Introduction

Streamflow is a vital freshwater resource, an important component of the global water supply1. Understanding changes in streamflow and their causation over an extended period is crucial for effective water resources management and availability analysis. Over recent decades, the Earth’s land has undergone dramatic climate variations, expected to result in noticeable alterations in streamflow.

Atmospheric CO2 plays a pivotal role in driving climate change, modulating the global water cycle, and influencing land surface dynamics. Elevated atmospheric CO2 (eCO2) can impact changes in streamflow through direct regulation of vegetation physiology and structure2,3,4,5,6,7,8, as well as through indirect effects on radiation and temperature9,10,11,12 that influence precipitation and potential evapotranspiration4,13,14,15. Regarding direct regulation, eCO2 can induce two major opposing impacts on streamflow: an increasing effect resulting from reduced leaf transpiration due to stomatal closure3,7,8 and reduced soil evaporation due to expanded leaf area16,17. There is also a reducing effect stemming from increased transpiration and intercepted evaporation6,18 caused by expanded leaf area. Although precipitation, meteorological inputs, and CO2 concentrations are typically treated as separate inputs in land surface models, the regulation of eCO2 on climate and associated feedbacks are often integrated into climate change assessments2,18,19,20,21,22,23. Therefore, the impact of eCO2 on streamflow in this study specifically refers to the direct regulation outlined in Supplementary Fig. 1.

How the eCO2 influences on streamflow via the direct and indirect regulations, or whether eCO2 increases or decreases streamflow, remains controversial and uncertain. Some studies emphasize a strong and positive contribution of eCO2 to increased streamflow due to the water-saving effect caused by stomatal closure3,7,17,24. Others indicate that recent global streamflow changes are primarily attributed to climate2,13,25,26,27 and land use changes2,28,29. Gedney et al. 3 and Piao et al. 2 obtained inconsistent results on streamflow attribution over the last century through different global models, suggesting uncertainty in global modeling30. Importantly, a lack of observational support contributes to low confidence in eCO2 impact modeling results8,31. This is mainly because available studies on historical eCO2 impact on streamflow have focused on the second half of the last century2,3,28 or before 20106,13,32, or on short periods2,5,24 ranging from one to three decades. Despite a 21.8% increase in atmospheric CO2 concentration from 1981 to 2020 triggering pronounced global warming33,34, how vegetation response to eCO2 influences streamflow at catchment and global scales remains largely unknown. Thus, we aim to utilize a large streamflow dataset along with two state-of-the-art modeling frameworks to unravel the role of eCO2 in streamflow changes over the past four decades via the direct vegetation regulation.

Results

Catchment scale contributions

We initiated our study by extracting the influences of climate change and eCO2 on streamflow components from catchments with lengthy observation records, with little human activities in the past 40 years. We employed observed streamflow data from 1116 unimpacted catchments, carefully selected from a vast dataset encompassing over 20,000 catchments worldwide. These specific catchments boast more than 30 years of streamflow observations, exhibit minimal human intervention, and maintain consistent vegetation types (Methods). This unique selection allows us to meticulously disentangle the impacts of precipitation, potential evapotranspiration, and atmospheric CO2 concentration on streamflow through a fully differential method based on the observed datasets.

The analysis at the catchment scale reveals that precipitation is the primary driver of streamflow changes (Fig. 1a), contributing over 70% to the overall absolute relative contribution (Fig. 1d). While an increase or decrease in precipitation can respectively lead to increases or decreases in streamflow for different catchments, the selected catchments overall exhibit a positive contribution from precipitation (Fig. 1d). Potential evapotranspiration accounts for less than 20% of the absolute relative contribution to overall streamflow changes (Fig. 1d), and in most catchments, it contributes negatively to streamflow changes (Fig. 1b, d).

