Climate change is a global problem, but the impacts and associated vulnerability are not homogeneous. There is therefore a demand for robust projections of changes in regional climate, particularly water availability. At the largest scales, the majority of the literature on projected changes in aridity suggests a global land-drying tendency : a consequence of ubiquitous increases in potential evapotranspiration (Ep) but mixed signals in precipitation (P). This has been challenged, however, by some recent studies . At the river catchment scale, direct human impacts (non-climatic, human interventions directly affecting the partitioning of P into runoff – Q – and evapotranspiration – E) are already having a significant, but poorly quantified, effect on water availability . For the Indus River catchment showed that current direct human impacts on water availability (decreases due to water consumption for irrigation) are expected to be greater in magnitude than end-of-21st-century climatic impacts on water availability. Increasing E due to irrigation is commonly observed in heavily populated catchments, especially across southern and eastern Asia .

The literature on future water availability projections has typically been framed around the net atmospheric supply of water versus the net demand for water resulting from direct human impacts (land-use change, dam construction and reservoir operation, and surface water and groundwater consumption for irrigation). Recent studies have considered (1) the projected human water demand using integrated assessment models, with water supply fixed to present conditions ; (2) the projected water supply using global climate models (GCMs) to force offline global hydrological models (GHMs), with human water demand fixed to present conditions ; or (3) both projected water supply and projected human water demand .

Using GCM output alone in hydrological projections is not considered suitable, because GCMs have coarse resolution; simplified land surface schemes; and, crucially, biases in simulating hydrological cycle components. The usual approach for generating hydrological projections is to use bias-corrected and downscaled GCM output to force offline GHMs . Using GHMs in addition to GCMs greatly increases the computational expense of a study. Here, we propose an approach for refining projections of water availability from GCM models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5). We use Q as a measure of water availability. The term “refine” is used in the sense that we expect to generate projections of Q on an improved physical footing, compared to using GCM output directly. The approach uses model-simulated aridity and a bias correction, within the Budyko framework . We do not consider future human water demand, only future net atmospheric supply of water, of which aridity is a key determinant.

We consider a simple water balance and assume that changes in storage are negligible: P=Q+E. GCM variables require bias correction to be of value at catchment scales . Bias-correcting a GCM-simulated future Q or E is a complex process. To illustrate this point, we introduce the Budyko framework . Within this framework the partitioning of (annual to long-term mean) P into Q and E scales as a non-linear function of aridity. Aridity, within the Budyko framework, is the dimensionless ratio of Ep to P. The evaporative index, the dimensionless ratio of E to P, is dependent on Ep/P. The relationship is represented by the non-linear Budyko curve, which is constrained by the physical limits of the atmospheric demand for water (E<Ep; the red dashed 1:1 line in Fig. ) and the atmospheric supply of water (E<P; the blue dashed horizontal line in Fig. ).

The original deterministic and non-parametric Budyko formula was developed using data mainly from European river catchments : EP=EpPtanh⁡PEp1-exp⁡-EpP1/2. The trajectory taken in the Budyko space due to a change in P, Ep, or E is dependent on the initial values of these three fluxes (the mean state) . Therefore, an accurate representation of the observed climatology is important in any modelling study looking at hydrological projections, especially since changes in variables are typically small compared with climatology. If the present-day aridity is biased, then the future-minus-present changes in runoff (ΔQ) and evapotranspiration (ΔE) will also be biased, even if the future-minus-present changes in precipitation (ΔP) and evapotranspiration (ΔEp) are correctly simulated. Section S1 in the Supplement further demonstrates this point with an example that, although arbitrary, is illustrative of the magnitude of aridity biases in CMIP5 models.

Recent work has shown that aridity can only explain part of the differences between catchments e.g.. This has led to the derivation of a number of parametric forms of the Budyko curve. One of the more popular forms is the Fu equation , a one-parameter function expressed as EP=1+EpP-1+EpPω1/ω, where ω is an empirical parameter that is calibrated against local data. The traditional Budyko curve (Eq. ) corresponds to ω=2.6 in Eq. () .

