A set of 18 GCM simulations (see Table ), produced within the framework of the High Resolution Model Intercomparison Project (HighResMIP v1.0) for CMIP6 , force the river routing model used to evaluate the rivers in the near future. The selection of these HighResMIP GCMs was contingent upon the availability of surface and subsurface runoff data within the Earth System Grid Federation (ESGF) servers, which host the HighResMIP simulations. The simulations include five different GCM families: CNRM-CM6 , EC-Earth3P , HadGEM-GC31 , MRI-AGCM3-2 , and NICAM16 , which vary in terms of the simulation type and the horizontal resolution. The simulation type can be either atmosphere–land (AMIP) or ocean–atmosphere–land (COUPLED). All GCMs present AMIP simulations, but only CNRM-CM6, EC-Earth3P, and HadGEM-GC31 have COUPLED simulations. In addition, all GCMs produced a low- and a high-resolution simulation, except for the HadGEM-GC31 family, which also provides an intermediate-resolution simulation. To reconcile the variety of grid topologies used by the different GCMs (rectilinear, reduced Gaussian, icosahedral, etc.) in the comparison of the GCMs' resolutions, we provide the atmospheric horizontal resolution at 50° N. This middle latitude serves as a representative point for assessing resolution, particularly given the significant variation in resolution from the Equator to the poles in models using rectilinear grids. The atmospheric resolution at 50° N ranges from 25 to 134 km for the set of simulations (Table ). For COUPLED simulations, we also provide the ocean resolution, which varies from 1° for low-resolution simulations to 0.25° for high-resolution simulations. Note that there is only one member per resolution and simulation type, which may limit the robustness of this study, because of internal climate variability. To shed light on this, we perform a comprehensive internal variability analysis of a set of 58 individual realizations across different GCMs in Appendix . The results show that the intermodel variability is much larger than the internal variability, which suggests strong robustness of the set of simulations used in this study.

The total runoff (surface and subsurface) produced by each GCM simulation is used to force the TRIPpy (Total Runoff Integrating Pathways in Python) river routing model , a standalone implementation of the original TRIP model developed by in FORTRAN. TRIPpy collects runoff from each grid cell and drives it through the river network to estimate the river storage and outflow of each grid cell. The simulations are run globally (excluding Antarctica) using the nearest-neighbour method to regrid the runoff from the original GCM resolutions to the target grid at a common resolution of 0.25°. The quarter-degree river network is based on the flow direction of the Dominant River Tracing dataset .

TRIPpy employs a simple advection method within a water balance model to route total runoff through the topography. This method calculates changes in river channel storage within each grid cell by accounting for the difference between the inflow and the outflow. The inflow includes both local runoff and contributions from upstream grid cells. The outflow is estimated using a linear function of storage considering the river flow velocity and the river length between two connected grid cells. Detailed TRIPpy equations can be found in the appendix of , who evaluated simulated river flow across 334 monitored catchments, revealing promising performance compared to observed data. The model's key attribute lies in its simplicity, enabling long-term global simulations with minimal computational resources, all while delivering commendable performance.

The hydrological simulations span from 1950 to 2050 at a monthly timescale, with 1950–2014 being the present climatology (hereinafter PRESENT) and 2015–2050 being the near future (hereinafter FUTURE). Note that the projections in HighResMIP consider a scenario as close to CMIP5 RCP8.5 as possible within CMIP6 ; i.e. the hydrological predictions are appraised in the context of a high-emission scenario. Table  indicates the change in global temperature between the FUTURE and PRESENT as an indicator of the assumed scenario impact on the projections. AMIP projections present a warming of ∼1.2 °C, while COUPLED projections present a change ranging from 1.3 to 2 °C. Although such changes may seem large for short-term climate predictions (36 years), they are likely to occur in the long-term.

To ensure the robustness of both the model and the forcing GCMs for our specific objectives, we undertake a comprehensive validation of the 18 hydrological simulations and the 18-model ensemble mean simulation for the PRESENT period. The validation involves assessing four metrics which evaluate diverse aspects of the simulations, computed by comparing our simulations with monthly observations of 346 selected near-coast gauge stations from the dataset. The selection criteria for observations focused on data availability (>120 observed values for the PRESENT period), a minimum size of the catchment (>14 grid cells), and a minimum agreement between catchment area in the model and the observations (>65 %). The selected monitored rivers cover approximately 42 % of the global land and contribute to about 45 % of the global river discharge (see Fig. a).