Fig. 1: Contributions of precipitation (P), potential evapotranspiration (ETp), and elevated atmospheric CO2 concentration (eCO2) to streamflow changes across 1116 unregulated catchments during the period 1981–2020.
figure 1

a Spatial patterns illustrating the relative contribution of precipitation to streamflow. b Spatial patterns illustrating the relative contribution of potential evapotranspiration to streamflow. c Spatial patterns illustrating the relative contribution of elevated atmospheric CO2 concentration to streamflow. d Box plots showing the relative contributions of the three factors to streamflow across the 1116 catchments. In each box plot, the whiskers represent the 90th and 10th percentiles, and the box is outlined by the 75th, 50th, and 25th percentiles.

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In contrast, the contribution of eCO2 to streamflow is considerably lower than that of climate change factors (precipitation and potential evapotranspiration), as depicted in Fig. 1d. The absolute relative contribution of eCO2 is less than 8% overall, with a median real relative contribution close to 0. No clear statistical evidence shows that eCO2 provides either a positive or negative contribution to streamflow overall (Fig. 1d). Moreover, the contribution of eCO2 to streamflow shows certain spatial pattern (Fig. 1c). For example, eCO2 in southeastern North America shows an overall positive contribution to streamflow, while eCO2 in eastern Oceania shows an overall negative contribution to streamflow.

Global scale attribution

Subsequently, we employed 14 global ecological models, which were simulated based on observed annual streamflow constraint scenarios of large basins. We then derived four observationally constrained models for our analysis, attribution, and uncertainty studies on global streamflow changes. The regularized optimal fingerprinting method (ROF) was applied for streamflow attribution, utilizing a dataset of pre-industrial revolution-controlled streamflow variability from 47 Earth System Models to represent internal variability. The ROF is a statistical method for attribution by evaluating the internal variability of streamflow and combining it with the statistical relationship between changes in streamflow itself and changes in streamflow driven by external forcing variables to obtain a “fingerprint” or a scale factor. In this paper, an uncertainty analysis was also conducted to evaluate internal variability using different datasets (see Methods).

The attribution analysis results indicate that global streamflow remains relatively stable overall, evident in both the global trend pattern and the area-weighted streamflow trend. More than 80% of global grids exhibit a non-significant increase in streamflow trends, with less than 5% showing a significant change (Fig. 2a). The global area-weighted streamflow displays a non-significant increase, with a trend of 0.09 ± 0.05 mm/yr² over the last 40 years (Fig. 2b). Excluding deserts for the global average obtains a similarly non-significant increase trend of 0.13 ± 0.05 mm/yr² (Supplementary Fig. 9b). In essence, the globally insignificant changes in streamflow are attributed exclusively to climate change, with no compelling evidence supporting a significant impact of eCO2 on streamflow.

Fig. 2: Trends, changes and attribution of global streamflow based on observation-constrained models in 1981-2020.
figure 2

a Spatial pattern of 40-year streamflow annual trends obtained from four observation-constrained models. SD, D, I, SI denote significant decrease, insignificant decrease, insignificant increase, and significant increase at the significant level of α = 0.05 (Mann–Kendall test), respectively. Purple dots in global map indicate that the trend is significant. b 40-year global area-weighted anomaly streamflow time series and trends for the four observation-constrained models (mean ± 1std), and pmin represents the minimum p value from the four models. c Attribution results for global area-weighted streamflow changes for the four observation-constrained models, with 90% upper and lower bounds and median values for the scale factor of the regularized optimal fingerprinting method being the median of the corresponding values for the four models. If the range of the scale factor at the 90% significance level is greater than 0 and contains 1, the driving factor (climate change (CLI), elevated CO2 (eCO2), and land-use change (LUC)) can be attributed; otherwise, it cannot.

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In Fig. 2c, the scale factor for climate change exhibits strong consistency in both single and multifactor cases, consistently greater than 0 and inclusive of 1. This suggests that the annual changes in streamflow over the past 40 years can be consistently and reliably attributed to climate change (also in Supplementary Fig. 17). However, eCO2 and land-use change cannot be reliably linked to these streamflow changes, especially in the multifactor case. In the multifactor scenario, the scale factors for these two variables fluctuate drastically, implying that their impact on streamflow is much less significant than their influence on climate change.

