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\begin{document}

\title{Global Observations of Riverbank Erosion and Accretion from Landsat
Imagery}



\author[1]{Theodore Langhorst}%
\author[1]{Tamlin M Pavelsky}%
\affil[1]{University of North Carolina at Chapel Hill}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Riverbank migration has historically been seen as a risk to
infrastructure that can be combatted through channelization, bank
stabilization, and sediment trapping. The physical processes involved
with riverbank erosion and deposition are well defined, yet the
solutions to these equations are computationally and data intensive over
large domains. While current understanding of large-scale river channel
mobility largely comes from reach- and watershed-scale observations, we
need global observations of riverbank erosion and accretion to
understand sediment processes within and across river basins. In this
work, we create the first global dataset of riverbank erosion for
\textgreater{}370,000 kilometers of large rivers using 20 years of water
classifications from Landsat imagery. We estimate uncertainty by
propagating water classification errors through our methods. Globally,
we find riverbank erosion for rivers wider than 150 m to have an
approximately log-normal distribution with a median value of 1.52 m/yr.
Comparing our dataset to 25 similar estimates of riverbank migration, we
found an normalized mean absolute error of 42\% but a bias of only
5.8\%. We definitively show that river size is the best first-order
predictor of riverbank erosion, in agreement with existing literature
that used available data. We also show that the relationship between
size and bank erosion is substantially different among a sample of
global river basins and suggest that this is due to second-order
influences of geology, hydrology, and human influence. These data will
help improve models of sediment transport, support models of bank
erosion, and improve our understanding of human modification of rivers.%
\end{abstract}%



\sloppy


Theodore Langhorst\textsuperscript{1}, Tamlin
Pavelsky\textsuperscript{1}

\textsuperscript{1}University of North Carolina at Chapel Hill,
Department of Earth, Marine and Environmental Sciences. Chapel Hill, NC,
USA.

Corresponding author: Theodore Langhorst (tlang@live.unc.edu)

Key Points:

\begin{itemize}
\tightlist
\item
  We developed the first global dataset of riverbank erosion and
  accretion for rivers wider than 150m.
\item
  We confirm that regional first order relationships between river size
  and riverbank erosion apply globally.
\item
  We show large interbasin differences in riverbank erosion that arise
  from the unique geography of each river basin.
\end{itemize}

Abstract

Riverbank migration has historically been seen as a risk to
infrastructure that can be combatted through channelization, bank
stabilization, and sediment trapping. The physical processes involved
with riverbank erosion and deposition are well defined, yet the
solutions to these equations are computationally and data intensive over
large domains. While current understanding of large-scale river channel
mobility largely comes from reach- and watershed-scale observations, we
need global observations of riverbank erosion and accretion to
understand sediment processes within and across river basins. In this
work, we create the first global dataset of riverbank erosion for
\textgreater{}370,000 kilometers of large rivers using 20 years of water
classifications from Landsat imagery. We estimate uncertainty by
propagating water classification errors through our methods. Globally,
we find riverbank erosion for rivers wider than 150 m to have an
approximately log-normal distribution with a median value of 1.52 m/yr.
Comparing our dataset to 25 similar estimates of riverbank migration, we
found an normalized mean absolute error of 42\% but a bias of only
5.8\%. We definitively show that river size is the best first-order
predictor of riverbank erosion, in agreement with existing literature
that used available data. We also show that the relationship between
size and bank erosion is substantially different among a sample of
global river basins and suggest that this is due to second-order
influences of geology, hydrology, and human influence. These data will
help improve models of sediment transport, support models of bank
erosion, and improve our understanding of human modification of rivers.

\textbf{Plain Language Summary}

Riverbank erosion presents a serious risk to people and infrastructure.
These risks are becoming increasingly hard to predict because of direct
modification of the rivers by damming and bank stabilization, as well as
indirect modification by climate change and land use change.
Geomorphologists have developed scaling relationships based on watershed
characteristics; however, these relationships are very coarse and
limited by the available data. This research uses twenty years of
satellite imagery to develop the first global dataset of riverbank
erosion, which both confirms existing knowledge and opens new avenues of
research.

