1. Introduction
River runoff is an important term in the global land and ocean water balances. On global average, roughly 30%–40% of precipitation falling over land reaches the oceans as river runoff (e.g., Baumgartner and Reichel 1975; Trenberth et al. 2007). In addition to its role in the global water balance, humans depend on river flows to provide municipal and agricultural water supply, transportation, electricity, recreation, and many other uses. Several recent studies have examined trends in global river discharge over the twentieth century, with varying results (e.g., Dai et al. 2009, hereafter D09; Gedney et al. 2006; Gerten et al. 2008; Labat et al. 2004). As we seek to understand the implications of climate change, which is inherently a global issue, and human impacts on the water cycle through land use and water management, a baseline for historical global discharge is important.
Despite the critical role of discharge in the global water cycle, the magnitude of global runoff is poorly known because large portions of the land surface have never been gauged, have only been gauged for brief periods, or have restricted data access (Alsdorf et al. 2007). As a result, some past studies have relied on land surface and hydrologic models (LSMs) to estimate runoff in ungauged basins. However, modeled runoff is biased because of the missing physical processes (such as reservoir management, irrigation, and wetland and lake storage), lack of constraints on model parameters (soil, vegetation, and elevation), or lack of observations for accurate atmospheric forcings (precipitation and temperature). How to best utilize available data and models to estimate runoff in ungauged basins remains an open question.
Attempts to estimate global runoff to the oceans date to at least the late 1800s. Reclus (1888) argued that existing estimates, which at that time ranged from 49 000 to 63 000 km3 yr−1, were far too high. Based on direct streamflow observations from about one-tenth of Earth’s land surface, he reasoned that the total should be closer to 26 500 km3 yr−1(excluding Greenland and Antarctica). Over the last 50 yr, many estimates of river discharge into the world’s oceans have been made, ranging from 22 310 (Oki et al. 1995) to 42 500 km3 yr−1(Korzun 1978). While not all estimates are equally defensible, given the large range in these estimates, we review the various methods used in deriving them and provide a new set of estimates.
Previous approaches to estimating global runoff fall into four general categories, as outlined in Syed et al. (2009): 1) interpolation of in situ gauge observations (Baumgartner and Reichel 1975; Grabs et al. 1996; Korzun 1978; L’Vovich 1979; Shiklomanov and Sokolov 1985; Shiklomanov 1999); 2) global land surface or atmospheric model simulations (Nijssen et al. 2001; Oki et al. 2001); 3) combination of model simulations and observations, which we refer to as “hybrid” methods (Dai and Trenberth 2002, hereafter DT02; D09; Döll et al. 2003; Fekete et al. 2000; Fekete et al. 2002, hereafter F02); and 4) inferences from the land surface water balance, specifically precipitation P minus evapotranspiration E minus storage change ΔS, where storage change often is assumed to be small when averaged over multiyear periods (Oki et al. 1995; Syed et al. 2009; DT02). Here, we use a variation of the third approach to produce a new range of estimates at the continental and global level, which we compare with previous estimates.
We generate monthly and annual (water year) time series of global runoff, which facilitate the calculation of long-term means over specific time intervals. Most interpolation or hybrid studies use in situ gauges, which arguably provide the most accurate measurements of river discharge. However, the fact that the length and timing of records vary complicates the use of discharge observations (Table 4). Following other hybrid studies, we combine river discharge observations, where available, with a physically based LSM forced with observed climate data to create time series of seasonal and annual discharge for those locations where and when observations are not available. We apply bias corrections to the model based on observations, where available, to create a time series that accounts for variations in climate over time, which are missing from short gauge records. This is particularly useful for global water budget closure studies, like the NASA Energy and Water cycle Study (NEWS; L’Ecuyer et al. 2015, manuscript submitted to J. Climate; Rodell et al. 2015, manuscript submitted to J. Climate), in which consistency between long-term mean estimates of each component is important.
Our general approach is to merge semidistributed estimates of runoff produced by two implementations of the Variable Infiltration Capacity model (VIC; Liang et al. 1994; Gao et al. 2010), one for the period 1950–2008 and the other for 1960–2001, with streamflow observations for the period 1950–2006. In doing so, we develop relationships between modeled and observed flow for areas with gauge observations and use these relationships to estimate runoff from ungauged areas. The methods we employ are similar to those of DT02 and D09, respectively; however, they vary in some important aspects that we explain in section 2. In section 3, we present our estimates and compare them with previous estimates on a continent-by-continent basis. We diagnose reasons for the differences, provide some additional context, and identify areas where additional observations would be most useful in reducing uncertainties in section 4. Section 5 concludes with a summary of our primary results.
2. Methods
We follow an approach similar to that outlined by DT02 and D09 to estimate continental streamflow to the world’s oceans based on a hybrid of streamflow gauge data and streamflow simulated by an LSM. DT02 focused on global-mean runoff to the ocean and based their analyses for ungauged areas on runoff fields from F02, which essentially are outputs of a climatically driven water balance model rescaled to match observations where available. D09 focused on long-term trends in global runoff using a similar approach; however, because the F02 dataset only contains long-term means, D09 used runoff simulated by the Community Land Model, version 3 (CLM3; Oleson et al. 2004), to fill in gaps in observed time series and as a basis for estimating flows in ungauged basins.