Here, an attempt is made to utilise biased but plentiful GCM output without the need for GHMs. We apply our approach to two major catchments in China, the Yangtze and the Yellow. There is a wealth of literature that uses the Budyko framework to understand water changes in other Chinese basins . The Yangtze and Yellow rivers dominate the wetter south and drier north, respectively (Fig. ). The spatial variability in P means that the north of the country, which is poleward of the east Asian monsoon rains, is more water-stressed than the south. This is exacerbated by the fact that the north has 65 % of the total arable land in China .

The mismatch in water supply versus water demand could be the reason behind the stark decline in Yellow River streamflow (the temporally lagged, spatial integral of upstream Q) seen in recent years . The contributions of climate change (which incorporates not only aridity change but also changes in seasonality, snow dynamics, storminess, and many other factors; ) and direct human impacts to this “drying up” are widely discussed in the recent literature . Most studies suggest a significant contribution of direct human impacts, including afforestation and land-use change , although methods and attributed contributions vary.

We can also use the Budyko framework to quantify the contribution of aridity change alone (changes in P and Ep only) to the 20th-century decrease in Q in the Yellow River catchment. Qualitative agreement with previous studies will serve to validate the use of the Budyko framework in refining 21st-century projections, while hopefully shedding new light on 20th-century observed changes. The 20th-century Budyko framework estimate is compared with an estimate of Q simulated by an offline land surface model (LSM) that does not include a representation of direct human impacts, with the exception of land-use change. If these estimates reconcile, it suggests that the Budyko framework is suitable for this attribution, since Q simulated by the LSM should largely reflect changes in P and Ep only. Further, we ask if the difference between the total change in Q and the component attributed to aridity change, for the Yellow River catchment, is in close agreement with a simple estimate of the change in Q due to direct human impacts.

Section  details the observed and modelled data used, and Sect.  describes the methodology. Results are presented in Sect. , first applying the Budyko framework to the 20th-century observed water availability (Sect. ), before extending the approach to constrain 21st-century model projections of water availability (Sect. ). We finish with a discussion (Sect. ) and conclusions (Sect. ) The two-pronged approach of this paper is summarised in Fig. . It shows how the approaches share the same theory and use many of the same equations but are independent in their objectives. However, the 20th-century application of the Budyko framework supports the suitability of the 21st-century application, as indicated (Fig. ).

Before using the Budyko framework in tandem with CMIP5 output, we considered whether it could be used to quantify the contribution of aridity change to the measured decrease in Yellow River runoff between 1951 and 2000. Encouragingly, for both the Yangtze and Yellow River catchments, the Q trend due to aridity change was found to be near-identical to that simulated using the LPJ LSM (which is forced by observed P and Ep). This suggests that the Budyko framework is suitable for determining the relative contribution of aridity change to the measured decrease in Yellow River runoff, calculated as 27 %. Therefore, the relative contribution of all other factors besides aridity to the measured decrease in Yellow River runoff is expected to equal 73 %.

With time series of water consumption derived using low and high year 2000 water consumption estimates, the component due to direct human impacts is calculated as 43 % and 71 %, respectively. Therefore, we can account for nearly all of the measured decrease in Yellow River runoff (98 %) using aridity change and the high consumption estimate alone, but we stress that such estimates are highly uncertain. We are not able to dismiss a significant contribution from the net effect of all other factors (besides aridity and direct human impacts), which ranges from 2 % to 30 %. Given that the estimate of the contribution of aridity change appears to be the most robust result, we can instead state that the majority of the measured decrease in Yellow River runoff appears to be due to direct human impacts and all other factors. Also, despite the uncertain water consumption estimates, the contribution from direct human impacts is approximately 2 times greater than the contribution from aridity change. Other studies have estimated the climate change (all non-human) and human components. attribute 55 % of the reduction in Yellow River water discharge to humans, with giving a value of 49 %, compared to our range of 43 % to 71 %. Note that these studies use different methods and periods to estimate the contributions of the two components but focus on the second half of the 20th century. Our estimate of the component due to direct human impacts is consistent with these previous estimates, although we add detail by finding that this contribution is markedly greater than the contribution from aridity change alone.

