Geomorphometry of drainage basins : a global view from the Shuttle Radar Topography Mission

Introduction Conclusions References


Introduction
The Shuttle Radar Topography Mission (SRTM) created a near global digital elevation model (DEM) with 3 arc second spacing, about 90 m (Farr et al., 2007).Despite some voids in mountainous terrain and sandy desert regions, the SRTM DEM remains the best freely available dataset and several projects have worked to fill the voids (Jarvis et al., 2008;Lehner et al., 2008a, b).The SRTM's greatest weakness is the lack of coverage for Antarctica and latitudes north of 60 • .
The Hydrosheds project (Lehner et al., 2008a, b) created a hole-filled version of the SRTM DEM, conditioned the dataset for hydrologic applications, and released a drainage network and basins outlines from a 15 arc second version of SRTM.This data set includes 3.46 million stream segments in 2.48 million basins; most of the basins are small and contain at most one stream segment.A segment connects two nodes, with a node being either the terminus of a segment or the junction of two segments.The largest 1.06% of the basins, those over 100 km 2 in area, contain 98.64% of the stream segments.
Geomorphometry performs quantitative land-surface analysis (Pike et al., 2009), and the SRTM data provides a data set at an appropriate scale for global analyses.results with the US National Elevation Dataset, and further described 30 parameters computed worldwide from SRTM (Guth, 2009).Those analyses used small rectangular areas (0.5 million in the United States, 7.4 million in the entire world) which can be considered random sampling areas.This study seeks to use the Hydrosheds drainage basins, natural sampling areas of varying size, and computes both geomorphometric parameters from the DEM, metrics of the drainage basin and channel networks, and characteristics of the channel thalwegs.

Methods and limitations
Appendix A lists the processing steps used with the Hydrosheds data.I excluded basins with an area less than 100 km 2 .With the 15 DEM used to compute the drainage network, each pixel is about 464×461 m at the equator and 232×464 m at 60 • , the limit of the SRTM data.These represent about 0.2 km 2 and 0.1 km 2 respectively, so a 100 km 2 drainage basin contains 500-1000 elevation points.These basins are likely to have only a single channel, and produce statistics of limited validity.While this size limit is somewhat arbitrary, over 85% of the drainage basins identified by Hydrosheds have areas less than 1 km 2 and most of these have no channel segments.
Most of these small basins occur on the coastline, or large areas of interior drainage (Fig. 1).
The scale of the DEM used to create the drainage network limits the scale of features visible in the drainage networks.The smallest segments will be a single pixel, about a half kilometer, and will influence parameters like sinuosity, so care must be taken in comparing these results with those from different scales.Computed thalwegs (the major channel in the basin) are based solely on landforms in the SRTM data, and not on hydrology; some channels might be intermittent or almost always dry.The thalwegs start from the last river segment in the basin, which has the largest contributing area and no downstream connections.I trace the thalweg Figures upstream, at each junction taking the tributary with the larger contributing area.This algorithm can be fooled in cases where climate does not produce rainfall and runoff proportional to area; the Nile, highlighted in Fig. 1, shows the computed thalweg following the Bahr el Ghazal and Bahr al-Arab west into Darfur, tributaries of the White Nile, instead of following the water up the Blue Nile.The number of basins in the data set precludes a manual search to correct this limitation.Figure 2 compares the Hydrosheds drainage network with the medium resolution network from the US National Hydrography Dataset (NHD; Simley and Carswell, 2009).At regional scales they line up very well, and because the NHD reflects a larger scale, it generally shows additional tributaries.The number of additional tributaries varies with landforms and the resulting channel patterns.Brief qualitative assessment suggests that the Strahler order 1 streams in this region range from order 1 to 4 in the NHD data, and most commonly are order 2 or 3. Figure 2 also shows the bimodal distribution of small basins (<100 km 2 ): a great many tiny basins along the coast with no stream segments, and a much smaller number of first and some second order drainage networks between the outlets of the larger basins.

