Optimization of cropping pattern under seasonal fluctuations of surface water using multistage stochastic programming Open Access

Water resource shortage is one of the critically important issues facing humanity in the 21st century (Eliasson 2015; Li et al. 2017; Lu et al. 2018). The important factors impacting on water resource shortage are climate change impacts on snowfall pattern and rainfall (Kaini et al. 2020b) and changes in precipitation and temperature patterns (Hock et al. 2019; Kaini et al. 2021). Extreme variability of seasonal rainfall and prolonged dry seasons due to climate change have led to water shortage (Payus et al. 2020). Today, a global concern is a need for a balance of water demand between competing sectors (Hatamkhani & Moridi 2019). Moreover, the water shortage has become a major constraint on socio-economic development and has become a threat to livelihoods across much of the world (Liu et al. 2017). Over the past 60 years, global demand for water has increased due to a number of reasons such as rapid population growth and economic growth (Kaur et al. 2010), expansion agriculture to provide food security (Tilman et al. 2002), expansion of urbanization and industrialization (Biswas 2010), increasing environmental damage (Vörösmarty et al. 2000), climate change impacts on snowfall pattern and rainfall, changes in temperature patterns (Hock et al. 2019; Kaini et al. 2021), land use change (Sophocleous 2004) and water policy makers' problems (Ward 2014). Today, desalination of water resources can meet the increasing demand for freshwater in urban and industrial sectors (Panagopoulos 2021, 2022). However, different approaches are needed for the agricultural sector.

The agricultural sector is the largest consumer of water resources. Today, the share of harvested water in the agricultural sector is about 69% worldwide, 84% in the Middle East and 92% in Iran (Mohammad Jani & Yazdanian 2014). As the agricultural sector is the underlying development sector of developing countries, the need for agricultural water management is inevitable. In this matter, water resources management is important in arid and semi-arid regions due to the lack of average annual rainfall (Belaqziz et al. 2014; Mirzaei et al. 2021). The growing dangers induced by water resources shortage have noticeably affected agricultural production in many parts of the world (Li et al. 2018). Water stress can lead to a decrease in agricultural production and, consequently, fluctuations in agricultural prices, and can affect various economic sectors and environments (Hoekstra 2014; IPCC 2014). As such, saving on water consumption and optimal use is essential due to the high share of water consumption in agriculture and the presence of intermittent droughts in arid and semi-arid regions.

In arid and semi-arid regions, excessive consumption of groundwater resources has dropped water tables and disturbed the balance of discharge and recharge of aquifers, and this issue has made regional and national sustainable water resources systems degrade (Dai & Li 2013). Groundwater resources are exploited for agricultural purposes due to inadequate surface water resources (Dai & Li 2013). Thus, efficient methods for surface water management are beneficial to many factors such as economy profit and groundwater protection.

Surface water resources management is possible through improvement of cropping intensity based on cropping pattern (Parvin et al. 2017). Cropping pattern and cropping intensity are greatly influenced by irrigation. Cropping intensity is the frequency of crops planted on the irrigated land per year. Cropping intensity is an important determinant of irrigation efficiency to reduce rural poverty. Increase in the cropping intensity and improvement in productivity of crops are affected considerably by the management of irrigation facilities and availability of water for crops (Sivasubramaniyan 2000). The biggest factors affecting cropping pattern are existing agricultural and irrigation practices (Kaini et al. 2020a), and cultural, political, technological and infrastructural factors (Ganguly & Patra 2016). The physical and technical factors include soil, climate, weather, rainfall, nature and availability of the inputs such as irrigation, power, technology etc. Economic factors include price and income maximization, changing consumption pattern, farm sizes etc., and government agrarian policy such as subsidies on farm inputs such as seeds or fertilizer (Raghuvanshi 1995; Erb et al. 2013).

Thus, regarding the limitation of surface water resources, some efficient and practical solutions must be considered to optimize water allocation through increasing water economic productivity and by generating the optimal cropping pattern. As a result, surface and groundwater resources management in areas facing water shortages is inevitable (Nouri et al. 2019). Estimating the water saving potential, showing how much water can be saved by adopting water saving criteria and measures, is desirable and beneficial for agricultural water management (López-Mata et al. 2016; Zhang & Guo 2016). Hence, an investigation of different irrigation strategies and optimal water allocation is a critical principle (Tong & Guo 2013). Water allocation is a principal planning method for managing water supplies to agriculture in dry climates (Barton et al. 2019).

