Earth Interactions
Design of Total Runoff Integrating Pathways(TRIP)—A Global River Channel Network
Taikan Oki, 1 NASA/Goddard Space Flight Center, Greenbelt, Maryland
E-mail: taikan@climate.gsfc.nasa.gov
Y. C. Sud, NASA/Goddard Space Flight Center, Greenbelt, Maryland
E-mail: sud@climate.gsfc.nasa.gov
PAPER ID: EI013
ABSTRACT: As a first step toward designing a comprehensive model for
validating land surface hydrology and river flow in Earth system models, a
global river channel network has been prepared at 1° latitude × 1° longituderesolution. The end product is the Total Runoff Integrating Pathways (TRIP)
network. The aim of TRIP is to provide information of lateral water movement
over land following the paths of river channels. Flow directions were
determined from vector data of river channels and river pathways available intwo recent atlases; however, an automatic procedure using a digital elevation
map of the corresponding horizontal resolution was used as a first guess. In thisway, a template to convert the river discharge data into mean runoff per unit
area of the basin has been obtained. One hundred eighty major rivers are
identified and adequately resolved; they cover 63% of land, excluding
Antarctica and Greenland. Most of the river basin sizes are well within a 20%
difference of published values, with a root-mean-square error of approximately
10%. Furthermore, drainage areas for more than 400 gauging stations weredelineated. Obviously, the stream lengths in TRIP are shorter than the naturallengths published as data. This is caused by the meandering of rivers in the realworld. Meandering ratio (rM), the ratio of actual (published) river length to theidealized river length, has been calculated. Averaged globally for all available
data, rM is 1.4, although it is 1.3 for rivers with areas larger than 500,000 km2.
The rM data will be useful in the design of the Scheme for Total Runoff
Integrating Pathways (STRIP). In the current form, TRIP can be used as atemplate for producing a time series of river flow using a simple version of1

STRIP.
[KEYWORDS: Water cycles; Geomorphology; Networks; Runoff and streamflow;
Land–atmosphere interactions]
Copyright: ©1998 Earth Interactions 3

1. Introduction
General circulation models (GCMs) are now becoming sufficiently realistic insimulating the rainfall, biosphere–atmosphere interactions, and land hydrology. This has
been accomplished because of modern state-of-the-art land surface models are able togenerate realistic evaporation and precipitation, provided the soil moisture initialization
and rainfall forcing (inputs) are realistic (e.g., Oki et al., 1997). Chen et al. (Chen et al.,1997) estimated (Project for Intercomparison of Land-Surface Parameterization
Schemes 2A) that the majority of flux schemes could obtain annual mean latent andsensible heat fluxes within 5 W m−2 of observation. This is approximately 15% ofannual mean net radiation (41 W m−2). The authors believe that this accuracy is quite
useful for GCMs and global hydrologic models.
Since soil moisture depends upon the soil hydrology, which, in turn, involves soil
water storage and runoff, it is imperative that runoff in the hydrologic model isrealistically simulated. The river runoff generated in the real world must be routed
through a natural network of water flow paths, such as creeks, brooks, tributaries, andmajor river channels. These paths are naturally created by soil erosion and are
orographically modulated and temporally carved. A few exceptions represent scenarios
either where humans have created new paths for water-use needs or where small
passages have naturally broadened to provide cross-basin flows. In this way, these
intricate river pathways become a complex network of channels and flow routes thatmust be accurately sorted to generate a dataset of basin-scale water channels. Thisdataset should largely, if not entirely, represent the streams of water runoff pathways of
the real world. This provides the motivation necessary to create a database representing
approximate directions of water flow, river basins, and drainage areas. We hope thisdataset will be useful for evaluating the land hydrology simulated by GCMs.
All GCMs include a runoff parameterization; even though not enough attention has
been paid to the simulated river discharge in global climatological studies (discharge isdefined as a water flow rate through a river cross section). On the other hand, riverdischarge is vital for investigating climate variability and/or validating the global waterbalance estimated by GCMs. Indeed, errors in runoff can vitiate the soil moisturecalculation and produce errors in evapotranspiration. Thus, a primary requirement of a2realistic hydrologic balance is an accurate calculation of each of the component terms of
the water balance.
The problem is that meteorological and climatological data on the global scales areoften given as spatial (raster) data of grid points, whereas the river discharge ismeasured at a single location as integrated runoff in its drainage area.
Geographical information that defines drainage area for each gauging point isrequired in order to convert the river discharge data into spatial data or to summarize
spatial data to areal mean data for the drainage area. Russell and Miller (Russell andMiller, 1990) pioneered the design and use of global templates of major river basins forhydrologic cycle studies on local as well as global scales. They converted the runoff
simulated by the Goddard Institute for Space Sciences (GISS) GCM into areal meanvalues by a template of 2° × 2.5° grid boxes and compared them with observations.
Later, Oki et al. (Oki et al., 1992; Oki et al., 1993) used a template of 35 river
basins in 2.5° × 2.5° grid boxes. Atmospheric water vapor convergence estimated fromfour-dimensional data assimilation products of the European Centre for Medium-Range
Weather Forecasts from 1985 through 1988 were compared with observed runoff using
the above template. Subsequently, Oki et al. (Oki et al., 1995a; Oki et al., 1995b)
extended the analysis to 70 river basins and found that the procedure was usable forinvestigating and evaluating global water balance studies using river flow data fromobservations.
Coe et al. (Coe et al., 1995) and Levis et al. (Levis et al., 1996) used continent andocean templates in 4.4° × 7.5° and 2° × 2° grid boxes, respectively, and examined thewater budgets in their numerical simulations.
In these studies, the templates are the converters between distributed areal data,such as model generated runoff, and areal mean hydrologic data, such as river discharge.
In recent years, Vörösmarty et al. (Vörösmarty et al., 1989) prepared a river routing
network for the Amazon River basin in 0.5° × 0.5° grid cells. They coupled a waterbalance model with a linear transfer model in river channels to simulate river discharge.
Subsequently, a similar system was applied for the Zambeze River basin by Vörösmarty
et al. (Vörösmarty et al., 1991). Miller et al. (Miller et al., 1994) employed a linear
routing model to simulate monthly discharge based on runoff by the GISS GCM. Sausen
et al. (Sausen et al., 1994) used their river routing model in approximately 5.6° × 5.6°
grid boxes and simulated monthly runoff as well. Even though only for the Mississippi
River basin on a 2° × 2.5° resolution, Liston et al. (Liston et al., 1994) made a river
channel network and compared simulated results with observations at a few discharge
stations within the basin. Kanae et al. (Kanae et al., 1995) applied the river routing
3

model of Miller et al. (Miller et al., 1994) to GCM outputs using their river channel
network with an approximate 5.6° × 5.6° resolution. Coe et al. (Coe et al., 1997) used asimilar linear reservoir model in a 2° × 2° grid and coupled it to their model to predict
surface waters. Costa and Foley (Costa and Foley, 1997) simulated river discharge for
56 stations in the Amazon River basin on a 0.5° × 0.5° resolution.
A continental-scale system of rivers at 0.5° × 0.5° spatial resolution was developed
and used in Vörösmarty et al. (Vörösmarty et al., 1997) to estimate the mean residential
time of water. The Global Soil Wetness Project has been sponsored under theInternational Satellite Land Surface Climatology Project (ISLSCP) to evaluate landhydrology schemes in GCMs and to produce a reliable distribution of global soil
wetness (Dirmeyer et al., 1997).
All the required atmospheric forcing data and physical parameters for land surface
parameterizations (LSPs) has been provided in a set of five CD-ROMs (Meeson et al.,
1995; Sellers et al., 1995) by 1° × 1° grid boxes over land for a 2-yr period: 1 January
1987–31 December 1988.
Various modeling groups have run their land–biosphere schemes to simulate allcomponents of the land hydrology. Validation efforts have included the comparison ofmodel products with river discharge. This requires delineating a river basin and a river
routing network, along with a realistic hydrologic flow scheme.
Since there has been little information about global river basins in 1° × 1° gridboxes, as a first step we have produced a global river channel network on a 1° × 1°
resolution, hereafter known as the Total Runoff Integration Pathways (TRIP) network.
In this framework, annual and climatological water balance can be studied with atemplate alone, and the seasonal and monthly water balance can be examined using
channel network information with a river routing model of sufficient accuracy. One of
the merits of TRIP is that it is accompanied by the locations of gauging stations and theirdrainage areas, which is helpful for model evaluation.
Most of the previous works based on templates of coarse resolution were unable toresolve between the whole river basin and the largest drainage area of existing gauging
stations in the river basin. With a 1° mesh, we hope to define the drainage areas moreaccurately for major gauging stations in each river basin on a global scale.
The procedure to develop TRIP is described in section 2; it is succeeded by the
diagnostics of the obtained TRIP in section 3. Summary and applications of TRIP are
discussed in section 4.

