Stream ow simulations for continental-scale river basins in a global atmospheric general circulation model

Transcription

1 Advances in Water Resources 24 1) 775±791 Stream ow simulations for continental-scale river basins in a global atmospheric general circulation model Vivek K. Arora * Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, University of Victoria, P.O. Box 17, STN CSC, Victoria, BC, Canada V8W 2Y2 Received 4 August ; received in revised form 29 November ; accepted 8 December Abstract Stream ow simulations for 23 major river basins from the third-generation general circulation model GCM) of the Canadian Centre for Climate Modelling and Analysis are assessed. Precipitation and runo data are used from the AMIP II simulation in which the GCM is integrated for a 17-yr period with speci c sea surface temperatures and sea-ice concentrations. Compared to the observations, the components of the global hydrological cycle and, the globally averaged precipitation and runo over land, are well simulated. There remain, however, discrepancies in the simulation of regional precipitation and consequently runo amounts, which lead to di erences in basin-wide averaged quantities. Mean annual model precipitation is within 2% of the observed estimates for 13 out of 23 river basins considered. Model mean annual runo is within 2% of the observed estimates for only 4 out of these 13 river basins. Analysis of basin-wide averaged monthly precipitation and stream ow data, and the errors associated with the mean, and amplitude and phase of the annual cycles, indicate that model stream ow simulations improve with improvement in GCM precipitation. Ó 1 Elsevier Science Ltd. All rights reserved. 1. Introduction Rivers are a major component of earth's hydrologic cycle and they provide the critical link for returning water from the land surface to the oceans. Until recently river ow was not modelled explicitly in general circulation models GCMs). The simplistic treatment of land surface runo in some GCMs meant either the distribution of land surface runo over all ocean cells in some predetermined manner [12] or moving runo from land cells to their respective target ocean cells with no time delay [23,1]. At present, there are a number of GCM which incorporate ow routing in one form or the other. Modelling of river ow in GCMs is important for at least three reasons. First, from a climate modelling perspective, freshwater ux from rivers into the ocean at the continental edges alters the salinity of the ocean and may a ect both ocean convection and thermohaline circulation and consequently ice formation [28,,54, 55]. Second, stream ow being a spatial integrator of hydrological processes is a conceptually attractive variable to assess land surface scheme/gcm simulations at * Fax: address: vivek.arora@ec.gc.ca V.K. Arora). large spatial scales [2,39,58]. Stream ow is routinely measured and one of the most easily available quantities which can be used to evaluate the performance of GCMs on a climatological basis. Third, the ability to reliably simulate stream ow at large spatial scales has water management implications. For example, runo and stream ow simulations from GCMs are now used for studying the impact of climate change on water resources and hydrology of major river basins either directly [4,37], or by downscaling GCM data at the appropriate catchment scales [11,2]. The approaches used to model river ow in GCMs can be broadly classi ed as those: 1) which assume a uniform constant ow velocity or transfer coe cient [16,17,38,41,42,44,53], 2) which parameterize ow velocities as a function of the topographic gradient [15,18,21,25,35,38,45], 3) which use empirical relationships between velocity and discharge [33,52], and 4) physically based approaches that relate ow velocity to slope, discharge, and river cross-section simultaneously with the help of Manning's equation [3,5]. GCMs results are subject to a range of limitations, in particular their coarse resolution. The spatial resolution of GCMs is seldom as ne as 2:5 2:5 or approximately 65 km 2 ), while most hydrological applications /1/$ - see front matter Ó 1 Elsevier Science Ltd. All rights reserved. PII: S )78-6

