1. Introduction

In a steady state, precipitation P exceeds evaporation E (or evapotranspiration) over land and the residual water runs off and results in a continental freshwater discharge into the oceans. Within the oceans, surface net freshwater fluxes into the atmosphere are balanced by this discharge from land along with transports within the oceans. The excess of E over P over the oceans results in atmospheric moisture that is transported onto land and precipitated out, thereby completing the land–ocean water cycle. While E and P vary spatially, the return of terrestrial runoff into the oceans is mostly concentrated at the mouths of the world's major rivers, thus providing significant freshwater inflow locally and thereby forcing the oceans regionally through changes in density (Carton 1991; Nakamura 1996).

To study the freshwater budgets within the oceans, therefore, estimates of continental freshwater discharge into the ocean basins at each latitude are needed. Baumgartner and Reichel (1975, BR75 hereafter) derived global maps of annual runoff and made estimates of annual freshwater discharge largely based on streamflow data from the early 1960s analyzed by Marcinek (1964). Despite various limitations of the BR75 discharge data (e.g., rather limited station coverage, areal integration over 5° latitude zones, no seasonal values), these estimates are still widely used in evaluations of ocean and climate models (Pardaens et al. 2002) and in estimating oceanic freshwater transport (Wijffels et al. 1992; Wijffels 2001), mainly because there have been few updated global estimates of continental discharge. The primary purpose of this study is to remedy this situation.

Correct simulations of the world river system and its routing of terrestrial runoff into the oceans has also become increasingly important in global climate system models (Miller et al. 1994). For evaluating climate models, a few streamflow datasets have been compiled (e.g., Dümenil et al. 1993), although many studies included only 50 or so of the world's largest rivers. Other approaches (e.g., Hagemann and Gates 2001) utilize daily precipitation and parameterized evaporation to compute runoff that is then fed into a hydrological discharge model. This approach makes no use of actual measurements of discharge. Perry et al. (1996) gave an updated estimate of annual-mean river discharge into the oceans by compiling published, gauge-data-based estimates for 981 rivers. However, although they used the farthest downstream gauges, the distances to the river mouths ranged from 100 to 1250 km and they made no adjustments for this. They estimated the contributions from ungauged small rivers by fitting a power law to the dataset and extrapolating.

For years hydrologists have been improving terrestrial runoff fields. One such example is the work by Fekete et al. (2000, 2002), who used a global river discharge dataset from the Global Runoff Data Centre (GRDC) coupled with a simulated river network and a water balance model to derive a set of monthly global maps of runoff at 0.5° resolution. This merging approach offers the best estimate of the geography of terrestrial runoff, with the magnitude of runoff constrained by the observed discharge, while at the same time preserving the spatial distribution of the water balance. For oceanic water budget analyses, however, only the discharges at coastal river mouths are of interest. To estimate continental discharge using the runoff fields, a river transport model that routes the terrestrial runoff into the correct river mouths is needed. Alternatively, estimates can be made from gauge records of streamflow (e.g., Grabs et al. 1996, 2000), but then the issue of ungauged streams has to be addressed and extrapolation from the gauging station to the river mouth is needed. To our knowledge, neither of these approaches has been done thoroughly in estimating continental discharge, and much improved estimates are the main purpose of this study.

In a steady state, P–E is a good proxy of runoff over land (BR75). Short-term P–E may, however, differ from runoff because of changes in storage and, in particular, snow accumulation and melt and infiltration of water into the ground. On a day-to-day basis, runoff greatly depends upon the frequency, sequence, and intensity of precipitation and not just amount, as these factors alter the extent to which water can infiltrate and be stored in the soil. Changes in soil moisture can be important, and it is only on annual and longer timescales that conditions may approximate a steady state.

Another problem is human interference with the natural water flows. The mining of groundwater effectively changes the subterranean water storage, although it is offset to some extent by the filling of surface reservoirs. The biggest human influence comes from irrigation and water usage, although this should be reflected in the P–E used in this study, which was derived from atmospheric moisture budget analyses. For the Mississippi River basin, for instance, Milly and Dunne (2001) estimate precipitation as 835 mm yr⁻¹ and total evaporation as 649 mm yr⁻¹, of which consumptive use contributes 12 mm yr⁻¹ (1.8%); surface reservoir filling provides a loss of 1 mm yr⁻¹; and groundwater mining adds 2 mm yr⁻¹. Overall, the changes in storage over land, such as in lakes and reservoirs, and through melting of glaciers are manifested as changes in sea level. Estimates of glacier contributions are 0.2 to 0.4 mm yr⁻¹ and terrestrial storage −1.1 to 0.4 mm yr⁻¹ (Church et al. 2001). Note that 1 mm yr⁻¹ globally is equivalent to a volume of 357 km³ yr⁻¹ and is approximately the mean annual flow of the river Amur in Russia (Table 2). Nevertheless, these values are small compared with regional P–E values.

