Channel Migration in Experimental River Networks Mapped by Particle Image Velocimetry
Abstract
Deltaic river networks naturally reorganize as interconnected channels move to redistribute water, sediment, and nutrients across the delta plain. Network change is documented in decades of satellite imagery and laboratory experiments, but our ability to measure and understand channel movements is limited: existing methods are difficult to employ efficiently and struggle to distinguish between gradual movements (channel migration) and abrupt shifts in river course (channel avulsions). Here, we present a method to extract channel migration from plan-view imagery using particle image velocimetry (PIV). Although originally designed to track particles moving in a fluid, PIV can be adapted to track channels moving on the delta surface, based on input estimates of channel width, migration timescale, and maps of the wet-dry interface. Results for a delta experiment show that PIV-derived vector fields accurately capture channel-bank movements, as compared to manually drawn maps and an independent image-registration technique. Unlike other methods, PIV targets the process of channel migration, excluding changes associated with channel avulsions and overbank flow. PIV-derived migration rates from the experiment span an order of magnitude and are reduced under lower sediment supply and during sea-level rise, supporting recent models. Together, results indicate that PIV offers a fast and reliable way to measure channel migration in river networks, that channel migration rates under non-cohesive conditions can displace channels a distance comparable to their width in the time needed to aggrade ∼10% of the channel depth, and that migration direction is ∼60% orthogonal to mean flow direction and ∼40% flow-parallel overall.
Key Points
-
Particle image velocimetry (PIV) can be adapted to accurately capture channel-bank motions in experimental river networks
-
PIV specifically targets the process of channel migration, excluding changes associated with overbank flows and channel avulsions
-
Experimental channels migrated ∼10 channel widths between avulsions, with ∼60% of migration directed normal to the mean flow
Plain Language Summary
River deltas change over time as channels move to distribute water, sediment, and nutrients across the coastal plain. Channel movements are documented worldwide in decades of satellite imagery, but are difficult to measure efficiently and precisely with existing approaches. Here, we present a new automated method to extract channel motion data from overhead images using particle image velocimetry (PIV). Originally designed to track particles moving in a fluid, the PIV algorithm can be adapted to track channels migrating on a delta surface. Using data from a laboratory experiment, we show that PIV-derived channel motions are accurate and comparable to manually drawn maps and an independent image-registration technique. Unlike existing approaches, PIV specifically measures gradual channel migration, excluding other types of change such as river floods and diversions. Application of PIV to river networks can provide new insight into how rivers migrate; for example, results from the experiment indicate that rivers migrated more slowly during sea-level rise and that ∼40% of channel migration was directed upstream and downstream rather than sideways.
1 Introduction
River deltas commonly display a branching network of interconnected river channels that distribute water, sediment, and nutrients across the delta plain (Passalacqua, 2017; Wohl, 2017). These river networks naturally reorganize themselves over time as individual channels grow, move, and are eventually abandoned. Network change is an important ingredient for the long-term sustainability of wetland ecosystems (Passalacqua et al., 2021; Temmerman & Kirwan, 2015), but also poses flooding and erosion hazards to human life and property (Singh & Awasthi, 2011; Sinha, 2009). It remains unclear how river networks might respond to modern climate change and land use, which are subjecting river networks to relative sea-level rise and altered sediment loads (Jerolmack, 2009; Syvitski & Saito, 2007). In addition, channel motion is an important determinant of sand distribution in the subsurface, which in turn influences porous-media flow and connectivity (Goodbred et al., 2003; Larue & Hovadik, 2006; Michael et al., 2010). Thus, it is imperative to measure and understand how river networks move.
In a river network, channels move through two main processes: channel migration, and channel avulsion (Figure 1). Channel migration involves the gradual, mostly sideways, translation of existing channels (Einstein, 1926; Hickin & Nanson, 1984). In contrast, channel avulsion involves the abrupt rerouting of water into new or abandoned channels (Slingerland & Smith, 2004). In the event of partial or failed channel avulsion, overbank flows can also alter the river network; for example, spreading as sheets that inundate the floodplain or carving crevasses (Edmonds et al., 2009; Smith et al., 1989; Figure 1). While both migration and avulsion contribute to channel network mobility, here, we focus on the channel migration process, and specifically on how best to quantify it using minimal assumptions about the form and direction of the migration.
Conceptual framework of river network mobility. (a) Initial river network, showing land (dark teal) and water in the river network and sea (light teal). Flow is from left to right. (b) The river network at a later time. The river network changes due to channel migration (yellow arrows), channel avulsions, and overbank flow (labeled). White dashed lines are initial network from (a).
Our aim is to measure channel migration from plan view. Diverse examples of channel migration are documented worldwide by roughly a half century of satellite imagery (Baki & Gan, 2012; Chakraborty & Mukhopadhyay, 2015; Constantine et al., 2014; Gupta et al., 2013; Ielpi, 2019; Peixoto et al., 2009; Rowland et al., 2009; Yang et al., 2015). These case studies have provided numerous insights into the kinematics of channel networks, but also highlighted the difficulty of making efficient, precise measurements of migration (Hooke, 2003; Schwenk et al., 2017). Migration rates are commonly measured in terms of the displacement of channels between satellite images collected at different times, which we refer to as the displacement-based approach. The direction of displacement can be identified manually, which is a labor-intensive process that is inherently subjective, and ideally should be coupled with on-site validation (Ielpi, 2019). The displacement-based approach is especially difficult to apply to river networks, where interconnected channels are not always spatially coherent. Alternatively, migration direction may be calculated assuming that the direction of movement is bank-perpendicular (Eke et al., 2014; Schwenk et al., 2017). However, channel bank positions are at times ambiguous due to vegetation cover, turbidity, and other features (Baki & Gan, 2012; Gupta et al., 2013). The assumption of bank-perpendicular movement, while reasonable, may have important exceptions.
Laboratory researchers have made progress developing automated procedures to extract river network mobility from plan view. Using published experimental data, Wickert et al. (2013) measured mobility in terms of the number of image pixels that changed from dry to wet, or wet to dry, between consecutive images, which we refer to as the pixel-based approach. Unlike displacement-based measurements, the pixel-based approach does not require spatially coherent channels. Due to this advantage, the pixel-based approach has since been adopted in experiments, numerical simulations, and field studies (Bufe et al., 2016, 2019; Lauzon et al., 2019; Liang et al., 2016; Perignon et al., 2020). However, the pixel-based approach also comes with a disadvantage: it does not differentiate between motion due to channel migration and channel avulsion, nor does it provide information about the direction of motion. Differentiating between channel migration and avulsion is important, because each process has distinct effects on river planform morphology and alluvial architecture, and can respond differently to sea-level rise and sediment supply changes (Blum & Törnqvist, 2000; Jerolmack & Mohrig, 2007; Slingerland & Smith, 2004). For example, sea-level rise causes delta-top aggradation, which increases the rate of channel avulsion in laboratory experiments (Jerolmack, 2009; Martin et al., 2009). However, careful investigation of non-avulsive areas in the experiments shows that migration rate may remain constant or even slow down during sea-level rise (Bufe et al., 2019; Wickert et al., 2013). Instead, migration rate is thought to be sensitive to the downstream sediment flux (Constantine et al., 2014; Wickert et al., 2013).