2 776 V.K. Arora / Advances in Water Resources 24 1) 775±791 use information at a scale of about 1 km 2. A range of downscaling and disaggregation techniques are available which are used to transfer climate data from GCM scales for application at the catchment scales [7,27, 29,56]. While the spatial resolution of GCMs is too coarse compared to typical hydrological applications, the hydrological behaviour can be fairly well studied for large river basins which cover a reasonable number of GCM grid cells. For example, Miller and Russell [37] study the impact of global warming on river runo for major river basins using output from the Goddard Institute for Space Studies GISS) GCM. In order to place con dence in GCM simulations of stream ow, and to be able to use GCMs as a tool for studying climate change impact on water resources and hydrology, it is necessary to reliably assess their stream ow simulations for the current climate. Global sets of observed river ow are now becoming available [51] and provide opportunities to validate GCM stream ow simulations. Stream ow depends on GCM precipitation, how precipitation is processed by the land surface scheme, and how runo is transported downstream to the mouth of the river. Stream ow comparisons thus make a rigorous test of GCM's overall hydro-climatological performance. In this paper, the mean annual precipitation and runo and, stream ow simulations of the Canadian Centre for Climate Modelling and Analysis' CCCma) third-generation GCM are analysed for 23 major river basins. Precipitation and runo data are obtained from the model simulation for the second round of the Atmospheric Model Intercomparison Project AMIP II), and the model runo data are used to obtain stream ow at the mouth of the major rivers using ow routing. In Section 2 a brief description of the GCM, its land surface scheme, and the AMIP II simulation is given. Salient features of the ow-routing algorithm are described in Section 3 and analysis of simulated stream ow and water balance for individual river basins is presented in Section The CCCma third-generation GCM and the AMIP II simulation The CCCma third-generation atmospheric GCM N. McFarlane et al., personal communication, ) follows the CCCma second generation model GCM2) as described by McFarlane et al. [36]. The results analysed here are obtained with the T47 L32version of the model, in which dynamic terms are calculated at triangular T47 spectral truncation, and the physical terms are on the associated ) horizontal linear grid. The vertical domain extends to 1 hpa and the thicknesses of the model's 32layers increase monotonically with height from approximately 1 m at the surface to 3 km in the lower stratosphere. While many of the parameterised physical processes in the third-generation model are qualitatively similar to GCM2, key new features include: 1) a new parameterisation of cumulus convection [6], 2) an improved treatment of solar radiation which employs four bands in the visible and near infrared region, 3) an ``optimal'' spectral representation of topography [26], 4) a revised representation of turbulent transfer coe cients at the surface [1], 5) a hybrid moisture variable [9], and 6) the introduction of Canadian Land Surface Scheme CLASS), a new module for treatment of the land surface processes [49,5]. The land surface in GCM2is described by a bucket scheme whose depth is spatially variable and assumed to be a function of the soil and vegetation type. Compared to the bucket scheme, several improvements are made in the new land surface scheme module. CLASS comprises of three soil layers with prognostic liquid and frozen soil moisture contents), a snow layer where applicable, a vegetative canopy layer, and soil surface properties e.g., surface roughness heights and albedo) which are functions of soil moisture conditions and the soil and vegetation types. The thicknesses of the top, middle, and bottom soil layers are.1,.25, and 3.5 m, respectively. For the canopy, interception of rainfall and snow and their subsequent evaporation and sublimation, respectively, are all modelled. CLASS generates two runo components: 1) surface runo is generated when the amount of ponded water exceeds a speci ed limit and ponds form when the precipitation intensity exceeds the in ltration capacity of the soil, and 2) deep soil percolation or drainage from the bottom-most soil layer is assumed equal to the hydraulic conductivity of the soil, which itself is a function of soil moisture. The GCM and the land surface scheme operate at a time step of 2 min. In AMIP II simulations the atmospheric GCMs are integrated for the 17-yr period 1979±1995) with speci- ed lower boundary conditions of observed monthly sea surface temperatures SST) and sea-ice concentrations [22]. The Atmospheric Model Intercomparison Project AMIP), initiated in 1989 undertook the systematic validation, diagnosis, and intercomparison of the performance of the atmospheric GCMs [24]. For this purpose, participating models simulated the evolution of the climate during the decade 1979±1988. AMIP II is an extension of AMIP, with improvements in experimental design, additional diagnosis of an expanded model output and establishment of new standards and protocols for data analysis. 3. The ow-routing algorithm The variable velocity algorithm of Arora and Boer [3] designed for use in GCMs is used to perform ow routing at 3.75 resolution and is described brie y. The