The validation metrics are as follows:

The relative bias (RB) measures the percentage difference between total simulated and observed mean flow for all monitored rivers, indicating whether simulations tend to overestimate or underestimate river flows (range of [-100,∞), perfect score of 0).

To understand the projected changes in rivers in the next decades, we perform a three-steps analysis. First, we identify the main differences between the FUTURE and PRESENT periods in terms of key hydrological variables. Second, we estimate the ToE of river discharge worldwide. Lastly, we focus the evaluation of river flow on regions exhibiting notable anomalies and where there is a clear consensus among model simulations regarding the projections.

In the comparison of the FUTURE vs. PRESENT, we assess the projected anomalies of land precipitation and total runoff in the near future (2015–2050) with respect to the recent past (1950–2014), used as a reference climatology. Particular attention is given to the level of agreement among GCMs in terms of such changes, which ensures robustness in the climate change signal (if any). Then, we centre the analysis in river flow to understand how anomalies in runoff end up affecting the different rivers of the world.

The river discharge S/N ratio and ToE are calculated following the approach proposed by . The goal of the method is to decouple the climate change signal (S) from the natural variability (the noise N). In our work, the method is applied to the river discharge annual anomaly (Q) of each simulation. PRESENT is used as the base period to calculate the anomalies in the entire period (1950–2050).

At the global scale, the signal SG(t) is a low-pass-filtered version of the original QG time series. The filter is based on the convolution of the signal with a scaled window of a 41-year length, resulting in a smoothing effect of the signal interannual variability. On the other hand, the noise is a fixed value calculated as NG=σ(QG(t)-SG(t)) over the base period, where σ is the standard deviation. At the local scale (grid cell), the signal is a linear regression of the local river flow annual anomaly QL(t) with respect to the global signal SG(t); that is, SL(t)=mSG(t)+b, where m and b are the regression coefficients (slope and intercept, respectively). The local noise is then estimated similarly to the global case as NL=σ(QL(t)-SL(t)) over the base period. The logic behind the methodological decisions (e.g. choice of filter, linear regression) results from a comprehensive analysis summarized in Appendix .

Both scales (global and local) use the corresponding noise as a threshold to determine the year in which the signal of climate change emerges from the natural variability. Following the terminology used by and , the year t in which |S(t)|>N is described as the ToE of “unfamiliar” climate, while the year in which |S(t)|>2N is described as the ToE of “unusual” climate conditions. Conversely, |S(t)|<N means that the projections of river flow remain in the range of its historical variability.

The previous analysis enables the identification of regions where river flow predictions (1) indicate a transition from their established climate to an unfamiliar or even unusual climate and (2) exhibit a significant consensus among models. Further assessment of these regions aims to determine the timing of the shift and its potential impact.

The evaluation of the high-resolution hydrological simulations across 346 monitored catchments provides a nuanced understanding of model performance. These results not only offer valuable insights into the models' consistency but also underscore their effectiveness in capturing key hydrological features. The metrics employed, including RB, OC, r, and npKGE, offer distinct perspectives on the models' performance.

Figure b summarizes the scores for the set of simulations. The relative bias (RB) provides insights into the mean volume biases between simulated and observed flows, ranging from -4.2 % to 27.7 %. The overlapping coefficient (OC) assesses the agreement in flow volumes, while correlation (r) focuses on the ability of the models to capture observed river flow variability. Both scores range from 0.51 to 0.72. Lastly, the non-parametric Kling–Gupta efficiency (npKGE), the most demanding metric, evaluates flow volume, variability, and dynamics, resulting in scores ranging from 0.39 to 0.58. Despite the diversity of these metrics, there is consistency across models, with all exhibiting values in a narrow range. Notably, the ensemble mean simulation outperforms most individual models, with RB=6.8 %, OC=0.63, r=0.72, and npKGE=0.58. Among the top-performing models are the GCMs of the EC-Earth3P and MRI-AGCM3-2 families.

