Introduction

Water is vital for survival and supports the health, resilience, development, and prosperity of humans and the planet alike (WWAP, 2023). Two of the 17 Sustainable Development Goals (SDGs) explicitly refer to water-related issues, namely, SDG 6: Clean Water and Sanitation and SDG 14: Life below Water. Several other SDGs are indirectly related to water. For example, SDG 3 concerns health and well-being and pertains to the reduction of ambient pollution, including water pollution (Tsani et al., 2020). SDG 12 targets the efficient use of natural resources, including water (Tsani et al., 2020). SDG 1 addresses poverty reduction, and SDG 8 emphasizes sustainable economic growth and employment (UN, 2015), both of which require job growth through economic advancement, which in turn increases resource consumption. Water pertains to both production and ecology, playing a vital role in sustainable development, and river basins serve as the foundation for the formation and utilization of water resources. In China, regions with high levels of socioeconomic development and high population density tend to be concentrated along major rivers (e.g., the Yangtze, Yellow, and Ganges Rivers). In this context, water resource carrying capacity (WRCC) refers to the ability of the available freshwater in a region to support the population while achieving a certain level of urbanization and meeting a certain level of per capita welfare (including per capita domestic water use for urban and rural residents as well as continuous per capita gross domestic product (GDP) growth) (Shi and Qu, 1992; Xia and Zhu, 2002; Jia et al., 2004; Wang et al., 2017). At present, WRCC is evaluated using dimensionless indexes that characterize regional or basin water availability in a general way. For example, Li et al. (2023) constructed a composite index to simulate the suitability of water resources, while Peng et al. (2023), Wang et al. (2023), and Chen et al. (2023) evaluated trends in water resources and environmental carrying capacity using values ranging from 0 to 1. However, dimensionless indexes are relative in nature and lack effective, concise visual depictions of regional carrying capacity. To overcome such limitations, this study aimed to characterize WRCC by simulating population size and economic scale.

The Yellow River has experienced unprecedented levels of flooding (Yu et al., 2023) while facing water-scarcity issues as a result of inadequate natural resources and contamination (Niu et al., 2023). Reductions in the Yellow River’s runoff have been obvious since the 1950s (Wang et al., 2019; Dai et al., 2023). Wang (2015) projected that from 2021 to 2050, runoff would decrease by 0.53–9.67% compared with the rate of decrease from 1991 to 2010, with a peak of 13.26% during 2021–2030. The “Yellow River Basin Comprehensive Planning (2012–2030)” suggested that surface river runoff in the Yellow River basin (YRB) will be reduced to 51.48 billion m3 by 2030 (YRCC, 2013), reducing the amount of available freshwater. At the same time, the YRB accounts for 12.4% of China’s population, 14% of its GDP, and 2% of its water resourcesFootnote 1 (Tang et al., 2019; Omer et al., 2020; Bai et al., 2022). Thus, in 2019, as a major national strategy, China set higher requirements for water resource allocation, environmental protection, and high-quality development in the YRB, emphasizing stable economic growth and environmental sustainability. To this end, the “Yellow River Protection Law” was implemented in April 2023. Meanwhile, as far back as 1987, a province-based Water Allocation Plan was proposed for the YRB (also called the 1987 scheme) (SPC and MWREP, 1987). However, with ongoing population growth and decreases in runoff, the 1987 scheme could not effectively address the contradiction between socioeconomic development and environmental sustainability. With runoff decreases expected to peak by 2030 (Wang, 2015; Yuan et al., 2016), the abovementioned “Yellow River Basin Comprehensive Planning (2012–2030)” issued a water resource allocation plan for the nine provinces of the YRB (Table 1). It is projected that by 2030, the available freshwater will be 39.485 billion m3 and the population size will be 0.13094 billion. Against this background, this study aimed to address the following research questions.