3 V.K. Arora / Advances in Water Resources 24 1) 775± Mackenzie Volga Ob Yenisey Lena Yukon Columbia Mississippi Orinoco Amazon Tocantins Danube Nile Indus Ganges Mekong Yangtze Amur Brahamaputra Congo Parana Zambezi Murray Fig. 1. Model discretisation of the 23 major river basins, at 3.75 resolution, considered in this study and their river ow directions as per Arora and Boer [3]. river ow directions at the GCM resolution are obtained from global 1 ow direction data set of Oki and Sud [43]. Fig. 1 shows the model discretisation of the 23 major river basins considered in this study and their river ow directions as per Arora and Boer [3]. Flow routing is performed via surface and ground water reservoirs. The water balance within a grid for the surface water store, S, is given by ds ˆ I Q; dt 1 where I is the in ow and Q is the out ow. Input into the surface and groundwater reservoirs, surface runo and drainage estimates, respectively, are obtained from land surface parameterisation scheme used in the GCM. Fig. 2shows the schematic of the ow-routing algorithm. The scheme uses Manning's equation to determine time-evolving channel ow velocities that depend on the amount of runo generated in the grid cell V ˆ 1 n R2=3 s 1=2 ; 2 where V is the channel velocity, n the Manning's roughness coe cient, R the hydraulic radius area of ow divided by the wetted perimeter), and s the channel slope. Manning's roughness coe cient of. corresponding to natural channels is used [13,14,47,57]. The surface water storage, S, is assumed to be a linear function of out ow discharge, so S ˆ sq ˆ L AV ˆ LA ˆ LWh; V 3 where s is the travel time between the grid cell under consideration and its downstream neighbour given by s ˆ L=V, where L is the distance between the grid cells. W and h are the river width and ow depth, respectively, and A is the cross-sectional area of the river. The out- ow Q is given by Q ˆ AV ˆ WhV ˆ Wh 1 2=3 Wh s 1=2 ; 4 n W 2h and substituting 3) and 4) into the continuity equation 1) yields d h dt Surface runoff, f s Deep soil percolation, f p Groundwater store, G Land surface scheme outputs f p ˆ 1 LW I W 5=3 h 5=3 n W 2h f s Groundwater store G Inflow from neighbouring cells, f n Surface water store, S Groundwater flow into the river channel, f g Surface water store S 2=3 s1=2 Flow to the downstream cell, f o Fig. 2. Schematic of the variable velocity ow-routing algorithm of Arora and Boer [3] used to perform ow routing.! : 5 Eq. 5) describes the ow in terms of the rate of change of ow depth for a given river section. An explicit f g f n f o W h

4 778 V.K. Arora / Advances in Water Resources 24 1) 775±791 forward step nite di erence approximation of 5) is used to determine ow depth.! h t 1 ˆ h t Dt LW I t W 5=3 h 5=3 t s1=2 : 6 2=3 n W 2h t With the ow depth known, the ow velocity and out- ow discharge at any time step can be obtained using Eqs. 2) and 4). The river channel cross-section is approximated rectangular in shape and the river width along the network is obtained using a geomorphological relationship between width and mean annual discharge. The residence time for the ground water reservoir is related to the major soil type in the GCM grid cell following Arora et al. [5]. The groundwater reservoir used in the routing algorithm does not simulate the water table depth or saturated groundwater ow, rather it is used to parameterize the delay that is experienced by drainage runo before it reaches the stream. The routing scheme is run o ine and takes daily input of surface runo and drainage from the land surface scheme. It operates at a time step of 1/1th of a day 2.4 h) and subdaily surface runo and drainage values are interpolated between the daily values before using them as input into the routing algorithm. The variable velocity routing algorithm of Arora and Boer [3] has been compared with a typical routing algorithm used in hydrological models at small spatial scales WATROUTE) by Arora et al. [6]. WATOUTE uses routing algorithms of the WATFLOOD distributed hydrological model [31]. The results suggest that, despite the large spatial scale at which routing is performed in the GCM, the monthly stream ow values simulated by the variable velocity routing algorithm and those simulated by WATROUTE compare well. Arora et al. [6] conclude that for the purpose of realistically modelling monthly stream ow in GCMs, ow routing at large spatial scales gives results similar to those obtained by small scale routing schemes. Although based on physical ow-routing parameterisations used in traditional small scale hydrological models, the variable velocity algorithm su ers from one limitation. It does not model the reduction of annual cycle amplitude and mean annual discharge caused by large dams and reservoirs, and does not take into account the extraction of water for irrigation and drinking purposes. This is likely to make comparisons with observed hydrographs somewhat di cult, especially for heavily regulated rivers such as the Parana [15]. 4. Model simulation ofthe moisture budget components Precipitation and runo data from the 17-yr period 1979±1995) of the AMIP II simulation are used. To obtain stream ow at the mouth of the major rivers, daily values of overland runo and deep soil drainage generated by the land surface scheme are used as input into the ow-routing algorithm in an o ine mode. The model components of the global moisture budget are compared with observations in Section 4.1, and comparisons for model precipitation and runo over land are performed in Section 4.2. Simulated mean monthly precipitation and stream ow for major river basins are analysed in Section The global hydrological cycle Fig. 3 compares the simulated components of the global hydrological cycle with observation-based estimates of Baumgartner and Reichel [8] and L'vovich [34]. The GCM simulates a slightly more active global hydrological cycle compared to the estimates of Baumgartner and Reichel [8] but compares well with L'vovich [34] estimates. The simulated value of vapour transport from ocean to the land surface is slightly higher than both observed estimates, while the fresh water ux or runo ) from the land surface to the ocean compares well with observations. The imbalance of 3 km 3 /yr over land in the model implies that the vapour transport from the ocean to the land surface is not balanced by the runo from the land surface to the ocean. In the GCM this is the result of moisture storage on land as snow over the Greenland and the Antarctica. The mass balance of Greenland and Antarctica, in particular the breaking of shelf ice which returns this excess moisture to ocean, is not modelled explicitly in the GCM Mean annual comparisons Table 1 compares model estimates of globally averaged mean values of precipitation and runo over land excluding the Greenland and Antarctica) with observation-based estimates of L'vovich [34]. Observed pre- Land All values are in 1 3 km 3 /year Freshwater flux Vapour Transport Precipitation Evapotranspiration Evaporation Precipitati Globally Averaged Precipitation/Evaporation Ocean AMIP II Run Baumgartner and Reichel [1975] L vovich [1979] Fig. 3. Comparison of simulated components of the global hydrological cycle with estimates of Baumgartner and Reichel [8] and L'vovich [34]