Uncertainty analysis

Utilizing observation-constrained modeling significantly diminishes the uncertainty inherent in the original 14 models when estimating global streamflow trends and attribution results. Initial estimates of streamflow trends from these models exhibit considerable variation, with some suggesting a noteworthy increase in global streamflow and one model proposing a decline, covering a range of −0.20 to 0.40 mm/yr² (Supplementary Fig. 2). The application of observation-constrained modeling effectively reduces this uncertainty, achieving a 62.0% reduction in standard deviation. This results in a more precise and stable trend estimate (Fig. 3a).

Fig. 3: Global comparison of annual trend and attribution uncertainty.
figure 3

a Estimates of global streamflow trends. Observed modeling is the mean ± 1 std of the trends from the four observation-constrained models, and the unconstrained is the mean ± 1 std of the trends from the 14 global ecological models. b Probabilities of attributing global streamflow to climate change (CLI), elevated CO2 (eCO2), and land-use change (LUC) for observation-constrained modeling and all models in TRENDY when different datasets are selected to assess the internal variability of streamflow. The bar error in (b) is the one standard deviation of a truncated normal distribution, ranging in 0–100%.

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In the application of the optimal fingerprinting method, the choice of diverse datasets for internally assessing global streamflow introduces significant uncertainty into the attribution results across all the TRENDY models (Fig. 3b). There exists a probability of attributing a change in global streamflow either to eCO2 or not attributing it to climate change. However, when utilizing the observation-constrained results, the change in global streamflow consistently attributes to climate change but not to eCO2. This highlights a substantial reduction in uncertainty in the attribution results.

Discussion

Our study uses two frameworks to investigate the impacts of the recent rise in CO2 on streamflow, focusing on direct vegetation regulation with different considerations. At the small catchment scale, we use the fully differential method, which is not specifically designed to isolate the effects of land-use change on streamflow. Therefore, we carefully select stable catchments that are minimally affected by anthropogenic impacts and vegetation type changes, while also excluding potential impacts of groundwater-streamflow interactions35. At the global scale, we use the optimal fingerprinting method to isolate the impacts of eCO2, climate change, and land-use change on global streamflow. Both frameworks show robust results, indicating that vegetation responses to the recent rise in CO2 exert limited impacts on streamflow at both catchment and global scales.

It is worth noting that neither of the two frameworks has the capability to investigate the response of climate variables (e.g., precipitation) to vegetation feedback under eCO2. On one hand, variables such as precipitation are used as forcing data for land-surface and statistical models, and vegetation feedback is embedded within climate forcing. On the other hand, it is challenging to validate the accuracy of vegetation feedback simulations based on observations. These limitations restrict our study to investigating how eCO2 has influenced streamflow changes over the past four decades through direct vegetation regulation.

We notice that several factors contribute to the uncertainty of the increment-based fully differential method for small catchments (see Methods), including catchment selection and multicollinearity issues among the driving factors, model structural errors and uncertainty in forcing and training datasets. The uncertainty in the fully differential method increases with the size of the catchment area (Supplementary Fig. 10). Larger catchments are more susceptible to anthropogenic change impacts. In our study, more than 74% of the selected catchments have a catchment area of less than 2000 km2, indicating that the majority of catchments have a low likelihood of experiencing strong anthropogenic changes. In the small catchments, it is also impossible to completely eliminate the anthropogenic impacts. Furthermore, precipitation, potential evapotranspiration, and eCO2 used in the fully differential method are relatively independent, and there are no collinearity issues36, as indicated by Variance Inflation Factor values of less than 5.0 (Supplementary Fig. 11). We also notice that the possible impacts from streamflow observation errors that largely vary from 3% to 6%37,38,39,40. To test the impact magnitude, we conduct the Monte Carlo simulations (see Supplementary Method 4), and find the impact is very small. Specifically, the 10% maximum streamflow error produces an uncertainty in contribution of eCO2 less than 0.5% for 50% of the selected catchments and less than 0.6% for 75% of the selected catchments (Supplementary Fig. 18). Compared to that, the errors in precipitation generate slightly higher uncertainty in annual streamflow, but it is smaller than the reported precipitation-streamflow error propagation simulated using a process-based hydrological model41. Based on the uncertainty analysis, we suggest that the fully differential approach is applicable and robust.

