HYDROLOGICAL PROCESSES
Hydrol. Process. 25, 1114– 1128 (2011)
Published online 23 July 2010 in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/hyp.7795
Global-scale river routing—an efficient time-delay algorithm
based on HydroSHEDS high-resolution hydrography
L. Gong,1,2 * S. Halldin1 and C.-Y. Xu1,2
1
2
Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36 Uppsala, Sweden
Department of Geosciences, University of Oslo, P.O. Box 1047, Blindern, NO-0316 Oslo, Norway
Abstract:
Coupling of global hydrologic and atmospheric models is difficult because of the highly nonlinear hydrological processes
to be integrated at large scales. Aggregation of high-resolution data into low-resolution spatial distribution functions is one
way to preserve information and account for the nonlinearity. We used HydroSHEDS, presently the most highly resolved
(300 ) global hydrography available, to provide accurate control on global river routing through a computationally efficient
algorithm. The high resolution of HydroSHEDS allowed discrimination of river-channel pixels, and time-delay distributions
were calculated for all such pixels. The distributions were aggregated into network-response functions (NRFs) for each lowresolution cell using an algorithm originally developed for the 1-km-resolution HYDRO1k hydrography. The large size of
HydroSHEDS required a modification in algorithm to maintain computational efficiency. The new algorithm was tested with
a high-quality local and a more uncertain global weather dataset to identify whether improved routing would provide a gain
when weather data quality was limiting. The routing was coupled to the WASMOD-M runoff-generation model to evaluate
discharge from the Dongjiang River and the Willamette River basins. The HydroSHEDS-based routing, compared with the
HYDRO1k-based routing, provided a small gain in model efficiency, for local and global weather data and for both test basins.
The HydroSHEDS-based routing, contrary to the HYDRO1k-based routing, provided physically realistic wave velocities. The
most stable runoff-generation parameter values were achieved when HydroSHEDS was used to derive the NRFs. Routing
was computed in two steps: first, a preparatory calculation which was a one-time effort and second, the routing during each
simulation. The computational efficiency was four to five orders of magnitude better for the simulation step than that for the
preparatory step. Copyright  2010 John Wiley & Sons, Ltd.
KEY WORDS
river routing; HydroSHEDS; computational efficiency; global scale; time-delay algorithm; aggregation;
high-resolution hydrography
Received 17 September 2009; Accepted 13 May 2010
INTRODUCTION
Global water resources are commonly assessed by global
hydrological models, whereas the interaction between
the global hydrological cycle and the atmosphere is
commonly studied with land-surface schemes. The two
approaches differ in complexity and in land-surface
parameterization. Global hydrological models are commonly simpler than land-surface schemes and require less
input data and computational resources. However, the
lack of feedback mechanisms and their weaker physical
foundation lower their ability to predict changes in the
hydrological system under changing land use or changing climate. Land-surface schemes, however, commonly
lack ability to represent direct anthropogenic influence
on the water cycle, are computationally more demanding, and have seldom, if ever, been tested for equifinality or parameter and model-structure uncertainty. Both
approaches are weak when it comes to parameterization
of the lateral transport of water. This parameterization
often uses low-resolution flow networks and routing algorithms developed for smaller scales. This introduces bias
* Correspondence to: L. Gong, Department of Geosciences, University of
Oslo, P.O. Box 1047, Blindern, NO-0316 Oslo, Norway.
E-mail: lebing@gmail.com
Copyright  2010 John Wiley & Sons, Ltd.
in transport time and scale dependency in model performance and model parameters (Gong et al., 2009).
Large-scale hydrologic and atmospheric modellers put
much effort on the scale dependency of their algorithms. Hydrological processes that are integrated to, e.g.
a 0Ð5° global cell are nonlinear over widely different
smaller scales. The use of average values of climate
forcing and land-surface properties reduces the spatial
variation of those inputs, which in turn reduces the
chance of the simulated discharge to cover low and
high extremes in space and time. Most global hydrological models currently calculate the water balance on
daily or sub-daily scales, whereas validation is carried
out over latitude bands and continental and global totals
at monthly or annual time scales. Uncertainties at finer
scales are seldom dealt with. Although high-resolution
flow networks exist, e.g. the 1-km HYDRO1k (USGS,
1996), the lateral transport of water is normally simulated with low-resolution flow networks, the spatial
resolutions of which typically range from 0Ð5° ð 0Ð5°
to 4° ð 5° latitude–longitude (Miller et al., 1994). A
0Ð5° ð 0Ð5° grid (Hageman and Dumenil, 1998; Graham et al., 1999; Renssen and Knoop, 2000; Vörösmarty
et al., 2000b; Döll and Lehner, 2002) has been found
suitable for a broad range of global water-resource and
GLOBAL-SCALE RIVER ROUTING WITH HydroSHEDS
water-quality studies (Vörösmarty et al., 2000a), and it
has been adopted by a number of global water-balance
models (Arnell, 1999; Fekete et al., 2002; Döll et al.,
2003). Most large-scale routing models apply storagebased routing algorithms based on mass conservation
and relationships between river-channel storage and river
inflows and outflows. Linear reservoir-routing methods
are widely used on large-scale networks because of their
conceptual simplicity. Examples are the routing models
by Sausen et al. (1994), Miller et al. (1994), and Liston et al. (1994), the HD model (Hagemann and Dumenil, 1998), Total Runoff Integrating Pathways (TRIP)
(Oki et al., 1999) and its applications (Oki et al., 2001;
Decharme and Douville, 2007; Falloon et al., 2007),
HYDrological Routing Algorithm (HYDRA) (Coe, 2000)
and its application (Li et al., 2005), Water Transport
Model (WTM) (Vörösmarty et al., 1989) and its application (Fekete et al., 2006), River Transport Model (RTM)
(Branstetter and Erickson, 2003), and the routing model
of WaterGap Global Hydrological Model (WGHM) (Döll
et al., 2003).
The quality of global runoff routing depends on both
flow network and routing algorithm. Du et al. (2009)
present the effect of grid size on the simulation of a
small catchment (259 km2 ) in the humid region in China.
They show that changes in the spatial model resolution
affect the simulation because of different values of Geographic Information System (GIS)-derived slopes, flow
directions, and spatial distribution of flow paths. Three
types of Digital Elevation Models (DEMs) with grid sizes
of 100, 200, and 300 m were used to simulate storm discharge in their study. They concluded that results are poor
when grid size is larger than 200 m. Arora (2001) compared runoff routing at 350- and 25-km scales with the
same runoff input and concluded that discharge is biased
at large scales and also more error-prone at high and low
flows. The method of Guo et al. (2004) to scale up contributing area and flow directions is designed to improve
decreasing model performance with decreasing spatial
resolution. Although the overall performance improves
and reaches a maximum at 7Ð50 , model performance
decreases continuously at increasingly lower resolutions.
