Application of Positive Mathematical Programming (PMP) in Sustainable Water Resource Management: A Case Study of Hetao Irrigation District, China

Abstract

Water scarcity and soil salinization pose significant challenges to sustainable agricultural development in arid and semi-arid regions globally. This study applies Positive Mathematical Programming (PMP) to analyze agricultural water resource management in the Hetao Irrigation District (HID), China. The research constructs a comprehensive multi-stress-factor integrated PMP model to evaluate the compound impacts of water resource constraints, pricing policies, and environmental stress on agricultural production systems. The model incorporates crop-specific salinity tolerance thresholds and simulates farmer decision-making behaviors under various scenarios including water supply reduction (0–100%), water pricing increases (0.2–1.0 CNY/m³), and soil salinity stress (0–10 dS/m). The results reveal that the agricultural system exhibits significant vulnerability characteristics with critical thresholds concentrated in the 60–70% water resource utilization interval. Water pricing policies show limited effectiveness in low-price ranges, with wheat demonstrating the highest price sensitivity (−23.8% elasticity). Crop salinity tolerance analysis indicates that wheat–sunflower rotation systems maintain an 85% planting proportion even under extreme salinity conditions (10 dS/m), significantly outperforming individual crops. The study proposes a hierarchical water resource quota allocation system based on vulnerability thresholds and recommends promoting salt-tolerant rotation systems to enhance agricultural resilience. These findings provide scientific evidence for sustainable water resource management and agricultural adaptation strategies in water-stressed regions, contributing to both theoretical advancement of the PMP methodology and practical policy formulation for irrigation districts facing similar challenges.

1. Introduction

Water scarcity has become one of the most pressing challenges facing the world in the 21st century. The global agricultural sector consumes approximately 70% of freshwater resources, with this proportion reaching as high as 95% in some developing countries [1]. Climate change has led to increasing frequency and severity of extreme weather events, further disrupting water supply and agricultural cycles, exacerbating water stress and threatening agricultural sustainability [2]. This challenge is particularly acute in global arid and semi-arid regions. Against this backdrop, arid and semi-arid regions have become focal areas for research on agricultural water resource planning and management optimization methods [3,4,5]. Scholars have applied agricultural economic models to optimize water resource allocation from multiple perspectives including hydrology, economics, technology, and policy, providing support for agricultural system decision-making in arid and semi-arid regions [6,7,8,9,10,11,12,13,14]. Among these approaches, Positive Mathematical Programming (PMP) has demonstrated good applicability in analyzing farmers’ responses to water pricing policies and evaluating the economic impacts of various water resource management policies [15,16,17,18,19,20,21].

Positive Mathematical Programming is a modeling method commonly used in agricultural economics, resource allocation simulation, and farmer behavior modeling, particularly suitable for research on irrigation districts, water resources, and crop structure optimization. The theoretical foundation of this method was established by Richard E. Howitt in 1995 [22], effectively addressing the problem that traditional linear programming could not accurately simulate farm production plans. With continuous methodological development, PMP has been refined and widely applied under different agricultural environmental policy contexts. Heckelei and Britz extended the PMP method, enhancing its flexibility and accuracy [23]. Mérel and Howitt systematically analyzed the theoretical and applied evolution of PMP, emphasizing its importance in bioeconomic models and policy analysis [24]. In practical applications, Jansson and Heckelei utilized the PMP method to estimate crop supply models in EU regions, providing data support for agricultural policy formulation [25]. Cortignani and Severini analyzed the adoption of water-saving irrigation at the farm level, demonstrating the application potential of PMP in water resource management [19].

In recent years, PMP has been used to assess the impacts of uncertainty and climate change on agricultural environment and policy. Ghaffari et al. considered the uncertainty of climate change and used PMP to analyze the economic impacts of drought on agriculture [26]. Mardani, Najafabadi et al. studied sustainable planting patterns in southern Iran, considering resource allocation and environmental constraints, providing recommendations for regional agricultural sustainable development [27]. Layani et al. combined PMP with system dynamics models to analyze the impact of government policies on agricultural environmental sustainability, emphasizing the potential of PMP in policy evaluation [28]. Randall et al. focused on crop planning optimization under climate change uncertainty, demonstrating the application of PMP in irrigation water resource management under uncertain conditions [29].

Despite significant progress in PMP method research for agricultural water resource management, existing studies still have several limitations. First, regarding regional applicability, existing PMP research has mainly concentrated on Europe and parts of the Middle East, with relatively few application studies in China’s northern arid and semi-arid irrigation districts. The climatic conditions, agricultural systems, and water resource management systems in these studies differ significantly from those in China’s HID. Second, regarding environmental-constraint-factor consideration, most existing studies primarily focus on water resource constraints and economic factors, but inadequately consider soil salinization, a key environmental constraint factor prevalent in arid and semi-arid irrigation districts. Third, regarding multiple stress factor analysis, existing studies often analyze individual stress factors separately, lacking comprehensive assessment of the interactive effects of multiple stress factors. Fourth, regarding crop rotation system modeling, although some studies involve crop selection optimization, the representation and optimization analysis of rotation systems in PMP models is relatively weak. Finally, regarding policy tool evaluation, existing studies mainly focus on water pricing policies, with relatively insufficient modeling and evaluation of other policy tools.