Recent progress suggests particle image velocimetry (PIV) could provide a new means to measure channel migration in a manner that integrates the advantages of both pixel-based and displacement-based approaches. PIV is a technique designed to extract displacement-based vector fields using automated, pixel-based image correlation (Keane & Adrian, 1992; Westerweel, 1997). Originally used to track moving particles in a fluid, PIV has also been adapted to riverine settings, for example, to measure the trajectory of sediment particles across a dune (Tsubaki et al., 2018) and secondary-flow characteristics during floods (Muste et al., 2008). In a recent study of global satellite imagery, Jarriel et al. (2021) demonstrated that PIV can be used to track the migration of channel centerlines. The full potential of PIV for measuring channel migration has yet to be explored; it remains unclear how PIV-derived measurements compare to those from existing approaches, and the extent to which PIV differentiates between channel migration and avulsion. Furthermore, PIV may be capable of tracking the migration of channel banks—rather than channel centerlines—allowing for broader applicability to multi-thread river networks where channel centerlines are poorly defined (Jarriel et al., 2019; Schwenk et al., 2017).
The goal of this study is to build on this previous work by measuring local channel migration across interconnected river networks in a way that is flexible, objective, and requires no assumptions about the direction of channel motion. We adapt established PIV methods originally designed to track moving particles in a fluid. We find that the PIV algorithm can be set to measure displacement vector fields associated with channel migration, while largely ignoring other changes due to channel avulsions and overbank flow processes. After validating PIV results against human-drawn maps of channel migration and an independent image-registration technique, we characterize the distribution of migration rate and direction mapped by PIV and place results into a nondimensional framework. Finally, we provide an example of how PIV results can be used to test theoretical predictions under controlled changes in sea-level and sediment supply.
2 Materials and Methods
2.1 XES10 Experimental Data
We developed our method using archived data from the XES10 experiment (Hajek et al., 2014), which we briefly review here. The experiment was conducted over 310 hr within a 5.72-m-long, 2.98-m-wide rectangular basin at the St. Anthony Falls Laboratory (Figure 2a). At the upstream end, water and sediment were supplied at a single point source, allowing for the natural formation of a laboratory-scale delta. The upstream portion of the basin featured a V-shaped expansion to allow a smooth transition from the single feed point to the full basin width. Water and sediment were supplied at a constant rate of 
and 
, respectively, although an error in the sediment feeder caused higher sediment supply (
) during the first 132 hr of the experiment (Figure 2b). The sediment supply mixture was composed of 63% quartz sand (
), 27% anthracite sand (bimodal: 
and 
), and 10% kaolinite. The water was dyed cyan for visibility.
Experimental setup for XES10. (a) Schematic view of the XES basin, modified from Kim et al. (2006). The tank coordinate system is defined such that the primary flow direction is eastward. (b) Upstream sediment supply during the experiment. (c) Downstream sea level during the experiment. Background shading highlights periods of constant sea level (white), sea-level fall (light gray), and sea-level rise (dark gray).
At the downstream end, basin sea level was controlled by a computerized weir-siphon system. Sea level was varied in an isolated slow cycle (108-hr period, 10-cm amplitude), followed by an isolated rapid cycle (9-hr period, 10-cm amplitude), and finally a superposition of one slow cycle with six rapid cycles (Hajek et al., 2014; Figure 2c). The basin floor consisted of a flexible rubber membrane, underlain by a layer of well sorted pea gravel. The basin floor subsided over time, which was achieved through controlled extraction of the gravel from underneath the membrane. The subsidence profile formed a back-tilted ramp-style pattern, such that subsidence rate was highest near the upstream end (
) and decreased linearly downstream. Subsidence was also reduced very close to the sediment feeder, in order to reduce sediment accumulation in the zone where the sidewalls caused prominent edge effects (Hajek et al., 2014). Further details on the XES facility are available online (https://cse.umn.edu/safl/experimental-earthscape-basin) and reported in previous work (Hajek et al., 2014; Kim et al., 2006; Paola, 2000).
An overhead camera captured photos of the experimental basin every 10 s (Figure 2a). Images were taken with a wide-angle lens and orthorectified using built-in image-processing tools in MATLAB. After orthorectification, photo resolution was 
with a pixel size of approximately 
. However, due to shifting distance between the overhead camera and delta surface, pixel size slightly increased over time, to a maximum of 5% (∼
) by the end of the experiment. The position of the shoreline was mapped from the photos approximately every 10 min and was originally reported in Hajek et al. (2014).
2.2 Image Preparation for PIV
The PIV algorithm was designed to track the motion of discrete spatial patterns in a time series of binary (black-and-white) images. To prepare the experimental photographs for PIV, we converted raw color images into binary images of the channel network (Figure 3), similar to previous studies (Cazanacli et al., 2002; Isikdogan et al., 2017; Kim et al., 2010; Martin et al., 2009; Tal & Paola, 2010; Wickert et al., 2013). Image preparation involved two steps. First, we conducted a principal component analysis (PCA) of color photos and isolated the component that was most strongly correlated to the presence of surface water (Figure 3). The result was an intensity map, ranging in values from 0 to 255, where higher values were associated with generally deeper flows on the delta surface. We masked the flume exterior as well as the offshore basin, using manually drawn maps of the most recent shoreline collected every 10 min.
(a) Example of a raw image from XES10. Flow is from left to right. (b) Principal component of the raw image most strongly correlated with the presence of surface water. White rectangular box highlights area enlarged in Figure 4a.
