Characterizing Erosion and Deposition in and Around Riparian Vegetation Patches: Complex Flow Hydraulics, Sediment Supply, and Morphodynamic Feedbacks

Riparian vegetation plays a fundamental role in alluvial channel evolution by modifying flow and sedimentation dynamics. To elucidate the roles of sediment supply, flow‐dependent transport capacity, and morphodynamic feedbacks on the evolution of emergent vegetation patches over a single hydrograph, we conducted two experiments with different reach‐scale sediment supplies: a high‐supply experiment (HSE) and low‐supply experiment (LSE). We measured flow velocities, bedload transport, and topographic changes around a full‐scale patch of live emergent willows in an outdoor laboratory flume. Erosion occurred in the patch‐adjacent channel areas irrespective of the sediment supply, whereas deposition within the patch interior was suppressed in the LSE and enhanced in the HSE. The magnitude of patch deposition in each experiment was controlled by the local sediment supply to the patch and local sediment mobility during each discharge in the hydrograph. The local sediment supply was affected by bed morphodynamics at the patch head, which modulated the reach‐scale sediment supply by redistributing the bedload in the channel. Sediment mobility within the patch was flow‐dependent and a function of velocity and turbulent kinetic energy. For different discharges, the velocity in the patch changed proportionally with the freestream velocity; however, the turbulent kinetic energy was more sensitive, being elevated compared with the freestream during high flows and inhibited at low flows. Therefore, deposition and erosion within vegetation patches are not simply functions of the reach‐scale sediment supply or patch flow characteristics, as is often assumed, but additionally depend on the local sediment supply to the patch interior.

Further uncertainty regarding patch-scale sediment dynamics occurs because many vegetation experiments are performed under steady-flow conditions (e.g., Follett & Nepf, 2012;Kim et al., 2015;Lightbody et al., 2019;Liu et al., 2022;Shan et al., 2020), which neglects the potential for erosion versus deposition at various locations around a patch during different flow conditions (e.g., Cotton et al., 2006;Vesipa et al., 2017).Recent vegetation experiments incorporating both bedload dynamics and sequences of unsteady flows in a small flume indicate that depositional and erosional areas varied around vegetation patches and depended on the flow magnitude, bed composition, and patch density (Waters & Curran, 2016).Consequently, an explanation is lacking for what controls deposition and erosion around vegetation patches, which ultimately affects the temporal persistence of vegetated morphologic features in the landscape such as bars and islands (e.g., Guo et al., 2023;Gurnell et al., 2019;Osterkamp, 1998;Tranmer et al., 2018).
The role of sediment supply in streambed evolution around discrete vegetation patches has also not been fully documented.In an experimental channel, Lightbody et al. (2019) observed that discontinuing the reach-scale sediment supply limited deposition and reduced the overall topographic variation of a vegetated bar.This was supported by smaller flume experiments showing that the influence of vegetation on morphologic changes is diminished when the sediment supply is less than the transport capacity (Diehl, Wilcox, et al., 2017;Manners et al., 2015).Alternatively, field-scale results are limited, as field studies often have incomplete sediment supply data (e.g., Gaeuman et al., 2005;Gran et al., 2015) and therefore cannot easily address the spatial evolution of vegetation patches relative to sediment supply.
To address these knowledge gaps, we conducted two field-scale laboratory experiments subjecting the same patch of mature live willows to high and low reach-scale sediment supplies.Similar to bed changes over a hydrograph in natural rivers, these experiments were not intended to represent equilibrium conditions.Instead, they simulate the peak and falling limb of a flood regime to examine bedload dynamics and resultant channel evolution around a vegetation patch on the timescale of a single hydrograph.The unidirectional flow experiments characterize riparian vegetation-sediment interactions in and around emergent vegetation patches growing in floodplains, deltas, as well as secondary and ephemeral channels that are exposed to sediment transport during a flood hydrograph.Specifically, we sought to (a) evaluate the influence of flow hydrographs and reach-scale sediment supply on topographic changes in and around a real riparian vegetation patch, (b) identify potential feedbacks between flow and bed morphodynamics that can alter how the reach-scale sediment supply is distributed in and around the patch, and (c) mechanistically explain patch-scale deposition and erosion using quantitative metrics of transport capacity and local sediment supply.

Experiment Setup
We performed two hydrograph experiments in a straight trapezoidal test section of an outdoor flume (150 m long, 4.5 m base width) at the Korea Institute of Civil Engineering and Building Technology-River Experiment Center (Figure 1a).The flume banks had side slopes of 1:1.5 (V:H) and were covered in mowed, native perennial grasses (Figure S1 in Supporting Information S1).The bed was constructed with 50 cm of a sand-gravel mixture that was overlaid with an additional 50 cm of sand that was screeded flat before each experiment.The median grain size (D 50 ) of the sand was 1.0 mm, which was mobile in the unvegetated section during each discharge.The bed was longitudinally divided into four sections (supply, slug, freestream, and study) (Figure 1a).The study section was 15 m long and extended approximately two patch lengths upstream of a riparian willow patch to capture any potential morphologic bed changes near the vegetation.A portion of the study section near the patch was subdivided into five smaller zones: the patch head, patch interior, patch wake, and adjacent main and side channels (Figure 1a).Individual zones were determined by their location relative to the vegetation patch and the maximum spatial extent of the morphologic bed responses in either experiment.
The rectangular vegetation patch (3.99 m long, 1.5 m wide) was planted directly in the flume bed and grown for 3 years prior to the experiments.The centerline of the patch was located 1/3 of the way across the channel and the ratio of the patch to channel base width was 1/3 (1.5/4.5 m).The patch consisted of 89 willows (Salix subfragilis) with an average plant height of 1.31 m and stem and branch densities of n s = 14.9/m 2 and n b = 110.9/m 2 , respectively.Willow morphology has a vertical gradient of vegetation density, with higher branch density near the top of the plants.Average stem (d s = 26.09mm) and branch (d b = 10.32 mm) diameters provided φ values of 0.0079 and 0.0093, respectively.However, given the range of relative plant submergence, we used a composite stem solid volume fraction of φ = 0.0086.The patch maintained emergent conditions throughout each experiment with relative submergence values ranging from 0.55 to 0.91.