The Hetao Irrigation District (HID), located in the upper reaches of the Yellow River Basin in China, represents a typical example of the contradiction between water resource scarcity and food production in arid and semi-arid regions. The increasingly prominent contradiction between water resource shortage and intensive agricultural production brings complex challenges to local food security and economic development. This irrigation district is an important region for grain and cash crop production in northern China [30], with approximately 3 million tons of annual grain production relying on about 5 billion m³ of water diverted from the Yellow River annually, accounting for approximately one-sixth of the Yellow River’s transit flow. As competition for water resources intensifies among different water-using sectors including agriculture, industry, urban areas, and ecological environment, HID requires scientific agricultural water resource models to quantify the effects of water resource management policies.

Based on the above research on background and limitations of existing studies, this research aims to construct a multi-stress factor integrated PMP model applicable to HID, systematically analyzing the compound impacts of water resource constraints, pricing policies, and environmental stress on agricultural production systems. This study expects to provide scientific evidence and decision support for sustainable agricultural development and water resource management in HID and similar regions globally, while promoting theoretical development and practical application of the PMP method under complex environmental constraint conditions.

2. Materials and Methods

2.1. Study Area

HID is located in Bayannur City, Inner Mongolia Autonomous Region, China, representing one of China’s three mega-scale irrigation districts and a major production area for wheat, corn, and sunflower seeds in China [31]. The total irrigated area of the district is 769,300 ha, including 623,700 ha of Yellow River irrigation, 89,800 ha of combined well and Yellow River irrigation, and 55,900 ha of pure well irrigation [32]. Agricultural production in this region relies almost entirely on water diverted from the Yellow River, with agricultural irrigation accounting for 95% of the total water diverted from the Yellow River [33]. The irrigation district has a typical temperate continental arid and semi-arid climate. Annual average precipitation ranges from 130 to 210 mm, with 70% concentrated from July to September. Annual potential evaporation reaches 2100~2300 mm. Water scarcity and soil salinization are the main limiting factors constraining agricultural production in this irrigation district. Soil survey data show that 63.6% of the irrigated area in the district faces salinization problems, with mild salinization areas accounting for 45.5%, moderate salinization areas for 16.0%, and severe salinization areas for 3.1% [34]. The irrigation district consists of five sub-districts: Wulanbuhe, Jiefangzha, Yongji, Yichang, and Wulate (Figure 1). The district supports the livelihoods of 1.4 million people through intensive agricultural production.

2.2. Current Agricultural Production Status

The high dependence on external water sources makes this region extremely vulnerable to Yellow River water resource allocation policies. Currently, HID mainly implements measures such as irrigation channel lining, water-saving irrigation technology, planned water use implementation, and volume-based charging systems to alleviate water scarcity problems in the region and achieve sustainable agricultural development [35,36]. HID has currently formed a diversified agricultural production system with grain crops as the main body and cash crops as supplements. Major crops account for more than 80% of the area and they include wheat, corn, and sunflower; cash crops include tomatoes, melons (watermelons and cantaloupe), and vegetables, with relatively small planting areas but high economic value. Crop rotation has become a common practice in HID to improve land utilization, increase yields, improve soil fertility, and control pests and diseases [37,38,39,40]. Among these, wheat–corn rotation and wheat–sunflower rotation are the main rotation patterns.

HID faces multiple challenges in water resource utilization. Firstly, the water resources supply is lower than demand and the scarcity has been exacerbated by accelerated urbanization and growing industrial development demand. Secondly, climate change has led to increased inter-annual and seasonal variations in Yellow River flow [41], increasing uncertainty with regard to the water resource supply. Thirdly, soil salinization problems are severe [42]. During the dry season, the proportion of farmland with groundwater mineralization above 2 g/L in HID reaches 60.9% (

Table 1. Groundwater mineralization during dry season in HID (2023), unit: ha.

Range of Salinity	Area (ha)	Percentage of Total Area (%)
Fresh water (<1 g/L)	143,420	13.2
Slightly saline water (1~2 g/L)	282,120	25.9
Slightly saline water (2~3 g/L)	115,110	10.6
Saline water (3~5 g/L)	216,150	19.8
Saline water (5~10 g/L)	215,040	19.7
Brine (>10 g/L)	118,160	10.8

), seriously affecting crop selection and yields.