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2. Development of a global river channel network
2.1. TRIP architecture
TRIP design is required to satisfy the following criteria.
1. The locations of each river basin are correct.
2. The river basin size and the drainage area to each gauging station point (GSP) arereasonably accurate.
3. The length from each grid to GSPs or to the river mouth reflects their real length.
The first requirement is obvious, because TRIP will be used to overlay various
climatic data. Since most of the continents are covered by major river basins, theirlocations and boundaries should be realistic. The only exceptions where this becomesdifficult are the regions next to arid areas, where major runoff does not occur.
The second requirement, although obvious, is nevertheless important. Using thepredetermined drainage area to the GSP, discharge is converted into runoff, which has adimension of water depth per unit time and can be easily compared with precipitationand evapotranspiration. Therefore, the error in the drainage area directly affects theaccuracy of conversion from discharge to runoff. Fortunately, the areas of major river
basins have been published, and most GSPs are attributed with their drainage areas.
Comparison of the areas obtained from TRIP with these values provides validationnecessary for evaluation of TRIP design. This comparison also serves as a verification
for the first requirement.
The last requirement is related to the application of TRIP with runoff routing
models. The histogram of the length from each grid point to the GSP may have a major
influence on the hydrograph formation of a large river basin. Consequently, it isdesirable that the length of the river is reasonably accurate.
In constructing the water flow channel network for TRIP, each grid point was
idealized to have only one outflow direction with reference to its eight neighboring grid
points: N, NE, E, SE, S, SW, W, and NW. It may be classified as “D8” and its
disadvantages are discussed in Costa-Cabral and Burges (Costa-Cabral and Burges,
1994). They show that statistical or partial treatment of river channel network, in which
each grid may have two or more outflow grids, may be more realistic in some cases,
particularly for regions with complicated boundaries. For the global domain, however,the simple format amply satisfies the requirements stated in the previous section; that is,
it represents the area size adequately and relates to the lateral flow directions
5

realistically. The numbering of direction is set 1 to 8 clockwise from north. The 0 value
is used for a sea grid, and 9 is used for a “river mouth” grid defined as a grid that has nooutflow to its neighboring land grids.
2.2 River flow directions in TRIP
There are two known methods of obtaining river flow directions: 1) digitizing waterflow directions that can be delineated manually from published maps or 2) extracting thewater path directions by a numerical analysis procedure from digital elevation models(DEMs) objectively (automatically). Even though laborious, the first method guarantees
accuracy, while the second method is also bound to produce the valid results in a
majority of the cases, provided that the quality of the DEM used is accurate over all thetarget region and the automatic algorithm is able to sort out the pathflows accurately.
River channel information on Earth is already available as vector data. Dirmeyer(Dirmeyer, 1995) converted the vector information into raster data. Nevertheless, it isstill helpful to extract river channel information from DEMs, because the density andquality of the existing vector data of river channels are not sufficient, as was also
pointed out by Dirmeyer (Dirmeyer, 1995).
There have been earlier attempts in making a river channel network from DEMs(e.g., Tarboton et al., 1991), but most of them were applications for high-resolution
situations in which DEMs were used on 1–100-m horizontal resolution. On such a small
scale, automated techniques, for defining river channels, can extract detailed water flow
paths on small river basins. Our goal is to create TRIP for the use in global models thathave a much coarser resolution and requires resolution to capture the large-scale picture.
Because of the scale difference, the following issues must be addressed.
1. Valley floors are not well represented by DEMs, because a 1° mesh corresponds toapproximately 100-km horizontal resolution.
2. The treatment of “pits” or “hollows” in the continents, where the altitude of the gridbox is lower than all the neighboring grid boxes, is a major problem to be dealt with.
Generally these pits and hollows are artificially filled up in the DEM in order toprevent the dead ends of streams produced by automatic procedures. However, there
are inland river basins on the continental scale and the dead ends of streams for such
rivers are correct.
3. TRIP design should identify lakes. Some of them are inland lakes, and some of them
have outlets for streams that eventually lead to the ocean. On smaller scales,
generally lakes were not treated by automatic techniques, but for the larger scales
lakes should be included.
4. Most of the previous studies extracted river channels for a specific river basin from6

DEM, but the number of river basins in TRIP is not prescribed.
Problems 1 and 2 are related to the horizontal resolution of the DEM used, while 3
and 4 are related to the target region being global. In studies of small scales, results fromautomated techniques were validated vis-à-vis published maps or air photos, but such avalidation is not viable for TRIP, because our goal is to extract the broad features ofwater flow that emerges from subgrid-scale water flow structures. We believe any river
channel network produced by automated techniques needs to be verified against
real-world atlases, and wherever the outcome differs from the actual direction of riverflow, we introduce manual correction. As a consequence, the river channel network
extracted by an automated technique was viewed as a first guess, and it was modified bymanual corrections to address the difference between real versus ideal world.
2.3. Automated extraction of TRIP from a DEM
To produce the first guess of TRIP, river flow directions were determined from a
global DEM called ETOPO5 (Edwards, 1986). ETOPO5 has 5′ × 5′ horizontal
resolution; thus, it has 12 × 12 cells in each 1° × 1° grid box. In each grid box, meanelevation of 5′ × 5′ cells above 0 m was calculated and used for the extraction of river
channel network. The values of medium, maximum, and minimum elevations in each 1°
grid box were also prepared.
The delineation of land and sea followed the land–sea mask of the ISLSCP
Initiative I CD-ROM (Meeson et al., 1995; Sellers et al., 1995). Large lakes wereclassified as sea in the land–sea mask, but some of them are parts of drainage systems ofrivers. Therefore, such a sea grid box in the land–sea mask was changed into a land gridbox, and its outflow direction was attributed during the manual correction step. Thus thelakes in current TRIP are grid boxes that have flow directions but are classified as sea inthe land–sea mask of the ISLSCP Initiative I CD-ROM.
As for most D8-type river channel networks, the idea of “hydrological flow
modeling method,” as illustrated by Chorowicz (Chorowicz, 1992), was employed. The
outflow direction was toward the lowest land point of the eight neighboring grids,
provided the point was lower than the originating point. It might appear that thedirection toward the steepest slope should be the obvious choice but considering that
there is meandering and unevenness within the subgrid scale, it is assumed thatsomehow water will find a way to reach the lowest level. We shall show that the choice
between steepest slope and lowest neighbor was not a clear one because both methods
produced a similar number of grid cells requiring subjective correction (see section 3.2).
In fact, approximately 70% of the directions determined by these two algorithms were7

identical. Therefore we opted for the simplest choice, that is, lowest neighbor method. If
more than one outflow directions were found, the median, maximum, and minimum
values of neighboring 1° × 1° grid boxes were examined in this order. If a grid point was
lower than all neighboring grids, it was marked as “hollow” and was left for the
subjective evaluation and manual correction. If such a hollow grid box had a sea grid in
its immediate neighborhood, it naturally became a river mouth.
Antarctica was processed differently. Lateral flow in this area is glacier flow andnot river (water) flow; therefore, the river channel network merely represents internalconsistency of TRIP. If ice height was lower in the grid box to the north, northeast, or
northwest, outflow direction was set to that direction. In all other cases, outflow
direction was set to the north.
The result obtained from the above algorithm showed fairly realistic pathways ascompared to the observed pathways. Rough stream structure and the drainage system tothe ocean were well represented by the automatic procedure. The hollow grids were
found to be located appropriately in areas such as at marshes and lakes or at theconfluence of large tributaries.
2.4. Manual correction of TRIP
A manual correction was applied to the TRIP network, obtained from the automatedmethod, by comparison with published geographical information on water flow
networks. This is done by overlaying TRIP on the actual river channels using theGeneral Mapping Tools of Wessel and Smith (Wessel and Smith, 1995). Global
continents were divided into 27 regions, and the river channel network was carefully
examined and corrected. Refer to Figure 10 as an example of overlaid maps. Additional
information to verify and correct TRIP was obtained from two atlases (Teikoku-Shoin,
1985; Rand McNally, 1995).
Some of the problems encountered in the river channel network are as follows. The
first problem relates to the diversion of a river channel into two or more major streams.
This is a common occurrence at a delta near the river mouth. There are only a few rivers
whose deltas are resolved on a 1° × 1° grid; however, when it gets resolved, it is
impossible to assign the flow directions because TRIP design allows only one outflow
direction. For example, this situation arose in the Amazon, the Nile, and the Lena River
pathways. For all these cases, one direction of outflow was assigned as a major pathway
referring to the atlases referenced above. Since there are no major gauging stations inthese areas, these approximations are not likely to cause a serious problem forsimulating/evaluating river flows from runoff at grid points.