The spatial pattern of eCO2 contribution to streamflow depicted in Fig. 1c can be attributed to vegetation types (density) and climate regimes. We observed that in forest-dominated catchments with a high leaf area index (as detailed in the Methods), eCO2 exhibits an overall positive contribution to streamflow in North America (Supplementary Fig. 12a), an overall negative contribution in Oceania (Supplementary Fig. 12c), and a transition from an overall negative to a positive contribution in South America (Supplementary Fig. 12b). In catchments dominated by various vegetation types, the absolute relative contribution of eCO2 to streamflow in tropical regimes is generally higher than in temperate and cold climate regimes (see Supplementary Fig. 3). However, despite the above discussion, the contribution of eCO2 to streamflow remains very limited, with an absolute relative contribution of about 10% or less for the selected catchments, and an overall relative contribution close to 0 (Fig. 1d, Supplementary Fig. 3 and Supplementary Fig. 12d). This is far behind precipitation and potential evapotranspiration.

Furthermore, we investigated whether considering vegetation phenology would noticeably impact our results. We focused on catchments outside the equator and conducted the same analysis but only for vegetation growing seasons (April to October for the Northern Hemisphere and October to April for the Southern Hemisphere). The results obtained from the growing seasons mirrored those obtained from the entire calendar year (see Supplementary Fig. 13), further affirming the robustness of our findings.

In the global models, the direct impact of eCO2 on streamflow is influenced by two opposing factors. On one hand, an increase in vegetation water use efficiency due to eCO2 can lead to a direct increase in streamflow, as dictated by the stomatal conductance equation in the models42,43,44,45. Conversely, eCO2 is a dominant factor in global greening18, causing an expansion in leaf area and consequently an increase in vegetative water consumption, ultimately reducing streamflow6. The substantial eCO2 levels observed from 1981 to 2020, coupled with the overall insignificant increase in annual streamflow and the minimal attribution of eCO2 to streamflow (in Fig. 2, and the same results are in the non-desert region, as shown in Supplementary Fig. 9), suggest that the response of global streamflow change to eCO2 is highly limited, which may be attributed to several factors. Firstly, the effects of global greening and stomatal closure may counteract each other at a regional to global scale. Secondly, the impacts of eCO2 on vegetation could be relatively small. Thirdly, complex feedback mechanisms remain poorly understood, although observation-constrained models show that the interactive effects of eCO2 and climate change on streamflow (see Methods) are of the same order of magnitude as the effects of eCO2 on streamflow, and both are much smaller than the effects of climate change on streamflow (Supplementary Fig. 19).

We also analyze trends in individual water balance components over the past 40 years based on the TRENDY models. These models obtain overall the increasing trends in global evapotranspiration and streamflow, but have a large range in their values. Furthermore, there exists a high uncertainty in these models for partitioning evapotranspiration comments: transpiration, canopy evaporation, and soil evaporation (Supplementary Fig. 20). However, these models achieve reasonable balance in the water balance trends, i.e. trends in precipitation similar to the sum of trend in streamflow and trend in evapotranspiration (Supplementary Figs. 20, 21). These models show the competing effects between the trend in streamflow and the trend in evapotranspiration, i.e. a high trend in streamflow companied by a low trend in evapotranspiration, and vice versa.