2.3. Methods

2.3.1. Positive Mathematical Programming (PMP)

The Positive Mathematical Programming (PMP) method, first proposed by Howitt [22], is a multi-stage modeling approach designed to calibrate agricultural production models to observed data, ensuring that the model accurately reflects the baseline production activities. This method is particularly well-suited for analyzing the impacts of policy changes, resource constraints, and environmental stresses on agricultural systems. The PMP approach typically involves three main stages:

Stage 1: Linear Programming (LP) Model

The first stage involves solving a standard linear programming model to maximize the total gross margin (TGM) of the agricultural production system, subject to resource constraints. The objective function and constraints are as follows:

Maximize $\mathrm{T}\mathrm{G}\mathrm{M}=\sum \left(p_i\times y_i-c_i\right)\times x_i$

Subject to

$$\begin{array}{l}\Sigma x_i⩽L\left(\mathrm{L}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\right)\\ \Sigma w_i\times x_i⩽W\left(\mathrm{W}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\right)\\ x_i⩽{x\_obs}_i+\epsilon \left(\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{b}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}\right)\end{array}$$

where $p_i$ is the price of crop $i$, $y_i$ is the yield of crop $i$, $c_i$ is the variable cost of crop $i$, $x_i$ is the area of crop $i$, $L$ is the total available land, $W$ is the total available water, $w_i$ is the water requirement per unit area for crop $i$, ${x\text{\_}obs}_i$ is the observed area of crop $i$, and $\epsilon$ is a small positive number.

The dual value (shadow price) of the calibration constraint, denoted as ${\lambda }_i$, is obtained from this stage and used in the subsequent stages;

Stage 2: Calibration of the Cost Function

The second stage involves calibrating a non-linear cost function using the dual values obtained from the first stage. The most common functional form used is a quadratic cost function:

$$\mathrm{C}(x_i)=(d_i+g_i\times x_i)\times x_i$$

where $d_i$ and $g_i$ are parameters of the quadratic cost function. These parameters are calibrated such that the marginal cost of production equals the marginal revenue at the observed production level:

$$p_i\times y_i-c_i-{\lambda }_i=d_i+2\times g_i\times {x\text{\_}obs}_i$$

Stage 3: Non-Linear Programming (NLP) Model

The final stage involves solving a non-linear programming model with the calibrated quadratic cost function. The objective function is to maximize the total gross margin, which now includes the non-linear cost term:

Maximize TGM = Σ ($p_i\times y_i\times x_i-$ ($d_i$ + 0.5 × $g_i$ × $x_i$) × $x_i$)

Subject to the same land and water constraints as in the first stage. This non-linear model is then used for policy scenario analysis.

In this study, we constructed a multi-stress factor integrated PMP model to analyze the agricultural decision-making in HID. The model considers the impacts of water scarcity, water pricing, and soil salinization on crop selection and production. The decision variables and their corresponding ranges are presented in

Table 2. Decision variables and their ranges.

Variable	Description	Unit	Range/Value	Type
xi	Planting area of crop i	ha	0 ≤ xi ≤ L	Decision variable
α	Water resource reduction ratio	dimensionless	0 ≤ α ≤ 1	Policy parameter
S	Soil salinity concentration	dS/m	0 ≤ S ≤ 10	Environmental parameter
pwater	Water price	CNY/m3	0.2 ≤ pwater ≤ 1.0	Policy parameter
λi	Dual value of calibration constraint for crop i	CNY/ha	λi ≥ 0	Model parameter
di	Intercept parameter of quadratic cost function for crop i	CNY/ha	di ≥ 0	Calibrated parameter
gi	Slope parameter of quadratic cost function for crop i	CNY/ha2	gi > 0	Calibrated parameter
yi	Yield per unit area of crop i	kg/ha	yi > 0	Input data
wi	Water requirement per unit area for crop i	m3/ha	wi > 0	Input data
L	Total available land area	ha	L = 769,300	Fixed parameter
W	Total available water supply	m3	W = 5.0 × 109	Fixed parameter
Ti	Salinity tolerance threshold of crop i	dS/m	1.7 ≤ Ti ≤ 6.0	Input data
si	Sensitivity coefficient of crop i to salinity stress	%/(dS/m)	0 ≤ si ≤ 10	Input data

.

The method of analysis is based on a mathematical programming model that simulates the farmers’ decision as a response to changes in the economic, political, or environmental context. We selected Positive Mathematical Programming (PMP) to construct an agricultural decision model for HID, as it has been frequently used to simulate farmers’ changes in many world regions. This model framework includes three interrelated core modules: first, a baseline calibration module used to accurately reproduce currently observed crop planting structures and resource allocation patterns; second, a behavioral response function module used to capture farmers’ adaptive adjustment behaviors to changes in external conditions; and third, a scenario analysis module used to evaluate system response characteristics under different policy measures and environmental change scenarios [43]. This optimization model aims to maximize regional agricultural total gross margin under given resource constraints and policy constraints.