In this study, we focus on long-term mean runoff (albeit we retain the capability to specify different averaging periods). For ungauged areas, we base our analysis on VIC simulations and use a somewhat different approach to combine model estimates for ungauged areas with observations. Furthermore, we use two VIC implementations to test the sensitivity of our results to some of the assumptions and forcings inherent in the LSM. Because the time periods and duration of observations vary greatly from gauge to gauge, F02 note that their long-term means are not fully consistent. Here, we create annual and monthly time series from 1950 to 2008 and from 1960 to 2001 (depending on the VIC simulation) from which we calculate long-term mean annual and seasonal discharge to the ocean over consistent time periods. Processes that are missing from VIC, such as water management and lakes and wetlands, will impact monthly discharge more than annual. Therefore, we calculate annual and monthly estimates separately.
a. Observations
DT02 assembled monthly streamflow measurements at 921 near-coastal gauging stations worldwide from Bodo (2001; archived at NCAR ds552.1, ds553.2, and ds550.1) and R-ArcticNET, version 2.0 (Lammers et al. 2001). These are compilations of data from the State Hydrological Institute of Russia (SHI); Environment Canada; the United Nations Educational, Scientific and Cultural Organization (UNESCO); Global Hydroclimatic Data Network (GHCDN); United States Geological Survey (USGS); and Global Runoff Data Centre (GRDC), among other sources [see Bodo (2001) and Lammers et al. (2001) for more details]. Records varied in length from 1 to 100 yr, with the most current ending in 2000. These gauges were selected to be the farthest downstream gauges on each river so as to make observations as representative as possible of continental runoff to the ocean. D09 incorporated new observations that allowed the previous analysis to be extended to 925 stations, with a consistent reference period of 1900–2006. They sourced new observations from GRDC, the University of New Hampshire (UNH), USGS, the Water Survey of Canada, Hydrological Cycle Observation System for West and Central Africa (AOS-HYCOS), Brazilian Hydro Web, and Milliman et al. (2008). They also filled in as many gaps in the observed time series as possible by performing a linear regression of downstream on upstream observations during overlapping data periods. This updated dataset [downloaded from NCAR (2013)] was the starting point for this study. We manually checked the drainage network for each station against Hydrological Data and Maps Based on Shuttle Elevation Derivatives at Multiple Scales (HydroSHEDS), version 1.0 (Lehner et al. 2006), Macmillan (1995), and Google Earth and removed stations that either did not have any data between 1950 and 2006 or were located upstream of another station in the dataset, leaving 836 stations that are closest to the mouths of their respective rivers. Excluding 89 stations had little impact on total gauged area (0.67 × 106 km2; see Table 1). The 836 gauges provide observations for 58% of exorheic areas (draining to an ocean) globally, excluding Greenland and Antarctica (Table 1; Fig. 1). Excluding 15.9 × 106 km2 of desert area that arguably produces little or no runoff from the exorheic land area (per Dai and Fung 1993), the gauged portion is about 68% of the exorheic, nondesert global land area. This is less than the 80% referenced by D09, apparently because they include ungauged areas downstream of the most downstream gauge in their gauged area estimate.
Drainage areas by continent for river basins draining to the ocean in STN-30p, the gauged areas by continent for the 839 gauges used here, and the percent of exorheic drainage areas represented by the observed dataset. “Gauged area excluded in this analysis” is the area upstream of the 86 gauges from D09’s original 925 stations that were not used here because they either had no data or were located upstream of other gauges based on tracing flow paths in HydroSHEDS, version 1.0 (Lehner et al. 2006); Macmillan (1995); and Google Earth imagery.
Map of global river basins, excluding Greenland and Antarctica, draining to the ocean, plotted using an equal area projection. Continent boundaries are color coded based on definitions from the NASA NEWS (L’Ecuyer et al. 2015, manuscript submitted to J. Climate; Rodell et al. 2015, manuscript submitted to J. Climate). The blue areas are unobserved, either containing no gauging stations in the coastal station dataset compiled by D09 or downstream of these gauging stations. Runoff from the brown areas is reported in the coastal station dataset. White areas are endorheic. Gauged areas are plotted based on the STN-30p 0.5° resolution drainage dataset. In some cases, the gauged areas are <0.5° grid cell or the boundaries of the drainage area do not line up exactly with the boundaries of a 0.5° grid; as a result, the true gauged areas are smaller than those shown here (66.2 × 103 vs 76.1 × 103 km2).
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Map of global river basins, excluding Greenland and Antarctica, draining to the ocean, plotted using an equal area projection. Continent boundaries are color coded based on definitions from the NASA NEWS (L’Ecuyer et al. 2015, manuscript submitted to J. Climate; Rodell et al. 2015, manuscript submitted to J. Climate). The blue areas are unobserved, either containing no gauging stations in the coastal station dataset compiled by D09 or downstream of these gauging stations. Runoff from the brown areas is reported in the coastal station dataset. White areas are endorheic. Gauged areas are plotted based on the STN-30p 0.5° resolution drainage dataset. In some cases, the gauged areas are <0.5° grid cell or the boundaries of the drainage area do not line up exactly with the boundaries of a 0.5° grid; as a result, the true gauged areas are smaller than those shown here (66.2 × 103 vs 76.1 × 103 km2).
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Map of global river basins, excluding Greenland and Antarctica, draining to the ocean, plotted using an equal area projection. Continent boundaries are color coded based on definitions from the NASA NEWS (L’Ecuyer et al. 2015, manuscript submitted to J. Climate; Rodell et al. 2015, manuscript submitted to J. Climate). The blue areas are unobserved, either containing no gauging stations in the coastal station dataset compiled by D09 or downstream of these gauging stations. Runoff from the brown areas is reported in the coastal station dataset. White areas are endorheic. Gauged areas are plotted based on the STN-30p 0.5° resolution drainage dataset. In some cases, the gauged areas are <0.5° grid cell or the boundaries of the drainage area do not line up exactly with the boundaries of a 0.5° grid; as a result, the true gauged areas are smaller than those shown here (66.2 × 103 vs 76.1 × 103 km2).
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
b. Model simulations
Estimates of runoff from ungauged areas (either downstream of the most downstream gauge in a river basin or completely ungauged basins) depend upon the relationship between model-simulated runoff and observed runoff in nearby gauged areas. D09 used CLM3 as a basis for estimating runoff from ungauged areas. In this version of the Community Land Model (CLM), runoff is computed using the conceptual TOPMODEL runoff generation scheme (Beven and Kirkby 1979). Beven (1997) describes several potential limitations of TOPMODEL, including the requirement of a very high–resolution, accurate digital elevation model (DEM) in order to represent flow pathways in the derivation of the topographic index. Li et al. (2011) also point out that runoff generation is less topographically controlled in arid regions (where infiltration excess dominates), flat areas, or in areas with thick soils or deep groundwater; they argue that VIC, which simulates runoff as the sum of surface runoff based on the variable infiltration capacity curve and base flow as a nonlinear function of subsurface soil moisture, may be more appropriate in some locations because it relaxes the TOPMODEL assumptions and is less dependent on topographic representations.
