Vegetation enhances curvature-driven dynamics in meandering rivers

Domain: earth_science
Published: 2024-03-04
Editorial outcome: major_revision

Abstract
Stabilization of river banks by vegetation has long been considered necessary to sustain single-thread meandering rivers. However, observation of active meandering in modern barren landscapes challenges this assumption. Here, we investigate a globally distributed set of modern meandering rivers with varying riparian vegetation densities, using satellite imagery and statistical analyses of meander-form descriptors and migration rates. We show that vegetation enhances the coefficient of proportionality between channel curvature and migration rates at low curvatures, and that this effect wanes in curvier channels irrespective of vegetation density. By stabilizing low-curvature reaches and allowing meanders to gain sinuosity as channels migrate laterally, vegetation quantifiably affects river morphodynamics. Any causality between dense vegetation and higher meander sinuosity, however, cannot be inferred owing to more frequent avulsions in modern non-vegetated environments. By illustrating how vegetation affects channel mobility and floodplain reworking, our findings have implications for assessing carbon stocks and fluxes in river floodplains.

Introduction
Meandering rivers are widespread in fluvial lowlands and represent one of the most dynamic landforms on Earth1,2. Besides being of critical importance for geological and engineering applications3,4, the dynamics of river meandering also exert primary controls on the biogeochemical cycles that make Earth’s climate suitable for life5–8.

The formation and development of meandering rivers have long been considered intimately linked to the stabilizing influence of vegetation on river banks. This includes bank strengthening provided by plant roots, as well as vegetation-enhanced generation and retention of pedogenic muds9–11. This hypothesis has been corroborated by physical experiments where vegetation facilitated the transition from multi- to single-thread rivers12,13. Moreover, the appearance of known indicators of river meandering in the geologic record has been observed to broadly coincide with the emergence of plant life on Earth ca 440 million years ago. Specifically, mud-rich sedimentary deposits characterized by laterally-accreting inclined heterolithic stratifications, which have classically been considered diagnostic of meander point bars, are uncommon prior to the evolution of vascular plants9,10,14. This observation led to the hypothesis that vegetation was instrumental to the spread of meandering rivers in the Paleozoic15–18. However, recent empirical evidence19–22 and physics-based modeling23 indicate that meandering rivers can also develop in landscapes devoid of plant life—including on Mars, where records of ancient vegetation are missing23,24. Unvegetated meandering river systems have now been recognized on several continents, displaying a diverse set of geomorphic units akin to those observed in vegetated alluvial floodplains, including subtle channel levees, crevasses plays, and point bars5,15,20,21,25–29. These observations suggest that single-thread meandering rivers can be sustained even in the absence of land plants, given favorable conditions of channel slope and as long as other cohesive agents, such as mud or ice, provide the necessary bank strength5,26,30. Yet, these observations also prompt new questions regarding the extent to which vegetation, or lack thereof, affects river meander morphology and dynamics, both directly and indirectly28,31,32.

Here, we analyze a globally distributed sample of modern meandering rivers spanning a range of riparian vegetation densities, with the goal of elucidating how vegetation influences the planform shape and evolution of meanders. We first demonstrate how denser riparian vegetation correlates with enhanced meander sinuosity, skewness, and curvature, although planform controls by vegetation are rather subtle and cannot be completely isolated from the effects of high aridity and flashy hydrological regimes. This is especially relevant in modern unvegetated rivers, where meander growth and evolution are prematurely disrupted by meander chute cutoffs and frequent avulsions. Nonetheless, we confirm that vegetation demonstrably reduces the rate of river lateral migration, and enhances the coefficient of proportionality between migration rate and channel curvature. This enhancement is most evident at relatively low curvature and wanes in curvier channels regardless of vegetation density. Irrespective of aridity, vegetation effectively stabilizes low curvature reaches and allows meanders to gain sinuosity as they migrate laterally, thereby leaving measurable imprints on the morphodynamics of meandering rivers.

