A nonlinear mathematical model integrated with the CROPWAT decision support tool to optimize cropping patterns under different climate conditions

Today, the rapid growth of the global population has increased the demand for agricultural products. Agricultural productivity is highly dependent on reliable sources of water, which itself is seriously influenced by climate change. Accordingly, for sustainable agricultural development, any long-term fluctuations of climatic variables (climate change) and their impact on agricultural activities should be considered in macro-economic decisions and policies. Therefore, special attention should be paid to the selection of optimum cropping patterns and optimal use of water resources under climate change. Selecting the optimal cropping pattern while minimizing water consumption can increase irrigation efficiency, increase crop yields, improve soil properties, increase farmers’ income levels, prevent the migration of families from rural to urban areas, and promote the agricultural, social, and economic development of a country. Therefore, cropping pattern optimization is an important step towards sustainable agriculture. Designing an optimum cropping pattern is a complex process influenced by a variety of factors and analysing them requires the gathering of large amounts of data and information. Solving such complex problems requires a robust and efficient method.

Previous researchers suggested different methods to optimize the cropping pattern. Zhenmin (1994) used a simple linear optimization model in the Yellow River Chengai irrigation project in China and reported that this optimization model could increase the production level while saving irrigation water. Darwish et al. (2007) optimized the cropping pattern in northern Lebanon by a linear programming (LP) method with the purpose of increasing farmers' profits. Regarding the several limitations of LPs, which make them unable to optimize complex engineering problems, nonlinear programming (NLP) methods have demonstrated promising results in such problems. Garibay-Rodriguez et al. (2017) proposed a mathematical NLP model for sustainable water management in treatment units in macroscopic systems. Aljanabi et al. (2018) developed a mixed-integer NLP optimization model to optimize the agricultural reclaimed water allocation over 84 agricultural farms in Iraq. They documented that irrigation with reclaimed water has the potential to increase agricultural and economic activities. Grové (2019) presented an NLP model to formulate deep percolation and evapotranspiration (ET) as functions of the soil-moisture content. The results of this study demonstrated that ignoring the increasing efficiencies may overestimate the impact of deficit irrigation on maize yields by a maximum of 2.2 tons/hectare. Li et al. (2019) proposed an NLP-based integrated model for the sustainable management of agricultural water–energy–food nexus under uncertainty and successfully employed the developed model for a real case study in northwest China. Cervantes-Gaxiola et al. (2020) proposed a multi-period mixed-integer NLP model for optimal crop allocation for several planting cycles based on future crop price and freshwater availability. The results demonstrated that the optimal allocation can be determined by the optimal relationship between the crop price, water availability, and costs by employing mass water integration. Barati et al. (2020) used a system dynamics approach by Vensim-Pro and multi-objective mathematical programming to optimize the cropping pattern in an agricultural region in Iran. The results showed that the ratio of the benefit to the consumed water in the optimized condition was always higher than in the nonoptimal condition. Yan et al. (2021a) successfully used a cloud-based dual-objective NLP model for the irrigation water allocation in northwest China. The results showed that the net economic profit and irrigation system efficiency are influenced by evapotranspiration more than surface water availability. Yan et al. (2021b) developed a stochastic multi-objective NLP model for irrigation water allocation under uncertainty and reported that the developed model can generate solutions that save irrigation water while ensuring net economic benefit. Marzban et al. (2022) developed a multi-objective NLP model to optimize the cropping pattern in Lorestan, Iran, for maximization of the net profit and minimization of the consumed energy. Akbari et al. (2022) linked the Soil and Water Assessment Tool to the well-known MODFLOW model to simulate agricultural production and groundwater-level variation in the Eshtehard watershed in Iran and used the particle swarm algorithm to optimize the cropping pattern. They reported that in the optimal cropping pattern, the dramatic rate of groundwater depletion was reduced. Ajudiya & Yadav (2023) utilized an artificial intelligence (AI) model to derive the optimal policies for a multi-reservoir system in a semi-arid river basin in India with the purpose of maximizing the net benefits subject to the land and water allocation. They validated the proposed model with the results of the LP model. The result revealed that the proposed AI model was superior. Mardani Najafabadi & Ashktorab (2023) developed a multi-objective fractional LP to determine the optimal cropping pattern under uncertainty. They reported that the consumption of fertilizers and chemical pesticides decreased by 5.9% and 8.19%, respectively, in the optimal cropping pattern. Darzi-Naftchali et al. (2024) provided a sustainable cropping pattern by developing a multi-objective model that maximizes profit while minimizing environmental problems and raising social indicators. The results of their study indicated that by sustaining a cropping pattern, the proposed model can help reduce social conflict while generating a synergy between economic and environmental benefits.