Substantial problems still exist in analyzed fields of precipitation and evaporation based upon four-dimensional data assimilation (Trenberth and Guillemot 1996, 1998; Trenberth et al. 2001b; Maurer et al. 2000). In fact problems exist in all precipitation products (e.g., Yang et al. 2001; Adler et al. 2001; Nijssen et al. 2001), and evaporation is not measured but can only be estimated from bulk formulas. Potential evapotranspiration is measured from pans, but is not a measure of actual evaporation, and over the United States, estimated trends in actual evaporation and pan evaporation are opposite (Milly and Dunne 2001) because increased clouds reduce the latter, while increased soil moisture from increased precipitation (associated with the cloud increase) increases the availability of moisture for evaporation. Therefore, we believe that the P–E used here, which was computed as a residual of the atmospheric moisture budget, is potentially much more promising.

Relatively new P–E estimates were derived from the atmospheric moisture budget based on the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR, NCEP hereafter) reanalyses (Kalnay et al. 1996) by Trenberth and Guillemot (1996, 1998) and the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-15 reanalyses (Gibson et al. 1997) by Trenberth et al. (2001a). New P–E estimates will also be produced for the ERA-40 reanalyses that are under way. One test for the P–E fields is to compute the implied continental discharge and compare with that derived from gauge data. Unfortunately, the results using model-based P and E are not good (Oki 1999) because these are purely model-predicted fields. Although not problem free, P–E estimates as a residual of the atmospheric moisture budget are better partly because atmospheric wind and moisture fields were calibrated every 6 h by atmospheric sounding and satellite observations in the reanalyses. They depend critically on atmospheric low-level divergence fields, which have considerable uncertainties, but small-scale errors naturally cancel as averages are taken over larger areas, and the global mean is guaranteed to balance. If the reanalysis data are evaluated to be reliable for estimating continental discharge, then they can be applied¹ to study the interannual to decadal variations of continental discharge because the reanalysis data are, or will be, available for the last 40–50 yr, and are likely to be updated regularly. This could become a valuable application of the reanalysis data given that many rivers have no or only short records of streamflow and that there has been a widespread decline in the number of river gauges during the last few decades (Shiklomanov et al. 2002).

In this study, we analyze station records of streamflow for 921 of the world's largest rivers to provide new estimates of long-term mean annual and monthly continental freshwater discharge into the oceans through each 1° latitude × 1° longitude coastal box. We make use of the composite runoff fields of Fekete et al. (2000, 2002), a state-of-the-art database of the world river network, and a river transport model (RTM) to translate information from the farthest downstream station to the river mouth, and to estimate contributions from unmonitored river basins. We also derive continental discharges using RTM simulations forced with various estimates of terrestrial runoff, including P–E from the reanalyses from NCEP–NCAR and ECMWF. Hence we compare the runoff-implied continental discharges with the gauge-based estimate.

Our goal is to update and improve the continental discharge estimates of BR75 and provide an evaluation of the P–E fields from the reanalyses, and at the same time provide useful data (e.g., river mouth flow rates) for climate model evaluations. The continental discharge can then be applied to produce detailed estimates of mean meridional freshwater transport by the oceans that can also be used in climate and ocean model evaluations.

2. Datasets

We used a number of observational and reanalysis data sets in this study, as listed in Table 1 and described below. The P–E data were remapped onto the 0.5° grid for driving the RTM.

Gauge records of streamflow rates are the basic data for estimating continental discharge. We used monthly streamflow datasets compiled by Bodo (2001) and others that are archived at NCAR (ds552.1, ds553.2, ds550.1; available online at http://dss.ucar.edu/catalogs/ranges/range550.html), together with the R-ArcticNET v2.0, a dataset created by C. J. Vörösmarty [University of New Hampshire (UNH)] et al. (online at http://www.R-ArcticNET.sr.unh.edu) that contains streamflow data for the Arctic drainage basins. These datasets were created using various sources of streamflow data, including those collected by the United Nations Educational Scientific and Cultural Organization (UNESCO), the United States Geological Survey (USGS), UNH, Russia's State Hydrological Institute, the GRDC in Germany (only an earlier version of its collection), and many national archives such as those for South American nations. Data quality controls were applied during the compilation, primarily for errata and inconsistencies in metadata. Undoubtedly, errors and discrepancies remain, although the majority of the streamflow records are thought to have an accuracy to within 10%–20% (Fekete et al. 2000).

After eliminating duplicate stations (mainly through locations), there were 8878 gauge records of monthly mean river flow rates with varying lengths, ranging from a few years to over 100 yr. The latest year with data is 2000, although most records end earlier (many in the 1990s). For estimating continental discharge, we selected 921 near-coastal (i.e., the farthest downstream) stations (Fig. 1) from this merged global streamflow dataset using a procedure described in section 3. Most of the selected stations are close to river mouths and have 10 or more years of data, although a few of them are located far from the ocean [e.g., Niger (∼1000 km), Mekong (∼850 km), Irrawaddy (∼800 km)] or have only a few years of data that may not be representative of long-term means (cf. Table 2 and the appendix). The mean streamflow and drainage area data from these coastal stations were used to derive the river outflow into ocean at the river mouth, as described in section 3. Because of the varying time periods of records, the mean river flow rates derived from these gauge records may be inconsistent temporally among the rivers.