Results
Our dataset consists of 54 single-thread meandering rivers found in distinct biomes worldwide (Fig. 1a). We quantified the planform morphology of individual reaches by manually digitizing river banks from aerial and satellite images, and estimated the density of riparian vegetation from multi-annual statistics of the remotely sensed Normalized Difference Vegetation Index (NDVI) (Fig. 1a and Methods). We defined three classes of rivers based on the computed NDVI: unvegetated (NDVI≤0.2; n =16), semi-vegetated (0.2<NDVI≤0.4; n =11), and vegetated (NDVI>0.4; n =27) (Fig. 1a, b).

For each class, we analyzed the width-adjusted morphometric properties of meander planforms at both the scale of single meander bends and individual meandering river reaches, using classical uni- and multivariate statistical methods in the river-meander literature33–36 (Fig. 1a and Methods). Finally, to unravel the role of vegetation in driving meander-planform evolution, we integrated measurements of river curvature (C*[m−1]) and lateral migration rates (M* [m/yr]) derived from dynamic time-warping (DTW) analyses37,38 (Fig. 1d) applied to a subset of actively migrating rivers (n=32, Fig. 1a) where pairs of aerial images were available at sufficient pixel resolution to reconstruct the position of channel centerlines over multiannual time spans (Methods).

Effects of vegetation on meander planforms
Scaling relationships between fundamental morphometric characteristics of meander planforms (Fig. 2) are remarkably similar among unvegetated, semi-vegetated, and vegetated rivers (Fig. 2a–d). We find that meander morphometric features—namely Cartesian (L* [m]) and intrinsic (ℓ* [m]) wavelengths, meander amplitude (A*[m]), and radius of curvature (R*[m])—all exhibit statistically significant (p<0.01) power-law relationships of the form z*= a⋅(B*)b, where z* is a given meander morphometric variable and B* ([m]) represents the channel width averaged along individual meander bends (Fig. 2a–d). Notably, whereas power-law prefactors (a) differ slightly among distinct vegetation classes, power-law exponents (b) closely approximating 1 imply linear scaling relationships between B* and all analyzed morphometric descriptors. Thus, to compare meandering rivers of different sizes, we investigate the distributions of dimensionless, width-adjusted meander wavelengths (L=L*/B*; ℓ=ℓ*/B*), amplitude (A=A*/B*), radius of curvature (R =R*/B*), and curvature (C= C*⋅B*), as well as the distributions of width-independent meander sinuosity (χ=L*/ℓ*) and asymmetry (A) (Fig. 2e–k). The latter parameter is computed as A=(ℓ*u -ℓ*d)/ℓ*, where ℓ*u and ℓ*d denote the distance between the meander apex and its upstream and downstream endpoints (Fig. 2, Inset), respectively, so that negative (positive) values of A indicate meanders skewed in the upstream (downstream) direction.

Two-sample Wilcoxon Rank Sum (WRS) and Kolmogorov-Smirnov (KS) tests, performed at a standard 5% significance level on river-aggregated data, highlight statistically significant differences in morphometric relationships between vegetated rivers (used as the control group) and both unvegetated and semi-vegetated rivers. The KS tests all reject the null hypothesis that the morphometrics of unvegetated and semi-vegetated rivers come from the same distribution as those of vegetated rivers. Additionally, the WRS tests reject the null hypothesis that the morphometric parameters of both unvegetated and semi-vegetated rivers have the same median as vegetated rivers in all cases except for the meander amplitude in unvegetated rivers and meander wavelengths and curvature in semi-vegetated rivers.

Compared to their vegetated counterparts, rivers in unvegetated settings typically feature longer meander wavelengths and larger radii of curvature relative to channel width, with lower meander sinuosity and width-adjusted curvature (Fig. 2e, f, h, i, k). Specifically, whereas in vegetated rivers 26% of meanders have a sinuosity χ>2 and 13% have a curvature C>0.3, these percentages decrease to 7% and 5%, respectively, for unvegetated rivers. Vegetation also appears to correlate with bend asymmetry: meanders in vegetated and semi-vegetated rivers are more strongly upstream-skewed (i.e., lower values of A) whereas unvegetated rivers host more symmetric bends on average (Fig. 2j).