Although estimates of water consumption are highly uncertain, there are also uncertainties in our estimate of the aridity change contribution to Q change. This estimate, as well as runoff simulated by the LPJ LSM, rely on an uncertain observed Ep dataset (see Sect. ). An energy-only EP estimator is expected to be more appropriate but is not available because of insufficient observed data. Meanwhile, the observed P dataset is likely to contain biases and inhomogeneities . Many grid boxes in China are poorly gauged (some not at all) in the period investigated (see Fig. S1), especially in the mountainous Tibetan Plateau region, where P is scarce but highly variable . These are largely insurmountable obstacles facing all hydroclimatological studies.

Within the Budyko framework all climatic and non-climatic factors besides aridity are integrated by the ω parameter. In Eq. () we separate this “residual” into a component due to direct human impacts and a component due to all other climatic and non-climatic factors besides aridity change and direct human impacts. The low water consumption estimate means that we are not able to dismiss a significant contribution from the net effect of all other factors. Support for a negligible contribution from all other factors comes from the strength of agreement between Qa and Qal. This is because the LPJ LSM includes a realistic representation of vegetation, which has been shown to be a useful indicator of these other factors that are integrated by ω (although this may only hold for larger catchments) (see Sect. S3). Further, Fig. S3 shows that CMIP5 models simulate no obvious changes in ω over the second half of the 20th century.

In estimating direct human impacts from just water consumption there remains the possibility that other direct human impacts could account for a significant contribution to the decrease in Yellow River runoff. We present evidence that the contribution from land-use change is negligible. On the other hand, catchment runoff can abruptly decrease during the filling of large reservoirs following dam construction, causing anomalously low annual runoff. Following filling, runoff should return to pre-dam levels, and such projects are only thought to affect seasonal water storage and not introduce trends in long-term runoff. Rather, dam and reservoir construction facilitates access to water resources and leads to more water withdrawal and consumption. The influence of dams and reservoirs are likely accounted for in the water consumption estimates .

The agreement between the Budyko framework and the LPJ LSM for the observed period also increases our confidence in using the Budyko framework for projections. The CMIP5 Budyko-corrected projected changes in runoff rely on the assumption that 21st-century changes in P and Ep are not dependent on existing climatology biases in CMIP5 models. Across the CMIP5 multi-model ensemble we did not find compelling evidence for relationships, supporting this assumption (Fig. ). This is broadly consistent with expectations, given recent research showing that the “wet gets wetter, dry gets drier” paradigm does not hold over global land surfaces . However, the mean state can undoubtedly have some influence on the simulated changes in P and Ep due to land–atmosphere feedbacks . We note that when correcting Ep (Eq. ; with P replaced with Ep) we calculate the correction offset as the observed climatology (Penman–Monteith estimator) minus the model-simulated climatology (energy-only estimator). Using these different estimators will likely introduce some error in the calculation.

It is also important to note some potential limitations of using Eq. () to separate the measured decrease in Yellow River runoff into various components. This approach assumes a linear relationship and therefore that the individual components are independent. showed that cross-correlations exist between many of the factors suggested to influence runoff through ω. Testing for dependencies between ΔQh and other components is unfortunately limited by the poor temporal resolution of the irrigated-area time series of . Although we find that interannual variations in Qa and the residual Qh+Qo are correlated (-0.35), this correlation is weak and reverses sign when considering multi-year means. Further, our approach considers long-term trends/changes in runoff, which means that any dependencies at shorter timescales should not influence conclusions.