8

Most of the other problems were encountered in arid and dry land regions. There are
a number of wadis in dry regions, and small streams from these regions occasionally run
into a main stream. It is difficult to decide whether to include such a stream flow in a
major river basin, but lateral flow of water in this region would be inactive for allpractical purposes and the decision of flow direction would have an inconsequential
effect, particularly for GCM-scale models. Some grid boxes with inland lakes were
attributed to river mouths, and river mouths are also arbitrarily put into arid areas inorder to terminate water flow from mostly dry channels into episodic ponding. This isindeed realistic, but the automatic algorithm was unable to handle it appropriately.
The following features of TRIP were checked in order to correct possible
inaccuracies caused by manual operations.
1. No river channels are allowed to crisscross.
2. All river channels flow from one land grid box to another.
3. Every land grid box has one, and only one, river mouth toward its downstream,
which eliminates the possibility of grid boxes counterflowing toward each other.
2.5. Postprocessing of TRIP
TRIP divided the entire land into river basins. Each river mouth was given a
temporary river basin number (RBN). To assign an RBN to a grid point without an
RBN, the downstream grid point was examined, and the upstream grid point received thesame RBN as the downstream grid point. This procedure was followed for all grid points
and repeated until all the land grid points had an RBN. The chosen values of RBNs wereallocated in the descending order of basin sizes. Thus, a larger river basin has a smaller
RBN.
In order to demarcate the river basin boundaries, color-coded numbers were
attributed to each river basin. Diagonal grid boxes were considered to be in contact andthey were given different color codes if they belong to different river basins. In thecurrent TRIP, seven colors were sufficient to distinguish adjoining river basins.
The order of streams was determined by an automated procedure. We define
headwaters as the grid points with no inflow from any of their eight neighbors; thestreams from the headwaters were assigned the river order of 1. The headwater grid cells
were identified first, then each stream was given the grid distance from headwaters. All
the grid points with 1 grid distance from the headwater grids were tested for water
inflow. If two or more streams of river order 1 flow into the grid box, the outflow stream
was attributed the river order of 2; otherwise, it continued to be river order 1. The
9confluence of two or more streams of n order produces an (n + 1)-order stream. All thegrid boxes were examined in this way in order from the shorter grid distance to theheadwaters. Because more than three tributaries can make a confluence, the river ordersof all inflow streams were stored during these steps, and the river order was increased by+1 when the highest river order and the second highest river order were the same.
A river catalog has been prepared that identifies the river basins (see Table 1). The
location of river mouth, its name, and its official river basin size are given in the catalog.
Major river basins with areas larger than 100,000 km2 are all included in this catalog.
Since we recognized the possibility of estimation errors, we extracted river basins with
official areas of more than 50,000 km2 from Korzun (Korzun, 1978, hereafter referred toas KU78) and compared with the basin sizes in TRIP.
4(Click on icon to view Table 1.)

A similar catalog, but for selected gauging stations of river discharge, has been
prepared as well. The selections and the locations of gauging stations are from the
Global Runoff Data Centre catalog (GRDC, 1992). Some of them are from ISLSCP
Initiative I datasets. Drainage area numbers were attributed to each grid point by analgorithm similar to the one used for the river basin numbering described above.
The distance between grid points was computed by an algorithm described inappendix A. The length of the stream from the grid point to its river mouth was also
computed. The stream length at the grid box of the river mouth was set to zero. The
longest stream length in each river basin was taken to be the representative length scaleof the river basin. Indeed, that is not the case in some river basins such as theMississippi. Itasca Lake, in Minnesota, is defined as the origin of the Mississippi River,and the length from Itasca to the river mouth, New Orleans, is approximately 3800 km.
However, the Missouri River has the longer stream length, with more than 6200 km forthe entire Mississippi River.

3. Diagnostics of TRIP
3.1. Configuration
The global network invoked by TRIP is shown in Figure 1. Only the streams of theorder of 2 or higher are drawn in the figure. Major drainage systems are also identified.

10

Figure 1. Global illustration of the 1° mesh TRIP. The thickness of the line
corresponds to the river order of streams, and only the streams of the order of
2 or higher are drawn. [Click on icon 12(approx 126 kbyte) to view full
figure.]Figures 2–7 illustrate further details of TRIP configurations for six major
continents. The thicknesses of connecting lines represent the river order of streams. The
river heads, the farthest grid points from the river mouth (origin for calculating the river
length), and the gauging stations of identified river basins in Table 1 are highlighted by“ ,” “ ,” and “ ,” respectively. Lake grid points are overlaid by “ .” A total of 3560
basins are identified in TRIP; some of them are one grid cell basins, where the rivermouth grid itself is the only one in the basin.

Figure 2. One-degree mesh TRIP of North America. River mouths are plottedby “ .” The thickness of the line corresponds to the river order of streams.
For identified rivers, the river mouth, the farthest grid from the river mouth,
and the gauging stations are marked by “ ,” “ ,” and “ ,” respectively.
Lake grids are marked by “ .” [Click on icon 13(approx 316 kbyte) to viewfull figure.]

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Figure 3. Same as Figure 2 but for South America. [Click on icon 14(approx
239 kbyte) to view full figure.]

Figure 4. Same as Figure 2 but for Africa. [Click on icon 15(approx 353
kbyte) to view full figure.]

Figure 5. Same as Figure 2 but for Asia. [Click on icon 16(approx 329 kbyte)
to view full figure.]

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Figure 6. Same as Figure 2 but for Europe. [Click on icon 17(approx 374
kbyte) to view full figure.]

Figure 7. Same as Figure 2 but for Australia. [Click on icon 18(approx 203
kbyte) to view full figure.]
As described in the previous section, river basins with an area larger than 100,000
km2 in TRIP were identified, and the river basins with official areas over 50,000 km2 aredelineated; this yielded 180 rivers that are listed in Table 1. Antarctica and Greenland
water flow channels are excluded; consequently, the sequential number of river basins is
not continuous. Some rivers have more than two names, and representative names areshown in Table 1. The location of the river mouth is identified from atlases(Teikoku-Shoin, 1985; Rand McNally, 1995), but when a few river mouths happen to beclose to each other in the observations, a 1° × 1° resolution is not sufficient to resolve
such details, and their locations are adjusted within plus/minus one grid box. River basin
area AT in TRIP is compared with published values AO from Matsuyama and Oki(Matsuyama and Oki, 1992, hereafter referred to as MO92), AK from KU78, and AM
contained in Milliman and Meade (Milliman and Meade, 1983, hereafter referred to asMM83). River length in TRIP (LT) is compared with LK from KU78 and LR from theJapanese National Astronomical Observatory (Japanese National Astronomical
Observatory, 1993, hereafter referred to as JNAO93). The number of 1° × 1° grid boxes
in each river basin is also shown in Table 1; clearly, the ratio of the number of gridboxes to basin area varies with latitude, because grid cells do not represent equal areas.

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Figure 8 is the illustration of the river basins identified in Table 1. These basinscover 84 × 106 km2 or 63% of land (excluding Antarctica and Greenland). Most of thenoncovered areas are arid regions, and they have minimal influence on the global river
runoff.

Figure 8. Coloring of identified major river basins of the globe. [Click on icon
19
(approx 69 kbyte) to view full figure.]
Figure 9 is the illustration of drainage areas for selected gauging stations. Currently,
more than 400 gauging stations are available, and their own drainage areas are from lessthan 10,000 km2 to more than 1,000,000 km2. The median size is approximately 70,000
km2, while mean size is 150,000 km2, and the standard deviation is 300,000 km2. Since
the area of the 1° × 1° grid box is approximately 10,000 km2, the mean size of 150,000
km2 implies that the continents are effectively divided into 4.0° × 4.0° boxes. Thesedrainage areas currently cover 62 × 106 km2, which corresponds to 47% of land
(excluding Antarctica and Greenland). Further compilation of runoff data will increase
these numbers.

