 5 degrees Celsius. The region receives low annual rainfall of 100–150 mm, predominantly during winter and spring, and suffers from generally low relative humidity, especially in the summer months. Commonly cultivated crops include wheat, barley, vegetables like lettuce and tomatoes, and medicinal plants such as saffron and rose.

Fig. 1
figure 1

Location of the Borkhar plain in the Zayandehroud basin in Iran.

Full size image

In addition to farming plains, there are major municipal, rural, and industrial demands in the region, and water allocation is a significant concern for governing entities. The water shortages the region faces spark unrest and struggles between various stakeholders43.

The main purpose of this research is to investigate how farmer agents react to different strategies and regulations that a government agent imposes. Government agent allocates water under different rules and situations, and this would affect farmer agents’ decisions during the simulation. To model the farmer agents’ behaviors, several agent-based techniques are employed that are presented in detail in the following sections. To determine the risk-taking factor which is essential in modeling farmer agents’ behaviors, their age and income dependency are taken into account39,44,45,46,47. The monthly water demand of each farmer is calculated with the hydrologic balance equation according to the studied area and crop characteristics, and farmer agents declare their demand at the beginning of each month to the system. The water allocation problem is solved with network flow programming in MODSIM-DSS.

Irrigation and water demand formulation

Six of the most cultivated crops in the Borkhar plain are selected for the modeling purposes of this study: wheat, barley, sunflower, sorghum, alfalfa, and sugar beet. To simplify the model, each farmer agent only cultivates one crop and does not change it during the simulation. Each farmer has a specified farmland area and decides what percentage of their land will be cultivated each year. The water demand per unit area of each crop is calculated with water balance equations48:

$$\:RZD\left(c\right)\times\:(z\left(c,t+1\right)-z\left(c,t\right))=NW\left(c,t\right)+ER\left(t\right)-{E}_{a}\left(c,t\right)-RF(c,t)\:$$
(1)

Total amount of water demand per farmer is calculated with:

$$\:WD\left(f,t\right)=NW\left(c,t\right)\times\:\frac{1}{{e}_{i}\left(f\right)}\times\:LU\left(f,T\right)\times\:A\left(f\right)\:$$
(2)

where, RZD is the depth of the root zone (water holding capacity), z is the monthly soil moisture content in the root zone as a percentage of the root depth, \(\:ER\) is the effective monthly rainfall, \(\:{E}_{a}\) is actual values for evapotranspiration and \(\:RF\) is the volume of runoff that leaves crop root zone. WD is a farmer’s water demand for time step (month), NW is net water demand of crop, ei is irrigation efficiency, LU is the percentage of the land the farmer has decided to cultivate, A is the total available area a farmer owns. Indices f, t, c, and T are for individual farmer, monthly time step, crop, and yearly time step, respectively. As there might be water shortages during the simulation, the actual crop yield when water-stressed should be calculated49.

$$\:1-\frac{{Y}_{a}\left(c\right)}{{Y}_{p}\left(c\right)}=K\left(c,t\right)\times\:(1-\frac{{E}_{a}\left(c\right)}{{E}_{p}\left(c\right)})$$
(3)

The ratio between actual/potential evapotranspiration and available/required water can be considered approximately equal50:

$$\:\frac{{E}_{a}\left(c\right)}{{E}_{p}\left(c\right)}\approx\:\:\frac{{W}_{a}\left(c\right)}{{W}_{r}\left(c\right)}\:$$
(4)

where, Ya and Yp are actual and potential yield, Ea and Ep are actual and potential evapotranspiration, Wa and Wr are available and required water for crops and K is yield response factor. The profits for each farmer are calculated using the following Eq. 

$$\:Profit\left(f\right)=\left({Y}_{a}\times\:LU\left(f,T\right)\times\:A\left(f\right)\times\:P\left(c\right)\right)-\left(C\left(c\right)\times\:LU\left(f,T\right)\times\:A\left(f\right)\right)$$
(5)

where, P and C are selling price and cultivation cost for each crop per area unit respectively.

Agent-based model

Farmers’ decision making process

In this research, agent farmers are characterized through three important metrics: their age, income independence in agriculture, and their level of education. The general theories for simulation of the farmers’ social behavior used in the agent-based model are based on the work of Aghazadeh et al.39, and necessary modifications are implemented to accommodate the needs of this research project. It has been reported in various studies that these factors can affect farmers’ decisions51,52,53. To determine a risk-taking factor, farmers’ age and income dependency are used and calculated with the following equation51:

$$\:\alpha\:\left(f\right)=\frac{\sqrt{{\left(80-Age\left(f\right)\right)}^{2}+{\left(100-ID\left(f\right)\right)}^{2}}}{\sqrt{{\left(80-20\right)}^{2}+{\left(100\right)}^{2}}}$$
(6)

where, Age is the age of each farmer ranging from 20 to 80, ID is each farmer’s income dependency ranging from 0 to 100% and \(\:\alpha\:\) is risk-taking factor calculated in a range of zero to one. The aforementioned characteristics are assumed fixed during simulation to simplify the model. As it can be gathered from the equation, a 20 years old farmer with zero income independence would be considered the highest risk-taker. For the simulation, 18 agent farmers are considered, and their age (Mean = 50, Standard Deviation = 15) and ID (Mean = 50, Standard Deviation = 25) are randomly generated with a normal distribution. The education level is randomly generated with a uniform distribution. For the simulation, 24 agent farmers are randomly generated, and they are divided into six groups based on the crop they are cultivating: wheat, barley, sunflower, sorghum, alfalfa, and sugar beet. Each crop’s farming land is divided equally among four farmer agents. Different farmers and their characteristics in each farming group and the calculated risk factor (\(\:\alpha\:)\) are presented in Table 1.