Yildiz and Barros (2005) found a strong dependency in
the Monongahela River basin between simulated runoff
components and flow-network resolution, in particular,
when using a 5-km resolution instead of a 1-km resolution. Less sub-surface and more surface runoff was
simulated as a result of the lower hydraulic gradients.
The runoff-generation mechanism was inconsistent with
observations at the lower spatial resolution, and it not
only resulted in a bad fit to observed discharge but also in
the hydraulic-conductivity parameter that had to be given
non-realistic values to compensate the lower gradients at
this resolution (Yildiz and Barros, 2005).
Gong et al. (2009) show that cell-to-cell reservoirrouting algorithms are strongly scale dependent. Such
a dependency can significantly alter the routing performance, while at the same time introducing, through calibration, a strong influence on the water-balance parameter
Copyright  2010 John Wiley & Sons, Ltd.
1115
values. It can also, especially in combination with the lack
of convective time delays (Beven and Wood, 1993), i.e.
an upstream input will have an immediate effect on the
downstream output, lead to a considerable drop in performance at large scales. The aggregated network-response
function (NRF) algorithm (Gong et al. (2009) aims at
overcoming these problems. The NRF algorithm transfers spatially distributed time-delay information extracted
from HYDRO1k in the form of simple delay histograms
to lower resolution spatial grids. The algorithm is shown
to perform equally well and independent of scale for
spatial resolutions ranging from 50 to 1° . Storage-based
routing methods are computationally at a disadvantage
because they require time steps much shorter than the
time steps of the runoff-generation algorithms used in
global models (Liston et al., 1994; Coe, 1998; Kaspar,
2004; Sushama et al., 2004). The time steps may ultimately be too short for available computational capacity
when global water-balance models are extended to finer
spatial scales than that commonly used today. NRF routing, however, only requires large computational capacity
at an initial stage to aggregate the time-delay distribution to the lower resolution grid for which the runoffgeneration algorithm is intended. The application of the
NRF algorithm then does not require a time step different
from the runoff-generation algorithm, nor significantly
different computational capacity.
HydroSHEDS (Lehner et al., 2008), an even more
detailed hydrography than HYDRO1k, was published
soon after conclusion of the work by Gong et al. (2009).
HydroSHEDS has a spatial resolution of 300 and covers
the globe approximately within š60° latitude. Few studies on HydroSHEDS have been reported because the data
have been available only for a short time. Getirana et al.
(2009) discuss the algorithms used by HydroSHEDS to
extract the drainage structure from the Shuttle Radar
Topography Mission (SRTM) data and compare them
with more alternative ones. Li et al. (2009) use the
HydroSHEDS flow-direction dataset at 300 resolution to
drive a combined time-delay and linear reservoir method
for operational flood prediction in Lake Victoria.
The main purpose of this investigation was to test
the costs and benefits of using HydroSHEDS instead of
HYDRO1k data in the NRF algorithm to derive spatially
distributed time-delay information for runoff routing. The
goal was met by comparing routing performance, routing
parameters, and runoff-generation parameters between
HydroSHEDS- and HYDRO1k-based NRF-routing models (Gong et al., 2009). The HydroSHEDS data were used
at its native 300 resolution with the NRF routing in two
well-studied basins to demonstrate the potential of the
method at continental and global scales. Special emphasis
was put on the computational efficiency of the new algorithm. A second purpose was to evaluate whether there
was any significant gain when time delays were derived
from the detailed HydroSHEDS database, compared with
HYDRO1k, in a situation where precipitation input was
based on the locally uncertain, globally covering data
Hydrol. Process. 25, 1114– 1128 (2011)
1116
L. GONG, S. HALLDIN AND C.-Y. XU
rather than on more certain data, interpolated from dense
local high-quality observations.
MATERIALS AND METHOD
River basins, climate data, and hydrography
We used two well-documented, medium-sized basins,
the Dongjiang (East River) basin in southern China [used
by Gong et al. (2009)] and the Willamette River basin
in north America, to ascertain that the routing-algorithm
properties would not be influenced too much by poor
climatic and hydrological data or disturbed by nondocumented regulations by dams and reservoirs or water
abstraction. Both basins are still large enough to retain
generality of the result in a study of global hydrology.
The Dongjiang River is a tributary to the Pearl River
with a 25 325-km2 drainage area above the Boluo gauging
station. The basin has a dense network of meteorological and hydrological gauging stations, and its hydrology is well studied (e.g. Chen et al., 2006, 2007; Jiang
et al., 2007; Jin et al., 2009, 2010). The climate is subtropical with an average annual temperature of around
21 ° C and only occasional sub-zero winter temperatures
in the mountains. The average annual precipitation for the
period 1960–1988 is 1747 mm, and the average annual
runoff is 935 mm or 54% of the average annual precipitation. About 80% of the annual rainfall and runoff occur
during the wet season from April to September. The basin
presents a complex mixture of Pre-Cambrian, Silurian,
and Quaternary geological formations showing as granites, sandstone, shale, limestone, and alluvium. The landscape is characterized by 83% mountains and hills, 13%
plains, and 3Ð8% inland water area. The basin is covered
by forest at higher altitudes, whereas intensive cultivation
dominates hills and plains. Local daily hydrometeorological data were retrieved for the Dongjiang basin for the
period of 1982–1983. The National Climate Centre of the
China Meteorological Administration provided data on
air temperature, sunshine duration, relative humidity, and
wind speed from seven weather stations inside or close
to the basin. Precipitation data from 51 gauges and discharge data from 15 gauging stations were retrieved from
the Hydrological Yearbooks of China issued by the Ministry of Water Resources. Potential evaporation was calculated from air temperature, sunshine duration, relative
humidity, and wind speed with the Penman–Monteith
equation in the form recommended by the Food and Agriculture Organization (FAO) (Allen et al., 1998).
The Willamette River is located upstream of the
Columbia River at Portland. The basin has an area
of 29 000 km2 above the Portland gauging station. The
Willamette is a large river with a gravel-dominated bed
(Hughes and Gammon, 1987), which drains a humid alluvial valley with extensive active and relict floodplains
(Parsons et al., 1970). The Willamette Valley lies roughly
80 km from the Pacific Ocean, and prevailing westerly
marine winds give it a Mediterranean-type climate (Taylor et al., 1994). The average daily temperature for the
Copyright  2010 John Wiley & Sons, Ltd.
period 1996–2009 is around 8 ° C and average annual precipitation is around 1180 mm. About 5% of the precipitation falls as snow. Winters are cool and wet, summers
warm and dry. Most runoff and flooding are caused by
winter rains. Winter rainfall on melting snow is the primary mechanism of generation of flood flows (Waananen
et al., 1971; Hubbard et al., 1993). Melting snow at high
elevations at the Cascade Range adds a seasonal runoff
component during April and May. We did not have access
to high-quality local weather data from the Willamette
River basin but ran the model only with weather data
from global datasets.