To derive estimates of continental discharge independent of those based on the streamflow records and to estimate the discharge from the land areas that were not monitored by the gauges, we used the composite monthly and annual runoff fields of long-term means of Fekete et al. (2000, 2002). Although only 663 gauges were used and biases are likely over regions with little calibration, their composite fields at 0.5° resolution probably represent one of the best estimates of terrestrial runoff currently available.

We used the P–E fields derived from atmospheric moisture budget analyses based on the NCEP reanalyses for 1979–95 (Trenberth and Guillemot 1998) and ECMWF reanalyses for 1979–93 (Trenberth et al. 2001a). These data are available online from NCAR's Climate Analysis Section catalog (http://www.cgd.ucar.edu/cas/catalog/). We did not use the individual E and P fields from the reanalysis products.

We also used monthly and annual precipitation over land, derived by averaging the Climate Prediction Center Merged Analysis of Precipitation (CMAP) and the Global Precipitation Climatology Project (GPCP) climatology (Table 1). These products are based mainly on rain gauge measurements over land and, therefore, depend on the distribution of gauges. In many open areas this is adequate, but it is typically inadequate in mountainous areas, where gradients of precipitation are very large. Much more detailed estimates of precipitation by the Parameter-elevation Regressions on Independent Slopes Model (PRISM) at resolution of 2.5′ for the United States by Daly et al. (1994) have been compared with GPCP results by Nijssen et al. (2001), who found substantial discrepancies, usually underestimates of precipitation, over mountains in GPCP. Nevertheless, the CMAP- and GPCP-averaged precipitation was used to compute the river-basin-integrated precipitation and to help evaluate the P–E products.

For estimating snow effects on the annual cycle of runoff, we used a simple scheme that requires daily surface air temperature. The latter was interpolated from the New et al. (1999) monthly climatology.

To perform areal averaging and integration and to obtain estimates of drainage area for individual river basins, a database for the world river network is needed. We used the simulated river database STN-30p (Vörösmarty et al. 2000), a global simulated topological network at 30′ spatial resolution. The STN-30p contains 397 named large river basins and 5755 unnamed small river basins for the world river network. In this database, each 0.5° cell of land surface belongs to a river basin. The database includes, among others, the upstream drainage area for each cell and the exact location where the runoff generated in any given cell enters an ocean or sea.

3. Analysis procedure

b. Estimating continental discharge

1) Discharge based on station data

To estimate continental discharge into each ocean basin at each latitude from the station data of streamflow, one can sum up the river outflow within each latitude band for each ocean basin. Before this can be done, however, we need to estimate the streamflow at the river mouth from the coastal station data and the contributions from rivers (or drainage areas) that are not monitored by the stations.

Although most of the selected coastal stations are close to river mouth, it is rare that a gauging station is right on the coast. For many rivers (e.g., Niger, Mekong, Amazon), the farthest downstream stations available are quite distant from the coast and thus streamflow measurements are not representative of the actual outflow into ocean. Although including the contributions separately from the rivers that enter downstream partly solves the problem (e.g., for Amazon), many downstream rivers are not monitored.

We used an RTM to estimate river mouth outflow from the upstream station data. The RTM was developed by M. L. Branstetter and J. S. Famiglietti and is described by Branstetter (2001) and Branstetter and Famiglietti (1999). The RTM is used in the NCAR Community Climate System Model (CCSM; Blackmon et al. 2001) for routing surface runoff into the oceans. Using a linear advection scheme at 0.5° resolution, the RTM routes water from one cell to its downstream neighboring cell by considering the mass balance of horizontal water inflows and outflows (Branstetter 2001):

View Expanded

where S is the storage of stream water within the cell (m³), F_out is the water flux leaving the cell in the downstream direction (m³ s⁻¹), ΣF_in is the sum of inflows of water from adjacent upstream cells (m³ s⁻¹), R is the runoff generated within the cell (m³ s⁻¹), υ is the effective water flow velocity [=0.35 m s⁻¹, following Miller et al. (1994)], and d is the distance between centers of the cell and its downstream neighboring cell (m).

The water flow direction is one of eight directions chosen as the downstream direction for each cell, based on the steepest downhill slope. Note that stream channel losses to groundwater recharge, reservoirs, and irrigation are not included in this version of the model. Tests showed that the choice of υ only affects the time for the model to reach an equilibrium under a constant runoff field. This time is about 6 months with υ = 0.35 m s⁻¹ (for the Amazon) starting from empty river channels. We used the river flow rates after 200 model days in annual simulations, and used the data of the second year in monthly simulations.

To simulate the annual-mean streamflow of the world river systems, we forced the RTM with the annual runoff from Fekete et al. (2000, 2002). In general, this simulation, which was run with daily time steps, produced comparable river flows at the coastal stations of most major rivers (see Table 2 and the appendix). We used the ratio of the simulated streamflow at the river mouth to that at the farthest downstream station to scale up (on monthly and annual timescales) the observed station flow as the river mouth outflow (vol in the tables) for the world's top 200 rivers listed in Table 2 and the appendix. In some cases (e.g., no. 23 Uruguay and no. 29 Essequibo in Table 2), where this simulated-flow ratio was unreasonable (<0.9, or >2.0 except for Niger), we instead used the ratio of drainage areas (based on STN-30p) at the river mouth to that at the station for the scaling. The estimated river mouth outflow was then used to compute continental discharge. All branch rivers above the mouth of the main river channel were excluded in this calculation. These excluded branch rivers are no. 12 Tapajos, no. 18 Xingu, no. 52 Bénoué, no. 60 Chindwin, no. 89 Red, no. 105 Jari, and a few smaller rivers. For other smaller rivers, not listed in Table 1 and the appendix, station streamflow was treated as river mouth outflow and used in estimating continental discharge. The use of the river mouth outflow increases the estimates of the global continental discharge by 18.7% and the total monitored drainage area by 20.4%.