\section*{Introduction}

{\label{introduction}}

Humans have long relied on rivers as a source fresh water, as a means of
transportation, and because of their role in shaping the landscape. Our
attraction to rivers consequently means people, buildings, and
agriculture are at risk from riverbank erosion. For example, in
Bangladesh, an estimated average of 60,000 people per year are displaced
by riverbank erosion of the Ganges-Brahmaputra-Jamuna system (Mutton and
Haque, 2004). In this context, it is easy to understand why the United
States Army Corps of Engineers spends more than \$200 million per year
managing the Mississippi River (James, 2019). However, sediment
deposition and riverbank accretion create natural riparian habitats and
fertile floodplains (Florsheim et al., 2008). Humans are dramatically
modifying river sedimentation, both directly through river management,
infrastructure, and land use development (Shields et al., 2000; Kondolf
et al., 2002), as well as indirectly through climate change (East and
Sankey, 2020). Land development has greatly increased the total sediment
transport of rivers, but trapping in reservoirs has resulted in a net
reduction in sediment export from land (Syvitski et al., 2005). These
changes in water and sediment supply alter riverbank migration rates as
the morphology adjusts to the new conditions (Brandt, 2000). The
deposition and erosion of material on the banks acts as a temporary
store of sediment, attenuating the impact of changing sediment supply,
and as such is an important input to sediment flux models (Kronvang et
al., 2013). As we think about the consequences of human impacts on
climate and the landscape, assessing large-scale patterns in
geomorphology is becoming increasingly valuable (Grill et al., 2019).

The many applications and broad importance of riverbank erosion has
resulted in diverse measurement methods. On annual timescales and local
spatial scales, bank migration and channel sedimentation can be measured
volumetrically with bank and bathymetry surveying techniques (e.g., De
Rose and Basher, 2011). Tectonic geomorphologists collect sediment cores
and use radiometric dating to relate sediment accumulation rates (which
are largely transported and deposited by river processes) to
mountain-building uplift processes over geologic time scales (e.g.,
Walling, 1999). Over annual to decadal time scales and large spatial
scales, fluvial geomorphologists rely on remote sensing methods like
repeat lidar and optical remote sensing (e.g., De Rose and Basher,
2011). Several methods have been developed to allow efficient analysis
of large domains from satellite or aerial imagery (Peixoto et al., 2009;
Monegaglia et al., 2018). Many of these methods find and track the
movement of the river centerline, which works well for well-behaved
single-threaded channels, but have difficulty representing the
complexity of anabranching or braided rivers (Parker et al., 2011;
Schwenk et al., 2017). Other approaches quantify bank migration by the
area that changes between river and non-river pixels (Rowland et al.,
2016; Nagel et al., 2022). Because these methods calculate change on a
pixel-by-pixel basis, they can more easily capture complex morphologies
and irregular change that are not well represented by a river
centerline. Among these many methods, there are also many ways to define
riverbank migration; some consider only the erosion of stable, vegetated
banks and bars (Boruah et al., 2008), while others include the shifting
of channel bars (Lane et al., 2010). None of these methods have been
used at global scales to produce a consistent dataset of riverbank
migration across all climates and geographies. As a result, our existing
geomorphological understanding of riverbank erosion and accretion are
limited to, and biased by, the patchwork of studies and locations where
we have observations.

Predicting and modeling bank erosion as a means of understanding
sediment processes has a long history in geomorphology. Over that
history, variables that describe the overall size of a river, such as
catchment area, discharge, and width have all been found to be highly
correlated with bank erosion (Hooke, 1980; Nanson and Hickin, 1986).
River size is considered a ``first order'' control on bank migration
(i.e. big rivers move faster than small rivers), and many researchers
now investigate ``second order'' influences on bank erosion by first
normalizing bank migration by the river width (Jarriel et al., 2021).
Regardless of scale, we know from physical modelling that the rate of
bank erosion is a balance between shear stress and bank resistivity
(Ikeda et al., 1981). This balance points to second order controls that
affect the interaction between flow and the banks. However, unlike the
first order controls described above, the results of these studies are
varied. For example, Constantine et al. (2014) found that suspended
sediment flux is the primary control of width-normalized bank migration
rate for 20 river reaches in the Amazon Basin. Ielpi and Lap\selectlanguage{ngerman}ôtre (2020)
showed that the presence of vegetation slowed down width-normalized bank
migration by an order of magnitude using a global sample of 983
meanders. Both of these variables can be heavily modified by human
interventions, such as damming (Shields et al., 2000) and bank
stabilization with concrete or vegetation (Grizzetti et al., 2017).
These examples show the range of second order controls in the literature
which arise from the different subsets of rivers studied. The
interactions and hierarchies of these controls at the global scale have
not yet fully been evaluated.