We chose to use the VIC macroscale LSM, which has been applied to estimate streamflow at continental and global scales in a number of previous studies (e.g., Haddeland et al. 2007; Maurer et al. 2002; Nijssen et al. 1997, 2001; Schaner et al. 2012; Sheffield and Wood 2007; Voisin et al. 2008). To test the sensitivity of our estimates of continental runoff to model runoff, we used two VIC-simulated runoff datasets. The first, referred to hereafter as Sheffield, was a global implementation of VIC, version 4.0.5, at 1° latitude by longitude and a 3-hourly time step in full energy balance mode (which iterates land surface temperature for the closure of the energy and water budgets) forced with the atmospheric forcings of Sheffield et al. (2006). Model parameters were specified following Nijssen et al. (2001) and calibrated to monthly streamflow in 25 large basins globally (Sheffield and Wood 2007). Sheffield et al. (2006) forcing data used daily precipitation from NCEP–NCAR reanalysis (Kalnay et al. 1996; Kistler et al. 2001), rescaled to match the monthly climatology of interpolated precipitation from Climatic Research Unit (CRU; New et al. 1999, 2000; Mitchell and Jones 2005), corrected for gauge undercatch following Adam and Lettenmaier (2003) and the number of rain days of CRU and the analysis of Nijssen et al. (2001) and finally disaggregated to 3-hourly based on TRMM Multisatellite Precipitation Analysis satellite retrievals (Huffman et al. 2007) between 50°S and 50°N latitude. Poleward of 50°S and 50°N latitude, Sheffield et al. (2006) assume that probability distribution functions of 3-hourly and daily precipitation are uniform across Köppen climate zones (see Critchfield 1983) for each continent.
The second simulation, referred to hereafter as WATCH, is based on a ½° latitude-by-longitude global implementation of VIC, version 4.1.1, at daily time step and in water balance mode (no prediction of surface temperature, which is assumed to be equal to surface air temperature). This model run was performed by van Vliet et al. (2012, 2013) as part of the EU Water and Global Change (WATCH) project and was forced with atmospheric forcings from Weedon et al. (2010, 2011) for the period 1958–2001. Weedon et al. (2010, 2011) used daily precipitation from the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40), resampled to match the number of wet days in CRU and bias corrected to match the monthly precipitation climatology from the Global Precipitation Climatology Centre (GPCC). Van Vliet et al. (2012, 2013) disaggregated the Nijssen et al. (2001) elevation, land-cover classifications, and soil characteristics from 1° to ½° spatial resolution. Nijssen et al. (2001) calibrated soil parameters at 22 basins and transferred these parameters to other basins based on climate zone and proximity.
Simulated at station and river mouth streamflow values were calculated from both datasets by routing the model runoff through the simulated topological network at 30-minute spatial resolution (STN-30p, version 6.01; 2004–07) flow network [Vörösmarty et al. 2000; downloaded from Water Systems Analysis Group (2007)] at ½° latitude-by-longitude resolution using the Lohmann et al. (1996, 1998) routing model. In the case of Sheffield, each ½° grid cell within the routing model was assumed to have the same runoff as the 1° grid cell containing it. The flow direction file was modified so that water upstream of the Hulun Nur Lake, in Mongolia, drains into the Amur River. Gauging stations were located along the STN-30p flow network to ensure that they drained to the correct river mouth [based on tracing flow paths in HydroSHEDS, version 1.0 (Lehner et al. 2006), and Macmillan (1995) and Google Earth imagery]. In addition, some stations were relocated to minimize differences in simulated and observed drainage areas upstream of the gauging stations. As a result, in 388 cases, the latitude and longitude of simulated station locations differ slightly from the latitude and longitude reported with the observational dataset [downloaded from NCAR (2013)]. In defining basin boundaries, D09 used the STN-30p, version 5.12, flow network, which differs from version 6.01 in several locations. The exorheic flow estimated from each simulation is shown in Table 2.
VIC-simulated discharge from continents to ocean for Sheffield and WATCH. Streamflow from Greenland and Antarctica is not included.
c. Gauged basins
At many stations, gauged monthly streamflow records had some months with no data. We filled in data gaps through linear regression of monthly or annual gauged streamflow on VIC-simulated streamflow, following the decision tree shown in Fig. 2, for those locations where the regression equations were statistically significant. D09 used a similar strategy. To maximize the extraction of information for available observations, we allowed for month-by-month predictions (all January data were used to develop January regression equations; all February data were used to develop February regressions; and so on) even if an annual regression was not possible (cases c5 and c6 in Fig. 2); this applied to less than 1% of stations. For hybrid estimates based on Sheffield, we also extended the observational record to include the period from 2006 to 2008 using the same regression equations. Annual regressions were performed separately from monthly regression when possible because we assume that the annual regressions more accurately predict annual flows than the sum of monthly regressed flows.