When running a global water-balance model, only
global weather datasets can be used. The water balances of both selected basins were, therefore, modelled for 6–10 years with weather data from three
global remotely sensed or reanalyses datasets. Precipitation data were constructed by combining a 0Ð25° and
a 1° dataset: the Tropical Rainfall Measuring Mission
(TRMM) 3B42 dataset (Huffman et al., 2007), which
has a coverage between 50 ° S and 50° N, and the GPCD
1DD dataset (Huffman et al., 2001), which covers the
whole globe. TRMM is a recently developed precipitation database based on a combination of infrared
measurements from geostationary satellites and passive
microwave measurements from polar-orbiting satellites.
TRMM has a spatiotemporal resolution of 3 h and 0Ð25°
latitude–longitude. We rescaled the combined precipitation to 0Ð5° through linear interpolation. Air and dewpoint temperatures were obtained from the ERA-interim
reanalysis dataset (Simmons et al. 2007). The comparison between local and global datasets for the Dongjiang
basin allowed us to assess whether the weather data quality could mask routing improvements.
HydroSHEDS (Lehner et al., 2008), a gridded global
hydrography with the highest resolution publicly available today, was used to delineate the hydrography of
both the basins. HydroSHEDS provides hydrographical information in a consistent and comprehensive format for regional- and global-scale applications. It offers
a suite of geo-referenced datasets (vector and raster)
at various scales. Available resolutions range from 300
(approx. 90 m at the equator) to 50 (approx. 10 km at
the equator) with seamless near-global extent between
56 ° S and 60° N. The dataset includes river networks,
watershed boundaries, drainage directions, and a number of ancillary datasets. HydroSHEDS is derived from
elevation data of the SRTM at 300 resolution. The original
SRTM data have been hydrologically conditioned using
a sequence of automated (void-filling, filtering, stream
burning, and upscaling techniques) and manual procedures. Lehner et al. (2008) indicate that the accuracy of
HydroSHEDS significantly exceeds that of other existing global watershed and river maps. The HydroSHEDS
dataset does not include upstream areas, so these were
derived from flow directions in this work. The high resolution of HydroSHEDS made it possible to identify river
pixels, so channel network routing was performed for
river pixels only.
Hydrol. Process. 25, 1114– 1128 (2011)
GLOBAL-SCALE RIVER ROUTING WITH HydroSHEDS
1117
The HYDRO1k hydrography dataset (USGS, 1996)
was used for a comparison with HydroSHEDS for
the Dongjiang River basin. HYDRO1k is derived from
the GTOPO30 3000 global-elevation dataset and has a
spatial resolution of 1 km. The HYDRO1k dataset was
developed on a Lambert azimuthal equal-area projection
in order to maintain uniform grid-cell area. HYDRO1k
is hydrographically corrected such that local depressions
are removed and basin boundaries are consistent with
topographic maps. HYDRO1k includes hydrology-related
data layers, such as aspect, flow direction, drainage area,
elevation gradient, compound topographic index, basin
and sub-basin boundaries, and DEM-derived stream lines.
The lower resolution of HYDRO1k did not allow river
identification, so we assumed that each HYDRO1k pixel
contains some river channel.
A global-scale flow network conserving local-scale
information
0Ð5°
We aggregated the hydrography dataset into
cells
(referred to as ‘global cells’ in the following), and then
connected those global cells through the flows occurring
at the borders, i.e. through flow paths that transport water
from one cell to another. The procedures to construct
HydroSHEDS hydrography for individual cells, to define
border flows, and to construct NRFs for runoff routing
are described in subsequent sections.
The HydroSHEDS dataset is distributed as 5° tiles
covering latitude bands between 56 ° S and 60° N. Two
types of data, the hydrologically conditioned elevations,
and flow directions were split into 0Ð5° tiles coinciding
with the model cells. Prior to the construction of the
flow network, slope was calculated for each pixel with
the neighbourhood method (Srinivasan and Engel, 1991),
which calculates the slope for a centre pixel by considering all its eight neighbour pixels. The area of each
pixel was calculated by assuming a spherical earth model.
Upstream area and basin boundaries are among most
important hydrological features but are usually poorly
defined with low-resolution global flow networks. The
use of HydroSHEDS ensured that any large river basin
could be delineated accurately.
Upstream area identification and river-channel routing
required an efficient way to index the large number
of HydroSHEDS pixels. The position of a pixel in a
global cell was indexed by the global cell and its relative
position in that cell. Global cells were indexed by a
number C depending on their positions. With global
cells covering the whole earth, the northwest-most cell
(centred on the zero meridian) got an index of 1, its
immediate southern neighbour 2, the immediate eastern
neighbour cell 361, and so on. Because the resolution
of HydroSHEDS is 300 , there are 600 ð 600 pixels within
each global cell. Those pixels were indexed with P in the
same manner as the global cells. In this way, any pixel
can be located by two indices (C, P). The HydroSHEDSconditioned DEM, flow directions, and the derived pixel
slopes and areas were stored as individual files for each
Copyright  2010 John Wiley & Sons, Ltd.
Figure 1. Schematic chart showing the five-step procedure of extracting
flow-path structure and constructing NRF for large-scale, low-resolution
cells from the high-resolution HydroSHEDS hydrography. The procedure
is performed on HydroSHEDS pixels within each low-resolution cell
(local), on pixels bordering low-resolution cells (global), and finally for
all cells covering a given basin (basin)
global cell. The flow network, derived from the flowdirection data, was first constructed as ‘local flows’
within each cell and then as ‘border flows’ between cells.
The border flows were sorted by the flow-accumulation
order at the global cell scale. They were then used to
derive time-delay distributions and total upstream area
for each pixel. A schematic chart (Figure 1) demonstrates
the five-step procedure.
Step 1. Each cell was treated as an independent catchment with multiple inflows and outflows that exchange
water at the border lines. The eight possible flow directions provided by HydroSHEDS were translated into a
two-column flow-path vector, each row of which represents a single transport from a source pixel to a sink
pixel. The sequence of the rows was sorted by the flowaccumulation order, i.e. a pixel that released its water to
its downstream pixel would never receive its upstream
input again. The sequence in the sorted flow-path vector
ensured the correct flow accumulation within each global
cell in this way. Once the sorted flow-path vector was
constructed for each cell, two by-products were derived,
namely the local upstream and downstream pixels for all
border pixels, i.e. the pixels that have one or two sides
on the border of a cell.
Step 2. For each global cell, except single-cell islands,
there are always some flow paths that start with a border pixel and end with a border pixel in another cell.