The total drainage area monitored by the 921 ocean-reaching rivers (at river mouths) is 79.5 × 10⁶ km², which accounts for about 68% of global nonice, nondesert land areas [≈117 × 10⁶ km²; Dai and Fung (1993)]. Therefore, approximately one-third of the world's actively drained land area is not monitored by the available gauging stations. Earlier studies (e.g., Marcinek 1964) estimated runoff from these unmonitored areas on the basis of comparable regions (i.e., nearby regions having runoff data). Fekete et al. (2000) showed that simply using the ratio of global actively drained area to the monitored area to scale up the global continental discharge estimate resulted in a number (28 700 km³ yr⁻¹) that was too low compared with other estimates. Perry et al. (1996) used a power law size distribution found for large rivers to estimate the total contribution from all small rivers.

Here we made use of the ratio of runoff (based on Fekete et al. 2000) between unmonitored and monitored areas to account for the contribution of the unmonitored areas to continental discharge using the following formula:

RjR₀jrjA_ujA_mj(2)

where R(j) is the continental discharge for 1° latitude zone j (for individual ocean basins), and R₀(j) is the contribution from the monitored areas only (i.e., the sum of river mouth outflow for all rivers with data within latitude zone j); A_u(j) and A_m(j) are the unmonitored and monitored drainage areas, respectively, whose runoff enters ocean in latitude zone j (i.e., A_u and A_m may be outside latitude zone j), and r(j) is the ratio of mean runoff over A_u and A_m. Equation (2) was first applied to individual ocean basins. To create the discharge from individual 1° coastal boxes, the contribution from A_u was further partitioned into the individual coastal boxes within the 1° latitude zone j for each ocean basin based on the allocation of A_u on the coasts. For display purposes, the 1° discharge was aggregated onto a 4° latitude × 5° longitude grid. Note that there are inconsistencies in Table 2 and the appendix between the two drainage areas listed, as the station drainage area comes from the station datasets while the river mouth drainage area comes from STN-30p; presumably the latter should be greater.

In this calculation, the coastal outflow location for the runoff generated over each 0.5° land cell was first derived based on STN-30p, and the runoff over A_u is put into the ocean at the correct location. Here, r(j) was computed using monthly and annual runoff fields from Fekete et al. (2000). It was found necessary to smooth r(j) over 4° latitude zones, because for narrower zones A_m can be zero or small. These r(j) values were then used in monthly and annual calculations of R(j) at 1° latitude resolution. Typical values of r(j), together with A_u(j)/A_m(j), averaged over the drainage area of each ocean basin, are shown in Table 3. The value of r(j) varies from 0.29 for the Indian Ocean in July, owing to very dry unmonitored regions in the summer monsoon, to 4.30 for the Pacific Ocean in January, where the unmonitored wet regions of Indonesia come into play. For the global land areas, however, this ratio is close to one, which supports the notion that the unmonitored landmass as a whole is unlikely to be significantly wetter than the monitored land areas (Fekete et al. 2000). Table 3 also shows that the drainage areas into the Atlantic and Arctic oceans are well monitored by the 921 river network, while the monitoring network is poor for the Indian Ocean [partly due to large unmonitored arid areas where r(j) is small and thus has little effect on R(j); cf. Fig. 1]. Globally, the unmonitored areas (including arid regions) account for about half of the monitored areas, or one-third of the total drainage areas.

Implicit in our approach is that we are dealing with the actual flows into the oceans, not the natural flows that would occur without dams and other interference by humans. This aspect does causes complications because comparisons with climate models that do not include or allow for effects of human interference should expect discrepancies. The gauge records reflect the actual flow, regulated or not, and as this may well have changed over time, the more recent records may differ from those of previous decades. Moisture from irrigation can be evaporated, which should be reflected in measurements of atmospheric moisture and thus in our P–E estimates.

Compared with earlier studies, our method for estimating the discharge from the unmonitored areas has some unique features that should improve our station-data-based estimate of continental runoff. For example, it makes use of runoff information over the monitored and unmonitored areas. It also integrates the runoff from the unmonitored areas and puts it into oceans at correct locations with the help of the river database. Most earlier studies merely scale up the global total discharge derived from the monitored areas and fail to do this geographically.

2) Discharge based on runoff fields

Continental discharge can also be estimated based on runoff fields. BR75 used the runoff field (in mm) derived by Marcinek (1964) to estimate continental discharge for each 5° latitude zone using simple areal integration. However, as many large rivers (e.g., Mississippi, Paraná, Nile, Niger, and most Russian rivers) flow mostly north–south, simple zonal integration of runoff does not provide correct estimates of continental discharge for a given latitude zone.

