Topography‐Based Particle Image Velocimetry of Braided Channel Initiation

River channels shape landscapes through gradual migration and abrupt avulsion. Measuring the motion of braided rivers, which have multiple channel threads, is particularly challenging, limiting predictions for landscape evolution and fluvial architecture. To address this challenge, we extended the capabilities of image‐based particle image velocimetry (PIV)—a technique for tracking channel threads in images of the surface—by adapting it to analyze topographic change. We applied this method in a laboratory experiment where a straight channel set in non‐cohesive sediment evolved into a braided channel under constant water and sediment fluxes. Topography‐based PIV successfully tracked the motion of channel threads if displacements between observations were less than the channel‐thread width, consistent with earlier results from image‐based PIV. We filtered spurious migration vectors with magnitudes less than the elevation grid spacing, or with high uncertainties in magnitude and/or direction. During braided channel initiation, migration rates varied with the channel planform development, showing an increase as incipient meanders developed, a decrease during the transitional braiding phase, and consistently low values during the established braiding phase. In this experimental setup, migration rates varied quasi‐periodically along stream at the half scale of initial meander bends. Lateral migration with respect to the mean flow direction was much more pronounced than streamwise migration, accounting for approximately 80% of all detected motion. Results demonstrate that topography‐based PIV has the potential to advance predictions for bank erosion and landscape evolution in natural braided rivers as well as bar preservation and stratigraphic architecture in geological records.

Sediment transport in braided channels can cause various morphological changes, including bar development and migration, local scour and fill, and channel bifurcation (Ashmore, 2013;Ashmore & Parker, 1983).These processes have been documented in laboratory experiments that evolve braided channels in non-cohesive sediment (e.g., Ashmore, 1982;Friedkin, 1945;Kasprak et al., 2015).The experiments usually begin with flow entering a straight channel, which then develops single, alternate bars that occupy most of the channel width.The flow is then topographically steered by these bars, leading to bank erosion and ultimately increasing the channel's sinuosity (Ashmore, 2013;Limaye, 2020).Multiple channel threads form when individual bars are cut off or bifurcation takes place around mid-channel bars (Ashmore, 2013).Braided patterns are then maintained by the continued formation and development of bars that divide channels and divert flow (Ashmore, 1982).
At a larger scale, the braided river channels and adjoining areas previously occupied by the channel form a composite feature called the channel belt (Figure 1, Bridge & Lunt, 2006;Dong & Goudge, 2022;Lunt et al., 2013).In laboratory experiments with initial shear stress higher than the threshold for sediment transport, braided channel threads tend to widen and shallow, resulting in lowered shear stress and decreased sediment transport capacity (Limaye, 2020).The channel belt eventually approaches a quasi-equilibrium width (Bertoldi et al., 2009;Limaye, 2020).During this evolution, the initially straight channel develops meanders that are likely to influence, and/or be influenced by, the channel thread migration.For example, in natural meandering rivers, the rate of channel migration is systematically larger downstream of the point of highest curvature (e.g., Y. Li & Limaye, 2022;Sylvester et al., 2019).
While these experiments suggest consistent trends in the evolution of braided-river channel belts, there are few measurements from either the laboratory or the field for the local directions and rates of change at the scale of individual channel threads.These smaller-scale motions impact bar preservation (Barefoot et al., 2022;Chamberlin & Hajek, 2019;Wang et al., 2022), landscape evolution (Allen, 2008;Kwang et al., 2021), and stratigraphic architecture (Paola & Borgman, 1991;Sahoo et al., 2020).These aspects are essential for reconstructing paleoenvironments from the sedimentary records of Earth and Mars (Jerolmack & Mohrig, 2007;Jerolmack et al., 2004) as well as assessing flood and erosion risks in riparian areas (Mutton & Haque, 2004).
Previous studies have quantified the network of channel threads and bars in laboratory braided rivers (Gardner et al., 2018;Kasprak et al., 2015) and analyzed channel thread migration in laboratory deltas (Chadwick, Steel, Williams-Schaetzel, et al., 2022;Jarriel et al., 2021;Scheidt et al., 2016;Wickert et al., 2013).A recent advance in tracking channel dynamics is through the application of particle image velocimetry (PIV)-a technique originally developed to track the motion of individual particles.PIV works by cross-correlating small sub-images, known as interrogation areas, in successive images to determine the best-fit displacement between image pairs (Keane & Adrian, 1992;Westerweel, 1997).This method has been used to track the motion of channel centerlines from satellite images (Chadwick et al., 2023;Jarriel et al., 2021) and track the motion of riverbanks in laboratory deltas from overhead photographs (Chadwick, Steel, Passalacqua, & Paola, 2022;Chadwick, Steel, Williams-Schaetzel, et al., 2022).Importantly, PIV does not track channel thread displacements that exceed the width of the largest interrogation area (Nogueira et al., 2001;Sciacchitano, 2019;Westerweel, 1997).By specifying an interrogation area at the scale of the characteristic channel thread width, PIV can specifically extract motion associated with gradual channel migration and exclude channel avulsions (Chadwick, Steel, Williams-Schaetzel, et al., 2022).
In this study, we explore the spatiotemporal features of braided channel thread migration based on the experimental data set of Limaye (2020).The braided channel belts underwent three distinct phases: incipient meandering (IM), transitional braiding (TB), and established braiding (EB), which correspond to the originally termed phases of meandering, braiding, and maturity by Limaye (2020).Within these phases, the extent of the channel belt showed quasi-periodic variations at the scale of initially formed meanders.Previous studies have shown the relationship between channel migration and channel width evolution (e.g., Eke et al., 2014;Mason & Mohrig, 2019) specifically in meandering rivers.Notably, a robust correlation has been identified between curvatures and migration rates within these meandering systems (e.g., Sylvester et al., 2019).We anticipate observing analogous dynamics and characteristics in braided rivers and hypothesize that: (a) the IM and transitionally braiding phases will exhibit high migration rates as the belt widens until the belt matures and the migration rate slows down; (b) the channel thread migration rate is influenced by local curvatures at the half scale of initial meander bends (i.e., half of the full meander).
Moreover, we aim to expand beyond the existing methods that track channel threads based on plan-view images using particle image velocimetry (image-based PIV) (Chadwick, Steel, Williams-Schaetzel, et al., 2022;Jarriel et al., 2021) by incorporating topographic data.Image-based PIV identifies channel threads by the extent of pixels classified as belonging to the water surface.Several factors can reduce the reliability of this proxy including differences in wetted extent due to discharge variation, variable color contrast between water and sediment, vegetation encroachment/dying, and overbank flooding (Chadwick et al., 2023).However, if topography data are available, channels could be more accurately identified and tracked based on local lows in channel cross-sections.We term this coupling of PIV and topography data topography-based PIV and apply it to the topography data presented by Limaye (2020).Section 2 introduces the data set and analysis methods.Section 3 tests the effectiveness of topography-PIV in tracking channel thread motion and analyzes the  ,New Zealand (43.7°S,171.5°E).In increasing scale, the annotations indicate a subset of channel threads (white lines), the channel (blue), and the broader channel belt (orange).(b) A definition sketch for these geomorphic features.Bars are shallow, often sandy, areas that are exposed at relatively low flow.Channel threads are wet areas separated by bars.The channel refers to the entire network of interconnected channel threads flowing around bars.The channel belt refers to the wider corridor imprinted by past channel occupation.The figure illustrates two alternative cases for measuring motion, each contingent on the choice of reference coordinate axis.Specifically, we refer to the mean flow direction aligned with the x-axis as the regional coordinate axis, and the local flow direction such as the b-b' line as the local coordinate axis.In the first case, regional migration is measured relative to the mean flow direction (i.e., the x-axis in the x-y coordinate system).For this case, we define migration directed within ±45°of the mean flow direction as regionally streamwise migration, and migration within ±45°of perpendicular to the mean flow direction as regionally lateral migration.In the second case, local migration is measured relative to the local orientation of the channel thread and can be oblique to the mean flow direction.For this second case, migration can be decomposed of locally bank-perpendicular migration (e.g., within ±45°of the a-a' direction) and locally bank-parallel migration (e.g., within ±45°of the b-b' direction).The following analysis will focus on the first coordinate system.direction and rate of migration through time and space.In Section 4, we compare results to previous research on channel thread migration and braided river morphology and discuss implications for interpreting landscapes and stratigraphy shaped by braided rivers.

