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Dramatic Change in the Hydrologic Cycle Anticipated at Regional Scale Qiuhong Tanga* **et al.** and Dennis P. Lettenmaier a Department of Civil and Environmental Engineering Box 352700, University of Washington, Seattle, WA 98195 * Email: [email protected] Abstract It is essential to assess the possible future changes in the hydrologic cycle at regional scale for developing adaptation strategies to anthropogenic climate change. A quantilequantile (Q-Q) relation between observation-based and estimated relative change from general circulation model (GCM) ensemble was developed in the last half of the twentieth century for three hydrologic variables, land precipitation, evaporation, and runoff. The relations were used to scale the GCM predicted changes in the twenty first century. The scaled relative change has a spatial pattern consistent with the probability of the change direction with pattern amplitude constrained by recent climate change. The results show that the land area that will experience large change in the hydrologic variables increase, indicating more dramatic change in the hydrologic cycle is anticipated at regional scale in the next couple of decades. The portion of global population that lives in the area with more than 30% change in runoff increases from one quarter in the twentieth century to near half in the twenty first century. The land areas with both wet and dry condition increase and the area with moderate condition decreases. The fingerprint pattern of climate impacts on the hydrologic cycle is generally consistent with the distribution of climatic zones with drier arid area and wetter humid area. Most nonpolar arid areas and the Amazonia become drier, likely because of the weakening of the tropical circulation systems. The northern high latitudes and Asian monsoon regions become wetter. It suggests the enhanced land-sea thermal contrast and warmer sea surface may intensify monsoon and enhance atmospheric moisture convergence over land. 1. Introduction It is essential to assess the impact of climate change and future climate variability on hydrology at regional scale for determining the adaption water management policy responses to anthropogenic climate change. Although current general circulation models (GCMs) are able to project the response of the climate system to anthropogenic changes into 2100, the uncertainty in forecasts is high (Allen et al. 2000). Ideally, the forecasts of climate change should be constrained objectively by the observed climate and recent climate change. Precipitation is the primary forcing of the terrestrial hydrologic cycle and is a determining parameter of land surface evaporation and runoff. Quantifying the possible changes in precipitation is fraught with difficulties because the constraints on future changes are considerably weak (Allen and Ingram 2002). Runoff, which represents a major portion of freshwater resources to terrestrial inhabitants, has more significant impacts on a wide range of social and environmental systems. The forecast of runoff change may be constrained by recent runoff observations and physical control: precipitation forecast. However, runoff forecast is expected to be more uncertain than that of global mean temperature and precipitation. Runoff is generally not spatially observed. The observed runoff is usually constructed from streamflow, a temporally lagged, spatial integral of runoff over a river basin. Streamflow observations have shorter record and less global coverage than precipitation and surface temperature observations (Peel and McMahon 2006; Fekete et al. 2002; Dai et al. 2009). Furthermore, the runoff observations are of a matter of substantial uncertainty because of human impounding and impeding the flow of rivers (Postel et al. 1996; Vitousek et al. 1997). For example, only half of the observed streamflow decrease in Yellow river during the last half of the twentieth century was caused by climate fluctuation (Tang et al. 2008). The other half was attributed to the irrigation water withdrawals. Physical constrains of runoff forecast are weaker than that in global mean temperature and precipitation. Annual runoff is largely determined by precipitation and annual evaporation in a region. It is anticipated that runoff increases (decreases) when precipitation increases (decreases). The ratio of annual runoff to precipitation (runoff coefficient) is about 36% over the global land (Gleick 1993; Oki and Kanae 2006) although with large spatiotemporal variations (Agarwal and Singh 2004). The impact of relative small human-induced fluctuation in global temperature and its consequent fluctuation in precipitation would cause much larger fluctuation in runoff (Langbein, 1949; Revelle and Waggoner 1983; Karl and Riebsame 1989). Another difficulty for assessing the change in the hydrologic cycle is its spatial scale. The regional hydrologic change is of more interest than the global mean change. Previous studies have projected the global change patterns of hydrologic variables based on single climate model (Arnell 1999; Vorosmarty et al. 2000; Arora and Boer 2001). However, different individual model could project much different spatial pattern of the hydroclimatic changes (Dessai et al., 2006; Nohara et al. 2006; Cai et al. 2009). It was suggested that climate change projections from any single model should be treated as only one of a range of possibilities (Forest et al. 2000). The Program for Climate Model Diagnosis and Intercomparison (PCMDI) archived coupled climate models results from many climate-modeling centers for the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC) (Meehl et al. 2007). The multimodel data are increasingly being used to reduce the single model’s uncertainty and increase the reliability of the projections (Giorgi and Mearns 2002; Held and Soden 2006; Zhang et al. 2007). Statistical methods are developed to produce probabilistic projections of ensembles of GCMs and to evaluate the probability distribution of global mean temperature change under different forcing scenarios (Allen et al. 2000; Stott and Kettleborough 2002; Tebaldi et al. 2005; Lopez et al. 2006). A common method, called multi-model ensemble mean or median (MM), is to calculate the (weighted) mean or median of the response-patterns of an ensemble of GCM simulations (Allen and Tett 1999). The variance in the response patterns from an ensemble is smaller than the variance in the observations (if all distributions are Gaussian).The model simulated trajectory is then needed to be linearly scaled to match the magnitude of the observed anthropogenic signal for the predictions of anthropogenic warming (Allen and Tett 1999; Allen et al. 2000). This approach is justified for temporal pattern of global mean results (see Lambert and Boer 2001; Reichler and Kim 2008). It is therefore increasingly being used to analyze the spatiotemporal pattern of the hydroclimatic variables at regional scale (Nohara et al. 2006; Milly et al., 2005; Seager et