The ability of a GCM-forced hydrological model to reproduce global discharge variability

The ability of a GCM-forced hydrological model to reproduce global discharge variability F. C. Sperna Weiland, L. P. H. van Beek, J. C. J. Kwadijk, and M. F. P. Bierkens Department of Physical Geography, Utrecht University, P.O. Box 80115, 3508 TC, Utrecht, The Netherlands Deltares, P.O. Box 177, 2600 MH, Delft, The Netherlands Deltares, P.O. Box 80015, 3508 TA, Utrecht, The Netherlands Received: 19 January 2010 – Accepted: 19 January 2010 – Published: 29 January 2010 Correspondence to: F. C. Sperna Weiland (frederiek.sperna@deltares.nl) Published by Copernicus Publications on behalf of the European Geosciences Union.


Introduction
Because runoff regimes might change significantly as a result of climate change, strategies for water management are sought for that either mitigate the undesired effects of a changing climate or gain from the positive effects.The search for these strategies relies on reliable assessment of the effect of climate change on river discharge.Consequently much research has been conducted, investigating the hydrological response to climate change, both on local (Christensen and Lettenmaier, 2007;Prudhomme and Davies, 2008;Buytaert et al., 2009), regional (Lehner et al., 2006;Strzepek and Yates, 1997;Hagemann et al., 2009) and global scale (Arnell, 1999(Arnell, , 2003;;Alcamo et al., 2000;Alcamo and Henrichs, 2002;Milly, 2006).Climate datasets from General Introduction

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Full Circulation Models (GCM) are often used as input for hydrological models to investigate the possible change.Unfortunately, different GCM model results can produce quite varying and even contradictory results (Varis et al., 2004) and the modelled past climate does not always agree with the observed one.Deviations are especially apparent for precipitation, when evaluating historical predictions against observations (Covey et al., 2003;Perkins and Pitman, 2009).Climate models tend to simulate too many days with light rain, at the same time they underestimate the frequency and amount of heavy rain events (Dai, 2006).Many studies concluded that a multi-model ensemble of GCM's should be used to obtain a reliable impression of the spread of possible regional changes and their accompanying uncertainties (Murphy et al., 2004;Boorman and Sefton, 1997;IPCC, 2007).Furthermore it has been widely recognized (Wood et al., 2004;Leander and Buishand, 2007;Fowler and Kilsby, 2007;Wilby et al., 1998) that precipitation data needs to be bias-corrected before it can be used.
In this study we force a single global scale hydrological model with results of the 20 century control experiment from an ensemble of 12 GCMs for which complete climate datasets with a daily time-step are provided by the IPCC-PCMDI data portal.We compare discharges calculated from the GCM data with observed discharges, as well as with discharges calculated from the CRU TS2.1 time-series (New et al., 2000) downscaled by ERA-40 (Uppala et al., 2005).Contrary to previous studies (Milly et al., 2006;Nohara et al., 2006) we do not focus on the correct reproduction of mean discharge or river regimes, but on the ability of a GCM-forced hydrological model to reproduce global discharge variability (extremes, seasonal variation and inter-annual correlation), parameters that are of importance to water management.We realize that a correct reproduction of current discharge variability is no guarantee that projected discharge variability is correct as well (Prudhomme and Davies, 2008).However we want to investigate the influence of deviating GCM variability on the resulting hydrological variability.And an incorrect projection of current discharge variability is likely to preclude accurate projections, which makes the comparison useful.Introduction