Laboratory Data Set
This study examines the patterns of channel thread migration in a braided channel using a data set from a physical experiment conducted at St. Anthony Falls Laboratory, University of Minnesota (Limaye, 2020).The experiment took place in a large basin, 37 m long and 2.7 m wide, which minimized boundary effects from the basin walls and inlet/outlet (Figure 2).There were a total of four runs with varied discharge and slope in Limaye (2020), and we analyzed data from a single, base run of the experiment that corresponds to Run 1 described by Limaye (2020).In this run, water discharge was held constant (Q = 0.25 L/s) and the initial down-basin slope (S = 0.01) did not change significantly during the experiment.The experiment used medium sand with a unimodal grain size distribution (D 50 = 0.42 mm) supplied at a constant feed rate (Q s = 0.001 L/s).This sediment feed rate was adjusted to minimize scour or deposition near the inlet, and due to the large scale of the basin, did not affect the overall topographic slope (Limaye, 2020), which is similar to the approach by Bertoldi et al. (2009).
To contextualize the experiment with respect to other laboratory and natural cases, we reformulated three equations for dimensionless stream power (ω*) from Bertoldi et al. (2009) into a single equation where g is gravitational acceleration, d s is mean grain size (approximated by the median, D 50 ), and R = ρ s ρ w ρ w is the submerged relative density of sediment, where ρ s is the sediment density (2,630 kg/m 3 ) and ρ w is the water density (1,000 kg/m 3 ).
We calculated ω * = 3.2 using parameter values from the experiment (Q = 0.25 L/s; S = 0.01; g = 9.8 m/s 2 ; R = 1.63; and d S = 0.042 mm).This value is lower than most values (2-6) reported by Bertoldi et al. (2009), who  2020)).Water and sediment were fed at constant rates to a channel initially carved in a bed of non-cohesive sediment (medium sand, D 50 = 0.42 mm) at a constant down-basin slope (S = 0.01).The x, y, and z coordinates align with the directions of downstream, cross-stream, and vertical, respectively.(b) A view from above.(c) A cross-section aligned with the direction of the flow.The bullseye signifies the flow out of the page, h 0 is initial channel depth, and w 0 is initial channel width.found a positive correlation between the number of braided channel threads (i.e., braiding intensity) and ω * .Therefore, the presented experiment should be viewed as a case with relatively low stream power and low braiding intensity.

Water Resources Research
Figure 2 illustrates the design of the initial channel, which had a rectangular cross-section and straight planform geometry (Limaye, 2020).The initial channel depth (h 0 ) was set at 3 cm to ensure a flow depth capable of sediment transport at the initial bed slope (Figure 2c, Shields, 1936).The initial channel width (w 0 ) was set to 18 cm (Figure 2c).Digital elevation models (DEMs) were collected using an optical and laser-line scanner during pauses in flow, with a grid spacing (Δx) of 2 mm and sub-millimeter vertical precision.The time interval between topography observations was 1 hr through the first 45 hr of the run and increased to 5 hr thereafter until the end of the run (t = 60 hr) as the rate of surface change diminished.
As the channel belt developed, the channel widened and shallowed, resulting in overall aggradation with no change in overall bed slope, as previously documented for similar experiments (Hirano, 1973).Limaye (2020) identified three distinct phases in the planform evolution of the channel and channel belt in the experiment, which are referred to as the meandering phase (t = 0-4 hr, where t is run time), braiding phase (t = 4-18 hr), and maturity phase (t = 18-60 hr), respectively.To better contextualize the experiment relative to other laboratory and field studies, we redefined these phases.During the IM phase, the channel belt widened rapidly.In the TB phase, the mean width of the channel belt grew logarithmically over time (Limaye, 2020).During the EB phase, shear stress dropped near the threshold for sediment transport, leading to minimal growth of the channel belt width (Limaye, 2020).The duration of each phase and the growth rate of the channel belt width varied across the four runs that varied discharge and initial bed slope in Limaye (2020).However, durations and growth rates were similar across runs when cast in terms of dimensionless time (t * ) The experiment showed quasi-periodic variations in the width of the channel belt, with a maximum wavelength of ∼2 m corresponding to the wavelengths of initial meanders (Limaye, 2020).Channel belt sinuosity ranged from 1.02 to 1.07 during the IM phase and 1.06 to 1.14 during the transitional and EB phases.
During the experiment, channel threads migrated in different directions, and quantifying this movement requires defining conventions for describing this motion.Figure 1 shows two end-member possibilities for defining the reference coordinate axis: (a) Regional migration, which we define as occurring relative to the mean flow direction (i.e., the longitudinal axis of the basin).Regional migration can be decomposed into streamwise migration (i.e., aligned with the mean flow direction within ±45°) and lateral migration (i.e., perpendicular to the mean flow direction within ±45°).(b) Local migration, which we define as occurring relative to the local orientation of the channel thread that can be oblique to the mean flow direction.Local migration can be decomposed into bankperpendicular and bank-parallel migration (i.e., aligned with or perpendicular to the local channel thread orientation within ±45°).In this study, we mainly focus on quantifying the regional migration.Regionally lateral migration was more common than regionally streamwise migration during the experiment.The regionally streamwise migration arises due to the downstream migration of mid-channel bars, but also due to locally bankperpendicular migration along a sinuous channel thread (Chadwick, Steel, Williams-Schaetzel, et al., 2022).Sinuosity increased over time in the Limaye (2020) experiment and thus we expect an increase in the amount of regionally streamwise migration through time.
Since the morphologic change is abrupt due to the straight geometry of the initial channel during the first time step between topography observations (i.e., t = 0-1 hr) but it is minimal during the EB phase (Limaye, 2020), we limited the analyses to the time interval t = 1-22 hr in Run 1.This period covers the full periods of IM and TB phases and a few hours at the onset of the EB phase.

