Frasson, R. P. D. M., Pavelsky, T. M., Fonstad, M. A., Durand, M. T.,
Allen, G. H., Schumann, G., Lion, C., Beighley, R. E., & Yang, X.
(2019). Global Relationships Between River Width, Slope, Catchment
Area, Meander Wavelength, Sinuosity, and Discharge.
Geophysical
Research Letters
,
46
(6), 3252-3262.
https://doi.org/10.1029/2019GL082027
Publisher's PDF, also known as Version of record
License (if available):
Other
Link to published version (if available):
10.1029/2019GL082027
Link to publication record in Explore Bristol Research
PDF-document
This is the final published version of the article (version of record). It first appeared online via Wiley at
https://doi.org/10.1029/2019GL082027 . Please refer to any applicable terms of use of the publisher.
University of Bristol - Explore Bristol Research
General rights
This document is made available in accordance with publisher policies. Please cite only the
published version using the reference above. Full terms of use are available:
http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/
Global Relationships Between River Width, Slope,
Catchment Area, Meander Wavelength,
Sinuosity, and Discharge
Renato Prata de Moraes Frasson
1
, Tamlin M. Pavelsky
2
, Mark A. Fonstad
3
,
Michael T. Durand
1,4
, George H. Allen
5
, Guy Schumann
6,7
, Christine Lion
8
,
R. Edward Beighley
9
, and Xiao Yang
2
1
Byrd Polar and Climate Research Center, The Ohio State University, Columbus, OH, USA,
2
Department of Geological
Sciences, University of North Carolina, Chapel Hill, NC, USA,
3
Department of Geography, University of Oregon, Eugene,
OR, USA,
4
School of Earth Sciences, The Ohio State University, Columbus, OH, USA,
5
Department of Geography, Texas
A&M University, College Station, TX, USA,
6
Remote Sensing Solutions, Inc., Monrovia, CA, USA,
7
School of Geographical
Sciences, University of Bristol, Bristol, UK,
8
FluroSat Pty, Ltd, Eveleigh NSW, Australia,
9
Department of Civil and
Environmental Engineering, Northeastern University, Boston, MA, USA
Abstract Using river centerlines created with Landsat images and the Shuttle Radar Topography
Mission digital elevation model, we created spatially continuous maps of mean annual flow river width,
slope, meander wavelength, sinuosity, and catchment area for all rivers wider than 90 m located between
60°N and 56°S. We analyzed the distributions of these properties, identified their typical ranges, and
explored relationships between river planform and slope. We found width to be directly associated with the
magnitude of meander wavelength and catchment area. Moreover, we found that narrower rivers show a
larger range of slope and sinuosity values than wider rivers. Finally, by comparing simulated discharge from
a water balance model with measured widths, we show that power laws between mean annual discharge and
width can predict width typically to −35% to +81%, even when a single relationship is applied across all
rivers with discharge ranging from 100 to 50,000 m
3
/s.
Plain Language Summary For years, scientists and engineers have been using aerial
photography to study the shapes of rivers, how they change over time, and how they relate to other river
characteristics, such as river width, the slope of the water surface, and flow. These studies served as basis for
the development of theories describing erosion, sediment transport, the speed at which flood waves travel
through a basin, and serving as guidance for the measurement of river flow. However, such studies were
often conducted in person, or done by combining results from other authors, leading to a very limited
coverage of world rivers, most of which were in North America. As images of world rivers obtained by
satellites became available and adequate computational power became affordable, we were able to describe
the shape of worldwide rivers and how other properties, such as slope, width, and flow relate to meander
characteristics. We showed that although classical geomorphic studies had limited geographical coverage,
their results could generally be applied to typical rivers over the world. Additionally, with our results, rivers
with atypical meander characteristics can be better identified, allowing the advancement of our
understanding of how rivers work.
1. Introduction
Responding to the need for better understanding of rivers at continental and global scales, recent studies
have explored existing remote sensing data to trace river networks (e.g., Allen & Pavelsky, 2015; Lehner
et al., 2008; Lehner & Grill, 2013; Yamazaki et al., 2014), extract basin and floodplain parameters and fea-
tures (Nardi et al., 2019; Shen et al., 2017), map the extent of flooding and flood risk (Andreadis et al.,
2017; Brakenridge, 2018; Van Dijk et al., 2016), and estimate discharge (e.g., Brakenridge et al., 2007;
Gleason et al., 2014; Gleason & Smith, 2014; Gleason & Wang, 2015; Tarpanelli et al., 2013; Tourian et al.,
2013; Tourian et al., 2017). However, additional information about rivers can be extracted from currently
available satellite imagery, particularly descriptors of shapes of rivers and meanders.