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We restrict ourselves to a bias-correction of monthly averages of GCM precipitation, temperature and derived potential evaporation, where monthly scaling factors are calculated from the difference in long term monthly mean between CRU and GCM quantities.Although a correction on monthly means does not guarantee that rainfall marginal distributions are well reproduced (Dai, 2006), no additional correction on GCM variability is applied for two reasons: First, several climate change experiments have shown that GCM variability will change, especially for precipitation, where frequency and storm duration is likely to decrease and intensity will increase resulting in heavier rain events (Trenberth et al., 2003;Allan and Soden, 2008;Meehl et al., 2000).Corrections based on past deviations between modelled and observed variability, although often applied (Leaner and Buishand, 2007;Ines and Hansen, 2006;Wood et al., 2004), may therefore not hold in future.Applying variability corrections might mask important changes, since changes in rainfall distributions may have a much larger effect on the hydrological cycle than changes in mean precipitation (Allen and Ingram, 2002).Second, as discussed before, the very goal of this study is to examine the effect of GCM variability on modeled hydrological variability, i.e. assessing the ability of GCMforced hydrological models to reproduce extremes and intra-and inter-year variability in discharge, thereby assessing the usability of these data for water management related climate effect studies.Replacing the differences in variability between GCMs to a single current observed variability (i.e.CRU) would rule out such an analysis.

Methods
The distributed global hydrological model PCR-GLOBWB (van Beek and Bierkens, 2009;Bierkens and van Beek, 2009) is run on a daily time-step with bias-corrected meteorological time series from 12 GCMs for the period 1961-1990.To evaluate the quality of the hydrological model on reproducing observed discharge when using biascorrected GCM data as input, resulting runoff regimes are compared with observed regimes.Furthermore calculated maps for the ensemble mean thirty year average, Introduction

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Q 10 , Q 90 , timing of peak discharge, inter-annual variability and lag-1 correlation are compared with maps derived from a run based on a reference meteo data set, created from ERA-40 (Uppala et al., 2005) and CRU (New et al., 2000) data.

Existing global hydrological models
Obviously, the macro-scale hydrological model (MHM) PCR-GLOBWB follows in a long line of existing MHMs.Without attempting to be complete, we refer to short reviews given by Arnell (1999) andD öll (2003) describing VIC (Nijssen, 2001), Macro-PDM (Arnell, 1999), WBM (V ör ösmarty, 1998) and WGHM (D öll, 2003), four models frequently used in large-scale hydrological studies.Similar to PCR-GLOBWB, the last three models calculate for each time-step the water balance of all individual grid cells.The grids of WBM and WGHM have a resolution of 0.5 • , corresponding to the finest resolution of most climate datasets available, within Macro-PDM grid cells can either be regular or catchment shaped.All three models contain at least one soil water layer and total runoff consists of a fast overland and a slow groundwater component.Size and partitioning of these fluxes depend on the degree of saturation of the soil water layer(s) that is calculated either physically based or described by a statistical relation.The models all apply some form of routing to obtain realistic river discharge.WGHM (D öll, 2003) is the sub model of the global water use and availability model WaterGAP (Alcamo, 2003).
Besides by stand-alone hydrological models, global water balances have also been modelled by coupled vegetation water balance models by land surface schemes (LSS) used in global climate models.Examples of global coupled vegetation water balance models are GEPIC (Liu et al., 2009) and LPJ (Gerten et al., 2004).GEPIC focuses on the calculation of crop yield and crop water productivity.a global dynamic vegetation model that describes the interaction between the terrestrial biosphere and the water cycle.Runoff is one of the outputs of this vegetation model and exists of excess over field capacity from the upper two soil layers and percolation from the second soil layer.However, no lateral flow between cells or river routing is applied.At this stage the global water balance and basin runoff is represented less reliable by most LSSs than by hydrological models (Gerten at al., 2004) and the resolution is too coarse for hydrological studies.A notable exception is global VIC (Nijssen et al., 2001).VIC is designed to be a land surface scheme for climate models and solves both the energy and the water balance.At the global scale it currently has a resolution of 1 • (Sheffield et al., 2009), where vegetation, soil moisture and the application of precipitation are modelled using sub-grid variability schemes.Runoff, existing of baseflow from the lower soil moisture store and fast response flow, is routed along a routing network using a convolution approach.VIC is one of the few LSSs that is frequently used in stand-alone hydrological studies.
The main focus of this study is the reproduction of variability in river regimes.Therefore the hydrological model used should be designed to calculate this variable, including a good representation of hydrology.In addition to the models described above the model used in this study, PCR-GLOBWB, contains an advanced scheme for the subgrid parameterization of surface runoff, interflow and baseflow and an explicit routing scheme for surface water flow using the kinematic wave approximation that includes retention and evaporation loss from wetlands, lakes and reservoir (van Beek and Bierkens, 2009).