As pixels were indexed by (C, P), border flows could
be identified with different C numbers for source and
sink pixels. Those border (global) flows were identified at
this stage, and they served as linkages for internal (local)
flows inside each global cell. Contrary to previous global
flow networks, a global cell in our case was allowed to
have multiple inflows and outflows on its border as well
Hydrol. Process. 25, 1114– 1128 (2011)
1118
L. GONG, S. HALLDIN AND C.-Y. XU
Figure 2. The connection of global-scale flows through downstream pixels of border pixels for (a) the Dongjiang River basin and (b) the Willamette
River basin. The global flow paths are used to connect flows between cells and to update upstream areas. The global flow paths derived only from
pixels at the low-resolution cell borders greatly simplify the flow-structure complexity, which is used for the basin-scale flow accumulation
as ‘loop flows’ entering another cell and coming back
later. Each large river basin and each continent has a very
large number of flow paths at a 300 resolution. This large
number could be handled with present-day computational
resources by separating the flows into border (global) and
within-cell (local) flow paths. The independency of local
flows allowed local flow structures to be constructed in
parallel for all cells before any large-scale hydrographical or routing calculations were initiated. Only global
flows were needed to construct global-scale hydrological
features, such as upstream area, and time-delay distribution for large basins and continents. This greatly reduced
computation time and memory demand.
Step 3. The most important procedure in the conversion
of HydroSHEDS flow-direction data into NRFs was
to sort the global (border) flows to represent correct
flow accumulation. The border flows served as links
to transport discharge from one cell to its downstream
neighbour. To achieve a correct flow accumulation at the
global scale, the same rules were applied to pixels in
neighbouring cells as for within-cell pixels, namely any
border pixel that released water to a downstream cell was
prohibited from receiving water from an upstream cell.
The border flows were internally linked with the local
downstream pixel at each border, a by-product created
in step 1. The local downstream pixel for each border
pixel, except for ocean outlets or inland sinks, always
started in a border pixel and ended in another border
pixel. This feature offered an easy way to combine flows
at border pixels with local downstream pixels to form
complete flow paths. A global flow-path vector could be
constructed in this way for a basin or a continent and then
sorted by the flow-accumulation order. The global flowpath vector (Figure 2) was much simplified compared
with the full flow paths of HydroSHEDS.
Step 4. The within-cell (local) upstream area of each
border pixel was obtained in step 1 for all global
cells. The time delay from each upstream pixel to the
corresponding border pixel was calculated simultaneously
with the method detailed in step 5. The upstream area
and time delay were updated by continuously adding
Copyright  2010 John Wiley & Sons, Ltd.
the upstream area and time delay of a certain border
pixel to its downstream pixels inside its downstream cell.
Each time a border flow path was used for this updation
process, the order was taken from the sorted global flowpath vector to ensure that the updation was carried out
in the order of flow accumulation. For the 25 325-km2
Dongjiang basin, 12 992 border flows had to be updated
before all local values of upstream area and time delay
could be converted into global values.
For basins where discharge data were available,
upstream delineation could quickly be done with the aid
of the local upstream pixels of each border pixel. The
calculation of an upstream area for a given gauging station started in the cell containing the station and then
extended into neighbouring cells as defined by the border flows. The border flow indicated the border pixels of
the upstream cell that had direct contact, and the upstream
area within the cell of those border pixels were immediately included in the total upstream area of the gauging
station. This process was iterated until no more upstream
cells were found. The registration of a discharge station
in HydroSHEDS was done by first assigning the closest pixel to the reported station coordinates and then
by searching for the closest major river channel to the
assigned pixel. As the precision of a station location may
not always be sufficient, we marked surrounding riverchannel pixels with distinctly high upstream areas. The
pixel that best matched the published upstream area for
the discharge station was then selected.
Step 5. The NRF was obtained for each global cell
by aggregating time delays of all river pixels. Whereas
each HYDRO1k pixel was assumed to contain a river
channel, a HydroSHEDS pixel was required to exceed a
certain threshold area (TA) to be recognized as a river
pixel.
River-channel identification
One of the major differences between HYDRO1k and
HydroSHEDS was the possibility of identifying individual river-channel pixels in the latter dataset. The identification of such pixels was analysed in terms of the
Hydrol. Process. 25, 1114– 1128 (2011)
1119
GLOBAL-SCALE RIVER ROUTING WITH HydroSHEDS
trade-off between the gain in keeping as much detailed
information as possible and the need to meet computational requirements. The trade-off was analysed by an
upstream TA for each pixel, and a range of TA values between 0Ð5 and 1000 km2 was tested. Time delays
in days, when assuming a unit V45 (see subsequent
sections), were obtained for each river pixel and plotted against their corresponding upstream area in order
to identify the influence of river-channel detail on the
time delays. Time-delay distributions were then compared for four intervals of upstream area, viz. 0Ð5–10,
10–100, 100–1000, and 1000–10 000 km2 . Whole-basin
NRFs were constructed with the four corresponding TA
values of 0Ð5, 10, 100, and 1000 km2 to show the integrated effect of the time-delay distributions. Runoff generation was assumed to be evenly distributed into the
river pixels before the routing was implemented, so only
river-channel delay was considered. River-channel identification was only performed on the Dongjiang basin
and the selected TA value was then also used on the
Willamette basin.
Calculation of time delays by HydroSHEDS
We used the NRF method of Gong et al. (2009), based
on the HYDRO1k hydrography, to calculate flow delays
at a 0Ð5° latitude–longitude resolution but had to extend
it in some respect to account for the native 300 resolution
of HydroSHEDS. The slightly modified method is briefly
described in subsequent sections.
Once the river pixels were chosen, a 24-h response
function was calculated with the diffusion-wave solution
of the full St Venant equations for all river pixels. A daily
response function was obtained by integrating the 24-h
response functions. The diffusion-wave equation requires
both a dispersion coefficient D and a wave velocity c to
be calibrated against downstream discharge observations.
We found this to introduce equifinality between the two
parameters without any performance gain. To simplify
the method, we made the same assumption as Gong
et al. (2009) that the daily pixel-response function could
be obtained by integrating the 24-h response functions
with near-zero D. The 24-h response function is well
approximated by a pure translation of the daily inflow
according to the wave velocity in this case.
The daily response function was specific for each river
pixel, so it was named river-response function (RRF) and
was used as the source of aggregation:
RRFtd D
Q24 tdt
1
td
where t is the time after runoff generation, td the days
after runoff generation, and Q24 the 24-h response function. Each RRF consists of a number of percentages of
runoff (p1 , p2 , . . . , pn ) arriving on days (d1 , d2 , . . . , dn )
following the runoff-generating day. When D is assumed
to be near zero, the RRF is reduced to two percentages
of arriving discharge (p1 , p2 ) for two consecutive days
(d1 , d2 ), which are sufficiently described by p1 and d1 .
Copyright  2010 John Wiley & Sons, Ltd.
This simplification is shown by Gong et al. (2009) to
considerably lower the computational demand, while still
providing correct travel time for discharge.