al. 2007; Barnett et al. 2008). The problem of using GCM results in regional study is that variability on small spatial scales is likely to be under-represented in any finite representation of a continuous turbulent system. Most importantly, the MM method has significantly reduced spatial variability. Previous researches had shown that MM method would give more spatially homogeneous pattern associated with climate change (Giorgi and Mearns 2002; Delworth and Knutson 2000; Milly et al., 2005). Although some studies had evaluated the facility of using the multi-model simulations to depict regional changes (Dessai et al. 2005; Watterson 2008), few of them had used objectively information, i.e. the observed recent change, to constrain the forecast of hydrologic variables. In this study, we present a mathematical framework that attempts to assess the regional change in hydrologic cycle in a changing climate. The spatial variance, which is suppressed in the MM method in statistical inference, is linear scaled to observed spatial variance. We present probabilistic forecasts of hydrologic changes at regional scale, obtained with multi-model simulations and constrained by the observed hydroclimatic changes. 2. Data and Method The PCMDI/AR4 archive of GCM outputs was used. Most of the GCMs performed historical simulations (20C3M) of climate with prescribed external forcing for the late nineteenth century and the whole of the twentieth century. Future climate simulations with an assumed forcing based on the IPCC Special Report on Emissions Scenarios (SRES) were also performed. The SRES A1B scenario, which represents a very rapid economic growth with increasing globalization into the future, is chosen for this study. Three hydrologic variables, precipitation (P), evaporation (E), and runoff (R), of the 20C3M and SRES A1B simulations were analyzed. P, E, and R were obtained from the monthly mean precipitation flux (pr), surface upward latent heat flux (hfls), and runoff flux (mrro) data of the IPCC standard output from the PCMDI/AR4. The outputs of the GCMs were of different atmosphere resolution (Gleckler et al 2008). The resolution is typically at the order of 4 degree. The GCM outputs were converted to a common 0.5°×0.5° latitude-longitude grid. We consider only one realization (“run1” in the archive when available) for each variable from each of 22 models (listed in Table 1). There are 21 models for P and 20 models for E and R. Global P, E, and R data from observations or observation-forced simulation using land surface model in the period of 1950-99 were collected from various sources. One set of monthly P observation was obtained from the 5°×5° grid dataset of the Global Historical Climatology Network (GHCN) (Peterson and Vose 1997).The GHCN dataset comprises over 30,000 stations with varying temporal coverage. It has been carefully quality controlled and considered to be sufficient to describe global scale land precipitation change, particularly after 1950 (New et al. 2001). Another set of monthly P observation was taken from Dai et al. (2009). The P data, thereafter referred as NCAR P, were derived by observation-based analyses of monthly precipitation with intramonthly variations from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis over global land areas (Dai et al. 1997; Chen et al. 2002; Qian et al. 2006). The NCAR P and other observed atmospheric forcing were used to force the Community Land Model (CLM; Dickinson et al. 2006) and to generate global land surface E and R (Qian et al. 2006; Dai et al. 2009). The CLM simulated monthly E and R, thereafter referred as CLM E and CLM R, and the NCAR P were collected in the period of 1950-99 at T42 (~2.8°) resolution. The data were converted to the same 0.5°×0.5° grid as the GCM outputs. A set of historical monthly streamflow at the farthest downstream stations for the world’s 925 largest ocean-reaching rivers was gotten from Dai et al. (2009). The network of the stations covers for ~80% of global ocean-draining areas and accounts for about 73% of global total runoff. The drainage basin associated with each station was determined using the Simulated Topological Network (STN-30p) at 0.5°×0.5° spatial resolution (Vörösmarty et al. 2000). The relative change in each hydrologic variable between the first 20 yr and the last 20 yr of the last half of the twentieth century was examined. The relative change was computed as 100 times the difference between 1980-99 and 1950-69, divided by 1950-69 value. Computing the PCMDI/AR4 ensemble median of the relative changes at each 0.5°×0.5° grid yielded a spatial pattern of the relative change. The PCMDI/AR4 change was then compared to the observed changes. The MM is widely applied to seasonal weather forecasting and climate change projections (see Harrison et al. 1999; Giorgi and Mearns 2002). The forecast skill of MM is usually superior to that of each ensemble member (Fritsch et al. 2000; Pierce et al. 2009). Pierce et al. (2009) found that the superiority of MM was largely caused by the cancellation of offsetting errors in the individual global models. The superiority of MM may be interpreted in statistics. If the GCM ensemble is assumed to be a sample of the full potential climate model, the ensemble mean or median is approximately where the peak of the probability density function is (exactly so if the distribution is Gaussian). Statistically, the ensemble mean is the center of mass and the median is the halfway point (half the population has a lower value) for the probability density. The peak of the probability density function is the most likely value (“best guess”) of the ensemble. Although the mean or median value can depart from the peak value (for different distribution), previous studies (see Stott and Kettleborough 2002; Tebaldi et al. 2005; Lopez et al. 2006) have shown that the discrepancy may be small for GCM ensemble that is most likely normally distributed (exactly be normally distributed if the number of ensemble member is sufficiently large and the ensemble members have identical distribution with finite mean and variance). Since the GCM ensemble is usually very sparse, the ensemble median is used in this study in order to give more robust guess. Another particular reason for using median not mean is that the median is order statistics, and this permits a relative direct interpretation of the probability distribution function. The direction of change, i.e. positive or negative change, is of great interest at regional scale. The probability of a positive change (Pp) is approximately the ratio of the number of the ensemble member showing a positive change to the total. The probability of a negative change (Pn) is 1–Pp. The range of Pp [0, 1] can be linearly transformed to the range of [-1, 1] using the transfer function f(Pp) = 2 Pp – 1 = Pp – Pn. Therefore Pp – Pn ranges from -1.0 indicating high probability of negative change, to 1.0 indicating high probability of positive change. The estimated probability of the direction of change, i.e. Pp – Pn, was