This study quantifies the uncertainty in discharge calculations caused by uncertainty in precipitation input for 294 river basins worldwide. Seven global gridded precipitation datasets are compared at river basin scale in terms of mean annual and seasonal precipitation. The representation of seasonality is similar in all datasets, but the uncertainty in mean annual precipitation is large, especially in mountainous, arctic, and small basins. The average precipitation uncertainty in a basin is 30%, but there are strong differences between basins. The effect of this precipitation uncertainty on mean annual and seasonal discharge was assessed using the uncalibrated dynamic global vegetation and hydrology model Lund–Potsdam–Jena managed land (LPJmL), yielding even larger uncertainties in discharge (average 90%). For 95 basins (out of 213 basins for which measurements were available) calibration of model parameters is problematic because the observed discharge falls within the uncertainty of the simulated discharge. A method is presented to account for precipitation uncertainty in discharge simulations.
There is a growing concern about increasing water scarcity in many regions of the world, as climate change on the one hand and increasing human water use on the other can put increasing pressure on the world’s water resources (CSD 1997; Kundzewicz et al. 2007; World Water Council 2000).
Understanding the processes leading to (repetitive) droughts and floods requires an extensive understanding of the global hydrological cycle and its interactions with vegetation, climate, and humans (Kabat et al. 2004). Not only should average annual water availability be quantified with certainty but also the spatial and temporal distribution of water availability. There are several studies that calculate soil moisture, runoff, and its accumulation in discharge based on climate input, soil, and vegetation characteristics using global-scale hydrological models (e.g., Alcamo et al. 2003; Arnell 1999b; Gerten et al. 2004; Nijssen et al. 2001; Oki et al. 2001; Vörösmarty et al. 1998). Most of these models have been used to simulate current discharge patterns, but a number of global assessments on the influence of climate change on future water resources exist (e.g., Alcamo et al. 2007; Arnell 1999a, 2003; Barnett et al. 2005; Bergström et al. 2001; Milly et al. 2005; Vörösmarty et al. 2000a).
For a reliable quantitative assessment of future water resources, it is important to first gain trust in the simulation of current water availability. This can be done by validating the global model to observed discharges, for which data are available globally (Global Runoff Data Centre 2007). Discharge is the integrator of the water balance over large areas and can be regarded as the water availability in different sectors.
Few global hydrological models have been validated and calibrated to discharge observations so as to reduce the bias between observations and simulations. This was done by adjusting the model parameters (Nijssen et al. 2001) or by applying a simple correction parameter (Döll et al. 2003). However, the bias between observations and simulations cannot always be attributed to the model designs. If, for example, the precipitation input data in a particular basin is too low, it is logical that the simulated streamflow becomes too low, even though the parameterization of the runoff generation process may be physically correct. Tuning the model to observed discharge can thus result in a compensation of the underestimated or overestimated precipitation, leading to an unrealistic partitioning of precipitation between runoff and other water balance terms. Therefore, the uncertainty in model simulations arising from different factors should be taken into account before calibrating the model parameters.
Wind-induced undercatch of solid precipitation (Adam and Lettenmaier 2003) and underestimation of precipitation in topographically complex regions (Adam et al. 2006) are well-known sources of errors in precipitation products derived from rain gauge measurements. Tian et al. (2007) compared water balance calculations with undercatch-corrected and uncorrected precipitation data and demonstrated that using bias-corrected precipitation resulted in an increase in computed streamflow of 5%–25% in northern latitudes.
The question of which precipitation dataset is the most accurate for forcing of hydrological models is posed in several studies, but has not yet been answered with consensus. Berezovskaya et al. (2004) showed inconsistencies between runoff data and three precipitation datasets for three large Siberian rivers. Their analysis suggests a poor quality of either the runoff or precipitation datasets, or both. Pavelsky and Smith (2006) used discharge observations of 198 arctic rivers to assess the quality of four global precipitation sets and concluded that observational datasets cover the trends significantly better than two reanalysis products. At global scale, however, Voisin et al. (2008) evaluated a reanalysis precipitation product more suitable than a satellite-derived precipitation dataset for use in a hydrological model, mainly because of the high temporal resolution of the reanalysis product.