Decision tree used in linearly regressing observed flows against VIC-simulated flows in order to estimate missing observations in the annual and monthly time series at each gauging station, adapted from Fig. 4 in D09. The N is the number of months with observations. Which regression is used depends on whether the correlation coefficient between simulated and observed flows (R) is statistically significant (|R| ≥ Rs) at a 95% significance level, based on a two-tailed Student’s t test. Subscripts on R are as follows: a indicates the annual time series, m is the monthly time series by each individual month, am is the monthly time series for all months treated together, and lag is the monthly time series but with VIC simulations offset by anywhere from 5 months earlier to 5 months later than observations, whichever has the best correlation. The percent of stations for which each method was used is shown in parentheses, with regressions against Sheffield first (S), followed by regressions against WATCH (W), followed by the percentages reported by D09 against CLM3.5 (D). Categories c5 and c6 were not used in D09, and category numbers differ. For the case of each month being treated individually, if the number of months for which correlations are significant (M) is more than 8 but less than 12, the missing observations in those 1–4 months are filled in using a cubic spline. If the result of the spline is negative, we linearly interpolate the two adjacent months. If the result of this is still negative, we either assign that month zero (if more than 80% of observations for that month are zero) or use observed climatology.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Decision tree used in linearly regressing observed flows against VIC-simulated flows in order to estimate missing observations in the annual and monthly time series at each gauging station, adapted from Fig. 4 in D09. The N is the number of months with observations. Which regression is used depends on whether the correlation coefficient between simulated and observed flows (R) is statistically significant (|R| ≥ Rs) at a 95% significance level, based on a two-tailed Student’s t test. Subscripts on R are as follows: a indicates the annual time series, m is the monthly time series by each individual month, am is the monthly time series for all months treated together, and lag is the monthly time series but with VIC simulations offset by anywhere from 5 months earlier to 5 months later than observations, whichever has the best correlation. The percent of stations for which each method was used is shown in parentheses, with regressions against Sheffield first (S), followed by regressions against WATCH (W), followed by the percentages reported by D09 against CLM3.5 (D). Categories c5 and c6 were not used in D09, and category numbers differ. For the case of each month being treated individually, if the number of months for which correlations are significant (M) is more than 8 but less than 12, the missing observations in those 1–4 months are filled in using a cubic spline. If the result of the spline is negative, we linearly interpolate the two adjacent months. If the result of this is still negative, we either assign that month zero (if more than 80% of observations for that month are zero) or use observed climatology.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Decision tree used in linearly regressing observed flows against VIC-simulated flows in order to estimate missing observations in the annual and monthly time series at each gauging station, adapted from Fig. 4 in D09. The N is the number of months with observations. Which regression is used depends on whether the correlation coefficient between simulated and observed flows (R) is statistically significant (|R| ≥ Rs) at a 95% significance level, based on a two-tailed Student’s t test. Subscripts on R are as follows: a indicates the annual time series, m is the monthly time series by each individual month, am is the monthly time series for all months treated together, and lag is the monthly time series but with VIC simulations offset by anywhere from 5 months earlier to 5 months later than observations, whichever has the best correlation. The percent of stations for which each method was used is shown in parentheses, with regressions against Sheffield first (S), followed by regressions against WATCH (W), followed by the percentages reported by D09 against CLM3.5 (D). Categories c5 and c6 were not used in D09, and category numbers differ. For the case of each month being treated individually, if the number of months for which correlations are significant (M) is more than 8 but less than 12, the missing observations in those 1–4 months are filled in using a cubic spline. If the result of the spline is negative, we linearly interpolate the two adjacent months. If the result of this is still negative, we either assign that month zero (if more than 80% of observations for that month are zero) or use observed climatology.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
In two cases, neither annual nor monthly regressions were statistically significant. In these cases, we used the best-fitting, all-month lagged regression, based on the full period of overlap between observations and simulations, and summed monthly values to obtain annual totals. The lagged regressions cannot be used to fill in missing observations at the beginning (or end) of the model simulation because they require simulated flows before (or after) the month of interest, depending on the lag. Instead, we used climatology for these months. This only occurred at Hino at Fukadani, Fukui Prefecture, Japan (1283 km2), for Sheffield and at Rompido de Samaria at Reforma, Mexico (9000 km2) for both Sheffield and WATCH. Hino has only three calendar years of data (1958, 1961, and 1963); of these, 1958 has an inverted hydrograph relative to the simulated climatology. Since 1958 is not present in the WATCH simulation, the WATCH regression is significant for Hino. The discrepancy could be a result of dam operations in this basin. Also, because the basin boundaries for Hino do not align well with the STN-30p basin boundaries, some flow from the headwaters is directed to another basin. Rompido de Samaria only has observations from 1976 to 1978 and is a bifurcation of the Grijalva River. The routing model we used cannot accommodate split flow situations, so it is not too surprising that the models would not simulate this well. There is another gauge in parallel on the Grijalva River that accounts for a much larger portion of the total Grijalva flow. Three other stations had no observations during the 1960–2001 WATCH simulation and had to be excluded when using WATCH: Rinda at Rinda, Russia (980 km2); Pulonga at Pulonga, Russia (670 km2); and Mapocho at Las Condes, Chile (500 km2).
d. Ungauged basins
To apply information from gauged rivers to ungauged rivers, DT02 defined geographical zones of influence. Their study focused on ocean basin inflows, so they allowed the relationship between observed and mean runoff fields (for the same area as observations) from F02 within each 1° latitude band draining into an ocean basin to influence the estimate of discharge from ungauged basins draining into the same zone (see Fig. 3a for areas draining into each ocean basin); in the remainder of this document, this scheme for zones of influence is referred to as Ocean. We are most interested in runoff from the continents and also in exploring the sensitivity of estimates in ungauged basins to the region of influence, so we also consider a case in which the geographical zone of influence is each 1° latitude band draining from a continent (see Fig. 3b for areas draining each continent); in the remainder of this document, this zone of influence is referred to as Land.