The use of aerial imagery for measuring river morphological traits such as meander wavelength and sinuos-
ity has long been common practice in fluvial geomorphology (Allen et al., 2013; Constantine et al., 2014;
©2019. American Geophysical Union.
All Rights Reserved.
RESEARCH LETTER
10.1029/2019GL082027
Key Points:
• Using satellite image ry, meander
wavelength and sinuosity were
computed globally for the first time
• Even when extended to global
scales, classical relationships
between river width and meander
wavelength and discharge still hold
• We found strong associations
between sinuosity, width, meander
wavelength, slope, and discharge
Supporting Information:
• Supporting Information S1
Correspondence to:
R. P. de Moraes Frass on,
frasson.1@osu.edu
Citation:
Frasson, R. P. d. M., Pavelsky, T. M.,
Fonstad, M. A., Durand, M. T.,
Allen, G. H., Schumann, G., et al.
(2019). Global relationships between
river width, slope, catchment area,
meander wavelength, sinuosity, and
discharge. Geophysical Research Letters,
46, 3252–3262. https://doi.org/10.1029/
2019GL082027
Received 11 JAN 2019
Accepted 8 MAR 2019
Accepted article online 15 MAR 2019
Published online 25 MAR 2019
FRASSON ET AL. 3252
Marcus & Fonstad, 2008). Using measurements collected through either topographic surveys or aerial photo-
graphs, relationships between planform properties such as width and meander wavelength (e.g., Leopold &
Wolman, 1960; Richards, 1982; Williams, 1986) have been identified. These relationships supported the
development of theories regarding the dynamics of river meanders (e.g., Edwards & Smith, 2002;
Seminara, 2006), and they continue to guide the definition of spatial scales over which to evaluate flow resis-
tance (Bjerklie, 2007; Bjerklie et al., 2005) and to compute sinuosity (e.g., Kiel, 2015). Nevertheless, such rela-
tionships are usually derived based on data with limited geographical coverage. For example, Leopold and
Wolman (1960) examined 49 rivers in the United States and Williams (1986) worked with 194 reaches, most
of which are located in the United States and Canada, though a few sites are in India, Pakistan, Sweden, and
Australia. This rather limited geographical coverage may impact the applicability of such relationships in
underrepresented regions of the world.
Automated centerline tracing tools such as RivWidth (Pavelsky & Smith, 2008) allow the extraction of river
centerlines from satellite imagery, from which one can identify river meanders and compute meander wave-
length and sinuosity. Given the quasi worldwide coverage and recently improved ease of access to such
images, we can now explore how these classical relationships hold when applied to rivers distributed over
the globe. Moreover, by cross‐referencing river extents obtained by Allen and Pavelsky (2018) with eleva-
tions measured by the Shuttle Radar Topography Mission (SRTM), water surface slopes can be estimated
(LeFavour & Alsdorf, 2005), allowing, for the first time, an examination of global relationships between
slope and river width and the evaluation of classical relationships between river width and meander wave-
length at the global scale.
This work takes advantage of the river centerlines contained in the Global River Width from Landsat data-
base (Allen & Pavelsky, 2015, 2018), which is briefly described in section 2.1, to compute meander wave-
length and river sinuosity (section 2.2). Subsequently, we extracted water surface elevations from the
digital elevation model obtained from the SRTM and computed water surface slopes a after LeFavour and
Alsdorf (2005) and mapped HydroSHEDS (Lehner et al., 2008; Lehner & Grill, 2013) catchment areas into
our river centerlines as detailed in section 2.3. The resulting multivariable data set allowed quasi‐global com-
parisons between river width, meander wavelength, sinuosity, water surface slopes, and mean annual flow
obtained from the water balance model WBMsed (Cohen et al., 2014; section 3). Our analysis aims to eval-
uate how well previously established relationships between river properties hold when extended to global
scales and to generate a range of hypotheses suitable for future studies that may benefit from our novel
data set.
2. Data and Methods
2.1. River Centerlines and Widths
The methodology for the extraction of river centerlines and estimation of river widths is described in
detail by Allen and Pavelsky (2015), and more recently by Allen and Pavelsky (2018). The major steps
in the tracing of river centerlines and calculation of widths are the identification of the time of the year
most likely to correspond to mean annual flow, which is executed using monthly discharges from the
Global Runoff Data Center (GRDC, 2011); selection of the closest ice‐ and cloud‐free Landsat scenes to
the identified date; creation of a land‐water mask based on dynamic thresholding (Li & Sheng, 2012)
applied to the modified normalized difference water index calculated from Landsat reflectance values
(Xu, 2006); and finally processing of the masks by employing the RivWidth software (Pavelsky &
Smith, 2008) to trace centerlines and calculate river widths. This method allows the tracing of centerlines
of rivers as narrow as 30 m, however, as widths of rivers narrower than 90 m tend to be overestimated
(Allen & Pavelsky, 2015), streams narrower than 90 m were kept in our data set but excluded from our
statistical analyses.