Identifying Channel Threads From Topography Data
Image-based PIV works by tracking channels in plan-view images.Each pixel in these images is classified as either "river" or "non-river" based on its spectral characteristics (Chadwick, Steel, Williams-Schaetzel, et al., 2022;Chadwick et al., 2023;Jarriel et al., 2021).However, this approach has significant limitations and is impossible under certain conditions.For instance, in laboratory environments, shallow, clearwater flows with depths less than 1 m are difficult to distinguish from dry surfaces unless opaque dyes are introduced.Figure 3 illustrates this challenge using an image from the experiment, which did not use dyes; the image quality is also affected by inconsistent lighting.Despite the common use of dyes in other experiments, depth inference remains convoluted, influenced by parameters such as dye concentration, mixing efficiency, optical properties, and fluid dynamics (e.g., settling and resuspension, hydraulic residence time, flow velocity) (Ghilardi et al., 2014).In natural settings, additional complications arise.Seasonal water level fluctuations generate waterline variations that are decoupled from channel migration processes.Overbank flooding and channel cover by clouds and vegetation further confound the pixel-to-channel correlation (Chadwick et al., 2023).Consequently, these factors constrain the applicability of image-based PIV.
To address these inherent limitations, we introduce topography-based PIV as an alternative method to measuring surface change.Although image data are often more readily available, topography data offer a more direct metric for determining bank positions.This method circumvents complications prevalent in image-based approaches, such as shallow, clear water; variations in wetted extent due to discharge variation; and cloud and vegetation cover.Channel threads were identified as elongated areas that were lower than the surrounding topography.To illustrate, we chose the center of the basin at a downstream distance of 15-20 m, which had minimal boundary effects (Figure S1 in Supporting Information S1); this segment is henceforth referred to as Reach 3. Other reaches are delineated in Figure S1 in Supporting Information S1 and will be introduced in Section 2.3.To systematically identify channel threads from topography, their elevation must be differentiated from the prevailing streamwise slope (S) (Figure 4a).Over scales of meters, the elevation in the channel belt also develops local convexities that depart from the overall linear trend in slope.Therefore, for each cross-section (i.e., a column of pixels) perpendicular to the mean flow direction, we subtracted the median elevation from each pixel's elevation to obtain the residual elevation (Z r ).Channel threads that are subtle in the original topography are clearly distinguished as areas with Z r < 0 (Figure 4b).PIV is designed to track objects in binary image masks.Therefore, to generate a map of channel threads that is compatible with PIV, we generate binary masks that distinguish channel threads from bars and areas outside the channel belt by applying a threshold value of the residual elevation (Z r,t ), which has a median (50th percentile) of 0 m.We tested several values of Z r,t with a range of 30th-70th percentiles of Z r (Figure 4c).While all cases highlight channel threads, the mapped extent of these channel threads increases systematically as Z r,t increases (Figures 4d and 5).By visually inspecting the binary masks (Figure 5), we find that the 40th, 50th, 55th, and 60th percentiles of Z r are reasonable threshold values for distinguishing channel threads from bars and the surrounding topography outside the channel belt.As will be shown in Section 2.3, we use these alternative realizations of the extent of channel threads as part of a procedure to test the uncertainty in calculated migration vectors.
While these binary masks effectively capture the locations of channel threads, they also include small-scale features, some because of sub-millimeter noise in the topography data, that could cause spurious migration vectors using PIV (Figure 6).Therefore, to reduce this effect and sharpen the interface between channel threads and bars in the binary masks, we applied a median filter to the image masks with a window scale of 10 × 10 pixels (2 × 2 cm) (Figure 6), which is much smaller than the characteristic channel-thread width (i.e., 16 cm).Applying this process to image masks before processing with PIV will systematically increase the migration rate by reducing the effects of spurious cross-correlation between small-scale features in the binary image masks.In this way, the resulting map of channel thread migration predominantly reflects the displacements of channel threads that are consistent for along-stream scales >2 cm (Figures 6c and 6d).We applied these processing steps to identify channel threads in all available DEMs. Figure S1 in Supporting Information S1 shows the binary masks that identify channel threads for the whole basin during the first 10 hr of the run.