calculated at each 0.5°×0.5° grid for each hydrologic variable. The spatial pattern of the ensemble median provides the most likely pattern with amplitude of hydroclimatic change predicted by the GCM ensemble. The variance in the spatial pattern from an M-member ensemble is 1/M times the variance in the spatial pattern of the ensemble member if the ensemble members have the same normal distribution. This will significantly underestimate the pattern-amplitudes. Denote the variable value at time t by xt, the relative change between time n and time 1 can be expressed as 100 times change ratio minus 100, where the change ratio is defined as the X= xn/x1. The change ratio between time n and time 1 can be expressed as: X=xn/x1=xn/xn-1 xn-1/xn-2 … x2/x1=(1+ε1) (1+ε2)… (1+εn-1) where εt denotes the relative change divided by 100. By assuming the increments εt to be independent random variables, the change ratio can be thought of as the multiplicative product of many independent random variables each of which is positive. It may be modeled as lognormal distribution. A Q-Q plot (quantile-quantile plot) was used to compare the observed and estimated probability distributions of the logarithm of the change ratios. The linear regression of the Q-Q relationship for the logarithm of the change ratio of each hydrologic variable between the observation and estimation was obtained based on the data in the historical period of 1950-1999. If the logarithm of the GCM ensemble change ratio X20 is normally distributed with mean μ20 and standard deviation σ20, the scaled change ratio X20s=X20/a –b/a using the Q-Q relationship is also normally distributed with mean μ20–b/a and standard deviation σ20/a, where a is the slope and b is the intercept of the linear regression of the Q-Q relationship. The scaled change ratio has the same standard deviation (i.e. pattern-amplitude) as the observation. It indicates the observation can be approximated by scaling the standard deviation and offsetting the GCM ensemble mean with –b/a. The Q-Q relationship was used to constrain the GCM ensemble estimate in future time period. Denote the logarithm of the GCM ensemble change ratio in a future period by X21, the mean of X21 by μ21 and the standard deviation by σ21. Assuming standard deviation difference between the scaled X21 and scaled X20 is the same as that between X21 and X20, the scaled X21 can be expressed as X21s=X21[σ20/a+(σ21– σ20)]/σ21 –b/a. The scaled X21 was used to approximate the change ratio in the future period. The GCM ensemble relative change in each hydrologic variable between the first 20 yr and the last 20 yr of the twenty first century was computed using the ensemble median of the available GCMs. The GCM ensemble relative change was then scaled using the relationship developed in the historical period. The scaled relative change in the twenty first century was compared to that in the twentieth century. The impact of climate change on hydrology and its potential consequences on human society were discussed. 3. Results and Analysis Figure 1 shows the last half of the twentieth century change in precipitation estimated using the GHCN P data, the NCAR P data, and the PCMDI/AR4 GCM ensemble, and the probability of the direction of change estimated by the GCM ensemble. The estimated spatial patterns based on observations (i.e. GHCN P and NCAR P) bear a considerable resemblance to each other with positive change over the United States, southeastern South America and Western Australia and negative change over large part of Siberia and Africa. There are large regional differences, however, between the observations and GCM ensemble in the western United States, Siberia, and middle Africa. The probability of the direction of change shows a pattern generally corresponding to that of the change from GCM ensemble. The amplitude of the change estimated by the GCM ensemble is much smaller than those of the observations (as expected from ensemble averaging). Figure 2 shows the last half of the twentieth century change in evaporation estimated using the CLM E data and the PCMDI/AR4 GCM ensemble, and the probability of the direction of change estimated by the GCM ensemble. The direction of change in CLM E is consistent with that in NCAR P (see Figure 1) except for relative large regional differences in Canada, eastern Siberia and South Asia where NCAR P shows negative change while CLM E shows positive change. The direction of change in evaporation estimated by GCM ensemble corresponds to that in GCM ensemble precipitation with relative large regional differences in northwestern United States where precipitation decreased while evaporation increased. Both the observation-based and GCM ensemble estimates show areas of increased evaporating grow. The change amplitude of the observation-based estimates is greater than that of the GCM ensemble as expected. Figure 3 shows the last half of the twentieth century change in runoff estimated using the observed R data, the CLM R data, and the PCMDI/AR4 GCM ensemble, and the probability of the direction of change estimated by the GCM ensemble. The number of the runs showing valid data is also shown. Some of the GCMs give invalid runoff (but not for precipitation and evaporation) output (e.g. negative runoff or constant value). The invalid values were removed from the ensemble. Most of the invalid values appear in hyper-arid area in Sahara, Middle East and Central Asia, and the Greenland. The Greenland was masked out in the runoff analysis later because the ice sheet runoff is not well presented in the models and the runoff observation is absent. The hyper-arid area with less valid runs was not masked out since the regions are of interest. The small number of the runs may decrease the reliability of the ensemble estimates over these regions. The observed R change was reconstructed from the CLM R data and streamflow observations. A scaling factor of each river basin was computed as the observed streamflow change divided by the CLM estimated change of the accumulated runoff over the corresponding drainage area. The scaling factor was extended to the surround grid if the grid was in a basin that was not covered by the streamflow observations. The observed R change was computed as the difference between the scaled runoff in 1980-99 (using the scaling factor times the CLM estimated runoff) and the CLM estimate runoff in 1950-69, divided by the 1950-69 value. Large regional difference between the observed R and the CLM R is found in Siberia where the observed R increased but the CLM R decreased. The change in CLM R shows a spatial pattern generally consistent with that in NCAR P, although amplified. The runoff change estimated by GCM ensemble coincides with the precipitation change estimated by GCM ensemble over most part of the land, while the region with decreased precipitation in western United Station and Europe expanded to a greater area with decreased runoff. Comparing with the observed R, the GCM ensemble R reproduces the positive changes in