Second, we generated binary images of the channel network using a range of PCA pixel-intensity values that were associated with the wet-dry interface (Figure 4). The distribution of PCA pixel intensity was bimodal, with peaks at 75 and 180 associated with dry and wet areas respectively (Figures 4a and 4b). Through visual inspection, we concluded that any intensity value between 
and 
was a reasonable representation of the wet-dry interface. Within this range, identification of the wet-dry interface from imagery was inherently subjective. To account for this uncertainty, we selected four different values evenly spaced within the range 
to serve as our threshold (Figure 4b). The result was four distinct but reasonable realizations of the wet-dry interface, represented by different contour lines in Figure 4a. Along well-defined riverbanks, there was a sharp spatial gradient in pixel intensity, and so all four realizations yielded the same position for the wet-dry interface (i.e., contour lines in Figure 4a overlap). In contrast, some riverbanks were more uncertain: gradual spatial gradients in pixel intensity caused differences in the wet-dry interface across realizations, resulting in significant spacing between contour lines in Figure 4a. Generally, we observed that riverbanks were more ambiguous along bank-attached bars or shallow secondary channels. Gradual changes in dye concentration and ambient lighting over the experiment also caused apparent shifts in the wet-dry interface, but these shifts were small compared to differences between realizations. We converted each PCA image into four separate binary images of the channel network (Figures 4c–4f), each produced with a different threshold value for the wet-dry interface (Figure 4b). In the thresholding process, pixels with an intensity value greater than or equal to the threshold were mapped as wet and assigned a value of 1. In contrast, pixels with an intensity value less than the threshold were mapped as dry and assigned a value of 0. To a good approximation, the wetted area in the binary images represented the channel network because the vast majority of water on the delta surface was flowing through river channels. Binary images were produced for the entire experiment (310 hr) resulting in four different realizations of the channel-network time series, which were used as input for PIV.
(a) Identification of four different, reasonable choices for the wet-dry interface, based on threshold pixel intensity values in the principal component. Base image is from Figure 3b, and black contours show wet-dry interface for each threshold. Examples of coherent and ambiguous channel banks are annotated. (b) Probability density of pixel intensity, showing that threshold values were evenly spaced in the valley between peaks in the bimodal distribution. (c–f) Four binary images representing different realizations of the channel network. Each realization was generated by thresholding the base imagery from panel (a) using one of the four threshold pixel intensity values in panel (b).
2.3 Implementation of Particle Image Velocimetry
We implemented PIV using PIVlab, an open-source MATLAB package (Thielicke & Stamhuis, 2014) that has been successfully applied to track the motion of tracer particles in a fluid flow (Pirbodaghi et al., 2015; Torres et al., 2017; Viola et al., 2019; Zheng et al., 2018). Comparable software has been adapted to riverine settings (Jarriel et al., 2021; Muste et al., 2008; Tsubaki et al., 2018). Here, we applied PIVlab software to track channel networks moving on the delta surface of XES10. While the application is unconventional, the mathematical principles are the same and we made no changes to the underlying algorithm. Here, we briefly summarize the PIVlab algorithm, and how we applied it to the XES10 data set. A summary of PIVlab input parameters is provided in Table 1.
| Parameter name | Parameter value | |
|---|---|---|
| Software version | 2.31 | |
| PIV algorithm | FFT window deformation | |
| Sub-pixel estimator | Gauss 2 × 3-point | |
| Correlation Quality | Extreme | |
| PASS 1 | Interrogation area | 0.5 × 0.5 m |
| Step | 0.25 m | |
| PASS 2 | Interrogation area | 0.25 × 0.25 m |
| Step | 0.125 m | |
| PASS 3 | Interrogation area | 0.125 × 0.125 m |
| Step | 0.0625 m |
, the PIV algorithm estimates motion of the channel network from the binary image at 
to a subsequent image captured at 
. Channel motions are expressed in terms of velocities, representing the distance that channels are displaced between images divided by 
. Channel displacement is evaluated through the cross-correlation of many small sub-images, referred to as interrogation areas (Figure 5). The correlation yields the most probable displacement for channels traveling in a straight line within an interrogation area (Keane & Adrian, 1992; Westerweel, 1997; Figures 5c–5e). The correlation matrix 
is given by the cross-covariance function (Huang et al., 1997; Thielicke & Stamhuis, 2014),
(1)
is the set of pixels within the interrogation area at 
, and 
is the set of pixels within the interrogation area at 
. The variables 
and 
denote the row and column locations of pixels in the correlation matrix 
and 
and 
denote row and column locations of pixels in 
. When displacing the first interrogation area by 
rows down and 
rows to the right yields good agreement with the second interrogation area, Equation 1 yields larger values of 
. The most probable displacement vector (
), in units of pixels, is defined by the pair (
) that yield the peak value of 
(Figure 5e). Using PIVlab, we solved Equation 1 in the frequency domain using a Discrete Fourier transform, window deformation algorithm (Thielicke & Stamhuis, 2014).
Example implementation of the particle image velocimetry (PIV) algorithm for a single timestep, starting at run time 100 hr 43 min (a), and ending 1 min later (b). Yellow vector fields show displacement of the channel network between images detected by PIV. In panel (a), colored squares show the PIV interrogation area, which was refined using three passes of decreasing size. The interrogation areas were chosen to be comparable to the characteristic channel width. Location of panels (c) and (d) are labeled. (c and d) Magnified view along a channel bank in panels (a) and (b), respectively. (e) Heat map of the correlation matrix 
(normalized) for the interrogation area considered in panels (c) and (d). The peak value in the correlation matrix determines the best-fit displacement in the x-direction (
) and in the y-direction (
), which together define the displacement vector.
The PIV algorithm is sensitive to the size of the interrogation area, which is a user-specified input parameter (Keane & Adrian, 1992; Westerweel, 1997). When tracking conventional PIV particles in a moving fluid, the interrogation area is chosen based on particle size and expected flow conditions. Ideally, the interrogation area should be large enough to contain a spatially distinct pattern of particles, but not so large that it contains significant spatial gradients in velocity. We followed this guideline as closely as possible in our application of PIV to river networks. The interrogation area, 
, was chosen to be comparable to, but less than, the characteristic channel width (cyan square in Figure 5a). At this size, the interrogation area was large enough to capture a distinctive stretch of the channel bank. At the same time the area was not large enough to contain noticeable spatial gradients in channel migration. Following this guideline, we expect measurement error from PIV on the order of 
(Foucaut et al., 2004; Sciacchitano, 2019). Increasing the interrogation area size leads to an increase in random error. Reducing the size reduces random error, but also increases computer-processing time, and can introduce systematic errors as the interrogation area size approaches the pixel size (Nogueira et al., 2001; Sciacchitano, 2019).