Table 1 Water allocation scheme for the Yellow River Basin Comprehensive Planning unit: billion m3.
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  1. (1)

    Can 39.485 billion m3 of available freshwater meet the needs of 0.13094 billion people?

  2. (2)

    What population size and economic scale can be supported by 39.485 billion m3 of available freshwater?

Study area

The YRB is an important ecological barrier as well as an economic zone in China. About one-third of China’s grain and meat production originates from this area. The YRB is also an important energy, chemical, raw materials, and industrial base. Thus, water shortages in the YRB could seriously affect China’s food, energy, and ecological security (Niu et al., 2023). The Yellow River flows through nine provinces in northern China, including Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shaanxi, Shanxi, Henan, and Shandong. Its limited freshwater resources support large populations. Most of the YRB is in arid and semiarid areas, with an average annual precipitation of 446 mm and per capita water resources of 473 m3, only accounting for 23% of the national average while also supplying water outside the YRB (Niu et al., 2023). The exploitation and utilization rate of YRB water resources is as high as 80%, far exceeding the ecological warning line of 40% (Niu et al., 2023). A fragmented ecology and significant soil degradation pose great challenges. To address such challenges, water-diversion schemes have been improved, and the Yellow River Protection Law was promulgated, among other measures.

Considering existing water distribution schemes (Table 1) and data availability, this study was conducted at the provincial level within the YRB. We aimed to simulate population size and economic scale under various scenarios in the YRB based on the concept of WRCC.

Methods

Water resources carrying capacity forecasting model

Based on the concept of WRCC and previous work using a WRCC model for historical periods (Guo et al., 2022) (see SI), we constructed a WRCC prediction model. Generally, in the WRCC model, the maximum population and economic scale can be calculated based on per capita GDP times population size. The mathematical expressions are described as follows:

$${{{\mathrm{Objective}}}}\,{{{\mathrm{function}}}}:MAX\left( P \right).$$
(1)

Total water use, domestic water use, and production water use are expressed by Eqs. (2), (3), and (4):

$$TW_{2030} \ge W_{D - 2030} + W_{P - 2030} + W_{E - 2030},$$
(2)

where TW is the available freshwater—that is, total water use, also called the upper limit of water use in 2030. WD, WP, and WE represent the water used for domestic purposes, production (i.e., agriculture and industry), and ecology, respectively. The subscript 2030 refers to the year 2030 (the same applies below).

$$W_{D - 2030} = P_{2030} \times ur_{2030} \times Q_{U - 2030} + P_{2030} \times \left( {1 - ur_{2030}} \right) \times Q_{R - 2030},$$
(3)

in which P denotes population, and ur represents the degree of urbanization, which is the proportion of the population living in urban areas. QU and QR denote per capita domestic urban and rural water use, respectively.

$$W_{P - 2030} = P_{2030} \times Y_{a - 2030} \times Q_{GDP - 2030},$$
(4)

in which Ya is per capita GDP; QGDP is defined as water use per CNY10,000 of GDP, which represents water use efficiency. WI and WA denote water use for industry and agriculture, respectively.

$$Y_{a - 2030} = Y_{a - 2020} \times \left( {1 + gr} \right)^{10},$$
(5)
$$Q_{GDP - 2030} = Q_{GDP - 2020} \times \left( {1 - dr} \right),$$
(6)
$$Q_{GDP - 2020} = \left( {W_{I - 2020} + W_{A - 2020}} \right)/GDP_{2020} = W_{P - 2020}/GDP_{2020},$$
(7)

where the annual growth rate (gr) of per capita GDP and decreased ratio (dr) of water use per CNY10,000 of GDP are set using 2020 data. The subscript 2020 indicates the year 2020.

Regarding the ecological water use of each province in 2030, there are no relevant regulations. For the whole YRB, average ecological water use remained at 12 m3 from 2011 to 2015 and 22 m3 from 2016 to 2021 (MWR, 2011–2021). With ongoing environmental improvements, ecological water use will decrease by 2030. Thus, each province will have reduced ecological water use in 2030, which is assumed to be close to 0.