The agricultural sector is the largest consumer of water resources. Today, employing mathematical programming models has a special place to determine appropriate agricultural patterns and water allocation. Optimization of crop patterns plays an essential role in high-benefit agricultural management and water conservation (Niu et al. 2016). Here it should be noted that in arid and semiarid regions, the profitability of irrigated agriculture depends on the availability of irrigation water and the cropping pattern of the irrigation area (Su et al. 2014). Therefore, optimization models can be an effective tool for water management of crops (He et al. 2018). In the following, a number of studies on the composition of water allocation and cropping intensity to optimize cropping pattern are mentioned. Keramatzadeh et al. (2011) developed a multi-objective linear programming model to maximize farmers' net income by optimizing cropping pattern as well as water allocation. It was concluded that many of the uncertainties caused by some factors of agricultural water management systems should be paid attention to. Hassanvand et al. (2018) utilized a positive mathematical programming method to investigate farmers' reaction to the price change policy as well as the amount of available water in Neka city. Their results showed that by taking a policy of increasing the water price up to 4 times, and reducing the available water up to 20%, there is no significant change in the baseline. Besides, in the policy of reducing the available water, the cropping pattern was not changed from irrigated and rainfed agriculture, but there was a significant saving in water consumption. Howitt et al. (2012) introduced a separate calibration model of agricultural production and water management by utilizing a positive mathematical programming approach. Their results showed that income increased by 30% through more flexible allocation of water market under drought conditions. Dai & Li (2013) described the Multi-stage Irrigation Water Allocation Model (MIWA) for agricultural water management. This model employed some distance parameters within the framework of the multistage mathematical programming model and was then used to plan agricultural water management and crop patterns in China. In a similar way, Hao et al. (2018) described an integrated crop pattern optimization model by considering uncertainty about water availability and future water savings potential, to maximize the net profit per unit of water for farmers in Gansu Province, China. They indicated that if the irrigation water saving rate increased to 10%, then the net water saving would be 21.5–22.5 million cubic meters, whereas the gross water saving would be increased from 275.7 to 303 million cubic meters. Li et al. (2018) investigated the allocation of agricultural water under uncertainty using an economic model and then analyzed how water shortage risk can affect farmers' irrigation decisions, basing their analysis on water right data, water resources and land use of farmers. The results revealed that increasing the risk of water shortage could significantly weaken the percentage of land allocated to irrigation among young water right holders. Kuil et al. (2017) provided a hydrological-social model framework, and then explained how farmers' perceptions of water access could affect water allocation and crop selection. This model can simulate an almost ‘optimal or satisfactory’ cropping pattern when farmers use simple decision-making rules, which have different perceptions of water availability. Kaini et al. (2021) investigated the impact of socio-economic factors on cropping intensity in an irrigation scheme. The results showed that areas were not fully utilized and farmers' socio-economic status and their socio-cultural practices affected cropping intensity.

In the present study, the management of water resources demand in the agricultural sector due to the uncertainty of those resources is considered by combining the issues of surface water resources release management in irrigation networks, and crop pattern optimization under seasonal fluctuations of surface water resources in irrigation networks. Attention has also been paid to the intensity of cultivation and consumption of groundwater resources as an alternative to surface water resources. Therefore, the main difference between the present study and review studies is the simultaneous attention to these three issues.

In order to achieve the purpose of the present study, a model of irrigation surface water allocation was designed and then developed in the framework of a multistage stochastic programming model to optimize a cropping pattern to cope with the fluctuations of available surface water. The use of a multistage stochastic programming model can promote the practical application of uncertainty models as well as providing a valid scientific basis for economical use of surface and groundwater resources. This model was designed for the irrigation network of Jiroft plain in Kerman Province, which encounters a severe shortage of surface water resources and the tendency of farmers to overuse groundwater resources (Regional Water Company of Kerman Province in Iran 2017). Jiroft plain is one of the most important agricultural areas in Iran with suitable climatic conditions. In this area, the groundwater resources are well known as the most important source of water supply due to shortage and fluctuations of surface water resources (Amir Teimoori 2017; Mirzaei & Zibaei 2021). Here, it is worthwhile to mention that groundwater resources are a valuable water supply throughout the world (Triska et al. 1993). Excessive pumping of groundwater resources will threaten sensitive ecosystems and sustainable water supply (Gleeson et al. 2012). The average amount of groundwater pumping in the Jiroft irrigation network is about 368 million cubic meters, about 15 times that of surface water harvesting. Therefore, how to allocate surface water to each crop to maximize the economic benefits of farmers and to modify groundwater consumption is a major issue for the region.