(a) Map of exorheic basins used to define each ocean basin over which 1° latitude zones are processed for Ocean—sky blue = Atlantic, dark blue = Pacific, bluish green = Indian, yellow = Mediterranean, and orange = Arctic basins. (b) Map of exorheic basins used to define each continent over which 1° latitude zones are processed for Land—yellow = Africa, bluish green = Eurasia, sky blue = South America, orange = North America, and blue = Australia–Oceania. Black stars show locations of gauging stations used in this study. White areas are interior closed basins. Greenland and Antarctica are not included in this analysis.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
(a) Map of exorheic basins used to define each ocean basin over which 1° latitude zones are processed for Ocean—sky blue = Atlantic, dark blue = Pacific, bluish green = Indian, yellow = Mediterranean, and orange = Arctic basins. (b) Map of exorheic basins used to define each continent over which 1° latitude zones are processed for Land—yellow = Africa, bluish green = Eurasia, sky blue = South America, orange = North America, and blue = Australia–Oceania. Black stars show locations of gauging stations used in this study. White areas are interior closed basins. Greenland and Antarctica are not included in this analysis.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
(a) Map of exorheic basins used to define each ocean basin over which 1° latitude zones are processed for Ocean—sky blue = Atlantic, dark blue = Pacific, bluish green = Indian, yellow = Mediterranean, and orange = Arctic basins. (b) Map of exorheic basins used to define each continent over which 1° latitude zones are processed for Land—yellow = Africa, bluish green = Eurasia, sky blue = South America, orange = North America, and blue = Australia–Oceania. Black stars show locations of gauging stations used in this study. White areas are interior closed basins. Greenland and Antarctica are not included in this analysis.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
In summary, our approach differs from that of DT02 and D09 in several important ways: First, we extrapolate gauged flows to the STN-30p basin outlet for all gauges, even those that are unnamed, by assuming that they drain to the ocean at the outlet of the STN-30p basin that contains them. Second, we allowed the bias correction of the ungauged area downstream of the gauges to vary in time; this was only possible by using VIC simulations instead of the F02 runoff fields. To facilitate this, we applied an area correction to the VIC-simulated, at station flows to match the observed station area. Using the VIC-simulated flows for this bias correction also makes more sense because the F02 runoff fields are already bias-corrected upstream of the farthest downstream gauge, such that the area upstream of the gauge has less bias than the ungauged area downstream. Third, we used VIC instead of F02 runoff fields or CLM to estimate flows in ungauged basins. As with corrections of the ungauged areas below a gauge, applying the bias-corrected F02 runoff fields to estimate biases in neighboring ungauged basins likely underestimates biases in ungauged areas. The VIC simulations are more likely to have a consistent bias regionally. Fourth, in addition to correcting bias in ungauged basins on the basis of observations in the same latitude band draining to the same ocean, we also correct bias on the basis of observations in the same latitude band draining from the same continent. Finally, in the interest of preserving as much spatial heterogeneity as possible, we apply bias corrections directly at each STN-30p river basin outlet rather than lumping all river discharge draining to the same 1° latitude band together.
e. Error estimates
Sources of uncertainty in our predictions include observation errors, uncertainty in simulations, errors in the fitted regression equations, and errors in the assumptions of localized bias corrections. Observation errors are difficult to quantify given inconsistencies in data quality control inherent in the compilation of global datasets; for the purposes of this study, we assume that the errors in the in situ data are small relative to the errors in unobserved basins. Uncertainties in simulations include uncertainties in modeled runoff generation processes and parameterization, errors in atmospheric forcing data, including precipitation, and errors in river routing/basin delineation. As noted previously, VIC was calibrated in the case of the Sheffield dataset, and calibrated parameters were taken from Nijssen et al. (2001) for WATCH. The parameters from Nijssen et al. (2001) were calibrated VIC at a spatial resolution of 2° × 2°, so the nearest neighbor disaggregation of these parameters to 0.5° × 0.5° resolution likely produced some errors in the scaling of subgrid variability in runoff generation. Neither of the VIC simulations represents lakes and wetlands and human controls on river flows (locks, dams, reservoirs, and interbasin water transfers). Precipitation in the Sheffield et al. (2006) forcings differed from CRU, version 3.2.2 (Harris et al. 2014; Harris and Jones 2014), and GPCC, version 6 [Becker et al. 2013; 0.5° resolution data accessed from DWD (2011)], by less than 3% on a continental average. The WATCH precipitation forcing is wetter on a global average by 6%, which partially explains why the highest runoff estimate is from the raw WATCH VIC simulations. As noted by Haddeland et al. (2011), the wetter conditions in WATCH are the result of undercatch correction factors. The bias correction procedure in unobserved basins is meant to correct for these forcing and model simulation errors; however, particularly in the case of interbasin water transfers, the simulation bias in neighboring river basins is unlikely to be transferable. The fact that the correction factors are computed using all observations within a 4° latitude zone reduces sensitivities to these singular effects to some extent.
To estimate errors in our predictions, we used a jackknife approach. Observation-based discharge for each gauged STN-30p basin was left out of the analysis one-by-one [in Eq. (3)], and discharge was recalculated following the above procedures as though that basin were ungauged. At each river mouth, variance was calculated from all unique solutions (the number of unique solutions at a river mouth varied depending on the number of stations impacting calculations at that mouth) then summed to get a total variance for each continent. For example, the runoff estimate for the area draining the Nemanus basin (Lithuania) to 55.75°N is influenced by 43 gauged basins draining from Eurasia and North America into the Atlantic Ocean between 53° and 58°N. Consequently, the variance for the Ocean method at that mouth is based on 44 unique solutions, including the solution in which all available observations are used. For the Land method applied to this basin, the variance is based on 37 unique solutions, including 36 solutions that individually exclude each gauged basin draining from Eurasia between 53° and 58°N and one solution that uses all available gauges. Several small basins at the southern tip of South America are corrected based on a single gauge on the Santa Cruz River, which enters the ocean at 50.25°S. As a result, the variance in these basins is based on only two unique solutions, one including this gauge and one excluding this gauge (in which case, the next southernmost gauge was used). This error estimate does not account for errors in gauged flows, errors in simulations, or errors in the regression applied to fill in the gauge record. It does account for the sensitivity of the method to the given gauging stations, which we discuss in more detail in section 4. We calculate a best estimate of runoff as the average of the four hybrid estimates (Sheffield-Ocean, Sheffield-Land, WATCH-Ocean, and WATCH-Land), with the average variance from their respective jackknife error estimates presented as the best estimate of uncertainty.
3. Results
Although the regression method used to fill gaps in gauged station streamflow is quite similar to that used in D09, the 
Sum of gauged annual average streamflow from 839 stations (836 for WATCH because of the lack of concurrent simulation and observation at three stations) after filling missing observations with regression against each model simulation. For D09, not all stations had full time series after regression, and values presented here are the averages of those available.