5 V.K. Arora / Advances in Water Resources 24 1) 775± Table 1 Globally averaged mean annual model and observed, precipitation and runo over land area excluding the Greenland and the Antarctica Precipitation Runo mm/day mm/yr mm/day mm/yr This study L'vovich [34] Xie and Arkin [59] Legates and Willmott [32] Cogley [19] cipitation estimates of Xie and Arkin [59] and Legates and Willmott [32], and runo estimates of Cogley [19], are also used. Xie and Arkin [59] constructed global 2.5 gridded monthly precipitation estimates based on gauge data, satellite estimates from three di erent sources, and predictions produced by the operational forecast model of European Centre for Medium-Range Weather Forecasting ECMWF). Legates and Willmott [32] compiled observations of long-term monthly precipitation at.5 resolution using gauge and shipboard estimates mostly from 192±198. Cogley [19] derived his runo estimates from water balance maps from a considerable number of sources, of which Korzun et al. [3] was the most important. The model values of mean annual land precipitation compare well with observations and lie between the estimates of Xie and Arkin [59] and Legates and Willmott [32]. The model estimate of mean annual runo compares well with L'vovich [34] but is lower than estimate of Cogley [19]. Mean annual runo value of upto 5 mm/yr in southern South America close to Chile) are shown in Cogley [19] estimates, while Fig. 4. Di erences between model and observed, mean annual precipitation and runo estimates over land. Observed precipitation and runo estimates of Xie and Arkin [59] and Cogley [19] are used, respectively.

6 78 V.K. Arora / Advances in Water Resources 24 1) 775±791 L'vovich [34] estimates show maximum values not exceeding mm/yr in this region. Cogley [19] estimates may therefore be on the higher side. Fig. 4 shows the global plots of di erences between simulated and observed mean annual precipitation and runo over land. The observed precipitation and runo estimates of Xie and Arkin [59] and Cogley [19], respectively, are used. While the simulated globally averaged precipitation and runo estimates compare well with observations see Table 1) there remain discrepancies in the regional precipitation and consequently runo estimates. The model produces more precipitation over northern North America, Central America, central Africa, south-west China, and southern South America. For regions where model precipitation is less than observed, the decrease is most signi cant in the Amazonia region. As expected, the land surface scheme produces more less) runo in areas characterised by high low) GCM precipitation. The model runo is signi cantly less than observed in the Amazonia, and higher in northern North America, central Africa, and south-west China. The di erences in regional simulation of precipitation and runo lead to di erences in basin-wide averaged values calculated for individual river basins and the di erences in stream ow Basin-wide averaged mean annual precipitation and runo Basin-wide averaged quantities are calculated by averaging precipitation and runo over the grid cells which collectively form a river basin see Fig. 1). The model and observed river basin areas obtained from 1 1 discretisation of Oki and Sud [43]) are compared in Table 2. The error in discretised basin areas at the GCM resolution is less than 5% for most river basins. Comparisons between simulated and observed mean annual amount of precipitation, and runo, for 23 major river basins are made in Fig. 5. Basin-wide averaged model precipitation estimates are compared with estimates of Xie and Arkin [59] and Legates and Willmott [32]. Model runo estimates are compared with estimates of Cogley [19]. Table 3 shows the di erence between the model and observed precipitation and runo estimates. The river basins are sorted in an ascending order according to the di erence in model and observed precipitation, and runo. The observed precipitation estimate used in Table 3 is the average of estimates obtained from Xie and Arkin [59] and Legates and Willmott [32]. Out of 23 major river basins considered in this study, model precipitation is within 2% of the observed estimates for 13 river basins. The di erences between simulated values and observed estimates are bigger for runo than for precipitation, because of the errors associated with the land surface scheme. Consequently, model runo is within 2% of the observed Table 2 Comparison of model and observed river basin areas obtained from 1 1 discretisation of Oki and Sud [43]) River basin Model area at 3.75 resolution km 2 ) Observed river basin area km 2 ) Model area expressed as a percentage of observed area Amazon Congo Zaire) Mississippi Ob Parana Nile Yenisey Lena Amur Yangtze Mackenzie Volga Zambezi Murray Ganges Indus Orinoco Tocantins Yukon Danube Mekong Columbia Brahamaputra estimates for only 4 of these 13 river basins. For most river basins high low) GCM precipitation results in high low) runo. However, there are river basins for which although the precipitation estimates are close to observations, such as the Zambezi and the Danube, the model runo simulations are poor. For the Volga and the Indus River basins the di erence between model and observed values have opposite signs for precipitation and runo. The model simulations imply that on an annual scale the land surface scheme does not partition the precipitation into runo and evapotranspiration realistically and thorough evaluation of the land surface scheme is required in these river basins. Nevertheless, Table 3 shows that the errors in mean annual runo, for most river basins, are the result of errors in mean annual precipitation Mean monthly precipitation and stream ow comparisons Model-simulated mean monthly stream ow is compared with observations obtained from UN Educational, Scienti c, and Cultural Organisation [48] and Vorosmarty et al. [51]. Comparisons between basin-wide averaged GCM precipitation and observation-based estimates are also made to relate de ciencies in the simulated river discharge to the GCM precipitation. Figs. 6±11 compare the annual average stream ow cycle at the mouths of the 23 major rivers geographic