In the current research, the irrigation network of Jiroft plain including the PC0, PC1 and PC2 canals in Jazmourian basin is regarded as the study area (Figures 1 and 2). Three stochastic states (low, medium and high) were considered concerning the amount of surface water supplied to Jiroft irrigation canals (including PC1 and PC2 canals) for four seasons (autumn, winter, spring and summer) and the probabilities were calculated by monthly surface water supply values over the last 8 years (Table 1). It should be noted that during the different seasons, the range of surface water supply for each of the stochastic situations is determined using the mean and standard deviation of the monthly surface water supply over the last 8 years.

The data reported in Table 1 indicate that the states of high (15%) and medium (44%) available water for canals are the least and most likely to occur, respectively. This result indicates Jiroft irrigation network has been faced with surface water shortage problems in recent years, which may be interpreted to be due to numerous droughts in this area and inadequate management of water resources upstream of Jiroft reservoir. Comparison of the amount of water supplied in the irrigation canals between different periods confirms that the least amount of surface water supply occurred in the autumn (between 2.2 and 16.5 million cubic meters) and summer (between 5.4 and 16.5 million cubic meters) seasons. It can also be said that in winter and especially in spring, the supply and consequent water harvesting in the canals noticeably increased, due to the water requirement of different crops and increased rainfall in these seasons.

As the amount of water consumed in the agriculture sector depends strongly on the amount of water available as well as the amount of land allocated to each crop, there is a need to optimally estimate the amount of land allocated to each crop according to the amount of available water, under stochastic conditions during different seasons. To achieve this aim, four main crops of wheat, potato, cucumber and tomato were considered, accounting for 80% of the total area under cultivation in these areas. Table 2 provides the gross water requirement per hectare of crops selected during the different seasons (Regional Water Company of Kerman Province in Iran 2017).

Accordingly, irrigation of land takes place for cultivation of wheat from November to April, potato from December to May, cucumber from December to March and tomato from December to May. Therefore, irrigation of the main crops in the region occurs in the three seasons of autumn, winter and spring, with the highest and lowest water demand for the crops studied being in winter and autumn, respectively. Moreover, the highest annual water consumption is for tomato and potato crops consuming more than 10,000 cubic meters, compared to the lowest water consumption for cucumber and wheat crops of 5,418 and 6,060 cubic meters, respectively.

Due to the inherent complexity and uncertainties of real-world water resources systems, the use of conventional deterministic optimization methods is limiting. Accordingly, many researchers have used stochastic programming to address these issues (Huang & Loucks 2000; Maqsood & Huang 2003; Maqsood et al. 2005; Chen et al. 2017; Zhang et al. 2019a). In other words, the uncertainties in the main factors in the planning of irrigation water resources, such as random seasonal runoff, uncertainty in data collection and limited water allocation to several users in a multi-period planning horizon, make the use of multi-stage programming inevitable (Figure 3) (Guo et al. 2018; Zhang et al. 2019b). The difference in the amount of water available in different seasons as well as in the stages of crop growth, along with the uncertainty of water inflow, have made the allocation of water between different stages a complex dynamic process (Wang et al. 2016). Therefore, the application of a multi-stage stochastic programming (MSP) model to deal with these problems and make full use of the collected data and accurate description of practical cases can be useful (Li & Huang 2007).

High flexibility in modeling the decision-making process and defining scenarios when the dimensions of the scenarios are large is the main advantage of MSP (Birge 1985). The MSP method takes into account the probabilistic uncertainties on the right-hand side (which usually indicates the amount of resources availability). However, the ability of this model to deal with the independent uncertainties on the model's left-hand side and cost coefficients is low. In addition, it is difficult to reflect probability distributions in large-scale stochastic models (Huang et al. 1992; Watkins et al. 2000; Li et al. 2006).

In the above equation, is the decision variable and is specified by water availability constraints for irrigation ⁠. The distribution of is expressed as a discrete function and contains the values of with the probability level for scenario k in period t such that is probability of scenario k in period t and and ⁠. ⁠, is the number of scenarios in period t.

The ratio of multiple total cropped land (L_s,i) of crop (i) under different stochastic states (s) and duration of crop (i) to the command land of the scheme crop (CL_s) is defined as cropping intensity.