Siberia, eastern United States and Western Australia, and the negative changes in Northwestern and Southwestern United States, western Africa, and eastern Australia. The amplitude of the GCM ensemble change is much smaller than that of the observations. The GCM ensemble approach, which gives change in R (increase or decrease) less than 20% over most of the land girds, apparently underestimates the pattern amplitude of the change at regional scale. The amplitudes of the GCM ensemble changes in the hydrologic variables are smaller than those of the observation-based changes. The Q-Q plot of the logarithm of the observation-based change ratios versus GCM change ratios and the cumulative probabilities of the relative changes over the global land are shown in Fig. 4. Comparing the cumulative probabilities of the changes in the hydrologic variables (Fig. 4b, 4d, and 4f) among GCM ensembles or CLM estimates, it is shown that the dispersion from zero change is largest in R and smallest in E. One hypothesis is that both P and E increase (decrease), but the former increases (decreases) by a larger amount, introducing a large change in (P-E) which equals to R for a long period mean. The hypothesis was supported by previous studies (see Seager et al. 2007; Chou and Chen 2010). The Q-Q plots of the logarithm of the GHCN P change ratio versus GCM ensemble P change ratio and NCAR P change ratio follow linear lines, although that of the GCM ensemble change is flatter than that of the NCAR P change and the 1:1 line. This indicates the distribution of the logarithm of the GCM ensemble P change ratio can agree with that of observation after linearly transforming the values. And the distribution of the observed P change ratio is more dispersed than that of the GCM ensemble. With the assumption that the model simulation of internal variability is correct and each member of the M-member ensemble has the same distribution, the dispersion of the logarithmic ensemble change ratio, which is measured by the slope the linear regression, would be 1 M (i.e. 0.22 when M is 21) in the observations. The regression of slope of 0.17 shows the strict conditions in the above assumption do not hold. The empirical Q-Q relationship was used to scale the GCM ensemble distribution to the observation. The dispersion of the logarithmic NCAR P change ratio is slightly smaller than that of the GHCN observation. It is clear in Fig 4b which gives the cumulative probabilities of P relative changes. The GCM ensemble approach shows the P relative change at almost all the land girds is in the range of -10 to 10% while the GHCN observation shows P has decreases 10% at about 20% land grids and increases 10% at about 10% land girds. If the regression relationship was used to constrain the GCM ensemble estimates, the shifted and scaled probability distribution agrees fairly with the observations (Fig. 4b). The Q-Q plots of the logarithm of the GHCN P change ratio versus P change ratio predicted by individual GCM are often arced with outliers, indicating that the P change distribution of individual GCM is often more skewed than the observed distribution. Most of the individual GCM underestimate P change amplitude. Although the amplitude of the GCM ensemble change is even smaller than that of individual GCM, the probability plot correlation coefficient of GCM ensemble is higher than that of individual GCM. The distribution of GCM ensemble should agree better with the observed distribution than the distribution of individual GCM if both are scaled to fit the observation. Both GHCN and NCAR P observations show precipitation decreased over half of the land grids, but the large decrease area was not detected by the GCM ensemble. The Q-Q plot of the logarithm of the CLM E change ratio versus GCM ensemble E change ratio follows linear line. The Q-Q plot of the logarithmic CLM E change ratio versus logarithmic individual GCM E change ratio is often curved with outliers. It confirms that the GCM ensemble is more closely related to observation than individual GCM. Again, most of the individual GCM underestimate E change amplitude. Using the regression relationship between the GCM ensemble and the observation, the scaled probability distribution from GCM ensemble agrees well with the CLM estimate (Fig. 4d). Both the scaled GCM ensemble and CLM E show a slightly higher probability of increase in evaporation. The Q-Q plot of the logarithm of R change ratios (Fig. 4e) shows strongly nonlinear patterns for the distributions predicted by individual GCM, suggesting the R change from individual GCM does not appear to have a common distribution with the observation. Meanwhile the linearity of the GCM ensemble change ratio suggests a common distribution to the observed distribution if the quantiles are shifted and scaled. Figure 4f shows that the GCM ensemble R change is generally between -20 and 20% at global land girds while the observed R change is smaller than -20% at 20% land girds and greater than 20% at 15% land grids. Most of the individual GCM underestimate R change amplitude. The GCM ensemble has also significantly underestimated the amplitude of R change as expected. The dispersion of the CLM R change is smaller than that of the observation. It should be noted that the observed runoff has taken into account of direct human interruption of streamflow (such as irrigation water withdrawal and dam operation) while the models have not. Using the regression relationship between the GCM ensemble and the observation, the scaled probability distribution from GCM ensemble is closer to the observations than the unscaled one. The CLM R shows a higher probability of decrease in runoff (i.e. the potential area extent with decreasing runoff is larger than that with increasing runoff) but the observed R and the scaled GCM ensemble do not show the same change. Figure 5 shows the GCM ensemble and the scaled relative change in P between the first 20 yr and the last 20 yr of the first half of the twenty first century. Both the GCM ensemble and the scaled relative change show a pattern generally consistent with that of the probability of the direction of change. Comparing with the probability of the direction of change in the last half of the twentieth century (Fig. 1d), the direction of P change in the first half of the twenty first century tends to have higher probability to be positive in high latitudes, Far East, South Asia, and equatorial regions, and higher probability to be negative in southern Europe, Middle East, North and South Africa, Australia, eastern equatorial South America, and southwestern North America. The scaled pattern amplitude, which is much greater than that from the GCM ensemble, was constrained by the observation in the last half of the twentieth century. The scaled relative change should be a better guess of the GCM ensemble in the twenty first century. The results show that P increases more than 10% in the high latitudes of North America and Eurasia and decreases more than 10% in southern Europe, Middle East, southwestern