Deriving PIV-Based Migration Vectors and Analyzing Uncertainties
We processed binary masks of channel thread locations with the software PIVlab (release 2.59, Thielicke & Stamhuis, 2014).Unlike traditional particles, channel threads are typically longer than the interrogation area, which introduces a systematic bias toward detecting channel thread migration aligned with the rectilinear PIV grid (Chadwick, Steel, Williams-Schaetzel, et al., 2022).To quantify the uncertainty associated with this directional bias, we followed Chadwick, Steel, Williams-Schaetzel, et al. (2022) and performed PIV analysis on four stacks of input images with different tilt angles relative to the PIV grid (i.e., 0°, 15°, 30°, and 45°; Table 1).The combination of four tilt angles and four threshold elevations (Section 2.2) yields a total of 4 × 4 = 16 realizations of the PIV vector field for each time step.
A further technical consideration arises from the elongated geometry of the source elevation data that spans the basin.Rotating binary masks based on these DEMs to oblique angles causes an increase in the size of the image mask, which must retain a rectangular geometry for input to PIV.This rectangular geometry is created by padding the image with additional false pixels, which increases the computational burden.Therefore, we divide each binary mask of channel threads into several smaller reaches at a 5 m scale.To reduce boundary effects, the division was started at a downstream distance of 5 m and ended at 35 m; these reaches are numbered sequentially Following Chadwick, Steel, Williams-Schaetzel, et al. (2022), we set the smallest interrogation area (i.e., we use 8 cm; equivalent to 40 pixels) to be comparable to, but less than, the characteristic channel thread width (i.e., 16 cm).Moreover, we used four interrogation areas (referred to as "Pass" in the PIVlab software; Table 1) to improve the signal-to-noise ratio (Westerweel, 1997), with lengths of 320, 160, 80, and 40 pixels, respectively, each of which is given a step size of half the interrogation area length (Table 1).The signal-to-noise ratio can be further improved if the displacement of the characteristic channel thread is adjusted to around 25% of the interrogation area length (Keane & Adrian, 1992).By doing pilot analyses, we obtained an initial estimate of the distribution of the channel thread migration rates, and we used the largest values to determine a characteristic displacement for one time step between topography observations.Accordingly, we chose to use a time step between observations (Δt) equal to 1 hr for IM and TB phases (t = 1-18 hr) and Δt = 2 hr for the EB phase (t = 18-22 hr).
After raw versions of all the vector fields across the 16 realizations were generated, we used the following criteria suggested by Chadwick, Steel, Williams-Schaetzel, et al. (2022) to discard vectors that were associated with high uncertainties (Figure 7): (a) the standard deviation of vector magnitude (M σ ) is larger than the mean (M μ ) (i.e., uncertain magnitude); (b) the standard deviation of vector direction (θ σ ) exceeds 90°(i.e., uncertain direction); and (c) vectors appear in fewer than four realizations out of the sixteen (i.e., false positive).A significant advantage of using topography data is that it enables a further test of the significance of each vector by requiring that it be associated with a change in topography.Therefore, we considered a further criterion to exclude vectors that are associated with minimal topographic changes, which are defined as locations where the difference between two successive DEMs is below the vertical precision of approximately 0.1 mm.However, we observed that the impact of applying this additional criterion was negligible, as over 99% of the topographic changes in this study occurred at scales exceeding the vertical precision.Therefore, we opted to use the first three criteria to generate filtered vectors for channel thread migration over the full basin length, and for each pair of topography observations, during which 60%-80% of the vectors were discarded.The result is a time series of mean vector fields that describe the motion of channel threads for the entire basin and over 22 hr of experimental run time.
After deriving vector fields of channel thread migration from PIV, we tested their accuracy by comparison to an independent analysis of channel threads mapped manually from DEMs of difference (DoD) that spans a 1-hr interval in the experiment.Additionally, we compared residual elevation (Z r ) and DoD (ΔZ) values along cross-sections.As will be shown, these independent measurements affirmed the PIV measurements and provided a complementary, three-dimensional view of surface change.

Developing Metrics for Quantifying Channel Thread Migration Rate
The PIV-derived vectors have horizontal and longitudinal components that can indicate the resultant migration magnitude and direction.We quantified three metrics related to channel thread migration.The first metric is the migration rate (M), described in terms of the reach-averaged PIV-derived vector magnitudes that exceeded 1 pixel/frame (our threshold for mobility; Chadwick, Steel, Williams-Schaetzel, et al., 2022).The second metric is the reach-normalized mobile perimeter (P), which describes the fraction of the bank that is migrating at speeds above our threshold for mobility over the studied reach (Chadwick, Steel, Passalacqua, & Paola, 2022).The reachnormalized mobile perimeter is estimated by dividing the mobile perimeter (U) over the along-stream distance of the reach analyzed (L): where N is the number of vectors that exceed 1 pixel/frame, and Δx is the grid spacing that approximates the length of the bank associated with each PIV vector.The third metric is the bank-integrated migration rate (M p ), defined as the product of the previous two metrics (M p = M × P = M × U L ; Figure 8c).This definition effectively divides the rate of areal reworking by channel thread migration (M × N × ∆x) by the reach length (L) to yield a migration rate (M p ) that averages across both mobile and immobile parts of the channel.M, P, and M p may capture different aspects of channel thread kinematics.For instance, a river reach that is slowly migrating everywhere will have a lower M value, a higher P value, and a possibly higher M p value (Figure 8b), compared to a reach where only a few places are migrating quickly (Figure 8a).Therefore, M p can be used as a more effective proxy for comparing migration rates.

Analysis of Vectors for Channel Thread Migration From PIV
To quantify spatiotemporal variations in migration rate, we analyzed the temporal variation of the bank-integrated migration rate (M p ) using moving average windows with different widths.These windows are: 30 m, which corresponds to the full length of the basin analyzed; 5 m, which is the length of each subdivided reach and corresponds to approximately 2.5 meander wavelengths (Figure S1 in Supporting Information S1); 1 m, which is the half scale of a meander bend; and 0.05 m, which is intermediate between half a meander wavelength and the grid spacing (Δx = 2 mm).
As noted in Section 1, the width of the channel belt in this experiment developed quasi-periodic variations linked to the scale of initial meanders that have maximum wavelengths of approximately 2 m (Limaye, 2020).To quantitatively test whether the bank-integrated migration rate (M p ) exhibits similar behavior, we implemented power spectrum analysis on the spatial series of M p using the REDFIT algorithm in the software PAST (version 4.03, Hammer et al., 2001).We used the abovementioned 0.05 m window to calculate the moving average of M p .We set both the oversampling and segmentation intervals to 1 and applied a Blackman-Harris window (Foreman & Straub, 2017).We used 1,000 Monte Carlo simulations of the autoregressive (AR1) process (Schulz & Mudelsee, 2002).This process involved analyzing the relationship between one value of M p and its previous one in space, along with a random noise term that accounts for unexplained variation or randomness in the time series.The resulting AR1 spectrum provides information about the distribution of power across different frequencies.We estimated the significance of detected peaks in the power spectrum of M p by comparison to the AR1 model, and we employed a threshold of 99% confidence level, which means that the likelihood of observing such periodicity in the along-stream M p measurements due to random chance is less than 1%.-e).The length of the vector represents the mean vector magnitude (M μ ), while the pointing direction of the vector represents the mean vector direction (M σ ).The upper and lower limits of the swath indicate the deviation from the mean vector magnitude (i.e., M μ + M σ and M μ M σ ).The opening of the swath is twice the standard deviation in direction (2θ σ ) centered at the mean vector direction (θ μ ).(b, c) Unfiltered vector fields include vectors with high uncertainty in magnitude and direction (circled) and vectors with small magnitudes (<1 pixel).(d, e) Filtered vector fields, after removing vectors with high uncertainties.It is important to note that the red circles illustrate a selection of removed vectors as examples; they do not encompass all instances.
Figure S2 in Supporting Information S1 presents a flowchart that outlines the above-presented methodological framework from Sections 2.2-2.5, including data preparation, PIV analysis, developing metrics to quantify migration rates, and spatiotemporal examination of migration vectors.