While all models successfully simulate annual variability in streamflow when compared to observations (Supplementary Fig. 4b), significant uncertainty persists in trends and attribution results at a global scale (Fig. 3). The application of observational constraints can substantially reduce uncertainty among different models46. However, it is important to acknowledge the challenge in achieving high accuracy in both simulated streamflow interannual trends and variations (Supplementary Fig. 4b, c). Constraining models based solely on streamflow variability might lead to higher estimates of global trends (Supplementary Fig. 2). This realization underscores the importance of not only constraining models based on annual streamflow values but also considering annual streamflow trends. The global model uncertainty on a broad scale underscores the need for cautious assessments of streamflow changes14.

Methods

Observed streamflow data and forcing data

We utilized annual streamflow data from a comprehensive dataset comprising over 20,000 catchments, gathered from publicly available sources47,48,49,50,51,52,53 and national statistical bulletins. A subset of 1116 small to medium catchments and 44 large basins were chosen for our study. To align with our research objectives, specific criteria were applied to select 1116 unimpacted catchments: catchment areas below 100,000 km², land use/vegetation types area changes under 5% (dataset from HILDA+ (HIstoric Land Dynamics Assessment + )54,55 including: urban areas, cropland, pasture/rangeland, forest, unmanaged grass/shrubland, and sparse/no vegetation), absence of reservoir regulation (reservoir capacity divided by multi-year average streamflow is 0), irrigated area less than 5% (Global Map of Irrigation Areas (GMIA), https://www.fao.org/land-water/land/land-governance/land-resources-planning-toolbox/category/details/en/c/1029519/), consistent vegetation types, and continuous observations spanning over 30 years (see Supplementary Fig. 5a). Among these catchments, 48.7% had an area less than 500 km², 25.4% ranged between 500 and 2000 km², 18.6% fell between 2000 and 10,000 km², and 7.3% exceeded 10,000 km². To strengthen our results, we further excluded catchments with abrupt shifts in runoff coefficients, resulting in 550 catchments. Details are provided in Supplementary Method 1 and Supplementary Fig. 14, and the corresponding results are summarized in Supplementary Fig. 15, which is similar to the results presented in Fig. 1.

Additionally, 44 large basins, each larger than 100,000 km², were selected having good data availability (each having no less than 36 years of observation and more than 90% catchments with missing percentage less than 1%) (see Supplementary Data 1 for details), covering 24.3% of the global land area (see Supplementary Fig. 5b). For the large basins, missing monthly data were interpolated through the G-RUN dataset56, subject to a Nash-Sutcliffe efficiency threshold57 of not less than 0.6 for non-missing months in both G-RUN and these catchments. Basins failing this criterion were excluded, and the boundaries of large basins were separately delineated58.

Climate classifications are derived from the Köppen-Geiger climate classification maps59. A catchment is considered to have a consistent vegetation type if the percentage of one vegetation type is greater than 50% for all 40 years of the catchment. A catchment is dominated by a particular climate or vegetation type if that climate or vegetation type constitutes the largest portion of the catchment. Three types of reservoir data were used in the screening of the 1116 catchments: Basin ATLAS60, GRanD V1.361, and GDAT62. Reservoir impacts were calculated by dividing the reservoir flow by the average multi-year streamflow in the catchment, with a reservoir impact of 0 indicating the absence of reservoir regulation. Precipitation and potential evapotranspiration for the fully differential method were sourced from MSWEP V2.863 and MSWX64. Leaf area index data were sourced from GIMMS3g_V4_165.

Trend analysis

Trends were determined using the robust Sen-slope estimator66, known for its resilience against outliers. The significance of the trends was assessed through the Mann-Kendall test67,68. A trend was deemed significant if the p value of the statistical test was less than 0.05; otherwise, the trend was considered not significant.