When the assessment is restricted to the 20 largest monitored rivers, most scores are increased, especially for r and npKGE (see Fig. c). For instance, for the ensemble mean simulation, this targeted analysis yields notable improvements, with the RB reducing to -1.5 %, the correlation enhancing to 0.76, and the npKGE rising to 0.71. These results suggest that GCMs demonstrate a greater capacity to accurately simulate the variability and dynamics of runoff generation in large catchments compared to smaller ones. The consistency in performance across models, independently of the resolution and the type of GCM forcing the hydrological simulations, and the enhancement in scores when focusing on major rivers collectively demonstrate commendable performance. This showcases the simulations' abilities to reproduce observed large-scale hydrological patterns, reinforcing our confidence in the models' suitability for our study objectives.

Precipitation, evapotranspiration, and runoff are the main components of the long-term land water budget and, thereby, are the key hydrological variables required to understand long-term changes in rivers. Figure  compares how global mean values of these variables change in the projections with respect to the climatology. Notably, all the models agree with regard to the prediction of wetter conditions for the next decades, independently of the type of simulation (AMIP or COUPLED) and the model's resolution. However, the positive changes in the projections of precipitation and runoff tend to be stronger for the COUPLED simulations, likely due to the higher level of global warming they simulate for the FUTURE period (see Table ). On the other hand, for each GCM family, increasing the resolution results in higher values for both the PRESENT and FUTURE periods. That is because high-resolution models enhance ocean–land moisture transport, producing more realistic mesoscale circulation patterns and synoptic systems . Moreover, the better-resolved orography at a high resolution favours the organization of convective precipitation and improves the representation of orographic jets, producing more orographic precipitation and thereby more runoff in the headwaters . The differences that arise with resolution and the level of warming produce a spread in the global mean values of the various GCMs. Even so, it is noteworthy that the values for all GCMs remain in the range of the observational uncertainty for the three variables.

Despite the global land precipitation increase of 3.6×103 km3 yr-1 in the ensemble mean, which represents just 3 % more precipitation, a large fraction of the extra water ends up in runoff, which is augmented by 2.4×103 km3 yr-1, representing a positive change of 6 % in the global average. The remaining extra precipitation is returned to the atmosphere through evapotranspiration, which rises by 2 % in the ensemble mean. The global rise in land precipitation and evapotranspiration is mainly explained by two factors that have the general consensus of most GCMs: a strengthening of the intertropical convergence zone (ITCZ) and an overall wettening in the northern high latitudes (a discussion about such phenomena is given in Appendix ).

Positive anomalies in precipitation are amplified in runoff (in terms of percentage change) when the extra water falls over either wet regions, where there is no more room for evapotranspiration, or over mountainous areas, where horizontal fluxes prevail . Figure  shows that positive and negative changes in runoff are unevenly distributed throughout the world. Central Africa is the most extensive region with strong wetter conditions, but also, more runoff is predicted for southeast South America; India; the Maritime Continent; and the windward side of orographic barriers like the tropical Andes, the Alaska Range, and the Himalayas. On the other hand, the main reductions in runoff are projected in parts of the Amazon Forest and southern Chile. There is agreement among most models about the regions presenting notable changes (either positive or negative) but also about the slight increase in runoff in the northern high latitudes, which is related to the strong signal of warming projected for that area (see Fig. c and its description in Appendix ).

The predicted global enhancement in runoff has a direct effect on river flow. Figure a presents the percentage change in river discharge between the FUTURE and PRESENT periods for the catchments of the world, while Fig. b depicts similar information but detailed for all river tributaries. Consistently with the analysis of runoff, the stronger positive changes appear in African, Australian, and boreal rivers. In Africa, many important rivers increase the mean discharge by more than 20 %, including the three major rivers, the Congo (+20 %), the Nile (23 %), and the Niger (26 %), but also the Okavango (+21 %), the Volta (+33 %), and the rivers feeding Lake Chad, whose catchment presents the largest percentage increment (+49 %). In Australia, the major river, the Murray, is augmented by 14 %, while other small rivers in northern Australia (the Victoria, Ord, and Fitzroy) and those discharging into Lake Eyre (the Cooper and Warburton, among others) increase their flow by more than 35 %. In the boreal zone, nearly all rivers simulate more drainage of freshwater into the Arctic Ocean. In particular, those located in eastern Russia (e.g., the Lena, Yana, and Kolima), Alaska (e.g., the Yukon), and Greenland are projected to experience at least 10 % increase in freshwater discharge. In South America, only the Uruguay River presents a significant rise in discharge (15 %). On the other hand, a few small rivers in the world present reduced flow for the FUTURE. For instance, rivers originating in the southern Andes (e.g. the Maipo, Maule, Limay, Negro, and Chubut) and Colorado in the USA decrease their flows by ∼15 %, while most rivers of the Iberian Peninsula project a decay of about ∼10 %. Interestingly, several southern tributaries of the Amazon present dry anomalies, but they are not sufficient to significantly alter the downstream discharge into the Atlantic Ocean. In summary, a 6 % extra global runoff in the near future may seem irrelevant, but the changes are heterogeneously distributed throughout the globe, with many important rivers changing their mean flow by more than 15 %, which suggests a clear signal of climate change.