Fekete et al. (2004) demonstrated the impact of uncertainties in precipitation input on runoff estimates at a grid scale by forcing a global water balance model with six different global precipitation datasets. This analysis showed that the uncertainty in precipitation translates to at least the same and typically much greater uncertainty in runoff in relative terms. Although the sources of the differences between the datasets were not identified, the Fekete et al. (2004) study demonstrated the importance of taking a close look at the climate input data that is used to force the hydrological model. However, they did not compare the datasets on a basin scale, which is the common scale for water resources assessments. The problem of uncertainties in input data for global hydrological models and the resulting over- or underestimations of streamflow in several basins has been identified in several papers (e.g., Döll et al. 2003; Gerten et al. 2004; Nijssen et al. 2001), but its individual contribution to overall uncertainty has, to our knowledge, not yet been quantified at global scale. Although there are possible uncertainties in all input datasets (e.g., soil, land use, temperature), in this paper we will focus on the impact of uncertainty in precipitation data, which we expect to be the largest source of uncertainty from input data.
For water resources assessments, the intra-annual dynamics of discharge are important, because both water demand and supply vary throughout the year. Therefore, the impact of uncertainty should also be investigated on a seasonal time scale.
The objective of this paper is to quantify the global distribution of the uncertainty in annual as well as seasonal estimates of precipitation on a basin scale and the resulting uncertainty in discharge estimates as computed by the Lund–Potsdam–Jena managed land (LPJmL) model (Bondeau et al. 2007; Rost et al. 2008). Based on the results, consequences of this uncertainty for validation and calibration of global hydrological models are discussed. Specifically, we compare the variations between seven global gridded precipitation datasets at a basin scale, analyze the simulated variations in discharge on a mean annual and a mean seasonal time scale, and compare the outcomes with observations for 294 basins around the world. More detailed analyses are presented for a selection of 16 basins located in different climate zones and with different hydrological properties. The analysis for all 294 basins is available in an online database (http://www.climatexchange.nl/projects/JHM).
Section 2 gives an overview of the method: the seven global precipitation datasets used, other input data for the LPJmL model, a brief model description, and the data used for validation. In section 3 the results of the analysis are presented in three parts: (i) the precipitation uncertainty, (ii) the impacts of this uncertainty on discharge simulations, and (iii) comparison with observed discharge. Section 4 discusses the implications of these results for validating, developing, and calibrating global hydrological models and concludes with the representation of uncertainty in modeling results.
2. Method and data
a. Precipitation input
In this study we use seven global gridded precipitation sets (Table 1) and compare them at basin scale. These datasets differ with respect to the original data sources that are used, the interpolation method, and the eventual correction factors applied. The datasets are selected based on their spatial coverage (global) and their temporal coverage (at least a 20-yr time series).
The Climate Research Unit (CRU) of the University of East Anglia developed the CRU dataset. It consists of a climatology (New et al. 1999) and monthly anomalies to this climatology (New et al. 2000) at a global 0.5° resolution, of which monthly values for precipitation, temperature, cloud cover, and number of wet days per month are used for the present study. The dataset has recently been updated (CRU TS 2.1) (Mitchell and Jones 2005) for the years 1901–2002. CRU is chosen as our reference dataset because it provides a full forcing dataset to run the model (precipitation, temperature, number of wet days, and cloud cover).
Österle et al. (2003) showed that the time series of temperature and precipitation in the first CRU database that covers the period 1901–98 (New et al. 2000) were corrupted with inhomogeneities. These inhomogeneities were adapted for each grid cell using a correction procedure (Österle et al. 2003). To extend the data to 1999–2003, an earlier version of the Global Precipitation Climatology Centre (GPCC) data (described below) for each 1° × 1° grid cell was used and interpolated onto a 0.5° grid based on the correlations between the grid cells derived from the original CRU precipitation data between 1986 and 1998. The precipitation dataset that has been developed by Österle et al. (2003) is referred to herein as CRU–Potsdam–Institut für Klimafolgenforschung (CRU–PIK).