A substantial advance can be made by using the RTM to route the excess water (runoff) within each 0.5° cell into the ocean and then estimate continental discharge by totaling the simulated coastal river outflows within each 1° latitude zone. Maps of coastal discharges at 1° and 4° latitude × 5° longitude resolution were obtained from the RTM simulations. Three different runoff fields were used: (i) the composite runoff fields of Fekete et al. (2000), and runoff estimated using the multiyear mean monthly and annual P–E fields from the (ii) NCEP and (iii) ECMWF reanalyses (Table 1). Daily runoff was interpolated from monthly mean fields and used to drive the RTM. These discharge estimates provide additional checks for the gauge-based estimate, as well as an evaluation of the reanalysis P–E fields.

Fekete et al. (2000) simulated snow accumulation and melt using some simple empirical equations in producing the composite runoff. We adopted a simple scheme from Haxeltine and Prentice (1996) to simulate the effects of snow on runoff in using the monthly P–E from the reanalyses for driving the RTM. The climatological daily surface air temperature (t_d in °C), interpolated from the monthly climatology of New et al. (1999), is compared with a constant t_s. When t_d < t_s, then positive P–E accumulates as snowpack and runoff is zero; if t_d > t_s, then snow melts at a rate sm (mm day⁻¹) = k (t_d − t_s), where k is a constant in millimeters per (day °C). Haxeltine and Prentice (1996) used −2.0°C for t_s and 0.7 for k. We tested a number of values for these two parameters in order to produce the best match between the simulated and observed annual cycle of continental discharge and selected 0.0°C for t_s, which is physically reasonable, and 0.7 for k. In reality, of course, temperatures vary considerably within a month, so that even if the monthly mean is less than 0°C, several days could be above that threshold, but the simplification we use is consistent with the other shortcomings in approximating runoff by mean P–E, rather than employing hourly, or at least daily, data to properly deal with issues discussed in the introduction.

4. Comparison among runoff estimates

To help understand discharge differences discussed below, we first compare annual means of the Fekete et al. runoff and the P–E derived from the NCEP and ECMWF reanalyses. Figure 2 shows the annual-mean runoff from Fekete et al. (2000), the P–E fields, and the mean precipitation (average of CMAP and GPCP) (left column), together with the implied E (i.e., the precipitation minus the runoff or P–E) and the difference between the NCEP and ECMWF P–E (right column). First, both the NCEP and ECMWF P–E fields show negative values over many regions of all continents, especially in central and western Asia and northern Africa. While it is physically possible to have negative P–E over land (e.g., due to water flowing into the region, groundwater mining, and evaporation from reservoirs and lakes), negative P–E cannot be used as runoff. Some of these regions indicate deficiencies in P–E arising from insufficient atmospheric observations (especially in Africa). We set the negative annual P–E to zero in forcing the RTM. The negative P–E over many coastal areas, such as eastern Africa, appears to result from extensions of oceanic P–E patterns. This problem may stem from the relatively low horizontal resolution of the reanalysis P–E. On the other hand, some regions, such as southern California, are heavily irrigated using, for instance, water from aqueducts. As a result, negative P–E values are plausible.

Second, the implied E for both the P–E fields and, to a smaller extent, the Fekete et al. runoff, has negative values over a number of land areas. Some of these negative values of E suggest that the Fekete et al. runoff and the P–E are too large since the CMAP and GPCP precipitation climatologies are generally reliable over nonmountainous land areas and they cover similar data periods (Table 1). These areas with negative E (especially nonmountainous areas), together with those land areas with negative P–E for the reanalyses cases, contribute to errors in estimating continental freshwater discharge.

Third, substantial differences exist on regional scales over both land and ocean between the P–E fields derived from the NCEP and ECMWF reanalyses, even though the large-scale patterns are comparable. While the difference patterns are noisy, the NCEP P–E is generally lower than the ECMWF P–E over the southern subtropical (20°–40°S) oceans, the eastern Pacific and the Atlantic around 3°–12°N, and much of the western North Atlantic. Over the continents, the NCEP P–E also has a dry bias compared with the ECMWF P–E. On the other hand, the ECMWF ERA-15 reanalysis data have a major problem over Africa, namely a spurious southward shift of the intertropical convergence zone (ITCZ) after 1987 (Stendel and Arpe 1997; Trenberth et al. 2001b).

The implied E fields are spatially correlated with the precipitation field, with the correlation coefficient r ranging from 0.66 to 0.79 over land and slightly lower over ocean for the reanalysis cases. This is expected since precipitation provides the main water source for evaporation over most land areas.

5. Freshwater discharge from the world's major rivers

Table 2 and the appendix present the annual-mean river flow rate and drainage area at the farthest downstream station and the river mouth for the world's largest 200 rivers. The river mouth flow was estimated using the method described in section 3b. The drainage area at the river mouth was estimated using the river database STN-30p. The river flow simulated at the station by the RTM forced with the annual runoff field of Fekete et al. (2000) is also shown next to the observed volume.