The d1 and p1 parameters were directly obtained from
the travel time t, which is a function of the network wave
velocity and network topology. We assumed that the
wave velocity was only a function of slope. Following the
delay calculation developed by Beven and Kirkby (1979),
we denoted the distances of the flow-path segments from
any HydroSHEDS pixel down to the reference pixel as
l1 , l2 , . . . , ln and the corresponding slopes as tan(b1 ),
tan(b2 ), . . ., tan(bn ). We also postulated a normalized
network wave velocity (V45 ) for a slope of tan(45° ). We
adopted the finding of Gong et al. (2009) that velocity is
less sensitive to slope for large-scale than for small-scale
water transport and assumed that
Vi D V45 tanbi 2
This time-constant velocity led to the following
equation for time delay from any given pixel to the reference pixel:
n
li
tD
3
V
45 tanbi iD1
where V45 should be calibrated against observed discharge. There is no need to use meandering factors for
the flow–path–segment distances because V45 represents
an effective network speed.
Like other large-scale water-balance studies, we did
not calculate runoff generation at the pixel scale. A
cell-response function (CRF) was, therefore, derived by
aggregating all the RRFs within a cell and normalizing
to unit volume:
1
RRFi td n iD1
n
CRFtd D
4
where n (360 000) is the number of pixels in a cell. The
aggregation from RRF to CRF transfers distributed delay
information, in the form of a daily NRF, to any lower
resolution defined by the size of the cell. Equation (4)
takes the simplest form of the aggregation by assuming
that runoff generation is constant throughout the cell, a
condition that could be relaxed to dynamically weigh
the aggregation by the sub-cell variation of runoff input.
The CRF offers flood-peak attenuation by redistributing a
1-day upstream discharge downstream over 2 (for a pixel)
or more (for a cell) days.
An NRF to a distributed daily runoff input was finally
calculated as
NRFtd D
m
Qj Ð CRFj td 5
jD1
where m is the number of cells covering the basin
and Qj is the runoff-generation volume of the jth
cell. Equations (4) and (5) indicate that although channel
response is represented at the cell level, it still contains
all the delay information from the pixel level. This is
Hydrol. Process. 25, 1114– 1128 (2011)
1120
L. GONG, S. HALLDIN AND C.-Y. XU
equivalent to directly using contributing area instead of
the number of channel reaches at a given distance away
from the outlet. The downstream hydrograph is obtained
by the convolution of NRF with the input runoff time
series.
The CRF derived in this way for a low-resolution
cell preserves the full delay information from all
HydroSHEDS river pixels. It tells explicitly on which
day (½2) the generated runoff reaches the reference pixel
and the percentage of discharge arriving on each day. The
efficiency of the algorithm stems from the fact that the
demanding calculations of the RRFs and the CRFs are
done before the convolution as a one-time preparatory
effort for all subsequent simulations.
Runoff generation
The global water-balance model WASMOD-M is based
on the WASMOD (Xu, 2002) monthly conceptual waterbalance model, which has been successfully applied in
many parts of the world. Other global water-balance
models route their runoff with a finer time step than
used for runoff generation (e.g. Döll et al., 2003). The
daily version of WASMOD-M was used in this study. It
required daily climatic input and generated runoff in each
cell with a daily time step. Compared with the monthly
WASMOD-M (Widén-Nilsson et al., 2007), the daily
version required its fast- and slow-runoff formulations
to be modified, in this case, to a nonlinear exponential
form:
SP D 1 ec1 ÐLM
6
F D Pn ð SP
7
S D LM ð 1 ec2 ÐLM 8
All other parts of WASMOD-M took the same form
as in Widén-Nilsson et al. (2007), e.g. actual evaporation
(E):
9
E D min[Ep ð 1 a4 AW/Ep , AW]
where SP is the percentage of each cell area that is
saturated, LM is the land moisture (water available in
each cell for actual evaporation and runoff), F is the
fast runoff, S is the slow runoff or base flow, Pn is
the net rainfall, AW is the water available for actual
evaporation, Ep is the potential evaporation. c1 [mm1 ],
c2 [mm1 ], and a4 [] are parameters, all of which have
a potential range from 0 to 1. The equations for Pn ,
AW, and LM are given by Widén-Nilsson et al. (2007).
The daily WASMOD-M version was used to simulate
runoff generation for each cell. In a snow-free region
such as the Dongjiang basin, WASMOD-M had only
three parameters: the evaporation parameter a4 , the fastrunoff parameter c1 , and the slow-runoff parameter c2 . In
the Willamette basin, two additional snow parameters, a1
and a2 , were used (Xu, 2002).
Calibration of model parameters
One thousand parameter-value sets were obtained by
Latin-Hypercube sampling (McKay et al., 1979) with
Copyright  2010 John Wiley & Sons, Ltd.
prior uniform distribution. Initial parameter-value ranges
were set with the same empirical values as reported by
Gong et al. (2009) and Xu (2002) for snow parameters.
WASMOD-M was run with the same 1000 parametervalue sets and the resulting 1000 runoff-generation time
series were saved as input to the routing models.
The runoff time series for each of the 1000 simulations
were used to calibrate the best wave velocity for both
HydroSHEDS- and HYDRO1k-derived NRFs. The Nash
and Sutcliffe (1970) efficiency was used as objective
function. The calibration was done with a range of V45
from 3 to 30 ms1 in steps of 1 ms1 . Calibrations were
performed for each of the 28 velocities, each one using
the same 1000 runoff time series to derive the NRF
in order to obtain 1000 model efficiencies for both the
basins studied. The wave velocity that gave the highest
efficiency was then chosen for the calibration of runoffgeneration parameters, and the top 2% parameter-value
sets were chosen as behavioural (in the Generalised
Likelihood Uncertainty Estimation (GLUE) sense, Beven
and Binley, 1992).
The calibration was done with local meteorological
data for the Dongjiang basin for the period 1982–1983.
Three years preceding the calibration period were used
to warm up the model. Monte-Carlo simulations with the
same 1000 parameter-value sets were then carried out for
1997–2002 in the Dongjiang basin and for 1997–2008 in
the Willamette basin with the combined TRMM–GPCP
precipitation and ERA-interim temperature and dew temperature data as weather input. Potential evaporation was
calculated by FAO-56 recommended equations (Allen
et al., 1998) from temperature and dew-point temperature
data. The top 2% simulation results for response functions derived from HYDRO1k and HydroSHEDS were
also used in these cases.
Computational efficiency
The computational time was recorded on a Windows
XP PC (Intel Pentium 4, 3 GHz CPU, purchased in 2005)
for three different tasks for the Willamette River basin
using the HydroSHEDS hydrography: (1) the calculation
of upstream area through the use of border flows, (2) the
computation of time delay for river pixels under a unit
V45 velocity, and (3) routing with the aggregated NRF
for a 10-year runoff simulation. The first two tasks
represent computationally demanding one-time efforts
for all subsequent simulations, whereas the third task
represents the computational requirements for an actual
simulation.