Figure 9. Coloring of drainage areas for selected gauging stations. [Click on
icon 20(approx 72 kbyte) to view full figure.]
3.2. Results of manual corrections
The outcome of manual correction of TRIP is summarized in Table 2a. The
numbers of the grid boxes before and after the manual correction are shown. Sixty-two
grid boxes were relabeled from “sea” to “land,” because they contain lakes in continents
on the pathways to river mouths.
21(Click on icon to view Table 2a.)14

Approximately half of land grid boxes are subjected to some manual correction,
while the other half required no correction. The authors believe the main reason for thisis the coarseness of the horizontal scale. Individual slopes and river channel valleys are
not well represented in the DEM, and the actual stream flow network is not welldetermined by the mean topography on a 1° × 1° resolution.
From past experiences in smaller scales, the steepest slope algorithm may seemappropriate for the first guess, but for our 1° × 1° DEM, the steepest slope algorithm wasfound to produce virtually the same number of the river flow discrepancies as the lowest
neighbor algorithm. The statistics on how many manual corrections are required for thevis-à-vis lowest neighbor algorithm are compared. The similarity can be seen between
Table 2a by lowest neighbor algorithm and Table 2b by steepest slope algorithm in thenumbers of “changed” grids and their percentage.
22(Click on icon to view Table 2b.)

For example, in the Amazon River basin, the first guess by the lowest neighboralgorithm is shown in Figure 10a, and the first guess by a corresponding steepest slope
algorithm is in Figure 10b. The grid boxes marked by “ ” indicate that the flow
direction of the box should be changed in order to obtain the desired pathways shown in
Figure 10c. The grid boxes marked by “H” indicates no lower grid box was found intheir neighbor, and “T” indicates two or more candidates were found as the outflow
direction. We believe whatever may be the deficiencies of the first-guess algorithm, ourmanual correction process eliminates them.

Figure 10a. First guess of TRIP in the Amazon River basin by the lowest
neighbor algorithm. The grid boxes marked by “ ” were changed afterward.
Numbers indicate the outflow directions. Grid boxes of “H” has no outflow
direction, and grid boxes of “T” has two or more candidates of outflow
direction and could not decide one. Sixty-one percent of grid boxes required15

the correction. [Click on icon 23(approx 264 kbyte) to view full figure.]

Figure 10b. Same as Figure 10a but for the steepest slope algorithm.
Sixty-four percent of grid boxes required the correction. [Click on icon 24(approx 246 kbyte) to view full figure.]

Figure 10c. Final illustration of TRIP in the Amazon River basin after the
subjective improvement. Marks are the same as in Figure 2. Numbers indicate
the outflow directions. [Click on icon 25(approx 236 kbyte) to view full
figure.]3.3. Validation by area size
The comparison of river basin size from TRIP (the fifth column of Table 1) withpublished numbers from MO92 (the sixth column), KU78 (the seventh column), andMM83 (the eighth column) is shown in Figure 11. The area of each grid cell in TRIP is afunction of latitude and was calculated following the algorithm described in appendix A.
MO92 compiled river basin sizes from several sources, including JNAO93. The largest
drainage area of a gauging station within the river basin is sometimes substituted for theriver basin area in Table 1 of MO92. Such a number is not appropriate here and is16

excluded from Table 1 in this paper. KU78 included the Tocantins in the Amazon.
MM83 compiled UNESCO publications, including KU78, but some of their numbers
were different, especially for the Niger and the Euphrates.

Figure 11. Major river basin areas (104 km2) in TRIP are compared withpublished numbers from MO92, KU78, and MM83. Most of the plots arewithin ±20% of error. [Click on icon 26(approx 58 kbyte) to view full figure.]
According to this comparison, river basin sizes are well reproduced, but somerivers, particularly in arid regions such as the Amu-Darya and the Syr-Darya, reveal
large differences vis-à-vis their official basin sizes. In fact, the corresponding values
from KU78 and MO92 are also quite different from those generated by our analysis; thiseither may be the outcome of the specific criteria used to define the river basin, or theofficial numbers may be outdated. Actually, in arid regions, there are some tributaries
that connect to the main stream only when there is large runoff; for these cases, river
basin boundaries where surface discharge is often inactive are unclear. Except for suchcases, most of the river basins in TRIP have a difference of less than ±20% of previously
published numbers. Root-mean-square errors are 11% for KU78 and MO92, and 15%
for MM83.
Figure 12 compares the drainage area of more than 400 gauging stations. The area
sizes in TRIP generally correspond well with official values from GRDC associated withthe runoff data, even though official numbers may be inaccurate for some stations. For
example, the drainage area at Tarbert Landing of the Mississippi River is 3,923,799 km2
according to GRDC (3,052,500 km2 in TRIP); however, it is more than the total river
basin area of 3,248,000 km2 given by MO92. On the other hand, Matamoros is locatedclose to the mouth of the Rio Grande (Bravo River), whose basin size is approximately
570,000 km2 (610,000 km2 in TRIP). It is expected that the drainage area of Matamoros
is close to the basin area, but GRDC gives it a value of 450,000 km2. The drainage areafor Yankton, Missouri, in GRDC is 273,900 km2, but it is 726,000 km2 in TRIP. Afteran inquiry to GRDC, it was found that there was a typographical error and the correct
17

value is 723,900 km2.

Figure 12. Drainage areas (104 km2) in TRIP for selected gauging stations arecompared with official numbers attributed to each gauging station. Most of theplots are within ±20% of error. [Click on icon 27(approx 55 kbyte) to viewfull figure.]
Some stations in regions of lakes and marshes also have relatively large differences.
In TRIP, the areas of water surface are included in the total drainage areas, but they may
have been excluded in the official numbers. For example, MM83 may have excluded thearea of Great Lakes from the river basin size of the St. Lawrence. In view of the above,
we believe that the overall accuracy of TRIP is quite adequate for global models despitea few issues with difficult stations. The mean bias of drainage areas larger than 50 × 103
km2 is 4.0 × 103 km2 (1.4%) and the root-mean-square error is 67 × 103 km2 (13%).
In Figure 13, the area of each river basin is plotted against its global ranking. The
plot shows a linear relation between basin areas of approximately 3,000,000 km2
through 100,000 km2 on a log–log plot. There are two clear steps in different areas, atranks from 12 to 13 and from 37 to 38.

Figure 13. Ranking of area size in the globe and river basin area (104 km2).
[Click on icon 28(approx 39 kbyte) to view full figure.]18

3.4. Examination of river length
The longest river length in each river basin of TRIP is compared with therepresentative river length from KU78 and JNAO93 (Figure 14). The published river
length is significantly larger than that depicted in TRIP. It is mainly because themeanderings of actual river channels are a subgrid-scale feature that cannot be outlined
in TRIP. Consequently, we calculate the “meandering ratio” (rM) as the ratio of
published river length to that calculated from TRIP. It represents a factor by which thestream length in TRIP must be multiplied to obtain the actual (observed) stream length.
The isolines of rM = 1.2, 1.4, and 1.6 are also drawn in Figure 14. It shows that rM for
most large rivers is close to 1.6. Large variability is seen for rM of river basins smaller
than approximately 500,000 km2 (which carry rivers with a length shorter than 1500
km). This reflects not only the meandering of the stream, but the effect of idealization of
the pathways of the main stream, which itself is not well reproduced in 1° × 1°
resolution. The traveling time for 1500 km is of the order of 2 weeks, if the flow
velocity in the streams is of the order of 1 m s−1. The error in estimating traveling time,caused by the poor reproduction of stream length, can be in the 10%–25% range if such
errors appear randomly. Its effect could be neglected, particularly for monthly waterbalance studies, but it could be crucial for flood forecasting.

Figure 14. River lengths (km) in TRIP for major river basins are comparedwith published numbers from KU78 (by “ ”) and the Japanese National
Astronomical Observatory (JNAO93) (by “ ”). Rivers whose area size islarger than 10,000 km2 are plotted by “ ,” else by “ .” Most of the actual
river lengths are larger than the length in TRIP. [Click on icon 29(approx 88
kbyte) to view full figure.]
The dependency of rM on river basin size is illustrated in Figure 15. Mean rM isplotted in each of the 200,000 (and larger than 1,000,000) km2 bins. One can apply rM
depending on the area size, or use different rM values in each river basin. Overall mean19

rM of 1.4 (compared to KU78), or 1.3 for the rivers larger than 500,000 km2, seem toemerge quite universally. This rM factor can be used to apply a meandering correction asa first-order approximation.