PCR-GLOBWB
PCR-GLOBWB is a global distributed hydrological model with a resolution of 0.5 • (van Beek and Bierkens, 2009;Bierkens and van Beek, 2009).Each model cell consists of two vertical soil layers and one underlying groundwater reservoir.Sub-grid parameterization is used to represent short and tall vegetation, surface water and for calculation of saturated areas for surface runoff as well as interflow.Water enters the cell as rainfall Introduction

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Full and can be stored as canopy interception or snow.Snow melt or accumulation occurs depending on temperature.Melt water and throughfall are passed to the surface.
Evapotranspiration is calculated from the potential evaporation and soil moisture conditions.Exchange of water is possible between the soil and groundwater layers in both downward and upward direction depending on soil moisture status and groundwater storage.Total runoff consists of non-infiltrating melt water, saturation excess surface runoff, interflow and base flow.For each time-step the water balance is computed per cell.Runoff is accumulated and transferred as river discharge along the drainage network using kinematic wave routing.The drainage network is taken from DDM30 (D öll and Lehner, 2002) which includes lakes, wetlands and large reservoirs.Information on model performance is given in Appendix A.

GCM data
In 1997 the IPCC developed a set of emission scenarios, representing possible future climate change and provided boundary conditions to be used in GCM runs.These scenarios are widely used in climate impact studies.Besides boundary conditions for studies based on these scenarios, the IPCC also provided boundary conditions for a 20th century control experiment.Climate modelling centers around the world conducted GCM runs with this data.The Program for Climate Model Diagnosis and Intercomparison (PCMDI) has collected the results and made these available through the PCMDI data portal (https://esg.llnl.gov:8443/index.jsp).The PCMDI provides results on a daily time-step, while the IPCC data portal only provides derived monthly averages.Although it has been said that daily values are less reliable (Prudhomme et al., 2002), we prefer to use daily data, since it provides more information on extremes and climate variability.We collected data from the GCMs for which complete model datasets are provided on a daily time step for both the 20C3M control experiment  and the future scenario A2, which we will analyze in future research.For those models where multiple ensemble runs were available the first run was selected.Although the data portal does Introduction

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Full not provide all required parameters for the Hadley centre climate models, HADGEM1 has been included for we are interested in its performance.HADGEM1 data has been retrieved from the CERA-gateway, http://cera-www.dkrz.de.Table 1 gives an overview of the selected models.

Derivation of potential evaporation
Both temperature and precipitation are directly available at the data portal for all selected climate models.Evaporation had to be derived from other variables, using the Penman-Monteith equation (Monteith, 1965).For those models where the required surface pressure fields were not directly available, surface pressure is derived from the pressure at sea level using a global DEM.Air humidity fields, required to calculate the actual vapor pressure, could not be retrieved from the data portal for the complete period for some of the GCMs.Therefore we used a simplified method to calculate the actual vapor pressure from the minimum air temperature (Allen et al., 1998).For arid regions the assumption that the air is saturated when the temperature is at its minimum might not hold and therefore the minimum temperature will not equal the dew temperature.As suggested by Allen (1998) we subtracted 2 • from the minimum temperature in the arid regions.Arid regions have been selected using the climate moisture indices of the WWDRII (UN, 2006).For those models where time-series for other required parameters were missing or incomplete we used the Blaney-Criddle equation (Brouwer and Heibloem, 1986;Oudin et al., 2005) instead of Penman-Monteith.We realize this may have introduced additional noise between the model results (Kay and Davies, 2008).Potential evaporation calculated with the Blaney-Criddle equation is too high for Europe, North-America and the north of Asia during summer and too low for Africa and Asia.Especially the first difference can result in deviations because, particularly at the beginning of summer, evaporation will not be limited by water availability and actual evaporation will be too high as well.However, hydrological model studies are forced to use what has been reported on by the GCMs host institutes and evaporation is not provided for most of the models.Introduction