In calculating Q* (Eq. ) ω values are calculated for the 1951–2000 period, using Eq. (), then taken to be constant for the period 1951–2100. While the relationships of variations in Q with variations in such catchment-specific parameters are understood , the full complexity of the influence of changes in catchment properties on these parameters is not. However, showed that, for large catchments, the long-term averaged annual vegetation coverage explains as much as 63 % of the variance in the catchment-specific ω. With 21st-century increases in total vegetation coverage projected , we expect this parameter will increase in magnitude. This is found to be the case in the CMIP5 multi-model ensemble, and these increases in ω need to be included when verifying the Budyko framework on the CMIP5 models themselves (see Sect. S3 and Figs. S2–S4). The influence of changes in ω on projected changes in Q is small compared to the influence of correcting Ep and P (see Sect. S3 and Fig. S5). Demonstrating this, the CMIP5 multi-model mean ΔQ* for the Yellow River catchment in RCP8.5 with constant ω (0.09±0.09 mm day-1) is not significantly different to the CMIP5 multi-model mean ΔQ* for the Yellow River catchment in RCP8.5 with time-varying ω (0.07±0.08 mm day-1). Therefore, our conclusions are not sensitive to the choice of ω (constant or time-varying).

We show that aridity change (changes in P and Ep only) is of greatest importance in shaping projected changes in runoff in CMIP5 models, and all other factors (ω) play a secondary role. We expect our CMIP5 Budyko-corrected Q projections to be substantially more reliable than the original CMIP5 model-simulated Q projections. In the case of the Yellow River catchment, the 5 %–95 % range of the future-minus-present (2080–2099 minus 1980–1999) change in Q is reduced by 34 % and 35 % in RCP8.5 and RCP4.5, respectively. Importantly, constraining Q projections using the Budyko framework increases confidence that the Yellow River catchment will see increases in Q by the end of the 21st century – the best-guess (CMIP5 multi-model mean) change of 0.09 mm day-1 is significantly different from zero at the 90 % confidence level. Greater confidence in the range of Yellow River catchment water availability projections could be of great value to policymakers. More generally, the Budyko framework serves as an inexpensive tool to rapidly update projections from biased GCM simulations without the need for offline GHMs. However, further research is needed. Specifically, we believe that an ensemble of GHMs, driven by at least one set of bias-corrected and downscaled GCM projections, should be used as a means of verification.

Most applications of the Budyko framework consider spatial rather than temporal variations. demonstrate that spatial and temporal variations are not necessarily tradable. We stress that the Budyko framework is not employed here to robustly determine interannual variability in water availability but is instead used to understand long-term trends (Sect. ) or the difference between 20-year means at the end of the 20th and 21st centuries (Sect. ).

We have demonstrated how the Budyko framework can be used to place water availability projections from readily available GCM output onto a more physical basis by correcting for biases in aridity, using the example of the Yangtze and Yellow River catchments in China. The approach is inexpensive, does not need the use of offline GHMs, and could be used to provide rapid updates on water availability projections for new GCM scenarios. Wherever GCMs simulate significant biases in representing observed aridity, we expect to generate significantly altered projections. In the Yellow River catchment, considerable negative biases in simulated aridity lead to a substantial narrowing of the range of future GCM projections. In catchments where GCMs simulate positive biases, we would expect to see broadening of the range of GCM projections. Meanwhile, in the Yangtze River catchment, simulated aridity biases are small, meaning that projections are little changed by our approach.

We stress again that these refined water availability projections account for aridity change only. In the hypothetical case where future aridity change is known, the projected Q will not be realised due to the effect of all other factors, especially highly uncertain future changes in direct human impacts (these are not represented in CMIP5 models). Current human impacts on Q are possibly greater than end-of-21st-century aridity change impacts on Q in the Yellow River catchment . Therefore, the current water shortages are not likely to be alleviated without improved agricultural practices and water management. Importantly though, reducing the range of water availability projections gives planners an improved idea of what needs to be done to reduce water stress in the Yellow River catchment for future generations. Moreover, our conclusions underline the need for imminent action and highlight the fact that increases in Q due to aridity change will not offer much relief in the absence of serious and concerted action to minimise direct human impacts.

Chinese authorities have recently attempted to alleviate the drying in the north of China, by diverting water there from the wetter south (the South-to-North Water Diversion Project). It remains to be seen whether this will reduce the imbalance in atmospheric water supply and human water demand across China and whether it could even place additional water stress on the more resilient south . Generating refined water availability projections in these two key river catchments should underpin decisions made on future engineering projects.