Sediment Supply and Flow Hydrographs
The two stepwise flow experiments (Figure 1b) were subjected to different reach-scale sediment supplies, a high-supply experiment (HSE) and low-supply experiment (LSE).Owing to the difficulties in feeding sediment in a field-scale laboratory flume, the reach-scale sediment supply was provided by a sand pile in the upstream supply section that was allowed to freely erode over the hydrograph (Figure S1 in Supporting Information S1).
The HSE and LSE had identical initial bed and sediment conditions except for the supply pile that was approximately 20 cm higher in the HSE than the LSE.The sediment supply piles were oversupplied to ensure that no supply limitation occurred in either hydrograph, with initial volumes of 23.9 m 3 (HSE) and 21.8 m 3 (LSE).In each experiment, the supply pile partially eroded and advanced downstream as a sediment slug into a 35 m-long slug section before stabilizing into a 30 m-long freestream section that was not impacted by the vegetation patch.
Before and after each hydrograph, the entire bed was scanned (all sections and zones) using a Riegl LMS-Z390i laser scanner.The vegetation was removed from the 3D point clouds using geoprocessing software (CloudCompare 2.12.4,Telecom ParisTech and 3D Point Cloud Editing Tools (KICT, 2023)) and the point clouds of the channel bed were converted to digital elevation models (DEMs) with a constant cell size of 0.085 m using a nearest neighbor interpolation scheme.The cut-fill tool in GIS was used to compute the total volume of sediment deposited or eroded from each section in an experiment.The reach-scale sediment supply was defined as the total sediment flux supplied to the study section over the hydrograph and calculated by summing the cut-fill volumes in the supply, slug, and freestream sections.The total reach-scale sediment supply was 3.6 times greater in the HSE (14.9 m 3 ) than during the LSE (4.1 m 3 ).
The difference in reach-scale sediment supply between experiments was driven by the height of the supply pile and by changing the flow hydrographs between experiments.During each discharge, reach-scale water surface 10.1029/2023WR034859 5 of 21 slopes were monitored upstream and downstream of the vegetation patch with a total station over a distance of 80 m.The higher supply pile height in the HSE increased the reach-scale water surface slope (Figure 1c) and caused greater supply pile erosion and, therefore, higher reach-scale sediment supply.To further ensure a higher supply during the HSE, the magnitude and duration of the HSE hydrograph were scaled to have 100% greater total transport capacity than the LSE based on the Engelund and Hansen (1967) transport relation.In each experiment, the bed was initially wetted with a nominal flow and the discharge was slowly ramped up over 3 hours to prevent a sudden change in the initial bed conditions.The two experiments had identical peak flows that were incrementally reduced in a series of constant discharges to simulate hydrograph falling limbs (Figure 1b).The discharge was controlled by pumps with established rating curves located 400 m upstream of the patch in the reservoir section of the flume (Berends et al., 2020).The HSE and LSE hydrographs were run for 41 and 49.7 hr, respectively, with each discharge lasting at least 8 hr.

Bed Elevation, Flow, and Bedload Measurements
The morphologic bed change in a given experiment was examined by differencing the pre-and post-experiment DEMs using the raster calculator in GIS to create DEMs of difference (DoD) for each individual section and zone (Figure 1a).The vertical accuracy of the laser scanner was 6 mm, and the composite vertical accuracy in each DoD was calculated as where ε b and ε a = vertical accuracies of the DEM (mm) before and after the experiment, respectively (e.g., James et al., 2012;Waters & Curran, 2016).The resultant ε DoD ≤ 8.4 mm defined the threshold for the minimum significant geomorphic change.We compared median bed elevation change in each zone to that in the freestream to examine how vegetation affects nonequilibrium change over a hydrograph relative to the unvegetated conditions.Median bed elevation changes in each section and zone were assessed using non-parametric Mann-Whitney tests (α = 0.05).Topographic variation within each section and zone was assessed using the final bed elevation variance in each experiment.Differences in bed variance in each section and zone between experiments were evaluated using one-tailed F tests (α = 0.05).
During each discharge, we measured flow velocities and bedload transport rates from mobile bridges.We began sampling approximately 5 hr after each change in discharge (Figure 1b) to provide sufficient time for the bed and hydraulics to respond to the new discharge and reach-scale sediment supply but retain nonequilibrium conditions in the patch-scale zones, which allowed us to monitor spatial changes in local sediment transport through the individual zones over the hydrograph.We performed 7-10 Acoustic Doppler Velocimeter (ADV) vertical profiles (circles in Figure 1a) in cross-sections located 4 m upstream of the vegetation patch (D 0 ), through the midsection of the patch (D 2 ) and 2 m downstream of the patch (D 4 ).No ADV measurements were performed through the patch head (D 1 ).The raw ADV data were filtered by discarding values with signal-to-noise ratio and correlation lower than 15 dB and 70%, respectively.In each vertical profile, we used the closest ADV measurement to the bed that converged to a stable velocity during the sampling period using a modified Z-score.The modified Z-score was calculated as Z = 0.6745(u i − u)/MAD (U), where u i are individual velocity measurements, u is the mean measured velocity, and MAD (U) is the median absolute deviation for U = {u 1 ,u 2 , ⋯,u n } as MAD (U) = Med {|U−Med (U)|} (Bae & Ji, 2019).Velocities with values of Z < 5 were marked as outliers and eliminated during the sampling period.Because dunes were present in the freestream at D 0 , the closest consistent measurements we could obtain near the bed for all discharges were at a relative flow depth (z/h) of 0.25.Therefore, we used the velocity measurements at similar relative flow depths in cross sections D 2 (z/h = 0.2) and D 4 (z/h = 0.25), which did not have bedforms.We measured flow at cross-section D 2 using a Sontek microADV (50 Hz, 120 s) and cross sections D 0 and D 4 using a Nortek Vectrino ADV (25 Hz, 60 s).The ADV measured streamwise, lateral, and vertical velocities were decomposed into mean (u, v, w) and fluctuating (u′,v′,w′) velocity components to calculate the turbulent kinetic energy as   = 0.5 where the overbar indicates time-averaged values.The depths from ADV measurements were used to compute the local water surface slope over a distance of 10 m through the study section (Figure 1d).
For each discharge, the spatial median (denoted by angular brackets) near-bed hydraulic variables were calculated for each zone (D 2 and D 4 ) and were normalized by the respective median near-bed freestream conditions (D 0 ) (e.g.,  ⟨   0