The global precipitation dataset (MW), developed by Matsuura and Willmott (2007), covers the period 1900–2006 and comprises monthly time series at 0.5° resolution. This precipitation dataset is based only on station data from several sources. Station climatology from the Legates and Willmott (1990) unadjusted (for rain gauge undercatch) archive were used as a part of the background climatology. Station precipitation values were not adjusted to reduce rain gauge undercatch bias. The stations were not checked for temporal heterogeneities because the main goal of this dataset was to represent spatial patterns of rainfall rather than homogenous time series.
The most recent version of the GPCC global precipitation dataset (Beck et al. 2005) consists of monthly precipitation fields on a 0.5° grid for the period 1951–2000. The dataset is based only on station observations that have met high demands concerning the quality and temporal coverage; therefore, this dataset is mainly suitable to study temporal variability. Interpolation has been done using ordinary kriging.
The Global Precipitation Climatology Project (GPCP), which is a part of the Global Energy and Water Cycle Experiment (GEWEX), developed a monthly precipitation dataset for 1979–2003 (Adler et al. 2003). The resolution of this dataset is 2.5°. It is based on a previous version described by Huffman et al. (1997) and was derived by merging satellite and surface rain gauge data. The gauge data have been corrected for systematic errors using a monthly correction factor as derived by Legates (1987).
The Climate Prediction Center Merged Analysis of Precipitation (CMAP) is a dataset that comprises both pentad and monthly analyses of global precipitation (Climate Prediction Center 2008; Xie and Arkin 1997). Observations from rain gauges were merged with precipitation estimates from several satellite-based algorithms (infrared and microwave). The analyses were performed on a 2.5° grid and extend back to 1979. The dataset with monthly values is used here.
The global precipitation dataset developed by Adam et al. (2006) (ADAM) is based on a previous version of the Matsuura and Willmott database (Willmott and Matsuura 2001). This dataset has been adjusted to correct for systematic wind-induced undercatch and wetting losses from rain gauges (Adam and Lettenmaier 2003) as well as for orographic effects (Adam et al. 2006). The combination of both adjustments resulted in a net increase of 17.9% in global land precipitation, as compared to Willmott and Matsuura (2001). The monthly data is available on a 0.5° grid for 1979–99.
First, the precipitation datasets are analyzed. For each basin determined by the validation stations (described in section 2c), the mean annual precipitation for the overlapping period 1979–99 is derived for all seven precipitation datasets:
where Ps,c,m,y is the precipitation in dataset s, cell c, month m, and year y; Ac is the area of cell c, Ab is the area of the basin b, and n is the selection of cells that fall within the basin b. The GPCP and CMAP data are only available onto a 2.5° grid but were projected onto a 0.5° grid. No interpolation method was applied, but each 2.5° grid cell was divided in 25 grid cells of 0.5° with the same values.
The maximum mean annual precipitation per basin b is determined by
and the minimum mean annual precipitation is derived analogously.
The absolute range in precipitation, representing the absolute uncertainty, is then given for each basin by
The relative range in precipitation, which is representing the relative uncertainty in precipitation, is given by
The area-weighted relative uncertainty is calculated as
Subsequently the minimum and maximum of the mean annual precipitation calculations per basin are used to create the models’ precipitation forcing. This is done by using the minimum and maximum values calculated in Eq. (2), multiplied by the original CRU data for all basins:
The minimum precipitation forcing Pminc,m,y was created analogously.
Thus, this created input data that covers the range in precipitation estimates per basin but retains the spatial and temporal pattern of CRU. Two model runs were made to determine the resulting minimum and maximum simulated discharge for each basin.
For the uncertainty in seasonality of precipitation the same procedure was followed: for each precipitation dataset the mean seasonal [December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON)] precipitation for 1979–99 was derived for each basin. The minimum and maximum of those seasonal totals were used to scale the respective seasons of the CRU dataset.
It is not our aim to give a quality judgment on the precipitation data in this study. Therefore, the seven precipitation sets are all given equal weight, and the range of precipitation values derived from these sets is assumed to represent the uncertainty in precipitation.