Objective Function:

Maximize ${\mathsf{\Sigma }}_i\left(p_i\times y_i-c_i\right)\times x_i-0.5\times {\mathsf{\Sigma }}_i{\gamma }_i\times x_i^2$

where $p_i$ = market price of crop $i$ (CNY/kg), $y_i$ = yield per unit area of crop $i$ (kg/ha), $c_i$ = variable cost per unit area of crop $i$ (CNY/ha), $x_i$ = planting area of crop $i$ (ha), and ${\gamma }_i$ = calibration parameter for crop $i$.

Main Constraints:

The land resource constraint is $\sum _i x_i\le L$

The water resource constraint is $\sum _i w_i\times x_i\le W\times (1-\alpha )$

The salinity stress constraint is $y_i=y_i^o\times max\left(0,1-s_i\times max\left(0,S-T_i\right)\right)$

The specific meanings of parameters in constraints are $L$ = total land area available for agricultural production in the region (ha), $w_i$ = water requirement per unit area for crop $i$ (m³/ha), $W$ = total water resource supply under baseline scenario (m³), $\alpha$ = water resource reduction ratio coefficient (range 0~1), $y_i^o$ = potential yield of crop $i$ under ideal conditions (kg/ha), $s_i$ = sensitivity coefficient of crop $i$ to salinity stress (%/dS/m), $S$ = soil salinity concentration (dS/m), and $T_i$ = salinity tolerance threshold of crop i (dS/m).

2.3.2. Data Sources and Processing

The data used in this study comes from comprehensive surveys of agricultural production, water resource utilization, and economic benefits in HID, as well as relevant socio-economic statistical yearbooks. Crop planting areas were obtained from actual survey data from the Inner Mongolia HID Water Conservancy Development Center and verified with remote sensing satellite image interpretation analysis to ensure accuracy. Crop yield data were obtained from the “Bayannur Statistical Yearbook” (2022–2024). Economic parameters including crop purchase prices and crop production costs were obtained through interviews with typical farmers in the irrigation district and public information published on the official website of Bayannur Statistical Bureau. Crop salinity tolerance parameters referenced salinity tolerance data published by FAO [44]. Crop water-requirement data came from irrigation management records of the Inner Mongolia HID Water Conservancy Development Center and crop water-requirement experiments conducted by relevant agricultural research institutions [32]. Water quality data were obtained from water quality monitoring data maintained by the Yellow River Conservancy Commission of the Ministry of Water Resources. The Yellow River diversion volume data was obtained from the Yellow River Water Resources Bulletin (2021–2023), officially released by the Yellow River Conservancy Commission of the Ministry of Water Resources of China. Based on [45] Figure 2 shows the main crops’ phenological information.

2.3.3. Choice of Modeling Approach

While metaheuristic algorithms are powerful optimization tools for a wide range of problems, the PMP method was chosen for this study due to its specific strengths in agricultural economic modeling. PMP is designed to perfectly calibrate the model to a single-year baseline, which is crucial for policy analysis where the starting point must be the observed reality. Furthermore, PMP is grounded in economic theory, providing a clear interpretation of the model parameters and results in the context of farmer behavior. Metaheuristic algorithms, while effective in finding optimal solutions, often lack this direct economic interpretation.

The implementation of the PMP model was carried out in the General Algebraic Modeling System (GAMS). For the optimization, this study utilized the CONOPT solver for the nonlinear aspects and the CPLEX solver for the linear portions of the model.

2.3.4. Scenario Design and Analysis Framework

To comprehensively evaluate the multi-dimensional impacts of water resource management policies, the study designed three main scenarios:

Scenario 1: Water Resource Supply Scenario

This scenario simulates the impact of gradually reducing Yellow River water resource allocation on agricultural production systems, setting the reduction range of Yellow River water resources from the current baseline level gradually to 100%, analyzing farmers’ adaptive adjustment behavior patterns through crop planting structure modification and water resource allocation optimization;

Scenario 2: Water Pricing Policy Scenario

This scenario focuses on analyzing the actual effects of water pricing mechanisms as water resource demand management policy tools, setting water prices gradually increasing from 0.2 CNY/m³ to 1.0 CNY/m³, systematically evaluating the degree of influence of price signals on farmers’ water use behavior and crop selection decisions;

Scenario 3: Soil Salinization Scenario

This scenario evaluates the vulnerability and adaptive capacity of agricultural production systems for continuously increasing soil salinity concentrations, setting soil salinity concentrations gradually increasing to 10 dS/m and analyzing yield responses and economic losses of various crops under different salinity levels.

In summary, the overall methodological framework of this study is presented in Figure 3.

3. Results and Analysis

3.1. Baseline Agricultural Production Characteristics in HID

Table 3. Crop production characteristics in HID.