Figure 15. The dependency of rM on river basin size. Meandering ratio rM isestimated as the ratio of published river length from the Japanese National
Astronomical Observatory (JNAO93) (by “ ”) or KU78 (by “ ”) to thelongest stream length from a grid point in each river basin to the river mouthof TRIP. [Click on icon 30(approx 62 kbyte) to view full figure.]

4. Summary and discussion
A global river channel network, Total Runoff Integrating Pathways (TRIP), at 1° ×
1° horizontal resolution has been constructed for the entire Earth. Its aim is to give
directions for lateral water movement by creating an idealized network of river channels.
First, an automatic algorithm based on grid-averaged topography was deployed todetermine a “first guess” of river flow directions from a digital elevation map. Of thetwo possible choices, one using river outflow in the direction of lowest elevation
direction and one using river outflow in the direction of steepest gradients, we adopted
the first for simplicity and comparable accuracy. On comparing TRIP with the actual
river channel information in atlases, we had to apply a number of subjective corrections.
The TRIP map was used to prepare a template to convert the point data of riverdischarge into the areal data of mean runoff.
One hundred eighty rivers with more than 100,000 km2 of basin area in TRIP (ormore than 50,000 km2, if in KU78 have been delineated. These rivers cover 63% of land
(excluding Antarctica). Most of the river basin areas are within 20% of thecorresponding published values (KU78; MM83; MO92).
The stream lengths in TRIP are shorter than the observed (KU78; JNAO93). Morethan 400 gauging stations were selected from the Global Runoff Data Centre (GRDC,
1992). Continents were divided into their own drainage basins. The size of drainage
20

basins feeding a gauging station is well captured in TRIP. Compared with the official
numbers associated with the discharge data, the areal bias in TRIP for drainage areas
larger than 50 × 103 km2 is roughly of the order of 4.0 × 103 km2 (the mean of relative
bias errors is 1.4%), and the corresponding root-mean-square error is roughly 67 × 103
km2 (13%).
The stream lengths in TRIP are shorter than the observed (KU78). It is mainly
because of the influence of the meandering of rivers on the subgrid scale, which TRIP
cannot handle. Meandering ratio (rM), the ratio of actual river length to the idealized
pathway length in TRIP, was calculated. Averaged for all available data, rM is 1.4. It issmaller for larger basins; for example, it is only 1.3 for the rivers larger than 500,000
km2. All these comparisons were viable for regions where a major river exists. However,an exhaustive validation of the accuracy of TRIP could not be carried out in arid regions.
It is hoped that TRIP will contribute to several future modeling studies. Gridded
runoff data can be arranged using the template of drainage areas, and it will help
climatological as well as annual water balance studies. Oki et al. (Oki et al., 1997) showthat the standard deviation of annual runoff error estimated by various land surface
models were approximately 100 mm yr−1. Since observed precipitation is the forcing
data in the numerical experiments, the standard deviation of evapotranspiration has thesame standard deviation error. Mean annual evapotranspiration over the globe isapproximately 600 mm yr−1; therefore 100 mm yr−1 corresponds to approximately 17%of error. This accuracy is something we need to evaluate further and improve upon.
Several LSP modeling groups are involved with improving upon the accuracy ofsimulated evapotranspiration and runoff. Indeed, if the main objective is to simulate therunoff in the river, one requires better accuracies with lower standard deviation.
Evidently, for hydrological evaluation of models as well as real hydrological data
analysis, we still have a long way to go.
Combining TRIP with a river routing model will help to evaluate LSPs of GCMs,
particularly the water balance of major rivers in a seasonal to monthly basis. We believethat inclusion of river routing in a GCM using information such as TRIP is very
important when water availability and use for irrigation is an issue; in these situations,soil moisture downstream is affected by the runoff from upstream. TRIP will provide thenecessary information for the better modeling of the global hydrological cycle, as well as
in helping to integrate the water balance of the atmosphere, the land, and the ocean.
TRIP will also be used for the on-line coupling of river routing models with GCMs; thiswill help to close the water cycle in GCMs. Off-line testing of a linear routing modelwith TRIP has been already applied and a better model, called the Scheme for Total
Runoff Integrating Pathways (STRIP), is under development. Invoking a linear routing
model of Miller (Miller et al., 1994) using the current TRIP dataset was employed by21

Oki (Oki, 1997); the model was successful in simulating the behavior of the annual cycleof the rivers identified in the TRIP design. Our more sophisticated scheme for TRIP
(called STRIP) is currently under development. It is being designed to better represent
the hydraulics of river flow and surface water storages. TRIP information in digital form
is attached to this manuscript (appendix B).

Appendix A: Calculating the Area and the Length on Earth's Surface
The area for various grid cells was calculated assuming Earth to be a spheroid in themeridional plane. The assumption of a perfect sphere has systematic biases ofoverestimation areas in the Tropics, and underestimation areas in polar regions.
Discharge is generally large in the Tropics and runoff per unit area may beunderestimated by the overestimation of the area size, and vice versa in polar regions.
As a result, global mean runoff may be slightly underestimated. The ellipticity of theequator, however, was ignored; it is less than that of meridians in the order of 2–3.
A.1. Area size per longitude
From the table of “Rika-Nenpyo” (meaning “scientific charts” in Japanese;
JNAO93) the length of the latitudinal arc (lx) and the meridional arc (ly) per unit angle
are given asa cosφ(1 − e2 sin2φ)1/2
a cosφlx =(1 − e2 sin2φ)1/2
lx =

(A1)
and
a(1 − e2)(1 − e2 sin2φ)3/2
a(1 − e2)ly =,(1 − e2 sin2φ)3/2
ly =

(A2)
where a is the equatorial radius of Earth, φ is the latitude, and e is the ellipticalness.
From (A1) and (A2), the surface area from latitude φ1 to φ2 per 1° in longitude, S(φ1,φ2),
can be obtained from the equation
S(φ1,φ1) = ∫φ1φ222πlxly dφ180=πa2(1 − e2)
cosφdφ.
∫φ1φ2
180(1 − e2 sin2φ)2(A3)

Substituting sinθ = e sinφ in (A3),S(φ1,φ1) =πa2(1 − e2)
dθ
∫θ1θ2
180e
cos3θ
(A4)

is obtained, where θ1 = e sinφ1 and θ1 = e sinφ1. Since,
∫

dθ
1
1
1 dθ
=∫(
−
) dθ + ∫2 cosθ
cos3θ
cos3θ 2 cosθ
1 sinθ
1
1 + sinθ=+ log||,
2 1 − sin2θ 4
1 − sinθ
(A5)

S(φ1,φ1) =πa2(1 − e2) 1 e sinφ1
1 + e sinφ+ log||).
(
180e
2 1 − e2 sin2φ 4
1 − e sinφ(A6)

For a = 6378.136 (km) and e2 = 0.00669447, surface area from latitude φ1 to φ2 per 1° inlatitude can be calculated from (A6).
The values calculated from (A6) are compared in Figure A1, with other estimatessuch as Baumgartner and Reichel (Baumgartner and Reichel, 1975), Bryan and Oort(Bryan and Oort, 1984), and the “gridarea.grz” file on the ISLSCP CD-ROM (Meeson etal., 1995; Sellers et al., 1995). The curves indicate the relative difference (%) of the area
size at each 5° latitudinal zone compared to the estimates by this algorithm. The
difference, if the area sizes are calculated assuming that Earth is a perfect sphere withthe actual radius of the equator (= 6378 km), is also shown in Figure A1. It was foundthat the area sizes in the ISLSCP CD-ROM and by Bryan and Oort (Bryan and Oort,
1984) correspond to the area sizes that were calculated with the perfect sphereassumption using radii equal to 6371 and 6366 km, respectively. The radius of 6371 km
may be derived inversely from the whole Earth's surface area of 510 × 1012 m2. The
radius of 6366 km is close to the mean of the equatorial and the polar radii. Residual to
the total of 510 × 1012 m2 might be allocated to polar regions, and that may be the reason
why the area by Bryan and Oort (Bryan and Oort, 1984) at 85°–90° is larger than theothers. Baumgartner and Reichel (Baumgartner and Reichel, 1975) have considered theellipticity of Earth, and their estimate is very close to the result of this study as seen from
Figure A1.
23