North America, North and South Africa, and Australia. The (scaled) P change pattern amplitude in the first half of the twenty first century is larger than (scaled) that in the last half of the twentieth century (Fig. 5d), indicating more dramatic change in the hydrologic cycle is anticipated at regional scale. The area extent with increasing precipitation becomes larger because of the positive P change in high latitudes. Figure 6 shows the GCM ensemble and the scaled relative change in E between the first 20 yr and the last 20 yr of the first half of the twenty first century. The scaled relative change shows that E increases more than 10% in the high latitudes of North America and Eurasia and decreases more than 10% in the Middle East, North Africa, and southern Australia. The amplitude of E change in the first half of the twenty first century is larger than that in the last half of the twentieth century (Fig. 6d), showing more dramatic change is anticipated in E at regional scale. The spatial pattern of the relative change in E is generally consistent with that of the change in P although the pattern amplitude is smaller and the area with negative change shrinks. Figure 7 shows the GCM ensemble and the scaled relative change in R between the first 20 yr and the last 20 yr of the first half of the twenty first century. The scaled relative change shows that R increases more than 20% in the high latitudes of North America and Eurasia, South Asia, and the La Plata basin of South America and decreases more than 20% in southern Europe, Middle East, southwestern North America, North and South Africa, and Australia. The spatial pattern of the relative change in R corresponds with the spatial pattern of the change in P although the pattern amplitude in R is greater. The spatial pattern is generally consistent with the finding in Milly et al. (2005) while their study shows a wetter Australia and North Africa. The pattern amplitude of R change of Milly et al. (2005) is slightly greater than that of the GCM ensemble. The relative change in R in Milly et al. (2005) was calculated as the difference between period 2041-60 and 1900-70. The size of the ensemble (i.e. the number of the members, 20) in this study is larger than the size of the ensemble (12) in Milly et al. (2005). It is expected that the estimated amplitude from a larger member ensemble is smaller. The scaled pattern amplitude of R change, which was constrained by the observation in the last half of the twentieth century, is greater than that from the GCM ensemble and that in Milly et al. (2005). The scaled GCM ensemble approach shows R will change (increase or decrease) more than 20% at about half land grids and will change more than 50% at 14% land grids. It delineates a vision of future hydrologic cycle with more dramatic change at regional scale than we expected before. The scaled relative change in P, E and R between the first 20 yr and the last 20 yr of the twentieth and twenty first centuries are shown in Fig 8. For either the twentieth or twenty first century, the spatial patterns of the change in E and R are generally consistent with that in P because precipitation is the primary forcing variable of the land surface hydrology. The spatial patterns of the changes between the first 20 yr and the last 20 yr of in the twenty first century are similar with those in the first half of the twenty first century (Fig. 5, 6 and 7), but with large pattern amplitude. The pattern amplitude of change in E is the smallest and that in R is the greatest. Significant differences are found in the pattern amplitudes between the twentieth century and twenty first century. The large relative change (decrease or increase more than 10%) in P occurs at 43 and 70% land grids in the twentieth century and the twenty first century, respectively (Table 2). The relative change (decrease or increase) is greater than 10% at 17% land grids in the twentieth century, but at 58% land girds in the twenty first century. These indicate more dramatic regional change in hydrologic cycle is anticipated in the twenty first century. The portion of global land girds (i.e. potential area) with large decrease change in P slightly increases (by 2%) in the twenty first century, comparing with the portion in the twentieth century. Comparing with the twentieth century, the potential area with large increase change in P in the twenty first century enlarges by 30, 27, and 16% of land for an increase magnitude more than 10, 20, and 30%, respective. It indicates the climate is globally turning wetter but dry area may be drier at regional scale. It implies the area with high risk of both flooding and drought may increase in the twenty first century. The potential area with large decrease change in E is similar in the twentieth and twenty first centuries. However, the land area with large increase change in E is predicted to increase in the twenty first century. E will increase more than 10% over about half of the land area. The increase in E over large land area is likely due to surface warming. The land girds with large R relative change (decrease or increase more than 30%) in the twenty first century is about twice than that in the twentieth century. The potential area with deceasing R increases. The potential area with >30% decrease in R increases from 13% land area in the twentieth century to 18% land area in the twenty first century. The expansion of the area with decreasing R is likely caused by the expansion of the area with increasing E. Dai et al. (2004) found a subsequent expansion of global very dry area since 1970s based on the ground observations from 1870 to 2002. Our results suggest that expansion of dry area will continue in the twenty first century. The potential area with increasing R also increases. The potential area where R increases more than 30% increases from 13% land area in the twentieth century to 31% land area in the twenty first century. It indicates the global land areas in very wet condition will increase. Dai et al. (2004) showed that the global very wet land areas declined by 5% from the early 1980s to early 1990s. The GCM projection suggests the global very wet land area may expand in the twenty first century, reversing the trend in the late twentieth century. On the basis of this analysis, large hydroclimatic changes are anticipated to occur in the next couple of decades. The hydroclimatic changes would directly influence human society. Domestic and industrial water demand was determined by population and socioeconomic factor such as gross domestic product (GDP). The geography of contemporary population was obtained from the Gridded Population of the World, version 3 (GPWv3) data at 0.5° resolution (CIESIN 2005a). The global GDP distribution was gotten from the Global Gridded Gross Domestic Product for 1990 dataset at 0.5° resolution (CIESIN 2005b). Comparing with the twentieth century, the area with large (increase or decrease) change in R is anticipated to cover more people in the twenty first century (Table 