Here, we present the first global observations of decadal-scale average
riverbank erosion and accretion for all rivers wider than 150 meters. We
use a surface water occurrence dataset derived from Landsat satellite
imagery, a river centerline dataset, and cloud computing to efficiently
estimate decadal-scale average bank erosion and accretion rates. We
analyze these data in the context of previous literature to show that
existing methods of estimating riverbank erosion and accretion
accurately capture large-scale patterns. However, the specific form of
these relationships between geomorphic predictors and riverbank erosion
and accretion varies from basin to basin. These data importantly confirm
geomorphic scaling theories and present a new, uniform dataset that can
help advance geomorphic modeling efforts.

\section*{Materials and Methods}

{\label{materials-and-methods}}

Our data collection and processing are done entirely in the free,
cloud-based geospatial platform Google Earth Engine (GEE) (Gorelick et
al., 2017). GEE allows us to analyze large spatial datasets in the cloud
without downloading the source imagery, which means our methods scale
without having to manage storage or bandwidth issues. Our methods are
optimized to run quickly on GEE's framework by calculating all change
metrics using raster operations and then reducing the data to a table
format before exporting. We used Python 3 and Geopandas for post
processing and analysis of the vector data (Jordahl et al., 2021).

\subsection*{Water classification data}

{\label{water-classification-data}}

Accurate classification of water and land from satellite images is
foundational to our calculations of bank migration. As such, we compare
two widely used and validated water occurrence datasets based on the
Landsat series of satellites. The first is the Joint Research Centre's
(JRC) yearly water classification dataset, where each pixel is marked as
either no data, not water, seasonal water, or permanent water (Pekel et
al., 2016). Pixels marked seasonal water are pixels that were classified
as water for at least one month but not every month with valid
observations. The permanent water classification represents pixels that
were observed to be water in all months with valid observations. We
considered both permanent and seasonal water classifications for our
binary water masks because permanent water classification is sensitive
to omission errors and often results in disconnected river reaches. The
other water classification dataset we use, by Pickens et al. (2020), is
a classification tree model applied to the Landsat archive starting in
1999. Unlike the JRC dataset, each pixel in the yearly composites from
the Pickens dataset represent the percentage of images that were
classified as water. We selected a 70\% occurrence threshold in the
Pickens dataset which approximated the JRC seasonal and permanent
classifications well. Visual inspection of this threshold showed stable
river forms with minimal flooding or disconnected river reaches. The JRC
dataset ranges from 1984 to 2020 at the time of writing and is currently
updated annually. However, data are not equally available through time
and space. Notably, some regions in northeast Siberia do not have any
images before 1999 due to limited downlink capability and no on-board
image storage on the Landsat-5 satellite. The launch of Landsat-7 in
April 1999 increased spatial coverage when operating in tandem with
Landsat-5 and included on-board image storage, enabling the capture of
up to 10 scenes to be stored and transmitted later when the satellite
was in range of a ground station (Goward et al., 2001). As such, we
begin our analysis in 2000, when Landsat-7 records became fully
available. Still, there are unavoidable problems with optical remote
sensing that impact the quality and continuity of the Landsat record.
Clouds, smoke, and the seasonal lack of sunlight at high latitudes can
all limit the utility of images. Any dataset that uses optical satellite
images, including the two water occurrence datasets used in this study,
are prone to incompleteness and biases because of these problems and
limitations. Even so, temporal continuity and relatively high resolution
make the Landsat archive the most viable satellite dataset for
morphological analyses of the world's large rivers over time.

\subsection*{River data}

{\label{river-data}}

We rely on the SWOT River Database (SWORD, Altenau et al., 2021) to
inform our search area for river classification and to organize our
pixel-level data into a vector product that includes river topology,
unique identifiers, and other morphological variables. SWORD is based on
the Global River Widths from Landsat dataset (Allen and Pavelsky, 2018)
but with several improvements that increase the topological continuity,
add additional reach identifiers that relate to other hydrographic
datasets, and resample reaches to a more uniform length of approximately
ten kilometers. Within each reach, the river is divided into nodes
approximately every 200 meters that track the river centerline. We also
use SWORD to filter small river reaches that we will not be able to
reliably measure with Landsat. We limit migration calculations to river
reaches with a mean width greater than 150 m, or approximately 5 Landsat
pixels. We based this threshold on manual inspection of river
classifications as well as our uncertainty estimates (section 2.5).