All four hybrid estimates (Sheffield-Ocean, Sheffield-Land, WATCH-Ocean, and WATCH-Land) of global runoff are higher than those of D09 and are generally near the upper end of estimates in the literature (Table 4; Fig. 4). Our hybrid estimates are closest to the average of published estimates in Africa but are nearly double most previously published estimates over Australia–Oceania. Over Eurasia and North America, all of our hybrid estimates are within approximately 10%–15% of the mean of previous estimates. Over South America, our Sheffield-based hybrid estimates are within 15% of the mean of previous estimates, but our WATCH-based hybrid estimates were 20% and 27% higher than the mean of previous estimates. Both WATCH-based hybrid estimates for South America are also higher than the raw WATCH VIC simulations. The highest global estimate is the uncorrected WATCH VIC simulation (49 700 km3 yr−1, in total; Table 4). For the WATCH-forced VIC simulation, the anomaly (relative to previous estimates) is mostly driven by large values over Eurasia. The second highest estimate was the raw Sheffield-forced VIC simulation (45 300 km3 yr−1). Both simulations had much higher runoff in Australia–Oceania than previous literature estimates. Some of the previous estimates do not include all of the islands in Oceania; moreover, the land areas included in each continent are often poorly defined in the literature. Our hybrid estimates indicate that the islands of Oceania and Southeast Asia are important contributors to the global water budget. We estimate discharge of approximately 2940 km3 yr−1from the islands in Oceania (86% of the Australia–Oceania total) and 2622 km3 yr−1from islands in Southeast Asia (16% of the Eurasia total). Combined, these islands account for approximately 12% of the total global discharge to the ocean. The hybrid estimates are sensitive to the performance of models in ungauged basins, which likely accounts for our hybrid estimates being higher than those of previous studies. For example, if two models performed the same in gauged basins, the ratio correction factors used in Eq. (3) would be equal. However, if one of the models simulated lower flow in ungauged basins than the other, applying these same correction factors would still yield lower hybrid flows. In reality, the model estimates are higher in some cases and lower in others. In the aggregate, this effect yields higher estimates from the models used in this study. For Australia–Oceania, in particular, the VIC simulations were lower than observations in the wettest basins of Papua New Guinea and New Zealand, likely because of the lack of orographic precipitation correction, the importance of which is described in Adam et al. (2006); therefore, hybrid flows after the correction of the VIC simulations were increased in those latitude bands.
Estimates of continental discharge (km3 yr−1) from the literature and this study grouped by methodology. Max values are in boldface, min values are in italics, and not applicable is indicated by an em dash.
Boxplot showing distribution of annual average estimates of continental and global streamflow, grouped by methodology (for explanation see Table 4). For simulated, the red open circle is Sheffield-VIC and the blue open circle is WATCH-VIC. For hybrid, the red open triangle is Sheffield-Ocean, the red dot is Sheffield-Land, the blue open triangle is WATCH-Ocean, the blue dot is WATCH-Land, and the black diamond is D09. Gray horizontal line in each box is the median, box edges are 25th and 75th percentiles, whiskers extend to 1.5 times the interquartile range, and black stars are outliers, where applicable.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Boxplot showing distribution of annual average estimates of continental and global streamflow, grouped by methodology (for explanation see Table 4). For simulated, the red open circle is Sheffield-VIC and the blue open circle is WATCH-VIC. For hybrid, the red open triangle is Sheffield-Ocean, the red dot is Sheffield-Land, the blue open triangle is WATCH-Ocean, the blue dot is WATCH-Land, and the black diamond is D09. Gray horizontal line in each box is the median, box edges are 25th and 75th percentiles, whiskers extend to 1.5 times the interquartile range, and black stars are outliers, where applicable.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Boxplot showing distribution of annual average estimates of continental and global streamflow, grouped by methodology (for explanation see Table 4). For simulated, the red open circle is Sheffield-VIC and the blue open circle is WATCH-VIC. For hybrid, the red open triangle is Sheffield-Ocean, the red dot is Sheffield-Land, the blue open triangle is WATCH-Ocean, the blue dot is WATCH-Land, and the black diamond is D09. Gray horizontal line in each box is the median, box edges are 25th and 75th percentiles, whiskers extend to 1.5 times the interquartile range, and black stars are outliers, where applicable.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
The results of the jackknife error analysis for the annual estimates are shown in Table 5. The standard deviations based on the leave-one-out jackknife approach are generally small [(2490–2940) km3 yr−1, globally]. In some cases, for example, North America, the annual jackknife average (calculated as the sum of the average of all realizations for each river mouth) differs from the annual average (calculated using all observations) by as much or more than the standard deviation estimated from the jackknife. This occurs because the number of observations contributing to the streamflow correction is low in many basins, with the result that the variance between jackknife estimates in that basin is based on a small sample size (number of unique solutions in a basin range from 2 to 47, with an average of 12). The jackknife approach only represents the sampling errors in applying the relationship between model and observations to other basins. It does not consider model errors, station errors, or errors in the river routing network. The standard deviation of our four hybrid global estimates (approximately 510 km3 yr−1) gives a sense of the sensitivity to model selection and the choice of the zone of influence; however, the small sample size (two models, two zones of influence) limits the applicability of this term in assessing this aspect of uncertainty.
Results of jackknife error analysis. Mean is the sum of the average of jackknife realizations at each river mouth; 1σ is the square root of the sum of variance of jackknife realizations at each river mouth.
4. Discussion
Our results differ from those of previous studies for several reasons. We explore these reasons on a continent-by-continent basis. As noted earlier, the largest differences are in South America and Australia–Oceania. We also discuss briefly the sensitivity of our results to the averaging period.
Because our method is essentially a derivative of that of D09, we outline here the impacts of differences in methodology. The extrapolation of observed streamflow to the mouth differs from D09 in three ways: First, D09 (and DT02) multiplied observed station flow by a ratio of long-term mean runoff from F02 upstream of the river mouth to long-term mean F02 runoff fields upstream of the station. We adjusted station flow using a time-varying ratio of routed VIC-simulated runoff at the river outlet to routed VIC-simulated runoff at the station. F02 long-term, mean, monthly runoff fields essentially weight the simulated runoff from the water balance model (Vörösmarty et al. 1998) so that the long-term mean integrated runoff above a given gauge matches the long-term mean observed streamflow at that gauge. As noted previously, the long-term means in F02 are not all from the same time period. Because we want mean discharge to the ocean over a consistent time period, we allowed for temporal variations in the relationship between flow at the gauging station and at the river outlet [Eq. (1)]. Also, because F02 applied bias corrections upstream of the gauges, the bias correction applied to the ungauged portion of the basin is lower than the actual water balance model bias.