Many of the world's largest river systems, with the exception of the Yenisey, Lena, Ob, and Amur, are located at low latitudes, where precipitation rates are highest. River discharge in general increases with drainage area, but the river flow to drainage area ratio varies from about 1 km³ yr⁻¹ per 1000 km² in the Tropics (equivalent to P–E of 1 m yr⁻¹) to less than 0.1 km³ yr⁻¹ per 1000 km² in high latitudes and dry areas.

The total global freshwater discharge, excluding that from Antarctica, is about 37 288 ± 662 km³ yr⁻¹ (Table 4), which is ∼7.6% of global precipitation or 35% of terrestrial precipitation (excluding Antactica and Greenland) based the averaged precipitation of CMAP and GPCP. Since a time series of global discharge is not easy to derive because of a changing number of gauges, this uncertainty range was estimated as the square root of the sum of the variance of long-term mean annual flows at the farthest downstream stations of all the 921 rivers multiplied by 1.187, the global-mean factor for converting the farthest downstream station flows to the river mouth outflows. Hence it is based on the assumption that the covariance of streamflow among large rivers is small. The world's 50 largest rivers (Table 2) account for ∼57% of the global discharge, while their total drainage area is ∼43% of the global actively drained land areas (i.e., excluding glaciers and deserts). Adding the next 150 largest rivers (the appendix) increases these to 67% and 65%, respectively, while adding the next 721 rivers in our dataset of coastal stations changes the numbers only moderately (to 73% and 68%, respectively). This suggests that an increasingly large number (in the thousands) of smaller rivers are needed to improve the coverage of the station network for monitoring global freshwater discharge.

Table 2 and the appendix show that the farthest-downstream station data underestimate—by 10% to over 100%—the river discharge and drainage area at the river mouth in many cases (e.g., Amazon, Orinoco, Mississippi, Paraná, Mekong, Irrawaddy, St Lawrence, and Niger). Most earlier estimates of streamflow and drainage area for the world's largest rivers used unadjusted data from the available farthest downstream station (e.g., Probst and Tardy 1987; Perry et al. 1996; Grabs et al. 1996, 2000). These unadjusted estimates not only underestimate the true river outflow, but also contribute to the large range among various estimates of flow rate for world's major rivers because the distance from the farthest downstream station to the river mouth varies among different studies from hundreds to thousands of kilometers (Perry et al. 1996). For example, Perry et al. (1996) listed the Amazon with a mean flow rate of 6088 ± 465 (std dev) km³ yr⁻¹ based on 11 different sources, while it is 6000 km³ yr⁻¹ in BR75. Although these are higher than our mean flow rate (5330 km³ yr⁻¹) at station Obidos, they are about 10% lower than our estimate of Amazon mouth flow (6642 km² yr⁻¹).

When forced with the annual runoff from Fekete et al. (2000), the RTM simulates the station flow rates reasonably well for most major rivers (Fig. 3a, also see Table 2 and the appendix). This suggests that both the Fekete et al. runoff and the RTM routing scheme are likely to be correct over most regions. However, problems are evident over a few river basins such as the Nile (no. 83) and Zambeze (no. 36), where the RTM greatly overestimates the river channel flow. For the Nile, river channel water losses due to evaporation and human withdrawal contribute to the smaller-than-simulated flow rate. The drainage areas derived from the STN-30p are close to those given in the station datasets (Fig. 3b), except for a few cases (e.g., Zambeze) where drainage areas from the streamflow datasets are likely to be incorrect, as the STN-30p provides one of most reliable estimates for the total drainage areas of world's largest rivers.

When the RTM is forced by the P–E fields derived from the NCEP and ECMWF reanalyses, the simulated station flow rate generally agrees with the observed at most of the major rivers (Fig. 4). Substantial differences exist, however, for the world's largest rivers. For example, the simulated flow rate is 3063 and 3833 km³ yr⁻¹ for the Amazon at Obidos in the NCEP and ECMWF cases, respectively, where the observed rate is 5330 km³ yr⁻¹. In general, the Fekete et al. runoff resulted in better simulated station flow rates, especially for the world's largest rivers.

The third column in Table 2 and the appendix lists the standard deviation (std dev) of year-to-year variations of river flow rate at the farthest downstream station. It can be seen that for the large rivers the std dev is ∼10%–30% of the mean flow. This ratio increases to over 100% for smaller rivers (the appendix), suggesting that streamflow rates of small rivers are much more variable from year to year than those of large rivers. This result arises because river flow rates are areal integrals of surface runoff and an integral over a larger basin is usually less variable than one over a smaller region.