2). About one quarter of global population are in the area with >30% change in R in the twentieth century. The portion will increase to near half if the geography distribution of population remains. It shows more people are heading to a wetter climate with large increase in R because the nations with large population size (i.e. China and India) are anticipated to receive more precipitation. Coinciding with the increase of population portion to a wetter climate, the population portion to a drier climate decreases. However, the population portion that will live in a much drier climate (with >30% decrease in R) does not change, indicating the globally wetter climate may not relieve drought at regional scale. The portion of global GDP at area with large change (increase or decrease) in R will increase, suggesting that more socioeconomic essential infrastructure will be exposed to the dramatic change. The portion of GDP at area with large increase in R increases because climate is becoming wetter over large portion of the land area. The portion of GDP at area with large decrease in R also increases. It is attributed to the anticipated drier conditions in the region with high GDP such as southern Europe, Middle East and southwestern North America. Figure 9 shows the spatial pattern of global aridity map. The climatic aridity index (AI) is defined as the ratio of annual precipitation to potential evapotranspiration (UNEP 1997). The aridity index data was obtained from the Global Aridity Index dataset (Trabucco and Zomer, 2009). The global land is classified into five zones of aridity: hyper-arid zone (AI < 0.03), arid zone (0.03<AI<0.2), semi-arid zone (0.2<AI<0.5), sub-humid zone (0.5<AI<0.65), and humid zone (AI>0.65). Comparing the spatial pattern of the changes in hydroclimatic variable (Fig. 8) with the global aridity map, it is found that most arid area (AI<0.2) tends to become drier and most humid area (AI>0.65) tends to be wetter in the twenty first century. A few arid and humid areas will change to a more moderate climate. These areas include Amazon and southern Europe where the humid condition is predicted to become drier and a line across southeastern Sahara, Middle East to Central Asia where the arid condition is predicted to become wetter (Fig. 9a). Intense drought in the Amazon was reported in 2005 and the causes and the implications of Amazonian drought for future climate change were widely discussed (Malhi et al. 2007; Marengo et al. 2008; Cox et al. 2008; Phillips et al. 2009). Figure 9a shows the risk of Amazonia drought increases in the twenty first century. The drying of Amazonia may be associated with a weakening of tropical circulation systems (Cook and Vizy 2008). Large part of the area with moderate climate condition (0.5<AI<0.65) is predicted to turn to dry or wet condition (Fig. 9b). The area where the climate is predicted to depart from moderate condition is larger than the area approaching moderate condition, indicating the marginal areas between arid and humid zones will shrink under climate change. On the base of this analysis, the semi-arid zone in cold area will shrink as the high latitude of North Hemisphere is moisturized. In arid and semi-arid regions, water is often a limiting factor for crop growth. The crop water requirement must be by irrigation if the precipitation in the growing season is inadequate for the plant’s needs. Irrigation is usually taken from the renewable water resources which can be estimated by R. The semi-arid regions in northern China, western India, Ethiopia, and north and central Argentina are becoming more humid (increase in R is more than 20%) and more favorable to crop growth. These regions are the important centers of food production and productive agricultural areas. This suggests climate change is expected to benefit the agriculture in the above developing nations. On the other hand, the semi-arid regions in the Great Plains area of the United States, northern Mexico, southern Europe, Turkey, Afghanistan, South Africa, and east coast of Australia will be adversely affected. These regions are susceptible to desertification, land degradation and drought. The drying climate is expected to make the agriculture and ecosystems more vulnerable in these regions. As a result of shrinking of the transition zone between arid and humid area, most non-polar desert will expand. The Sahara will extend to its north and southwest. The Syrian Desert and Arabian Desert will grow to the Black Sea. The Kalahari Desert (Africa) may expand to the India Ocean. The deserts in Australia are growing to the Pacific coast. The area of the Great Basin Desert, Sonoran Desert and Chihuahuan Desert will expand in the northeast to the Great Plains and in the south to the coastal plains of the northern Mexico. One exception is the Gobi Desert (Asia) which tends to diminish. The weakening of the tropical circulation may explain the imminent transition to a more arid climate in the subtropics (Vecchi et al 2006; Seager et al. 2007; Chou and Chen 2010). The location of the Gobi Desert is quite far north for a non-polar desert. It t is a continental interior desert which is separated from ocean moisture by topographic barriers and large distances (Broccoli and Manabe 1992). Atmospheric flow may transport more moisture into this region. Most of the cold semiarid area will become more moisturized, expanding the global humid area. The moistening is due to the apparently robust increase in high latitude precipitation (Allen and Ingram 2002; Zhang et al. 2007). The Asian monsoon regions such as North China and India become wetter. A possible explanation is the enhanced land-sea thermal contrast will intensify the Asian monsoon and the warmer sea surface will supply an enhanced moisture source to fuel stronger monsoon rainfall. The model studies that found increased monsoon rainfall relative to control simulations (Kitoh et al 1997; Douville et al 2000; Hu et al 2000; Meehl and Arblaster 2003) support this possibility. The areas with humid condition at high latitude tend to merge with the east coast humid area of the Eurasian continent, form two humid belts along the north and east coast of the North American and the Eurasian continents. The tropic humid belt may slightly shift to south in South America and to north in Eastern Africa. These changes indicate climate change is shaping the global pattern of arid and humid area. More concentrated arid or humid belts and narrower margin area between the belts are expected. 