$$\:Farmer\:number:$$
$$\:\left|\begin{array}{cc}Age&\:Income\:dependency\\\:Education\:level&\:Risk\:factor\end{array}\right|$$
Table 1 Farmer agents in each crop farming group and their characteristics
Full size table

Each farmer agent owns a specific amount of land and, at the beginning of each year, decides how much of their land should be cultivated. This is one of the two decisions being investigated in this study. Farmer agents are considered cognitive, processing data and information for their decisions to maximize their profits. They compare and analyze what has happened to them and their neighbors previously and how much of their land should be cultivated in order to maximize the profits. So, there are no obligations for them to be water savers, but the formalization of the social behavior in the following sections mimics how an individual farmer would like to avoid cultivating his land without getting the water they need. In other words, the farmers may waste money by plowing and sowing most of their land without sufficient water to reap the benefits. To simulate these types of information analysis and decision making, the first four parameters are calculated for each farmer agent.

$$\:{P}_{1}\left(f,T\right)=sgn(\text{m}\text{a}\text{x}(0,\frac{Profit(f,T-1)}{(\sum\:_{f}^{Nf}Profit(f,T-1))/Nf}$$
(7)
$$\:{P}_{2}\left(f,T\right)=sgn(\text{m}\text{a}\text{x}(0,\frac{\sum\:_{i=T-6}^{T-1}Profit(f,i)}{(\sum\:_{f=1}^{Nf}Profit(f,T-1))/Nf}$$
(8)
$$\:{P}_{3}\left(f,T\right)=sgn(\text{m}\text{a}\text{x}(0,\frac{{W}_{a}(f,T-1)/{W}_{r}(f,T-1)}{\left(\sum\:_{i=T-6}^{T-1}\frac{{W}_{a}\left(f,i\right)}{{W}_{r}\left(f,i\right)}\right)/5}$$
(9)
$$\:{P}_{4}\left(T\right)=sgn(\text{m}\text{a}\text{x}(0,\frac{\sum\:_{f=1}^{Nf}\frac{{W}_{a}\left(f,T-1\right)}{{W}_{r}\left(f,T-1\right)})\:}{\sum\:_{i=T-6}^{T-1}\sum\:_{f=1}^{Nf}\frac{{W}_{a}\left(f,i\right)}{{W}_{r}\left(f,i\right)})}$$
(10)

In Eq. (7) to (10), Nf is the number of farmer agents. The rest of the parameters have been explained before. With P1 and P2, farmer agents compare their short and long-term profits against those of other farmers and this effectively influences future economic decisions. Parameters P3 and P4 simulate farmer agents reaction to the operator agent’s decision and water availability condition. A summation of the parameters Pi is calculated for farmers, and a β parameter is calculated based on ∑P and risk factor α, which is reflective of a farmer’s perception of the existing condition and available water for them in the coming year13.

$$\:\sum\:P\left(f,T\right)={P}_{1}\left(f,T\right)+{P}_{2}\left(f,T\right)+{P}_{3}\left(f,T\right)+{P}_{4}\left(T\right)$$
(11)
$$\:\beta\:\left(f,T\right)=\left\{\begin{array}{c}\alpha\:\left(f\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\sum\:P\left(f,T\right)=4\:\\\:\alpha\:\left(f\right)-0.3\:\:\:\:\:\:\:\:\:\:\:\:if\:\sum\:P\left(f,T\right)=3\:\\\:\alpha\:\left(f\right)-0.5\:\:\:\:\:\:\:\:\:\:\:\:if\:\sum\:P\left(f,T\right)=2\:\\\:\alpha\:\left(f\right)-0.7\:\:\:\:\:\:\:\:\:\:\:\:if\:\sum\:P\left(f,T\right)=1\:\\\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\sum\:P\left(f,T\right)=0\:\end{array}\right.$$
(12)

\(\:\beta\:\) is the violation rate, which indicates a farmer’s presumption of the water available to him in the coming year. With \(\:\beta\:\) calculated, each farmer decides how much of their land should be cultivated in the next year. They take into account how much water was available to them in the previous year and their violation rate (\(\:\beta\:\)).

$$\:LU\left(f,T+1\right)=\frac{{w}_{a}\left(T\right)}{{w}_{r}\left(T\right)}\times\:\left(1+\:\beta\:\left(f,T\right)\right)\times\:LU(f,T)$$
(13)

Land-use factor indicates how much of their land each farmer would cultivate in the coming year, and based on this, calculates a water demand and declares it to the system and operator agent.