Channels cannot be correlated where they enter or exit the interrogation area, resulting in a reduced signal in the correlation matrix 
(Equation 1) which can obscure the peak of most probable displacement. Previous work has shown that the signal is optimized when displacement is about one quarter (25%) of the interrogation area (Keane & Adrian, 1992). This optimum displacement can be achieved for a given velocity through adjustment of the timestep between images 
. Here, we inspected a small subsample of images from XES10 and determined that the fastest-migrating channels typically migrated a distance comparable to 25% of the interrogation area over timescales of ∼1 min. We subsampled our binary imagery to this timescale, such that 
between consecutive images, which optimized the PIV signal for these faster-migrating channels. Slower-migrating channels necessarily incurred higher measurement error, on the order of 
(Foucaut et al., 2004; Sciacchitano, 2019), but this was negligible compared to uncertainty in the wet-dry interface (Figure 4). Importantly, no channels in the experiment migrated fast enough to traverse an entire interrogation area within one timestep (
); if they had, they would suffer significant systematic errors in PIV (Nogueira et al., 2001; Sciacchitano, 2019).
The signal in the correlation matrix 
was further improved by running three consecutive passes of the algorithm for each image pair (Scarano & Riethmuller, 1999; Westerweel, 1997). The grid of interrogation areas was refined with each pass, and results from the initial pass were used to offset the grid in subsequent passes. Previous work has demonstrated that this multiple-pass approach improves signal-to-noise ratios in the final correlation matrix, and also allows for a final velocity field with a high spatial resolution (in this case 
, or 
, between grid points). We used 50% overlap between adjacent interrogation areas, achieved in PIVlab by setting the grid spacing of interrogation areas (i.e., the step parameter) to 50% the size of the interrogation area (Table 1).
PIV is traditionally implemented to track particles whose edges are well defined. However, the edges of a river channel—the riverbanks—are not always so clear (Baki & Gan, 2012; Gupta et al., 2013). To account for this uncertainty, as discussed above, we applied PIV to our four, separate realizations of the binary-image time series to capture the range of possible bank positions. An example is given in Figure 6. PIV vectors were broadly similar across realizations, in this example showing northwestward motion of the channel in all realizations. However, differences arise due to different choices of the wet-dry interfaces, and different rates of motion for each interface. No displacement was detected in areas that were identified as dry in all realizations, or areas that were channelized but remained fixed between images. The four PIV fields were compared, averaged, and filtered in post-processing, as described below.
Implementation of particle image velocimetry on 16 separate stacks of binary images, corresponding to four different realizations of the wet-dry interface (rows) and four different tilt angles of the imagery (columns). Tilted imagery and vector fields are re-tilted back to 
for comparison (Figure S1 in Supporting Information S1). Each image stack contains 18,500 images spanning 310 hr of experimental run time.
We also found that vector direction identified by PIVlab was influenced by the orientation of the input imagery relative to the rectilinear PIV grid (Text S1 and Figure S1 in Supporting Information S1). The effect stems from our application of PIV to river channels, which unlike conventional PIV particles are much longer than they are wide. Displacements along the channel's long axis cause little change in the channel's shape—at least in the local interrogation window—and are difficult to constrain via image correlation (Equation 1). We were not able to modify the open-source PIVlab algorithm to eliminate the influence of image orientation, so instead we opted to quantify associated uncertainty in a manner similar to how we tackled uncertainty in the wet-dry interface: we tilted each binary image at four different angles relative to the PIV grid (Figure 6) and applied PIV to each. We calculated the average vector field across all four realizations and four tilt angles, as well as uncertainty in this field, in post-processing.
2.4 Post-Processing of PIV Data
and magnitude 
are given by,
(2)
(3)
and 
are the components of the 
th velocity vector, 
, and 
(Curray, 1956; Miall, 1974). The subscript 
denotes the stack of binary images (Figure 6), which ranges from 1 to 
, where 
is the number of stacks in which PIV detected displacement (
). Together, Equations 2 and 3 are used to define the mean vector: 
(Figure 7a).
Post-processing of particle image velocimetry (PIV) data. (a) An example PIV vector field of the mean (yellow vector) and 
uncertainty (pale yellow swath) in channel-network displacement across all 16 stacks of binary images. Base image shows principal component most strongly correlated with the presence of surface water, and black contours show wet-dry interface for each realization. Location of panels (b) and (c) are labeled. (b) An example of a vector with high uncertainty in vector magnitude across realizations. (c) An example of a vector with high uncertainty in vector direction across realizations. (d) PIV vector field of channel-network displacement after filtering, which discarded vectors with high uncertainty.
and magnitude 
are given by,
(4)
(5)
is the direction of vector 
, and 
is the magnitude of vector 
measured along the average direction, that is, 
. The standard deviation in Equation 4 was weighted by the vector magnitude 
, following Miall (1974), and the difference in angle 
was wrapped to 
. Together, Equations 4 and 5 describe a swath in vector displacement representing 
uncertainty in measurements across all 16 stacks of imagery (Figure 7a).Next, the mean field was filtered to remove vectors with high uncertainty. Vectors were discarded in cases where the uncertainty in vector magnitude exceeded the mean (
; see, for example, Figure 7b), or if the uncertainty in vector direction exceeded 180° (
; Figure 7c). Furthermore, if only a single of the four realizations detected a vector at a given location and time, then the vector was deemed unreliable and was discarded. Filtering in this way removed roughly half of the vectors in a field (Figures 7a and 7d). Most discarded vectors were located on the dry delta surface, channel interiors, or ambiguous channel banks. Measurements were also discarded when the time between consecutive image pairs exceeded 1 min, and during brief periods of dry or clear-water conditions on the delta surface, which were associated with temporary pauses in the experiment. We deemed that vectors with detected displacements of less than 1 image pixel per frame (0.5 cm/min) were effectively immobile, and we did not consider them in our analysis.
2.5 Method Validation and Comparison to Theory
As a test of the PIV method, we compared PIV results to maps of channel migration drawn by hand. Manual measurements were made independently by three of the authors of this study. First, a sample raw image was selected at run time 
, and 12 control points were assigned approximately along channel banks. Each person was assigned the task of tracking control points through the following three images, until run time 
, without any guidelines beyond tracking the channel migration. Afterward, the displacements of control points and the image timestep 
were used to calculate 12 vectors per image, per participant.
As a second test, we also compared the PIV results to velocity measurements from an entirely different image-registration technique, called the demons algorithm (Cahill et al., 2009; Thirion, 1998). The demons algorithm calculates the deformation field required to alter a given image into a target image. The best-fit deformation field is chosen by minimizing the amount of required deformation, using a Monte-Carlo approach that is repeated at multiple spatial scales.