7 V.K. Arora / Advances in Water Resources 24 1) 775± Moisture flux (mm/yr) Moisture flux (mm/yr) Amazon Congo Mississippi Ob Moisture flux (mm/yr) Moisture flux (mm/yr) Parana Nile Yenisey Lena Amur Yangtze Mackenzie Volga Moisture flux (mm/yr) Moisture flux (mm/yr) Zambezi Murray Ganges Indus Orinoco Tocantins Yukon Danube 25 Moisture flux (mm/yr) Mekong Columbia Brahamaputra Precipitation Model Precipitation Xie and Arkin (1996) Runoff Model Runoff Cogley (1998) Legates and Willmott (199) Fig. 5. Comparison between simulated and observed mean annual values of basin-wide averaged precipitation and runo for the major river basins considered in this study. locations shown in Fig. 1) with their observed hydrographs. These gures also compare the basin-wide averaged GCM precipitation with observation-based estimates. The observed monthly precipitation shown in these gures is the mean of estimates obtained from Xie and Arkin [59] and Legates and Willmott [32]. In Fig. 6 the seasonality of GCM precipitation estimates compares well with observations for the Amazon River basin, although the simulated precipitation is considerably less throughout most of the year. This results in less stream ow at the mouth of the river but the seasonality of model stream ow values compares well with observations. In Fig. 7, the monthly GCM precipitation for the Yenisey and the Lena River basins compares extremely well with observations and consequently the simulated stream ow also compare reasonably well. In Fig. 8, although the GCM preserves the seasonality of monthly precipitation amounts in the Yangtze River