Irrigation method

For the sake of simplification, all the farmer agents are assumed to use a traditional, not efficient, irrigation technology (surface irrigation) at the start of the simulation. In the simulation of water demands and cultivation calculations, the traditional irrigation efficiency is considered to be 0.35. Throughout the simulation, farmer agents face different levels of water shortages based on their own decisions, the hydrological conditions, and the operator agent’s strategies. As farmer agents face water stress during various stages of cultivation, they begin to search for ways to alleviate this water stress. One of the ways farmers can do this effectively is by changing their irrigation technology. Modern irrigation technology (drip irrigation) can increase efficiency to 0.854, so farmer agents adopting this new technology can cultivate more crops in water shortage conditions. This adaptation happens in multiple stages.

The first stage in the adoption of modern irrigation technology is acquiring knowledge. This stage involves simulating conditions that would convince a farmer agent to seek information about modern irrigation technology. The conditions that would trigger this knowledge-seeking state in farmer agents are based on the water stress experienced by the farmer, the level of education, and the farmer agent’s risk factor. Farmers who experience water stress are more likely to seek information about modern irrigation technology as they are looking for ways to improve their crop yields. Education is another factor that can affect a farmer’s willingness to seek information about modern irrigation technology. Farmers with higher education are more likely to be aware of the benefits of modern irrigation technology and to be able to understand the information that is available. They are also more likely to be able to afford the cost of modern irrigation technology. Farmers with a higher risk factor are more likely to be willing to take risks. They are also more likely to be motivated to find ways to improve their crop yields, even if it means taking on some financial or operational risks.

A farmer with higher education and a risk-taking factor is more prone to seek information about modern technologies when facing lower water stress levels. This is because they are more aware of the benefits of modern irrigation technology and are more willing to take on the risks associated with adopting it.

The conditions that would trigger a knowledge-seeking state are formulated as follows39:

$$\:AD=\:\frac{\sum\:_{t=T-6}^{T-1}Def\left(T\right)}{6}$$
(14)
$$\:Knowledge\left(f,T\right)=\left\{\begin{array}{c}trigger\:if\:AD\ge\:0.30\:,\:\:0\le\:\alpha\:\left(f\right)\le\:0.3,\:\:Edu\left(f\right)=high\\\:\:\:\:\\\:trigger\:if\:AD\ge\:0.25\:,\:\:0.3\le\:\alpha\:\left(f\right)\le\:0.5,\:\:Edu\left(f\right)=high\\\:\:\\\:trigger\:if\:AD\ge\:0.20\:,\:\:0.5\le\:\alpha\:\left(f\right)\le\:0.7,\:\:Edu\left(f\right)=high\\\:\:\:\\\:trigger\:if\:AD\ge\:0.15\:,\:\:0.7\le\:\alpha\:\left(f\right)\le\:1,\:\:Edu\left(f\right)=high\\\:\:\:\:\\\:trigger\:if\:AD\ge\:0.35\:,\:\:0\le\:\alpha\:\left(f\right)\le\:0.3,\:\:Edu\left(f\right)=low\\\:\:\:\:\:\:\:\\\:trigger\:if\:AD\ge\:0.30\:,\:\:0.3\le\:\alpha\:\left(f\right)\le\:0.5,\:\:Edu\left(f\right)=low\\\:\:\:\:\:\:\\\:trigger\:if\:AD\ge\:0.25\:,\:\:0.5\le\:\alpha\:\left(f\right)\le\:0.7,\:\:Edu\left(f\right)=low\\\:\\\:trigger\:if\:AD\ge\:0.20\:,\:\:0.7\le\:\alpha\:\left(f\right)\le\:1,\:\:Edu\left(f\right)=low\\\:\:\:\\\:do{n}^{{\prime\:}}t\:trigger\:if\:else\end{array}\:\right.$$
(15)

In the above equations, AD is the average deficit experienced by the farmer in the last five years and the Def is the amount of water deficit or shortage. In the next step, if the farmer agent is triggered to gain knowledge, the personal opinion of each farmer is simulated. As different characters can look at innovations and technologies differently, it is imperative to take into account these personal views and simulate how they may affect other farmer agents. Farmers with higher education, income, and risk-taking factor are more sympathetic to newer technology45,46. To simulate this personal view based upon farmer characteristics, the following formulation is used.