RESULTS
The HydroSHEDS representation of the Dongjiang basin
The HydroSHEDS representation of the Dongjiang
basin is presented here to show the degree of detail
elaborated by the algorithm. The numerical characteristics for the Willamette River basin were similar. The
downstream Boluo station of the Dongjiang basin was
Hydrol. Process. 25, 1114– 1128 (2011)
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GLOBAL-SCALE RIVER ROUTING WITH HydroSHEDS
Figure 3. Pixel upstream areas (logarithmic scale) for downstream cell of the Dongjiang basin: (a) upstream area based on HydroSHEDS, obtained by
only considering flow accumulation inside each low-resolution cell, (b) upstream area based on HydroSHEDS, taking into account flow accumulation
from all upstream cells, and (c) upstream area of all upstream cells deduced from HYDRO1k. Pixels with less than 1 km2 upstream area are shown
in white
registered to the HydroSHEDS pixel (211814, 203809).
In this study, 21 upstream cells were identified, each of
which partly or fully contributed to the drainage area of
the downstream station. The complete upstream area was
identified as 25 381 km2 with HydroSHEDS as a basis
but as 25 886 km2 with HYDRO1k as a basis (Gong
et al., 2009).
There were 3 234 541 HydroSHEDS pixels identified
upstream of the Boluo station, about 125 times more
than the number of pixels identified in HYDRO1k. The
3 234 541 flow paths were constructed to represent the
complete flow dynamic, which included transport both at
hillslope scale and in river channels. The use of combined local-scale (within cell) and global-scale (between
cells) flow paths allowed a great degree of simplification
(Figure 2) for the global-scale flow accumulation. Only
12 922 global flow paths, i.e. 0Ð4% of the complete number of flow paths, were needed to derive pixel upstream
area and time-delay distribution by the continuous updation procedure that added upstream-cell values to downstream cells. The updation started with individual pixel
values (Figure 3a) and ended when all upstream pixel
areas and time delays had been added to the upstream
area (Figure 3b). Figure 3b shows that stream channels
retained the same shape at the end of the updation
procedure but the upstream area of the main channel
was greatly increased by adding all upstream contributions. A comparison with the HYDRO1k upstream area
(Figure 3c) showed that only the main stream of the river
was correctly represented in HYDRO1k. A considerable
loss in local-scale delay information, together with some
disagreement in the basin delineation, can be seen. The
range of upstream area values, however, remained similar
for both HydroSHEDS and HYDRO1k.
The resolution of the flow network had a considerable
effect on slope. The spatial distribution of pixel slope,
as demonstrated in Figure 4, showed large differences
when based on HYDRO1k compared with HydroSHEDS
data in both the basins studied. The spatial variation
pattern agreed but the range differed between the two
slope maps. The maximum slope for the Dongjiang basin
Copyright  2010 John Wiley & Sons, Ltd.
increased from 18° to 50° , and for the Willamette basin
from 27° to 57° , when introducing HydroSHEDS instead
of HYDRO1k.
River-channel identification
Time delays (Figure 5a) showed a wide and stable
range for upstream areas of less than 100 km2 in the
Dongjiang basin. The range of time delays quickly converged towards lower values when TAs were larger than
100 km2 , suggesting a shorter transport time for the
major downstream channels. The time-delay distributions showed similar bimodal behaviour for the intervals 0Ð5–10 and 10–100 km2 , with peaks at 10 and
20 days, indicating a similarity in transport times for
small tributaries. This could be understood as a compensation effect between slope and distance (Figure 5b).
The bimodal trend was visible but less apparent for the
100–1000 km2 interval. Stream channels with upstream
TAs in the interval 1000–10 000 km2 showed a uniform
response function with a shorter concentration time than
that for smaller channels. NRFs with TAs of 0Ð5, 10,
and 100 km2 values gave similar bimodal distributions,
whereas the 1000-km2 threshold value gave a more uniform response (Figure 5c). This meant that TA values
between 0Ð5 and 100 km2 for river identification gave
similar time-delay distributions. The number of river cells
for TAs of 0Ð5, 10, and 100 km2 were 240 464, 61 248,
and 19 413, respectively, for the Dongjiang basin. If the
computational cost is a concern, a TA of 100 km2 would
give similar result but only require 8% of the computational time compared with a 0Ð5-km2 TA. Computational
time was not a concern in this work, so we used the 0Ð5km2 TA to guarantee that all the local-scale information
was extracted from HydroSHEDS.
The aggregated NRF
The aggregated NRFs showed clear differences when
based on HYDRO1k and HydroSHEDS (Figure 6). The
HYDRO1k-based NRFs had a wider distribution, indicating a slower basin response. This behaviour was the
Hydrol. Process. 25, 1114– 1128 (2011)
1122
L. GONG, S. HALLDIN AND C.-Y. XU
Figure 4. Slopes derived from 1-km HYDRO1k (a, c) and 300 HydroSHEDS pixels (b, d) for the Dongjiang River (a, b) and the Willametter River
basins (c, d). Note the different scales
Figure 5. (a) Time delays for each HydroSHEDS pixel having more than 0Ð5-km2 area upstream of the Boluo station of the Dongjiang basin, as a
function of its upstream area, assuming unit V45 wave velocity. (b) Time-delay distributions for river-channel pixels for four upstream TA intervals:
0Ð5–10, 10–100, 100– 1000, and 1000– 10 000 km2 . (c) Time-delay distributions for river-channel pixels obtained by assuming TAs of 0Ð5, 10, 100,
and 1000 km2
same for both Dongjiang and Willamette basins. With a
normalized wave velocity, V45 , of 5 m s1 , the maximum
time delays were 37 days for Dongjiang and 15 days for
Willamette when HYDRO1k was used but only 7 and
6 days, respectively, when HydroSHEDS was used.
Routing performance
The top 2% simulation results using NRFs derived
from HYDRO1k and HydroSHEDS gave the best fit
during the recession period in early spring of 1982
and during the wetting-up period of 1983 when using
HydroSHEDS (Figure 7a,b). A comparison between
Copyright  2010 John Wiley & Sons, Ltd.
HYDRO1k and HydroSHEDS for one randomly picked
behavioural discharge time series showed that both
routing models underestimated low flows. This might
indicate a less efficient algorithm for the runoff generation. HYDRO1k significantly overestimated high flows,
whereas HydroSHEDS showed less bias (Figure 7c).
Equifinality was found between calibrated snow parameters a1 and a2 , confirming the results of Widén-Nilsson
et al. (2009).