The streamflow of many rivers has a large annual cycle. Figure 5 compares the mean annual cycle of discharge (thick, solid curve) with those of basin-integrated precipitation (thin, solid curve), runoff, and P–E for the 10 largest rivers. Note that the RTM is not used in these basinwide summation and therefore the differences between the river discharge and the basin-integrated values illustrate the effects of snow and the time delay of water traveling downstream to the river mouth. The Amazon has the highest flow from May to June, while its basin-integrated precipitation, runoff, and P–E peak in early spring. This lag reflects the time needed for surface runoff to travel to the river mouth. For the Changjiang, Brahmaputra/Ganges, Mississippi, Mekong, and smaller rivers, this time lag is shorter (about 1 month or less), suggesting that the seasonal changes in surface runoff occur in the area not far away from the river mouth. The Congo and Paraná have relatively small annual cycles, even though precipitation and runoff (for Paraná only) exhibit large seasonal variations. There are several reasons for this to happen. First, evaporation positively correlates with precipitation and thus reduces the seasonal variation of surface runoff, which is the case for the Congo. Second, for large rivers like the Paraná, which runs through different climate zones, regional variations of surface runoff within the river basin, combined with the time lag due to river channel transport, tend to compensate and thus reduce the seasonal variation of downstream river flow. More fundamentally, the relative uniformity of river flows throughout the year in spite of large precipitation variations is a sign of large and diverse lags and obstructions, such as lakes, that help smooth out and regulate the flow.

The big Russian rivers (Yenisey, Lena, Ob, etc.) have large peak flows in June, which result from spring (April–May) snowmelt as precipitation does not peak until July–August in these regions (Fig. 5). In fact, the drainage-area-integrated discharge and precipitation for the entire Arctic region (cf. Fig. 12; also see Grabs et al. 2000) are very similar to those for Yenisey and Lena (Fig. 5). Early spring snowmelt over the Mississippi basin also appears to be the main reason for the April peak discharge from the Mississippi, whose integrated precipitation peaks in May–June.

At low latitudes, the basin-integrated P–E generally agrees with the Fekete et al. runoff, indicating that the monthly P–E fields are reasonable proxies of monthly runoff provided the areas are large enough. One exception is the ECMWF P–E over the Congo River basin, where it follows the precipitation annual cycle rather than the runoff (Fig. 5). This bias is reflected in the high values of P–E in tropical Africa (Fig. 2) and is mainly due to the higher-than-observed precipitation in the ECMWF data resulting from the spurious ITCZ shift over Africa noted earlier. As noted, spring snowmelt results in peak river flows in late spring or early summer at northern mid- and high latitudes. It also disrupts the general agreement between surface runoff and the P–E seen at low latitudes. This suggests that on a monthly timescale the P–E fields at mid- and high latitudes cannot be used as a proxy of runoff without including the effects of snow accumulation and melt.

6. Latitudinal distribution of discharge into the oceans

In this section, we consider the continental discharge from the ocean perspective, with a view toward their use in oceanic freshwater transport and budgets. We start from the total discharge into the global ocean and then discuss individual ocean basins separately, with a focus on the latitudinal distribution.

7. Discussion

Our freshwater discharge estimates have various sources of errors. For example, the 921-river-based discharge contains uncertainties associated with 1) the estimate of discharge from the unmonitored areas, 2) the adjustment for river mouth flow rates, 3) varying length and periods of streamflow records, and 4) varying human influences on the natural streamflow. We also did not include groundwater runoff and the runoff from Antarctica. For the reanalysis P–E fields, there are many documented regional biases such as those related to moisture convergence and the atmospheric circulation (Trenberth and Guillemot 1998; Trenberth et al. 2001a), as well as known problems in ERA-15 over Africa (e.g., the spurious ITCZ shift) and South America (Trenberth et al. 2001b). The Fekete et al. runoff has uncertainties arising from its use of limited streamflow data and a water balance model over many regions (Fekete et al. 2000). The strength of the Fekete et al. (2000) runoff is in its patterns of the distribution, but the calibration for the total amount contains uncertainties over many regions.

Nevertheless, we believe that the estimates based on the 921-river streamflow data, the Fekete et al. runoff, and the ECMWF P–E are likely to be close to the truth. In particular, we think the 921-river-based estimate is the most reliable, except perhaps for the Mediterranean and Black Seas where the estimate seems to be a bit too low (Table 4). This conclusion follows because the 921 rivers cover over two-thirds of world's actively drained land areas and the errors in computing the discharge from the unmonitored areas result primarily from the uncertainties in the Fekete et al. runoff through r(j) in Eq. (2); that is, these errors are also in the Fekete et al. runoff-based estimate. The freshwater discharges implied by the reanalysis-derived P–E fields generally agree with the 921-river-based estimate, although large regional biases exist (cf. Fig. 2), especially for the NCEP P–E. This result suggests that the P–E products could be used as proxies of runoff over most land areas and, with some tuning and information about variability of groundwater, may be applied to study the interannual to decadal variations in continental freshwater discharge. The NCEP reanalysis is available for the last 50 years or so and an improved ECMWF reanalysis (ERA-40) for a similar period will soon become available. For such applications, however, improvements in accounting for the effects of snow accumulation and melt on seasonal to interannual timescales are needed. Furthermore, changes in human influences on the natural streamflow and evaporation over the last several decades will also be important considerations.

We have shown that comparisons of basinwide discharges (Table 4) have only limited value. It is obviously a more challenging task to derive correct estimates of discharge from all major rivers than just for the total discharge. For detailed evaluation of climate models and for estimating meridional transport of freshwater in the oceans, discharge from individual rivers (e.g., Table 2 and the appendix) and spatial distributions of discharge (Fig. 6) are needed. Because the freshwater fluxes from the large rivers are substantial, use of the unrealistic discharge distribution from BR75 in estimating oceanic meridional freshwater transport (e.g., Wijffels et al. 1992; Wijffels 2001) is likely to induce significant errors. Using the BR75 discharge for evaluating climate models (e.g., Pardaens et al. 2002) is also not a good choice.