Parameters of an MSP model including prices, amount of water required for crops, total amount of available water, cost of inputs and crop yields were obtained and extracted from the Regional Water Company of Kerman as a set of irrigation and drainage reports, from the Jihad Agriculture Organization in the south of Kerman Province and from a sample of 214 farmers.

The optimum land allocation for each crop was obtained by solving a multistage stochastic water programming model with all stochastic states of available surface water and their water requirements. It should be mentioned that as the water requirements of the selected crops for the three seasons of autumn, winter and spring, as well as the number of stochastic states of surface water supply, are considered to be low, medium and high, the total number of stochastic states is 27 (3³=27). By solving the MSP model, the decision variables related to the optimal cultivation level of the four selected crops are achieved for all stochastic states. Therefore, the total number of model decision variables was estimated to be 108 (4*27=108). The optimum cropping pattern was extracted for 27 stochastic states, for example, with only the optimum-cropping pattern of 11 states presented so that the overall conclusions can be deduced from the finding (Table 3).

The results confirm that the highest and lowest share of crops in the optimal cropping patterns for all stochastic states of available surface water are dedicated to potato and cucumber, respectively. Comparing the optimal patterns with the current conditions in the region shows that the farmers in the Jiroft irrigation network did not allocate optimally because the share of wheat crop in the current pattern is higher than other crops whilst, in optimal patterns, the potato has the largest share of the area under cultivation. Also, under the current conditions, net profit is about half of the expected net profit under optimal stochastic states. Therefore, by modifying the cropping pattern, one can hope for the better economic status of farmers in the region. Here, the high share of potato crop in optimum cropping patterns is due to its profitability. Meanwhile, the results reveal that despite the low surface water supply in all seasons (L-L-L), the potato crop, which has a high-water consumption pattern compared to other crops, has a high share in the optimal cropping pattern. This finding is due to the easy access to groundwater resources in the region, and the low cost of that access. Thus, the pressure exerted by farmers on groundwater resources can clearly be seen.

A comparison of the results of the optimal cropping pattern and the amount of land cover through surface water resources for different stochastic states shows that if the available surface water level is low or medium in winter, the amount of water supply in other seasons will have a significant impact on the optimal cropping pattern. As all crops in the pattern have high water requirements in the winter season, low or moderate available surface water cannot improve cultivated area covered by surface water resources. Also, the impact of spring surface water availability can be significant when the amount of available surface water in winter is high. To confirm this result, the L-H-L via L-H-H stochastic states can be compared. This comparison reveals that there is a difference between the optimal cropping patterns covered by surface water resources. Thus, in the L-H-L state, available surface water can cover 11, 9, 11 and 8% of wheat, potato, cucumber and tomato cultivated areas respectively, whilst it covers 3, 13, 2 and 12% of the respective crops in the L-H-H state. Therefore, it can be found that if the surface water level in the spring season is increased, by assuming high water availability for the winter, the percentage of cover area for potato and tomato crops increased through surface water, whereas the wheat and cucumber crops decreased.

Surface water and groundwater consumption in the region, the total area under cultivation by surface water resources and the amount of groundwater to meet the needs of farmers in optimal cropping patterns under different stochastic states are presented to better understand the findings (Table 4).

It can be interpreted from the results in Table 4 that, in general, the surface water resources do not cover a significant cultivated area even at the best state of surface inflow (high-high-high). Therefore, it can be concluded that the surface water resources are inadequate in this area. The results show that if the available surface water is low in winter, the cultivated area covered by surface water resources is between 4.93 and 5.04%. If surface water inflow is considered medium for winter, 6.04% of arable land is covered by surface water resources. In contrast, if the water availability is high in winter, more than 9% of arable land is provided by surface water resources. Therefore, it is concluded that by increasing the amount of water available in winter, the percentage area under cultivation through surface water sources increases. However, the fluctuations in the available surface inflow of the autumn and spring seasons did not have a significant effect on the area of cultivation covered by surface water resources.

In the optimal patterns, comparing the amount of groundwater consumption for different stochastic states indicates the fact that increasing the amount of water available in winter can moderate the amount of groundwater consumption, so that the optimal cropping pattern in low-high-low and high-high-low stochastic states reduces the average consumption of groundwater resources from 368 million cubic meters to about 323 million cubic meters. This reduction in the consumption of underground resources is not significant, when compared to the volume of these resources used in the area concerned. Therefore, it is not expected to reduce the consumption of groundwater resources under optimal patterns. On the other hand, increasing surface water supply in the spring season does not reduce the consumption of groundwater resources but does also increases the consumption of these resources.