2.2. Meander Wavelength and Sinuosity
We calculated the meander wavelength as twice the distance between successive inflection points iden-
tified over river centerlines, as defined by Leopold and Wolman (1957). The inflection point identification
followed a modified version of the method proposed by Bjerklie (2007): we operated one river segment at
a time, defined here as a continuous section of a river centerline broken at the location of confluences.
We projected the entire segment centerline using the Universal Transverse Mercator zone containing the
10.1029/2019GL082027
Geophysical Research Letters
FRASSON ET AL. 3253
centroid of the segment. Next, we smoothed the projected centerline using a 5‐point moving average to
remove jagged edges caused by the finite raster resolution of the Landsat images. Finally, moving along
the river segment, we identified the direction of the curvature of the river by the sign of the cross‐
product between two vectors: one beginning at the immediate upstream point and ending at the evalu-
ated point and the second beginning at that point and ending at the immediate downstream point.
Locations where the cross‐product changed signs marked the locations where curvatures changed direc-
tions, therefore delimiting the meanders. We computed sinuosity over all identified meanders, regardless
of whether the channel formed a symmetric S shape. We used the meander endpoints to delimit the
length over which sinuosity is calculated according to its classic definition given in Leopold and
Wolman (1960), that is, the ratio between the length measured along the centerline to half the
meander wavelength.
2.3. River Slope and Catchment Area
Catchment area was derived from flow direction and corresponding flow accumulation grids based on
HydroSHEDS (Lehner et al., 2008), which provides river networks obtained from SRTM data analysis and
includes corrections based on observed hydrographic data sets. The flow accumulation grid describes, for
any location (i.e., pixel), the number of upstream pixels that drain to that location. HydroSHEDS pixels were
mapped into our centerlines using the nearest neighbor method. We translated flow accumulation given in
number of pixels into catchment area (in m
2
) by multiplying the number of pixels flowing to a location by
the average area covered by 3 arc‐seconds SRTM pixels according to the latitude of the centroid of the river
segment. We show a limited evaluation of the catchment areas over the Mississippi River in the section 5 of
the supporting information.
We matched SRTM pixels to river centerline points based on the nearest neighbor method. The matching
allowed the use of flow distance computed from the Global River Width from Landsat centerlines, which
accounts for river meanders not captured by HydroSHEDS, thus leading to better slope estimates than com-
puting slopes from SRTM/HydroSHEDS alone. We attenuated SRTM elevation noise by applying a Gaussian
filter over 10 km reaches, which were used to compute an initial estimate of the water surface slope using
either least squares linear regression or the Theil‐Sen estimator (Sen, 1968; Theil, 1992), a nonparametric
method for robust fitting of first degree polynomials. We selected the slope given with the highest coefficient
of determination as the initial estimate of the water surface slope. Next, we used the initial slope estimates to
identify optimal reach lengths (RL) according to LeFavour and Alsdorf (2005), who showed that for calculat-
ing a reliable slope from SRTM, RL need to extend sufficient distances to accommodate the height errors (σ),
given the minimum slope to be resolved (S
min
):
2 σ=RL ¼ S
min
: (1)
Using the initial slope estimates computed over 10 km reaches and assuming a constant SRTM error of
±5.51 m (LeFavour & Alsdorf, 2005), we estimated new RL with equation (1) for each river segment.
Finally, we recalculated water surface slopes over optimized RL. We omitted river reaches with slopes in
excess of 300 cm/km, which generally occur in mountainous areas where SRTM is known to be inaccurate
(Farr et al., 2007). As the SRTM data coverage is restricted to latitudes between 60°N and 56°S, the resulting
data set is also restricted to 60°N and 56°S.
2.4. Relating River Width With Catchment Area
We assumed that the relationship between river width and catchment area follows a power law of the form
W ¼ a·A
b
; (2)
where W stands for the river width, A for the catchment area, and coefficients a and b are fitted using
reduced major axis regression (Mark et al., 1977) applied in logarithm space. Reduced major axis was chosen
over ordinary least‐squares regression because it is robust to situations where the both variables, here width
and catchment area, are measured with significant error. Calibration was performed using the mcr R pack-
age (Manuilova et al., 2014) using Deming regression on log‐transformed widths and catchment areas. In
order to reduce redundancy, the calibration data included only a single width‐catchment area pair for each
river segment.