Crop Type	Yield (kg/ha)	Water Requirement (m3/ha)	Price (CNY/kg)	Area (1000 ha)	Production Cost (CNY/ha)	Gross Margin (CNY/ha)	Water Productivity (CNY/m3)	Salinity Threshold (dS/m)
Wheat	6375	3825	3	40.4	12,000	7177.5	1.88	6
Corn	17,145	4050	2	207.2	15,000	19,350	4.78	1.7
Sunflowers	3525	3000	8	254.5	8000	14,700	4.9	4.8
Tomato–Watermelon	55,000	4950	0.9	83.8	18,000	31,515	6.37	2.5
Wheat–Corn Rotation	12,300	6000	2.4	2.2	16,500	15,720	2.62	4.4
Wheat–Sunflower Rotation	7335	4800	4.8	0.7	14,000	21,618	4.5	5.4

presents the basic production characteristics of six main crop categories in the study region, including yield per unit area, irrigation water requirements, crop prices, planting areas, production costs, gross margins, water productivity, and salinity thresholds. The results show that high-value cash crops such as tomatoes and watermelons, while having the highest gross margins per unit area, also represent the crop types with the highest water requirements and those which show high sensitivity to soil salinity stress. In contrast, traditional field crops such as wheat and sunflower have relatively low water resource requirements and better salinity tolerance, but with correspondingly lower economic returns. The agricultural system in HID shows distinct structural characteristics and risk vulnerabilities. The crop structure shows significant imbalance, with sunflower and corn dominating. Economic efficiency differences are substantial, with the gross margins of tomatoes and watermelons exceeding those of wheat by 4.4 times. Water use efficiency shows severe differentiation, with the highest (tomato–watermelon) differing from the lowest (wheat) by 3.4 times. Salinity tolerance differences are considerable, with corn showing the highest sensitivity (1.7 dS/m) and wheat showing the highest salt tolerance (6.0 dS/m).

3.2. Water Resource Supply Scenario Analysis

Figure 4 shows that HID water resources exhibit significant vulnerability characteristics. Under the lower water supply scenario (water resource <20%) vs. normal supply), all crop systems show 100% total loss rates, completely withdrawing from production, revealing the region’s high dependence on irrigation water resources. Vulnerability thresholds refer to the critical water utilization level at which each crop system reaches a 50% loss rate. Vulnerability thresholds are concentrated in the 60–70% water resource utilization interval, with tomato–watermelon reaching the threshold (62%) and wheat and rotation systems having the highest threshold (72%). This interval emerges as the critical transition point for agricultural systems moving from stable to unstable states. All crop systems show nonlinear decline trajectories, maintaining relative stability when water resource utilization is over 80% and declining rapidly below 60%. Therefore, the 60–70% water resource utilization interval serves as a critical warning window, representing the optimal intervention timing for threshold-based warning and response mechanisms under the existing irrigation system.

Figure 5 illustrates the response relationship between water resource supply and changes in regional agricultural total gross margins. The research findings indicate (1) water resource availability and agricultural total revenue show a strong positive correlation (r = 0.962), exhibiting significant nonlinear characteristics; (2) the economic impact of water resource scarcity shows obvious threshold effects, with economic losses increasing dramatically when water resource availability falls below 80%; (3) extreme water scarcity (<1% availability) can cause economic losses as high as 96.3% (JPY 10.4 M), with a marginal loss rate of JPY 105 K per 1% of water resource; and (4) different degrees of water resource scarcity correspond to different risk levels, requiring the construction of graded warning and response mechanisms.

3.3. Water Pricing Policy Scenario Analysis

Figure 6 shows the relationship curves between water price levels and changes in crop planting areas, revealing relatively modest response characteristics in the low-to-medium price ranges. Specific characteristics include (1) wheat shows the highest sensitivity to water price changes, with the planted area responding to a water price elasticity coefficient of −23.8%, showing a significant negative response. This result is consistent with wheat’s characteristics as a traditional grain crop with relatively low profit margins. (2) Corn shows moderate price sensitivity (−9.7%), while other crop systems (sunflower, rotation systems, cash crops) show essentially negligible response to price changes, with price elasticity coefficients approaching zero. This result may stem from limited substitutability of cash crops; a small planting area base with limited adjustment space; and high returns per unit area with strong capacity to absorb price changes. (3) Water pricing policies show limited effectiveness in the low price range (0–0.5 JPY/m³), indicating water pricing policy limitations. Significant structural adjustment effects only appear in the high price range (0.5–1.0 JPY/m³). (4) Under the current policy framework, obvious challenges exist with water pricing tool ineffectiveness, requiring the construction of differentiated pricing mechanisms and supporting policy systems, as well as risk-sharing mechanisms.

3.4. Crop Response Characteristics to Salinity Stress

The six crop systems show different response patterns to salinity stress. As soil salinity concentration increases, the planting proportions of all crops show declining trajectories, but the decline magnitudes and critical thresholds differ substantially (

Table 4. Salinity critical thresholds for different crops.