Scheidt et al. (2016) applied the demons algorithm to track mobile river channels on experimental deltas, and we follow their approach here. In a manner similar to the PIV method, we applied the demons algorithm to image pairs captured 
apart, and the velocity field was calculated by dividing the deformation field by 
. Unlike PIV, the demons algorithm is designed to measure gradients of pixel intensity in a grayscale image, and so thresholding images was not necessary. Instead, we used grayscale images of the principal component for surface-water presence as input (e.g., Figure 3b). For analysis we selected a subsample of images from 
to 
, the same run-time window as manually drawn vector maps. Successful implementation of the demons algorithm required a shorter timestep 
than for PIV. For comparison to PIV vectors, which were collected with 
, demons displacement vectors were summed over each minute.
scales with the sediment flux,
(6)
is volumetric sediment flux, 
is channel width, and 
is channel depth. The constant of proportionality is expected to vary with river planform curvature, deposit porosity, and stabilization provided by vegetation or cohesive bank sediment. For our calculations, we used the characteristic wetted channel width 
, channel depth 
, and sediment supply 
(Figure 2b) of XES10.
(7)
is volumetric water discharge, 
is sediment grain size, and 
is channel bank height. We assumed channel bank height was equal to the channel depth (
) for simplicity, though autogenic and allogenic variability in bank height is expected (Bufe et al., 2019); in particular, bank height likely increases during the early stages of relative sea-level fall. Parameters 
were estimated by Bufe et al. (2019) using multi-variate regression (
, where 
indicates one standard deviation from the best-fit value). 
and 
are accommodation factors for sea-level rise and land subsidence, respectively, defined as,
(8)
(9)
is sea-level rise rate, 
is subsidence rate, and 
is the basin area. Accommodation factors scale linearly with created accommodation and inversely with destroyed accommodation (Bufe et al., 2019). Factors are always greater than 0, and equal to 1 when accommodation is constant. For our application to XES10, we used the spatially averaged subsidence rate 
and estimated basin area using the squared basin width 
following Bufe et al. (2019). 
is given by the sea-level curve (Figure 2c).3 Results
3.1 Validation of the PIV Procedure
To validate our PIV procedure, we compare manually drawn vectors and demons algorithm vectors to their nearest-neighbor PIV vectors within 3 cm. In terms of vector magnitude, all approaches show agreement within an order of magnitude (Figures 8a and 8b). Vector magnitude ranges between 
, except for a subset of demons algorithm vectors with substantially lower magnitudes 
. Manually drawn vectors show higher magnitudes than PIV on average, but the discrepancy is within measurement uncertainty in most cases (as illustrated by error bars of standard deviation in Figure 8a that intersect the 1:1 line). In terms of vector direction, PIV shows close agreement with manual mapping and the demons algorithm (Figures 8c and 8d). Discrepancy is within 
for over 85% of compared vectors, and in most cases discrepancy is within measurement uncertainty.
(a) Comparison of vector magnitudes mapped by particle image velocimetry (PIV) to nearest-neighbor vectors mapped manually (white diamonds) and the demons algorithm (magenta circles). Error bars indicate 
uncertainty from PIV (Equations 4 and 5). Solid black line indicates 1:1 agreement and gray shaded area indicates agreement within an order of magnitude. (b) Cumulative probability distributions of the discrepancy, measured as the distance to the 1:1 line in panel (a). Panels (c) and (d) are same as panels (a) and (b), but for vector direction. Gray shaded areas denote agreement within 90°.
Results are consistent among PIV, manually drawn vectors, and the demons algorithm because all approaches accurately track motion associated with channel migration (Figure 9). For example, from run time 100 hr 45 min–100 hr 46 min, PIV vectors, demons algorithm vectors, and manually drawn vectors all record northwestward migration of ∼2 cm along the north bank of the main channel (Figure 9b). Farther upstream, all three approaches captured an increase in migration magnitude to ∼5 cm, and a shift in migration direction toward the west (Figure 9c). In a nearby secondary channel (Figure 9d), the wet-dry interface was more ambiguous, leading to higher uncertainty in PIV, higher uncertainty in manually mapped vectors, and greater spatial variability in demons algorithm vectors. Despite ambiguity, however, all approaches agree upon northward migration of the southern bank. Results were similar for other image pairs.
(a) Comparison of vector maps produced by particle image velocimetry (PIV; yellow arrows), manual mapping (white arrows), and the demons algorithm (magenta arrows) for the image pair at run time 100 hr 45 min–100 hr 46 min. For PIV, arrow indicates the mean vector, and shaded swath shows 
uncertainty in vector magnitude and vector direction. Base image shows principal component most strongly correlated with the presence of surface water, and black contours show wet-dry interface for each realization. White rectangular boxes highlight areas enlarged in panels (b–d), and in Figure 10b.
Some demons algorithm vectors show poor agreement with PIV because they are found in channel interiors or on the dry delta surface. For example, inside of the channel, demons algorithm vectors show incoherent motion in all directions, whereas PIV detects no motion (Figure 9a). The demons algorithm detects motion because it tracks motion of grayscale patterns in the surface-water principal component, which in the channel interior were due in part to migrating bedforms and barforms, and in part to changing reflection patterns. In contrast, PIV targets motion of the wet-dry interface, ignoring changes within the channel. The demons algorithm also records low-magnitude, incoherent vectors across the dry delta surface (Figure 9a). PIV detects no motion in these cases. In this case, apparent motion detected by the demons algorithm can again be attributed to changes in ambient lighting.
Manually mapped vectors show higher magnitudes than PIV on average because human participants measured additional motion associated with overbank flow. For example, between 100 hr 44 min and 100 hr 45 min, sheet flow encroached 
cm over the east bank of the southern channel, leading to a wide zone of shallow flow and an ambiguous wet-dry interface (Figure 10a). Human participants mapped this displacement, but little to no motion is detected by PIV. The PIV vectors show little motion because sheet flow caused ambiguity in the displacement of the wet-dry interface, leading to a standard deviation in displacement greater than the mean displacement. Thus, uncertainty in motion is so large that PIV vectors are filtered out in postprocessing. In another example, overbank flow occurred upstream of a bend along the south bank (Figure 10b, see also Figure 9a). Human participants mapped 
cm of displacement downstream of the bend, whereas PIV detected only 
cm. This difference arises because PIV detected only the portion of displacement associated with channel migration and did not detect changes in the wet-dry interface associated with the overbank flow. The overbank flow created distinct new wetted areas on the delta surface, which cannot be described in terms of a single, best-fit displacement of the wet-dry interface within the PIV interrogation area. Thus, despite changes in the wet-dry interface, the peak in the correlation matrix (Equation 1) is not affected by overbank flow.
Examples of discrepancy between particle image velocimetry (yellow) and manual mapping (white) due to sheet flow (a) and overbank flow (b).