⟩
) in the patch, wake, main and side channels).As the measurements at D 2 (z/h = 0.2) were normalized using those at D 0 (z/h = 0.25), the reported variables in the patch and adjacent channels may have a slight bias.
Linear regression identified relations between the discharge and spatial medians of the normalized hydraulic variables in each zone.Regression slopes were compared using t tests (α = 0.05) to assess the differences between experiments in each zone.
Bedload measurements were performed at 5-6 locations within three cross-sections (diamonds in Figure 1a) located 4 m upstream of the vegetation patch (D 0 ), across the upstream head of the vegetation patch (D 1 ), and across the downstream end of the vegetation patch (D 3 ).Bedload cross-sections were selected to capture the sediment fluxes entering and exiting the patch and adjacent channels, whereas velocity measurements targeted the average patch, channel, and wake conditions.Bedload measurements used a mini bedload sampler with a 21.6 cm 2 orifice and were collected for 2-4 min at each sampling location depending on the discharge.Dried samples were sieved at half-phi intervals and weighed in the laboratory.In comparison to the reach-scale sediment supply, the local sediment supply in each experiment was defined as the median measured bedload transport rate entering a zone for a given discharge.To estimate the relative magnitude of deposition or erosion within the patch, main channel, and side channel for each discharge in the hydrograph, we used a mass-balance approach to calculate the ratio of the unit bedload transport rate exiting the downstream boundary to that entering the upstream boundary ( ) of each zone.The bedload measurement locations prevented us from using this approach in the patch head or wake zones.

Sediment Mobility Calculations
To help evaluate hydraulic conditions that influence the sediment mass balance results, we used co-located ADV and bedload measurements at D 0 (freestream) from the two combined experiments to calculate the dimensionless critical velocity (   * cr ) using the reference transport approach.Dimensionless velocity (u*) and unit bedload transport rate (q s *) were calculated as , where q s = unit bedload transport rate (m 2 /s), ρ s and ρ = density of sediment and water (kg/m 3 ), respectively, and g = gravitational acceleration (m/s 2 ).Values of q s * were plotted against u* and the onset of sediment transport (   * cr ) was determined for the reference value of q s * = 1 × 10 −4 using the methodology of Shvidchenko et al. (2001).To evaluate sediment mobility in the vegetation patch,   * cr was converted to u cr and adjusted for the influence of stem-generated turbulence using the relation of J. Q.Yang et al. (2016) as . Here C = 0.9*C D 2/3 /C b , where C D is the stem drag coefficient (C D ∼ 1).The bed roughness coefficient (C b = k t /   2 ℎ ) was calculated using the cross-sectional average of the near-bed turbulent kinetic energy (k t ) and depth-averaged velocity (u h ) in the freestream.Computed values of u cr and u crv were 0.32 and 0.26 m/s, respectively.
To estimate sediment mobility in each zone for a given discharge, we determined the ratio of the measured dimensionless near-bed velocity (u*) to the calculated critical velocity (   * cr ).Hereafter,   * cr represents the critical velocity in the unvegetated zones and turbulence-corrected critical velocity within the patch.Similar to the other near-bed hydraulic variables, we used the spatial median of these ratios in each zone to compute an index of mobility (

Flow Changes Over the Hydrograph
In the study section, the patch partially backwatered the flow and locally steepened the water surface slope with similar values in each experiment for a given discharge (Figure 1d).Similar water surface slopes resulted in the flow field in each zone (freestream, patch, wake, main and side channels) responding similarly to reductions in discharge during the falling limb in both hydrographs (Figure 2).The median near-bed normalized streamwise velocity (  ⟨   0

⟩
) and turbulent kinetic energy ) had linear responses to discharge in each zone, and no significant differences between linear regression slopes were evident between the HSE and LSE for a given parameter (p = 0.11-0.96).Therefore, a single linear regression between a given hydraulic parameter and discharge was applied in each zone using the combined data from both experiments, and subsequent reported p values are for the slope of these regressions.).
In the freestream, 〈u 0 〉 and 〈k t0 〉 decreased linearly (p < 0.001) as the discharge was reduced and served as baselines to evaluate the responses of each zone to changes in discharge (Figure 2a).In each hydrograph, the velocity in the main channel remained elevated above the freestream (  ⟨   0

⟩
< 1) within the patch and wake zones (Figure 2b).In each zone except the side channel,  ⟨   0

⟩
was insensitive to changes in discharge (p = 0.24-0.60),indicating that velocity in each zone changed proportionally with the freestream velocity over the hydrograph.2d), indicating that sediment mobility decreased over each hydrograph.

Freestream and Study Sections
In both experiments, the final bed slope over 51 m in the freestream and study sections was within 1% for the HSE and LSE (S = 0.0011).DEM differencing showed that the initial plane bed in the freestream section responded to an influx of sediment via bedform formation and slight deposition (Figure 3a).No significant differences were observed in the freestream median bed change between the experiments (p = 0.48), with median bed deposition of 0.011 m in the HSE and 0.012 m in the LSE (Figure 3b).In contrast to the deposition in the freestream section, the vegetation patch suppressed bedform formation and altered the study section to a net erosional condition (Figure 3a), with median bed elevation change of −0.013 and −0.030 m in the HSE and LSE, respectively (Figure 3b).The greater reach-scale sediment supply in the HSE resulted in lower erosion depths and increased topographic variability within the study section, with 24% higher bed elevation variance in the HSE than in the LSE (p < 0.001).

