Under the pressures of global climate change and human activities, the carrying capacity of water and soil resources in agricultural lands has decreased, and the traditional models of agricultural development are no longer sustainable. Land degradation, groundwater quality reduction and ecosystem instability are the consequences of agricultural development without considering sustainability indicators. This article aims to investigate the use of variable relationship analysis and Bayesian network methods to analyze and investigate the relationship between irrigation in agriculture and the sustainability of the groundwater ecosystem. Descriptive statistics of agriculture including cultivation pattern, time, precipitation, irrigation, and land slope were analyzed and combined with the simulated characteristics of groundwater including specific yield, hydraulic conductivity and hydrodynamic diffusion coefficients. Five crops of wheat, barley, paddy, alfalfa, and potato were studied to evaluate the effect of plants on the pattern of nitrate release due to irrigation and fertilization in agriculture. The results showed that managing the amount of fertilizer and the volume of irrigation can positively affect the nitrate distribution pattern in the groundwater even in a short period of time.

  • The relationships between variables are used to build a logical model for analysis.

  • The quantity and quality of irrigation water is incorporated into the system for estimating the nitrate concentration in groundwater.

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.

Study areas

The study takes place in the Loess Plateau, China (Figure 1). The Loess Plateau is located in northern China and is characterized by highly erodible thick Loess soil (92.2 m on average). It is traversed by the upper and middle reaches of the Yellow River and covers a total area of ∼640,000 km2 (Zhu et al. 2018; Zhang et al. 2022). Erosion and land degradation were main challenges in this region (Zhou et al. 2021) and some strategies such as revegetation have been used to cope with them. In the revegetation process, several studies showed that the vegetation cover in the Loess Plateau increased at an approximate rate of 6–8% during six years or 12.5% at local level in the Central Loess Plateau. The net primary production of regional ecosystems in the Loess Plateau experienced a significant increase or remained stable between 1999 and 2008. In general, the trend of improving soil conservation and grain production may indicate that these key ecosystem services act in synergy (Lu et al. 2021).
Figure 1

Loess Plateau in China.

Figure 1

Loess Plateau in China.

Close modal

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.

Table 1

Collected data for variable analysis

LocationTime periodIrrigation (mm)Fertilizer (kg·m−3)Nitrate (mg·L−1)
L1 (Wheat) T1 18 0.70 34 
T2 26 0.60 37 
T3 19 0.64 38 
L2 (Potato) T1 23 0.75 23 
T2 31 0.63 24 
T3 27 0.63 26 
L3 (Barley) T1 14 0.62 27 
T2 19 0.69 36 
T3 21 0.74 33 
L4 (Paddy) T1 17 0.60 41 
T2 16 0.67 42 
T3 24 0.74 48 
L5 (Alfalfa) T1 23 0.61 36 
T2 27 0.77 37 
T3 18 0.66 39 
LocationTime periodIrrigation (mm)Fertilizer (kg·m−3)Nitrate (mg·L−1)
L1 (Wheat) T1 18 0.70 34 
T2 26 0.60 37 
T3 19 0.64 38 
L2 (Potato) T1 23 0.75 23 
T2 31 0.63 24 
T3 27 0.63 26 
L3 (Barley) T1 14 0.62 27 
T2 19 0.69 36 
T3 21 0.74 33 
L4 (Paddy) T1 17 0.60 41 
T2 16 0.67 42 
T3 24 0.74 48 
L5 (Alfalfa) T1 23 0.61 36 
T2 27 0.77 37 
T3 18 0.66 39 

Variable relationship analysis

The univariate linear regression model that contains only one independent variable is used to describe a linear correlation between the dependent variable and the independent variable. Its basic structure is as follows:
(1)
where and are calibrated parameters, and are functions for the tth observation, and is the random error term. The multiple linear regression model is a type of regression model used to describe the linear correlation between the dependent variable and multiple independent variables. Its basic structure is as follows:
(2)
where are the functions for the tth observation.
A nonlinear regression model describes the nonlinear relationship between the dependent variable and the independent variable. It can set new variables as needed and use variable substitution methods to convert the existing nonlinear relationship into a linear relationship under the new variable. For example, on the hyperbola, the formula is as follows:
(3)
It can be transformed into a line form:
(4)
where and .

Probabilistic Bayesian networks

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.

These networks are optimized based on Bayes' theorem, which obtains the secondary probability based on the primary probability (Equation (1)) (Khakzad et al. 2011). Due to this ability and the structure of risks, which is in the form of cause and effect relationship, the use of Bayesian networks helps to analyze the risk in the interaction between water and ecosystem:
(5)
where P(EF) is the probability of occurrence E with condition F or the same posterior probability, P(FEi) is the probability of occurrence F with condition Ei, P(Ei) is the probability of observing Ei with the prior probability, and P(F) is the probability of observing F. Moreover, for n events E1, E2, … En where 1 ≤ in, P (Ei) ≠ 0.

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.

Groundwater model calibration

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.

