Population dynamics are driven by births, deaths, and migration (Fig. 3). Births are calculated based on exogenous total fertility rates derived from historical data (Eq. S2 in the Supplement) to reflect the strong influence of China's Family Planning Policy. Deaths are determined by the life expectancy, which is modeled as a function of human well-being (Eqs. S3–S6). Migration is calculated based on historical statistical data and per capita GDP differences between YRB and the national average (Eqs. S7–S8). The total population is characterized by age and gender with exogenous urbanization ratios. The output of Population sector drives Economy, Energy, Food, and Water Demand sectors through labor force, urban and rural populations.

The key variable, total population, is modeled using the age-structured mathematical method (Kemei et al., 2024), which categorizes individuals by one-year age group and gender (Eq. 1), 1Popg,a=IniPopg,a+∫Bg,a+NMg,a-Dg,adt,a=0∫Popg,a+NMg,a-Dg,adt,1≤a≤99,a=100and over where Pop is population, subscript g and a are gender (g=M for male, g=F for female) and age (a=0–100 and over); IniPop_g,a is the population in the initial year, Bg,a is the births, Dg,a is the deaths, and NM_g,a is the net migrants (i.e., immigrants – emigrations).

The Economy sector simulates production activities in agriculture, industry, and services, which in turn drive changes in the Population, Energy, and Water Demand sectors (Fig. 4).

The gross product of industry and services is calculated using the Cobb-Douglas production function (Cobb and Douglas, 1928) to account for multiple factors in the economy (Eq. 2). Exogenous variables (infrastructure, education, and elasticity), and endogenous variables (health and labor force) from the Population sector (Eqs. S10–S21) all affect the gross domestic product in industry and service (GDP_s), 2GDPs=IniGDPs×TFPs×LsIniLs1-αs×KsIniKsαs where subscript s represents industry and service, IniGDP_s is the initial GDP; TFP_s is the total factor productivity calculated from exogenous (infrastructure, education, and elasticity) and endogenous variables (health and labor force) (Eqs. S10–S13); Ls represents the labor force and IniL_s is its initial value (from Population sector); αs and 1-αs are capital and labor elasticities from T21-China (Qu et al., 2020) and calibrated using historical data; Ks and IniK_s refer to the capital stock and its initial level (Eqs. S14–S21).

Gross agricultural production includes crop and livestock production from Food sector, calculated by their respective prices (Eqs. S22–S23).

The Energy sector simulates production, consumption, and the structure of the energy system, encompassing fossil fuels (coal, oil, and gas) and electricity (Fig. 5). Energy production and consumption are always balanced in this sector. Electricity generation is divided into residential and production uses, the former is estimated from the linear fit of historical per capita GDP and residential demand, and the latter is calculated using GDP and electricity intensity data from the China Energy Statistical Yearbook (NBSC, 2020a) (Eqs. S24–S25). Cross-provincial electricity transmission is also incorporated according to the same yearbook. The shares of electricity generated from thermal, hydro, wind, solar, and nuclear sources are determined by exogenously specified ratios, as reported in the China Energy Statistical Yearbook (NBSC, 2020a). The fossil fuel consumption by economic production of industry and service sectors is modeled as a linear function of sectoral GDP based on historical data (Eqs. S26–S28). It combines with fossil fuel consumption for electricity generation and residential gas consumption to drive carbon emissions in the Carbon sector.

The Food sector simulates the production of livestock and crops, and food demand, and these productions directly affect gross agricultural production in the Economy sector (Fig. 6). Livestock production (Livestock_pro) is calculated by an empirical function, driven by economic development and population growth (Eqs. 3, S29), 3Livestockpro=Pop×ParaGL1+ParaGL2-ParaGL1×PCGDPPCGDP+ConstGL where Para_GL1, Para_GL2 and Const_GL are parameters obtained by fitting the historical per capita meat production and per capita GDP (PC_GDP) data.