$$\:POV\left(f\right)=\left\{\begin{array}{c}-0.5\:\:\:\:\:\:if\:\:\:\:0\le\:\alpha\:\left(f\right)\le\:0.3\:,\:\:Edu\left(f\right)=high\:\:\\\:0\:\:\:\:\:\:if\:\:\:\:0.3\le\:\alpha\:\left(f\right)\le\:0.5\:,\:\:Edu\left(f\right)=high\\\:+0.5\:\:\:\:\:\:if\:\:\:\:0.5\le\:\alpha\:\left(f\right)\le\:0.7\:,\:\:Edu\left(f\right)=high\\\:+1\:\:\:\:\:\:if\:\:\:\:0.7\le\:\alpha\:\left(f\right)\le\:1\:,\:\:Edu\left(f\right)=high\\\:-1\:\:\:\:\:\:if\:\:\:\:0\le\:\alpha\:\left(f\right)\le\:0.3\:,\:\:Edu\left(f\right)=low\\\:-0.5\:\:\:\:\:\:if\:\:\:\:0.3\le\:\alpha\:\left(f\right)\le\:0.5\:,\:\:Edu\left(f\right)=low\\\:0\:\:\:\:\:\:if\:\:\:\:0.5\le\:\alpha\:\left(f\right)\le\:0.7\:,\:\:Edu\left(f\right)=low\\\:+0.5\:\:\:\:\:\:if\:\:\:\:0.7\le\:\alpha\:\left(f\right)\le\:1\:,\:\:Edu\left(f\right)=low\\\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:else\\\:\end{array}\right.$$
(16)

where, POV is point of view of each farmer agent in regards to new irrigation technology. The impact of the various simulated POVs is calculated.

$$\:SigPOV=\:\sum\:_{f=1}^{Nf}POV\left(f\right)$$
(17)

Regardless of their personal views regarding new irrigation technologies, farmer agents that have adopted the innovation can have satisfaction with their decision or not. These farmers and whether they are happy or not can impact the decision of other farmer agents. To simulate this process, the following equations are used.

$$\:Satisfaction\left(f\right)=\left\{\begin{array}{c}+1\:\:\:\:if\:\:\:\:\frac{Def\left(f,T-1\right)-Def\left(f,T\right)}{Def\left(f,T-1\right)}\ge\:0.1\:,\:\:\:{e}_{i}\left(f\right)=0.8+\\\:-1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:else\end{array}\right.$$
(18)
$$\:SigSatisfaction=\:\sum\:_{f=1}^{Nf}Satisfaction\left(f\right)$$
(19)

With all the impacting factors calculated, the decision of the farmer agent regarding adopting a new irrigation technology can be simulated with the following Eq. 

$$\:Decision\left(f\right)=18\times\:POV\left(f\right)+2\times\:SigPov+SigSatisfaction\:\:$$
(20)
$$\:New\:Irrigiation\:System\:\left(f\right)\:=\left\{\begin{array}{c}Adopt\:\:\:\:if\:\:\:\:Decision\left(f\right)>0\\\:Reject\:\:\:if\:\:\:\:Decision\left(f\right)\le\:0\end{array}\right.$$
(21)

Through these steps, a farmer agent decides if they want to adopt the new irrigation technology to increase their efficiency from 0.35 to 0.8. The simulation is based on the farmer agents’ characteristics, and they will affect the other farmers’ decisions. It is important to simulate how the operator agent’s different strategies can influence the more conservative farmers to adopt the new technology.

Reservoir operator agent

The operator agent in this research is the dam operator, who controls the amount of water released from the reservoir at each time step (monthly release) and how much each demand node receives. The operator agent can assume different strategies when controlling the reservoir, and these various strategies can affect farmer agents’ behaviors. The ideal farmer behavior in the POV of the government or operator agent is that farmers would cultivate more of their land and switch to new irrigation technology. It is clear that adopting new irrigation technology would increase efficiency, and farmers can cultivate more crops for the same amount of water. As a farmer’s decision regarding the amount of land to use in the coming year is a form of prediction based on the previous time frame, this should be affected by the operator agent’s policies.

If a strategy can reduce the severity of water shortages in some time steps, this can lead to increased average land use of farmer agents, or at least decrease the fluctuations in land use and thus profits. Severe fluctuations in land use and profits would increase uncertainty for farmers, and this would be devastating, in particular for farmers who have a higher dependency on farming income. The strategies investigated in this paper are Standard Operation Policy (SOP) and Hedging Rules, and they are explained in the following sections.

Standard operation policy

In the Standard Operation Policy (SOP), the only objective of the operator agent is to meet the downstream demand as well as possible. Water would be released at each time step to fulfill the demand or reach the reservoir’s minimum capacity. If all downstream demand has been supplied, the surplus water would be stored in the reservoir. If the reservoir has reached its maximum capacity, the water would be released as a downstream overflow. In SOP, the optimum solution for release is not the objective. It is a simple policy to meet the demand at all times possible. This strategy can be formulated as follows:

$$\:RWB=\left\{\begin{array}{c}{R}_{t}={S}_{t}+{I}_{t}-{E}_{t}+{P}_{t}-{S}_{min}\:;\:{S}_{t+1}={S}_{min}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\:\:\:\:\:\:{S}_{t}+{I}_{t}-{E}_{t}+{P}_{t}<{S}_{min}+{D}_{t}\\\:{R}_{t}={S}_{t}+{I}_{t}-{E}_{t}+{P}_{t}-{S}_{max}\:;\:{S}_{t+1}={S}_{max}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\:\:\:\:\:\:{S}_{t}+{I}_{t}-{E}_{t}+{P}_{t}>{S}_{max}+{D}_{t}\\\:{S}_{t+1}={S}_{t}+{I}_{t}-{E}_{t}+{P}_{t}-{R}_{t}\:;\:{R}_{t}={D}_{t}\:\:\:\:\:\:\:\:\:\:\:\:\:if\:\:\:\:\:{S}_{min}+{D}_{t}\le\:\:{S}_{t}+{I}_{t}-{E}_{t}+{P}_{t}\le\:{S}_{max}+{D}_{t}\end{array}\right.$$
(22)