Whereas these differences emerge when data are treated as ensemble averages (i.e., binned over the entire dataset), distributions associated with individual rivers display a wide dispersion (Fig. 2e–k). Thus, meander morphologies overlap considerably among different vegetation classes.

Because the observed differences are subtle and yet systematic, correlations between planform expression and vegetation density might emerge more clearly from multivariate analyses of meander planform morphometrics33–36,39. We applied Principal Component Analysis (PCA) (Supplementary Method 1) to a set of distinct morphometric variables derived from river-aggregated distributions of meander planform features (Table 1 and Methods). As demonstrated by Howard and Hemberger35, morphological variations among freely meandering streams can be resolved by morphometric parameters related to meander wavelength, skewness, sinuosity, and curvature. Hence, we considered the first- to fourth-order statistics of the probability distributions of meander sinuosity (χ), asymmetry (A), and both width-adjusted curvature (C) and intrinsic wavelength (ℓ).

All variables were computed for both half and full meander bends (Table 1 and see Methods), except for C, for which we considered the reach-averaged values. Whereas the resulting dataset consists of 28 variables overall, we performed PCA on a subset of 17 variables (Fig. 3) that succinctly capture the variation in the original data while avoiding redundancy from cross-correlations. The first three principal components (i.e., PCs a1, a2, and a3) account for about 55% of the total variance in the dataset, with the relative importance of higher-order PCs decaying exponentially (Supplementary Fig. 1). Data from unvegetated and vegetated meandering rivers cluster in different parts of PC biplots, especially in the (a1; a2) and (a1; a3) spaces where unvegetated rivers cluster in the negative a1 half-plane opposite to the vegetated data (Fig. 3a–c; Supplementary Method 1). Data for semi-vegetated rivers, in contrast, do not form a well-clustered group and generally fall somewhat in between the unvegetated and vegetated data clusters (Fig. 3a–c). These results hold even when different ensembles of morphometric variables are considered (Supplementary Figs. 2 and 3), and altogether suggest that data separation is predominantly driven by higher meander sinuosity, curvature, and degree of upstream skewing (i.e., lower A) in vegetated rivers compared to their unvegetated and semi-vegetated counterparts. Higher χ, larger C, and lower A values are typically associated with late-stage meander growth40,41, suggesting that denser riparian vegetation correlates with the continued growth of meanders until they reach morphodynamic maturity. At this stage, bends become highly sinuous and are more likely to shortcut themselves through neck cutoff40, which marks the endpoint of a meander evolution (Fig. 1d).

Meandering river dynamics
To seek an explanation for the observed disparity in meandering river morphometrics as a function of riparian vegetation density, we also investigated differences in the dynamic evolution of meander planforms over time. Meander evolution is known to be controlled by flow-imparted sediment erosion and deposition at the outer and inner banks, respectively, driving the lateral migration and planform development of meandering rivers over time1,2.