\subsection*{River identification}

{\label{river-identification}}

Rivers occupy only about 0.6\% of earth's unglaciated land surface area,
and as such, about the same percentage of pixels in satellite imagery
(Allen and Pavelsky, 2018). We rely on the SWORD river centerline
dataset to limit the scope of our search for rivers and greatly reduce
the volume of pixels that we must process and classify. Identifying a
river in a multispectral image or binary watermask is visually easy but
often challenging with automated methods. In most environments, rivers
display a unique shape and or color when compared to lakes in the
floodplains. Rivers and lakes take on a wide range of morphologies, but,
in general, rivers form sinuous channels that traverse long distances,
whereas lakes are rounder and isolated. Identifying river pixels is
often done by intersecting the river centerline with a watermask, such
as in the RivWidthCloud algorithm (Yang et al., 2020). However, if the
static centerline is inaccurate, whether by error or because of
riverbank migration, using the intersection with a static centerline to
identify the movement of rivers will often fail. Other approaches for
identifying rivers include selecting polygons with high length to width
ratios (Isikdogan et al., 2017) or polygons that intersect the edge of
an image (Kyzivat et al., 2019). We combine these methods by selecting
the polygon with the largest perimeter within the area buffered on the
prior centerline dataset. We buffer the river centerline by 10 rivers
widths, which approximates the meander amplitude (Leuven et al., 2018),
and thus the approximate maximum distance the channel will move before
reversing direction. Selecting the largest polygon by perimeter would
identify many lakes and reservoirs in a global search, but we largely
avoid this issue by limiting our search to the area within 10 river
widths of the static river centerline and by excluding any pixels that
are included in the HydroLakes dataset (Messager et al., 2016). These
methods allow us to produce global annual maps of river pixels from
2000-2021 suitable for detection of bank migration over time.

\subsection*{Bank Migration}

{\label{bank-migration}}

We use an area-based approach to quantifying riverbank erosion and
accretion, similar to the SCREAM method from Rowland et al., (2016).
This approach is advantageous for global applications because it can
better represent multithreaded rivers than centerline-based methods do,
and raster operations are much faster than vector operations in GEE. We
measured riverbank erosion and accretion by comparing river inundation
masks from different years and counting the pixels that transition
between river and land. Pixels that transition from river to land are
marked as accretion, and pixels that transition from land to river are
marked as erosion (Figure 1b). Our first step is to calculate the area
and bank characteristics of the individual images. We locate the bank
pixels by dilating the river mask by one pixel, subtracting the original
river mask, and then calculate the bank aspect by convolving the bank
pixels with a directional kernel (Figure 1c). We measure the standard
deviation of local bank aspect as a proxy for bank curvature for each
side of the banks. Measuring bank curvature typically uses the radius of
a best fit circle for a section of river, which is a slow process in the
GEE framework. Next, we calculate the pixel-scale magnitude and
direction of change using the same methods in Rowland et al. (2016;
Figure 1d). The magnitude of erosion is calculated for each bank pixel
in the first image as the shortest path to any of the bank pixels in the
second image, where each path is constrained to only traverse pixels
that were eroded. For islands and bars that have entirely eroded, the
distance is calculated from the island perimeter to the island centroid.
The result of these distance calculations is a raster surface that
slopes between the banks in the two images, and we use the gradient of
this surface to calculate the direction of erosion. Accretion is
calculated in the same manner with the images switched and the paths
constrained to the accreted area. These change metrics are relatively
simple, efficient to calculate, and describe the change in
pixel-by-pixel detail. While the raster data preserve all the detail in
the original river masks and our change calculations, that fidelity
comes with high cost when exporting and analyzing the data. We exported
this data only in limited cases while developing the methods and
visualizing the results over small regions and are not available
globally.