Population size in 2030 is deduced from Eqs. (2–7):

$$P_{2030} \le \frac{{TW_{2030} - W_{E - 2030}}}{{ur_{2030} \times Q_{U - 2030} + \left( {1 - ur_{2030}} \right) \times Q_{R - 2030} + Y_{a - 2030} \times Q_{GDP - 2030}}}.$$
(8)

Approximately,

$$P_{2030} \le \frac{{TW_{2030}}}{{ur_{2030} \times Q_{U - 2030} + \left( {1 - ur_{2030}} \right) \times Q_{R - 2030} + Y_{a - 2020} \times \left( {1 + gr} \right)^{10} \times Q_{GDP - 2020} \times \left( {1 - dr} \right)}}.$$
(9)

Further, the economic scale can be calculated by the product of Eqs. (5) and (8).

$$TWGDP_{2030} = P_{2030} \times Y_{a - 2030} = P_{2030} \times Y_{a - 2020} \times \left( {1 + gr} \right)^{10},$$
(10)

where TWGDP2030 is the regional total GDP.

Materials and data processing

As stated earlier, by 2030, the YRB’s available water resources will change greatly, and runoff will continue to decrease. At that time, the western route of the South-to-North Water Diversion Project will begin transporting water to relieve water shortages in the YRB. Hence, the “Yellow River Basin Comprehensive Planning (2012–2030)” (YRCC, 2013) provides a water resource allocation scheme for the provinces of the YRB in 2030 (see Table 1), assuming the western route of the South-to-North Water Diversion project opens as scheduled.

Urbanization in 2030, ur2030, was derived from each province’s planning for population and city development in 2030. Per capita domestic water use in urban areas, \(Q_{U - 2030}\), and per capita domestic water use in rural areas, \(Q_{R - 2030}\), were determined based on historical rules. The Mann–Kendall method (Hamed, 2008) was used to detect trends in the time-series data from 2013 to 2020. When it presented a prominent rising trend, the predicted value was adopted using artificial neural network backpropagation autoregression (Al-Zahrani and Abo-Monasar, 2015). Meanwhile, the upper limit was set based on WHO standards and the literature, with 330 L/d as the upper limit of per capita domestic water use in urban areas and 165 L/d in rural areas (Luna et al., 1992; Howard et al., 2020). If no evident or downward trend appeared, the mean value was selected to meet human demand, owing to a certain distance between China and WHO standards in per capita domestic water use. QGDP was calculated by dividing the sum of industrial and agricultural water use by GDP rather than directly using official statistics from the China Water Resources Bulletin. This is because domestic and ecological water use is not included in the calculation of QGDP (see Eq. (7)). Thus, the official statistics can yield exaggerated results since they incorporate elements beyond production water usage. Annual growth rate (gr) and decreased rate (dr) were also derived from the historical trend. These two parameters facilitated the simulation of possible development scenarios for each province, as presented in the next section. Here, the year 2020 was adopted as the benchmark year.

Results and discussion

We built the WRCC prediction model based on a previous study. Since model performance was evaluated by Guo et al. (2022) (see SI), there was no need to further verify model validity.

Scenarios of steady reform and no major shocks

According to previous research, water use per CNY10,000 of GDP and per capita GDP is more sensitive to the estimation of WRCC than other indicators (Guo et al., 2022) (see SI). Consequently, the scenarios with steady reforms and no major shocks were simulated through the annual growth rate (gr) of per capita GDP and decreased ratio (dr) of water use per CNY10,000 of GDP. Combined with the water allocation scheme, the scenarios were conducted taking each province as the computing unit. The annual per capita GDP growth rate was set as 1%–8% with step increases of 1%. We set 40% as the baseline of the gross water use decrease ratio based on the National Comprehensive Planning of Water Resources issued in 2010, which indicated that water use per CNY10,000 of GDP should decrease by 40% from 2020 to 2030 (Jiao, 2011). Official data show that this rate fell by 28% between 2016 and 2020 (Li and Chen, 2022), averaging 5.6% per year. As a result, the water use per CNY10,000 of GDP decrease ratio was set from 40% to 70% with decreasing steps of 5%. Further, the population size and economic scale of each province across various scenarios were determined by Eqs. (9) and (10). Then, the totals for the nine provinces were the population size and economic scale of the YRB (Fig. 1).