Crop production (Crop_pro) is determined by the yield (Yield_c) and harvest area (PA_c) of seven major crop types (subscript c): rice, wheat, corn, soybeans, cotton, potatoes, and oil crops (Eq. 4). The harvest area is influenced by cropland area from the Land sector, exogenous cropping intensity and crop harvest ratio. Crop yields are positively affected by agricultural investment from the Economy sector, along with effects of precipitation, temperature, and CO₂ concentration from the Climate sector (Eqs. S30–S36). 4Croppro=∑c=17Yieldc×PAc

Food demand encompasses both staple and feed grain demand, which are determined by population size from Population sector and dietary patterns (Eqs. S37–S41).

The Water Demand sector simulates water withdrawal (WW) and consumption (WC) across multiple uses – irrigation, livestock, industry, services, and residential – in the nine provinces of the YRB (Fig. 7). Water consumption is derived as the product of water withdrawal and water use efficiency reported in the Water Resources Bulletin (YRCC, MWR, 2020) (Eqs. S42–S43), which affects the Water Supply sector.

Irrigation water withdrawal (WW_irr) is estimated through a physically-based function of exogenous irrigation water use intensity (WWI_irr), cropland irrigation ratios (IR) from the China Agricultural Yearbook (MARA, 2020), and cropland area (Area_Cropland) provided by the Land sector (Eq. 5). 5WWirr=WWIirr×AreaCropland×IR

The water withdrawal for livestock, industry, and services is also driven by exogenous sectoral water use intensities collected from the China Statistical Yearbook and National Long-term Water Use Dataset of China (Zhou et al., 2020), in combination with livestock production from the Food sector, economic output from the Economy sector (Eqs. S44–S48).

Residential water withdrawal (WW_res) is derived from a non-linear empirical function of economic development and population growth with an upper limit of per capita domestic water use (Flörke et al., 2013) because water demand per person cannot increase indefinitely (Eqs. 6, S49), 6WWres=Pop×ParaGD1+ParaGD2-ParaGD1×PCGDPPCGDP+ConstGD where Para_GD1, Para_GD2, and Const_GD are parameters obtained by fitting the historical per capita domestic water use with per capita GDP (PC_GDP).

The Water Supply sector simulates runoff, discharge, and their changes in each sub-basin (Fig. 8). Runoff (R) is determined by precipitation (Pre) and evapotranspiration (ET) based on the water balance principle derived from the Budyko equation, which is suitable for non-humid regions of China (Yang et al., 2009) (Eqs. 7, S50), 7R=Pre-ET where ET is calculated by various exogenous climate variables from the Climate sector, and vegetation coverage from the Land sector (Eqs. 8–9, S51–S53), 8ET=PET×PrePren+EPn1n9n=ParaE1×KsPIParaE2×FVCParaE3×eParaE4tan⁡β where PET is potential evapotranspiration at sub-basin, from the Climate sector; n is a parameter reflecting the basin landscape characteristics, related to saturated hydraulic conductivity (Ks), precipitation intensity (PI), average slope (β), and fraction of vegetation coverage (FVC); Para_E1, Para_E2, Para_E3, and Para_E4 are parameters fitted from historical data.

Runoff and the loss coefficient (defined by the ratio of natural streamflow to runoff) determine the natural streamflow due to the water loss during the confluence process (Eq. S54). Natural streamflow and ecological flow constraints define the upper limit of available water resources. By integrating human water consumption from the Water Demand sector across sub-basins, the model calculates the actual streamflow (Eqs. S55–S57). Actual streamflow is transferred following hydrological connectivity from upstream, midstream, and downstream, ultimately reaching the sea, which governs sediment transport processes within the Sediment sector.

The Sediment sector estimates sediment load (Sed) for each sub-basin using an empirical model in the literature (Yin et al., 2023b), which links actual streamflow from the Water Supply sector to sediment transport (Eqs. 10, S58–S59), 10Sed=ParaSS×AS+ConstSS where Para_SS and Const_SS are derived from linear fitting of historical hydrological station data on actual streamflow and sediment load.

The Land sector simulates the area changes of six land use types (cropland, forest, grassland, wetland, settlement, and others) based on the land transfer matrix obtained from historical remote sensing data (Xu et al., 2018). The land transfer matrix calculates the inflow and outflow of each land category and can be configured to represent the influence of future land use drivers (Fig. 9). This sector outputs vegetation area (including forest, grassland, and cropland), which influences the Water Supply sector. Cropland area changes impact the Food sector, while land use conversion also plays a role in the Carbon sector.