Channel Thread Migration From Topography-Based Particle Image Velocity (PIV)
Channel thread migration can be manually mapped by comparing riverbanks at different times both on the surface (Figure 9a) and in the cross-section residual elevation (Z r ) profile (Figure 8d).Alternatively, it can also be mapped by following the transition from positive to negative DEMs of difference (DoD) on the surface (Figure 9b) and in the cross-section (Figure 8e).By comparing PIV-derived vectors (Figure 9c) with visual inspection based on surface and cross-section differences, we find that the PIV effectively captures channel thread migration wherever the displacement is less than the width of the channel thread, such that there is an overlap in the extent of the channel thread in successive images (Figure 9d).However, PIV generates vectors with incorrect directions and magnitudes in instances of exceptionally high migration rates, because the displacement is greater than the channel thread width between topography observations (e.g., the rectangle in Figure 9a).This finding is consistent with image-based PIV (Chadwick, Steel, Williams-Schaetzel, et al., 2022).Increasing the interrogation window size degrades the signal-to-noise ratio, as the optimal displacement is roughly 25% of the width of the interrogation window (Keane & Adrian, 1992).These erroneous vectors can be avoided if a shorter time step is available, such that a channel thread in one image overlaps significantly with the same channel thread in the next image.The inset of Figure 9a highlights the wrong directions and magnitudes of these erroneous vectors.
The DoD method can detect such fast channel migration (Figures 9b and 9e), as it focuses on elevation changes in the vertical domain.Particularly, it can help us focus on channel threads with comparable dimensions in both extent (Figure 9b) and depth (Figure 9e).However, this approach requires user interpretation and pairs of negative and positive DoD values in proximity (Figures 9b and 9e) to determine migration direction.Furthermore, DoD does not differentiate between topographic change due to channel migration, channel avulsion, or channel aggradation/degradation.In contrast, PIV can exclusively target channel migration if input interrogation window size and timestep are selected appropriately, as described in Section 2. Overall, PIV is effective in tracking gradual channel thread migration, but produces incorrect vector directions and magnitudes if channel threads shift by more than their width.

Spatiotemporal Variation of Channel Thread Migration
The bank-integrated migration rate (M p ) shows order-of-magnitude variations in both time and space (Figure 10a).Spatially, M p averaged over a moving window of 0.05 m shows quasi-periodic along-stream variations (Figures 10a, 10b, and 10d).M p averaged over moving windows of 1 and 5 m vary within smaller ranges and indicate a higher migration rate in the central part of the basin compared to the upstream and downstream (c) Parameters used in defining the bank-integrated migration rate (M p ). M is the particle image velocimetry (PIV)-derived migration rate defined in the above text, U is the mobile perimeter, L is the along-stream distance of the reach analyzed, N is the number of vectors that exceed 1 pixel/frame, and Δx is the grid spacing that approximates the length of the bank associated with each PIV vector.Panel (c) is modified based on Chadwick, Steel, Passalacqua, and Paola (2022).
(Figure 10b).Comparison between channel belt morphology at t = 4 hr (Figure 10c) and the migration vectors during t = 4-5 hr (Figure 10d) indicates a relationship between channel belt extent and M p at the half scale of meander-bend (i.e., half meander).Specifically, high-magnitude vectors tend to cluster near the apex of meander bends (Figures 10c and 10d).We first implemented spectral analysis on M p averaged over a moving window of 0.05 m during t = 4-5 hr, which interval has been extensively analyzed above.The spectral power exceeds the 99% confidence level for wavelengths between 0.7 and 1.0 m (Figure 11a).The same analysis applied to M p in the other time intervals (t = 1-10 hr) indicates that the longest-wavelength peak during each time interval ranges from 0.8 to 1.2 m (Figure 11b).This range is approximately half the wavelength of the initial meander bends (approximately 2.0 m; Limaye, 2020).At the scale of the entire basin, M p varies during the successive phases of channel belt development, demonstrating a systematic trend over time (Figures 10e and 10f).The median value of M p at the basin scale increases from 3.1 mm/hr during t = 1-2 hr to 8.2 mm/hr during t = 5-6 hr within the IM and early TB phases (Figures 10e  and 10f).Subsequently, it decreases monotonically during the late TB and EB phases (Figures 10e and 10f).At the scale of the 5-m reach, taking Reach 3 as an example, the spatially averaged migration rate (M) increases during the IM phase, sharply declines and stabilizes during the TB phase, and ultimately drops and remains low during the EB phase (Figure 12a).The reach-normalized mobile perimeter (P) increases during the IM phase, peaks during the TB phase, and fluctuates at a low level during the EB phase (Figure 12b).M p increases during the IM  phase, undergoes a steep drop during the TB phase, and remains low during the EB phase (Figure 12c).The other 5-m-scale reaches show similar behavior (Figure S3 in Supporting Information S1).
Channel thread migration occurs in all directions, with regionally lateral migration (see definition in Figure 1) being much more common than regionally streamwise migration (Figure 13).In Reach 3, the proportion of regionally lateral migration vectors varies between 62% and 95% during t = 1-22 hr, with an average of 80% (Figure 13a).The proportion of regionally lateral migration decreases over time (Figure 13a).This decrease can at least partially be explained by the locally bank-perpendicular migration as the channel threads grew more sinuous over time (Figure S1 in Supporting Information S1) (Chadwick, Steel, Williams-Schaetzel, et al., 2022).Similar patterns were observed in the other reaches (Figure S4a in Supporting Information S1).The rose diagram of migration directions in all PIV-derived vectors during t = 1-22 hr in Reach 3 also shows that regionally lateral migration is much more common than regionally streamwise migration (Figure 13b).Similar patterns were observed in the other reaches (Figure S4b in Supporting Information S1).