Under the imposed high-emission scenario, all GCMs project a global rise in river discharge for the next decades, and there is an overall consensus among models on where the changes in river flow are likely to occur. However, there is an important spread in the magnitude of the change. Figure a presents the trends of global river discharge anomalies for each model. The differences among models get amplified over time and are more noticeable in COUPLED models; i.e. the stronger signals of change are simulated by the GCMs with higher warming (see Table ). The ensemble mean global river discharge for PRESENT is 42.6×103 km3 yr−1, while the anomalies by 2050 are in the range [0,4.9]×103 km3 yr−1 for AMIP and [0.4,8.1]×103 km3 yr−1 for COUPLED simulations. These anomalies represent a positive change of up to 11.5 % for AMIP and up to 19.0 % for COUPLED simulations by the end of the projected period.

However, are these anomalies within the natural variability range? Figure b presents the ToE estimation for the ensemble mean. As for individual models, the ensemble mean presents a steady-state until about the year 2000 and a strong positive trend thenceforth. The anomalies remain within the natural variability range (±N), i.e. within the familiar climate conditions, until the year 2017. From there on, the global river discharge enters an unfamiliar climate until 2033, when it shifts to unusual climate conditions.

The emergence of global river discharge can have severe implications for specific rivers around the world, such as an increased frequency of floods. Figure  displays the ensemble mean spatial distribution of the signal-to-noise ratio (S/N) by the year 2050, when the global signal is at its maximum (Fig. b). The pattern reveals that the majority of rivers worldwide will remain in a range of natural variability in the coming decades (|S/N|<1). However, most changes arise in high-latitude and tropical areas where |S/N|>0.3. The high-latitude changes can be attributed to polar amplification, while the tropical changes are likely due to a shift to intense precipitation in the ITCZ (see discussion in Appendix ), which is accurately simulated only at resolutions finer than 20 km. In this sense, the river network may act as a strong filter, partly compensating for precipitation errors. Within high-latitude and tropical areas, rivers originating in central Africa, eastern Russia, Alaska, and Greenland present signals of climate change (|S/N|>1). Figure a shows that the main courses of the Congo, Nile, Niger, and Chad present a ToE for familiar to unfamiliar climate during the years 2015–2025, while the Yukon and Lena present this after 2030. Moreover, the projections of river flow in the lower Congo, Oubangui (Congo’s north tributary), Chari (primary tributary of Lake Chad), and main Nile indicate a shift to unusual wetter climate conditions during the 2030s (Fig. b). Similarly, the flow of rivers discharging in the Greenland coasts is projected to move to unusual climate in the next decade.

The global evaluation of the river flow anomalies, the signal-to-noise ratio, and the time of emergence reveals that there are four regions that project strong changes for the coming decades and that present a general consensus among models: central Africa, the Arctic, South Asia, and Patagonia. Here, we focus the analysis on those regions where, according to the projections, the signal of climate change of mean flow either emerges or closely approaches the threshold of its familiar climatology (see Fig. ).