Based on the initial land use area (IniArea_i), the transfer matrix determines the area (Area_i) allocated to each land use type (Eqs. 11, S60–S66), 11Areai=IniAreai+∫∑i=16FTMi,j-∑j=16FTMi,jdt where FTM_i,j is the finial land use transfer matrix, indicating the area of land use i transferred to land use j (i and j represent six land use type).

The Carbon sector simulates the basin's carbon processes and their balance, including carbon emissions and absorption, adapted from the carbon cycle of ANEMI (Davies and Simonovic, 2011). Carbon emissions (CE) encompass fossil fuel emissions, and livestock emission, and ecosystem respiration, which are influenced by outputs from the Energy, Food, and Land sectors (Fig. 10).

Fossil fuel and livestock emissions are calculated based on fossil fuel consumption, livestock production, and their respective emission coefficients. Ecosystem emissions include carbon released from burning as well as from the decomposition of biomass, litter, humus, and charcoal, which are determined by carbon pools' lifespans, decomposition factor, and respiration coefficients (Eqs. S69–S93).

Carbon absorption (CA) is determined by net primary productivity (NPP) and land use area. NPP is influenced by climate factors, including CO₂ concentration, temperature, and precipitation (Eqs. 12, S67–S68), 12CA=∑i=16NPPi×Areai where i represent land use type and land use area (Area_i) is from the Land sector.

The Climate sector supplies both historical and projected future climate data essential for the Water Supply, Food, and Carbon sectors. The key climate variables comprise temperature and precipitation (at the sub-basin and provincial levels), as well as potential evapotranspiration, precipitation intensity, and CO2 concentration (at the sub-basin level). These variables are treated as exogenous inputs, without accounting for potential feedbacks from human activities or natural system responses on regional climate patterns.

The future baseline scenario represents a trajectory in which existing plans and policies continue to operate without substantial changes in external environments. The development of the baseline scenario primarily relies on variables from the Population, Economy, Water Demand, and Land sector based on available government planning documents, historical trends, and other projections (Table 2). For future projections, variables or parameters not specified in the Table 2 are held constant at historical levels from their most recent year. Future climate data (2015–2100) are from the ensemble mean of 11 CMIP6 models (ACCESS-CM2, CESM2, CMCC-ESM2, GFDL-ESM4, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, MIROC6, MRI-ESM2-0, UKESM1-0-LL, and HadGEM-GC31-LL) (available at https://cds.climate.copernicus.eu/datasets/projections-cmip6?tab=download, last access: 8 March 2026) for the SSP 2-4.5 because this scenario aligns more closely with the climate trends in the YRB. To ensure temporal consistency, CMIP6 historical climate data (1981–2014) were used instead of observed historical records. To reduce systemic biases in the raw CMIP6 data, we applied bias correction using CN05 and ground weather stations observations from 1981 to 2014. By statistically aligning the mean of the CMIP6 data with observation records, systemic bias is removed while retaining the temporal consistency required for long-term simulation.

We run the model under the future baseline scenario and analyze the projected evolution of CHANS in the basin from 2021 to 2100 (see Sect. S6 for details of the future scenario design and supplementary spreadsheet for the setting of exogenous variables).

The model simulates human and natural system dynamics under the future baseline scenario and produces outputs for nine provinces and their corresponding areas within the YRB. The simulation results are reported either at the provincial level (nine provinces) for human system sectors or at the basin level (basin boundary) for natural system sectors. The total population in the nine provinces and the YRB is projected to peak in 2023 and 2024, at 429 and 131 million, respectively, driven by declining fertility rates (Fig. 13a). The labor force peaks earlier, reaching 261 million in the nine provinces in 2012 and 79 million in the YRB in 2011 (Fig. 13b). After 2025, the labor force is projected to increase again due to the delayed retirement policy. GDP in the nine provinces is expected to increase until a peak in 2063, at 91 trillion CNY (three times the 2020 level in constant prices), under the influence of a labor force decline, with the YRB reaching its peak four years later (Fig. 13c). In contrast to total GDP, per capita GDP in all regions is projected to continue rising throughout the future period (Fig. 13d). Although all provinces demonstrate improvements in economic status and living standards, considerable regional disparities persist. Among the nine provinces, Shaanxi demonstrates the largest growth in average per capita GDP from 2021 to 2100 relative to the historical period (1981–2020), with a more than seventeenfold increase, while the YRB as a whole shows an over thirteenfold increase.