Fully differential method for catchment scale contribution analysis

We have developed a fully differential method to assess the contributions of eCO2 and climate change to streamflow. The observed streamflow (Qobs) within a catchment is expressed as a function of hydroclimatic variables (Eq. (1)):

$${Q}_{{obs}}=F\left({X}_{1},{X}_{2},\cdots,{X}_{n}\right)$$
(1)

where \({X}_{i}\left(i={1,2},\cdots,n\right)\) denotes hydroclimatic variables. The fully differential form for streamflow increment is represented as:

$${dQ}={\sum}_{i}\frac{\partial F}{\partial {X}_{i}}d{X}_{i}$$
(2)

where dXi is the increment in the driving variable. We hypothesize that streamflow trends primarily result from three key drivers: annual precipitation (P), annual potential evapotranspiration (ETp), and annual CO2 (CO2). We approximate Eq. (2) with the annual increments of the regression variables through a standardized multiple regression process (Eq. (3)):

$${\left\{\Delta {q}_{j}\right\}}_{j\in N}=\mathop{\sum }_{i}{k}_{i}{\left\{\Delta {x}_{i,j}\right\}}_{j\in N}+\delta$$
(3)

where \({\left\{\Delta {q}_{j}\right\}}_{j\in N}\) is the time series of the standardized streamflow increment, j is time point and N is the natural number indicator set, similarly, \({\left\{\Delta {x}_{i,j}\right\}}_{j\in N}\) is the time series of the standardized i-th driving variable increment, ki is the standardized regression coefficient of the i-th driving variable increment, δ is the uncertainty term. For a given variable \({\left\{{\hat{x}}_{i,j}\right\}}_{j\in N}\), the increment is calculated as \(\Delta {\hat{x}}_{i,j}={\hat{x}}_{i,j+1}-{\hat{x}}_{i,j}\) and the normalization process is \(\Delta {x}_{i,j}=\frac{\Delta {\hat{x}}_{i,j}-{{{\rm{MEAN}}}}\left({\left\{\Delta {\hat{x}}_{i,j}\right\}}_{j\in N}\right)}{{{{\rm{STD}}}}\left({\left\{\Delta {\hat{x}}_{i,j}\right\}}_{j\in N}\right)}\). It is noted that MEAN and STD are mean and standard deviation, respectively. By performing standardized linear regressions relating annual increments in these dominant factors to annual streamflow increments, we obtain regression coefficients for annual precipitation (kP), annual potential evapotranspiration \(({k}_{{{ET}}_{p}})\), and annual \({{{{\rm{CO}}}}}_{2}({k}_{C{O}_{2}})\). The standardized regression coefficients represent the relative contribution of the independent variables to the dependent variable, and trends are an expression of the accumulation of “increments”. Therefore, the streamflow changes driven by each factor (Xi) can be expressed as \(d{Q}_{{obs\_}{X}_{i}}={k}_{{X}_{i}}\cdot \left|{{{\rm{Trend}}}}\left(Q\right)\right|\), and CO2-driven streamflow changes are

$$\Delta {Q}_{{obs}{{\_}}C{O}_{2}}={k}_{C{O}_{2}}\cdot \left|{{{\rm{Trend}}}}\left(Q\right)\right|$$
(4)

where \({{{\rm{Trend}}}}\left(\cdot \right)\) is the trend of the annual variable. The absolute relative contribution and real relative contribution are calculated according to the formula: \(|\Delta {Q}_{{obs\_}{X}_{i}}|/ (|\Delta {Q}_{{obs\_P}}|+|\Delta {Q}_{{obs\_E}{T}_{p}}|+|\Delta {Q}_{{obs\_C}{O}_{2}}|),\Delta {Q}_{{obs\_}{X}_{i}}/ (|\Delta {Q}_{{obs\_P}}|+|\Delta {Q}_{{obs\_E}{T}_{p}}|+|\Delta {Q}_{{obs\_C}{O}_{2}}|)\), respectively.