To produce the structured global river erosion data product we summarize
the raster data to a vector product by reducing the pixels to their
nearest river centerline node in SWORD (Figure 1e). In our final data,
the vector dataset includes the original SWORD hydrography data
(centerline location, upstream and downstream connections, Pfafstetter
basin codes, flow accumulation values, slope, mean width, sinuosity,
etc.) and a summary of the change calculations (total river area in time
1 and time 2, accreted area, eroded area, average rate of change,
average direction of change, variance in direction, and uncertainty
estimates) at \textgreater{}2.2 million nodes spaced approximately 200 m
apart. We further aggregate the data up to the reach and watershed
scales for analysis, which allows flexibility in future analysis. For
example, while we present average bank migration values at large scales,
others may be interested in the maximum value for a particular reach.
The high-resolution node data also allows for resampling the data over
custom reaches and extents, beyond the reach and basin structure in
SWORD.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1. a) Overlapping watermasks from two years in red and blue;
purple indicates pixels classified as river in both years. b) Rivermasks
produced from the watermasks after identifying river pixels and a
closure operation. c) Bank aspect (only one image is shown, and the bank
pixels are dilated for visibility). d) distance or magnitude of change
for all river pixels that eroded or accreted. e) The SWORD centerline
overlain on erosion pixels. During vectorization, each pixel is assigned
to the closest river centerline node and a summary of geomorphic change
is calculated for each centerline node.

\subsection*{Uncertainty}

{\label{uncertainty}}

We first quantify the uncertainty of our estimates by propagating the
water classification errors through our methods. Both the JRC and
Pickens datasets include classification error rates. For the JRC
dataset, omission and commission errors are estimated for each
seasonality class (seasonal or permanent) and sensor (Landsat 5, 7, or
8). Errors are highest in the seasonal omission category, and lowest in
the permanent commission for all sensors. There is not as large of a
difference between sensors, however the downlink capability during
Landsat 5 was limited, and the scan line corrector failure on Landsat 7
limits the quality of the seasonality classifications. The Pickens
dataset takes a different approach, quantifying the omission and
commission error rates as a function of distance from the land-water
boundary for both the Pickens and JRC datasets. We use these
distanced-based uncertainties for both datasets because we believe they
better represents the sources and patterns of error and uncertainty in
classifications. Further, the seasonality classifications in the JRC
dataset do not validate well against the high-resolution, manually
trained and classified validation data from Pickens et al. (2020).

We apply these error rates to the annual water masks by randomly adding
omission and commission errors according to the distance-rate function
in Pickens et al., (2020). We repeat this process according to the
number of observations in each annual watermask and then average the
erroneous watermasks together, simulating the effect of the per image
pixel-scale errors to the annual water masks (Figure S1). Each time we
analyze two images for change detection, we also create two noisy
watermasks and process them with the same river classification and
change analysis methods (sections 2.3 \& 2.4). The difference between
our `clean' watermasks and the `noisy' watermasks is a quantification of
the erroneous planform change we would anticipate given no actual change
in planform (Figure S2).

Another source of uncertainty stems from variations in river stage. When
looking at water surfaces only in planform, changes in inundation cannot
be distinguished from changes in channel form. For example, if we happen
to observe a flood in year one and low flows in year two, our bank
migration data could suggest accretion along both banks. We reduce this
source of error by using the composited annual masks, though interannual
variability will still be present in our data. We investigate the
severity of interannual variation by performing our calculations on 9
combinations of years, in a 3x3 matrix of years from 2000-2002 compared
to 2017-2019 (Figure S3). Our final dataset incorporates these data by
presenting the minimum, maximum, and median riverbank erosion and
accretion values for each node.

\subsection*{Validation}

{\label{validation}}

To assess the accuracy of our riverbank migration estimates, we
calculated the bank erosion rate for river reaches where previous
studies have published rates of erosion. After filtering the dataset of
290 published studies (Rowland and Schwenk, 2019) down to studies that
obtain similar metrics (producing reach-averaged rates and over
decade-scale time intervals) and wider than 150 meters, there are 25
cases remaining (See supplemental S4 for a map of validation sites and
Supplemental T1 for full list of references and reach characteristics).
We limit the validation studies to decade-scale measurements because
year-to-year variations in discharge and erosion can bias or
misrepresent the characteristic erosion rate when the time scale of
observations changes (Donovan et al., 2019). Further, any change in
erosion rate over time could falsely add error to the validation, so we
exclude studies with data collection that ended before our satellite
record. The reach definition is not identical between the published
studies and our data so we compared the migration rate for each
validation reach to our observed migration rate nearest the reported
validation reach center.