Using Topography-Based PIV to Track Geomorphic Change
Building on traditional image-based PIV (e.g., Chadwick, Steel, Williams-Schaetzel, et al., 2022), this study establishes a method for topography-based PIV that provides more accurate criteria for identifying and tracking channel threads.Topography-based PIV has several advantages over image-based PIV.First, it is not affected by numerous factors that can complicate image-based detection, such as water level, wetted width, overbank flooding, color contrast between water and sediment, and encroachment/death of vegetation if present, amongst others.Second, topography provides three-dimensional information about the terrain that cannot be extracted from images alone.Third, channel threads identified by elevation data are more precise compared to those derived from optical images.Fourth, topography-based PIV has the potential to be applied to other geomorphic changes that are not readily detectable from the image by color contrast or limited by resolution, such as those associated with fluvial and aeolian ripples and dunes, earthflows, turbidites, and alluvial fans.
Topography-based PIV may, however, require more effort to implement than image-based PIV.In both laboratory and natural settings, topography data are generally more difficult to collect, and are collected less frequently, than images.This difference in typical sampling time would limit the ability to apply topographybased PIV if channels migrate by more than their width between consecutive observations; this behavior erpendicular to the basin axis direction; Figure 1) rather than streamwise migration (within ±45°along the basin axis direction; Figure 1).would cause erroneous migration vectors (Figure 9a) (Chadwick et al., 2023).Yet in some field settings amenable to image-based PIV, the application of topography-based PIV can be used to independently measure the motion of channel threads.Therefore, in situations with both satellite and topography data, in either single-or multiple-thread river settings, the temporal resolution of the data determines whether imagebased or topography-based PIV is more suitable for a given study.Nevertheless, topography-based PIV should outperform image-based PIV if the topography data are collected at a high frequency, or the river migration is relatively slow so that channel thread displacement is always less than its width between consecutive observations.For instance, implementing topography-based PIV for the Brahmaputra River is notably challenging.The river's extensive scale complicates the acquisition of repeated topographic data with the required spatial and temporal precision.Moreover, its high migration rate, reaching up to 800 m/yr (Coleman, 1969), causes channel thread displacements to surpass its width, undermining the applicability of topography-based PIV.

Water Resources Research
In the context of flooding events, field survey frequencies are generally lower than pre-and post-flood intervals, complicating both image-and topography-based PIV applications.Notably, PIV specializes in capturing vectors related to gradual bank migration while effectively ignoring those associated with abrupt morphological changes, such as avulsion or the sudden opening and closing of anabranches.This characteristic is supported by both laboratory (Chadwick, Steel, Passalacqua, & Paola, 2022;Chadwick, Steel, Williams-Schaetzel, et al., 2022) and remote sensing evidence (Chadwick et al., 2023) and differentiates PIV from other channel-tracking algorithms such as dynamic time warping (Lisiecki & Lisiecki, 2002), demon (Thirion, 1998), and SCREAM (Rowland et al., 2016)-which yield erroneous migration vectors in areas associated with abrupt morphological changes (Chadwick, Steel, Williams-Schaetzel, et al., 2022;Sylvester et al., 2019).To address the current data limitations on applying topography-based PIV, emerging methods including Light Detection and Ranging and Unmanned Aerial Vehicle (UAV)-enabled techniques could provide more efficient and frequent topographic measurements.Integration of these new methods could potentially enhance understanding of natural braided river dynamics, provided that the corresponding data sets offer adequate temporal and spatial resolution for channel-thread mapping.At present, both image-and topography-based PIV hold potential for practical applications, particularly given the increasing availability of high-resolution satellite images and topography data.

Factors Influencing Spatiotemporal Trends of Migration of Braided Channel Threads
Temporally, channel thread migration in this study follows a pattern similar to channel belt growth reported by Limaye (2020).Both processes slow down over time due to progressively decreasing boundary shear stress.This observation is corroborated by the fact that water flow may be present but unable to transport sediment in channel threads (Ashmore et al., 2011;Limaye, 2020).The cause of the temporal increase in M, P, and M p during some time intervals in the TB phase remains elusive, but we speculate that it may result from local variability in migration rates.The proportion of regionally lateral migration decreases over time (Figure 13), which can be partly explained by increasing sinuosity.Spatially, we observed quasi-periodic, along-stream changes in migration rates at the half scale of meander bends (Figures 10 and 11).This observation suggests that the migration of braided channel threads may also be curvature-driven at the half meander-bend scale, similar to meandering channels (Sylvester et al., 2019).If this hypothesis holds, it may further suggest that the development of the braided channel network, despite its complexity, is guided by the coherent motion of individual channel threads in this experiment setup.We note, however, that the imprint of meandering on the channel belt margin is a time-transgressive feature that does not directly reflect the formation of a single, sinuous channel (Limaye, 2020).Additionally, the curvature is not only present at the channel belt boundary but is also prevalent along the channel threads within the channel belt.Chadwick, Steel, Passalacqua, and Paola (2022) reported differential migration caused by faster bank erosion than accretion, which may be another factor controlling channel migration.Over spatial scales larger than the aforementioned half meander bends (e.g., 5 meander bends), we observed larger migration rates in the central part of the basin than those in the upstream and downstream.It is unclear whether this behavior results from the boundary effect or is a random occurrence.Nonetheless, this observation is consistent with the larger channel belt width in the midstream (Limaye, 2020), further indicating the interrelationship between channel thread migration and channel belt development.Notably, the study reveals the spatially quasi-periodic migration rates in the initiation of this laboratory braided river, which could be tested against other laboratory experiments and observations from natural rivers.

10.1029/2023WR035229
We underscore that specific geometries and rates observed are likely particular to the experimental setup characterized by (a) relatively low stream power and weak braiding intensity and (b) a distinct reduction in lateral mobility over time.This setup differs from several prior studies where rapid and common planform changes are documented (e.g., Bertoldi et al., 2010;Middleton et al., 2019;Peirce et al., 2018;Wheaton et al., 2013).Yet regardless of these differences in kinematics, the new approach of topography-based PIV presented in this study provides a method that can be applied more generally to quantify and compare changes in complex topography.