The reliability of the method is confirmed by goodness-of-fit (R²) spatial map and cumulative distribution figures (Supplementary Fig. 6a, b). R2 in 75% catchments is greater than 0.55, and in 50% catchments is greater than 0.7. Additionally, potential evapotranspiration is calculated using the improved FAO Penman Monteith method (FAO Penman Monteith [Yang])17, and the results from different potential evapotranspiration formulas exhibit extremely similar correlation coefficients and goodness-of-fit in Eq. (3), as shown in Supplementary Fig. 7. In addition, we evaluate the multicollinearity issue among the driving factors by the Variance Inflation Factor (VIF), where VIF less than 5 is considered to have no multicollinearity among the variables and VIF greater than 10 indicates a strong multicollinearity36. The expressions of the equations for the fully differential method and the elasticity coefficient method14,69 are similar. In contrast to the elasticity coefficient method, the fully differential method requires the consideration of all potential driving variables, which is the key reason for the rigorous screening of the catchments.

Global ecological models

We employed 14 state-of-the-art process-based global ecological models to assess and attribute streamflow changes, obtained from latest TRENDY phase 1121,70. These models, including CABLE-POP71, CLASSIC72, CLM5.073, DLEM74, IBIS75, ISAM76, ISBA-CTRIP77, JSBACH78, JULES79,80, LPJ-GUESS81, LPX-BERN82, ORCHIDEE83, SDGVM84 and VISIT-NIES85, are widely used for evaluating hydrological effects and attributions2,22,86.

The model results were provided through the TRENDY project (https://sites.exeter.ac.uk/trendy), specifically from the S3 scenario simulations, which consider all forcing data (eCO2, climate change, and land use change) as time-varying and are deemed to be most representative of the real world18,22. Half of these models have a spatial resolution of 0.5°×0.5°. To facilitate calculations, all model results were resampled to a spatial resolution of 0.5°×0.5° using bilinear interpolation, as needed, for consistency in spatial representation. Model details are summarized in Supplementary Method 3 and Supplementary Data 2.

Using TRENDY model experiments, we can partition the trend in streamflow into three components: CO2-driven, climate-driven, and interactive effects of climate change and CO2. The CO2-driven streamflow trend from TRENDY models is:

$$\Delta {Q}_{C{O}_{2}}={{{\rm{Trend}}}}\left({Q}_{S1}-{Q}_{S0}\right)$$
(5)

where \(\Delta {Q}_{C{O}_{2}}\) is the CO2-driven streamflow trend from TRENDY models; \({{{\rm{Trend}}}}\left(\cdot \right)\) is the function to calculate the trend, Sen-slope estimator is used here; \({Q}_{S0},{Q}_{S1}\) are the streamflow from S0, and S1 in the TRENDY control scenarios (see Supplementary Method 3).

The climate-driven streamflow trend from TRENDY models is:

$$\Delta {Q}_{{CLI}}={{{\rm{Trend}}}}\left({Q}_{S2}-{Q}_{S1}\right)$$
(6)

where ΔQCLI is the climate-driven streamflow trend from TRENDY models; \({{{\rm{Trend}}}}\left(\cdot \right)\) is same as Eq. (5); QS2 is the streamflow from S2 in the TRENDY control scenarios (see Supplementary Method 3).

The streamflow trend driven by CO2 and climate from TRENDY models is:

$$\Delta {Q}_{C{O}_{2}{{\_}}{CLI}}={{{\rm{Trend}}}}\left({Q}_{S2}-{Q}_{S0}\right)$$
(7)

where \(\Delta {Q}_{C{O}_{2}{\_CLI}}\) is the streamflow trend driven by CO2 and climate from TRENDY models; others are same as Eqs. (5) and (6).

Therefore, the streamflow trend driven by the interactive effects of climate change and CO2 from TRENDY models is:

$$\Delta {Q}_{{{{\rm{Interaction}}}}}=\Delta {Q}_{C{O}_{2}{{\_}}{CLI}}-\Delta {Q}_{C{O}_{2}}-\Delta {Q}_{{CLI}}$$
(8)

where \(\Delta {Q}_{{{{\rm{Interaction}}}}}\) is the streamflow trend driven by the interactive effects of climate change and CO2 from TRENDY models. The CO2-driven and climate-driven (combination of precipitation and potential evapotranspiration) streamflow trend calculated by the fully differential method can be deduced from Eq. (4), which corresponds to Eqs. (5) and (6).