Channel avulsions occurred frequently during XES10—approximately once per hour. Similar to cases of overbank flow, changes in the channel network due to channel avulsion are not detected by our PIV procedure. For example, an avulsion occurred at run time 
hr 
min as the network initiated a new path to the shoreline along the northern section of the flume (Zone 1 in Figure 11). Despite a major change in the channel network, no vectors are detected by the PIV in the zone of avulsion, save for a few high-uncertainty vectors at the breached channel bank. At the same time, however, PIV detects translation of a pre-existing channel in the southern section of the delta (Zone 2 in Figure 11). PIV does not detect the avulsion because the initiation of a new channel cannot be described in terms of a best-fit translation of the pre-existing network. In most interrogation areas, there was no prominent peak in the correlation matrix (Equation 1), resulting in no motion. In some cases, a peak was detected, but motion was so uncertain between realizations that the vectors were filtered out in post-processing.
An example of an avulsion during XES10, showing conditions before (a) and after avulsion (b). Yellow arrows are mean motion between images detected by particle image velocimetry, and shaded swath shows 
uncertainty in vector magnitude and direction. Outlined Zone 1 highlights the avulsion. Zone 2 highlights channel migration in the pre-existing channel network.
3.2 PIV Results for Channel Migration
With validation that PIV captures motions associated with channel migration, here, we explore the main features of PIV-derived migration vector fields. PIV-derived migration rates (
) span an order of magnitude, ranging from 
(Figures 12a and 12b; Movies S1–S19). The distribution exhibits a median migration rate of 
, with a 
quantile range of 
. Following previous work, we cast these results in a non-dimensional framework using the characteristic channel dimensions and aggradation rate (Jerolmack & Mohrig, 2007). Dividing the characteristic channel width (
cm) by the median migration rate, we find that a channel migrates a distance comparable to its own width in approximately 
min (with a 
quantile range of 
min), referred to as the migration timescale 
. For comparison, a channel requires 
hr to aggrade by one channel depth, referred to as the avulsion timescale 
, which we estimate by dividing the channel depth (∼
) by the mean subsidence rate (
). Thus, a channel migrates its own width in the time required to aggrade ∼10% of the channel depth (
), or, in other words, a channel migrates by roughly 10 channel widths between avulsions (
). This degree of channel mobility is within the range of depositional rivers in nature (
), and is comparable to mobile, braided rivers like the Brahmaputra (
) and unstable, ill-defined channels on alluvial fans (
) (Jerolmack & Mohrig, 2007; Sarma, 2005).
(a) Particle image velocimetry (PIV)-derived channel migration rate (
) over time, including the median (squares), 99th percentile (circles), and 16th–84th percentile range (gray envelope) measured over 9-hr-wide non-overlapping windows. More than 14,000 vector observations are represented in each window, for a total of 1,550,752 vectors observed over 310 hr of run time (18,500 image pairs). Background shading highlights periods of constant sea level (white), sea-level fall (light gray), and sea-level rise (dark gray; Figure 2c). (b) Cumulative frequency distribution of channel migration rate over the entire experiment (thick black curve) and over 9-hr subsamples. (c) Distribution of migration rates detected by PIV during higher sediment supply (solid line) and lower sediment supply (dashed line). (d) Distribution of migration rates detected by PIV during constant sea level (solid line), sea-level fall (dashed line), and sea-level rise (dotted line). Blue curves show prediction based on Equation 6 (Wickert et al., 2013), and red lines show prediction based on Equation 7 (Bufe et al., 2019). Propagation of uncertainty in Equation 7 predictions is provided in Figure S3 in Supporting Information S1.
XES10 exhibited systematic changes in migration rate under changing sea-level rise and sediment supply. For example, during run time 
hr, sea-level and sediment supply were constant, and PIV detects a median migration rate of 
cm/min, with a 
percentile range (66% of all observations) of 
cm/min, and a 99th percentile of 
cm/min (Figure 12c). Later in the experiment (run time 
hr), the system experienced a 15% reduction in sediment supply, and the migration rate distribution was reduced to a new median of 
cm/min, 
quantile range of 
cm/min, and a 99th percentile of 
cm/min (Figure 12c). Channel migration was also reduced during sea-level rise, consistent with recent experimental work (Bufe et al., 2019). For example, during slow sea-level rise (run time 
hr), the distribution of PIV observations is shifted toward slower migration rates, with a median and 
percentile range of 
cm/min, and a 99th percentile of 
cm/min (Figure 12d). Channel migration during sea-level fall was similar to that during constant sea level (Figure 12d). Further investigation of systematic trends and their comparison to theoretical models is provided in the Discussion.
PIV vector directions (
) show channel banks migrated in all directions (Figure 13a). Migration is predominantly north-south in most cases (∼60% of all vectors), indicating that migration is usually perpendicular to the mean flow direction (eastward), consistent with assumptions of existing displacement-based methods (Eke et al., 2014; Schwenk et al., 2017). However, east-west (i.e., landward–basinward) channel migration was not uncommon: ∼40% of all vectors exhibit a dominant component parallel to the mean flow direction. Channels migrated east-west in part because channel bends changed the local flow direction. For example, at 100 hr 45 min, a reach of the channel flowed northeastward (Figures 9a and 9b). Migration direction was locally bank-perpendicular, resulting in a significant westward component of motion. In other cases, migration direction was locally bank-parallel (e.g., Figure 9c), because distinct bends and islands along the channel bank moved upstream or downstream. We estimate that a channel of sinuosity of 
would be required to produce the observed 
migration parallel to mean flow, from curvature alone (Text S2 and Figure S2 in Supporting Information S1). Channel sinuosity was only ∼1.2 in XES10, suggesting that roughly half of east-west migration was locally bank-perpendicular, and half was locally bank-parallel. Besides the tendency for flow-perpendicular migration, we did not observe any prominent peaks and valleys in the probability density distribution of migration directions (Figure 13a). By sampling 9-hr non-overlapping windows of vector data, we find that the probability of a given vector direction varies by as much as a factor of two, and that there is no systematic trend in direction with changing sea levels or sediment supply (Figures 13b and 13c).
(a) Probability density distribution of particle image velocimetry-derived channel migration direction 
, measured over the entirety of XES10 (thick black curve) and over 9-hr subsamples. Gray shaded regions highlight vectors that are predominantly flow-perpendicular, that is, pointing within 45° of due north or south. Vectors outside of the gray shaded regions are predominantly flow-parallel. (b) Distribution during higher sediment supply (black line) and lower sediment supply (gray line). (c) Distribution during constant sea level (red line), sea-level fall (green line), and sea-level rise (blue line).