4. Discussion and Conclusions This study used the hydroclimatic observations in the late half of the twentieth century to constrain the ensemble predictions of the PCMDI/AR4 GCM models. Assuming GCMs are designed to reproduce the observed climate, the robust prediction in future climate should be as model independent as possible and be constrained by the only objective information. The ensemble median of the available GCMs provides a spatial pattern of the change which is less dependent to individual model but with smaller pattern amplitude than individual model and observations. A Q-Q plot was used to compare the observed and estimated probability distributions of the logarithm of the change ratios. The Q-Q relationships between the observations and GCM ensemble estimates were developed for P, E and R. Assuming the discrepancies in the spatial variance do not change, the relationships were used to scale the GCM ensemble estimates of the relative changes in the hydroclimatic variables in the twenty first century. The scaled estimate of the relative change has a spatial pattern corresponding to the probability of the change direction with pattern amplitude constrained by the observed climate and recent climate change. This approach used historical observations to constrain the GCM ensemble estimates and to provide the “best guess” of the future climate projection at regional scale. It differs from the Bayesian type of approach which is usually used to quantify the uncertainty in projections of regional climate change (Giorgi and Mearns 2002; Tebaldi et al. 2005). A basic assumption in the Bayesian type of approach is that the ability of a GCM to reproduce current mean climate (and future weighted ensemble mean) constitutes a measure of its reliability. However, this study assumes the ensemble median method gives the “best guess” of the spatial pattern although the pattern amplitude should be constrained using historical climate observations. The results show that the pattern amplitude of relative change in the twenty first century is larger than that in the twenty first century for P, E, and R, indicating more dramatic change in the hydrologic cycle is anticipated at regional scale in the next couple of decades. It is expected that both the land areas with wet condition and dry condition increase. More people (about one quarter of global population) are heading to a wetter climate with over 30% increase in R because the nations with large population size (i.e. China and India) are anticipated to receive more precipitation. However, the population portion that will live in a much drier climate does not decrease. The portion of global GDP at area with either large increase or large decrease in R becomes large, suggesting that climate change will increase existing risks of natural disasters such as flooding and drought. Globally, the GCM projection shows arid area becomes drier and humid area becomes wetter. The global large hot deserts will expand except for the Gobi Desert which tends to diminish. The areas with humid condition tend to merge together and form two humid belts along the northern and eastern coast of the North American and the Eurasian continents. These changes are shaping more concentrated arid or humid belts and narrower margin area between the belts. It suggests the mechanisms of atmospheric circulation that contribute to the dryness to arid area or wetness to humid area are generally strengthening. The change of the mechanisms may be different for different region. Most non-polar arid areas and the Amazonia become drier, likely because of the change of the tropical circulation systems. The Asian monsoon regions may become wetter because the intensified monsoon. It is expected the land warming faster than the ocean responding to increasing greenhouse gas concentrations in the atmosphere (Barnett et al. 2000; Brohan et al. 2006; Hansen et al. 2006). The enhanced land-sea thermal contrast may intensify monsoon and enhance atmospheric moisture convergence over land. The warmer sea surface might supply an enhanced moisture source to fuel continental interior. The change in the atmospheric moisture convergence might moisten the Gobi Desert and the northern high latitudes. One caveat should be noted in the results from the low resolution PCMDI/AR4 GCMs. High spatial resolution climate model may give results with important regional scale differences to low resolution GCMs, and sometimes reverse the direction of the change in hydroclimatic variables at regional scale (Duffy et al. 2003; Govindasamy et al. 2003; Ashfaq et al. 2009). Despite they may be challenged by fine scale climate process at regional scale, the PCMDI/AR4 GCMs can capture large scale climate feature and can be used to assess the relative impacts of climate change on different regions of the globe. Given that higher latitudes have warmed more than the lower latitudes in the past half century (Hansen and Lebedeff 1987; IPCC 2007), the temperature-related change, or “fingerprint”, in natural systems such as terrestrial organisms, climate and hydrology was thought to be generally in parallel with latitude (Myneni et al. 1997; Parmesan and Yohe, 2003; Root et al 2003; Reich and Oleksyn, 2004; Zhang et al. 2007; Deutsch et al. 2008). However, both model and observations showed large heterogeneity across latitude in the fingerprint of climate impacts on hydrologic cycle (see Dai and Trenberth; 2002; Nohara et al., 2006). Our results suggest that the fingerprint pattern of climate impacts on the hydrologic cycle is generally consistent with the distribution of climatic zones with drier arid area and wetter humid area. Besides local non-climatic influences, the fingerprint pattern of hydrology may complicate the latitudinal patterns of climate change impacts on the water-related natural or human systems. It is evident that the hydrologic fingerprint has potentially important effects on the global pattern of the biodiversity change (Bonebrake and Mastrandrea 2010), food supply (Rosenzweig and Parry 1994; Parry et al. 2004), and climate-related migration (Feng et al. 2010). Acknowledgements The work described in this paper was supported by **xxxx Projects**. We thank Dr Aiguo Dai of the National Center for Atmospheric Research (NCAR) for providing the global observed precipitation, and Community Land Model (CLM) simulated evaporation and runoff data. References Agarwal A, Singh RD (2004) Runoff modeling through back propagation artificial neural network with variable rainfall-runoff data. Water Resour Manage 18:285–300. doi:10.1023/B:WARM.0000043134.76163.b9 . Allen, M. R. and S. F. B. Tett. 1999. 