Fig. 1: The area of the Yellow River basin (Source: Guo et al., 2022).
figure 1

The Yellow River Basin is an important ecological barrier in China, and plays a crucial role in China’s socio-economic development and ecological security.

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Figure 2 shows that the economic scale had an uptrend with the decrease in water use per CNY10,000 of GDP and per capita GDP growth. Conversely, we can see in Fig. 3 that the limited freshwater resources can support a larger population size under a low per capita GDP growth rate while at the same level of water use per CNY10,000 of GDP. Under the baseline of 1% per capita GDP growth and 40% water use per CNY10,000 of GDP decrease ratio, limited freshwater resources of 39.845 billion m3 can carry a population of 0.18 billion, surpassing the predicted population of 0.13094 billion (YRCC, 2013). Correspondingly, the limited freshwater resources can support an economic scale of more than CNY12 trillion ($1.74 trillion)Footnote 2. Considering the differences in economic development and water use per CNY10,000 of GDP among the nine provinces, the WRCC of each province was analyzed to enhance simulation precision and realism.

Fig. 2: The economic scale of the Yellow River basin under different scenarios.
figure 2

The economic scale has an uptrend with the decrease of water use per CNY10,000 of GDP and per capita GDP growth.

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Fig. 3: The population size of the Yellow River basin under different scenarios.
figure 3

The limited freshwater resources can support more population size under a low per capita GDP growth rate while at the same level of water use per CNY10,000 of GDP.

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Most likely scenarios

To ensure the simulation’s reliability and accuracy, we analyzed each province’s scenario independently. Drawing on historical rules and practical knowledge, we still assumed that per capita GDP presented exponential growth while water use per CNY10,000 of GDP continued to decrease. The simulation scenarios were the same as in Guo et al. (2022). Specifically, the upper limit of each province’s annual per capita GDP growth rate was determined by the past three average values (NBS, 2019–2021). Meanwhile, the decelerating trend of the economic growth rate was also considered (World Bank and DRCSC, 2013). Moderate economic growth occurs when the per capita GDP growth rate declines by one percentage point, while a two percentage point decline is considered low economic growth. Based on historical trends and the water use per CNY10,000 of GDP decrease ratio over the last 10 years, as well as the experience of developed countries where this ratio gradually decreases, the upper limit of the water use per CNY10,000 of GDP decrease ratio for every province could be determined. Following the principle of proximity, the average annual value from 2011 to 2020 was used to determine the upper limit of each province. As mentioned above, 40% was the lower limit of each province’s water use efficiency enhancement (Jiao, 2011). The mean of the upper and bottom limits is a moderate development level. Thus, the cascading per capita GDP growth rate and decrease ratio for water use per CNY10,000 of GDP comprised three scenarios of high, moderate, and low development, as shown in Table 2.

Table 2 Scenarios setting.
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Further, based on Eqs. (9) and (10), population size (Table 3) and economic scale (Table 4) under different scenarios could be obtained.