4 Discussion
4.1 Comparison to Previous Work on Channel Mobility Under Changing Sea Level and Sediment Supply
Here, we compare PIV results to theoretical models of channel mobility under changing sea-level and sediment supply. We find that Equation 7 and Equation 6 well predict the median and maximum of the distribution of PIV-derived migration rates, respectively. For example, during constant sea level and sediment supply conditions (run time 
), Equation 7 predicts 
cm/min, which is similar to the median rate from PIV (
cm/min; Figure 12c). Equation 6 yields 
cm/min, which is similar to the highest rates observed by PIV (99th percentile of 
cm/min). Later, when sediment supply was reduced (run time 
hr), channels migrated more slowly and predictions from Equations 7 and 6 shift to track the median and maximum of the new migration-rate distribution (Figure 12c). Equation 6 does not account for sea-level change, but predictions from Equation 7 also shift to accurately reflect the reduced migration rate during sea-level rise (Figure 12d). During sea-level fall, Equation 7 appears to overestimate migration rates compared to PIV-derived measurements (Figure 12d). Overestimation likely stems from our simplified assumption of a constant bank height in Equation 7. Although bank-height time-series measurements are not available for XES10, a companion experiment XES02 documents a four-fold increase in bank height during the early stages of sea-level fall (Wickert et al., 2013) that indirectly reduced migration rates (Bufe et al., 2019). If a comparable increase in bank height occurred in XES10, then Equation 7 predictions for migration rate during sea-level fall would decrease from 
to 
cm/s, which is very similar to the PIV-derived median migration rate (
cm/sec; Figure 12c). Furthermore, some discrepancy between PIV-derived results and Equation 7 is expected because the exponents in Equation 7 were calibrated using pixel-based measurements of channel mobility (Bufe et al., 2019), which unlike PIV do not differentiate between channel migration and avulsion processes.
Based on our results, we suggest the predictions of Equations 6 and 7 may be used in tandem to constrain an expected distribution of migration rates for braided channels with non-cohesive sediment. Constraining the autogenic variability in migration rate may be more important than predicting allogenic changes: the PIV results indicate allogenic changes are relatively small compared to the overall scale of autogenic variability (Figures 12a and 12b). The variability can be explained at least in part by autogenic fluctuations in channel bank height, which have been shown to exert a first-order control on channel migration rate in similar experiments (Bufe et al., 2019).
PIV results support recent experimental work showing channels migrate more slowly during sea-level rise (Figure 12d; Bufe et al., 2019). Sea-level rise creates additional accommodation on the delta top, which decreases the sediment flux through the basin because sediment is lost to aggradation (Bufe et al., 2019). With reduced sediment transport, channels migrate more slowly (Constantine et al., 2014; Nanson & Hickin, 1983; Wickert et al., 2013). Our results also differ from previous work that measured higher channel mobility during sea-level rise (Liang et al., 2016; Martin et al., 2009). Unlike PIV, the approaches in these studies did not specifically target channel migration. Thus, we reason, the increased mobility observed in these studies could be explained by overbank flow and channel avulsions, which are expected to occur more frequently during sea-level rise (Chadwick et al., 2020; Edmonds et al., 2009; Jerolmack, 2009; Liang et al., 2016).
The PIV results imply that some rivers may migrate in a manner that is relatively insensitive to sea-level fall. Previous work suggests channel erosion during sea-level fall can enhance migration by providing additional sediment, but also has the potential to reduce migration rate by increasing channel bank relief and bank sediment yield (Bufe et al., 2019; Malatesta et al., 2017). Based on our results, we suggest that the two effects compensated for one another in XES10, leading to similar migration rates during constant sea-level and during sea-level fall (Figure 12d).
4.2 Challenging the Assumption of Bank-Perpendicular Migration Direction
Channel migration is thought to occur primarily sideways with respect to flow direction, hence the common term lateral migration (Einstein, 1926; Hickin & Nanson, 1984). However, our results indicate that ∼40% of channel migration in XES10 was oriented primarily parallel to the mean flow direction (Figures 11b), and locally bank-parallel motion was not uncommon (we estimate ∼20%; e.g., Figure 9c). These results challenge the assumption that channel migration is consistently bank perpendicular, a common simplification in field and modeling studies (e.g., Baki & Gan, 2012; Ikeda et al., 1981; Parker et al., 2011; Schwenk et al., 2017). Channel migration commonly occurs in all directions, at least for weakly constrained braided systems in non-cohesive sediment. Bank-parallel channel migration can be attributed in part to bar movements, as well as the propagation of distinct bends (e.g., Figure 9c). We expect bank-parallel channel migration may cause spatial changes in wetted width and could contribute to the braided channel planform morphology in nature. Bank-parallel migration may be less pronounced for systems with relatively uniform channel widths, such as meandering rivers (Eke et al., 2014; Mason & Mohrig, 2019).
4.3 Advantages of the PIV Method for Measuring Channel Mobility
The new PIV procedure we propose here provides objective, accurate estimates of migration of the channel network in XES10. PIV-derived vector fields show agreement with manually drawn vector maps and those produced by the demons algorithm (Figures 8-10). PIV is less subjective and is less time- and labor-intensive than manual mapping; PIV also more reliably captures channel migration compared to the demons algorithm, because the demons algorithm produces numerous incoherent vectors on channel interiors and the dry delta surface that are unrelated to channel migration (Figure 9a).
Unlike existing displacement-based approaches, PIV-derived migration directions are determined via best-fit translation of the channel planform (e.g., Figure 5), and do not require subjective visual assessment or the assumption that motion is bank-perpendicular. PIV results show that the majority of migration vectors are oriented perpendicular to the mean flow direction, but there is nonetheless a significant population of vectors (∼40% of the total) with a significant landward or basinward component (Figure 13a). Furthermore, the PIV procedure offers a means to quantify uncertainty in migration rate and direction (Equations 4 and 5) that arise from the inherent subjectivity in identifying channel-bank positions from plan-view imagery (Figure 4). Quantified uncertainty is an important advantage for application to natural rivers, where bank positions are often obscured by vegetation cover, turbidity, and other features (Baki & Gan, 2012; Gupta et al., 2013). The PIV procedure is also less labor intensive than existing displacement-based approaches: PIV implementation is fully automated, in our case extracting more than 1 million vector measurements from 
image pairs (Figure 12; Movies S1–S19). This is despite intensive filtering to reject poorly constrained vectors. We expect such volumes of data would require weeks, if not months, to extract manually using existing displacement-based approaches (e.g., Chakraborty & Mukhopadhyay, 2015; Constantine et al., 2014; Yang et al., 2015) but PIV extraction could be completed within 24 hr of computer-processing time. Furthermore, our PIV method tracks movement of the channel banks, rather than channel centerlines, which should allow for reliable application to both meandering river systems and braided river systems where channel centerlines are poorly defined.