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Bias correction and downscaling
Rainfall time-series from GCMs are often biased in monthly amounts, frequency and intensity.For other parameters deviations from observed quantities are present as well.Furthermore the resolution of GCMs is relatively course compared to the desired resolution for hydrological modelling.Therefore previous studies concluded that some kind of bias-correction and downscaling is needed before the data can be used in climate impact studies (Wilby et al., 1998;Ines and Hansen, 2006;Wood et al., 2004).
We calculated discharge time-series from the uncorrected GCM meteo data and concluded that deviations between modelled and observed discharges were that large that for our datasets bias-correction was necessary as well.A bias-correction was applied to monthly averages of GCM precipitation, temperature and derived potential evaporation.Adjustment of temporal distributions of time-series has been avoided where possible, in order to keep the GCM variability unchanged.Monthly scaling factors are calculated from the difference (temperature) or ratio (precipitation and evaporation) in long term monthly mean between CRU and GCM quantities.Applying these correction factors also implies downscaling of the GCM data to CRU resolution.For temperature an additive correction was used: Where T is the daily temperature and T is the 30 year average monthly temperature.For evaporation a multiplicative correction is used, to avoid the occurrence of negative evaporation.
For precipitation a similar multiplicative correction is used as in Eq. ( 2).For some regions (North-Africa, Amazone and Himalaya) differences between GCM and CRU Introduction

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Full monthly rainfall amount and number of wet days can be very large.A simple multiplicative correction in these cases resulted in unrealistic rainfall peaks in the bias-corrected rainfall time-series.Time-series obtained with additive monthly correction contained negative rainfall values.Therefore the bias-correction of precipitation is extended with a minimum daily precipitation amount that has to be exceeded by the GCM precipitation before the multiplicative correction can be used (van Beek, 2008).The threshold equals the mean daily CRU rainfall amount: With W CRU the 30 year average number of wet days for the specific month.When the precipitation threshold is not exceeded, the days with precipitation occurrence are calculated from a temperature limit below which a day becomes wet.
Where T min and T max are the minimum and maximum temperature (Kelvin) of the given month and N is the total number of days in the specific month.With this formula the number of wet GCM days per month is calculated (W GCM ) and the rainfall amount for these days equals: With this equation, rainfall is equally distributed over the wet days and the original temporal distribution of the GCM rainfall time-series is lost.However, this correction method is only applied for those months where relative differences between CRU and GCM time-series were that large that applying simple scaling factors resulted in larger deviations in discharge time-series.

Meteorological data
PCR-GLOBWB was run for the period 1961-1990 with a reference meteorological dataset to create reference modelled discharge maps and time-series for comparison with discharges calculated form GCM data.This dataset was created from the ERA-40 re-analysis dataset from the ECMWF (Uppala et al., 2005), the CRU TS 2.1 monthly time-series (New et al., 2000) and the CRU CLIM 1.0 climatology (New et al., 2002) according to the same method as described above for the GCM data (van Beek, 2008).The ERA-40 dataset is a representation of the weather system on a daily timestep, but precipitation is poorly approximated, particularly in the tropics (Troccoli and K ålberg, 2004).Therefore, we preferred the CRU monthly quantities, which are interpolated from observed meteorological time-series.The hydrological model run based on this reference meteorological dataset will be referred to as reference run.

Hydrological data
We selected 19 large catchments (Fig. 1) to be included in this study, which cover a variety of climate zones, latitudes and continents.For most of these catchments average monthly discharges are available from the Global Runoff Data Centre (GRDC, 2007).For the remaining catchments data from the Global River Discharge Database were used (V ör ösmarty et al., 1998).