Second, we extrapolated observed streamflow to the basin outlet for all basins that had at least one gauging station. D09 did not extend flows to the mouths of rivers that were not named in the STN-30p dataset (generally small rivers). Third, because we extrapolated the gauged streamflow from all gauges to the outlet of their STN-30p basin, we extrapolated flows from some smaller rivers, which did not typically align perfectly with the STN-30p flow network. To correct for this, we calculated the simulated runoff and applied it to the observed drainage area [Eq. (1)]. This extrapolation assumes that simulated runoff from ungauged areas has similar biases to the simulated runoff from gauged areas within the same basin. We prefer that assumption to applying bias corrections based on model performance in neighboring basins (as if the basin were completely ungauged). Conversely, this means that if the gauging station is located in an uncharacteristic portion of the larger STN-30p basin, the correction may be worse than if the basin were treated as ungauged. For example, if a station is located on a small, mountainous headwaters tributary with streamflow that is much higher than the simulation, and the correction is applied to the larger STN-30p basin, the mouth flows may be corrected to be higher than is appropriate. By extending observed flow to the mouth for the top 200 basins, D09 estimated flows for 12.3 × 106 km3 of area. Our corrections extended flows to 14.1 × 106 km3 of area (Table 6). The biggest percentage differences in area covered are in Australia–Oceania and Eurasia, which is reflected in higher amounts of flow treated as observed flows at the river mouth (Table 3) for the purposes of Eq. (3). It is worth noting that our total area was consistent with D09; the only difference is that we treated more area as “observed” for the purposes of Eq. (3).
Drainage areas (×106 km2) at the mouth of rivers to which gauged flows were extrapolated.
The second major difference from DT02 (and D09) is the calculation of streamflow in completely ungauged basins. Whereas DT02 calculated flows for ungauged areas on the basis of runoff fields, we used routed streamflow (which should be nominally the same as runoff times area at the monthly and annual scales). Also, instead of calculating a single combined runoff value entering the ocean at either end of the 1° latitude band and redistributing to 1° grid cells at the edge of each continent based on drainage area upstream of those grid cells, we calculate a single discharge value for each 0.5° river outlet. Equation (3) applies the timing of the observed flows from nearby outlets to unobserved basins; however, because 
Finally, one should note that this study does not account for direct discharge of groundwater into the ocean. Shiklomanov and Sokolov (1985) suggest that ~(0.5–1.0) km3 yr−1 of juvenile water enters the ocean directly from degasification of the mantle and that total direct underground runoff to the ocean is ~2200 km3 yr−1. Therefore, our estimates are likely lower than the true value.
a. Africa
On an annual average, hybrid estimates over Africa are within 4% of D09, even though runoff from only 51% of the exorheic areas is gauged. This is in part because much of the ungauged area is quite arid (Table 7). This is consistent with the observation of Fekete et al. (2004, p. 301) that in arid regions “the runoff estimate is completely insensitive to the precipitation estimates” because precipitation is so low that there is almost no runoff. The two largest ocean-reaching rivers, the Nile and Congo, are observed. Compared to observations, both VIC simulations model too much flow in these basins. The Congo River contains complex systems of wetlands, and the Nile is heavily managed; neither of these processes is represented in the version of VIC we used. In each case, the residence time of water is higher than simulated and more evapotranspiration is expected, as such, it is unsurprising that the LSMs would overestimate runoff in these basins. The correction results in lower African runoff in the hybrid dataset than the raw VIC simulations.
Percent of all exorheic area and of gauged exorheic area only for which VIC simulates <30 mm yr−1 runoff.
b. Eurasia
Although a large portion of Eurasia’s ungauged area is in the arid Arabian Peninsula, which has little influence on Eurasian runoff, some regions with extremely high monsoon precipitation in the Southeast Asia mainland and islands are also largely ungauged. As shown in Fig. 3, the ±2° latitude bands near the outlets of ungauged basins in these areas are poorly monitored for both Ocean and Land regions of interest. In fact, the lack of observations means that the Ocean-based hybrid estimates in Eurasia are sensitive to model performance in the Sepik River basin on Papua New Guinea, which has an observed drainage area of only 41 000 km2 and only 2 yr of observations. Syed et al. (2009) comment that their GRACE water balance–based estimates do not include the Southeast Asian islands and suggest that the fact that their estimates are low relative to others (see Table 4; Fig. 4) is evidence of the relative importance of these islands to Eurasian streamflow.
As shown in Fig. 5, our estimates agree with D09 to the extent that Eurasian discharge has its peak in June, presumably because of snowmelt in northern Eurasia; however, the Sheffield and WATCH simulations both show continued high discharge through September, likely because of the Asian monsoon. Since our corrections are applied on a month-by-month basis, the timing of the simulated seasonal cycle in our unobserved basin estimates follows that of the model simulations. This supports our argument that the lack of observations in basins impacted by the Asian monsoon is a major source of uncertainty in Eurasian streamflow.