Note that LPJmL is a dynamic vegetation model (see section 2d) in which the spatial pattern of vegetation is closely linked to that of precipitation. To initialize the carbon and water pools, the model has been spun up for 1000 years by repeating the CRU climate of 1901–30 before the transient simulations (refer to Sitch et al. 2003). To prevent differences in simulated discharge between the runs from arising due to factors other than precipitation (e.g., the changed vegetation), we kept the spatial pattern of CRU and only used the precipitation totals derived from the other datasets.
b. Other climate input
Other meteorological variables used to force the model are monthly temperatures, the number of wet days per month, and the average monthly cloud fraction per grid cell so as to calculate potential evapotranspiration. These variables are all taken from the CRU database (Mitchell and Jones 2005; New et al. 1999, 2000) and are used for all simulations in this study.
c. Validation basins and data
There are several global gridded drainage direction maps (Döll and Lehner 2002; USGS 2000; Vörösmarty et al. 2000b). To compare the modeled discharge with the observations in a basin, it is important that the contributing area reported by the discharge measuring station matches the contributing area upstream of the station as calculated by the river network. We, therefore, use the Simulated Tropical Network at 30-min spatial resolution (STN-30p) (Vörösmarty et al. 2000b) for the accumulation and routing of computed runoff and a subset of 663 discharge stations that were co-registered to this network (Fekete et al. 2000, 2002). From these, we have analyzed the 294 most downstream stations of nested basins (Fig. 1: four basins were eliminated because their gauges fell outside of the LPJmL land mask). The area covered by these stations is approximately 70% of the world’s actively discharging area (Fekete et al. 2002).
The 213 basins for which observation data are available (Global Runoff Data Centre 2007) for at least 5 years within the 1979–99 period are used to validate the model results with measured data.
d. Model description
We use the LPJmL dynamic global vegetation and water balance model (Bondeau et al. 2007; Gerten et al. 2004; Rost et al. 2008; Sitch et al. 2003) for the discharge simulations. LPJmL accounts explicitly for ecosystem processes such as the establishment, growth, and mortality of potential natural vegetation. In contrast to global hydrological models, it does not use a prescribed natural vegetation pattern but it dynamically computes (changes in) natural vegetation patterns from soil properties and climate. The vegetation competes for resources (water and light). The model calculates the full carbon and water balances, which are coupled, for example, through photosynthesis.
The LPJmL model uses a two-layered soil with a top layer of 0.5 m and a lower layer of 1 m thickness. The soil water balance is calculated daily, including precipitation, snowmelt, interception loss, soil evaporation, transpiration, percolation, and runoff. The total runoff is calculated as the sum of surface runoff from the top soil layer, subsurface runoff from the lower soil layer, and water percolating down through the lower soil layer. The surface and subsurface runoff are defined as the excess water above field capacity of the top and lower soil layers. Subsequently the runoff water is routed through the above-described gridded network with a constant velocity of 1 m s−1.
Gerten et al. (2004) evaluated the water balance of an earlier version of the model for a small set of basins and concluded that the model results for runoff and evapotranspiration agree well with the results reported by state-of-the-art global hydrological models. However, all models in that analysis showed systematic bias in many regions, for example, an overestimation in dry regions and an underestimation especially in high latitudes. Recently, LPJmL has been extended with a representation of prescribed agricultural land (Bondeau et al. 2007) as well as a routing (including lakes) and irrigation scheme (Rost et al. 2008). This latter version is used here, although the irrigation module was switched off.
1) Mean annual precipitation
At the global scale the seven precipitation datasets differ considerably in their global totals, although their interannual variability is largely similar (Fig. 2). The ADAM dataset gives substantially higher total land precipitation than the others, followed by GPCP. This can be explained by the application of correction factors for high elevation and snow-dominated areas in these datasets. The mean annual land precipitation estimates vary from 96 286 to 118 006 km3 yr−1 (743–926 mm yr−1) for the years 1979–99.
2) Mean annual precipitation per basin
Figure 3 shows the CRU mean annual precipitation as well as the relative range between the seven datasets for all basins [as Eq. (4)]. Although the largest absolute ranges can be seen in basins that have high precipitation (not shown), it is obvious from Fig. 3b that the largest relative ranges between the precipitation sets are found in mountainous and arctic regions and small catchments. This large uncertainty in precipitation in mountainous and arctic regions can be explained by the correction factors that have been applied in some datasets (ADAM and GPCP). The relative large ranges in small basins might be caused by the fact that variations between the datasets in the spatial distributions of precipitation are relatively more important for small basins, where it can be essential whether precipitation falls in a particular cell or a neighboring cell outside of the basin. In larger basins, those differences are more likely to average out over the total area. The weighted average precipitation range [Eq. (5)] per basin is 30%.