8. Summary

We have created and compared several estimates of continental freshwater discharge into the oceans. The first is built on discharge data from 921 ocean-reaching rivers selected from several comprehensive streamflow datasets. The drainage area of the 921 rivers is 79.5 × 10⁶ km², or about 68% of global non-ice, nondesert land areas. We estimated the river mouth outflow from the world's large rivers by adjusting the streamflow rate at the farthest downstream station using the ratio of simulated flow rates (or drainage areas in some cases) at the river mouth and the station. The discharge from the unmonitored areas was estimated based on the ratios of runoff and drainage area between the unmonitored and monitored areas at each latitude. A river transport model, the composite runoff field from Fekete et al. (2000), and a simulated global river database, STN-30p, were used in this analysis. Long-term mean annual and monthly freshwater discharge at each latitude into individual and global oceans were derived based on the adjusted river outflow and the estimated contribution from unmonitored areas.

Second, we have separately computed annual and monthly continental discharge at each latitude into the oceans by forcing the RTM with the Fekete et al. runoff and the P–E fields derived from the NCEP and ECMWF reanalyses with a adjustment for snow effects. These implied discharges were compared with that derived from the streamflow data. The main results are summarized as follows.

1. The use of river mouth outflow increases the global continental discharge by ∼18.7% and the total drainage area by ∼20.4% compared with estimates using the unadjusted data from the farthest downstream stations (cf. Fig. 1). This result suggests that using unadjusted streamflow data from the farthest downstream stations (e.g., Perry et al. 1996; Grabs et al. 1996, 2000) substantially underestimates global continental freshwater discharge.

2. Globally, the annual runoff rate over the unmonitored areas is comparable to that over the monitored areas, although their ratio varies from 0.29 for the Indian Ocean drainage basin in July to 4.30 for the Pacific Ocean drainage basin in January (Table 3).

3. Our 921-river-based estimate of global continental freshwater discharge (excluding Antarctica³) is 37 288 ± 662 km³ yr⁻¹, or 1.18 ± 0.02 Sv, which is ∼7.6% of global P and 35% of terrestrial P. Although this value is comparable to earlier estimates, large differences exist among the discharges into the individual ocean basins. The estimates of global discharge based on the Fekete et al. runoff and ECMWF P–E are slightly higher than the river-based estimate, while the NCEP P–E implies lower discharge (Table 4). In general, the reanalysis P–E fields underestimate discharge from east Asia and northern Africa (Fig. 6). About 57% of the global discharge comes from the world's 50 largest rivers (Table 2).

4. When forced with the Fekete et al. runoff and reanalysis P–E fields, the RTM simulates the station streamflow rates reasonably well for world's major rivers (Figs. 3, 4, and 6). This is especially true for the Fekete et al. runoff case (Table 2 and the appendix) and suggests that river transport models at 0.5° resolution, such as the one used in the NCAR CCSM, can realistically simulate the world river system and its routing of terrestrial runoff into the oceans.

5. The continental discharges into the oceans within each 1° latitude band implied by the Fekete et al. runoff and reanalysis P–E fields agree reasonably well with the river-based estimates, which we regard as the closest to the truth. This is particularly true for the Fekete et al. runoff and ECMWF P–E cases and for the global oceans and the Atlantic Ocean (Figs. 7 and 9). In general, the NCEP P–E underestimates continental discharge at many latitudes for all the ocean basins except for the Arctic Ocean.

6. The latitudinal distribution of accumulative discharge into the global oceans estimated based on the 921 rivers is similar to that from BR75, although the discharge at individual latitudes differs greatly. The BR75 estimate is unrealistically smooth (Figs. 7 and 8) even compared with our 5° smoothed discharge. Our continental discharge has realistic latitudinal distributions that are needed for reliable estimates of meridional transport of freshwater in the oceans. Earlier estimates (e.g., Wijffels et al. 1992; Wijffels 2001) may contain significant errors as a result of using the unrealistic latitudinal distribution of continental discharge from BR75.

7. Discharges from most of the world's largest rivers have large annual cycles. For example, the Amazon peaks in May–June, Orinoco peaks in August, Changjiang peaks around July; whereas large Russian rivers (e.g., Yenisey, Lena, Ob,) have a sharp peak in June arising from snowmelt (Fig. 5). Basinwide-integrated precipitation usually does not have the same seasonal phase as for river discharge, which illustrates the important effects of snow accumulation and melt and river transport. The total discharge into the Arctic, the Pacific, and the global oceans peaks in June, whereas the peak is in May for the Atlantic Ocean and in August for the Indian Ocean (Fig. 12). Snow accumulation and melt have large effects on the annual cycle of discharge into the Arctic, Atlantic, Pacific, and global oceans, but little influence on the discharge into the Indian Ocean and the Mediterranean and Black Seas.

The long-term mean values of river runoff and continental discharge reported here is available for free download from NCAR's Climate Analysis Section catalog (http://www.cgd.ucar.edu/cas/catalog/).