Figure A1. Comparison of the area size at each 5° latitudinal zone. The
difference error compared to the values used in this study are presented.
Previous studies except for Baungartner and Reichel (Baumgartner andReichel, 1975) have systematic biases in latitude. [Click on icon 31(approx 53
kbyte) to view full figure.]
A.2. Surface distance
As stated earlier, the river channel length in TRIP can be expected to be shorter thanobserved. Therefore, a relatively simple algorithm was used to calculate the length
between two grid points in TRIP.
The distance between grids is obtained from (A1) and (A2), respectively, if theirlatitudes or longitudes are the same. Otherwise, the distance L, between P(λ1, φ1) andQ(λ2, φ2), was calculated assuming that Earth is a sphere with an effective radius of Re atlatitude φh = (φ1 + φ2)/2.
From the law of cosines on a sphere,cosa = cosb cosc + sinb sinc cosA ,(A7)
where A is an interior angle, and a, b, and c are the length of opposite sides measured inradians. Let b and c be the longitudinal and latitudinal directions, and A makes a rightangle, then cosA = 0. The distance L = a is obtained by
L = arccos[cos(lx/Re) cos(ly/Re)] Re ,(A8)
where lx and ly are from (A1) and (A2). The effective radius of the earth at the latitude
φh, Re, is given by
Re = N (1 − 2e2 sinφh + e4 sin2φh )1/2
(A10)
24

N = a(1 − e2 sin2φh )−1/2.
(A11)
The results obtained from the above algorithm would be accurate enough for TRIP,
because the distances are calculated piecewise between neighbors of 1° grids.

Appendix B: TRIP Information
TRIP data and its derivative information are attached with this manuscript.
B.1. TRIP data
Each 1° × 1° grid box is allocated a number that indicates the outflow direction
from the grid box. Each grid box can have one outflow direction from eight candidates:
1) north, 2) northeast, 3) east, 4) southeast, 5) south, 6) southwest, 7) west, and 8)
northwest.
Missing value, indicating that grid point is water surface, is 0. The value “9” implies
that no outlet from that grid point to any neighboring land grids. It could be a rivermouth.
TRIP data are provided in several formats.
B.1.1. Binary format
Four-byte real of 360 × 180 data are written from (89.5°N, 0.5°E) to (−89.5°N,
359.5°E). The following program will read the binary data file of TRIP.
integer i, jreal trip(360, 180)
open(15, file='trip.bin', access='DIRECT'$, recl=4*360, form='UNFORMATTED')
do j = 1, 180
read (infile, rec=j) (trip(i, j), i = 1, 360)
end doclose (15)25The longitude (rlon) and latitude (rlat) for “trip(i,j)” can be calculated as
rlon = real(i) - 0.5
rlat = 90.5 - real(j).

The datafile “data1.zip” is attached. [Click on icon

to initiate a download.]

B.1.2. Two-byte integer file
The program below will read the binary data file.
integer i, j
integer*2 i2trip(360, 180)
open(15, file='trip.i2', access='DIRECT'$, recl=2*360, form='UNFORMATTED')
do j = 1, 180
read (infile, rec=j) (i2trip(i, j), i = 1, 360)
end doclose (15)The datafile “data2.zip” is attached. [Click on icon

to initiate a download.]

B.1.3. Text format
TRIP information is stored in a text file of 360 column by 180 lines from (89.5°N,
0.5°E) to (−89.5°N, 359.5°E). The “+” is used for “9,” and “.” is used for “0.”26The datafile “data3.zip” is attached. [Click on icon

to initiate a download.]

B.1.4. ASCII data
TRIP information is indicated by a line for each grid point over land. Each line has
longitude, latitude, and the TRIP direction number.

The datafile “data4.zip” is attached. [Click on icon

to initiate a download.]

B.2. Templates of major river basins in TRIP
Approximately 200 major river basins are delineated in TRIP. Data in the index file(data5.dat) indicate the correspondences between the river basin numbers and the rivernames. The longitude and the latitude of the river mouth in TRIP are presented as well.

The datafile “data5.zip” is attached. [Click on icon

to initiate a download.]

The river basin number may change in the future version of TRIP and one must use
the corresponding version of the index file. River basin numbers are given in thefollowing formats. Data can be read by the same manner as in the previous section.

A 4-byte real binary datafile, “data6.zip,” is attached. [Click on icon
initiate a download.]

A 2-byte integer binary datafile, “data7.zip,” is attached. [Click on icon
initiate a download.]

27

to

to

An ASCII datafile, “data8.zip,” is attached. [Click on icon
download.]

to initiate a

B.3. Vector data of basin boundaries of major rivers
Information on river basin boundaries is extracted from the current version of TRIP
in vector format (data9.tar).

The datafile “data9.tar” is attached. [Click on icon

to initiate a download.]Acknowledgments. The authors wish to thank the Global Runoff Data
Center for providing valuable datasets. Special thanks go to Dr. W.
K.-M. Lau and Mr. D. Mocko at NASA/Goddard Space Flight Center,
and Prof. E. F. Wood at Princeton University for their helpfulcomments. The authors are grateful to Mr. S. Kanae for his help in
appendix A. Figures were drawn by the General Mapping Tools. This
work was done during the first author's tenure as a visiting scientist at
the Laboratory for Atmospheres, NASA/Goddard Space Flight Center.
The visit was supported by Japan Society for the Promotion of Science
Postdoctoral Fellowships for Research Abroad in collaboration with
Universities Space Research Association.

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Wessel, P., and W. H. F. Smith, 1995: New version of the generic mapping tools
released. Eos, Trans. Am. Geophys. Union, 76, 329.
RECEIVED: 7 March 1997
REVISED: 23 July 1997
ACCEPTED: 10 November 1997 (in final form 3 December 1997)2

Permanent affiliation: Institute of Industrial Science, University of Tokyo, Tokyo,
Japan. E-mail: taikan@iis.u-tokyo.ac.jp

1

Corresponding author address: Taikan Oki, Institute of Industrial Science, University ofTokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8558, Japan. 2

3

Earth Interactions is published jointly by the American Meteorological Society, theAmerican Geophysical Union, and the Association of American Geographers. Permission touse figures, tables, and brief excerpts from this journal in scientific and educational
works is hereby granted provided that the source is acknowledged. Any use ofmaterial in this journal that is determined to be “fair use” under Section 107 or thatsatisfies the conditions specified in Section 108 of the U.S. Copyright Law (17 USC,
as revised by P.L. 94-553) does not require the publishers' permission. For
permission for any other form of copying, contact one of the copublishing societies.

5
6
7
8
9

River basin area in TRIP.
River basin area from MO92.
River basin area from KU78.
River basin area from MM83.
River length in TRIP.

10
11River length from KU78.
River length by JNAO93.

32

4

Table 1. River catalog identified in Total Runoff Integrating Pathways (TRIP). Riverbasins on Antarctica and Greenland in TRIP are excluded and the sequential
number in the order of area is not continuous. Representative names of rivers areshown. The river mouth may be shifted within ±1° to the actual location. Basinarea and river length in TRIP are compared with previously published numbers.
Number of 1° × 1° grid boxes in each river basin is listed at the end of each row.

33

River mouth
Name

No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
47
49
50
52
53
54
55
56
57
59
62
63
65
66
67
69
70
71
72
73
74
75
76
78
79

AmazonCongo
Mississippi
Ob
ParanaNile
Yenisey
Lena
Niger
Amur
Changjiang
Mackenzie
Volga
Zambeze
Lake Eyre
NelsonSt. Lawrence
MurrayGangesOrangeIndus
OrinocoChari
Tocantins
Yukon
DanubeMekongCubangoHuangheEuphrates
Jubba
Columbia
Brahmaputra
KolymaColorado
Rio Grande
SaoFrancisco
Dniepr
Amu Darya
LimpopoSenegalTarimDon
Syr Darya
Xi
Volta
Northern
Dvina
Khatanga
Irrawaddy
Indigirka
SaladoGodavari
Salween
Paranaiba
PechoraSaladoDulce
Magdalena
Churchill
Neva
Helmand
Tugaj
Krishna
Ural
FraserYana
Rhein
Huai He
OlenekOgooueRiver length (km)Basin area (104 km2)

5

6

7

8

9

10

11

Long

Lat

50.5°W
12.5°E
90.5°W
70.5°E
57.5°W
30.5°E
83.5°E
124.5°E
6.5°E
140.5°E
120.5°E
134.5°W
48.5°E
36.5°E
137.5°E
92.5°W
70.5°W
139.5°E
88.5°E
16.5°E
67.5°E
61.5°W
14.5°E
48.5°W
164.5°W
29.5°E
106.5°E
22.5°E
118.5°E
48.5°E
42.5°E
123.5°W
90.5°E
160.5°E
114.5°W
97.5°W
37.5°W