Under the future baseline scenario, land use patterns remain relatively stable along historical trajectories (Fig. 14a), as no new land use policies are introduced and cropland area in each province has to stay above a mandatory minimum threshold for food security (China's Cropland Red Line policy). The forest area is projected to increase gradually, reaching 62 % above the 2021 level by 2100, while the cropland area is expected continue declining, falling 12 % below the 2021 level. Total crop production in nine provinces and YRB is projected to peak in 2079 and 2062 (Fig. 14b), respectively, driven by the combined effects of declining cropland area and increasing crop yields. Food demand in both the nine provinces and the YRB as a whole peaked in 2013 (193 and 57 million t, respectively) (Fig. 14c), largely driven by population dynamics. In the future, per capita food production in the YRB is projected to consistently exceed the international food security threshold of 0.4 t per person (Fig. 14d). However, in certain years, provinces such as Qinghai and Shaanxi could fall below this standard.

Total water withdrawal in the nine provinces and the YRB is projected to peak in 2056 and 2058, reaching 162 and 64 km³, respectively (Fig. 15a). Irrigation water withdrawal is expected to decline, driven by reductions in cropland area and irrigation intensity, the latter resulting from improvements in irrigation efficiency assumed in the scenario. Peaks in residential, industrial, service, and livestock water withdrawals are primarily associated with projected peaks in population and GDP. Natural streamflow is projected to exhibit a fluctuating upward trend of 0.073 km³ yr⁻¹ basin-wide (Fig. 15b), with the most significant growth in the upstream region (0.068 km³ yr⁻¹). Considering the ecological flow requirement of 18.7 km³ (YRCC, MWR, 2015), water stress (calculated as water consumption divided by (natural discharge – ecological flow)) is expected to decline in the latter half of the century, largely due to the peak and subsequent reduction in water withdrawal. However, overall water stress is projected to exceed historical levels in 2041 and will stay above 1 in 62 % of the years (Fig. 15c), reflecting persistent human–water tensions and future trade-offs between ecological and human water use. As a result of reduced actual streamflow, sediment transport in the Yellow River is projected to decline sharply (Fig. 15d), with a 71 % decrease in sediment load relative to the historical period.

Since the energy system is transitioning to carbon neutrality goals under the future baseline scenario, thermal power generation is projected to decline sharply, while clean energy (hydropower, wind, solar, and nuclear) will become the dominant source for electricity generation (Fig. 16a). The large-scale adoption of clean energy will lead to a peak in carbon emissions from electricity generation in 2024 (Fig. 16b). In contrast, emissions from productive and livelihood activities are projected to rise substantially over time, with total human emissions in the YRB reaching a peak in 2044. NPP is anticipated to increase markedly in response to CO₂ concentration increase (Fig. 16c). Although the carbon balance of the YRB has remained positive (net carbon source), it is expected to gradually decline after 2068 (Fig. 16d), indicating that the basin's ecosystems alone cannot fully offset human-induced carbon emissions.

The above projections of future baseline scenarios highlight persistent challenges to achieving sustainable development in the YRB, underscoring the need for integrated policy responses to address these challenges. Priority should be given to enhancing water-use efficiency and establishing adaptive water resource allocation mechanisms that balance ecological and human water needs. Sediment management strategies, which combine ecological restoration with hydraulic regulation, are necessary to maintain river stability and delta health. To counter the decline in labor force, policies should promote industrial upgrading and technological innovation. Strengthening the basin's carbon mitigation capacity requires accelerating the clean energy transition and expanding ecological restoration to enhance carbon sequestration. Finally, a multi-sectoral, CHANS-based governance framework should be established to coordinate water, land, energy, and carbon management, enabling evidence-based scenario analysis and adaptive policy design for long-term sustainability.