As seen, during recent years, special attention has been dedicated to cropping-pattern optimization. In this way, less attention has been paid to the effect of climate change on the cropping pattern. Climate change directly impacts the irrigation water requirement and crop yields. Investigating the effects of climate change on agriculture is essential for addressing food security and the sustainable use of water. Accordingly, Harmsen et al. (2009) investigated the impact of climate change on the relative yield of crops in the three regions of west Puerto Rico and found that climate change impacted the crop yield in some emission scenarios. Jamshidpey & Shourian (2021) used the well-known MODSIM, IHACRES, and Hadley Centre Coupled Model version 3 (HadCm3) models to obtain the optimal amount of irrigation water and cultivation areas under two conditions, namely, the status quo and the climate-change-affected streamflow for the Zayandeh-roud River in Iran. They reported that the agricultural net benefit will decrease by up to 17.5% in the investigated climate-change scenarios. Chen et al. (2022) developed a multi-objective model for the optimization of cropping patterns in the Jinxi Irrigation District in China under climate-change with two goals: environmental pollutants' reduction and the economic benefit increment. They found that by adjusting the acreage of rice, maize, and soybean, the degree of harmony of the economy–society–environment system increased by 10.7% compared with the nonoptimal condition. More recently, Rudraswamy & Umamahesh (2024) employed the CROPWAT model to investigate the impact of future climate change on the irrigation and crop water requirements of Bhadra and Tungabhadra areas in India. The results showed that the future climate projections from the best global climate model indicate a consistent increasing trend from 2023 to 2100 in both areas under the two shared socioeconomic pathways. Kumari et al. (2024) investigated the impacts of climate change on the irrigation water requirements in the Lower Mahanadi Basin in India utilizing a CMIP6-based spatio-temporal analysis and future projections. They documented that the study region may experience more extreme weather events in the future, potentially leading to increased challenges in water management. They reported the importance of optimal water allocation and management scenarios to sustain agricultural activities in the study area.

As reviewed, climate change may pose significant challenges to agricultural productivity, global food security, and water resources (Reshmidevi et al. 2018). This highlights the urgency of the optimal cropping pattern and adaptive water-management strategies considering climate-change scenarios. Despite its great importance, limited studies have been conducted on this topic. In most of the related studies, such as those mentioned above, a holistic view that considers both natural (water) and human (farmer) resources considering the uncertainties (climate change) was not evident. Accordingly, there is still a great need for further research on this topic.

The objective of this study was to develop a framework for optimization of the cropping pattern in an agricultural region. The optimization procedure in the proposed framework was defined in such a way that the amount of agricultural water consumption was reduced while the farmer's revenue from the sale of agricultural products was increased. In the optimization model, several constraints regarding the available water resources, accessible cultivable areas, and food-security compliance for the indigenous people were considered.

In this study, a new framework was proposed for the optimization of the cropping pattern considering the effect of climate change. To investigate the effect of climate change and its future impacts, global climate models (GCMs) are the most appropriate tool (Rudraswamy & Umamahesh 2024). The GCM projections directly are not suitable for capturing climate at a local scale (Baft agricultural area) due to their coarse spatial resolutions (Anandhi et al. 2013). So, it is necessary to downscale the coarse GCM projections to a high-resolution scale that can characterize a representative condition (Tamang et al. 2023). In this study, the Long Ashton Research Station Weather Generator (LARS-WG) model (Semenov & Barrow 2002) as a stochastic weather generator was used to extract the local-scale future daily climate data from the selected GCMs (downscaling). To implement the LARS-WG model, the daily data in the base period, including the minimum and maximum temperatures, the precipitation, and the solar radiation, were used. These data were employed as the base-period climate and to simulate the future climate. The reproduced climate data were used as input to the CROPWAT model (Swennenhuis 2009) for estimating the irrigation water requirement of the study area and calculating the amount of agricultural water consumption. Next, a nonlinear optimization model was developed in LINGO to optimize the cropping pattern in the study area in such a way that while the farmer's revenue increases, the agricultural water consumption decreases. In the following sections, a brief introduction of the utilized models and the modelling procedure are provided.

LARS-WG: LARS-WG is a stochastic weather generator that can be used for the simulation of weather data under current and future climate conditions. These data are in the form of daily time-series, including the precipitation, maximum and minimum temperatures, and solar radiation. The first version of this model, LARS, was developed in Budapest in 1990, and a modified version (current version) of this weather generator, LARS-WG, was introduced in 2005. It is a robust model capable of generating synthetic weather data for a wide range of climates. It has been well validated in diverse climates around the world (Sha et al. 2019; Bayatvarkeshi et al. 2020; Ahmadi et al. 2021; Roushangar & Abdelzad 2023). The process of generating synthetic weather data includes three phases, namely, model calibration, model validation, and synthetic weather data generation. During the model calibration, the observed weather data are analysed to determine their statistical characteristics. In the model validation step, the statistical properties of the observed and synthetic weather data are analysed to specify if there are any statistically significant differences. In the final step, the parameters derived from the observed data during the calibration procedure are employed to produce synthetic data having similar statistical properties to the observed data but differing on a day-to-day basis. Synthetic data related to specific climate-change scenarios may also be produced based on GCMs, which have been used in the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Kikstra et al. 2022). In this study, the daily data of minimum temperature, maximum temperature, precipitation, and solar radiation in a 17-year statistical period from 2007 to 2023 have been used as the base-period data, and the prediction of these variables has been performed for the period of 2024–2054 under three IPCC emission scenarios, namely, A2, B1, and A1B. The A family of scenarios (here, A2 and A1B) describes a future world of very rapid economic growth, a global population that peaks in mid-century and declines thereafter, and the rapid introduction of new and more efficient technologies. The A1B is distinguished by its technological emphasis on a balance across all sources of energy. The B1 scenario family describes a convergent world with the same global population as in the A1 scenario but with rapid changes in economic structures towards a service and information economy, with reductions in material intensity and the introduction of clean and resource-efficient technologies. The emphasis is on global solutions to economic, social, and environmental sustainability, including improved equity, but without additional climate initiatives (IPCC 2000). The details of each scenario can be found in Kikstra et al. (2022). The LARS-WG weather generator has been widely used by many researchers (Mohebbi et al. 2024; Tikuye et al. 2024) because of its several advantages, e.g. it is computationally inexpensive, it provides climate scenarios that match the statistical properties of observed weather, and it furnishes daily-scale meteorological variables while preserving statistical interrelationships between variables.