10.1029/2019GL082027
Geophysical Research Letters
FRASSON ET AL. 3254
3. Results and Discussion
We created a data set of quasi‐global coverage, which allows the visualization of the evolution and the inter-
connection of river planform properties and flow profile characteristics. As an example, Figure 1 shows the
width, slope, meander wavelength, and sinuosity computed for the main stem of the Amazon River and tri-
butaries. A closer inspection of Figure 1a depicts river widths gradually increasing as the Amazon tributaries
flow from the Andes to the Atlantic Ocean, with abrupt width increases occurring at confluences. Similarly,
Figure 1b shows the transition from steeper to mild slopes as tributaries merge and flow to the ocean.
Contrasting Figures 1a and 1b, one can see that steeper slopes, for example, steeper than 70 cm/km, are more
frequent in narrower streams, with widths less than or equal to 100 m and, generally, as rivers become wider,
they tend to show shallower slopes. Figures 1c and 1d show the meander wavelength and sinuosity of chan-
nels, respectively, which, when compared to widths, illustrate the increasing wavelength and decreasing
sinuosity as width increases. The increase of meander wavelength with width is expected as several authors
have reported positive correlations between wavelength and width (e.g., Leopold & Wolman, 1960; Richards,
1976, 1982; Williams, 1986), however, we observed frequent deviations from previously reported linear rela-
tionships, which can be quantified by analyzing the histogram of the ratio between meander wavelength and
width (Figure 2e).
We summarized the distributions and quantiles of river width, sinuosity, meander wavelength, water sur-
face slope, ratio between the meander wavelength and width, and catchment area in Figures 2a–2f, respec-
tively. The presented histograms and quantiles of river properties account for channels that are at least 90 m
wide and with sinuosity greater than 1.01 at the 30 m point scale, that is, the number of occurrences per class
multiplied by 30 m can be interpreted as river length per property class. Right skewness is common to all
histograms in Figure 2, with higher skewness being associated with width, sinuosity, and catchment area.
The ratio between meander wavelength and channel width has been reported by many classical studies, for
example, approximately 11 by Leopold and Wolman (1960), 12.34 by Richards (1976) and Richards (1982),
and 7.5 by Williams (1986). Contrasting previous measurements with our findings, we see that the value
reported by Leopold and Wolman (1960) was located between the mode of the distribution, 9, and the med-
ian, 12.67, whereas Richards (1976) was remarkably close to the worldwide median. However, the spread of
the meander wavelength to channel width ratio (Figure 3b) indicates that significant errors may occur when
using width to predict meander wavelength of a river. Analyzing the spatial variability of this ratio and cross‐
referencing it with other properties such as soil type databases, for example, the 1° grid Global Soil Types
(Zobler, 1999), may shed some light on the reasons for the observed variability and possibly lead to an
increased understanding of the factors governing the geometry of meanders.
Although not immediately comparable to our sinuosity results, both Leopold and Wolman (1960) and
Richards (1976) also suggest that sinuosity is not normally distributed. An inspection of the histogram of
sinuosity over the 49 rivers reported by Leopold and Wolman (1960) shows strong right skewness similar
to that of Figure 2b. Nevertheless, sinuosity in both past studies is considerably larger than what we found,
with Leopold and Wolman (1960) showing an average sinuosity value of 1.53 and Richards (1976) reporting
an average between 1.25 and 1.38 depending on how reaches are defined for the computation of sinuosity.
Aside from the vastly different sample size in our study, another difference arises: Leopold and Wolman
(1960) only compute sinuosity at locations where meanders assumed a reasonably symmetrical S shape,
whereas we did not enforce any symmetry.
Figure 3 depicts how width, slope, meander wavelength, and sinuosity are interconnected. Figure 3a indi-
cates that, generally, water surface slope decreases as width increases. Figure 3b illustrates the coupling
between meander wavelength and width. Figures 3c and 3d show that as slope and width increase, the range
of possible sinuosity values decreases. Finally, Figure 3e relates river width and catchment area.
To assess the constancy of the meander wavelength to width ratio across different river widths, we split the
rivers into four subsets: narrower than 100 m, wider than 100 m and narrower than 200 m,
200 m ≤ width < 300 m, and wider than 300 m. We observed that as width increased, the mean meander
wavelength to width ratio decreased, showing values of 21.2, 17.7, 13.2, and 8.4 for the four subsets, respec-
tively, indicating a slowing down in the increase of the meander wavelength with width and offering another
reason for the discrepancy between our results and those of past studies. Future analysis of our data set could
10.1029/2019GL082027
Geophysical Research Letters
FRASSON ET AL. 3255