Table 2

Calibrated parameters by the model

ParametersValues
Hydraulic conductivity 0.6–9 m/day 
Specific yield 0.002–0.06 
Effective molecular diffusion coefficient 0.001 
Longitudinal dispersivity 4.8 
Distribution coefficient 0.0003 
ParametersValues
Hydraulic conductivity 0.6–9 m/day 
Specific yield 0.002–0.06 
Effective molecular diffusion coefficient 0.001 
Longitudinal dispersivity 4.8 
Distribution coefficient 0.0003 

Irrigation and nitrate concentration

A comparative model for evaluating the amount of irrigation and nitrate concentration is designed in Figure 2. The points show two values of irrigation volume (m3/ha) for a growing season and nitrate concentration at the end of the season for a sampled point. Samples are connected to each other based on the closest geographic distance. Therefore, the connection of points represents the shortest distance to other points. The pattern shown in Figure 2, which shows the current situation, argues that increasing the volume of irrigation causes a decrease in nitrate concentration. The accumulation of the specified points is a reason for the increase in the concentration of nitrates in the groundwater due to the reduction of irrigation and the increase in the use of fertilizers containing nitrogen. Changing the state of this pattern can indicate improved planning to improve the relationship between water and the ecosystem.
Figure 2

Distribution pattern of nitrate concentration in the existing condition.

Figure 2

Distribution pattern of nitrate concentration in the existing condition.

Close modal
Irrigation management cannot be a complete decision without considering the control of groundwater quality, which is one of the main components of a sustainable ecosystem. Figure 3 shows the increase in nitrate concentration as a result of updating water allocation management regardless of fertilizer. In this method, the amount of irrigation is allocated based on plant needs and increasing food security. This method of planning has caused leaching and increased infiltration and has increased the concentration of nitrates in the groundwater. The effect of the continuation of this process on the quality of groundwater has brought the nitrate concentration to an average of 50 mg/L. Around 50 mg/L is the upper limit of the water quality standard. Several researches have been conducted to confirm the negative impact of irrigation on the quality of groundwater (Lalehzari & Tabatabaei 2015).
Figure 3

Distribution pattern of nitrate concentration in the critical condition.

Figure 3

Distribution pattern of nitrate concentration in the critical condition.

Close modal
Water and fertilizer management for ecosystem sustainability, if based on fertilizer control, can significantly reduce groundwater nitrate in the long term. Figure 4 shows the distribution pattern of points for fertilizer control. The density of points shown in the figure confirms that the average nitrate concentration has reached 26 mg/L. The decrease in the distance between the points indicates the effect of the adductive phenomenon in nitrate diffusion (Lalehzari et al. 2013).
Figure 4

Distribution pattern of nitrate concentration in the suggested condition.

Figure 4

Distribution pattern of nitrate concentration in the suggested condition.

Close modal

Probabilistic variable analysis

The prediction of groundwater nitrate concentration in five locations that had agricultural use in three time periods is shown in Figure 5. The highest and lowest values are estimated based on the analysis of variables in the form of Bayesian network. The results showed that nitrate concentration increased at the end of the growing season. The difference between the available amount and the recommended amount is obtained based on the distribution patterns of nitrate relative to irrigation. Suggested values are achievable based on predetermined schedules. However, the maximum and minimum values are subject to probabilistic conditions.
Figure 5

Nitrate changes based on probabilistic Bayesian networks and variable analysis.

Figure 5

Nitrate changes based on probabilistic Bayesian networks and variable analysis.

Close modal
Water allocation management for the quality control of surface or groundwater is one of the interested topics of the past researches (Rafipour-Langeroudi et al. 2014; Naghdi et al. 2021; Norouzi Khatiri et al. 2023). In this section, in order to compare the suggested values of irrigation compared to the existing values, the depth of irrigation is reported in millimeters. Maximum and minimum possible limits for plant growth and quality control are also suggested. According to Figure 6, irrigation at T1 time had the lowest average among all locations and the highest amount was at T2 time. It is necessary to explain that in order to control the concentration of groundwater nitrate, it is necessary to increase irrigation to a level higher than the current values. This argument can be seen in all scenarios.
Figure 6

Irrigation changes based on probabilistic Bayesian networks and variable analysis.

Figure 6

Irrigation changes based on probabilistic Bayesian networks and variable analysis.

Close modal
The range of fertilizer changes was wider compared to irrigation (Figure 7). The high range of fertilizer changes in comparison to irrigation is due to the effective role of fertilizer in the decision-making system (Zhu et al. 2020) based on the analysis of variables. In the L2 and L4 ranges, the amount of fertilizer has decreased at the end of the growing season. This is to be expected because part of the production of the results is based on the experience of the farmers. Past researches have pointed the role of changes in fertilization in the growing season according to the needs of the plant (Ebrahimi et al. 2019; Agathokleous et al. 2023).
Figure 7

Fertilizer changes based on probabilistic Bayesian networks and variable analysis.

Figure 7

Fertilizer changes based on probabilistic Bayesian networks and variable analysis.

Close modal

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.

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