0.5°N
5.5°S
29.5°N
66.5°N
34.5°S
31.5°N
71.5°N
73.5°N
5.5°N
53.5°N
31.5°N
68.5°N
46.5°N
18.5°S
27.5°S
57.5°N
47.5°N
35.5°S
22.5°N
28.5°S
24.5°N
9.5°N
12.5°N
1.5°S
62.5°N
45.5°N
10.5°N
19.5°S
37.5°N
30.5°N
0.5°N
46.5°N
22.5°N
69.5°N
31.5°N
26.5°N
10.5°S

614
373
325
300
297
296
261
235
211
187
182
175
141
133
123
111
111
107
103
100
97
95
92
87
85
81
80
79
78
76
74
72
65
64
64
61
61

615
369
325
298
310
301
259
—
209
205
181
167
142
133
—
106
125
108
110
102
96
94
88
90
90
82
80
78
75
76
—
65
66
63
—
57
66

691
382
322
299
297
287
258
249
209
185
180
180
136
133
124
107
129
106
95
102
96
100
88
—
85
82
81
78
74
75
75
67
58
65
63
57
60

615
382
327
250
283
296
258
250
121
185
194
181
—
120
—
—
103
106
—
102
97
99
—
—
84
81
79
—
77
105
—
67
—
64
64
—
64

4434
3982
4023
4157
3113
5464
4757
4292
3475
3490
4327
3075
2973
2419
1178
2285
2794
1883
1970
1576
2518
2000
1415
2099
2665
2091
3383
1112
3823
1986
1603
1593
2769
1947
1578
2044
2228

6280
4370
5985
—
4700
6670
—
4400
4160
—
5520
4240
3350
2660
2000
2600
3060
3490
—
1860
3180
2740
1400
—
3000
2860
4500
1800
4670
2760
1600
1950
3000
2130
2180
2880
2800

6300
4370
6210
5200
4800
6690
4130
4270
4180
4350
6300
4240
3690
2740
—
2570
3060
2590
2510
2090
2900
2060
1400
—
3700
2860
4020
1800
5460
2800
1660
1850
2900
2600
2320
3030
3200

505
305
347
441
265
249
409
400
177
234
171
289
202
112
111
144
128
102
93
91
92
78
76
72
158
94
69
68
79
75
60
84
60
123
64
58
51

32.5°E
59.5°E
33.5°E
16.5°W
86.5°E
39.5°E
61.5°E
113.5°E
0.5°E
40.5°E

46.5°N
43.5°N
24.5°S
16.5°N
41.5°N
47.5°N
45.5°N
22.5°N
6.5°N
64.5°N

51
49
44
44
44
43
42
41
38
36

51
46
44
44
—
43
65
44
39
36

50
31
44
44
45
42
22
44
39
36

—
—
41
—
—
—
—
44
—
35

1534
1987
1084
1332
1379
1238
1703
1115
1129
1289

2200
—
1600
1430
2000
1870
2210
—
1600
—

2290
2540
1770
1630
2180
1970
2210
1960
—
1750

66
51
39
37
46
53
46
36
31
62

106.5°E
95.5°E
149.5°E
66.5°W
81.5°E
97.5°E
42.5°W
53.5°E
57.5°W
62.5°W
74.5°W
94.5°W
30.5°E
62.5°E
62.5°E
80.5°E
51.5°E
122.5°W
135.5°E
4.5°E
119.5°E
120.5°E
9.5°E

73.5°N
16.5°N
71.5°N
37.5°S
16.5°N
16.5°N
3.5°S
68.5°N
35.5°S
30.5°S
10.5°N
58.5°N
59.5°N
30.5°N
47.5°N
16.5°N
47.5°N
49.5°N
71.5°N
51.5°N
33.5°N
72.5°N
1.5°S

36
35
35
33
33
32
32
31
29
29
27
27
26
24
24
24
23
23
23
23
22
20
20

—
43
36
—
31
—
—
32
—
—
26
—
28
—
—
25
22
22
—
22
—
—
—

36
41
36
—
31
32
32
32
—
—
24
28
28
25
—
26
24
22
24
22
22
22
20

—
43
36
—
31
—
—
—
—
—
24
—
—
—
—
—
—
22
22
—
26
—
—

1092
1586
1607
1068
1007
2382
975
1407
887
948
1022
1483
711
769
630
751
1284
911
1002
986
663
1560
693

1636
2300
1726
—
1500
2820
1450
1810
—
—
1530
1600
—
1150
—
1290
2430
1110
872
1360
900
2270
850

—
2090
—
—
—
2410
—
1810
—
—
1540
—
—
—
—
—
2530
—
—
1320
—
2160
—

87
31
72
32
28
29
26
60
29
27
22
38
42
23
30
20
30
30
47
28
21
45
16

AT

AO

34

AK

AM

LT

LK

LR

Grids

80
81
82
83
84
86
88
89
91
92
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
110
111
112
113
114
116
118
119
120
121
123
124
126
127
129
131
132
133
134
135
137
138
139
141
142
143
144
145
146
147
148
153
158
159
170
172
174
178
186
191
195
200
201
224
225
238
240
241
247
248

Wisla
Anadyr
Liao
RufijiKura
P'asina
Chao Phraya
Hai
Taz
Lake Rudolf
AlbanyKoksoak
Ili
Red
Essequibo
CuanzaTelon
ElbeSantiago
Emba
BaritoFitzroy
MobileSanagaRuvumaCuneneUsumacinta
Mahanadi
Burdekin
NarmadaBrazosTedzenPur
Loire
Kuskokuim
KerulenChubutFlinders
Colorado
Save
Negro
Odra
Mattagami
Bandama
Komoe
Hayes
Santa Cruz
Rhone
Anabar
Tes-Chem
Back
SevernLa Grande
RiviereNeman
TaimyraBroadback
Tana
Saguenay
GambiaBalsas
Doce
Douro
Ebro
PanucoWestern
Dvina
Gascoyne
Garonne
Churchill
Tagus Tejo
Sacramento
NistruSarysuVictoria
FitzroySeine

18.5°E
176.5°E
122.5°E
38.5°E
48.5°E
86.5°E
100.5°E
117.5°E
78.5°E
35.5°E
81.5°W
68.5°W
74.5°E
105.5°E
58.5°W
13.5°E
100.5°W
9.5°E
104.5°W
53.5°E
114.5°E
150.5°E
88.5°W
10.5°E
39.5°E
12.5°E
92.5°W
86.5°E
147.5°E
72.5°E
95.5°W
61.5°E
77.5°E
1.5°W
162.5°W
116.5°E
65.5°W
140.5°E
96.5°W
34.5°E
63.5°W
14.5°E
80.5°W
4.5°W
3.5°W
92.5°W
68.5°W
4.5°E
113.5°E
92.5°E
96.5°W
87.5°W
78.5°W

53.5°N
64.5°N
40.5°N
7.5°S
39.5°N
73.5°N
13.5°N
39.5°N
67.5°N
3.5°N
52.5°N
58.5°N
45.5°N
20.5°N
6.5°N
9.5°S
64.5°N
53.5°N
21.5°N
46.5°N
3.5°S
23.5°S
30.5°N
4.5°N
11.5°S
17.5°S
18.5°N
20.5°N
20.5°S
21.5°N
29.5°N
36.5°N
67.5°N
47.5°N
60.5°N
48.5°N
43.5°S
17.5°S
28.5°N
21.5°S
40.5°S
53.5°N
51.5°N
5.5°N
5.5°N
56.5°N
50.5°S
43.5°N
73.5°N
50.5°N
67.5°N
55.5°N
53.5°N

19
19
19
18
18
17
16
16
16
16
16
15
15
15
15
15
14
14
14
14
14
13
13
13
13
13
13
13
13
13
12
12
12
12
12
12
12
12
12
12
12
11
11
11
11
11
10
10
10
10
10
10
10

—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

20
19
23
18
19
18
16
14
15
—
13
13
14
14
15
15
14
15
—
—
—
14
11
13
14
14
12
13
13
10
—
7
11
12
12
12
14
11
10
11
13
11
—
10
—
11
—
10
10
—
11
10
—

—
—
17
18
—
—
—
—
—
—
—
—
—
12
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
10
—
—
—
—
—
—
9
—
—
—
—
—