Patch Head
Within the patch head, we did not have the velocity or sediment transport measurements necessary to evaluate and   _exit  _enter through the zone; therefore, only the morphologic changes and distribution of q s_enter are reported.In the LSE, median bed erosion of −0.0065 m (below the threshold of change) occurred in the patch head at the end of the experiment (Figure 3b), which increased the magnitude of the median bed elevation change by 154% relative to the freestream (p < 0.001).In contrast, median deposition of 0.06 m occurred in the patch head at the end of the HSE, a 432% increase in the median bed elevation change compared with the freestream (p < 0.001).This difference resulted from a depositional sediment mound with a maximum height of 0.12 m that formed in the patch head during the HSE (Figure 4a).The patch head experienced the largest difference in bed elevation response between the two experiments, indicating that it was the most sensitive zone to reach-scale sediment supply.
In the HSE, we visually observed that the depositional mound formed in the patch head during the two highest discharges of the hydrograph and persisted throughout the rest of the experiment (Figure 4b).As the mound was forming during the two highest discharges, an initially high q s_enter entered the patch but q s_enter was reduced to nearly zero in the lowest two discharges in the hydrograph (Figure 4c) because the mound limited the bedload entering the patch interior and diverted it into the main channel.The influence of the mound is evident when 10.1029/2023WR034859 9 of 21 comparing the percentages of the total bedload flux through the D 1 cross-section that entered the patch and main channel (Figure 4d).In the HSE, the highest percentage of bedload flux (15%) entered the vegetation patch during peak flow but diminished to 0.1% as the discharge decreased, whereas the percentage of bedload entering the main channel increased from 85% to ∼100%.In contrast, no mound formed at the patch head in the LSE and the percentage of the total bedload flux in D 1 entering the patch interior increased from 5% to 40% over the falling limb of the hydrograph, with a corresponding decrease from 95% to 60% entering the main channel.The percentage of total bedload flux that entered the side channel was <0.2% for every flow in each experiment, effectively limiting the local sediment supply over the entire hydrograph.The different morphologic changes that occurred in the patch head between experiments modulated the reach-scale sediment supply by spatially redistributing the bedload transport within the channel and affecting the local sediment supply to individual zones.

Patch Interior
Within the patch,  ⟨ was less than that in the freestream throughout both hydrographs, indicating the patch sediment transport capacity was less than the freestream transport capacity and deposition would occur during all flows (Figure 2d).However, continuous deposition did not occur in either experiment because the patch head  In particular, q s_enter was 7.2 × 10 −6 and 2.7 × 10 −6 m 2 /s during the two highest discharges in the HSE, which was approximately seven and two times greater than the q s_enter for similar flows in the LSE (Figure 4c).The high local sediment supply in the HSE likely exceeded the transport capacity within the patch, resulting in measured deposition (   _exit  _enter < 1) for the two high discharges (Figure 4e).After mound formation at the patch head, q s_enter was reduced to near zero during the two lowest flows of the HSE, which was lower than q s_enter during similar flows in the LSE.This resulted in erosion (   _exit  _enter > 1) during the lowest two HSE discharges because the patch transport capacity exceeded the near-zero local sediment supply.The combination of deposition during the two high flows and erosion during the two low flows resulted in a measured median deposition of 0.037 m in the patch at the end of the HSE (Figure 3b).
Ultimately, median bed deposition within the patch interior was enhanced above that in the freestream by 226% at the end of the HSE (p < 0.001) but was 58% lower than that in the freestream at the end of the LSE (p < 0.001), making the patch interior the second most sensitive zone to sediment supply.The resultant topographic variation in the patch interior increased with greater reach-scale sediment supply, with 62.7% greater bed elevation variance in the HSE than in the LSE (p < 0.001).

Patch Wake
We did not have bedload measurements downstream of the wake zone to calculate   _exit  _enter ; therefore, bed changes in the patch wake during the hydrographs were monitored using bed elevation measurements performed with the bedload sampling rod 1 m downstream of the patch boundary (Figure 4f).These measurements indicate that a depositional mound formed rapidly in the wake zone during high flows, and the rates of deposition were reduced to varying degrees as discharge diminished in each hydrograph.At the end of the experiments, the cumulative median wake deposition in the HSE and LSE were 0.059 and 0.034 m, respectively (Figure 3b).Deposition in the patch wake was enhanced relative to that in the freestream in both experiments (p < 0.001), increasing the median bed elevation change by 422% (HSE) and 180% (LSE).This difference in median bed elevation change between experiments indicates that the patch wake was less sensitive to differences in sediment supply than the patch head and interior.The topographic variance in the wake zone was only 12.4% greater in the HSE than in the LSE.
During the three highest LSE flows,  ⟨  *  * cr ⟩ decreased from the patch to the wake indicating that sediment supply from the patch could exceed the transport capacity of the wake to cause sediment deposition and wake mound growth (Figure 4f).In the two lowest LSE discharges, the wake mound remained stable because the transport capacity was