Results
Figure 3 shows the drainage basins coded by Strahler order.The three largest streams on earth (Amazon, Congo, and Volga) have a Strahler order of 9, and very different geomorphic regimes due to significant differences in total basin relief (6211, 3955, and 1624 m respectively).Figure 4 shows a histogram of Strahler order for the 26 272 basins with an area greater than 100 km 2 , clearly demonstrating a logarithmic decline in the number of basins with increasing order.Limiting basin size to 100 km 2 removes many small order 1 streams; an alternative might be to restrict analysis to order 2 and larger streams.all of these maps, several characteristics stand out.The desert belts (North American Great Basin, Sahara, Arabian peninsula, central Asia, and western Australia) tend to lack large drainage basins, in both area and Strahler order.ELEV RELF (Fig. 5a) is the elevation-relief ratio computed from the DEM.The Dnieper River basin has the largest value of this parameter, due to an elevation distribution with almost all the points in the middle of the elevation distribution and very little area near the elevation of the Black Sea, and a thalweg which descends comparatively rapidly near its mouth at the Black Sea. Figure 5b shows the RATIO RELF parameter, which considers only the geometry of the thalweg and in essence computes its average slope.The largest values occur in small steep basins which do not show up well at this scale; of major rivers, the largest values are from the Mekong and Yangtze, which have thalwegs that ascend high into the central Asian mountains.Figure 5c shows BASIN RUGD, which is the ratio of basin's elevation range to its area, and this metric rewards small, steep basins along coasts and interior basins in central Asia; coloring by the logarithm emphasizes the huge range in values for this parameter, from nearly 0 for very large, flat basins to 36 for small steep basins.Figure 5d shows basin SINUOSITY, with low values for a straight thalweg and higher values for curved channels.The most sinuous major river that appears at this scale is the Don, which curves 1896 km to travel a straight line distance of 521 km.Figures 6 and 7 look at basin thalwegs, on a normalized plot of elevation and distance so that profile shapes can be compared.Figure 6 contours the density of thalweg shapes, in terms of the percentage of basin in each percent on the graph.Densities less than 1 are not shown, and the magenta includes values significantly larger than 5. Profiles tend to be very gentle near the mouth of the river, and steep near the headwaters, reflecting the traditional graded profile.The small basins, which dominate noise in the measured elevations where the channel goes through deep canyons; we are working on a satisfactory automatic filtering algorithm that will work with all 26 272 thalwegs.A number of the thalwegs in Fig. 7 lie outside the common zones seen in Fig. 6; for example, both the Amazon and Niger (Fig. 7b) have extremely steep headwaters, while the Nelson has an extremely abrupt descent into Hudson's Bay, as well as much lower overall relief compared to the others in this group.Several of these thalwegs, such as the Indus, show several distinct convex segments.
Figure 8 shows a correlation matrix for the 42 parameters in Appendix B, for all 26 272 basins.Blue represents the strength of positive correlations, and red negative correlations.Positive correlations >0.90 mostly demonstrate that many of the parameters really reflect different ways of expressing slope; the one correlation that is not directly related to slope is a high correlation between the log of the basin area and the Strahler order.The strongest negative correlations are for S2S3 and STRENGTH, negatively correlated with the slope measures because they are defined as inverse slope measures.

Discussion
Wechsler (2007) looked at uncertainties in DEMs and how they impacted hydrologic applications.He emphasized that the results of using DEMs depended on both the DEM quality, and its scale.The results reported here rely on 15 data, appropriate for global analysis, but could be extended to 3 scale by using the full resolution of the SRTM data.The most significant problem will be the holes in the data, and lack of coverage at high northern latitudes, but the SRTM appears to be the best candidate for a global dataset for the immediate future.Initial claims for the superiority of the 1 ASTER GDEM do not appear to be substantiated (Guth, 2010), and even the 1 SRTM data currently restricted to the United States military and publicly available only for the continental United States does not provide much improvement over the 3 data for geomorphometry (Guth, 2006).Introduction

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Full Despite the limitations of scale and data quality, the SRTM drainage data provides a real bonanza for quantitative geomorphology.The challenge will be to frame the correct comparisons, which will probably involve restricting analysis to basins with similar size or Strahler order, and looking at the subbasins within the global data set.The elevation data from SRTM consists of about 35 GB of data, and cheap processing and storage allows manipulation on common desktop computers.

Conclusions
The SRTM-derived Hydrosheds data set contains 26 272 basins with an area greater than 100 km 2 , and provides a near-global, internally consistent data set to investigate the gemorphological properties of both the basin and the thalweg profiles.The current resolution of this data is 15 (about 0.5 km), appropriate for global studies.Because most parameters depend on the scale of the data used for computations, these results cannot be readily compared to other studies.Parameters also depend on the size of the drainage basin as well as the resolution of the input data, but the SRTM data provides a fascinating picture of the world's drainage patterns.3. Create a DEM for each basin, using 6 SRTM data created by decimating the 3 Hydrosheds void-filled data.This size allows in memory manipulation of the largest drainage basins for fast processing, and is still higher resolution than the drainage basins.
4. Assign each drainage segment to a basin using a point in area function; segments in the small drainage basins are left unassigned.
5. Extract nodes and create topology for each basin from the nodes at the end of each drainage segment, and compute its Strahler order 6.Create thalweg for each basin as a 3-D shapefile with the elevations from the 15 Hydrosheds DEM (6 DEM produces similar results).
7. Compute geomorphometric parameters listed in Appendix B for each drainage basin.
8. Modify Hydrosheds river files to include the basin to which it belongs, its Strahler order, and whether it lies on the thalweg of the drainage system.9. Modify the Hydrosheds basin files to include Strahler order, the total length of channels in the basin, the length of the thalweg, and the perimeter of the basin.15.S2S3: terrain organization (Guth, 2003).High values correlate with strong tendency for ridges and valleys to align.Introduction

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Figure 5
Figure5shows maps color-coded by 4 of the basin geomorphometric parameters listed in Appendix B. Like Fig.3, the map visually emphasizes the large basins.On

Fig. 6a ,
Fig.6a, tend to have a much more linear profile; the larger streams tend to have a flatter downstream segment, steeper headwaters, and an overall more concave profile as seen in Fig.6b.Figure7shows the thalwegs of the 25 largest basins (defined as having over 500 m relief along the thalweg, and Strahler order 8 or 9).The graphs exhibit Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

10 .
Manually identify significant basins by reference to atlases and other reference material.Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .
Fig. 1.(a) Red symbols mark drainage basins smaller than 100 km 2 for Africa, with the thalwegs of the larger drainage basins shown in blue.The Nile is highlighted in black.The small basins effectively mark the coastline, with smaller numbers in interior drainage areas such as the Sahara.The size of the symbols greatly exaggerates the importance of the small basins.(b) Strahler order for the larger channels in Africa, down to order 4.