Table 3 The maximum population size under different scenarios unit: million.
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Table 4 The economic scale under different scenarios unit: trillion (CNY).
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As shown in Table 3, the available freshwater could support maximum population sizes of 0.16, 0.152, and 0.147 billion under the high, moderate, and low scenarios, respectively. According to the national population development plan, by 2030, the population will peak at 1.45 billion (SC, 2016) while the YRB can support 8.76–11% of China’s total population. The “Yellow River Basin Comprehensive Planning (2012–2030)” predicts that the YRB’s population will be 0.13094 billion in 2030 (YRCC, 2013), which is significantly lower than the maximum population sizes of 0.16 billion, 0.152 billion, and 0.147 billion under the high, moderate, and low scenarios. As a result, the available freshwater can adequately sustain population expansion in the YRB. Accordingly, the available freshwater can support maximum economic scales of CNY17.5 trillion ($2.52 trillion), CNY15.01 trillion ($2.18 trillion), and CNY13.2 trillion ($1.91 trillion) under the high, moderate, and low scenarios, respectively (Table 4). Further, the YRB can support 6.9–8.0% of China’s total economic scale.

Spatial analysis of WRCC under different scenarios

In terms of population size, in the middle and upper reaches of the YRB—Qinghai, Sichuan, Gansu, Ningxia, and Inner Mongolia—the maximum population sizes are about 42.39, 39.14, and 36.98 million under the high, moderate, and low scenarios, respectively. In the middle and lower reaches of the YRB—Shanxi, Shaanxi, Henan, and Shandong—the figures are 117.17, 112.43, and 109.60 million under the high, moderate, and low scenarios, respectively. Therefore, the middle and upper reaches of the YRB can only carry 25% of the total population across the YRB while the middle and lower reaches can carry 75%.

In terms of the economic scale, in the middle and upper reaches of the YRB—Qinghai, Sichuan, Gansu, Ningxia, and Inner Mongolia—the total maximum economic scales are about CNY3.69 trillion ($0.53 trillion), CNY3.13 trillion ($0.45 trillion), and CNY2.71 trillion ($0.39 trillion) under the high, moderate, and low scenarios, respectively. In the middle and lower reaches of the YRB—Shanxi, Shaanxi, Henan, and Shandong—the figures are CNY13.67 trillion ($1.98 trillion), CNY11.89 trillion ($1.72 trillion), and CNY10.50 trillion ($1.52 trillion) under the high, moderate, and low scenarios, respectively. Thus, the economic scale of the middle and lower reaches of the YRB is approximately 3.8–4.3 times greater than that of the middle and upper reaches.

In light of the above, by 2030, it is estimated that the middle and lower reaches of the YRB can carry about three times as many people as the upper and middle reaches and about four times the economic scale as the upper and middle reaches. Nevertheless, the water allocation of the middle and upper reaches is 18.14 billion m3, and that of the middle and lower reaches is 21.345 billion m3, which is 1.18 times higher than that of the middle and upper reaches (Table 1). Although the YRB might carry more population and economic aggregates, there are still significant differences in WRCC within the YRB.

Differential analysis of WRCC

Combined with the simulation scenarios, the disparities in regional economic growth and water resource utilization represent the primary factors. By 2030, the average per capita GDPs of the middle and upper reaches of the YRB are about CNY88,791, CNY86,689, and CNY78,766 under the high, moderate, and low scenarios, respectively; the average per capita GDPs of the middle and lower reaches are about CNY114,013, CNY103,743, and CNY94,314, respectively (Table 5).

Table 5 Per capita GDP and water use per CNY10,000 of GDP under different scenarios in 2030.
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Comparatively, the per capita GDP of the middle and upper reaches of the YRB under the high scenario is significantly lower than the average per capita GDP of the middle and lower reaches under the low scenario. This suggests that the five provinces in the middle and upper reaches are relatively less developed regions. Meanwhile, the regional variations in water use efficiency are significant. For example, water use per CNY10,000 of GDP across the middle and upper reaches is 37.74, 45.74, and 54.19 m³ under the high, moderate, and low scenarios, respectively (Table 5); however, across the middle and lower reaches, the figures were 12.50, 14.27, and 16.09 m³, respectively (Table 5), which represented a threefold disparity.