Main and Side Channels
The overall erosional condition of the study section in both experiments was driven by scour in the main and side channels (Figures 3a and 3b).In the main channel, sediment was mobile ( > 1 for all discharges in both hydrographs (Figure 5a).Consequently, the median bed elevation in the main channel at the end of the experiments decreased by −0.045 m in the HSE and −0.065 m in the LSE (Figure 3b).Relative to the freestream, erosion caused the magnitude of the change in the median bed elevation to increase in the main channel by 496% in the HSE and 640% in the LSE (p < 0.001).Owing to greater erosion in the LSE, the bed of the main channel became flatter and the bed elevation variance was 26.5% lower in the LSE than in the HSE (p < 0.001).
Greater scour occurred in the LSE because measured q s_enter to the main channel was approximately half of that in the HSE over the hydrograph (Figure 5b).The HSE had a higher q s_enter than the LSE, partly because its greater overall reach-scale sediment supply was locally increased by the mound in the patch head routing bedload around the patch and into the main channel (Figure 4d).In the LSE, no mound formed in the patch head, which enabled a greater percentage of the already low reach-scale sediment supply to enter the patch interior.Thus, limiting the local upstream sediment supply to the main channel.Consequently, the LSE often had a greater   _exit  _enter than the HSE for a given discharge (Figure 5a), which implies greater bed erosion during each discharge and corresponded to the larger total erosion depths measured at the end of the LSE.
Bedload transport was active in the side channel ( ∼ 1 (Figure 5c).Laser scans at the end of each experiment confirmed the calculated erosion during both hydrographs, with the median bed elevation decreasing by −0.026 m in the HSE and −0.034 m in the LSE (Figure 3b).This cumulative erosion enhanced the magnitude of the median bed elevation change in the side channel by 328% (HSE) and 384% (LSE) relative to the freestream (p < 0.001).
The measured q s_enter into the side channel ranged from 1.7 × 10 −11 to 8.1 × 10 −8 (Figure 5d), one to two orders of magnitude less than that in the freestream, and constituted only a small percentage of the total cross-sectional sediment flux (<0.2%) throughout both experiments.Because the local sediment supply was limited to the side channel and the flow hydraulics were similar during both hydrographs, the median bed elevation change was also similar between experiments.This sediment disconnectivity caused the side channel to be the least sensitive zone in the entire study section to differences in reach-scale sediment supply.Similar to the main channel, greater erosion in the side channel during the LSE led to 50.9% lower variance in bed elevation than in the HSE (p < 0.001).

Importance of Flow-Dependent Changes in Velocity and Turbulence in and Around Vegetation Patches
While the reach-scale water surface slopes differed between experiments to generate different sediment supplies, the patch-scale water surface slope and hydraulics responded similarly over the two hydrographs.This indicates that the flow conditions in and around the vegetation patch were primarily a function of vegetation characteristics rather than reach-scale conditions or bed morphology (e.g., Diehl, Wilcox, et al., 2017;Etminan et al., 2018;Ji et al., 2023;Västilä & Järvelä, 2018), at least at the scale of the morphologic changes observed in this study.In both experiments, streamwise velocity within the vegetation patch was reduced to 60%-75% of that in the freestream owing to increased vegetative roughness, while flow constriction in the adjacent main channel increased the velocity by approximately 5%-20% (Figure 2b), which agreed with previous research on sparse uniform vegetation in open channels (e.g., Caroppi et al., 2022;Kim et al., 2015;Lightbody et al., 2019;Valyrakis et al., 2021).Interestingly, the side channel had reduced flow velocities compared with the freestream, which contrasts with previous observations of flow acceleration (  ⟨   0

⟩
> 1) in the gap between narrowly spaced dense patches (e.g., Meire et al., 2014;Vandenbruwaene et al., 2011).Drawing an analogy between a gap between patches and our side channel (a gap between patch and flume sidewall), we speculate that if our vegetation patch had been as dense as in those previous studies (φ > 0.03), more flow would have been routed around the patch.This would have resulted in acceleration (  ⟨   0

⟩
> 1) in the side channel during higher flows, similar to the numerical results of Bywater-Reyes et al. (2018).Our sparse-patch results indicate that flow acceleration between riparian vegetation patches may not only be a function of patch and gap widths (e.g., Vandenbruwaene et al., 2011), but must also account for patch density (e.g., Bouma et al., 2009;Meire et al., 2014).

⟩
was relatively insensitive to discharge in all zones except the side channel.

⟩
in the channel between two vegetation patches decreased from ∼1.27 to ∼1 as the incoming discharge was reduced (calculated from their Figure 10).This further suggests that the flow acceleration in the channel between two porous obstacles should account for patch density, patch and gap widths, as well as the magnitude of the incoming flow.
Riparian vegetation also affected turbulent kinetic energy in zones near the patch.The values of  ⟨

𝑘𝑘 𝑡𝑡 𝑘𝑘 𝑡𝑡0
⟩ within the wake had the lowest magnitude in any zone, confirming the downstream sheltering effect of a full-scale willow patch, despite having a different plant size and morphology than other laboratory studies (e.g., Chen et al., 2012;Elliott et al., 2019;Shi et al., 2016).The main and side channels also exhibited  ⟨

𝑘𝑘 𝑡𝑡 𝑘𝑘 𝑡𝑡0
⟩ < 1, indicating the presence of the patch reduced the near-bed turbulence in the adjacent channels to below that in the freestream (Figure 2c).While a localized peak was observed in the turbulent kinetic energy along the boundary shear layer of the patch margin, similar to that observed in other studies (e.g., Caroppi et al., 2021;Zong & Nepf, 2010), it had a limited spatial extent and did not affect ⟩ values in both of our experiments, which occurred regardless of the reach-scale sediment supply, also likely resulted from the limited bedforms in the erosive main and side channels (Figure 3a).

