Supplying demands of aquatic ecosystems using bivariate optimization of water depletion strategies under uncertainty

Water and nutrients interact with each other to control the amount of production due to the coupling effect created (Sang et al. 2023). Studies have shown that there is a significant interaction between nitrogen consumption and water management on nitrogen uptake and utilization and grain yield in rice (Ashouri 2019). The aquatic environment of paddy fields is different from rivers and marine structures. The water in the paddy fields is shallow with little salt. If the water layer is shallow, the energy input by the Sun on the water at the surface of the field and at the bottom is almost the same (Park et al. 2013; Zhang et al. 2021; Zheng et al. 2023). At the same time, water convection and turbulence are weakened and nitrate conversion through diffusion and dispersion is reduced. But the unit's water level has a relatively high contact with the atmosphere and soil and is more sensitive to atmospheric and geographical conditions (Yang et al. 2018; Liu et al. 2023). In addition, the water surface is relatively small and easily contaminated. The lower the bleaching ability, the weaker the buffering capacity of the water zone, and the more difficult it is to regulate pH and dissolved oxygen. In addition, rice easily casts shadows, reduces light areas, and is affected by water temperature and other factors. Therefore, as a water ecosystem, the paddy field environment is more exposed to pollution than other water streams. On the other hand, the water returned from the paddy field is considered as healthy water and is reused in aquaculture or agriculture industries (Li et al. 2023). Therefore, it is necessary to pay attention to the water quality in the paddy fields (Mohammadi et al. 2017).

Nitrogen is very important for crop yield, and the use of nitrogen fertilizer in crop production systems is one of the critical aspects of modern crop management practices (Yu et al. 2024) and one of the determining factors for increasing crop yield and thus keeping pace with human population growth. However, most of the nitrogen fertilizers added to rice fields are not absorbed by the rice plants, but are lost to the environment as ammonia, nitrates, and nitrogen oxides. This pollutant causes serious environmental problems and harmful effects on human health (Gu & Yang 2022; Hu et al. 2022). One of the factors of increasing food production in the world in the past decades has been the use of synthetic nitrogen (N) fertilizer (Tilman 1999). However, the excessive use of nitrogen fertilizer and the reduction of its use efficiency have led to the problems of environmental pollution and nitrogen oxide emissions (Chen et al. 2022). Nitrate nitrogen (NO₃-N) leaching has had harmful effects on groundwater and thus has been a major concern for human health in China (Zhang 2016). Therefore, the effective control mechanism of NO₃-N leaching in irrigation water has become an important issue for the development of sustainable agriculture. Field experiments on cereals have shown the effectiveness of nitrogen use in China to be about 27% (Zhang et al. 2007).

The effect of nitrate (NO₃) on rice growth as well as N absorption and assimilation during different growth stages was examined using three typical rice cultivars (Duan et al. 2006). Dry weight and N uptake were measured with solution culture experiments. Results showed that some replacement of NH₄ with NO₃ could greatly increase the growth of rice plants, mainly on account of the improved uptake of NH₄ promoted by NO₃. Nitrogen deficiency usually occurs in almost all agricultural land, unless nitrogen is applied as fertilizer or manure in the water supply process. In the past decades, the amount of synthetic nitrogen fertilizers used in rice has increased dramatically. However, only less than half of applied fertilizer N can be taken up by crop plants, with most of the unused fertilizer N being uptake into water, which can have severe environmental consequences (Gao et al. 2023). Water is the component of nitrogen transfer, which plays an essential role in the control of pollution in the water cycle of rice cultivation (Yang et al. 2017; Fang et al. 2023).

Yang et al. (2018) conducted field experiments in rice-wheat rotation under conventional management to determine the effects of straw return on crop yield, nitrogen uptake, soil properties and soil NO₃-N. The results showed that the return of straw significantly increases crop yield and nitrogen absorption. To improve the current practice of rice irrigation in the future, long-term observations of crop yield and leaching of nitrogen nitrate are necessary to identify environmentally friendly practices. Rezayati et al. (2020) simulated water level fluctuations and nitrate transport during two crop years based on three irrigation regimes. The simulation results showed that the HYDRUS-2D model has a good ability to simulate water movement and nitrate transfer from chemical or compost sources. Therefore, it can be used to manage irrigation and fertilizer in the case of paddy fields to analyze different scenarios.

