Water resources carrying capacity to achieve a sustainable ecosystem using support vector regression

The water resources carrying capacity (WRCC) is an important factor for the sustainability of agricultural management. Exceeding the carrying capacity of water resources causes destructive environmental and agricultural effects such as erosion, reduction of water resources, increase in climate change, pollution and health risk, land degradation, reduction of biodiversity, destruction of ecosystem services, and reduction of productivity (Sun et al. 2023). In the agricultural sector, the reduction of production efficiency and the increase of planning risk are the most important consequences of the carrying capacity of water resources. Under normal circumstances, these damages will be irreversible or accompanied by environmental destruction and economic failure. Therefore, it is necessary to consider WRCC in planning for long-term agricultural development.

Several planning techniques have been developed to achieve the sustainability of water resources in agriculture including conjunctive exploitation of surface and groundwater, developing the optimal plans for water allocation (Ahmad & Zhang 2022), interbasin water transfer (Cánovas-Molina et al. 2023), optimal planning of irrigation (Lalehzari et al. 2016), uncertainty modeling, and water resources agricultural footprint analysis (Berger et al. 2021). Among these strategies, analyses of carrying capacity and agricultural water resources are widely used to formulate the evaluation systems for developing the sustainability of water resources (Kang et al. 2019; He et al. 2021; Li et al. 2023).

Considering the large spatial difference in water resources, water scarcity, and deterioration of water quality in Northeast China's economic circle, the WRCC was evaluated from the perspective of time and space by Wang et al. (2021). Gray correlation analysis and multiple linear regression models were combined to quantitatively predict water supply and demand in different planning years. In the selection of research indicators, the interaction of social economy, water resources, and water environment was also taken into consideration. Song et al. (2011) proposed the concept of WRCC to assess the economic and population scale that local water resources can support. In this study, the city of Tianjin, China, is considered as an example and its population size and economic scale were selected as two main indicators. Based on the historical statistical data, the carrying index (CI) and the balance of supply and demand index (IWSD) were evaluated, and then the current WRCC in Tianjin city and its dynamic trend were evaluated using the carrying capacity method. The results showed that the use of water resources in Tianjin is currently inefficient, and rational policies and measures should be established and implemented to ensure the optimal use of water resources in Tianjin city. Qi et al. (2021) evaluated the spatiotemporal changes in climatic factors and agricultural water resources carrying capacity (AWRCC) during the crop growing season in the Nenjiang River Basin. Precipitation, evapotranspiration, and meteorological drought were all key driving factors affecting the problem. Wang et al. (2023) indicated that the carrying capacity of agricultural water resources in Anhui Province has shown a fluctuating upward trend from 2000 to 2020. Furthermore, the carrying capacity in the southern region of Anhui Province is gradually increasing, while that in the northern region is decreasing. It is recommended that Anhui Province increase the construction of agricultural water resource management and field water conservation facilities to ensure the sustainable use of agricultural water resources.

The basic idea of support vector regression (SVR) is that a non-linear mapping can map the data into a high-dimensional feature space where linear regression is performed. SVR offers a better solution for small sample problems by minimizing the generalization error bound. In recent years, machine learning (ML) has been one of the most significant advances in the field of optimization technology. It is built on the established statistical learning theory (Morshed et al. 2024). Support vector machines (SVMs) are learning machines that can achieve better generalization on a limited number of learning patterns. There are two categories: one is support vector classification (SVC) solving classification problems and the other is SVR solving regression problems. In this paper, water resources footprints and carrying capacities are calculated and analyzed. Furthermore, with applying SVR, the prediction of water resources footprints is performed. Moreover, observational data were compared to evaluate the accuracy of SVR.

Three parameters of SVR should be optimized, that are kernel function, C, and ε. There are various forms of kernel functions, such as Gaussian radial basis function, exponential radial basis function, multilayer perceptron, and additive kernels function. Among these kernel functions, Gaussian radial basis function is usually preferable in practical problems.

The Gaussian radial basis function was developed as the kernel function. To find the optimal parameter combination (σ∗, C∗, ε∗), genetic algorithm can be used with fewer computing overheads. However, due to the greedy search used in the genetic algorithm to find the optimal solution, it may fall into local optimality. To tackle this problem, we repeat the genetic algorithm a given number of times (30 times in our experiment) to find the optimal combination, which has the smallest prediction error on the validation set. This process is finished through Libsvm, an SVM tool box, widely used in the implementation of SVM.

As shown in Figure 3, the change of agricultural footprints per capita in the study area can be roughly divided into two stages: while it has been relatively stable from 2010 to 2020, there has obviously been an overall decline compared with before 2010. As for agricultural carrying capacity per capita, it changes little except in some years such as 2013, 2015, 2017, and 2019, when it was clearly smaller than in the other years.

Water resources analysis from the perspective of water footprint contents in the study area is indicated in Table 2. The agricultural water resources footprint has occupied the highest proportion among four categories. Its proportion is not lower than 0.48. Agricultural footprint per capita has occupied the second highest proportion with a peak value of 0.64. The proportion of urban water resources footprint per capita is nearly equal to the proportion of household water resources footprint per capita every year.

In this paper, water resources footprints and carrying capacities from 2010 to 2020 in the study area are calculated and analyzed. The same indexes on the level of the whole study area are calculated as a comparison. Furthermore, by introducing SVR, which belongs to the field of ML, water resources footprints per capita from 2010 to 2020 are predicted via the use of a small sample. Experimental results show that SVR has less fitting and prediction errors compared with the classical methods. Although there is no a large sample of water resources, the established SVR model will provide some guidance for the sustainable development of water resources in the study area.

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

The authors declare there is no conflict.