8 782 V.K. Arora / Advances in Water Resources 24 1) 775±791 Table 3 Di erence between mean annual model and observed precipitation, and runo, for major river basins a River basin Di erence in model and observed precipitation %) basin, the amount of GCM precipitation is high, which results in higher stream ow. For most river basins, the di erence in observed and GCM precipitation is suspected to be the primary cause of di erence in the magnitude of stream ow. The stream ow simulations are further evaluated in terms of the error variance for precipitation and stream ow values. In the following equations, e ˆ f m f o ˆ f m f o f m f o ˆe e 7 is the error or the di erence between model-simulated, f m, and the observed, f o, climatological annual cycles, and f and f are the annual mean and deviations from the mean. After some algebra and writing r 2 o ˆ f 2 r 2 m ˆ f 2 m, and R ˆ f m f o =r or m where r 2 o and r2 m are the variance of observed and model values, respectively, and R is the correlation coe cient), the mean-square-error is written as n e 2 ˆ e 2 e 2 ˆ e 2 r m ˆ e 2 m e2 a e2 p : River basin Di erence in model and observed runo %) Tocantins )48.3 Tocantins )76.6 Amazon )25.6 Murray )69.4 Ganges )22. Ganges )62.9 Mekong )19.3 Amazon )52. Orinoco )17.6 Danube )49.4 Ob )16.8 Mississippi )49.1 Volga )1.2 Indus )38.5 Mississippi )7.5 Yenisey )36.3 Danube.6 Mekong )3.1 Zambezi.8 Orinoco )29.1 Yenisey 3.2 Ob )12.6 Murray 3.4 Amur )8.1 Yukon 9.8 Lena )4.5 Lena 1.2 Yukon 17.3 Congo Zaire) 11.8 Volga 2.2 Amur 11.9 Parana 26.4 Parana 2.6 Columbia 36.6 Brahamaputra 27.9 Yangtze 39.6 Indus 3.9 Mackenzie 41.7 Mackenzie 38.8 Brahamaputra 43.6 Yangtze 5.4 Congo Zaire) 68.3 Columbia 56.4 Zambezi 76.7 Nile 63.2Nile 52.9 a The river basins are sorted in an ascending order according to the di erence in model and observed precipitation and runo ). The river basins for which GCM precipitation and runo ) are within 2% of the observed estimate are given in italics. Observed precipitation estimates are the mean of estimates of Xie and Arkin [59] and Legates and Willmott [32]. Observed runo estimates are of Cogley [19]. o r o 2 2r o r m 1 R o, 8 W is de ned as the ratio between the error variance and the sum of variance of observations and the modelsimulated values. In Eq. 9), if the model-simulated values and observations are not correlated i.e., R ˆ ), then W equals 1. However, when model-simulated values are exactly similar to observations, then R ˆ 1; b ˆ 1, and W ˆ : W ˆ e2 r 2 m ˆ 1 2r or m r2 o r 2 m R ˆ 1 br; r2 o 9 S ˆ 1 W ˆ br: Skill, S coe cient of correlation weighed by b), is de- ned as 1 W, that equals 1 when model simulations are same as observations, when there is no correlation between the model-simulated values and the observations, and less than zero when the correlation is negative. The use of skill, S, is sought to gain information not only about correlation, but the absolute values as well. Fig. 12shows the skill of the stream ow values plotted against the skill of precipitation values as determined from Eq. 9)) for the major river basins considered in this study. If both model precipitation and stream ow were equal to the observations, both precipitation and stream ow skills would be equal to 1 and, a river basin would be plotted at the location shown by the star. Fig. 12shows river discharge simulations for river basins with good agreement between the observed and GCM precipitation are generally better than for river basins with poor GCM precipitation. The skill of precipitation values is above.8 for most river basins. In terms of precipitation and stream ow skill, the Amur, the Yenisey, and the Lena are the best simulated river basins. For the Murray and the Indus River basins the skill of stream ow values is negative because of the negative correlation between the simulated and observed stream ow hydrographs see Fig. 12). The skill of simulated stream ow values for the Ob, the Nile, and the Zambezi is poor, despite a value of precipitation skill above.92, implying poor performance of the land surface scheme in these river basins. The skill of simulated stream ow values for the Parana River is poor see Figs. 7 and 12) despite reasonably well-simulated monthly GCM precipitation, because the Parana is heavily regulated and the ow-routing algorithm used in this study does not model ow attenuation due to large dams and reservoirs. The three terms e 2 ; r m r o 2, and 2r o r m 1 R, in Eq. 8), are the errors associated with di erence in the mean, and the amplitude and phase of the annual cycles, respectively. As a fraction of the total mean square error these may be expressed as 1 ˆ e2 m e e2 a 2 e e2 p 2 e : 2 1

9 V.K. Arora / Advances in Water Resources 24 1) 775± Amazon AMIP2 Observed Amazon AMIP2 Observed Congo 3 Congo Mississippi Mississippi Ob Ob Precipitation Streamflow Fig. 6. Comparison between simulated and observed basin-wide averaged mean monthly precipitation and stream ow for the Amazon, Congo, Mississippi and the Ob River basins. The stream ow observations for the Amazon, Congo, Mississippi, and the Ob are at Obidos, Brazzaville, Vicksburg, and Salekhard, respectively. Observed precipitation estimates are the mean of estimates obtained from [59,32]. Observed stream ow data are obtained from [48,51]. p The root-mean-square error, RMSEˆ e 2, and the relative RSME, RRMSE ˆ RMSE/f o, are also calculated. Table 4 shows the RMSE and RRMSE values and the percentage of error associated with the mean, amplitude, and phase of the simulated values for precipitation and stream ow for the major river basins. As expected, the values of RRMSE for stream ow are generally higher than those for precipitation because of errors associated with the land surface scheme and the routing algorithm. The errors associated with the annual mean, and the amplitude and phase of the annual cycle about the mean, give further insight into the model simulations. For Amazon Basin precipitation, for example, most of the error is associated with the lowaverage GCM precipitation Fig. 6), which results in an error of similar magnitude in the mean of simulated stream ow values. The Yangtze, the Orinoco, the Tocantins, and the Nile behave in a similar manner. For