\section*{Results}

{\label{results}}

Our data compare very well to the 25 validation reaches, with a mean
absolute error of 2.84 meters per year and a bias of 0.39 meters per
year (Figure 2a). Unfortunately these limited validation sites are not
equally distributed around the world and do not represent a very broad
range of morphologies (Figure S5). Nevertheless, our validation results
suggest that our method and implementation in GEE can capture riverbank
erosion with similar accuracy to studies focused on smaller domains.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

The results of our classification uncertainty analysis show that the
global median bank migration rate (1.52 m/year) is more than an order of
magnitude higher than the median false erosion rate associated with
pixel misclassification error (.06 m/year). The distribution of the
observed riverbank migration rate is approximately log normal, while
false erosion rate is slightly bimodal when binned in log scale (Figure
2b). Of course, it is not true that the bank migration rate is an order
of magnitude higher than the false erosion rate everywhere, in fact many
reaches with low migration rates will have nearly equivalent rates of
false migration. 5.7\% of reaches have false erosion rates higher than
their median observed bank erosion rate. Narrow rivers and anabranching
rivers have more bank pixels per unit length than wide single channel
rivers, and as such will have higher average rates of classifcation
errors. The uneven distribution of Landsat images also greatly biases
the false erosion estimates, as areas with fewer images have higher
rates of classifcation errors in the annual watermask products (Figure
S3).

\textbf{Figure 2} . a) Validation of the riverbank erosion from REAL
(vertical axis) with references from literature (horizontal axis). b)
The distribution of global observed riverbank erosion rate is shown in
blue. The false erosion rate is shown in orange and indicates the
uncertainty from water classification errors.

Our global estimates of riverbank migration are mapped in Figure 3a
after averaging the data to Pfaffstetter level 6 basins. At the largest
scales, these data agree with our expectations: rivers like the Amazon,
Orinoco, Paran\selectlanguage{ngerman}á, Mississippi, Syr Darya, Indus,
Ganges-Brahmaptura-Meghna (GBM), Yangtze, and Niger show very high rates
of erosion. In contrast, rivers in Europe, much of Siberia, and the
Canadian Shield show low average rates of bank migration. European
rivers have been modified and stabilized since at least the
16\textsuperscript{th} century to serve the people that live near them,
and as such show very low rates of riverbank migration (Evette et al.,
2009; Grizzetti et al., 2017). The Canadian Shield region also shows
near-zero riverbank migration rates, but for very different reasons.
Rivers in the Candian Shield region are not heavily modified by humans,
but flow over highly resistive precambrian igneous and metamorphic rock.
Large swaths of the Arctic show low migration rates, with some notable
exceptions in the Russian Far East, Northern Siberia, and parts of the
Yukon River.

At finer scales we can see intrabasin and reach scale patterns. Within
the Amazon basin, the subbasins coming off of the Andes mountains show
the highest rates of erosion, while tributaries from the central trough
are more stable (Figure 3b). Upon closer inspection, and aggregated to
the 10km SWORD reaches, we can see high variability in bank erosion
between reaches, with a distinct drop in erosion downstream of a
confluence with a tributary (Figure 3c). Visual inspection of satellite
images suggests that this tributary (Ituxi River) typically has lower
sediment concentrations than the Purus River. At the finest scale of
REAL, the 200m node spacing, we see meander-scale sediment processes on
the Purus River (Figure 3d). Nodes near the apex of the meander bends
typically show high rates of erosion, while the straight connecting
sections show much lower rates of erosion. We also see a pattern of high
rates of erosion before and after the apex of the bend, indicating the
expected positive bias in erosion on the downstream bank faces.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}



Figure 3. a) Global riverbank erosion rates averaged at Pfafstetter
level 6 basins. b) Amazon basin inset showing Pfafstetter level 6
averages. c) reach averages using the approximately 10 km reaches in
SWORD. d) The finest scale of REAL data shown for a section of the Purus
River, node data spaced approximately every 200m.

Beyond the broad, global scale spatial patterns there is a lot of
potential analysis with regards to inter- and intra-basin relationships.
We show scatterplots of river width versus the observed bank erosion
rate for the 16 basins with the most valid observations to investigate
the first order scaling relationships (Figure 4). Generally, the
relationships show a spectrum from highly linear (e.g.
Ganges-Brahmputra-Meghna) to weak relationships and clustered values
near the low end of width and erosion rate (e.g. Yangtze and Yenisei).
In comparison to the global relationship proposed by Hooke (1982) shown
in dark red, some basins approximate this relationship well (e.g. Amazon
and Paran\selectlanguage{ngerman}á), while several notable river basins are biased low (e.g.
Congo, Ob', and Yukon).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4. Relationships between reach-averaged meander rate and width
for Pfafstetter level 3 river basins. The color of each hexagonal bin
represents the percent of all observed reaches in that basin that are
within the bounds of that bin. ``GBM'' refers to the
Ganges-Brahmaputra-Meghna river basin. The dark red dashed line
represents the M = 0.01W relationship proposed by Hooke (1982) as an
first-order estimate of riverbank erosion.