Statistics
For all models we calculated the thirty year average modelled and the thirty year average observed mean discharge, 10 (low flow) and 90 (high flow) percentile values for each catchment (see Table 2).From thirty year average quantities of the individual Introduction

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Full Screen / Esc Printer-friendly Version Interactive Discussion models we calculated the ensemble mean.To compare the temporal behavior of the GCM based model runs with the reference model run and the observations, we calculated the inter-annual discharge variability for the 30 year annual average discharges, the auto-correlation for a time-lag of one year and the yearly timing of the discharge peak occurrence.Inter-annual variability is of importance when GCMs are used to derive extreme value distributions.Reproduction of the lag-one autocorrelation is important for analyzing multi-year droughts related to persistent weather anomalies, for example those related to ENSO.

Map comparison
PCR-GLOBWB calculates daily maps with accumulative routed discharge per cell.For all statistical variables we calculated the GCM ensemble mean values and compared those with the statistics calculated from the results of the reference run.The performance is quantified by the relative difference between, respectively the yearly average mean discharge, the Q 90 , Q 10 and the inter-annual variability.For these variables we used relative values, because our main interest was to assess whether the GCM derived discharge statistics are relatively high or low compared to the calculated reference.For the yearly average month of peak occurrence we calculated absolute differences, revealing whether and where the timing of the peak discharge is in accordance with the results of the reference run.
Where Q REF and Q GCM are, respectively the thirty year average discharge statistics derived from the reference run and the thirty year average statistics derived from the ensemble hydrological runs based on the different GCMs.Furthermore we tested the significance of the calculated lag-1 correlation with a t-test for a significance level of 90%: Where r is the calculated lag-correlation coefficient and n is the number of lagged pairs that can be formed.To visualize the ensemble results, for each individual cell the number of models, for which significant correlation was calculated, was displayed on a map.
To reveal the areas where the spread between the 12 models is largest, we calculated maps with the standard deviation of the ensemble of 12 GCM derived fields for the Q 90 , Q 10 , Q mean , Q peak and IAV according to: Where i corresponds to the model number, M is the total number of models ( 12), Q can be Q mean , Q 90 , Q 10 , Q peak , IAV or Cor-lag1 and Q is the ensemble mean value of the 12 GCMs for the given parameter.

Hydrological regimes
For all catchments hydrological regimes have been calculated for: 1) simulated discharges for each individual bias-corrected GCM dataset, 2) the ensemble mean of the discharges calculated by these individual GCMs and 3) the reference run (see Fig. 2).Introduction

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The calculated regimes are compared with the observed regimes derived from the GRDC time-series.Overall the simple monthly bias-correction reduces the differences between the reference run and the GCM based runs and it also reduces the spread between the modelled discharge for the ensemble of GCMs.For rivers with a strong seasonal pattern, for example the Monsoon driven rivers Brahmaputra, Ganges and Mekong, the resemblance of the GCM runs is large.Also for both the Lena and the MacKenzie, which have a snowmelt driven discharge peak that rises as temperature increases in spring, differences are small for most GCMs, with the exception of two models (IPSL-CM4 and HADGEM1) where discharge is relatively constant throughout the year, indicating that temperatures in the GCMs are too high for too many days in the colder half of the year.For other catchments, that are influenced by both rainfall and snowmelt like the Rhine and the Danube, differences in regime pattern remain.For basins in the more arid regions of the world, such as the Murray, Zambezi, Niger and Orange River, the ensemble mean discharge is lower than the mean discharge calculated by the reference run for most of the year.This is a result of the bias-correction method.For months with too little rain in the GCM dataset, the CRU rain quantities are divided over the number of days that have temperatures below the calculated temperature threshold.Resulting in a larger number of rain days with relatively small equal rain quantities.From such a rainfall distribution more water can evaporate than from a more realistic distribution with rainfall peaks.One of the GCMs (IPSL-CM4) shows exceptional behavior.Deviations in regime are apparent for the Parana, Yellow river, Yangtze, Brahmaputra, Volga, Lena, MacKenzie and present for almost all rivers for this GCM.
From the regime plots it can be seen that there are also differences between observed discharge and discharge results of the reference run.For example for the MacKenzie and Lena, calculated discharges are too low due to snow undercatch problems (Fiedler and D öll, 2007).Discharges for the more arid basins in Africa and Australia are overall too high.In the calculated regime of the Indus the snow and glacier melt driven discharge occurs too early in spring, while the Monsoon influenced Introduction