This paper uses experiments to study the overall benefits of water allocation for the aquatic rice ecosystem to evaluate the effects of NO₃ fertilizer on environmental factors and yield production. Previous studies have confirmed that the water environment indirectly affects rice yield, but the simultaneous optimization of fertilizer application and water allocation has not been researched. The application of these two goals in the rice field provides the possibility of increasing water productivity and protecting the environment. On the one hand, the increase in water absorption reduces the nitrate concentration, and on the other hand, the increase in nitrate helps to improve production and increase economic profit. The optimization model with two objective functions has been developed using the extremal algorithm under uncertainty conditions.

Conducting field experiments to determine the optimal strategy for managing water consumption in paddy fields is very time-consuming and expensive (Rezayati et al. 2020). The use of decision-making models based on artificial intelligence in combination with experimental information is a solution for accurate and validated conclusions (Bortolan & Degani 1985). Therefore, a two-objective optimization model was developed for the paddy water ecosystem.

In solving multi-objective optimization problems, the objective functions are usually in conflict with each other. This means that with the improvement of one function, another function will decrease (Lalehzari et al. 2016). Therefore, the objective functions will be relatively improved at the same time. The concept of Pareto is defined for responses that have reached a level of progress corresponding to the objective function. The best solution in the multi-objective optimization system is that the response (1) should not be worse than the others in any of the goals and (2) should be optimal than others in at least one goal.

The extremal optimization algorithm is a heuristic algorithm developed by Boettcher & Percus (2003). The most obvious difference between the extreme optimization algorithm and other heuristic algorithms such as the genetic algorithm is that the competence of the cells (local competence) needs to be determined in addition to the overall competence of the solution. In fact, this feature is the core of the extremal optimization algorithm. Solving the problem has two steps: first, it needs to find an executable schedule, so that all the constraints are set. Second, this schedule must be optimal, in which case it is necessary that the objectives of the problem achieve the best value.

In this experiment, 24 quality samples of river water were measured for four rice fields (F1, F2, F3, and F4). The application rate of nitrogen fertilizer and the volume of water inflow and outflow to the plots were collected. The obtained information is summarized in Table 1. The concentration of fertilizer nitrate was measured from the combination with irrigation water. In other words, the concentration of irrigation nitrate before and after fertilization is recorded as river and fertilizer information.

The average decrease in nitrate concentration in F2 was 1.86 mg·L⁻¹, which is almost the same in all plots (Figure 5). The range of maximum and minimum estimated changes ranged from 1.2 mg·L⁻¹ (S2) to 1.67 mg·L⁻¹ (S6). In the best situation, using the optimal plan will reduce the nitrate concentration to 7 mg·L⁻¹.

Changes in F3 and F4 farms have been associated with more fluctuations. Plot F3S3 has the highest range of uncertainty and F4S2 has the lowest sensitivity (Figures 6 and 7). The reduction of nitrate concentration in river water is not limited to the calculations made in this research and other factors are also involved. The processes of convection, dispersion and diffusion are among the components that affect the quality of river water in different locations. The results of this research can be investigated from the aspect of nitrates coming out of the paddy field, and the role of other factors should be investigated separately.

With increasing population and demand for food, cultivation of rice and providing the needs of water ecosystems have become an effective model for increasing agricultural production and efficiency and increasing the efficiency of water allocation in one season. However, water recycling technology is not developed in every region, and farmers usually cannot manage the water allocation of the river ecosystem and thus cannot achieve maximum economic benefits. Therefore, it is necessary to experiment with the water allocation needs of the ecosystem in rice paddies to find the density range that can achieve the most benefit. This article has two research objectives: increasing the efficiency of water consumption and decreasing the nitrate concentration of the ecosystem downstream of rice fields. Compared to other research models, the data accuracy of the bi-objective optimization method proposed in this article has increased, and the practicability and accuracy are higher. In this way, it can provide a reference for increasing income and rational use of water resources for farmers. One of the main limitations of the research was the control of the quality of the output stream from paddy farming for the ecosystem, which can be considered in future studies.

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

The authors declare there is no conflict.