Among the nine provinces, Gansu, located in the middle and upper reaches, has the lowest per capita GDP, while Shandong in the middle and lower reaches has the highest. In fact, among the four provinces in the middle and lower reaches of the YRB, the per capita GDP of the other three provinces, excluding Shanxi, is significantly higher than that of the five provinces in the middle and upper reaches (Table 5). Similarly, under the high, moderate, and low scenarios, the water use per CNY10,000 of GDP of the four provinces in the middle and lower reaches remains below 20 m3 while that of the five provinces in the middle and upper reaches remains at 40–60 m3. Specifically, Ningxia’s water use per CNY10,000 of GDP is seven times higher than that of Shandong (Table 5). In conclusion, imbalanced economic development and water use efficiency among provinces perpetuate large disparities in the YRB’s WRCC.

Uncertainties and limitations regarding water use

Here, we discuss uncertainties and limitations related to water use purposes and efficiency. Specifically, it was assumed that water allocation for each province is used solely for production and domestic purposes, without considering ecological water requirements. The simulated population size and economic scale were also the maximum and ideal supported by the YRB’s 2030 water allocation scheme. According to official statistics, over the past decade, the average ecological water use of the entire YRB was about 1.5 billion m3 (MWR, 2011–2021). Water use for ecological purposes has been relatively low in each province. Moreover, in the coming decade, with environmental improvement, ecological water use is expected to decline substantially, potentially leveling at 0. Therefore, the population size and economic scale might have been slightly overestimated compared with the actual situation. Meanwhile, technological innovation and industrial structure changes could expedite enhancements in water use efficiency; however, water use efficiency was determined through a combination of individual knowledge and the historical trends of each province. The setting of water use efficiency has certain limitations and uncertainties owing to unknown technological and industrial developments. Thus, these uncertainties were also included in water use efficiency used to predict future development trends. However, water use efficiency has a greater effect on WRCC (Guo et al., 2022). Then, uncertainties regarding water use efficiency will result in uncertainties and biases in the simulated population size and economic scale in 2030. Nevertheless, the scenarios were all determined through long-term trend analysis, and predictions and simulations at the provincial level are characterized by higher credibility.

Conclusion

To investigate the carrying capacity of available freshwater, this study simulated population size and economic scale under limited freshwater using a WRCC prediction model. Combining various scenarios, we generated 56 narratives (Figs. 2 and 3) that present plausible storylines for the trajectories of the YRB’s freshwater and socioeconomic systems. The most likely scenarios (under high, moderate, and low development) were proposed. The results showed that (1) by 2030, 39.845 billion m3 of freshwater could support population sizes of 0.16, 0.152, and 0.147 billion under high-, moderate-, and low-development scenarios, respectively. These figures are greater than the 0.13094 billion predicted by the “Yellow River Basin Comprehensive Planning (2012–2030).” (2) By 2030, 39.845 billion m3 of freshwater could support economic scales of CNY17.5 trillion ($2.52 trillion), CNY15.01 trillion ($2.18 trillion), and CNY13.2 trillion ($1.91 trillion) under the high-, moderate-, and low-development scenarios, respectively, accounting for 22.4–24.6% of the nine provinces’ total economic scale. (3) There were significant differences in WRCC within the YRB, especially between the middle and upper reaches and the middle and lower reaches.

The main contributions of this study are as follows. (1) Using population size and economic scale to characterize WRCC helps overcome the limitation of measuring WRCC with a dimensionless index. (2) Quantifying the size of WRCC helps correct the defects of single-trend measurement. (3) This study’s narratives paint a clear picture of the YRB’s future water security and socioeconomic development. This could contribute to formulating policies for sustainable, high-quality development. Meanwhile, this study’s shortcomings include two points. (1) The projected population size did not take into account population density, which is assumed to be evenly distributed. (2) Compared with the provincial sample units of the YRB, the detailed spatial scale of municipal or county sample units was accurate, which would be more conducive to strengthening the rigid constraints of water-diversion schemes. As such, the next step should be to consider population density in the model and apply it at more detailed spatial scales.