This study collected hydrological and meteorological data from 291 catchments in mainland China with drainage areas ranging from 372 to 142 963 km2. These catchments cover all of the first-level basins of mainland China except the Huaihe River basin (Fig. 1). Annual restored discharge data from 1956 to 2000 for each catchment outlet were collected from the Hydrological Bureau of the Ministry of Water Resources of China. Here, the term “restored” means that the effects of human activities on discharge have been mostly removed via the water balance method or other methods. Specifically, the process of restoring the station-observed discharge consists of two major parts: replenishing the consumption and removing the supplement. The water consumption includes the net consumption in agricultural, industrial, and residential sectors as well as water loss in the reservoir owing to evaporation and leakage. The water supplement includes the water diverted from other watersheds and the part of the extracted groundwater supplied back to the river. Changes in the reservoir storage can depend on whether the change is positive or negative. Thus, the restored discharge can be considered as the approximate natural discharge. The records range in length from 21 to 45 years; 261 catchments have record lengths greater than 40 years.

Two meteorological data sets were used in this study. The first is the 10 km gridded data set interpolated by Yang et al. (2014) based on 736 stations of the China Meteorological Administration, which includes P and potential evapotranspiration (Ep) observations from 1956 to 2000. Based on this observed data set, the annual areal P and Ep of each catchment were calculated. The other is the daily bias-corrected (Piani et al., 2010; Hagemann et al., 2011) modelled data set from the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP; http://www.isi-mip.org) covering the period 1951–2050 under scenarios RCP2.6, RCP4.5, and RCP8.5, as released by the CMIP5. The modelled data were initially downscaled to a 0.5∘ × 0.5∘ latitude–longitude grid data set and were then extracted and transformed into the ASCII format by the Institute of Environment and Sustainable Development in Agriculture, Chinese Academy of Agricultural Sciences, China. The output data for each scenario include precipitation; mean, maximum, and minimum air temperature; solar radiation; wind speed; and relative humidity for the five models including GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM, and NorESM1-M. The daily Ep of each grid was estimated by adopting the Penman equation (Penman, 1948; Appendix A) based on the GCM outputs. The annual series of P and Ep were calculated as the sum of every daily P and Ep over one year. Then, the annual catchment-averaged P and Ep were calculated as the average of gridded P and Ep within one catchment.

In this study, two slightly different methods were used to estimate the runoff trend for the historical (1956–2000) and projected periods (2001–2050), respectively. The runoff trend for the historical period was estimated as the slope of the linear regression of the annual Q series, denoted as kQ, and can be calculated by kQ=∑i=1mti-t‾Qi-Q‾∑i=1mti-t‾2, where m is the observed record length of a catchment, i is the ith record, ti is the year of this record, t‾ is the average of all recorded years, and Qi and Q‾ are the observed annual runoff in ti and the mean annual runoff in the historical period, respectively. The significance of kQ was tested by using a t test. The runoff trend of the projected period, denoted as ΔQ‾, is defined as the change in mean annual runoff between historical and projected periods and can be computed as ΔQ‾=Q‾p-Q‾, where Q‾p denotes the projected mean annual runoff.

In the study of Greve et al. (2014), the DDWW pattern was sensitive to the assigned threshold for defining the dry and wet regions such that different thresholds may have led to different, and possibly conflicting, results. To remove the influence of the threshold, Allan et al. (2010) adopted percentile bins for P to define wet and dry regions, thereby successfully avoiding the pitfalls of selecting a convincing threshold. Therefore, this study does not define absolute wet or dry regions but instead identifies relatively wetter or drier ones. Specifically, two variables, Q‾ and φ, were chosen as indicators of the aridity degree. The term φ was introduced to maintain consistency with studies based on the climate model data where Q‾ is not available. The spatial distributions of Q‾ and φ are shown in Fig. 2, with Q‾ ranging from 0 to 1400 mm a-1 and φ ranging from 0.5 to 8. We divided Q‾ and φ into six intervals, where the intervals with larger Q‾ values and smaller φ values denoted wetter levels (Table 1). In each interval, the total catchments and catchments becoming wetter were counted, and then the proportion of catchments becoming wetter, denoted as d, was calculated. A larger d value implies that more catchments have become wetter in this level. This study compares the d values of different intervals to examine a new DDWW pattern.

Among various types of Budyko-like equations, two analytical equations proposed by Fu (1981) and Yang et al. (2008) should be highlighted. These two equations are able to better capture the role of landscape characteristics because the two studies each introduce a catchment property parameter, ω and n, respectively, as shown by the two examples of c in Eq. (1). Yang et al. (2008) showed a high linear correlation between ω and n. Therefore, this study adopted the equation derived by Yang et al. (2008), which has been rewritten as E‾P‾=E‾pP‾-n+1-1/n. Focusing on Q, this study transformed Eq. (4) into Q‾=P‾-P‾E‾pP‾-n+1-1/n. The parameter n can be calculated by using the observed Q‾, P‾, and E‾p of each catchment from the period 1956–2000. The differential form of Eq. (5) was derived as dQ=∂Q∂PdP+∂Q∂EpdEp+∂Q∂ndn, where dQ, dP, dEp, and dn denote deviations in the observed or modelled Q, P, Ep, and n with respect to long-term mean values. Equation (6) has widely been used to estimate changes in annual Q (e.g. Yang and Yang, 2011; Roderick and Farquhar, 2011; Roderick et al., 2014).