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Model Modeling center T P E R BCCR BCM2 Bjerknes Center for Climate Research v v v v Canadian Centre for Climate Modelling and CCCMA CGCM3.1 Analysis v v v v CCCMA CGCM3.1 Canadian Centre for Climate Modelling and T63 Analysis v v v v CNRM CM3 Center National de Recherches Meteorologiques v v v v Commonwealth Scientific and Industrial Research CSIRO MK3.0 Organisation (CSIRO) Atmospheric Research v v v v Commonwealth Scientific and Industrial Research CSIRO MK3.5 Organisation (CSIRO) Atmospheric Research v v v v GFDL CM2.0 Geophysical Fluid Dynamics Laboratory v v v v GFDL CM2.1 Geophysical Fluid Dynamics Laboratory v v v GISS AOM Goddard Institute for Space Studies v v v v GISS EH Goddard Institute for Space Studies v v v v GISS ER Goddard Institute for Space Studies v v v IAP FGOALS1 Institute for Atmospheric Physics v v v v INGV ECHAM4 Istituto Nazionale di Geofisica e Vulcanologia v v v INM CM3 Institute for Numerical Mathematics v v v v IPSL CM4 Institut Pierre Simon Laplace v v v MIROC(hires) Center for Climate System Research v v v v MIROC(medres) Center for Climate System Research v v v MIUB ECHO Meteorological Institute University of Bonn v v v v MPI ECHAM5 Max Planck Institute for Meteorology v v v v MRI CGCM2 Meteorological Research Institute v v v v NCAR CCSM3 National Center for Atmospheric Research v v v v UKMO HadCM3 Met Office’s Hadley Centre for Climate Prediction v v v v Table 2. Statistics of the scaled relative change in precipitation (P), evaporation (E) and runoff (R) for the twentieth and twenty first centuries (see Fig. 8). The area (percentage of global land grids) where the relative change (decrease or increase), decrease, and increase change magnitudes in P, E, and R are greater than 10, 20, and 30% are given. The percentage of global population (Pop) and gross domestic product (GDP) in the area where the relative change, decrease, and increase change magnitudes in R are greater than 10, 20, and 30% are given. Area (%) in P Area (%) in E Area (%) in R Pop (%) in R GDP (%) in R Century 20th 21st 20th 21st 20th 21st 20th 21st 20th 21st Change >10% 43 70 17 58 70 83 70 83 64 77 Change >20% 15 43 7 20 44 65 44 62 41 51 Change >30% 6 24 2 6 27 50 24 45 24 32 Decrease >10% 24 22 11 11 29 31 40 28 33 38 Decrease >20% 11 13 5 6 20 24 27 21 23 28 Decrease >30% 5 7 1 3 13 18 15 15 15 19 Increase >10% 19 48 7 46 41 51 29 55 31 39 Increase >20% 4 31 2 15 24 41 17 41 18 22 Increase >30% 1 17 1 3 13 31 9 30 10 13 Figure 1. Relative change in precipitation (P) between the first 20 yr and the last 20 yr of the last half of the twentieth century estimated using the GHCN P data (a), the NCAR P data (b) and the ensemble median of the PCMDI/AR4 GCM outputs (c), and the probability of the direction of change (Pp – Pn) (d). Figure 2. Relative change in evaporation (E) between the first 20 yr and the last 20 yr of the last half of the twentieth century estimated using the CLM E data (a) and the ensemble median of the PCMDI/AR4 GCM outputs (b), and the probability of the direction of change (Pp – Pn) (c). Figure 3. Relative change in runoff (R) between the first 20 yr and the last 20 yr of the last half of the twentieth century estimated using the observed R data (a), the CLM R data (b) and the ensemble median of the PCMDI/AR4 GCM outputs (c), the probability of the direction of change (Pp – Pn) (d), and the number of runs showing valid value (e). Figure 4. Q-Q plot of the logarithm of GHCN P change ratio versus that of GCM ensemble P change ratio, P change ratio predicted by individual GCM, and NCAR P change ratio (a), and cumulative probabilities of the P relative changes (b) over the global land (masked by the GHCN P coverage, see Figure 1a). Q-Q plot of the logarithm of CLM E change ratio versus that of GCM ensemble E change ratio, and E change ratio predicted by individual GCM (c), and cumulative probabilities of the E relative changes (d) over the global land. Q-Q plot of the logarithm of the observed R change ratio versus that of GCM ensemble R change ratio, R change ratio predicted by individual GCM and CLM R change ratio (c), and cumulative probabilities of the R relative changes (d) over the global land (excluding the Greenland). The change ratio is the proportionate rate and the change is the relative change (percentage) between the first 20 yr and the last 20 yr of the last half of the twentieth century. The twentieth quantiles of changes (the circles), the linear regressions of the twentieth quantiles of the GCM ensemble and CLM change ratios and the linear regression parameters (slope, intercept and correlation coefficient) are shown in the left panels. The relative changes which are shifted and scaled using the regression relationships are compared to the observed changes in the right panel. Figure 5. Relative change in P between the first 20 yr and the last 20 yr of the first half of the twenty first century estimated using the GCM ensemble (a) and the scaled GCM ensemble (c), and the probability of the direction of change (Pp – Pn) (b), and cumulative probabilities of the GCM ensemble and scaled P relative changes (d) over the global land. The cumulative probabilities of the GCM ensemble (P_20c) and scaled P (P_20c_scaled) relative changes between the first 20 yr and the last 20 yr of the last half of the twentieth century and the GCM ensemble (P_21c) and scaled P (P_21c_scaled) relative changes between the first 20 yr and the last 20 yr of the last half of the twenty first century are shown in Fig. 5d. Figure 6. Relative change in E between the first 20 yr and the last 20 yr of the first half of the twenty first century estimated using the GCM ensemble (a) and the scaled GCM ensemble (c), and the probability of the direction of change (Pp – Pn) (b), and cumulative probabilities of the GCM ensemble and scaled E relative changes (d) over the global land. The cumulative probabilities of the GCM ensemble (E_20c) and scaled E (E_20c_scaled) relative changes between the first 20 yr and the last 20 yr of the last half of the twentieth century and the GCM ensemble (E_21c) and scaled E (E_21c_scaled) relative changes between the first 20 yr and the last 20 yr of the last half of the twenty first century are shown in Fig. 6d. Figure 7. Relative change in R between the first 20 yr and the last 20 yr of the first half of the twenty first century estimated using the GCM ensemble (a) and the scaled GCM ensemble (c), and the probability of the direction of change (Pp – Pn) (b), and cumulative probabilities of the GCM ensemble and scaled R relative changes (d) over the global land. The cumulative probabilities of the GCM ensemble (R_20c) and scaled R (R_20c_scaled) relative changes between the first 20 yr and the last 20 yr of the last half of the twentieth century and the GCM ensemble (R_21c) and scaled R (R_21c_scaled) relative changes between the first 20 yr and the last 20 yr of the last half of the twenty first century are shown in Fig. 7d. Figure 8. Scaled relative change in P between the first 20 yr and the last 20 yr of the twentieth century (a) and the twenty first century (b); scaled relative change in E between the first 20 yr and the last 20 yr of the twentieth century (c) and the twenty first century (d); and scaled relative change in R between the first 20 yr and the last 20 yr of the twentieth century (e) and the twenty first century (f). Figure 9. Arid (AI < 0.2) or humid area (AI > 0.65) where the climate tends to become moderate in the twenty first century (a). The black arrow shows the arid area where R is predicted to increase more than 20% and the red arrow shows the humid area where R is predicted to decrease more than 20%. Area with moderate climate (0.2 < AI < 0.65) where the climate tends to become dry or wet in the twenty first century (b). The black and red arrows show the moderate area (0.2 < AI < 0.65) where R is predicted to increase or decrease more than 20%, respectively.