The cropping intensity index was considered to better understand irrigation efficiency to improve the economic situation of farmers (Table 5).

According to the results of Table 5, about 43% of the areas are fully utilized in terms of the current cropping pattern. However, optimal cropping patterns under different stochastic states can improve land use by 2–3%. The results show that current frequency of crops planted on the irrigated land in a year is not appropriate. Therefore, new crops must be planted to be able to improve cropping intensity.

In general, optimal cropping patterns under different stochastic states had no significant impact on adjusting water consumption and increasing crop intensity in the region, while the application of these patterns can achieve a significant increase in farmers' gross profit due to the change of cultivation from low-profit crops to high-profit crops. The reason for these findings is the improper crop frequency and the overuse of groundwater resources in the region.

On the one hand, the results of the present study clarify the need for planning in the release of surface water resources in irrigation canals so that the increase of land covered by the irrigation network can be seen when the rate of water release in the canals is high in winter. On the other hand, the results for the study area showed that surface water resources cannot meet the water needs of the region, even by using optimal cropping patterns, and this has led to overuse of groundwater resources in this area. Also, analysis of the cropping intensity index in the region suggests that even the optimal cropping patterns cannot significantly increase this index. Therefore, the need to use new crops in the cropping pattern is necessary. Finally, these results indicate the dynamic and space-time dependent nature of water resources management, which has been confirmed in other studies (Westerhoff & Smit 2008; Reidsma et al. 2010; Esteve et al. 2015).

It is clear that the amount of surface water resources fluctuates greatly under the influence of rainfall and climatic conditions in different regions. In this regard, groundwater resources have been heavily exploited by farmers as an alternative to surface water to reduce production risk and increase crop production, especially in arid and semi-arid regions. Therefore, surface water resources demand management in the agricultural sector is very important due to seasonal fluctuations and replacing groundwater resources with these resources. In this study, which has considered the release of surface water resources in irrigation networks, optimal cultivation patterns and cultivation intensity under seasonal fluctuations of surface water resources and the relationship between surface and groundwater resources consumption, an attempt has been made to efficiently manage water resources under uncertainty. Therefore, the framework and model used in the present study can be used as an efficient structure for managing surface water resources under the influence of seasonal fluctuations.

Iran is one of the countries with the highest consumption of water in the agricultural sector. In many areas, due to the natural connection between groundwater and surface water, groundwater depletion has caused damage to surface water. Therefore, in the current research, a surface irrigation water allocation model was employed in the framework of a multistage stochastic programming model to optimize crop planning to cope with the surface water fluctuations of Jiroft plain irrigation network in Kerman Province, Iran. The results, comparing groundwater consumption in optimal patterns for different stochastic states of inflow, confirmed that increasing the amount of water available in winter can moderate the amount of groundwater consumption. However, this reduction in the consumption of groundwater resources is not significant compared to the volume of these resources used in the area concerned. Therefore, one cannot hope to reduce the consumption of groundwater resources under optimal patterns. Also, the results for the spring season indicate that increasing the surface water supply in this season does not reduce the consumption of groundwater resources but does increase the consumption of these resources. This result indicates that if the surface water released into the canals increased in the spring, the increase in farmers' profits would be due to patterns in which high gross margins and water intakes would be greatly increasing. The share of high water consumption crops increases the amount of water consumed and increases the pressure on groundwater resources. Thus, the related policy of water release in the irrigation canals of Jiroft plain should be amended accordingly.

The results of the present study can help adoption of desired policies for irrigation water management through the proper release of these resources. Though rational solutions and surface water management policies have been found through a multistage stochastic model, more attention needs to be paid to the limitations of groundwater resources as well as the frequency of crops in the model. The applied model has extracted the optimal cropping patterns under stochastic states of surface water resources to improve the economic situation of farmers. Therefore, the findings of this model can be used by policy makers in different regions to improve farmers' livelihoods. However, it is possible to improve economic conditions without those improvements necessarily reducing water consumption and increasing cropping intensity in different areas. Finally, the model can be expanded not based on historical data but based on existing hydrological conditions. Therefore, the combination of such models with hydrological simulation models is proposed in future studies.

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

The authors declare there is no conflict of interest.