Average monthly streamflow estimates (1960–2001) from continents and globe to oceans. Observed is based on station observations after temporal gaps are filled in using regressions. As shown in Table 1, just over half of the exorheic area is observed.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Average monthly streamflow estimates (1960–2001) from continents and globe to oceans. Observed is based on station observations after temporal gaps are filled in using regressions. As shown in Table 1, just over half of the exorheic area is observed.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
Average monthly streamflow estimates (1960–2001) from continents and globe to oceans. Observed is based on station observations after temporal gaps are filled in using regressions. As shown in Table 1, just over half of the exorheic area is observed.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
c. South America
Our hybrid estimates are ~6% higher in South America than those of D09 if using the Sheffield simulations and 15%–21% higher than D09 if using WATCH simulations. The largest differences occur in the southernmost basins draining west from South America because there are almost no observations at these latitudes (Figs. 1, 3). Additionally, these western basins have high runoff, of which Schaner et al. (2012) estimate 5%–50% comes from glacier melt. The VIC implementations used here do not include glacier melt processes and underpredict runoff in the southernmost observed basins. As a result, the hybrid estimates are higher than simulations in the poorly observed southern part of South America.
d. North America
Our estimates of North American, average, annual streamflow are relatively close (within 15%) to those of D09 and agree well with D09’s seasonal cycle (Fig. 5). This is somewhat surprising since only 62% of the exorheic area (and ~50% of discharge to the ocean, based on the average of all estimates) from North America is gauged (Table 1). Because gauges are evenly distributed across latitude bands in North America, corrections in unobserved areas are well-constrained by several stations, leading to low variability between estimates. The Canadian Arctic Archipelago is poorly observed, but because it is relatively dry, this lack of observations has little influence on the continental estimates.
e. Australia–Oceania
The biggest difference between our hybrid streamflow estimates and D09 is in Australia–Oceania. Only 33% of this region is observed. Furthermore, the majority of the runoff comes from small islands to the north and east of Australia, rather than from the ungauged part of the continent, and these islands are poorly observed. In fact, in our hybrid estimates, only 14% of discharge to the ocean in this region comes from Australia. The two observed rivers with the largest flows are the Sepik and Purari Rivers in Papua New Guinea, and both of these basins only had 2 yr of observations. The combined average, annual, gauged flows for these two rivers after regression to fill in the time series account for 53% of gauged streamflow in Australia–Oceania (Table 3). Many of the island gauges have drainage areas smaller than a 0.5° grid cell and are located in the mountainous headwaters, which should have higher runoff than the grid cell as a whole. Similar to Eurasia, the reason that the lowest estimates for this region come from water balance methods is because they do not include these islands (Table 4). The number of islands included in the analysis and the accuracy of their estimated drainage areas is likely to have a large impact on any estimate of streamflow from Oceania to the oceans.
f. Reference period
To test the sensitivity to the selected reference periods, we computed 10-yr (water year), moving average discharge from each continent for each of our hybrid and raw simulation datasets. The global results are shown in Fig. 6. Globally, the lowest estimate of 10-yr average flow was 43 100 km3 yr−1 (Sheffield-Ocean 1962–72), and the highest was 45 500 km3 yr−1 (WATCH-Land 1981–91). WATCH-based hybrid estimates peak in the 1980s, while Sheffield-based hybrid estimates decrease. This is attributable to an increase over South America, which has the largest temporal variability in 10-yr average discharge. Averages are lowest in the late 1950s to early 1960s for both raw VIC simulations and all hybrid estimates. The range of estimates related to the reference period is within the uncertainty bounds found for the long-term estimate from the jackknife analysis. Even the lowest estimates are higher than those of DT02, D09, and F02, suggesting that the selection of reference period is not a driving factor in differences between datasets.
The 10-yr moving average discharge globally to oceans from all exorheic areas.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
The 10-yr moving average discharge globally to oceans from all exorheic areas.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
The 10-yr moving average discharge globally to oceans from all exorheic areas.
Citation: Journal of Hydrometeorology 16, 4; 10.1175/JHM-D-14-0183.1
5. Conclusions
Estimates of global and continental runoff vary widely depending on the method and the degree to which observational data are included. Our best estimate of mean discharge from the continents to the global oceans, based on the average of four combinations of VIC simulations of runoff and in situ streamflow observations, is 44 240 (±2660) km3 yr−1. Of this, 3820 (±720) km3 yr−1 comes from Africa; 16 640 (±750) km3 yr−1 comes from Eurasia; 13 240 (±2430) km3 yr−1 comes from South America; 7140 (±280) km3 yr−1 comes from North America; and 3400 (±120) km3 yr−1 comes from Australia–Oceania. In comparing our estimates of discharge to other estimates, we found the following:
Interpolated in situ gauge observations, LSM simulations, and hybrid estimates (combining streamflow observations with LSMs) generally produce similar global streamflow estimates, with the mean of previously reported estimates of 39 860 ± 4670 km3 yr−1 (38 770 ± 3760 km3 yr−1 if water balance methods, which are not strictly comparable to the others, are excluded). Our best estimate falls at the upper end of this range.
The water balance methods we included rely on spatially accurate evapotranspiration and precipitation from atmospheric reanalysis datasets. As such, they are a better indicator of uncertainty in reanalysis products than of uncertainty in the global runoff estimate. The water balance methods also excluded most islands, which are important sources of runoff, particularly in Oceania, which accounts for more than 6% of global discharge. These methods, on average, produced lower discharge estimates than any of the other methods except in North America.
Additional constraints—more in situ streamflow observations and/or better model simulations, including better forcing data—are needed in poorly observed regions of high runoff. These regions include the southern tip of South America and the islands of Oceania.
Without additional observations, it is not possible to determine whether or not the LSM we used (VIC) as part of our method to estimate discharge from ungauged basins is differentially biased in unobserved basins relative to neighboring observed basins from which bias correction factors are derived. This appears to be the basis for most of the differences in our runoff relative to F02 and D09, who used different LSMs.
Ensuring continuation of accurate observation of streamflow on the Congo and Amazon Rivers, which provide the majority of runoff from Africa and South America, respectively, is critical to quantifying global streamflow and tracking changes in the global hydrologic cycle.
Acknowledgments
The authors thank Hiroko Kato Beaudoing for processing the MERRA and GLDAS runoff estimates and the Global Modeling and Assimilation Office (GMAO) and GES DISC for the dissemination of MERRA and GLDAS. The authors thank Aiguo Dai for his thoughtful comments on early versions of this manuscript. We are grateful for funding from the NASA Energy and Water Studies (NEWS) under Grant NNX13AD26G to the University of Washington and from NOAA Grant NA14OAR4310218 to Princeton University. The runoff dataset will be made freely available (online at http://hydrology.princeton.edu) after the publication of this paper.
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