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Interactive Discussion discharge peak is relatively small, as the melt water peak that in reality more or less coincides with the Monsoon maximum, has already occurred.Besides by model deficiencies these differences are caused by errors in the observed discharges and in the CRU dataset, which is known to be inaccurate for parts of Africa and suffers from undercatch in snow dominated areas.By using the CRU dataset as reference for the bias-correction, the deviations present in the CRU set are introduced in the corrected GCM data as well.

Catchment statistics
Discharge statistics of the hydrological model runs are given in Table 3.For most rivers, discharge calculated from the ensemble of GCM results is lower than discharge calculated with the reference run.This originates from the fact that GCMs in general have more days with rain (Dai, 2006;Ines and Hansen, 2006) and therefore daily rainfall amounts will be lower than in the bias-corrected ERA-40 dataset.With this GCM rainfall distribution a larger part of rainfall can evaporate or infiltrate.Relative differences in Q mean , Q 90 and Q 10 for the reference and the ensemble mean derived discharge for the individual rivers range between −57 and +31% (leaving out the extreme outliers of 100% for the driest rivers).However 47% of the GCM derived values (Q 90 , Q 10 and Q mean statistics for 19 catchments) deviate less than 10%.Ensemble standard deviations for the Q mean , Q 90 and Q 10 are comparable in size.
For the Lena, MacKenzie and Volga, GCM derived mean discharge is higher than the reference mean discharge.For these three rivers there are two GCMs with deviating regime curves.These GCMs also cause the Q 90 to be too high for the Volga and MacKenzie.This illustrates that a few deviating GCMs can bias the discharge statistics derived from the multi-model ensemble.The ensemble mean Q 10 values exceed the reference value for half of the catchments.GCM calculated Q 10 values are relatively high, because the GCMs have a lower inter-annual variability and prolonged droughts occur less often.Introduction

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Inter-annual variability is smaller for almost all catchments in the ensemble GCM results than in the results of the reference run (up to 10 times).The MacKenzie is the only exception, but the ensemble standard deviation, and thus the uncertainty, is relatively large for this basin.Furthermore the MacKenzie is one of the few rivers for which GCM derived discharge is higher than discharge from the reference run and for which several regime curves show large deviations.
The lag-1 correlation coefficients calculated from the ensemble of GCMs show large deviations from the coefficients derived from the reference run.There is no clear trend in differences being positive or negative.Uncertainty between GCMs is large, the ensemble standard deviation of the lag-1 correlation exceeds the ensemble mean for more than half of the catchments.The reference run correlation coefficients also deviate from correlation coefficients derived from the GRDC data.In general GRDC values are higher.This is most likely due to regulation and presence of reservoirs in some of the large rivers.

Mean, 10th and 90th percentile discharge
Because the bias-corrections are based on thirty year average monthly precipitation and evaporation quantities, it can be expected that thirty year average mean annual accumulated discharges, derived from the ensemble of GCM based hydrological model run, are comparable to results of the reference run.However from Fig. 3 it can be seen that this does not hold for the entire globe.The Middle-East, Southern Africa and Australia are drier in the results of the GCM ensemble.This is caused by the equal division of rain over potential rain days, applied when GCM time-series contain not enough rain in a month.Overall GCM derived discharges are higher for the Northern Hemisphere and lower for the Southern Hemisphere.The maps with the standard deviation of the results of the ensemble of GCMs show that the spread between GCMs is largest for regions with high discharge.This is particularly the case in large rivers where biases are Introduction