The trends and most efficient V45 values differed
considerably between HYDRO1k and HydroSHEDS
(Figure 7d). Calibration against observed discharge
Hydrol. Process. 25, 1114– 1128 (2011)
GLOBAL-SCALE RIVER ROUTING WITH HydroSHEDS
1123
Figure 6. Aggregated CRFs at 0Ð5° resolution for the Dongjiang River (a, b) and the Willamette River basins (c, d) with a unit wave velocity of
V45 D 5 m s1 . The distribution gives the time taken for runoff generated in a given pixel to reach the reference point, in this case, the down-most
discharge station (marked by an open circle). The distributions are derived from HYDRO1k (a, c) and HydroSHEDS (b, d). The maximum time
delay is 37 days for the Dongjiang and 15 days for the Willamette basins. The y axes of each cell, scaled 0–1, show the fraction of arrived discharge
on each day
forced HYDRO1k-based routing to very large V45 values
with a best value of 26 m s1 , corresponding to a maximum Nash–Sutcliffe efficiency of 0Ð85. An opposite
trend was observed with HydroSHEDS which showed
a well-defined peak around 5 m s1 with a maximum
efficiency of 0Ð86. The basin-average velocities were
1Ð6 m s1 for HydroSHEDS and 7 m s1 for HYDRO1k
when the optimum V45 values were converted using
Equation (2) and the average slopes. The HYDRO1k
value was clearly less realistic when compared with other
global routing schemes (e.g. Oki et al., 1999; Döll et al.,
2003; Gong et al., 2009).
Simulations in Dongjiang with global weather data
gave lower Nash–Sutcliffe efficiency and more scattered
discharge simulations than that for the local weather
data case (Figures 7a,b and 8a,b). The HYDRO1k
routing overestimated high flows. Both HYDRO1k
and HydroSHEDS models underestimated low flows
and slightly overestimated flows in the range 1000–
2000 m3 s1 (Figure 8c). When local weather data and
HydroSHEDS were used (Figure 7c), the simulated flow
showed little bias for flow magnitude above 1000 m3 s1 .
This may indicate a bias in the global weather data.
Distinctly different wave velocities were also obtained
Copyright  2010 John Wiley & Sons, Ltd.
when global weather data were used to drive the model
(Figure 8d). The HYDRO1k-derived basin velocity again
showed an unrealistic optimal value, 30 m s1 , with an
efficiency of 0Ð76. The HydroSHEDS-derived velocity
of 5 m s1 was the same as when driven by local data.
The corresponding maximum efficiency was 0Ð77 in this
case. The advantage of HydroSHEDS was clear for the
Willamette basin than for the Dongjiang basin (Figure 9).
The steeper topography of the Willamette basin was better represented with HydroSHEDS, reflected in the significant differences of the model efficiency (Figure 9d).
The sensitivity of the runoff-generation parameters
a4 , c1 , and c2 of WASMOD-M was overall moderate
with respect to both hydrography and weather input
(Figure 10). The difference in probability–density functions for the two hydrographies was small for the fastflow (c1 ) and slow-flow (c2 ) parameter values, whereas
some deviation was seen for the evaporation parameter (a4 ). The difference was much larger when global
weather data was used instead of local. The use of global
weather data forced a4 and c1 to large values for both
hydrographies. When HYDRO1k was used, the slowflow parameter c2 reacted differently to global than to
Hydrol. Process. 25, 1114– 1128 (2011)
1124
L. GONG, S. HALLDIN AND C.-Y. XU
Figure 7. Observed (black line) and modelled discharge (grey lines) in 1982– 1983 for the Dongjiang basin at Boluo. Runoff generation is modelled
with WASMOD-M with local weather input and routed with NRFs derived from HYDRO1k (a) and HydroSHEDS (b). (c) Quantile–quantile plot
of observed versus simulated discharge using HYDRO1k (filled dots) and HydroSHEDS (open squares). (d) V45 wave velocity and corresponding
best efficiency of simulated discharge using HYDRO1k (filled dots) and HydroSHEDS (open squares)
local data, whereas the HydroSHEDS response remained
the same.
The computational requirements for two preparatory, one-time efforts and for an actual simulation in
the Willamette River basin showed order-of-magnitude
differences between the two types of calculations. The
updation of upstream area took 1 h and 35 min for the
4 717 638 HydroSHEDS pixels of the Willamette basin.
The computation of time delay for river pixels under a
unit V45 velocity took 35 min. The computation of routing delay for a 10-year simulation took less than 1 s.
DISCUSSION AND CONCLUSIONS
In the study preceding this, Gong et al. (2009) show
that storage-based routing algorithms are inherently scaledependent because they rely on flow networks that change
with spatial resolution. The inaccuracy of such algorithms
tends to increase with cell size, because the assumption
of zero convective delay becomes less and less valid
as cell size increases. The transfer of high-resolution
delay dynamics in the form of NRFs for low-resolution
grids is shown by Gong et al. (2009) as one way of
achieving accuracy and scale independency in the same
Copyright  2010 John Wiley & Sons, Ltd.
time. This study was based on the belief that successful
application of the method would rely strongly on the
quality of the hydrography used to derive the time-delay
distribution.
We had to develop an efficient algorithm to use
HydroSHEDS at its native 300 resolution for global-scale
applications. We found it important to demonstrate the
added value of using such a high-resolution dataset at a
global scale, given all other uncertainties in global waterbalance models. The comparison of routing algorithms
based on HYDRO1k (1-km resolution) and HydroSHEDS
(90-m resolution at the equator) gave insight into the
costs and benefits of using hydrographies with different
spatial resolutions. The use of HydroSHEDS instead
of HYDRO1k to derive NRFs did not significantly
improve overall model efficiency when calibrated against
observed discharge. The use of the lower resolution
HYDRO1k, however, resulted in non-realistically high
wave velocity and a positive bias for simulated high
flows. The bias for the HYDRO1k-derived wave velocity
could be explained by comparing the CRF of the two
routing models for the same V45 value of 5 m s1
(Figure 8). A much larger spread of behavioural models
was seen for HYDRO1k compared with HydroSHEDS
(Figures 7c, 8c, and 9c).
Hydrol. Process. 25, 1114– 1128 (2011)
GLOBAL-SCALE RIVER ROUTING WITH HydroSHEDS
1125
Figure 8. Observed (black line) and modelled discharge (grey lines) for the period 1997– 2002 for the Dongjiang River basin at Boluo. Runoff
generation is modelled with WASMOD-M with precipitation input from a combined TRMM–GPCD dataset and routed with NRFs derived
from HYDRO1k (a) and HydroSHEDS (b). (c) Quantile–quantile plot of observed versus simulated discharge using HYDRO1k (filled dots) and
HydroSHEDS (open squares). (d) V45 wave velocity and corresponding best efficiency of simulated discharge using HYDRO1k (filled dots) and
HydroSHEDS (open squares)
The scaling of flow-path length when using hydrographies with different spatial resolutions may be reflected
in the network meandering factor. This was found to take
a small value of 1Ð2 for the Dongjiang basin (Gong et al.,
2009) when based on HYDRO1k or 1Ð4 globally when
based on total runoff integrating pathways (Oki et al.,
1999). The significant delay for HYDRO1k indicated that
the lower resolution of HYDRO1k led to a decrease in
derived slope resulting in longer travel times which was
not compensated by the decrease in flow path. The underestimation of slope was likely the main reason for the
unrealistically large V45 value obtained for HYDRO1kbased algorithm. The good basin-area agreement between
both hydrographies came from our explicit accounting of
sub-cell area. Other algorithms commonly use the whole
area of a cell. The STN-30p network, e.g. only identifies
ten 0Ð5° ð 0Ð5° cells for the Dongjiang basin upstream of
Boluo compared with 21 in this study.