where, RWB is the reservoir water balance function, I, R, D, E, T are inflow, release, demand, evaporation and precipitation on the reservoir respectively. S, Smin, and Smax are reservoir storage values, minimum capacity, and maximum capacity. The parameter t denotes the time step (month). The model in this scheme is calibrated in a way that storage has the least priority, and all the demands are fulfilled before trying to store water in the reservoir. Also, there are no rule curves present in the model for this scheme for different storage releases based on the time of the year.

Hedging policy

The hedging rule theories are driven by finance and natural resources economics, which are usually employed. Reliability measures were used in reservoir operation, as it is rather difficult to calculate estimates of economic and social factors in many cases55. Hedging rules enable reservoir operators to introduce a few smaller shortages to the water system spread over time instead of a single period of severe shortage, which is known to be more damaging56. There are several forms of hedging rules introduced in various studies. A two-point linear hedging rule57 is shown in Fig. 2.

Fig. 2
figure 2

Two-point hedging rule scheme.

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The two-point hedging rule (solid line) replaces the SOP (dotted line) between these points, PA and PB, and outside this range, SOP operates. The x-axis represents available water during the period, meaning the sum of the current reservoir storage and the expected inflow, and the y-axis represents the release (for demands and potential spill). To implement the hedging rule scheme in MODSIM, the seasonal target storage and storage layering functionality of MODSIM is used. By denoting different priorities to layers of storage, the water storage and release in periods with a shortage or abundance of water can be controlled. This type of hedging rule enables maintaining a balanced water supply and allows operators to strategically introduce smaller, manageable shortages during times of abundance to ensure that water demands can still be met during low-flow periods58,59. Through strategic layering and prioritization of storage, impacts of severe shortages are minimized, and hedging rules prevent sudden catastrophic shortages and complete system failures60. For the watershed in this study, water availability period based on the historical flows to the reservoir was considered from the start of May until the end of December for each year, and the hedging rule was applied in that timeframe. This period also coincides with the typical irrigation season for the area.

Dynamic informed hedging policy

Forecast-Informed Reservoir Operations (FIRO) is an adaptive water management strategy that integrates advanced hydrological and meteorological forecasts into reservoir operation decision-making. By utilizing streamflow and precipitation forecasts, FIRO aims to enhance water supply reliability, flood risk reduction, and ecological resilience61. Studies have shown that FIRO can increase water supply reliability while maintaining flood control capabilities62. Forecasts can enhance the effectiveness of hedging policies by providing real-time or forecast-based triggers for initiating hedging actions63.

A dynamic informed hedging rule was developed to enhance reservoir operation by incorporating historical inflow data and forecasted hydrological conditions. Probability distributions of historical inflows were analyzed to characterize baseline hydrological patterns and subsequently used to classify the incoming year as dry, normal, or wet based on observed inflows at the start of the year in order to mimic forecasts available for the reservoir operator. These probability distributions were then utilized to dynamically adjust the hedging strategy across different months, allowing reservoir operations to align with seasonal inflow variability and anticipated water availability. Operational parameters, including storage layer values, their priority levels, and the timing of hedging, were adaptively modified in response to the hydrological condition of each month. This dynamic approach ensured water conservation during anticipated dry periods while maximizing storage and releases during wetter conditions.

River basin simulation model

MODSIM is a river basin management decision support system (DSS) developed by Labadie42. The idea behind MODSIM is that water resources systems can be simulated as flow networks and utilize network flow programming (NFP) for water allocation while considering various aspects of river basin management like hydrological, physical, and operational policies64. As mass balance dictates in the network, MODSIM uses an efficient minimum cost NFP to sequentially solve the following linear optimization problem65:

$$\:Minimize{\sum\:}_{l\in\:A}{c}_{l}{q}_{l}$$
(23)

Subject to:

$$\:{\sum\:}_{j\in\:{O}_{i}}{q}_{j}-{\sum\:}_{k\in\:{I}_{i}}{q}_{k}=0\:\:for\:all\:i\in\:N$$
(24)
$$\:{l}_{l}\le\:{q}_{l}\le\:{u}_{l}\:\:for\:all\:\:l\in\:A$$
(25)