Unlike pixel-based approaches for measuring channel network mobility (Bufe et al., 2019; Lentsch et al., 2018; Wickert et al., 2013), the PIV procedure specifically targets the process of channel migration, producing spatially explicit vector fields and excluding changes associated with overbank flow (Figure 10) and channel avulsions (Figure 11). The difference arises because the PIV algorithm is designed to measure only the best-fit displacement of discrete features—in our case, channels—and not the creation or destruction of such features (Keane & Adrian, 1992; Westerweel, 1997). Thus, in our application, PIV offers a way to disentangle channel migration from other forms of channel-network mobility. This is an important advantage, because channel migration leaves distinct signatures on the delta floodplain (Bradley & Tucker, 2013; Limaye & Lamb, 2016) and in the underlying stratigraphy (Paola et al., 2001; Straub et al., 2013). Moreover, the process of channel migration may respond differently compared to channel avulsion in the face of environmental change (Bentley et al., 2016; Blum & Törnqvist, 2000; Nanson & Hickin, 1986). For example, PIV results show that channel migration is reduced during sea-level rise, consistent with recent experiments (Bufe et al., 2019), whereas the frequency of river avulsions is expected to increase with sea-level rise (Chadwick et al., 2020; Jerolmack, 2009; Martin et al., 2009).
4.4 Implications for the Application of PIV to Natural River Networks
Though we developed our procedure using laboratory data, we believe the PIV approach can also be applied to natural river networks. This could be done using a range of satellite-derived indicators of surface-water presence (Du et al., 2016; Jarriel et al., 2019; Rokni et al., 2014). For example, the Landsat satellite suite has captured worldwide images every 2 weeks for the past half century, providing bountiful examples of channel migration (Constantine et al., 2014; Jarriel et al., 2020; Schwenk et al., 2017; Schwenk & Foufoula-Georgiou, 2016). For such systems, PIV offers an alternative to manual mapping that is both efficient and easily reproducible with large data sets. Jarriel et al. (2021) recently demonstrated the power of applying PIV-based techniques to river networks in Landsat imagery, showing that centerline migration rates on major deltas are sensitive to global variations in sediment supply, flood frequency, and offshore processes.
Our results imply that successful field application requires a specification of the PIV interrogation area such that the area dimensions are comparable to the width of the natural channels (Figure 5a). Furthermore, image timestep should be adjusted to allow channels to migrate ∼25% of their own width between successive images. Many rivers take several years to migrate 25% their own width, allowing for the acquisition of many satellite images that can then be downsampled at the required timestep and compiled into cloudless mosaics to improve PIV signals (Wang et al., 1999). These specifications are supported by more conventional applications of PIV, where interrogation area and image timestep are chosen based on particle size and mobility (Keane & Adrian, 1992; Westerweel, 1997).
Unlike conventional uses of PIV, applying PIV to river networks also requires careful treatment of the wet-dry interface. Channels commonly exhibit banks that can be only loosely constrained from plan imagery (Figure 4). Higher-resolution satellite images may allow for tighter constraints on the wet-dry interface, and thereby improve the precision of PIV channel-migration measurements. However, we expect this improvement is negligible in many cases because vegetation and turbidity obscure the wet-dry interface from clear overhead view regardless of image resolution. To account for this uncertainty in practice, the spectral ranges of riparian vegetation and turbidity should be identified either through visual inspection or automated classification methods (Liao et al., 2001). The range of pixel intensities for the wet-dry interface (e.g., Figure 4b) should then be expanded to span these spectral ranges.
5 Conclusions
-
Successful implementation of PIV requires that the input interrogation area be approximately equal to the squared width of a characteristic channel, and that the image timesteps allow for channels to migrate approximately ∼25% their own width between images (Figure 5). It also requires accounting for ambiguity in the wet-dry interface, which we did by applying PIV to a range of reasonable realizations of the channel network (Figure 6), as well as for potential directional bias, which we did by comparing PIV vector fields from four image orientations. We calculated the average and standard deviation of vector fields across realizations, and discarded vectors with high uncertainty (Figure 7).
-
PIV vectors show good agreement with manually drawn vectors in a blind exercise, as well as vectors produced by the demons algorithm. Vector magnitudes agree within an order of magnitude (Figures 8a and 8b), and vector directions agree within 90° (Figures 8c and 8d). Results are most consistent along migrating channel banks, because all three approaches accurately track motion associated with channel migration (Figure 9).
-
By design, the PIV algorithm does not detect channel avulsions (Figure 11) or overbank flows (Figure 10b), because the initiation of new flow pathways cannot be described in terms of a best-fit translation of the pre-existing network. Post-processing of the data also filters out sheet flows (Figure 10a), which exhibit too much uncertainty in the wet-dry interface to reliably track with PIV.
-
The maximum migration rate observed by PIV is set by the sediment flux divided by the channel cross-sectional area (Equation 6; Wickert et al., 2013; Figures 12a and 12b). The median migration rate is well predicted by a power-law relationship that also accounts for sea-level change and water discharge (Equation 7; Bufe et al., 2019). The full distribution of migration rates in XES10 spans an order of magnitude (
cm/min), which may be explained by autogenic fluctuations in channel bank height (Bufe et al., 2019). At the median rate, channels migrated ∼10 channel widths between avulsions. -
Consistent with theory, channels migrated more slowly after the sediment supply was reduced by 15% midway through the experiment (Figure 12c).
-
Channel migration was common in all directions, with ∼60% of vectors oriented perpendicular to the mean flow direction and ∼40% with a dominant component landward or seaward (Figure 13a). This distribution results from, in roughly equal measure, variability in channel direction and bank-parallel migration.
-
Channels migrated more slowly during sea-level rise (Figure 12d). We hypothesize that sea-level rise caused aggradation on the delta top, thereby decreasing the sediment flux that drives channel migration. Increased mobility during sea-level rise may be attributed to overbank flow and channel avulsions—not channel migration (Chadwick et al., 2020; Liang et al., 2016; Martin et al., 2009).
-
Migration rates during steady sea level were similar to those during sea-level fall (Figure 12d). Increased channel-bank height during sea-level fall, which hinders migration, was compensated for by the additional sediment flux generated by riverbed incision.
Acknowledgments
The authors thank Holly Michael, Teresa Jarriel, Jiyong Lee, Jayaram Hariharan, and Zhongyuan (Tymon) Xu for insightful discussions, and Aaron Bufe and two anonymous reviewers for constructive comments. This research was supported by the NSF grants EAR 1719492 and EAR 1719670 and the University of Minnesota George and Orpha Gibson Fund.
Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
Open Research
Data Availability Statement
The data and codes underlying this study, as well as step-by-step instructions and example code showing how to apply the PIV method, are publicly available in the SEAD repository (http://doi.org/10.26009/s0ECKYD5).