10 784 V.K. Arora / Advances in Water Resources 24 1) 775±791 Parana AMIP2 Observed Parana AMIP2 Observed Nile Nile Yenisey Yenisey Lena Lena Precipitation Streamflow Fig. 7. Same as Fig. 6 but for the Parana, Nile, Yenisey and the Lena River basins. The stream ow observations for the Parana, Nile, Yenisey and the Lena are at Corrientes, El Ekhsase, Igarka, and Kusur, respectively. the Mackenzie basin the GCM precipitation is higher than that observed Fig. 8) and thus a large error in the mean. This mean error in precipitation is not, however, translated into a similar error in the mean stream ow. In Mackenzie Basin, most of the winter precipitation falls as snow, so does not contribute to runo until spring. The high GCM precipitation thus contributes to a high peak discharge in spring Fig. 8), so most of the error in stream ow is seen as an error in the amplitude of the annual cycle. For the Volga River, although the mean annual runo compared well with observations see Fig. 5 and Table 3), the analysis of monthly stream ow show the errors in simulated amplitude and phase of the annual stream ow cycle see Fig. 8). For the Congo, the Ganges, and the Brahamaputra Rivers, most of the error is associated with the amplitude of the annual precipitation cycle see Figs. 6, 9 and 11) which results in an error of similar magnitude in the amplitude of the annual stream ow cycle. For the Ob, and the Indus Rivers Figs. 6 and 9), the timing of the simulated maximum discharge does not compare well with observations, so most of the error is associated with the phase

11 V.K. Arora / Advances in Water Resources 24 1) 775± Amur AMIP2 Observed Amur AMIP2 Observed Yangtze Yangtze Mackenzie Mackenzie Volga Volga Precipitation Streamflow Fig. 8. Same as Fig. 6 but for the Amur, Yangtze, Mackenzie and the Volga River basins. The stream ow observations for the Amur, Yangtze, Mackenzie and the Volga are at Komsomolsk, Hankou, Norman Wells, and Volgograd Power Plant, respectively. of the annual stream ow cycle. No signi cant relationships between the percentage errors associated with mean, amplitude, and phase for precipitation and the associated stream ow values are found. This is expected because the land surface scheme processes the precipitation in a di erent manner for every river basin depending on its hydrology and climate. If, however, the scaled error variances e 2 f ˆ and n ˆ e 2 2 f m fo r 2 m r2 o 2 are considered which normally vary between zero and 1 though n can have a value of up to 2if simulated and observed values are inversely correlated) as measures of error in the mean and deviation from the mean, there is some overall relationship between error in precipitation and the associated stream ow values. Fig. 13 shows the scaled error variances, associated with the mean f) and deviation from the mean n) for precipitation plotted against the corresponding stream ow values, for the major river basins. The errors associated with both mean and deviations from the mean in model stream-

12 786 V.K. Arora / Advances in Water Resources 24 1) 775±791 Zambezi AMIP2 Observed Zambezi AMIP2 Observed Murray Murray Ganges Ganges Indus 9 Indus Precipitation Streamflow Fig. 9. Same as Fig. 6 but for the Zambezi, Murray, Ganges and Indus River basins. The stream ow observations for the Zambezi, Murray, Ganges and Indus are at Matundu, Lock 9 Upper, Farakka, and Kotri, respectively. ow simulations increase when the corresponding error in the GCM precipitation increases, and model-simulated stream ow values improve with improvement in GCM precipitation. 5. Summary and conclusions Modelling of river ow in GCMs is of interest for at least three reasons: the role played by freshwater ux from rivers in a ecting both ocean convection and circulation, the ability to assess land surface schemes at large spatial scales, and the water management implications associated with, reliably simulating stream ow at continental scales and, climate variability and change. Various approaches, with varying degrees of complexity, are available to perform ow routing at large spatial scales and at present a number of GCMs incorporate ow routing. In order to place con dence in GCM simulations of stream ow, and to be able to use GCMs as a tool for studying climate change impact on water resources and hydrology, it is necessary to reliably assess

13 V.K. Arora / Advances in Water Resources 24 1) 775± Orinoco AMIP2 Observed Orinoco AMIP2 Observed Tocantins Tocantins Yukon Yukon Danube 12 Danube Precipitation Streamflow Fig. 1. Same as Fig. 6 but for the Orinoco, Tocantins, Yukon and Danube River basins. The stream ow observations for the Orinoco, Tocantins, Yukon and Danube are at Musinacio, Itupiranga, Ruby, and Ceatal Izmail, respectively. their stream ow simulations for the current climate. The dependence of stream ow on GCM precipitation, how this precipitation is processed into evapotranspiration and runo at the land surface, and how runo is transported downstream to the river mouth, make stream ow comparisons a rigorous test of GCM's performance. Stream ow simulations for 23 major river basins from the third-generation CCCma GCM are assessed in this study. Precipitation and runo data from the AMIP II simulation are used in which the GCM is integrated for the 17-yr period 1979±1995) with speci ed lower boundary conditions of observed sea surface temperatures and sea-ice concentrations. Daily runo estimates from the simulation are used as input into a ow-routing algorithm to obtain stream ow at the mouth of the major rivers. Compared to the observations the global hydrological cycle is simulated well in the model. The mean annual globally averaged estimates of model precipitation and runo over land excluding the Greenland and the Antarctica) also compare well with observationally