In the above equations, A is the set of all arcs or links in the network; N is the set of all nodes; Oi is the set of all links originating at node i (i.e., outflow links); Ii is the set of all links terminating at node i (i.e., inflow links); ql is the integer valued flow rate, ll is the lower bound and ul is the upper bound on flow in link l; cl is the cost (i.e., negative benefits in the minimization form), weighting factors or priorities per unit of flow rate in link l. The database for the network optimization problem is completely defined by the link parameters for each link l: [ll, ul, cl], as well as the sets Oi, Ii, N, and A. The reservoir and various demand nodes and their connection, modeled in MODSIM, are depicted in Fig. 3. All the major consumptions located in the Zayandehroud basin are implemented in the model and are considered in the water allocation. Their demand values in each month and their priority are the features that the model uses to determine how much water to allocate to each consumption node every month. These data are collected from local water management offices. The model extends beyond agricultural considerations to encompass the urban landscape, incorporating municipal and industrial water demands for several key cities within the basin, namely Kashan, Yazd, Ardakan, Naeen, and Isfahan. Each city’s water requirement is explicitly defined within the model, allowing for a comprehensive analysis of the region’s water distribution. This holistic approach facilitates the assessment of water management strategies, balancing the complex interplay between agricultural needs, urban consumption, and industrial requirements within the Zayandehroud Basin. The model’s ability to simulate these demands and the dam’s operational influence is crucial for strategic planning and sustainable water resource management in the region. In the Zayandehroud Basin, surface water has become the main source for meeting various water demands due to the severe depletion of groundwater resources over the past decade. This shift is largely attributed to the excessive withdrawal of groundwater, which has led to a significant drop in the water table and the drying up of many pumping wells. It is important to note that the location of nodes depicted in MODSIM Gui is not relevant, and only the links show the actual connection between nodes.

Fig. 3
figure 3

The Zayandehroud basin and Borkhar plain modeled in MODSIM.

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One of the key features of MODSIM-DSS is the ability to use custom coding to access various variables and parameters at runtime. Using these custom coding capabilities, all of the agent-based calculations and simulations are scripted and controlled in the MODSIM software. Changing parameters outlined in previous sections are calculated in the runtime and modified during the simulation period without needing to be changed manually in the GUI. The MODSIM-based allocation model for the Zayandehroud watershed integrates both groundwater and surface water sources and has been calibrated over a 40-year simulation period. Recognizing the real-world water distribution hierarchy, we assigned the lowest priority to the Borkhar Plain in accordance with its actual water rights status. The selection of Borkhar Plain was strategic due to the availability of extensive farming data and its relevance as a water-stressed region. The model’s farmers are not direct representations of actual individuals but rather generalized agents reflecting the wider situation in Iran’s arid zones.

Figure 4 shows the simplified flow chart of the simulation process, which cycles through decisions made by farmer agents for land use and monthly demand calculations, as well as water allocation by the reservoir operator agent.

Fig. 4
figure 4

Flowchart of the modeling process.

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Results

A 20-year period is considered for the simulation, and intended factors are investigated during this time. Farmer agents need a memory so that they can start the decision-making process. The first five years (of the 20-year period) are not included in agent-based modeling as a warm-up period. So, in effect, farmer behaviors are monitored within the model for 15 years.

Irrigation technology adoption

The farmer agents’ risk-taking factors, their education level, and their irrigation efficiency at the end of the simulation using the SOP, hedging rule, and informed hedging rule schemes are presented in Fig. 5. Farmer agents with an efficiency of 0.8 have adopted modern irrigation technology. Under the SOP, only 37.5% of farmer agents transitioned to modern irrigation systems, highlighting the reluctance of farmers to adapt new irrigation infrastructure when facing unpredictable water supply. The adoption rate improved to 45.83% under the Hedging Rule, while the highest adoption rate, 62.5%, was observed under the Dynamic Informed Hedging Rule, indicating that informed, forecast-driven water allocation policies significantly enhance farmer confidence in adopting modern irrigation techniques. The analysis of farmer characteristics reveals that education level plays a significant role in irrigation adoption. Under SOP, 66.7% of the adopters had higher education levels, suggesting that awareness and understanding of long-term water efficiency benefits influence decision-making. However, under the Hedging Rule and Dynamic Informed Hedging Rule, adoption rates among farmers with lower education levels also increased, suggesting that different water allocation policies can also play a crucial role in driving irrigation technology adoption rates.

Fig. 5
figure 5

Farmer agents’ education level, risk factor, and irrigation efficiency at the end of each policy simulation.

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Results also indicate that the risk-taking factor has a significant impact on farmers’ decisions. Younger farmers with lower income dependency on farming tend to make more risky moves. Few outside influences can affect a farmer’s risk-taking factor. While a risk-averse farmer would reject innovations, a highly risking farmer might misjudge the situations and existing conditions, which might lead to some non-recoverable losses.

Land use decisions

Simulated land use factors (ranging from 0 to 1) and averages for each year of the simulation period under each policy are depicted in Fig. 6.

Fig. 6
figure 6

Farmer agents’ land use factor in each year under different policy simulations.

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While farmers tend to exhibit similar patterns (increasing or decreasing land use), there is noticeable variability in the severity of their decisions. Some farmers even make decisions that completely diverge, showing opposite trends. This behavior is observed in both high and low-risk-taking farmers, complicating the task of controlling and predicting their land-use decisions.