3) Seasonality in precipitation per basin
The absolute ranges in precipitation [derived as in Eq. (3) but with mean seasonal precipitation] per basin were found to be season dependent and to occur mainly in the wettest seasons (figure not shown). The mountainous arctic regions and small basins again show the largest relative ranges in precipitation in all seasons. Furthermore, the relative ranges in precipitation are largest in the Nordic basins (in the United States, Canada, Russia, northern Europe, and northern China) in winter. This is as expected because in this season most precipitation falls as snow, which is more difficult to measure (Adam et al. 2006). In ADAM and GPCP, a snow undercatch correction has been applied, which additionally explains the large variation among the different datasets. In summer the relative ranges are lower in those basins. For the other basins, the relative ranges in precipitation are more or less constant throughout the year.
Figure 4 presents the ranges in mean monthly precipitation for 16 basins (see locations in Fig. 1). It can be concluded from these graphs, as well as for the other 278 basins not shown here, that the differences between the precipitation datasets are caused by a relative shift in total precipitation. The patterns of monthly precipitation distribution are similar. [See also the online database for all other basins (http://www.climatexchange.nl/projects/JHM)]. There are no datasets that report the same mean annual precipitation values but do show a completely different distribution throughout the year. This can probably be explained by the fact that all datasets are partly based on the same station data, and the differences are caused by the interpolation and correction method applied and the additional sources used. The bias between the datasets cannot be traced back to one particular season, except for the basins where an undercatch correction has been performed. These basins show a relative higher precipitation uncertainty in the winter season compared to other seasons (e.g., in the Mackenzie and Volga river basins).
1) Mean annual discharge per basin
The mean annual discharge simulated by LPJmL forced with CRU precipitation is shown in Fig. 6a. From Figs. 5 and 6b, it is clear that ranges in precipitation (Fig. 3) translate into similar patterns of ranges in discharge but with higher relative numbers (cf. Fig. 3b with Fig. 6b). Large uncertainties in discharge can be seen in the northern basins in Europe, Asia, and North America and in the mountainous regions and small basins. The area-weighted average uncertainty [as Eq. (5) but with discharge values] in the mean annual discharge calculations is 90% and thus is three times higher than the average uncertainty in precipitation.
Figures 6c and 6d illustrate the basin sensitivity to precipitation uncertainty. Figure 6c shows the fraction of precipitation uncertainty that results in runoff uncertainty. In regions where this fraction is high, the absolute uncertainty in discharge is almost the same as the absolute uncertainty in precipitation. Physically this means that in those areas the evaporative demand is largely met and the soil is very moist, causing extra precipitation to add to runoff immediately. Basins in the tropics and in high latitudes show a higher fraction than basins in temperate regions.
In relative terms, however, for almost all basins the relative discharge uncertainty is larger than the relative uncertainty in precipitation (if sensitivity >1 in Fig. 6d). This implies that the relative precipitation uncertainty is amplified in the discharge calculations.
2) Seasonality in discharge
As expected, the basins that have a large uncertainty in the precipitation input also have a large resulting uncertainty in the estimated discharge in each season (Figs. 7a–d). However, there are some clear seasonal differences. In Europe, the relative uncertainty in summer discharge is lower than in winter, although absolute precipitation is larger in summer. In high-latitude basins the uncertainty in winter discharge is low, although the precipitation uncertainty is high in this season. The uncertainty in precipitation input leads to ranges in discharge of more than 75% in those high-latitude basins, except in winter (Fig. 7a).
In general, for all basins the precipitation uncertainty is translated into discharge uncertainty (Fig. 4). However, the largest uncertainty in precipitation and discharge do not always occur at the same time (Figs. 8a–d). In northern basins, the uncertainty in winter precipitation does not directly translate into a range in discharge. During the winter months precipitation is stored in the snowpack and only released as discharge in spring and/or summer. Large basins such as the Nile and the Amazon also show a shift of the uncertainty signal in time because of the time lag that the water needs to reach the outlet of the river.
c. Validation with observed discharge data
Figure 9a suggests that the LPJmL model produces too little streamflow in the high latitudes and too much streamflow in the tropical and some midlatitude basins. Assuming reliable input and validation data, it can be concluded that model calibration is necessary to compensate for the over- and underestimates, or that some processes need a better representation.