Because we focused on the effects of climate change, n was assumed to remain unchanged, i.e. dn = 0 (Yang and Yang, 2011), and Eq. (6) became dQ=∂Q∂PdP+∂Q∂EpdEp. For convenience, we introduced εP and ε0 to represent ∂Q∂P and ∂Q∂Ep, which can be estimated on the basis of n, P‾, and E‾p: εP=∂Q∂PP‾,E‾p=1-1+E‾pP‾-n-n+1n and ε0=∂Q∂EpP‾,E‾p=-1+E‾pP‾n-n+1n. Roderick et al. (2014) showed that the runoff changes (= Δ(P - E) in this study) estimated by using Eq. (7) account for about 82 % of the variation in the GCM projections of Δ(P - E). Therefore, Eq. (7) can predict a reliable result under climate change projected by the GCMs. Based on Eq. (7), a framework can then be constructed to estimate the runoff trends and is interpreted in Appendix B: kQe=εPkP+ε0kEp,ΔQ‾e=εPΔP‾+ε0ΔE‾p, where kQe and ΔQ‾e are estimated runoff trends of the historical and projected periods, respectively; kP and kEp are the linear regression-calculated trends in annual P and Ep, respectively; and ΔP‾ and ΔE‾p are changes in P‾ and E‾p, respectively.

Equation (8a) and (8b) attribute the runoff trend to two major factors: the precipitation trend and the potential evapotranspiration trend. Equation (8a) estimates kQe according to the observed kP and kEp. Equation (8b) estimates ΔQ‾e according to the GCM projections, where ΔP‾ and ΔE‾p are calculated as the differences in P‾ and E‾p between 1956–2000 and 2001–2050. To measure the uncertainty of the GCMs, the coefficient of variance (Cv) in each catchment was estimated. Cv is defined as the ratio between the standard deviation and the absolute mean of the five ΔQ‾e outputs of the respective GCMs. Specifically, a lower Cv indicates less uncertainty in ΔQ‾e because the results of the different GCMs are similar.

Figure 3 presents the spatial distribution of the observed kQ in the 291 study catchments. At the significance level of 0.05, 39.9 % (or 116 of 291) of the study catchments are undergoing significant changes in annual Q. These catchments are hereafter referred to as significant catchments. Trends towards wetter conditions (positive trends) were found mainly in the upper and lower reaches of the Yangtze River basin and in the basins of the southwest, southeast, Pearl, and Inland rivers. The annual Q in the lower reaches of the Yangtze River basin and the northern Xinjiang Uyghur Autonomous Region robustly increased by more than 2 mm a-1, which was greater than the rates of most other catchments. The largest increasing trend of 10.3 mm a-1 was observed in the Yangtze River basin. However, the catchments in the middle reaches of the Yangtze River basin and in northern and northeastern China experienced the greatest reductions in runoff, generally with significant trends. Several catchments had negative trends of over 4 mm a-1; the most severe situation was in the Yellow River basin, where the annual Q decreased at a rate of 7.2 mm a-1.

The relationship between kQ and Q‾ is plotted in Fig. 4, which also shows the d for each interval. With an increase in Q‾, d increased from 0.18 to 0.88, which means that drier regions are more likely to become drier, whereas wetter regions are more likely to become wetter. The slight decrease in d to 0.79 in the last interval can be attributed to the small sample size of this interval; the number of catchments getting drier is actually equal in intervals 5 and 6 (Table 2). Therefore, these results indicate a new DDWW pattern, which emphasizes the fact that the distribution of water resources has become increasingly uneven in China since the 1950s. The process driving the uneven distribution of water resources in this study is powerful because nearly all of the wettest catchments became wetter, and the driest catchments became drier.

The DDWW pattern was also examined on the basis of kQ and φ data. Figure 5 shows that d decreased from 0.86 to 0.16 as φ increased, which implies that the DDWW pattern also holds if we adopt φ to describe the aridity degree in a manner similar to that reported by Greve et al. (2014). This result can be attributed to the monotonic decrease in Q‾ with φ (Fig. 6a). However, d increased sharply to 0.36 in the last interval, in contrast to the DDWW pattern. To understand this divergence, we marked 26 total areas of φ > 2 and kQ > 0 in Fig. 6b. Surprisingly, most of these areas (19 of 26) were located in areas of glaciers. Therefore, the change in water storage (ΔS) from the melting of glacial ice and snow also plays a key role in the runoff generation in such regions. However, φ does not consider the influence of ΔS, thereby leading to an overestimate of the aridity degree in these catchments caused by grouped into the wrong intervals. This reflects the weakness of φ in assessing the aridity degree with respect to water resources compared with Q‾. Moreover, by acquiring ΔS and redefining an adjustable aridity index (φ′) as (P - ΔS)/Ep, these catchments with high φ could also obey the DDWW pattern.