Figure 7 shows each farmer’s average land-use factor against their risk-taking factor under each policy. Under the SOP policy, farmers, particularly those with higher risk-taking tendencies, preferred maximizing land cultivation despite the uncertainty in water supply. The average land-use factor under SOP was 0.696, with noticeable fluctuations in land utilization across simulation years. This variability suggests that in the absence of strategic reservoir management, farmers tend to overestimate future water availability, leading to a cycle of expansion during wet years and contraction during dry years. In contrast, the Hedging Rule policy introduced a more structured water allocation framework, resulting in a decline in the average land-use factor to 0.636. The increased predictability in water availability encouraged more cautious decision-making, particularly among risk-averse farmers, who cultivated a smaller but more stable portion of their land. However, some variability persisted, indicating that while the hedging rule mitigates extreme fluctuations, it does not entirely eliminate the tendency of risk-prone farmers to expand cultivation when conditions seem favorable. The Dynamic Informed Hedging Rule further reduced land use, with the average land-use factor dropping to 0.540, the lowest among the three policies. This suggests that incorporating forecast-based policies significantly alters farmer behavior, encouraging more synchronized and conservative land use decisions. Farmers had greater confidence in the predictability of future water availability, leading to a more balanced and sustainable approach to cultivation. The Dynamic Informed Hedging Rule exhibited the highest degree of synchronization among farmers, as indicated by the high inter-farmer correlation in land-use decisions (R² = 0.813). This suggests that the policy fosters a well-coordinated and predictable response to water management challenges, significantly reducing variability and uncertainty in farmers’ land-use decisions.

Across all policies, there is a noticeable increasing trend in average land use with higher risk factors (\(\:\alpha\:\)), which can be inferred from the regression lines of each policy. This indicates that farmers with a higher propensity for risk tend to utilize more land, potentially driven by their willingness to invest in larger-scale operations despite uncertainties. The trend underscores the importance of understanding farmer behavior in designing policies, as risk-taking attitudes significantly influence land use patterns. Effective policy interventions may need to balance promoting sustainable land use while considering the diverse risk preferences of farmers.

Fig. 7
figure 7

Farmer agents’ risk factor and average land use factor in each policy simulation.

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Benefit/cost ratio analysis

Figure 8 shows the average Benefit/Cost Ratio for each farmer against their risk-taking factor. The benefit/cost ratio (BCR) is a key indicator of economic efficiency, especially in agricultural water management. A higher BCR suggests that the benefits derived from resource use significantly outweigh the associated costs (water usage, labor, and equipment). Policymakers rely on BCR analysis to evaluate resource-intensive practices’ sustainability and economic viability, particularly under scenarios of constrained water availability.

Fig. 8
figure 8

Farmer agents’ risk factor and average benefit/cost ratio (BCR) in each policy simulation.

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Across all policies, the average BCR remains relatively steady for each farmer, even as land and water use decrease from SOP to informed hedging rule. This is significant, as maintaining a stable BCR under reduced resource use reflects the efficiency of these policies in sustaining economic returns. The decrease in water usage and land utilization under the hedging and informed hedging rule policies highlights an improvement in resource allocation, ensuring decreased waste while maintaining profitability. The scatter plot and regression analysis show a clear trend: as the risk-taking factor increases, so does the average BCR. This is observed consistently across all policies. Farmers with higher \(\:\alpha\:\) values (risk-prone) appear to achieve better economic returns compared to more risk-averse farmers. This can be the result of Risk-prone farmers utilizing resources more aggressively to maximize yields. Figure 9 shows the heatmap of the BCR across the years for farmers under each policy.

Fig. 9
figure 9

Farmer agents’ risk factor and benefit/cost ratio (BCR) heatmap across the simulation in each policy.

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The color transitions indicate economic stability or instability, with more color variation signifying fluctuations in economic outcomes. Across all policies, the BCR values remain relatively steady for all farmers over the years, with minimal fluctuations, indicating a consistent economic performance. The SOP policy is the most stable, with minimal color variation, indicating highly consistent economic returns. The hedging rule introduces slightly more variation but remains mostly stable, with sparse shading shifts that reflect occasional, rather than frequent, adjustments. In contrast, the dynamic informed hedging rule shows more frequent but relatively subtle color changes, suggesting continuous but controlled adaptations in economic performance. While the hedging rule maintains steadier BCR values, the informed hedging rule allows for greater flexibility in resource use without causing extreme fluctuations. This variability likely stems from the tighter resource constraints introduced by the more advanced policy, which influences how resources are allocated to the farmers. The informed hedging rule, despite minor fluctuations, maintains economic resilience, demonstrating that adaptive resource allocation can optimize efficiency without significantly disrupting profitability. This highlights the potential for sustainable water and land-use policies that reduce waste while preserving economic viability as farmers adjust to achieve comparable economic results under more restrictive resource conditions.