Further, 𝐴𝐴 ⟨ 𝑘𝑘 𝑡𝑡 𝑘𝑘 𝑡𝑡0
⟩ was sensitive to discharge in all zones (Figure 2c), indicating the near-bed turbulence decreased with discharge in these locations than in the freestream.J. Q.Yang et al. (2016) demonstrated that k t through sparse emergent vegetation can be expressed as the sum of bed-induced turbulence (k tb ) and vegetation-induced turbulence (k tv ), where 2 ∕3  2 .In the simple case of unvegetated zones with a plane sandbed,  ⟨ ⟩ is the ratio of the bed drag coefficients of the zone relative to the freestream ( ∼ constant over the hydrograph.We expect that C bfree increases with the smaller bedform submergence present at low discharges, whereas bzone is a function of the consistently high relative grain submergence and remains relatively stable with discharge because of the lack of bedforms in the study section (e.g., van Rijn, 2006; S. Q. Yang et al., 2005).An exception was observed in the side channel, where  ⟨   0

⟩
was affected by the sidewall and was not constant over the hydrograph.Further research is required to explain the hydraulics in this complex zone.Within the patch, C D is principally a function of the stem Reynolds number and is nearly constant over a wide range of values (e.g., Liu & Nepf, 2016;Schlichting, 1982).Thus,  ⟨ in our experiments explains why some studies show that vegetation patches increase turbulence (e.g., Tang et al., 2019;Tinoco & Coco, 2016, 2018; J. Q.Yang & Nepf, 2018), whereas others show vegetation suppressing turbulence (e.g., Leonard & Luther, 1995;Pujol et al., 2013;Sand-Jensen & Pedersen, 1999).This flow dependence suggests that vegetation patches cannot be simply assumed to increase or decrease the near-bed turbulence intensities relative to the open channels that deliver sediment to them but must be evaluated over the range of flow conditions present at the site.Therefore, a better understanding of the mechanics of these discharge-dependent changes in k t is required to accurately predict bedload transport and sedimentation in vegetated fluvial and deltaic systems.

Mechanisms and Importance of Morphologic Changes in the Patch Head
Reach-scale sediment supply is a primary driver of sediment deposition within vegetation (e.g., Ganju et al., 2015;Lightbody et al., 2019;Zhang et al., 2020), but here we show that bed morphology in the patch head can modulate the reach-scale sediment supply by reducing or increasing local sediment connectivity to individual zones.In experiments and numerical models, deposition has been observed upstream of flume-spanning vegetation when the transport capacity through the vegetation is less than that supplied to the flume, thereby inducing channel slope adjustments (e.g., Caponi & Siviglia, 2018;Diehl, Wilcox, et al., 2017;Le Bouteiller & Venditti, 2014;Manners et al., 2015).Because vegetation generally does not span the entire width of fluvial channels, the depositional mechanisms observed in those experiments may differ from those observed in most rivers and deltaic channels.In comparison, laboratory experiments with discrete vegetation patches have found that depositional mounds can occasionally form immediately upstream of a patch, which has been attributed to localized flow deceleration and reduced transport capacity (e.g., Kim et al., 2015;Tsujimoto, 1999;van Dijk et al., 2013;Zong & Nepf, 2010).Our experiments show that the reach-scale bed slope is not necessarily affected by a discrete vegetation patch but that a mound formed only in the patch head during high reach-scale sediment supply, indicating that flow deceleration is not the only mechanism responsible for sediment deposition in the patch head.Furthermore, the depositional sediment mound in the patch head redistributed the reach-scale sediment supply by increasing the local sediment supply to the main channel and limiting it to the patch interior (Figure 4d), creating a morphologic control of equal importance to the reach-scale sediment supply for determining sediment storage within the patch.Thus, the formation of a mound in bedload dominated rivers may directly impact restoration efforts using riparian vegetation to trap sediment and build instream bars by limiting bar growth during flood events, even in high sediment supply channels.

Role of Sediment Supply and Flow-Dependent Transport Capacity in Patch Deposition
Our experiments demonstrated that reach-scale sediment supply, flow-dependent transport capacity, and morphologic changes in the patch head influence the sediment storage dynamics through a vegetation patch.In natural systems, any or all of these physical mechanisms may change over a single hydrograph.Therefore, predictions of sediment storage for a given vegetation patch may not scale as a function of only the reach-scale sediment supply or flow-dependent transport capacity owing to potential morphodynamic feedbacks that impact the local sediment supply.For example, considering only reach-scale sediment supply and ignoring the flow-dependent transport capacity and local sediment supply to a patch can lead to erroneous conclusions.A simple comparison between the final bed elevation changes in the patch and the reach-scale sediment supply in each experiment suggests that high reach-scale sediment supplies always cause patch deposition and low supplies limit deposition.However, both patch deposition and erosion occurred during each experiment because of changes in the flow-dependent transport capacity and the influence of the upstream bed morphology on the local sediment supply.If we had a longer moderate-flow duration in the HSE, similar to that of many snowmelt-dominated rivers, the sediment mound at the patch head would have continued to limit the local sediment supply into the patch.This would have resulted in greater erosion within the patch interior and possibly net erosional conditions later in the hydrograph despite the high reach-scale sediment supply.Therefore, interpretations of reach-scale sediment supply from long-term field measurements of patch deposition and erosion (e.g., Cordes et al., 1997;Rodríguez et al., 2019) may be complicated by the complex bed morphodynamics that occur under different flow conditions.
Alternatively, sediment mobility has often been used to explain deposition and erosion within vegetation (e.g., Liu & Nepf, 2016;van Oorschot et al., 2016;J. Q. Yang et al., 2016;Zong & Nepf, 2010).If only sediment mobility was considered and all sediment supply effects were disregarded in our experiments, deposition would be expected when > 1.In the LSE, measured erosion and deposition in the patch interior followed this expected pattern over the hydrograph (Figure 4e).However, ignoring sediment supply effects became problematic in the HSE, where erosion was expected throughout the experiment because Instead, the patch transitioned from depositional at high flows to erosional at low flows because of the feedbacks between the flow-dependent transport capacity (Figure 2d) and the mound-modulated local sediment supply (Figure 4c).These observed changes in patch deposition and erosion during a single experimental hydrograph can help explain the divergent results in the literature suggesting that vegetation patches enhance deposition (e.g., Cotton et al., 2006;van Dijk et al., 2013;Vargas-Luna et al., 2019;Västilä & Järvelä, 2018;Zong & Nepf, 2010), limit deposition (e.g., Bouma et al., 2007;Chen et al., 2012;Follett & Nepf, 2012;Kim et al., 2015;Rominger et al., 2010;Tinoco & Coco, 2014), or both under different forcing conditions (e.g., Bouma et al., 2009;Lightbody et al., 2019;Nardin et al., 2016;Olliver et al., 2020;Yager & Schmeeckle, 2013).
Ultimately, the occurrence of deposition or erosion within a patch results from complex interactions between the reach-scale sediment supply, flow-dependent transport capacity, and morphodynamic feedbacks that affect the local sediment supply.
In theory, the downstream change in using hydraulic models may be appropriate for identifying areas of erosion and deposition in vegetated channels if an appropriate grid size is selected to extract the necessary patch-scale boundary conditions.