The comparison between local precipitation data and
the combined TRMM–GPCP data showed that the routing performance was much more sensitive to the quality of precipitation input than to the choice of spatial
resolution in the hydrography. Both input-data errors
Copyright  2010 John Wiley & Sons, Ltd.
and routing-parameterization errors influenced the distribution of behavioural parameter values. This can be
a problem in a global water-balance model because its
parameters must be extrapolated spatially into ungauged
areas and temporally into the future for water-resource
predictions and assessments. The sensitivity study of the
runoff-generation parameters showed that they were more
sensitive to the quality of input precipitation data than to
the hydrography. However, a good routing algorithm is
always crucial. For example, Gong et al. (2009) show
that if a linear reservoir-routing algorithm is used for the
Dongjiang basin, a maximum Nash–Sutcliffe efficiency
of only 0Ð75 can be achieved at 0Ð5° resolution even with
high-quality local precipitation input. This is as poor as
the result obtained with the biased TRMM–GPCP data
in this study.
Our result indicated that the biased wave velocity for
HYDRO1k was caused by the reduction in slope at 1-km
resolution. A bias correction for the HYDRO1k slope
dataset, e.g. through the use of the downscaling algorithm
by Pradhan et al. (2006), might improve the results for
large-scale applications, while at the same time improving the quality of a slope-related product such as the
Hydrol. Process. 25, 1114– 1128 (2011)
1126
L. GONG, S. HALLDIN AND C.-Y. XU
Figure 9. Observed (black line) and modelled discharge (grey lines) for the period 1997– 2008 for the Willamette River basin. Runoff generation
is modelled with WASMOD-M with precipitation input from a combined TRMM–GPCD dataset and routed with NRFs derived from HYDRO1k
(a) and HydroSHEDS (b). (c) Quantile–quantile plot of observed versus simulated discharge using HYDRO1k (filled dots) and HydroSHEDS (open
squares). (d) V45 wave velocity and corresponding best efficiency of simulated discharge using HYDRO1k (filled dots) and HydroSHEDS (open
squares)
Figure 10. Posterior cumulative distribution functions, Fx, of the WASMOD-M parameters a4 , c1 , and c2 under different weather and hydrographic
inputs: global weather data and HYDRO1k (dashed grey); local high-quality weather data and HYDRO1k (dashed black); global weather data and
HydroSHEDS (solid grey); and local high-quality weather data and HydroSHEDS (solid black)
topographic index. However, there are more advantages
that are only offered by HydroSHEDS. For example, the
high-resolution, hydrologically conditioned DEM offered
by HydroSHEDS meets the resolution requirement to
implement TOPMODEL at a local-basin scale (e.g.
Quinn et al., 1995). Ongoing work by the authors has
successfully used topography-derived storage-capacity
Copyright  2010 John Wiley & Sons, Ltd.
distributions to formulate a runoff-generation algorithm at
the global scale. This algorithm also uses HydroSHEDS
data and will be coupled to the routing algorithm in this
study.
The HydroSHEDS dataset offers the possibility of
identifying individual river-channel pixels. This possibility has several implications for the modelling of routing
Hydrol. Process. 25, 1114– 1128 (2011)
1127
GLOBAL-SCALE RIVER ROUTING WITH HydroSHEDS
and runoff generation. We have shown in this paper that
the NRF, constructed for river channels, remains almost
unchanged when TAs vary in the 0Ð5–100 km2 range.
Although many more river-channel pixels were identified
at the higher resolution, the network topologies remained
similar. This feature can allow a simplification of the
algorithm because the routing quality is not significantly
lowered when using a large TA, i.e. when performing
routing only on major river channels. For runoff generation, however, model performance is most likely more
sensitive to the selected TA specified for river-channel
identification (e.g. Quinn et al., 1995). The HydroSHEDS
dataset has a potential to allow separation of overlandflow delay and channel delay, which must be lumped
when HYDRO1k is used. The explicit identification of
river pixels can also simplify the registration of dams and
reservoirs into the river network and their incorporation
into a routing model. More accurate basin delineation and
the high-resolution flow-path structure may make it easier to compare and validate global hydrological models
against regional models.
Computational efficiency is of central importance for
any kind of global model. We addressed the efficiency
problem by separating the total amount of calculation
into two stages: the preparation stage and the simulation
stage. The new algorithm allows the most computationintensive tasks, resulting in the NRF for the given
area and spatial resolution, to be accomplished in the
preparation stage, which is a one-time effort. Routing
during the simulation stage is done by the convolution of
runoff into the NRFs. The computational demand at this
stage is four to five orders of magnitude smaller than that
during the preparation stage. The convolution algorithm
is fast enough to allow calibration techniques based on
Monte-Carlo methods on the global scale. The two-stage
computational strategy separates not only heavy from
light computation but also the fine-scale data dependency
at the simulation stage. Once the NRF is constructed for
global cells, it can easily be coupled to runoff-generation
output from any other global or regional water-balance
model.
The short temporal coverage of high-quality daily
global climate data limits the application of global hydrological models. The mismatch between temporal coverage of precipitation and discharge data introduces
another challenge. For instance, TRMM, one of the
most homogeneous global precipitation datasets, covers only the last decade. This period coincides with a
trend of reduced number of discharge-gauging stations
and increased degree of river regulation. Therefore, we
believe that it is a large challenge to evaluate the new
routing algorithm in a large spatial and temporal domain,
as compared with local evaluation in this study. Further studies are being prepared to evaluate the new NRF
algorithm and the HydroSHEDS dataset at a continental scale. Because reliable global daily precipitation data
are only available for the last decade, future work will
also aim at developing a new calibration technique to
Copyright  2010 John Wiley & Sons, Ltd.
condition model parameters from statistical characteristics of previous discharge time series. This new technique will have a potential to be used when recent
discharge data are not available or are influenced by
regulation.
ACKNOWLEDGEMENTS
This work was funded by the Swedish Research Council Grants 629-2002-287 and 621-2002-4352, Grant
214-2005-911 from the Swedish Research Council for
Environment, Agricultural Sciences and Spatial Planning, Grant SWE-2005-296 from the Swedish International Development Cooperation Agency Department for
Research Cooperation, SAREC, and Grant CUHK4627/
05H from the Research Grants Council of the Hong
Kong. Parts of the computations were performed on UPPMAX resources under Project p2006015. We are grateful
to Prof. Yongqin David Chen of the Chinese University
of Hong Kong for providing the hydrological data for the
Dongjiang basin.
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