Crop System	90% Threshold (dS/m)	75% Threshold (dS/m)	50% Threshold (dS/m)	25% Threshold (dS/m)	Final Land Use at 10 dS/m (%)	Decline Rate (%/dS/m)	Tolerance Rank	Tolerance Level
Wheat–Sunflowers	8	>10.0	>10.0	>10.0	85	1.5	1	High
Sunflowers	8	>10.0	>10.0	>10.0	83	1.7	2	High
Wheat–Corn	5	6	>10.0	>10.0	52	4.8	3	Medium
Wheat	6	7	>10.0	>10.0	50	5	4	Medium
Tomato–Watermelon	4	5	6	9	20	8	5	Low
Corn	4	5	6	7	0	10	6	Low

). Based on planting proportions at 10 dS/m, the crop salinity tolerance ranking is wheat–sunflower rotation (85.0%) > sunflower (83.0%) > wheat–corn rotation (52.0%) > wheat (50.0%) > tomato–watermelon (20.0%) > corn (0.0%).

Different crops show significantly different salinity critical thresholds. Among high salt-tolerant crops (90% threshold ≥ 8 dS/m), wheat–sunflower rotation performs most consistently across the entire salinity range. Sunflowers show the strongest salt tolerance among individual crops. Among medium salt-tolerant crops (90% threshold 5–7 dS/m), wheat as a traditional salt-tolerant crop performs well, followed by wheat–corn rotation showing intermediate performance. Among low salt-tolerant crops (90% threshold ≤4 dS/m), tomato–watermelon as cash crops are relatively sensitive to salinity. Corn shows the highest sensitivity to salinity stress.

Rotation systems show clear advantages in salt tolerance (Figure 7). Under extremely high salinity conditions of 10 dS/m, the average planting proportion of rotation systems is 52.3%, significantly exceeding 44.3% of individual crops, with an advantage margin of 8.0%. This advantage is mainly reflected in the fact that rotation facilitates soil salt leaching and microenvironment improvement and differences in root depth and distribution of different crops from three-dimensional utilization patterns. The conclusion is that crop rotation can reduce salt stress risks faced by individual crops and enhance the stability and stress resistance of agricultural ecosystems.

3.5. Comprehensive Economic Efficiency Analysis

Figure 8 provides a comprehensive comparative analysis of main crop categories for two basic dimensions: water productivity and economic efficiency. Figure 9 summarizes the key results of three main scenario analyses, clearly showing the different impact levels of different types of stress factors on agricultural production performance.

The water productivity analysis results in Figure 8a show substantial differences among different crops in economic output per unit of water resource input. The tomato and watermelon combination shows the highest water productivity level, reaching 6.4 CNY/m³, mainly benefiting from the crops’ high market value and relatively good yield performance per unit area. This is followed by crop rotation systems that achieve efficient utilization through multi-seasonal water resource optimization allocation. Traditional field crops show relatively low water productivity, with wheat at 1.9 CNY/m³ and corn at 4.8 CNY/m³, but these crops play an irreplaceable basic security role in ensuring regional food security.

The economic efficiency scatter plot analysis results in Figure 8b show the complex trade-off relationships among production efficiency, economic profitability, and production scale in the current agricultural production system. High-value cash crops occupy the upper right quadrant of the chart, having both high yield and substantial economic return advantages, but their promotion and planting scale are relatively limited due to constraints from food security policy red lines, high requirements for irrigation water guarantee rates, and land salinization levels.

The comprehensive comparison of the scenario analysis results in Figure 9 indicates that through scientific crop selection strategies and rational planting-area allocation, substantial room exists for further optimization and improvement in the agricultural production system of HID. Moderately expanding the planting scale of crops with high water productivity such as sunflower, while optimizing the crop combinations of existing rotation systems, is expected to significantly improve overall water resource utilization efficiency while maintaining economic viability. However, such structural adjustments must comprehensively consider the impacts of realistic factors such as market demand constraints, technical management capability requirements, and farmers’ risk tolerance. Policymakers need to consider adopting alternative or complementary policy tools such as water resource quota systems and water-saving technology subsidies to more effectively achieve water resource conservation and utilization objectives.

4. Discussion

4.1. Hierarchical Water Resources Quota Allocation and Management System

Based on the model results indicating that the agricultural system in HID shows significant threshold response characteristics to water resource changes, this study recommends establishing a hierarchical water resources quota allocation and management system based on the identified vulnerability thresholds. The system design is grounded in the empirical findings from Section 3.2, which demonstrated clear threshold effects in the 60–70% water utilization range.

Green Alert Level (Water Supply ≥ 80% of normal supply): At this level, the agricultural system maintains stable operation with controllable economic losses. It is recommended to maintain the existing water resource allocation pattern while strengthening water-saving technology promotion and water use efficiency monitoring. According to model analysis, in this range, a 10% reduction in water resources only causes a 5.5% decline in total gross margins, indicating that the system has certain buffering capacity.