Implications for Channel Evolution
As individual vegetated features often constitute the building blocks of larger landforms, their stability and persistence have consequences for the ultimate morphology, resilience, and evolutionary trajectory of alluvial systems (e.g., Guo et al., 2023;Gurnell et al., 2019;Piliouras & Kim, 2019).Our experiments demonstrated that vegetation patches with identical characteristics (e.g., patch density, plant rigidity, and leaf area) can either enhance or inhibit sediment storage over a single hydrograph, depending on the reach-scale sediment supply, flow-dependent transport capacity, and vegetation-induced morphologic feedbacks on local sediment supplies.We expect these factors to be similarly influential for the stability of vegetated bars (e.g., Corenblit et al., 2020;Gran et al., 2015;Larsen, 2019), but further research is required to understand how certain morphodynamic and flow conditions lead to erosion within vegetation patches during high reach-scale sediment supply as well as how the elevation gradient of a bar would impact these results (e.g., Bridge, 1992;Nelson et al., 2010).This is critical for modeling the evolution of vegetated bars because vegetation is currently treated as an enhanced roughness element that generally leads to internal sediment deposition and storage (e.g., Baptist et al., 2007;Olliver et al., 2020;Wright et al., 2018).
Further, most vegetation-sediment research has focused on suspended sediment dynamics and limited information is available on bedload transport through patch-scale vegetation, with few exceptions (e.g., Kim et al., 2015;Shan et al., 2020;Waters & Curran, 2016).Our results illustrate that the stable depositional environment downstream of the patch provided the greatest volumetric sediment storage per unit area and was the least sensitive depositional zone to reach-scale sediment supply, indicating that the wake zone provides a dependable depositional area in bedload dominated streams for habitat formation and geochemical cycling (e.g., Gurnell, 2014;Sand-Jensen & Pedersen, 1999;Shi et al., 2016).Therefore, particularly in sparse patches, wake zone deposition may principally be related to the stem arrangement and density of vegetation (e.g., Chen et al., 2012;Waters & Curran, 2016).
Even when subjected to different reach-scale sediment supplies, the resultant wake mound had a similar bed elevation as the patch interior with a difference in median bed elevations <0.01 m in both experiments.Given the similar bed elevations between the patch interior and downstream wake, we propose that wake deposition downstream of sparse riparian vegetation patches can grow to the same topographic elevation as the patch interior in bedload dominated streams.In our experiments this was achieved by bedload ramping, a process where sediment was transported from the streambed onto a higher bar surface via rolling and saltation (e.g., Carling et al., 2006;Church & Rice, 2009).Bedload ramping was visually observed during bedload measurements for all mobile flows, as evidenced by grains exiting the patch interior and rolling over the wake mound crest.Alternatively, experiments and simulations indicate that high suspended sediment concentrations may facilitate wake mound deposition that exceeds the elevation in the patch interior owing to the different mode of transport (e.g., Chen et al., 2012;Kim et al., 2018;Liu & Nepf, 2016).Therefore, rates of wake mound growth may depend on the type of sediment and transport processes that exist in the system.Consequently, river restoration intended to maintain persistent vegetated bars in rivers and deltas must account for both reach-scale sediment supply and type of sediment transport to understand the potential evolutionary trajectories of vegetated bars during flood conditions.
Our experiments evaluated channel changes over a single hydrograph but would have benefited from replicate runs to reproduce the observed responses.Previous experiments using sequences of hydrographs to represent multiple flood events show variable bed responses around vegetation, which depended on how long the channel takes to respond to the given sediment supply, bed grain size distribution, and flow regime (Waters & Curran, 2016).Therefore, the future stability of the vegetation patch and surrounding channel is uncertain with respect to subsequent hydrographs and likely depends on the magnitude of flows, continued local sediment supply, and further colonization of stabilizing vegetation over time (e.g., Corenblit et al., 2016;Gurnell et al., 2012;Tranmer et al., 2020).
Additionally, the cumulative erosion in the main and side channels was responsible for changing the channel from a depositional bed in the freestream section to a net erosive bed in the study section (Figure 3b).Therefore, vegetation patches can locally store sediment but their presence can increase the patch-adjacent sediment transport capacity that results in overall bed erosion during high flows, even with a high reach-scale sediment supply.Previous observations have identified increased velocities and enhanced scour in channels adjacent to vegetation because of convective acceleration and flow constriction (e.g., Schwarz et al., 2014;Temmerman et al., 2007;Vargas-Luna et al., 2018), but our study quantified the magnitude of bed changes relative to the reach-scale and local sediment supply over a single hydrograph.Our results show that greater reach-scale sediment supply mitigated the magnitude of net bed erosion that occurred within the study section.This is important because riparian plantings are commonly used in river and floodplain restoration projects to reduce velocities and stabilize morphologic features (e.g., Gonzalez et al., 2018;Neary et al., 2012;Tranmer, Caamano, et al., 2022).Because greater channel erosion occurred during the LSE than during the HSE, this suggests stream restoration activities that introduce vegetation plantings in low-supply watersheds can potentially result in unintended erosion around vegetated features, particularly when recently manipulated streambanks and structures are sensitive to disturbance.It should be noted that our experiments had a limited grain size distribution and other complex bed responses like channel coarsening and armoring may limit near-patch erosion when a wider range of sediment sizes are present (e.g., Waters & Curran, 2016;Wintenberger et al., 2015).