Implications and Future Opportunities for Interpreting Landscapes and Stratigraphy Shaped by Braided Rivers
The migration of channel threads in braided rivers significantly impacts fluvial landscapes, and sedimentary deposits (Ganti et al., 2020;Morris et al., 2022;Steel et al., 2022;Wickert et al., 2013).This study analyzes the style of channel thread migration in a specific laboratory experiment and finds that patterns of migration exhibit spatial trends.If the behaviors from this experiment are also present in natural cases, they imply that zones of higher channel-thread curvature are associated with faster migration rates.This finding can be used to inform assessments of erosion hazards in natural braided rivers.
Whereas the experiment used constant boundary conditions, several other factors can influence the channel thread migration in laboratory experiments, including differences in water and sediment discharge, slope, base-level, and basin subsidence; and in natural settings, differences in vegetation, lithology, and grain size that impact bank stability (Braudrick et al., 2009;Bufe et al., 2019;Dunne et al., 2010;Limaye, 2020;Wickert et al., 2013).The braided channel studied here evolved in non-cohesive sediment, and thus findings of this study may be particularly relevant to pre-Silurian braided channels, where fine sediment and vegetation were likely scarce (Davies & Gibling, 2010, 2011;Gibling & Davies, 2012).
Although the down-basin slope was effectively constant in this experiment, it can evolve due to spatial variation in aggradation or degradation (Ashworth et al., 2004(Ashworth et al., , 2007;;Bryant et al., 1995;Bufe et al., 2019).In laboratory experiments, aggradation can be caused by factors such as high sediment supply, constant basin subsidence, or sea level rise, and tends to enhance channel migration (Ashworth et al., 2004;Bryant et al., 1995;Chadwick et al., 2020).In contrast, net degradation is typically associated with incised channel threads with relatively narrow widths, tall banks, and slow migration (Bufe et al., 2019).
The properties of autogenic migration by braided channel threads analyzed in this study provide a foundation for investigating the impact of external forcing, such as variations in water and sediment discharge, changes in base level, and alternating uplift and subsidence (Chadwick et al., 2020;Esposito et al., 2018;Kim et al., 2014;Q. Li et al., 2016;Wang, 2021).For example, a recent field study by Barefoot et al. (2022) indicates that high variability in water discharge, rather than high discharge magnitude, enhanced channel mobility and floodplain reworking during the Paleocene-Eocene Thermal Maximum.This finding challenges an earlier hypothesis that increasing water discharge alone enhances channel mobility (Foreman et al., 2012).To better understand the influence of high and variable discharge on geologic records, future studies could compare their effects on channel thread migration.

Conclusions
Using time-series measurements of topography, we quantified the direction and rate of channel thread migration during the initiation of a laboratory braided river with relatively low stream power.We find that: 1. Channel threads are consistently identified as local topographic lows relative to the median cross-stream elevation, enabling automated analysis of their kinematics.2. Topography-based PIV accurately captures the motion of braided channel threads, if the displacement is less than the width of the channel thread.We systematically quantified uncertainty in measured migration vectors by considering several threshold values for identifying channel threads in topography data, accounting for biases in PIV output due to grid orientation, and using the statistics of vector magnitude and direction to exclude negligible migration rates and/or uncertain migration magnitudes and directions across 16 realizations.3. Channel thread migration rates correlate with the developmental phases of the channel planform, with higher migration rates observed during the IM and early TB phases, and lower rates in the late TB and EB phases.
Water Resources Research 10.1029/2023WR035229 WANG ET AL.
4. Channel thread migration rates at the half scale of initial meander bends show quasi-periodic variations from upstream to downstream, indicating the strong influence of local curvatures.5.At the scale of several meander bends, regionally lateral migration is much more common than regionally streamwise migration, representing approximately 80% of migration vectors during channel belt development.6.The advancement in tracking channel threads using topography-based PIV can improve predictions for bank erosion, bar preservation, and environmental signal propagation by braided rivers, while the approach can be applied to tracking complex topographic change in other geomorphic settings.

Figure 1 .
Figure 1.An example of common features of braided rivers.(a) The RakaiaRiver, New Zealand (43.7°S, 171.5°E).In increasing scale, the annotations indicate a subset of channel threads (white lines), the channel (blue), and the broader channel belt (orange).(b) A definition sketch for these geomorphic features.Bars are shallow, often sandy, areas that are exposed at relatively low flow.Channel threads are wet areas separated by bars.The channel refers to the entire network of interconnected channel threads flowing around bars.The channel belt refers to the wider corridor imprinted by past channel occupation.The figure illustrates two alternative cases for measuring motion, each contingent on the choice of reference coordinate axis.Specifically, we refer to the mean flow direction aligned with the x-axis as the regional coordinate axis, and the local flow direction such as the b-b' line as the local coordinate axis.In the first case, regional migration is measured relative to the mean flow direction (i.e., the x-axis in the x-y coordinate system).For this case, we define migration directed within ±45°of the mean flow direction as regionally streamwise migration, and migration within ±45°of perpendicular to the mean flow direction as regionally lateral migration.In the second case, local migration is measured relative to the local orientation of the channel thread and can be oblique to the mean flow direction.For this second case, migration can be decomposed of locally bank-perpendicular migration (e.g., within ±45°of the a-a' direction) and locally bank-parallel migration (e.g., within ±45°of the b-b' direction).The following analysis will focus on the first coordinate system.

Figure 2 .
Figure 2. Schematic of the experiment setup (after Limaye (2020)).Water and sediment were fed at constant rates to a channel initially carved in a bed of non-cohesive sediment (medium sand, D 50 = 0.42 mm) at a constant down-basin slope (S = 0.01).The x, y, and z coordinates align with the directions of downstream, cross-stream, and vertical, respectively.(b) A view from above.(c) A cross-section aligned with the direction of the flow.The bullseye signifies the flow out of the page, h 0 is initial channel depth, and w 0 is initial channel width.

Figure 3 .
Figure 3. Attempted identification of channel threads following the workflow of image-based particle image velocimetry.(a) Orthorectified optical image captured at t = 5 hr.(b) Grayscale conversion of the image from panel (a).(c) Probability density distribution of pixel intensities.(d) Binary image that fails to effectively distinguish between channel threads, bars, and regions outside the channel belt by pixel intensity thresholding.Vertical dashed lines in panels (b, c) indicate threshold values of 75 and 100, employed to differentiate between dry (black pixels with the intensity of 75-100), wet (white pixels with the intensity of 0-75), and reflective regions (white pixels with the intensity of 100-255).This delineation is insufficient for segregating wet areas within the channel belt from dry areas outside it and is particularly inadequate for differentiating channel threads wetted by shallow, clear water.

Figure 4 .
Figure 4. Steps to separate channel threads from bars, taking Reach 3 (see Figure S1 in Supporting Information S1 for location) at t = 5 hr as the example.(a) The elevation (Z) variation in the Digital elevation model (DEM) dominated by the overall, streamwise bed slope (S).(b) The residual elevation (Z r ), obtained by subtracting the cross-stream median elevation from Z along each cross-section, indicating channel threads as local lows in topography.(c) Histogram of Z r with lower values representing topographic lows and vice versa.Vertical dashed lines indicate certain percentiles of Z r (i.e., 30th-70th) in the studied reach, and their roles of separating channel threads from bars are also shown in panel (d) and Figure 5.(d) Profile of Z r along the cross-section at x = 18 m indicated in panel (b).The channel thread in the cross-section view is defined as the part below a certain percentile of Z r , with larger values corresponding to wider channel threads.