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Full Screen / Esc Printer-friendly Version Interactive Discussion accumulated over the entire basin, resulting in large discharge deviations in the main rivers.The GCM based runs also show large deviations for Greenland, caused by both extreme biases and high correction factors for precipitation and evaporation and hydrological model deficiencies.Because of the limited information content of discharge changes in Greenland, this region has been excluded.
By correcting only monthly mean quantities, the daily rainfall distribution of the original GCM datasets remains practically unchanged.Herewith, the occurrence of extreme discharges should be less influenced than the average discharge.Figures 4 and  5 show maps of the Q 10 and Q 90 discharge values.Again differences are largest for Australia, North and South Africa and the Middle-East.The Q 10 for the ensemble of GCMs is higher for large parts of the world, except for arid and Monsoon influenced regions.The Q 90 is relatively high for the Amazone basin, Indonesia, India and parts of the Northern regions and too low for the same regions, but more extended, as for the Q 10 values.Relative difference between the GCM based runs and the reference run are smaller for Q 90 values than for Q 10 values.Apparently the variability is smaller in (corrected) GCM datasets, resulting in less extreme values for Q 10 and Q 90 .This shows that a simple bias-correction leaves part of the GCM behavior, the behavior that influences extremes, unchanged.This is an argument for correcting the total cumulative distributions of daily discharge or precipitation.However, there is no guarantee that such corrections may hold for a future climate.

Timing of discharge peak
The calculated global pattern of timing of peak occurrence of monthly mean discharge (Fig. 6) is comparable for the reference run and the ensemble of GCMs.Although in the GCM results discharge peaks occur more often in January.For the southern drier regions, this can be explained by the difficulty of distinguishing the month with highest discharge when there is little variation in discharge.For Western Europe and North-America peak discharges occur to early in the GCMs.Differences between GCMs are largest in northern and in drier regions.Introduction

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Inter-annual variability and persistence
Figure 7 shows that for most of the world the GCM derived inter-annual discharge variability is smaller than the inter-annual variability derived from the reference run.This difference is also present in discharges calculated from non-bias corrected GCM data, but is amplified in the runs using bias-corrected data.A lower inter-annual variability implies more resemblance between years and less extremes.This indicates that GCMs have difficulties in reproducing very dry and very wet years, possibly underestimating the frequency of floods and droughts.
To measure multi-year persistence, the lag-1 correlation is calculated.The variation between GCMs is large for the lag-1 correlation, especially in the more humid regions on the Northern Hemisphere.Overall positive correlation coefficients, ranging between 0.2 and 0.8, were found for both the reference run and the results of the ensemble of GCMs. Figure 8 shows maps with the significance of the calculated correlation for a significance level of 90%.For the reference run, regions with significant lag-1 correlation are indicated in black.When a significant correlation is present, predictability of next years hydrological conditions based on the current hydrological conditions is large.For regions where this is the case a same predictability, or correlation, should also be present in the GCMs.We stress however that the value of ERA-40 as a benchmark for correlation coefficients of individual rivers was found to be limited (see Table 4), probably because most large rivers are regulated, so that their results should be interpret with care.
For the ensemble of GCMs we calculated for each cell the number of models with significant correlation.Lag-1 correlation is significant in the Mississippi basin, Northern Europe and parts of Africa and Australia for both the reference runs and most of the GCMs.In the reference run significant correlation is also found for the Amazone and Lena basins, while only a few GCMs show this significance.There are only small areas where none of the GCMs give significant correlation.The consistency amongst models is small and while the values of the coefficient deviate from those calculated

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Full from the reference run for most of the world we conclude that lag-1 correlation is not well reproduced by most GCMs.