Discussion

The first point that we can infer from the results is that high-risk farmers tend to cultivate more land, significantly under SOP, which can lead to overuse during periods of water abundance and increased vulnerability during shortages. In contrast, the hedging rule moderates farmers’ decisions, making their actions more predictable and reducing risky behavior. The dynamic informed hedging rule policy scheme fosters the most synchronized and efficient land-use behavior, highlighting the value of shared information in promoting coordinated responses to water management challenges. The Benefit/Cost Ratio (BCR) analysis highlights the economic efficiency of each water allocation strategy. Despite notable reductions in overall land and water use from SOP through to the dynamic informed hedging rule, the average BCR across farmers remains remarkably steady. This consistency suggests that more advanced water allocation policies, and the associated decrease in resource inputs, do not come at the expense of profitability. In fact, they appear to enhance the efficiency of agricultural operations. This stability is vital as the policies effectively sustain economic returns while reducing resource consumption. Risk-taking behavior emerged as a significant determinant of BCR, with higher-risk farmers achieving better economic returns by utilizing resources more aggressively. Education level and risk-taking behavior significantly affect the adoption of modern irrigation technology. Farmers with higher education levels are more likely to adopt efficient irrigation systems, particularly under hedging and hedging rule schemes. In the SOP scenario, only 37.5% of farmers adopted modern irrigation systems, with most adopters having high education levels. Under the hedging rule, the adoption rate increased to 45.83%, with all high-education farmers and some low-education farmers with higher risk-taking factors transitioning to modern technology. The informed hedging rule scheme resulted in the highest adoption rate (62.5%), with adoption extending across both education levels, underscoring the importance of combining informed decision-making frameworks with educational support to promote widespread adoption. The conjunctive use of water resource allocation models with the Agent-Based Modeling (ABM) approach allows us to have a more comprehensive and realistic view of water resource systems, supported by earlier studies66. Modifications in reservoir operations directly alter on-farm water availability, which in turn motivates farmers’ subsequent land use and technology adoption decisions. Over time, these decisions feed back into system-wide water demand, creating a cycle that may mitigate or exacerbate scarcity. By combining these approaches, the conjunctive model enables a more accurate representation of the social, economic, and behavioral aspects that influence water allocation decisions while allowing a deeper exploration of the feedback loops and interactions between physical water management policies and individual decision-making processes. Our findings reveal how the ABM component captures farmer responses to changes in water availability and policy interventions, which are crucial in arid and water-scarce regions. In particular, the success of the dynamic informed hedging rule in driving up modern irrigation adoption rates highlights the potential of incorporating seasonal forecasts and advanced reservoir operations into water allocation protocols. Water managers can mitigate the severity of consecutive dry periods by using hedging rule schemas67 and influence farmer decisions by changing the cycles of water availability and magnitudes of water scarcity.

Conclusion

This study explores how farmer characteristics, such as age, education level, and income dependency, influence their decisions on land use and irrigation technology, and how an operator can affect these decisions through agent-based modeling (ABM). Farmer agents, modeled as autonomous entities, make cultivation and technology adoption choices based on their risk-taking behavior and perceived conditions. The operator agent uses either a Standard Operating Policy (SOP) or a hedging rule for water allocation, impacting water availability over time.

The models were linked using MODSIM-DSS software to simulate the Zayandehroud basin in Iran, a region facing severe water scarcity. Farmer agents request water based on their needs, and the operator allocates it using the selected water management strategy. MODSIM-DSS provides a quantitative framework to simulate the physical aspects of water allocation, including reservoir operations, water demand, and supply dynamics. On the other hand, ABM captures the complex interactions and decision-making processes of individual agents within the system, such as farmers, policymakers, and water managers. By linking these behavioral responses with the water systems impacts simulated by MODSIM-DSS, the study provides insights into how water allocation strategies influence agricultural practices.

The results showed that high-risk farmers tend to use more land under SOP, leading to potentially unsustainable expansions during wet periods, while the hedging rules moderate and synchronize decision-making to improve efficiency and reduce resource waste. Despite declining land and water use from SOP to informed hedging, farmers’ economic returns (BCR) remain stable, with risk-takers generally earning higher returns, but they may face greater vulnerability. Education strongly influences modern irrigation technology adoption, while more advanced water allocation schemes (hedging and dynamic informed hedging) substantially raise irrigation technology adoption rates, especially among less-educated farmers, highlighting the value of coupling policy frameworks with educational support.

Furthermore, the proposed approach enhances scenario analysis and policy evaluation capabilities. By coupling the models, it becomes possible to assess the effectiveness of different water allocation policies, infrastructure investments, and management strategies under various socio-economic and climatic conditions. The ABM component enables the representation of diverse stakeholder perspectives, preferences, and decision-making criteria, which can inform the evaluation of policy trade-offs and the identification of robust and sustainable water allocation solutions. Overall, the conjunctive use of water resources allocation models, such as MODSIM-DSS, with the Agent-Based modeling approach offers a powerful toolset for understanding and managing complex water systems. It enables a more holistic and integrated assessment of water allocation dynamics, facilitates the exploration of feedback effects, and supports evidence-based decision-making for sustainable water resource management.