Yellow Alert Level (Water Supply 60–80%): The model shows that when water supply availability falls below 80%, economic losses begin to increase dramatically. At this stage, it is recommended to initiate emergency water-saving measures, including (1) prioritizing crops with high water productivity, such as sunflower (4.9 CNY/m³) and corn (4.78 CNY/m³); (2) limiting the planting area of wheat with low water productivity, as its water productivity is only 1.88 CNY/m³; and (3) promoting rotation systems, particularly wheat–sunflower rotation (4.5 CNY/m³) and wheat–corn rotation (2.62 CNY/m³).

Red Alert Level (Water Supply < 60%): The model results show that in the 60–70% water resource utilization range, each crop system reaches the vulnerability threshold of 50% loss points, with tomato–watermelon reaching the earliest threshold at 62% water resource utilization. It is recommended to implement strict water resource quota systems at this stage, mandatorily adjust crop structures, and prioritize ensuring basic water needs for food security crops.

Emergency State Level (Water Supply < 20%): The model shows that under extreme water resource constraints, all crop systems show 100% total loss rates. It is recommended to initiate agricultural production emergency plans, including temporary cessation of irrigation, implementation of dryland agriculture, and activation of agricultural insurance compensation mechanisms.

4.2. Enhanced Water Rights Transfer System

The HID predominantly cultivates major agricultural commodities including wheat, corn, and sunflower, which exhibit limited economic returns per unit area. Concurrently, agricultural production confronts multifaceted risks encompassing climate change, market volatility, and pest and disease outbreaks, rendering farmers relatively vulnerable in their adaptive capacity. Under these circumstances, relying solely on increasing agricultural irrigation water pricing to achieve water conservation objectives not only lacks practical feasibility but may also adversely impact farmers’ livelihoods and regional food security.

Based on the practical experience of two phases of water rights transfer pilot programs in the HID [46,47,48], this study proposes further refinement of the water rights transfer system through the establishment of a “technology + ecology” three-dimensional collaborative framework. This framework leverages iterative upgrades in water-saving technologies to drive water rights release, while optimizing water rights allocation and transfer to promote coordinated development among agricultural, industrial, and ecological systems.

The specific measures involve constructing an intelligent water rights trading ecosystem, with a digital twin water rights management platform as its core component. The technological architecture comprises an Internet of Things (IoT) sensing layer for real-time monitoring of water usage status, an artificial intelligence (AI) algorithm layer for optimizing water rights allocation schemes, and a mobile application layer for facilitating user-friendly transactions. A dynamic pricing model will be established, implementing intelligent pricing based on supply–demand relationships, risk coefficients, and climatic factors. Furthermore, the integration of water rights trading with carbon sink trading will be implemented to achieve “water-carbon synergy.” An innovative water–carbon collaborative trading mechanism will be developed, whereby water-saving retrofits reduce energy consumption to achieve carbon emission reductions, and carbon sink trading revenues subsidize water rights trading, thereby realizing synergistic management of water and carbon resources.

4.3. Soil Management Strategy Based on Salinity Thresholds

The model analysis determined the salinity tolerance thresholds of different crops, providing scientific evidence for formulating precise soil salinization management strategies.

Soil Salinity Monitoring and Stratified Management: Based on salinity thresholds determined by the model, it is recommended to establish a four-level soil salinity management system: (1) safe zone (<4 dS/m): suitable for cultivating all crop types; (2) warning zone (4–6 dS/m): restrict cultivation of salinity-sensitive crops (corn, tomato–watermelon) and prioritize development of salt-tolerant crops; (3) restricted zone (6–8 dS/m): only permit cultivation of highly salt-tolerant crops (wheat, sunflower) and rotation systems; and (4) prohibited zone (>8 dS/m): suspend agricultural production and implement soil improvement measures.

Crop Layout Optimization Strategy: The model results show that under extremely high salinity conditions of 10 dS/m, the crop salinity tolerance ranking is wheat–sunflower rotation (85.0%) > sunflower (83.0%) > wheat–corn rotation (52.0%) > wheat (50.0%) > tomato–watermelon (20.0%) > corn (0.0%). Numerous studies have demonstrated [49,50,51,52,53,54,55] that sunflower exhibits salt–alkali tolerance and possesses the capacity to absorb certain quantities of salt, whereas wheat and corn lack this soil amelioration capability. Therefore, it is recommended to prioritize the promotion of sunflower cultivation in regions with severe salinization, as sunflower can maintain 83.0% of its planting proportion even under extreme salinity conditions while simultaneously contributing to the further remediation of salinized soils.

Rotation System Promotion Plan: The model analysis shows that rotation systems have an 8.0% advantage in salt tolerance (52.3% vs 44.3%). It is recommended to formulate a rotation system promotion plan, targeting an increase in the rotation area proportion from the current 0.5% (29,000 ha) to 15% (approximately 120,000 ha) within 5 years, focusing on promoting the wheat–corn rotation pattern.