However, as shown in the previous sections, the precipitation input is very uncertain, so, before validation and calibration of the model, the uncertainties in streamflow caused by the input uncertainties should be taken into account. When forcing the model with the minimum and maximum of precipitation for each basin, we determined that for 95 out of the 213 basins the observed discharge falls within the ranges of uncertainty of the simulated discharge. For another 23 basins, the difference between the observed and closest simulated discharge is less then 10% (Fig. 9b). For tropical basins in Africa and the Mississippi basin, the model still tends to overestimate the streamflow compared to observations, even after accounting for the uncertainty in precipitation. However, it should be noted that that these overestimations are probably caused by the fact that neither evaporation from the stream nor water extraction for irrigation are taken into account in the model run, which are both very high in those basins.
Figure 10 shows for the individual seasons that, by accounting for the precipitation uncertainty, the observed value can often be captured, whereas the model would fail more often when using a single precipitation set (CRU). However, there are some seasonal differences in that the performance is somewhat better in spring and autumn months as compared to the two solstice seasons.
d. Additional results
The model runs and analyses have been done for all basins shown in Fig. 1. For researchers with a particular interest in specific basins, these results can be consulted online. The supplemental information contains a database with information on the interannual and intra-annual variations in precipitation in each river basin as derived from the described global precipitation datasets. The resulting ranges in discharge are calculated with the LPJmL model and compared with GRDC observations, if available.
4. Discussion and conclusions
The comparison of seven global gridded precipitation datasets on a basin scale results in absolute and relative ranges in mean annual precipitation. The absolute total and relative differences in precipitation between the datasets found here at basin scale are typically lower than those found for the grid scale, as analyzed by Fekete et al. (2004). This is because a lot of the spatial differences between the datasets is averaged out when summed over a larger area. However, at basin scale the precipitation estimates still differ a lot for some basins—especially in mountainous areas where precipitation measurement errors are large and spatial interpolation is more difficult and in high latitudes where datasets not corrected for systematic wind-induced undercatch tend to underestimate the total precipitation (Adam and Lettenmaier 2003). Areas with low precipitation uncertainty typically have simpler topography, are not snow dominated, and have a dense precipitation network. Furthermore, the precipitation datasets follow the same seasonality pattern so that the main differences are in total rather than in temporal distribution of the precipitation. Exception to this pattern occurs in high-latitude basins where the uncertainty in the snow-dominated winter season is larger than in other seasons.
Our results show that the uncertainty in precipitation has a significant impact on discharge estimations. Typically, the uncertainty in precipitation propagates in larger relative uncertainty in discharge calculations. Although the relative precipitation uncertainty does not change a lot during the year, the resulting discharge uncertainty does sometimes show seasonal differences. In regions where the precipitation is stored as snow in winter and released as runoff in spring, the uncertainty in winter and spring precipitation leads to a large discharge uncertainty in spring.
This quantification of the large uncertainty in discharge calculations resulting from precipitation input uncertainty is important for hydrological modelers who estimate current or future water resources, for example, studies to be conducted in the European Union Integrated Project Water and Global Change (WATCH) (available online at http://www.eu-watch.org). It makes proper validation ambiguous and calibration difficult. Most current model calibration strategies ignore this input uncertainty and estimate model parameters based on one precipitation dataset as if the precipitation was known exactly (e.g., Döll et al. 2003; Nijssen et al. 2001), possibly leading to erroneous parameter estimates and simulation results (Kavetski et al. 2002; Vrugt et al. 2005).
Discharge estimations as simulated by the LPJmL model show that including precipitation uncertainty results in a discharge uncertainty that overlaps the observed value in 95 out of 213 basins. For 23 basins the observed discharge differs less than 10% from the simulated range. Under the assumption that all precipitation datasets have the same quality and their range reflects the uncertainty, for these basins a calibration cannot improve the model results. For the other basins, where forcing the model with the different precipitation sets leads in all cases to an under- or overestimation, a calibration could improve the simulated discharge. However, it is also possible that missing processes are causing the under- or overestimations. For example, for African basins the observed overestimation might be explained by the evaporative losses from stream and irrigation extractions that are not represented by the model. Another missing process that is significantly altering streamflow patterns is the operation of large reservoirs.