Conclusions
In order to evaluate the ability of the hydrological model PCR-GLOBWB to reproduce global discharge variability when being forced with GCM datasets that are biascorrected with a simple monthly correction method, we calculated the average hydrological regimes and various discharge statistics for the period 1961-1990 for the ensemble of 12 GCM datasets and compared the results with observed data and a reference hydrological model run based on the ERA-40 downscaled CRU dataset.
As expected, after bias-correction the spread between regimes calculated with the 12 corrected GCM datasets is decreased.Differences are smallest for basins with strong seasonal patterns; the Arctic and Monsoon driven rivers.GCM derived discharge is overall too low, as raw GCM data have too many rain days, resulting in many days with little rain from which a larger amount of rain can infiltrate or evaporate.For the Lena, MacKenzie and Volga deviations in regime curves are present for two of the GCMs (IPSL-CM4 and HADGEM1), these deviations increase the ensemble mean Q mean and Q 90 values.This illustrates that a few deviating GCMs can bias the discharge statistics derived from the multi-model ensemble.
All the GCM based runs show a lower inter-annual variability than both the reference run and observations, meaning an underestimation of the number of extreme years.
And indeed, overall the Q 90 values are lower and the Q 10 values higher than in the reference run.Inter-annual runoff persistence as present in the reference run is reproduced by the GCM based runs only for a few areas, while results between GCMs vary greatly.This shows that multi-year droughts resulting from large weather anomalies (e.g.ENSO) cannot be produced either.Overall the GCM based runs resemble the reference run reasonably well.However GCMs do, even after bias-correction, not represent Q 10 values, lag-1 correlation and inter-annual variability well for the current period, which questions their usefulness for investigation of future changes in extremes.

Model performance PCR-GLOBWB
Despite its coarse resolution PCR-GLOBWB can reproduce observed discharges reasonably well for most selected catchments.To assess its performance we ran the model for the period 1961 to 1990 with CRU TS 2.1 monthly time series (New et al., 2000) downscaled to daily values with the ERA-40 re-analysis data (Uppala et al., 2005) and compared the yearly mean modelled discharge with observed discharges per catchment (see Fig. 9).For most of these catchments average monthly discharges are available from the Global Runoff Data Centre (GRDC, 2007) for the remaining catchments data from the Global River Discharge Database were used (V ör ösmarty et al., 1998).Deviations are partly present because the hydrological model calculates natural flows and does not include water use.To investigate the influence of water use, calculated discharge are compared with the sum of observed discharge and estimated water demand.Water demand is estimated on a grid of 0.5 • and is the sum of estimated industrial, agricultural and domestic water demand (Wada et al., 2010).
The 30-year mean observed (Q GRDC ) and modelled (Q CRU ) discharge are compared.Beside through inadequacies of the hydrological model, differences between modelled and observed discharge can also be caused by errors in discharge measurements or deviations in meteorological data.From Fig. 9 it can be seen that for the Murray the deviations between observed and calculated discharge can partly be assigned to the lack of inclusion of water use.To a lesser extent this is also the case for the Danube, Ganges, Yellow River and Rhine.Deviations for the river Orange, Congo and Introduction

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Full Zambezi are present as well, however this difference can not be explained by water use.For the Mississippi and the Volga the inclusion of water demand indicates that model results are worse than expected, deviations are larger than when comparing with observed discharge only.The Lena and MacKenzie river show deviations as well.These deviations are caused by undercatch in the CRU snowfall amounts (Fiedler and D öll, 2007).Additionally 30 year average calculated hydrological regimes (CRU ERA) are compared with observed regimes (GRDC) for each catchments, see Fig. 9.The plots show that the difference between the CRU derived and the observed discharge regime is especially large for the MacKenzie as mentioned before.Furthermore the observed snowmelt driven discharge peak for the Lena is steeper than modelled.Large differences are also present for the Murray because of water use.In the calculated regime of the Indus, the snow and glacier melt driven discharge increase is too large and too early in spring, while the Monsoon influenced discharge peak is relatively small.For the Parana observed river flow is more constant through time, because of the presence of large reservoirs.Where j corresponds to the year number, N is the total number of years (30), Q j is the mean annual discharge for the calculated for the years 1961 to 1990, Q is the 30 year average mean discharge, Q is an array containing all day-values for the thirty year period and k is the time-lag of one year.

Parameter Description Equation
Q mean Thirty year average mean annual discharge Screen / EscPrinter-friendly Version Interactive Discussion

Table 2 .
Description of statistical quantities of interest.