Figure 5 .
Figure5.Binary masks created using different values of the threshold for residual elevation (Z r,t ) to map channel threads (i.e., 30th-70th percentiles of Z r ) in Reach 3 (see FigureS1in Supporting Information S1 for location) at t = 5 hr.From bottom to top, the area of individual channel threads increases as the binarization threshold value increases, indicating a transition from underestimation to overestimation of the channel thread extent.To account for ambiguity in the threshold choice, we incorporate representation with a Z r,t of 40%-60% in the analysis of channel thread migration using particle image velocimetry.

Figure 6 .
Figure 6.(a, b) Binary mask separating channel threads (white) from bars (black) and surrounding areas outside the channel belt (black), using the 50th percentile of the residual elevation (Z r ) as the binarization threshold.(c, d) Binary masks after median filtering using a 10 × 10-pixel window.

Figure 7 .
Figure 7. Unfiltered and filtered particle image velocimetry-derived vector fields for Reach 3 of Run 1 during t = 4-5 hr.The base image for (b-e) is a binary mask of channel threads.(a) A definition sketch for vectors and swaths in panels (b-e).The length of the vector represents the mean vector magnitude (M μ ), while the pointing direction of the vector represents the mean vector direction (M σ ).The upper and lower limits of the swath indicate the deviation from the mean vector magnitude (i.e., M μ + M σ and M μ M σ ).The opening of the swath is twice the standard deviation in direction (2θ σ ) centered at the mean vector direction (θ μ ).(b, c) Unfiltered vector fields include vectors with high uncertainty in magnitude and direction (circled) and vectors with small magnitudes (<1 pixel).(d, e) Filtered vector fields, after removing vectors with high uncertainties.It is important to note that the red circles illustrate a selection of removed vectors as examples; they do not encompass all instances.

Figure 8 .
Figure 8. Sketches illustrating the definition of migration rates in this study.(a) A reach where only a few places are migrating quickly.The length of the vectors indicates the rate of migration.(b) A reach that is slowly migrating everywhere.(c)Parameters used in defining the bank-integrated migration rate (M p ). M is the particle image velocimetry (PIV)-derived migration rate defined in the above text, U is the mobile perimeter, L is the along-stream distance of the reach analyzed, N is the number of vectors that exceed 1 pixel/frame, and Δx is the grid spacing that approximates the length of the bank associated with each PIV vector.Panel (c) is modified based onChadwick, Steel, Passalacqua, and Paola (2022).

Figure 9 .
Figure 9. Evaluation of particle image velocimetry (PIV)-derived vectors during t = 4-5 hr in Reach 3 of Run 1.(a) Extracted channel threads at t = 4 hr (black) and t = 5 hr (transparent green).The inset shows an example where PIV-derived vectors are incorrect due to the displacement of the channel thread exceeding its width.(b) A Digital elevation model of difference that shows the elevation change (ΔZ) from t = 4-5 hr.Adjacent areas of red (elevation increase) and blue (elevation decrease) correspond to elevation change caused by migration of channel threads.In general, red color corresponds to channel thread disappearance in a region, while blue color corresponds to channel thread appearance.(c) PIV-derived vectors for t = 4-5 hr.The lengths of the vectors are exaggerated compared to those in Figure 7, and the swaths indicating uncertainty are excluded for clarity.(d) Profiles of elevation at t = 4 hr (black curve) and t = 5 hr (green curve), measured at a downstream distance at x = 16 m as indicated in panels (a-c).Vertical black and green lines indicate the edges of channel threads defined by the 50th percentile of the residual elevation (Z r ) as the threshold value.The black arrows indicate example riverbank displacements of a channel thread that are detected by PIV (see corresponding vectors in panel (c)).(e) Profile of ΔZ during t = 4-5 hr, where colors indicate elevation increase (red; equivalent to channel thread disappearance) and decrease (blue; equivalent to channel thread appearance) as in panel (b).Black rectangles in panels (a-c) indicate areas where channel thread displacement is too large for PIV to derive the correct vectors (see inset of panel (a)).

Figure 10 .
Figure 10.Spatiotemporal variation of the length-adjusted bank-integrated migration rate (M p ) during t = 1-22 hr.(a) Space-time plot of the moving average of M p using a window width of 0.05 m.The vertical indicates the starting time for each observation interval, with Δt = 1 hr for the interval from 1 to 18 hr and Δt = 2 hr for the interval from 18 to 22 hr.(b) Downstream variation of M p measured over different sizes of moving windows (i.e., 0.05, 1, and 5 m) during t = 4-5 hr.(c) Binary mask separating channel threads (white) from bars and surrounding areas outside the channel belt (black), using the median value of the residual elevation (Z r ) as the binarization threshold for the whole basin at t = 4 hr.(d) Particle image velocimetry-derived vector fields on the base map shown in panel (c).(e) Cumulative probability distribution of M p averaged over a moving window of 30 m during different time frames.(f) Temporal variation of median M p averaged over a moving window of 30 m. Labels indicate the occurrence of each phase of planform change, including incipient meandering, transitional braiding, and established braiding.Panels (a-d) share the same horizontal axis extent that corresponds to a downstream distance of 5-35 m.

Figure 11 .
Figure 11.Power spectrum analysis of the spatial series of bank-integrated migration rate (M p ) averaged over a moving window of 0.05 m.(a) Power spectrum of M p during the time interval t = 4-5 hr.Only peaks with confidence levels higher than 99% are regarded as reliable.(b) Time series of the longest-wavelength peak in the power spectrum of M p during the time interval from t = 1-10 hr.

Figure 12 .
Figure 12.Measurements related to channel thread migration in Reach 3 during the time interval t = 1-22 hr.(a) Temporal variation of the spatially averaged migration rate (M).The horizontal, dashed line indicates the mobility threshold of 1 pixel/ frame (e.g., 2 mm/hr).(b) Temporal variation of the normalized mobility perimeter (P, Equation3).(c) Temporal variation of the normalized bank-integrated migration rate (M p ).As in Figure10f, the text labels indicate stages of planform development of the channel belt.

Figure 13 .
Figure 13.Migration direction of channel threads over 22 hr.(a) The proportion of lateral migration vectors for Reach 3 during the same time interval.As in Figure 10f, the text labels indicate stages of planform development of the channel belt.(b) The rose diagram of all migration vectors for Reach 3 over 22 hr indicates primarily lateral migration (within ±45°perpendicular to the basin axis direction; Figure1) rather than streamwise migration (within ±45°along the basin axis direction; Figure1).

Table 1
Parameters Used for Binary Image Preparation, PIVlab Analysis, and Migration Statistics WANG ET AL.