826
811
936
598
819
972
749
631
902
801
949
638
1059
666
442
817
541
783
616
478
535
457
698
646
547
698
461
720
373
1071
1006
681
744
624
811
911
653
720
1039
581
826
577
465
534
643
385
451
545
764
492
864
582
531

1090
1150
1350
1400
1360
818
1200
—
1400
—
975
1300
1000
1200
970
630
—
1110
960
—
—
960
1064
860
800
830
—
858
680
1300
1400
1124
—
1110
—
1264
850
830
1450
680
1000
907
—
780
—
—
—
810
939
—
960
976
—

1090
—
1430
—
—
—
—
—
—
—
—
—
1400
—
—
—
—
1170
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
1020
—
—
—
—
—
—
—
910
—
—
—
—
—
810
—
—
—
—
—

25
37
21
15
19
43
14
17
31
13
20
22
17
13
12
12
25
18
12
16
11
12
13
11
11
11
11
11
11
11
12
12
22
14
20
14
13
10
11
10
12
15
14
9
9
15
13
12
25
13
20
14
14

21.5°E
99.5°E
78.5°W
40.5°E
70.5°W
16.5°W
102.5°W
40.5°W
8.5°W
0.5°E
98.5°W
24.5°E

55.5°N
75.5°N
51.5°N
2.5°S
48.5°N
13.5°N
18.5°N
19.5°S
41.5°N
40.5°N
22.5°N
56.5°N

10
10
10
10
10
10
9
9
9
9
9
9

—
—
—
—
—
—
—
—
—
—
—
—

10
12
—
9
9
18
11
8
9
9
8
9

—
—
—
—
—
—
—
—
—
—
—
—

520
565
614
490
503
590
422
363
501
581
318
633

937
754
—
720
—
1200
—
600
925
930
—
1020

—
—
—
—
—
—
—
—
—
930
—
—

14
30
13
8
12
8
8
8
10
10
8
13

113.5°E
0.5°W
58.5°W
8.5°W
121.5°W
30.5°E
66.5°E
129.5°E
123.5°E
0.5°E

24.5°S
44.5°N
54.5°N
39.5°N
38.5°N
46.5°N
45.5°N
15.5°S
17.5°S
49.5°N

9
9
9
9
9
8
8
8
8
8

—
—
—
—
—
—
—
—
—
—

8
9
8
8
7
7
8
8
9
8

—
—
—
—
—
—
—
—
—
—

553
328
590
654
474
567
700
542
412
413

770
650
560
1010
610
—
761
570
520
780

—
—
—
—
—
—
—
—
—
780

8
10
12
9
9
10
10
7
7
10

35

257
267
269
281
284
285
305
313
316
317
323
324
331
342
356
368
371
385
392
415
420
421
426
435
443
451
462
471
473
476
509
514
529
533
579

Mezen
Ashburton
San Joaquin
Rio
Colorado
Guadiana
Penzina
Susquehana
Mamberamo
Sepik
MearimFly
Sassandra
Nottaway
Mitchell
Nadym
Paraiba
Attawapiskat
Murchison
Yalu
Apalachicola
Kuban
KouilouPo
Lurio
Alazeja
Guadalquivir
Chu
Kemi
Sakarya
Fortescue
CopperOnega
Saint John
SkeenaNarva

44.5°E
115.5°E
121.5°W
62.5°W

65.5°N
22.5°S
37.5°N
39.5°S

8
8
8
8

—
—
—
—

8
8
8
6

—
—
—
—

584
505
373
772

966
640
560
1000

—
—
—
—

15
7
8
8

7.5°W
164.5°E
76.5°W
138.5°E
144.5°E
44.5°W
143.5°E
6.5°W
79.5°W
142.5°E
72.5°E
41.5°W
82.5°W
114.5°E
124.5°E
84.5°W
37.5°E
12.5°E
11.5°E
40.5°E
154.5°E
6.5°W
105.5°E
25.5°E
30.5°E
116.5°E
144.5°W
38.5°E
66.5°W
129.5°W
27.5°E

37.5°N
62.5°N
39.5°N
2.5°S
4.5°S
3.5°S
8.5°S
5.5°N
51.5°N
15.5°S
66.5°N
21.5°S
52.5°N
27.5°S
40.5°N
30.5°N
45.5°N
4.5°S
45.5°N
13.5°S
70.5°N
37.5°N
19.5°N
66.5°N
40.5°N
21.5°S
60.5°N
63.5°N
45.5°N
54.5°N
58.5°N

8
8
7
7
7
7
7
7
7
7
7
7
7
7
6
6
6
6
6
6
6
6
6
6
6
6
5
5
5
5
5

—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—

7
7
7
8
8
9
6
7
6
7
6
6
5
7
6
5
6
6
7
6
6
6
6
5
6
5
6
6
6
5
6

—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
7
—
—
—
—
—
—
—
6
—
—
—
—

600
509
361
379
333
424
644
378
521
308
662
461
606
447
530
546
508
424
371
478
513
494
257
312
539
255
358
369
346
385
299

800
713
733
—
700
800
620
660
—
520
545
800
810
700
1500
880
870
600
650
560
498
560
1190
—
790
670
360
416
640
510
77

—
—
—
—
—
—
1130
—
—
—
—
—
—
—
—
—
—
—
680
—
—
—
—
—
—
—
—
—
—
—
—

8
14
8
6
6
6
6
6
9
6
13
6
9
6
7
6
7
5
7
5
13
6
5
12
6
5
9
9
6
7
7

12

36

13

14

37

15

38

16

39

17

40

18

41

19

42

20

21

Table 2a. Number of grid boxes with river channel of each direction, before and after
the manual corrections for the first guess by the lowest neighbor algorithm. There
are 1162 grid boxes pointing southwest (SW) after the manual correction (column
8, row 13), but 933 out of 1162 were SW as well before the manual correction(row 8). The grid boxes where the automatic algorithm could not determine the43directions are presented as "N/A" (row 12), and for example, 78 of these gridboxes are pointing north (column 3) after the manual correction. The statistic of
the correction shows the usefulness of the automated method. Similar statistics forthe steepest slope algorithm (Table 2b) showed that lowest neighbor method wasequally satisfactory.
Before
Sea
North
NE
East
SE
South
SW
West
NW
Mouth
N/A
Total
Changed
(%)

22

Sea
43,082
0
0
0
0
0
0
0
0
0
0
43,082
0
0

North
11
3597
210
29
73
35
59
46
242
8
78
4388
791
18

NE
5
54
2580
27
56
16
27
18
56
7
52
2898
318
11

East

SE

13
97
490
749
369
67
103
55
116
24
139
2222
1473
66

South
7
20
57
39
1090
52
48
11
24
4
55
1407
317
23

9
17
63
33
221
548
198
30
53
15
65
1252
704
56

SW
6
17
18
15
51
29
933
21
48
3
21
1162
229
20

West
8
82
130
60
118
76
353
749
353
21
94
2044
1295
63

NW
2
29
61
16
29
20
53
28
2507
4
36
2785
278
10

Mouth
1
166
257
284
230
223
223
256
228
1567
125
3560
1993
56

Total
43,144
4079
3866
1252
2237
1066
1997
1214
3627
1653
665
64,8007398
11Table 2b. Same as Table 2a but for the first guess by the steepest slope algorithm.
Before
Sea
North
NE
East
SE
South
SW
West
NW
Mouth
N/A
Total
Changed(%)

Sea
43,082
0
0
0
0
0
0
0
0
0
0
43,082
0
0

North
11
3692
113
141
38
50
35
146
118
2
42
4388
696
16

NE
5
920
1354
383
30
27
16
98
28
6
31
2898
1544
53

East

SE

13
144
224
1192
173
112
58
118
73
14
101
2222
1030
46

South
7
38
35
404
522
254
27
72
18
1
29
1407
885
63

23

44

9
27
32
143
124
629
97
112
28
8
43
1252
623
50

SW
6
38
11
70
34
166
440
349
33
1
14
1162
722
62

West
8
134
73
115
60
102
178
1124
170
10
70
2044
920
45

NW
2
861
36
91
21
40
32
356
1317
1
28
2785
1468
53

Mouth
1
759
229
472
165
264
153
398
216
821
82
3560
2739
77

Total
43,144
6613
2107
3011
1167
1644
1036
2773
2001
864
440
64.80010,627
16

24

45

25

46

47

26

48

27

49

28

50

29

51

30

52

31

53