Sustainable water–ecosystem management using the Bayesian network and variable relationship analysis

Paying attention to strengthening land degradation in China's agricultural areas, improving the stability of agricultural ecosystems and enhancing the efficiency of water resource utilization are effective ways to solve water resource problems (Ma et al. 2022). Ecosystem construction in agricultural areas is a systematic project that includes, in addition to natural factors and human activities, factors such as soil, climate, biology, meteorology and more. The relationship between water, food and ecosystem is the most important relationship in agricultural areas, and its influence and regulation on the construction of the environment is a major challenge that agricultural areas in China are currently facing. The structure of agricultural area protection systems and ecological environment construction has significant economic and social values that can promote the development of agriculture in China.

Risk analysis, and especially risks related to food and ecosystem security, has increased in recent decades with the development of advanced theories, methodological frameworks, and new tools. The definition of risk varies in different research areas, but, in general, it can be considered as the product of probability (or risk) and impact, consequence, or vulnerability. In this study, the risk of agricultural crops on the water ecosystem has been evaluated using two methods such as the Bayesian network and analysis of variables. Water management in agriculture is a process that promotes the sustainable development and management of all resources of an ecosystem to maximize the balance between socio-economic well-being and the sustainability of critical ecosystems. The increase in human activities in river basins causes destruction and serious problems for beneficiaries and managers, especially in arid and semi-arid areas. Although there are many techniques to solve these problems, it is not easy for watershed managers to apply them.

An integrated Bayesian network model framework was used to evaluate the sustainability of a semi-arid river catchment in the Habale Rood River Basin, which is located in the Central Plateau River Basin of Iran. The catchment has an area of 32.6 km² and is located in the northern part of the Central Plateau of Iran (Keshtkar et al. 2013). The river basin of this research shows the assessment of related management problems, the model framework and the techniques used to extract the input data. The results for the implementation of the study area and a proposal for management are described and discussed. Pham et al. (2021) identified Bayesian network approaches for evaluating ecosystem services and investigated the key factors driving changes and trade-offs between these services under different scenarios. Applying the designed system to the Taro River basin in Italy, the results showed that there is limited space for improving the potential of ecosystem services. This is mainly due to the trade-off between water performance and nutrient retention services, which are affected by changes in precipitation patterns and land use. The results indicate a low capacity to provide services in the medium term for the river, where water has been exploited for different competing purposes. Therefore, long-term spatial planning and water management strategies are needed to improve the potential of ecosystem services. The designed model represents a valuable decision support tool to rapidly evaluate the most appropriate management plan to maintain ecosystem benefits.

Bruen et al. (2022) presented a method for building a nondeterministic Bayesian model by combining water quality and watershed model output, data, and expert knowledge. This framework can support the integration of ecosystem sustainability in water resource management and analyze areas of agreement and disagreement among experts. This model was developed for four selected ecosystem patterns and to evaluate the consequences of management options. The implications suggested for the practical use of this type of model to support watershed management decisions showed the complexity of the relationship between management actions, water quality, and ecological responses. Therefore, it can be concluded that managerial decisions are usually related to the general characteristics of the solutions and not to their precise design. An ecosystem service network system was developed for the Jinghe River Basin by Tang et al. (2019), which utilized a distributed eco-hydrological model called the Soil and Water Assessment Tool (SWAT) model for water simulation. The Carnegie-Ames-Stanford model was used to estimate net primary productivity and the Universal Soil Loss Equation model was used to calculate soil erosion. In addition, a crop productivity model was developed to simulate agricultural productivity to quantify four ecosystem services. The results showed that the water yield, concentrated in the middle and downstream parts of the mountain and river areas, is increasing in the Jinge River Basin. In addition, there was a synergistic relationship between water yield and agricultural productivity, which could increase vegetation cover and lead to increased agricultural productivity. However, water yield can be reduced if necessary to balance water yield and soil erosion.

Ecosystem sustainability comprises all the positive components obtained from an optimal structure that improve life and increase utility. Since this stability is closely related to human life and survival, it is important to examine the changes in their temporal and spatial trends in natural conditions and in relation to the activities that humans have done both for their own survival and for the development of the Earth.

Today, the focus on sustainable resource development has increased, and economic, social, and environmental benefits are considered as a fundamental part.