14 788 V.K. Arora / Advances in Water Resources 24 1) 775±791 Mekong AMIP2 Observed Mekong AMIP2 Observed Columbia Columbia Brahamaputra Brahamaputra Precipitation Streamflow Fig. 11. Same as Fig. 6 but for the Mekong, Columbia and the Brahamaputra River basins. The stream ow observations for the Mekong, Columbia and the Brahamaputra are at Mukdahan, The Dalles, and Bahadurabad, respectively. Streamflowskill Danube Precipitation skill vs. Streamflow skill Congo Murray Indus Precipitation skill M ississippi M ackenzie C olum bia Nile Parana Ob Amur Yenisey based estimates. However, there remain discrepancies in the simulation of regional precipitation and consequently runo estimates, which lead to di erences in basin-wide averaged precipitation and runo amounts. Comparisons of basin-wide averaged mean annual precipitation with observations show that model precipitation is within 2% for 13 out of 23 major river basins considered. Compared to observations, the di erences in Lena Amazon Yangtze Orinoco Ganges Yukon Brahamaputra Tocantins Volga M ekong Zambezi Fig. 12. Skill of simulated monthly stream ow values plotted against the skill of monthly precipitation values for the major river basins. If model precipitation and stream ow were exactly same as observations a river basin would be plotted at the location shown by the star. model runo estimates are bigger because of the errors associated with the land surface scheme. Consequently, model runo is within 2% of the observed estimates for only 4 of these 13 river basins. Analysis of basin-wide averaged monthly precipitation and stream ow simulations suggest that river discharge simulations for river basins with good agreement between observed and GCM precipitation are generally better than for river basins with poor GCM precipitation. In terms of monthly precipitation and stream ow, the Amur, the Yenisey, and the Lena are the best simulated river basins. Stream ow can be used as a diagnostic variable. River basins for which stream ow simulations are poor despite reasonably well-simulated annual precipitation cycle indicate that either the spatial variability of model precipitation estimates is poor, or the land surface scheme partitioning of precipitation into evapotranspiration and runo is not realistic, or the ow-routing scheme performance is unsatisfactory. For example, the stream ow simulations for the Ob, the Nile, and the Zambezi rivers are poor despite reasonably well-simulated precipitation skill >.92). These river basins indicate the regions over which the performance of the land surface scheme and routing algorithm is

15 Table 4 Comparison of model-simulated and observed, precipitation and stream ow for major river basins River basin Precipitation Stream ow Percentage of error associated with Annual cycle RMSE mm/ month) RRMSE %) V.K. Arora / Advances in Water Resources 24 1) 775± Annual mean Amplitude Phase RMSE 1 3 m 3 =s) RRMSE %) Percentage of error associated with Annual cycle Annual mean Amplitude Amazon Congo Mississippi Ob Parana Nile Yenisey Lena Amur Yangtze Mackenzie Volga Zambezi Murray Ganges Indus Orinoco Tocantins Yukon Danube Mekong Columbia Brahamaputra Phase ς - streamflow (%) (a) Relationsip between precipitation and streamflow scaled error variance associated with the mean, ς-precipitation vs. ς-streamflow ς = f 2 e + f 2 2 m o R 2 = ς - precipitation (%) ξ - streamflow (%) (b) Relationship between precipitation and streamflow scaled error variance associated with deviations from the mean, ξ-precipitation vs. ξ-streamflow 2 e ξ = σ + σ 2 2 m o R 2 = ξ - precipitation (%) Fig. 13. Relationship between precipitation and stream ow scaled error variances associated with the mean panel a) and deviations from the mean panel b). needed to be evaluated thoroughly. The disagreement between simulated and observed stream ow for the Parana river highlights the importance of taking large dams and reservoirs into account in global ow-routing schemes. The analysis of errors associated with the mean, and the amplitude and the phase of the annual cycles indicates how the errors in precipitation are transformed into errors associated with the annual stream ow cycle. Compared to stream ow simulations in GCM2 not shown) the simulations in GCM3 improve, but the de ciencies in simulation of regional precipitation are found to be the primary cause of de- ciencies in stream ow. The land surface scheme CLASS) used in CCCma GCM3 does not currently account for sub-grid scale variability of soil moisture and precipitation intensity. A new version of the land surface scheme which includes sloping soil layers according to the sub-grid topography, to model inter ow, has been successfully tested at small spatial scales [46], but not yet included in the GCM simulations. More realistic representation of hydrologic processes in the land surface scheme is likely to improve

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