\section*{Discussion and Conclusion}

{\label{discussion-and-conclusion}}

Our results suggest that previous regional studies indicating that size
is the first order control on riverbank erosion at large scales (Hooke,
1980; Nanson and Hickin, 1986; Ielpi and Lap\selectlanguage{ngerman}ôtre, 2020) are largely
correct (e.g. Figure 4). However, upon closer inspection, we reveal the
limits of the global applicability of such relationships. We show large
regional differences in this first order relationship that arise from
the unique blend of secondary controls in each basin. For example,
riverbank erosion in the Congo basin, which is characterized by varied
drainage patterns due to localized geologic controls (Flügel et al.,
2015), is notably lower than the global average. The world's largest
basin by discharge, the Amazon, has a lot of spread in this first order
relationship, a result of the varied inputs of sediment load as shown by
Constantine et al. (2014) and seen in the REAL data in Figure 4b. The
Ob' basin is also biased low, however, likely due to low flows in the
winter and a discontinuous and sporadic permafrost setting. On the other
hand, riverbank erosion in the Ganges-Brahmputra-Meghna basin is higher
than the global average, which may be because of high relief and
sediment yield in the tectonically active headwaters and thick alluvium
downstream as well as frequent high discharge during monsoon season. As
shown in these examples, river size does provide a good first order
approximation of riverbank erosion for most basins globally, however
these specific relationships can vary greatly between regions. REAL
provides a starting point for analyzing these second order relationships
at the global scale, and further research may be able to show the
relative importance of geologic, hydrologic, and human influences on the
rate of riverbank erosion in different basins.

We have revealed and clarified some limitations in quantifying river
planform change using remotely sensed data products. First, the
resolution of Landsat (\textasciitilde{}30 meters) requires decades
between images to reliably detect the rate of change for all but the
most dynamic rivers. This long timeframe comes with an added challenge,
in that any changes in hydrology, human influence, or data quality over
the intervening years can result in biased estimates of planform change.
Higher resolution satellites like Sentinel-2 and the Planet
constellation will become increasingly viable for global riverbank
migration analysis as the length of record grows, and at the very least
would be useful for multi-source remote sensing data fusion with the
Landsat record. Second, the uncertainty in water classifications is a
well-known problem in remote sensing of planform change, however the
severity of the problem is in relation to the magnitude of actual
planform change. We found that classification uncertainties propagated
through our change calculations were greater than the observed planform
change for only about 5.7\% of rivers. Improving the representation of
all sources of uncertainty and the impact on change calculations is a
necessary next step remote sensing of river morphology change detection.

We have also provided the first global accounting of highly mobile
rivers that may present a problem to remote sensing applications which
treat rivers as immobile. Our earth observation satellite record is now
several decades long, yet most river morphology data are static in time.
As the satellite record grows, dynamic methods that track the movement
and change of rivers in time will be critical. Even satellite missions
over relatively short periods, like the SWOT satellite (Biancamaria et
al., 2016), which is currently planned to launch in 2022 and will be
operational for 3 years, will require some flexibility to accommodate
the mismatch between SWORD centerline locations and highly mobile
rivers. The REAL dataset provides the historical data to predict where
and how soon these problems may arise in the future.

\textbf{Acknowledgments}

Funding for this research came in part from a contract with the SWOT
project office at Caltech and the Jet Propulsion Laboratory. Funding was
also received from the The Preston Jones and Mary Elizabeth Frances Dean
Martin Trust Fund~from the Department of Earth, Marine and Environmental
Sciences at the University of North Carolina at Chapel Hill.

\textbf{Open Research}

The annual water classification data used to identify permanent water
bodies are available in the original publication and via
https://www.glad.umd.edu/dataset. SWORD, the river centerline dataset
used to separate rivers from lakes and other surface water, is available
online in netCDF and shapefile formats via
https://zenodo.org/record/3898570. The REAL dataset will be available
via Zenodo upon publication in shapefile and csv formats. Additionally,
the data can be viewed online in a Google Earth Engine Application at
https://tedlanghorst.users.earthengine.app/view/realnodes.



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