The most severe changes are projected for rivers originating in central Africa. Several important rivers, such as the Congo (which contributes the second-largest discharge of all rivers in the world); the Nile (considered to be the longest river in the world); and the Sanaga, Niger, Volta, and Lake Chad tributaries (with important populations living upstream), are projected to experience a strong rise in their mean flow for the coming decades. Projections indicate an extra average discharge ranging from ∼16 % for the Sanaga River to around ∼49 % for the Lake Chad tributaries (see map in Fig. a). The aggregated discharge anomaly of these rivers exhibits a steady evolution during the past century that changes to a positive trend at the beginning of the current century (see Fig. b). The ensemble mean simulated river flow rise of this group of rivers exceeds the upper threshold of the familiar climate by the year 2018, and it drifts from unfamiliar to unusual climate by 2037. While the ensemble dispersion suggests a clear consensus in surpassing the familiar threshold, some models remain in the unfamiliar climate, others shift to an unusual climate, and some models progress to an unknown climate (S>3N). This is closely related to the degree of global warming assumed by each GCM, with those projecting higher warming exhibiting a more pronounced signal of change.

The Arctic Ocean plays two roles in the global ocean circulation: it provides a pathway to connect the Pacific and the Atlantic oceans, and it receives Atlantic inflow, cools the water, and returns it to the Atlantic . According to the simulations, this circulation could be affected in the near future. The projections indicate an average extra freshwater inflow of ∼12 % to the Arctic Ocean, which means that it will experience a freshening of its waters. The main contributors to this freshening are the Yukon and Mackenzie in North America; the Greenland rivers; and the Ob, Yenisey, Lena, Indigirka, Kolyma, and Anadyr in Russia, which exhibit positive anomalies ranging from ∼6 % to ∼43 % (Fig. c). The evolution of the integrated discharge anomaly of these rivers (Fig. d) shows a rise in the signal after ∼2000, emerging to an unfamiliar condition by 2039 and from then on stabilizing the signal slightly above the upper natural variability threshold. The ensemble dispersion presents a small spread around the ensemble mean signal, with some models remaining within the natural variability range until 2050.

The South Asia region also exhibits noteworthy anomalies (Fig. e), and while these anomalies are projected to stay within the bounds of natural variability (see Figs.  and ), we specifically emphasize this region due to its status as the most densely populated area globally. The significance lies in the potential impact of these anomalies on millions of people. The main rivers in the area of interest are the Indus, which projects anomalies of ∼28 %, and the Narmada, Krishna, Godavari, Mahandi, Ganges–Brahmaputra, and Salween, which project anomalies of around 8 % (Fig. e). Similarly to the previous regions and to what is observed globally, there are no significant changes in the signal until the early years of the present century, when a positive trend begins and extends until 2050 (Fig. f). The signal dispersion indicates that most models remain within the familiar climate, with some exceptions emerging into unfamiliar conditions by ∼2040.

Although positive river flow trends dominate the projections, there are few regions of the world where models project drier conditions for the future. From these regions, Patagonia in South America stands out for the strong agreement among models (see Fig. ). In particular, the models predict that the river flow of rivers originating in the southern Andes and discharging into the Pacific Ocean (the Maule, Biobío, Tolten, Valdivia, Yelcho, and Panela) or into the Atlantic Ocean (the Negro and Chubut) will decline in a range that varies from 10 % to 18 % (Fig. g). The signal time series shown in Fig. h shows that these flow reductions are not strong enough to emerge from the natural variability range before 2050, but this is likely to occur in the second half of the century if its signal strengthens in the long term (S/N=-0.9 in 2050). Moreover, the signal spread indicates that some models shift to unfamiliar drier conditions after 2030. Patagonian rivers are snow-fed rivers that extend over arid to semi-arid regions. The river flow decline results from a combination of significantly reduced precipitation with increased evapotranspiration (see Fig. ), which produces snow loss in the headwaters .

Lastly, the regional assessment is complemented with a brief description of specific rivers that project significant changes in their annual cycle at their mouths, which could provide useful insights for planning purposes given the population living upstream. Figure a–c show the cases of the Congo, Niger, and Lake Chad tributaries in central Africa, which present two common features. First, all annual cycles in the FUTURE period (2015–2050) are above the mean annual cycle of the PRESENT period (1950–2014). Second, these differences are amplified during their corresponding peaks, which could double for the Niger and Lake Chad or could be up to ∼50 % higher than the climatological peaks for the case of the Congo. Focusing on the Ganges–Brahmaputra and Indus rivers (Fig. d and e), the results show exactly the same pattern, albeit slightly weaker. In these cases, the amplitude of most annual cycles will be exacerbated up to ∼40 % due to a strong increase in flow during the wet season.