Observation-constrained modeling

We developed four observation-constrained models based on the annual observed streamflow values and trends. For each continent, we pursued two approaches: (1) maximizing the Nash-Sutcliffe efficiency (NSE) of the model-simulated annual streamflow series against the observed annual streamflow series to derive the value-constrained models (two types: single, named Best-VAS-SM, and multi-model ensemble, named Best-VAS-EM), and (2) minimizing the Root Minimum Mean Square Error (RMSE) of the model-simulated annual streamflow trend against the observed annual streamflow trend to obtain the trend-constrained models (two types: single, named Best-TAS-SM, and multi-model ensemble, named Best-TAS-EM) (See Supplementary Method 2 for details). The multi-model ensemble models involved an averaging process, followed by an optimization algorithm (Strategic Random Search87) to identify optimal values. The results of the model selection are depicted in Supplementary Fig. 4a, and validation of modelled trends for the 44 large basins is shown in Supplementary Fig. 8 and Supplementary Fig. 16.

Regularized optimal fingerprint method for attribution analysis

We employed the optimal fingerprint method (OF) for global attribution analysis, specifically using the regularized OF (ROF), which enhances OF by eliminating the stage parameter determination in the Empirical Orthogonal Function projection. This refinement contributes to increased accuracy88. The core equation for ROF remains consistent with OF:

$$y=\mathop{\sum }_{i=1}^{l}{\beta }_{i}{x}_{i}+\epsilon$$
(9)

where y represents the streamflow (obtained from TRENDY models or observation-constrained estimates in this context), xi is the response to the i-th external forcing variable, derived from the TRENDY control scenarios described in Supplementary Method 3, βi is an unknown scaling factor, and ϵ denotes the internal streamflow variability, computed from the pre-industrial revolution-controlled (CTL) from the Earth System Models (ESMs) in CMIP689 (A total of 47 models were collected, as shown in Supplementary Data 3). y, xi, and ϵ consist of spatio-temporal vectors. When βi and its 90% confidence interval are both greater than 0 and contain unity, changes in streamflow can be attributed to the i-th external forcing.

In this study, both single-factor (or single-signal) and multi-factor (or multi-signal) analyses were employed throughout the attribution process. Single-factor analysis provides a quick and simple way to determine whether a variable can be attributed or not. In contrast, multi-factor analysis tests the robustness of the attribution results for a single-factor variable, especially when other variables are added to attribution simultaneously.

However, we observed a heavy reliance of ϵ on the CTL dataset. To construct noisy covariances of internal streamflow variability, we extracted non-overlapping 80-year data blocks (twice the length of 1981–2020) from various available CTLs in the Earth System Models (ESMs) randomly. For each experiment, no less than 24 ESMs were randomly selected through uniform distribution. Each 80-year data block was then split into two 40-year data blocks, from which we calculated the area-weighted annual mean streamflow anomaly. This process yielded two independent matrices, one for determining the noise covariance and the other for testing residual consistency88,90. Subsequently, this experiment was repeated 100 times to account for variations in results due to different CTL model selection processes.

To enhance the reliability of the results by reducing temporal dimensions, we chose multi-year non-overlapping means for further calculation. Previous studies often employed means over 3-year12,18,22, 5-year91, and 11-year92 periods. However, due to the limited 40-year streamflow data in this paper, we selected non-overlapping means of 3-year, 4-year, and 5-year durations for the calculation, resulting in a total of 300 sets of results.

If changes in streamflow can be attributed to a variable xi (climate change, eCO2, and land use change), then the probability that it can be attributed is given by:

$${P}_{{x}_{i}}=\frac{{A}_{{x}_{i}}}{N}\times 100\%$$
(10)

where Axi is the number of times that xi can be attributed, and N is the total number of times, which is 300 in this case.