Crossman & Pollino (2018) applied the Bayesian decision network concept to estimate the total benefit of water resource development according to social, economic, and environmental sustainability criteria in Australia. We focus on two remote, water-scarce catchments under consideration for development. The results showed that the Bayesian decision network has many features that make it useful for evaluating social, economic and environmental sustainability criteria, especially its ease of construction. From the point of view of sustainability assessment, the total desirability of developing water resources for new irrigation in the studied basin was negative. If irrigation development is sensitive to the environment and has a very little environmental impact, while achieving a much higher net economic return for irrigation, it can be positive. This can be achieved through higher commodity prices, lower capital costs of irrigation development, or the development of water resources. Ropero et al. (2022) proposed a Bayesian network-based regression solution to avoid missing a variable from the collected data, which uses fixed probabilistic graphical structures to impute the missing variable as accurately as possible. To solve the problem of lack of information, an unsupervised classification method based on the Bayesian network was developed to predict flood risk in the coastal area. The results showed that the proposed regression solution can predict the behavior of the continuous missing variable and avoid its early forms of rejection. In addition, the unsupervised classifier can classify all observations into a set of groups based on upstream river behavior and rainfall information. It can then return the probability of belonging to each group and provide appropriate predictions about flood risk in the coastal region.

Methods based on the analysis of variables are of interest to researchers in many research fields. The method of analyzing the relationship of variables mainly refers to the use of mathematical mechanisms to build a logical model based on random data or time series of two or more variables and then shows the change relationship between these variables and their change process. The data that have been selected possesses certain characteristics such as quantity, time, and trend. From the perspective of the quantity of variables, the relationship between variables can be divided into two categories: single and multiple. According to its overall change characteristics, it can be divided into two categories: linear and nonlinear. Based on the correlation between different variables, it can be determined whether there is a causal relationship or not. This article has estimated the depth of nitrate penetration into groundwater by combining variables such as cultivation patterns and the time series data of plant growth.

The data collected for the research consisted of five major groups of data for wheat, barley, paddy, alfalfa and potato plants, which are summarized in Table 1. The effect of irrigation and fertilizer has been investigated as two important factors of increasing nitrate concentration in underground water.

As discussed in the review of past research, there are different methods for risk estimation. In this research, the risk of using nitrate fertilizer for agricultural use on the ecosystem is calculated hierarchically. Another tool that is common among researchers to analyze risk is the use of probabilistic Bayesian networks.

The Bayesian network consists of two main parts such as quantitative and qualitative. Its quantitative part is a set of probabilistic relations or probability distributions for each cell of the presented problem, and the qualitative part is a directed linear graph in which each cell represents a variable and the nodes are an indicator of the relationship between the variables of the network. The connection between cells in a Bayesian network is known by the concept of family relations. If the cell has no parent, the cell will have a boundary probability table. If the node has a parent, it will have a conditional probability table.

The advantages of Bayesian networks include the possibility of combining expert opinions and existing data, displaying the variables of a model in the form of cells and analyzing the cause and effect in the form of relationships between cells, and using past information to predict the future situation. Bayesian networks are divided into three categories: continuous Bayesian network, networks with continuous cells, discrete Bayesian network, networks with discrete cells, and hybrid Bayesian network with both discrete and continuous cells. In this research, based on the input data, hybrid Bayesian networks were used, which were used first to analyze the risk of using nitrate fertilizer.

In order to calibrate and validate the model, cross-validation was done. The K-fold method is one of the cross-validation methods. In this method, the data series are divided into K subsets. Among the K subsets, each time one is used for validation and another K − 1 is used for training. This procedure is repeated K times, and all data are used exactly once for training and once for validation. Finally, the average result of these K validation times is chosen as a final estimate. Usually, the 5-layer or 10-layer validation method is used in modeling and forecasting studies. In this research, according to the number of data series, five layers were selected.

A number of input variables that were used to establish a logical relationship between nitrate concentration and irrigation are summarized in Table 2. These data were obtained from information calibrated by the groundwater modeling system (GMS v10.8) model and used as variables in the middle layers of the decision-making model. These variables included hydraulic head in initial and boundary conditions, specific yield, hydraulic conductivity, groundwater level, longitudinal slope, and land use (Siddik et al. 2022). Some uncertain coefficients of the aquifer were calibrated in the simulation stage. The plain results showed that the field soil has a relatively heavy texture with slow flow.

With the development of social economy and population growth, the demand for water resources by humans is increasing day by day. Due to the impact of climate change and human activities, global warming is intensifying, and the world population is constantly increasing. As a result, the demand for water resources is constantly increasing, thus causing the global water environment to deteriorate. At the same time, due to the rapid growth of population and the improvement of living standards, human demand for food and energy is also constantly increasing. Therefore, how to utilize limited water resources to meet the growing needs of socio-economic development is a major issue facing humanity. Therefore, solving the contradiction between humans and water, humans and energy, and achieving optimal resource allocation and sustainable development has become the focal point of attention in today's society. Compared with traditional agriculture, the new modern agriculture guided by ‘water-saving, efficient, and green development’ has significant advantages, but it has significant shortcomings in resource utilization efficiency. Under the water–grain–energy relationship, this model can achieve the optimal development mode selection for different types of agricultural wet areas. To achieve this goal, it is necessary to take the efficient utilization of soil and water resources as the foundation and the comprehensive management of water resources as the core.

This study was supported by Scientific and Technological Key Project in Henan Province (222102240049).

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

The authors declare there is no conflict.