Based on the comparison of the Budyko-estimated kQe with the observed kQ, the coefficients of determination (R2) (Legates and McCabe, 1999) were determined to be 0.70 and 0.86 for all catchments and for significant catchments, respectively (Fig. 7). Therefore, the majority of the runoff trends can be attributed to changes in the atmospheric forcing of water and energy. However, the slope of k was smaller than 1, at 0.60 and 0.62 for all catchments and significant catchments, respectively, which implies that the Budyko-based framework underestimates the changes in runoff. Nevertheless, despite underestimating the runoff trends, the framework can correctly note the direction of runoff changes in more than 80 % of the study catchments (Fig. 7). This is because the error rates in all and significant catchments, or the proportions of misestimated catchments having different signs of the observed and the estimated trends, are 18.6 and 6.0 %, representing 54 of 291 and 7 of 116, respectively. Furthermore, the DDWW pattern works well based on kQe (Fig. 8), which validates the DDWW pattern from the perspective of climate change based on historical meteorological observations. It also indicates the feasibility of using only P and Ep information to examine the pattern and serves as a reference for studies based on climate model outputs.

In catchments where the observed and the estimated signs are consistent, the parts of kQe generated from P (kQP, = εPkP) and Ep (kQ0, = ε0kEp) were compared to find the factor controlling the runoff changes owing to climate change. As shown in Fig. 9, kP makes an overwhelming contribution in 88.6 % (or 210 of 237) of these catchments because the ratios of absolute kQ0 to absolute kQP are smaller than 1. Moreover, when linking kP with Q‾ (Fig. 10), we observed a pattern similar to that of DDWW, i.e. more precipitation in wetter areas and less in drier areas. This pattern is the result of the dominant position of kP and the positive effect of kP on the runoff trends. Therefore, from the perspective of climate change, the more uneven precipitation resulted in more uneven runoff, thereby producing the DDWW pattern.

Based on the GCM projections, Eq. (8b) predicts the future runoff trends ΔQ‾e between the periods 1956–2000 and 2001–2050. The results showed great discrepancies in ΔQ‾e among the five GCMs even under the same scenario, whereas the model-averaged results under different scenarios were close (Fig. 11). The Cv values of ΔQ‾e in each catchment are presented in Fig. 12. Taking the RCP2.6 scenario as an example, over two-fifths (41.9 %) of the catchments have a Cv value larger than 0.5, which is indicative of considerable uncertainty in the various models reported by previous studies (e.g. Greve et al., 2014; Kumar et al., 2016). However, the proposed DDWW pattern is no longer suitable under the three scenarios regardless of the model selected because d decreased as Q‾ increased except for interval 6, which showed an increase in contrast to the DDWW pattern. These results do not imply an obvious alleviation of the uneven water resource distribution. Conversely, they suggest that most areas of China (more than 60 %, as calculated from Table 3) will experience water resource shortages under the projected climate changes, whereas the conditions of the driest (interval 6) and wettest (interval 1) areas will be relatively slight. Furthermore, the main meteorological factor controlling the future trends was identified on the basis of the mean results of the five GCMs. Figure 13 shows that the trend in P(ΔP‾) is no longer the controlling factor because only 40 % of the catchments had ε0ΔEp‾εPΔP‾ values smaller than 1.

The spatial distribution of model-averaged relative changes in Q‾(ΔQ‾e/Q‾) is shown in Fig. 14. The results under the three scenarios were similar. Red regions indicate catchments in which Q‾ will fall by more than 60 % relative to the historical value; most of these regions are located in the Yellow River basin with relatively high certainty (Cv < 0.5). The most severe situation occurred in a catchment situated in the Yangtze River basin, where the runoff is predicted to be nearly zero and the Cv was less than 0.2. In contrast, dark blue areas indicate catchments in which Q‾ is projected to increase by more than 40 %. These catchments are located primarily in the Inland River basin, except for northwest China, where catchments will suffer from a shortage of fresh water. Instead of continuing to become drier, catchments in northeast and north China are projected to generate more runoff in the future, whereas catchments in the lower reaches of the Yangtze River basin will experience considerable reductions in runoff despite historical increases. These are the most obvious distinctions between the projected and historical runoff changes. Thus, the DDWW pattern failed to accurately characterize these future patterns.

An inevitable concern about the GCM outputs is their uncertainty, which determines the reliability of the projected results. To examine the uncertainty, one workable method is to compare meteorological observations with simulations for the same period of 1956–2000. Taking the results of the GFDL-ESM2M model as an example (Fig. 15), P‾ was effectively simulated except for some obvious incorrectly estimated points far from the y = x line. However, simulations of E‾p show tremendous deviations, resulting in no obvious linear relationship between the simulated and observed values. This simple comparison directly highlights the unreliability of the GCM outputs.