CROPWAT: This is a decision support tool for the calculation of crop water requirements based on rainfall, crop, soil, and climate data. It was developed by the Land and Water Development Division of the Food and Agriculture Organization (FAO). This model can improve the computations of a scheme's water supply for different crop patterns under different irrigation schedules. Due to its simplicity and accuracy compared with other models, CROPWAT has been widely used and recommended by many researchers for estimating crop evapotranspiration, crop water requirement, irrigation water requirement, and irrigation scheduling (Mwanga et al. 2024; Niromand Fard et al. 2024; Yerli 2024).

LINGO: The LINGO optimization model, developed by Lindo Systems Inc., is a comprehensive tool for efficiently building and solving a variety of linear, nonlinear, and integer optimization problems. It has a friendly environment for building and editing optimization models and a collection of fast built-in solvers. Also, it has several other prominent features, such as its high capability for modelling optimization problems, enjoying various mathematical, statistical, and stochastic functions, and the ability to read information from other files, including Excel (Tulett & Ke 2023). LINGO has a comprehensive language to facilitate all the optimization models in a wide range of engineering fields. Due to the mentioned advantages and features, it has been widely used and accepted in several optimization studies (Mirzaei et al. 2024; Shoaib et al. 2024; Zečević & Jevremović 2024).

In this study, the water requirements of each crop in the region in both base and future periods were calculated for all the three IPCC emission scenarios of A2, A1B, and B1. The results showed that in all the investigated scenarios, the highest water requirement was for wheat and the least for bean. For the alfalfa, the highest water requirement was observed in June and the lowest in December. The reason for this is the decline of the precipitation in the study area during these months. For the bean and barley crops with the same planting and harvesting dates, the highest water requirement was observed in January and the lowest water requirement in April. Wheat had the highest water demand in June and the lowest water demand in November. Also, maize had the highest water demand in July and the lowest in September.

Climate change has led to extreme pressure on water resources and agricultural activities in the world. Optimization of cropping patterns considering climate change is an essential step towards sustainable agriculture. The purpose of this study was to optimize the cropping pattern considering climate change to reduce agricultural water consumption as well as to improve the farmers' economic conditions in Baft agricultural area in Iran. For this purpose, after the identification of the dominant crops in the study area, the water requirement of each crop was predicted by the CROPWAT model through the FAO – Penman–Monteith method, and thereafter, the total volume of water used by farmers to irrigate the agricultural areas was calculated for both base and future climate-conditions. Next, regarding the yield, price, and production costs of the crops, the total gross profit earned by the farmers was calculated. The calculations were carried out for two periods: current (2007–2023) and future (2024–2054). For the future period, the CROPWAT input data was obtained by simulating the climatic parameters using HadCM3 under the three IPCC emission scenarios of A2, B1, and A1B. For the downscaling of GCM data, the LARS-WG statistical model was used. Finally, a nonlinear optimization model was developed in LINGO-20 to optimize the cropping pattern. In the optimal cropping pattern, the farmer can achieve more profit while consuming less water to irrigate the crops. The results indicated that by applying the optimal cropping pattern, the farmer's profit could be increased up to 1.65 times compared with the nonoptimal cropping pattern, while the amount of agricultural water consumption could be decreased by 5%. It should be noted that the assumptions and uncertainties in the utilized data and modelling procedure may impact model performance, so it is recommended that the sensitivity of the utilized models to such error sources be investigated in future studies. Future directions for this study include the utilization of comparative models such as the water evaluation and planning system for projecting the irrigation water requirements under different climate-change scenarios, the statistical downscaling model for assessing the local climate-change impacts, remote sensing and geographic information system for acquiring huge amounts of spatiotemporal crop data from satellite information, and evolutionary algorithms for efficient optimization of cropping patterns.

N.B. collected the data, designed the model, carried out the simulations, and prepared the original draft. N.S. conceived the original idea, reviewed the paper, and supervised the project. B.B. reviewed the paper and contributed to the interpretation of the results. M.R.M. proofread the paper, analysed the data, and contributed to the interpretation of the results. All authors reviewed the results and approved the final version of the paper.

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The authors declare there is no conflict.