Because calculated discharge is to such a large extent dependent on uncertain input data, it might not be useful to calibrate a model with one particular dataset. This would give a false impression of the performance of the model. After calibration, the model seems to a large extent able to reproduce the observed discharge in river systems throughout the world. However, using a different input dataset gives other model results, thus using a different input dataset to calibrate the model could possibly lead to very different calibration parameters and, therefore, different hydrological behavior of the model.
There are three possible approaches to account for this uncertainty in global hydrological modeling (schematically illustrated in Fig. 11) to be used for future projections. Because the precipitation datasets do not differ in their representation of seasonality, these simple approaches are justified.
The first possible solution would be to calibrate the model based on multiple datasets to find the possible parameter space for the calibrated parameters. This parameter space could subsequently be used to project future water resources as a range instead of a single number. Instead of performing a calibration seven times, the precipitation coefficients in Table 2 can be used to obtain the range in precipitation estimates for each basin. The coefficients reflect the uncertainty in precipitation among the seven datasets relative to CRU and can be applied to scale the CRU dataset. The parameter space can then be obtained by performing two calibrations—one on the resulting maximum dataset and one on the minimum dataset. Another way to explicitly disaggregate different sources of uncertainty in model calibration was developed by Vrugt et al. (2005) and Kavetski et al. (2006a). Kavetski et al. developed a method (Bayesian total error analysis) to account for input uncertainty in model calibration and applied this method to a hydrological model on catchment scale (Kavetski et al. 2006b). To our knowledge, no global hydrological model has been calibrated in this way, and further research is required to explore the applicability of this method to a global hydrological model.
The second option is not to calibrate but, instead, use the current model parameters and the uncertainty in precipitation to project water resources. It requires that the model parameters have physical meaning, which can be estimated from existing literature. Models that use physical parameters and have not been calibrated are MacPDM (Arnell 1999b), the water balance model (WBM) (Vörösmarty et al. 1998) and, as used here, LPJmL. To estimate the impact of precipitation uncertainty on discharge at least two model runs have to be performed, respectively with minimum and maximum estimates of precipitation. Because we have shown that the datasets show the same distribution of precipitation in time, the CRU data and precipitation coefficients derived in this study (Table 2) can be used. The minimum and maximum precipitation datasets can be obtained by multiplying the CRU values with the coefficients in Table 2 for the required basins, as done in this study.
The third option is to apply the results from the analysis presented in this paper in discharge estimations as uncertainty bands. Under the assumption that using another model for this analysis would not significantly change the results, the basin uncertainty estimations for discharge can be obtained by multiplying the model results with the coefficients in the last columns of Table 2. These coefficients can be applied to any model result to present the uncertainties in discharge resulting from precipitation uncertainty, on the condition that the model has been run, forced with CRU precipitation data. The advantage of this option is that only one model run is required, and the uncertainty in results is estimated as a postprocessing procedure.
A general conclusion of this paper is that a deterministic approach, such as it is often used in water resources research, is too simplistic. The range of uncertainty in input data has a large influence on the output and may not be neglected in the communication of results. This is even more true when modeling water resources under climate change because the uncertainty in future precipitation produced by different climate models is even larger than the uncertainty in historical data (Meehl et al. 2007). Therefore, it would be better to change to a probabilistic way of presenting results and projections of future water resources.
In this paper we have chosen not to give a quality judgment of the precipitation datasets, but to give them equal weight in the analysis. An additional study may reduce the precipitation uncertainty by eliminating the datasets known to be of less quality. However, this paper clearly shows the need for more accurate precipitation datasets to be used for forcing hydrological models.
The authors thank three anonymous reviewers for their useful comments on an earlier version of this paper. The Global Runoff Data Centre is acknowledged for the provision of global discharge data.
Corresponding author address: H. Biemans, Earth System Science and Climate Change, Wageningen University and Research Centre, P.O. Box 47, Wageningen 6700 AA, Netherlands. Email: firstname.lastname@example.org