4.4. Climate Change Considerations and Future Implications

Climate change represents a critical long-term factor that could significantly influence the effectiveness of water resource management strategies in HID. Rising temperatures and altered precipitation patterns may exacerbate water scarcity and soil salinization challenges. Increased evapotranspiration rates due to higher temperatures could increase crop water requirements, potentially shifting the vulnerability thresholds identified in this study. Changes in precipitation timing and intensity may affect the reliability of Yellow River water allocations, requiring more flexible and adaptive management approaches.

Future climate scenarios suggest that extreme weather events, including droughts and floods, may become more frequent and severe. These changes could alter the effectiveness of current crop rotation systems and necessitate the development of more climate-resilient agricultural practices. The integration of climate projections into PMP models represents an important avenue for future research, enabling the development of long-term adaptive strategies that account for both current constraints and future climate risks.

4.5. Methodological Innovation and Contributions

This study successfully constructed a comprehensive agricultural economic modeling framework applicable to water resource management analysis of agricultural production systems in HID. The successful application of the Positive Mathematical Programming (PMP) method not only effectively captured farmers’ actual decision-making behaviors and adaptive adjustment strategies but also provided scientifically reliable analytical tools for policy effect evaluation. Particularly noteworthy is that this study incorporated soil salinization, an important environmental constraint factor, into agricultural economic models by constructing crop-specific salinity tolerance threshold functions. This methodological advancement makes the evaluation of agricultural production environmental constraints more realistic.

The three-dimensional scenario analysis framework developed in this study provides reference for other irrigated agricultural regions facing water resource stress and environmental degradation challenges. The integration of three scenario dimensions—water resource supply changes, pricing policy implementation, and environmental stress intensification—achieved comprehensive evaluation of agricultural production system vulnerability and adaptive capacity. Future related research can further expand the analytical framework based on this foundation, incorporating additional dimensions such as long-term impacts of climate change, agricultural technology progress effects, and institutional factors affecting farmer decision-making behaviors.

5. Conclusions and Suggestions

This study developed a comprehensive PMP framework integrating multiple stress factors (water scarcity, pricing policies, and soil salinization) to analyze water resource management in the HID. The three-stage PMP approach, incorporating linear programming calibration, cost function estimation, and non-linear optimization, successfully captured farmer decision-making behaviors and system responses to environmental and policy changes. The research provides insights for agricultural adaptation under environmental stress.

5.1. Key Research Findings

The PMP model showed critical vulnerability patterns in the HID agricultural system. Agricultural production has threshold-based responses to water availability. The 60–70% water utilization interval is a critical transition zone where all crop systems reach 50% loss rates. This finding helps develop early warning systems and management strategies.

Water pricing policy analysis showed limited effectiveness in low-to-medium price ranges (0–0.5 CNY/m³). Significant effects only appeared in higher price ranges. Wheat showed the highest price sensitivity with an elasticity coefficient of −23.8%. Cash crops and rotation systems showed a minimal response to price changes. These results suggest that water pricing alone cannot achieve water conservation objectives. Other policy instruments are needed.

The crop salinity tolerance assessment provided quantitative thresholds for different agricultural systems. Rotation systems have better salt tolerance than individual crops. Under extreme salinity conditions (10 dS/m), wheat–sunflower rotation maintained 85% of its planting proportion. This shows an 8% advantage over individual crop systems. This finding supports diversified cropping patterns as an adaptation strategy for salinized agricultural lands.

5.2. Policy Implications and Recommendations

The study recommends establishing a hierarchical water resource quota allocation system with four alert levels: Green (≥80% water supply), Yellow (60–80%), Red (<60%), and Emergency (<20%). Each level corresponds to specific management measures from routine monitoring to emergency agricultural production plans.

The research supports developing water rights transfer systems through “technology + ecology” collaborative frameworks. This integrates water-saving technology upgrades with water rights trading mechanisms. The water–carbon synergy approach offers innovative pathways for sustainable resource management.

For soil salinization management, the study recommends stratified management based on salinity thresholds: Safe zone (<4 dS/m), Warning zone (4–6 dS/m), Restricted zone (6–8 dS/m), and Prohibited zone (>8 dS/m). Priority should be given to promoting sunflower cultivation and wheat–sunflower rotation systems in salinized areas because of their superior salt tolerance and soil improvement capabilities.

5.3. Research Limitations and Future Directions

This study has limitations. The model focuses on short-term responses and may not capture long-term changes in agricultural systems. Climate change represents a significant limitation, as the current model does not fully incorporate the dynamic effects of changing temperature and precipitation patterns on crop water requirements and salinity stress. The static nature of the current PMP framework limits its ability to capture the temporal evolution of climate–agriculture interactions. Future research should include technological progress, climate change projections, and market conditions.

Future research should expand the framework to include climate change scenarios, develop integrated models linking agricultural, hydrological, and economic systems, and explore machine learning techniques to enhance PMP model accuracy. Specifically, incorporating stochastic weather patterns and long-term climate projections into the PMP framework would enhance its predictive capability and policy relevance for long-term planning.