Conclusions
To understand the influence of sediment supply and variable flow conditions on channel and patch evolution, we measured the flow, sediment transport, and topographic changes through a single emergent patch of live willows in two stepwise flow experiments with different reach-scale sediment supplies.The hydraulic responses over each hydrograph were similar between experiments, indicating flow within and near the patch was principally influenced by vegetation characteristics.In both experiments, erosion in the adjacent channels was greater than the quantity of sediment deposited through the patch zones, altering the net depositional channel in the unvegetated freestream section to an erosional condition near the patch.Greater reach-scale sediment supply enhanced the topographic variance and physical heterogeneity in all zones within the study section by 12%-63%.
While reach-scale sediment supply provided the upstream boundary condition for potential deposition and erosion, the geomorphic response of individual zones over the hydrograph depended on the combination of flow-dependent transport capacity and local sediment supply.Within the vegetation patch, both erosion and deposition occurred over the hydrograph as the flow-dependent sediment transport capacity changed relative to the local sediment supply.Morphodynamic change at the patch head was the physical mechanism in our experiments that modified the distribution of bedload transport through the channel, thereby altering the magnitude of erosion in the adjacent channels and the sediment storage dynamics through the patch.The sensitivity of the patch head and interior to reach-scale sediment supply indicates these zones may be the most geomorphically sensitive in river systems with naturally varying sediment supplies and mechanistically helps to explain the divergent results in the literature addressing whether vegetation patches enhance or inhibit sediment deposition.These experiments were partially funded by the Korea Institute of Civil Engineering and Building Technology, and the University of Idaho.This work was also supported by the Korea Environment Industry & Technology Institute (KEITI) through the Climate Change Research Program funded by the Korea Ministry of Environment (MOE 202200346002).We thank Inhyeok Bae and Son Truong Hong for their assistance at the River Experiment Center and for post-processing the ADV data.

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Relative to the open depositional channel located upstream, a single vegetation patch caused channel erosion that lowered the median bed elevations by up to 640% • The same vegetation patch can both inhibit and enhance interior sediment deposition depending on the flow-dependent transport capacity and local sediment supply • Morphodynamic bed changes modulated the reach-scale sediment supply in and around the patch by spatially redistributing bedload within the channel Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.(a) Side and plan views of experimental setup of channel sections and zones.In the plan view, the color-coded areas delineate the different zones within the study section and the solid black lines identify the boundary between the flume bed and side walls.Diamonds indicate bedload sampling locations, and circles show Acoustic Doppler Velocimeter (ADV) measurements.(b) Experimental hydrographs for the high-supply experiment and low-supply experiment with the X's identifying when ADV and sediment sampling began.Water surface slopes over each hydrograph for (c) the entire flume test section and (d) the study section near the patch.

Figure 3 .
Figure 3. (a) Digital elevation models of difference for the high-supply experiment (HSE) and low-supply experiment (LSE).Dashed box indicates location of vegetation patch.(b) Median bed change for the HSE and LSE in the freestream and study sections and by zone.Stippled lines depict range of the threshold of change (ε DoD ≤ 8.4 mm).Error bars indicate standard error values.

Figure 4 .
Figure 4. (a) Initial and final bed elevations across the patch head (D 1 ).Box indicates lateral extent of patch.(b) Example of mound in the patch head at the end of the high-supply experiment.(c) Measured unit bedload flux entering the patch interior at D 1 .(d) Percentage of total bedload flux in cross section D 1 entering the patch and main channel.The percentage of bedload flux entering the side channel remained <0.2% for each flow in the hydrograph.(e) Ratio of unit bedload flux exiting the downstream end of the patch (D 3 ) to that entering the patch head (D 1 ).(f) Timeseries of bed elevation in the wake 1 m downstream of patch.
in both the patch interior and wake, implying that no local sediment was supplied to the wake and no transport occurred in this zone.Similarly, the reduction in  ⟨  *  * cr ⟩ between the patch and wake for all the HSE flows implies the sediment supply always exceeded the transport capacity and sediment deposition should occur, which agreed with the continuous wake deposition and mound growth over the hydrograph (Figure 4f).In both experiments, using  ⟨  *  * cr ⟩ for both sediment mobility and change in relative transport capacity accurately predicted the occurrence of deposition or no elevation change in the wake during specific discharges of the hydrograph.

Figure 5 .
Figure 5. (a) Ratio of unit bedload flux exiting the downstream end of the main channel (D 3 ) to that entering the main channel (D 1 ).(b) Measured unit bedload flux entering the main channel.(c) Ratio of unit bedload flux exiting the downstream end of the side channel (D 3 ) to that entering the side channel (D 1 ).(d) Measured unit bedload flux entering the side channel.
channel.Lightbody et al. (2019) observed a similar reduction in turbulence in the channel adjacent to a vegetated bar when they eliminated the reach-scale sediment supply and bedforms were reduced.Mechanistically, the reduced  ⟨    0

⟩
similarly decreased in the patch because of the increase in C bfree whereas both C bzone and C D remained relatively stable over the hydrograph.Our results within the vegetation showed  ⟨ lower discharges, indicating that over a hydrograph, the same patch can enhance, have little effect, or suppress turbulent kinetic energy relative to open channel conditions depending on discharge.This is important as near-bed turbulence strongly affects sediment suspension and transport through vegetation (e.g.,Liu et al., 2021;Tinoco & Coco, 2016, 2018;Yager & Schmeeckle, 2013;J. Q. Yang et al., 2016).The change in  ⟨ The side channel was an exception, ⟩∼ 1 , indicating k t in the adjacent channels was generally inhibited relative to the freestream over each hydrograph.Within the willow patch, stem-generated turbulence enhanced  ⟨ cr ⟩ decreased in each zone as the discharge was reduced (p < 0.001) in both experiments (Figure was poor at identifying deposition or erosion in the patch interior and side channel.These differences in predictive success likely occurred because we did not have local hydraulic data to characterize the upstream boundary conditions of each zone.For example, this analysis used the change in  ⟨