Quantification of meander planform evolution through DTW (Methods) suggests statistically significant differences in rates of width-adjusted lateral migration (MR =M*/W* [yr−1]) between vegetated rivers (used as the control group) and both semi-vegetated and unvegetated rivers (p-value<0.01 for WRS tests performed at 5% significance level). Migration rates relative to channel width in unvegetated rivers (Munveg =0.019±0.022 yr−1, median ± standard deviation values reported) are almost twice as high as those in vegetated rivers (Mveg =0.010±0.058 yr−1), and about 58% higher than in semi-vegetated rivers (Msemiveg =0.012±0.051 yr−1) (Fig. 4a). This finding corroborates empirical observations that vegetation helps to stabilize river banks against migration13,23,42 and suggests that reach-averaged time-lapse analyses, as employed herein, attenuate differences in characteristic migration rates between unvegetated and vegetated systems when compared to measurements carried out at bend apexes32,43–45. More importantly, DTW analysis of river centerlines also allows for examining the functional relationship between channel curvature and river migration. The extensive literature on this topic1,4,38,46–50—which focused almost exclusively on relatively large, sand-to-gravel-bedded rivers in vegetated landscapes–has shown that the distribution of C vs. MR data is significantly scattered, such that a single value of MR cannot be generally associated with a single value of C (refs. 51, 52; see Supplementary Method 2). Nevertheless, a quasi-linear relationship emerges between C and both the mean and upper values of the MR distributions, pointing to a strong first-order control of C on meandering river morphodynamics37,38,44. This proportionality typically only holds for mildly curved channel reaches (i.e., for width-adjusted curvature values smaller than 0.25–0.5, taken here as C<0.3 for convenience) and breaks down at higher curvatures (C>0.3) where MR saturates due to the growth of hydrodynamic nonlinearities that effectively limit bank erosion, such as saturation of centrifugally driven secondary flows, enhanced secondary outer bank cells, and flow separation at the outer bank1,38,46,53,54 (Supplementary Method 2).

In order to explore the effect of vegetation on curvature-driven meander dynamics, we derived the relationship between dimensionless curvature (C) and width-adjusted migration rate (MR) for each river in our dataset, further adjusting migration rates by the reach-average spatial lag (Δ*CM[m]) between local maxima in channel curvature and migration rate37,44,51 (Supplementary Method 2). In all the river classes, a positive linear relation of the type MR=α+β⋅C is observed for curvature values C≤0.3 (Fig. 4b), a pattern consistent with theoretical and numerical predictions37,55–58. Linear correlations hold both for average and upper values of the MR distributions, represented here by the 50th (M50) and 95th (M95) percentiles, respectively, of equally sized sets of MR data binned according to increasing C values38 (Fig. 4b). Nevertheless, our results show that the coefficient of proportionality (β), computed for both M50 and M95 data corresponding to C≤0.3, are consistently larger in vegetated rivers than in unvegetated and semi-vegetated ones (Fig. 4b). Beyond the C=0.3 threshold, the correlations become negative as MR decreases with increasing curvature, with a steeper decline observed for vegetated rivers compared to unvegetated and semi-vegetated ones. Notably, the latter class of rivers exhibits significant data scattering, to the extent where all the linear relationships are not statistically significant.

These results still generally hold when we break the rivers out of ensemble vegetation classes and treat them individually by considering characteristic NDVI (Supplementary Fig. 4), even without adjusting curvature and migration values to account for the whole set of river widths in our dataset (Supplementary Fig. 5). Minor deviations of some rivers from the general trend described above are justified by variability in sediment grain size59, bank erodibility46, and floodplain heterogeneity39,60, which are not accounted for in our remote-sensing analyses. Moreover, morphodynamic feedbacks that arise from vegetation patterns and habits likely contribute to variability in (MR, C) that emerge even among rivers with similar NDVI values (Supplementary Figs. 4 and 5), and add to the variability observed in semi-vegetated river data (Fig. 4b). Plant density, as well as channel width and depth relative to plant stem diameter and rooting depth13,15,61–63, have been shown to influence channel dynamics. In sparsely vegetated landscapes, shrubby arborescent, drought-resilient plants will encroach into the moister and nutrient-rich thalweg zone of ephemeral channels, where groundwater is more accessible15,21. Especially in rivers narrower than 10m, such clusters of in-channel vegetation can enhance local scour and bank erosion, disrupt curvature-induced helical flow that sustains lateral migration, and limit meander growth by facilitating braiding and chute cutoffs15,62 (formed when the river cuts a new bypass channel through its own point bar64; see Supplementary Fig. 6). In contrast, deep-rooted trees can sustain large single-thread meandering channels (width>102m)15,63 in densely forested floodplains, aiding flow confinement through enhanced bank-erosion resistance and facilitating the continued development of highly sinuous meander bends until neck cutoff. On average, larger rivers are associated with higher NDVI values (Supplementary Fig. 7), but our analysis of normalized morphometric characteristics shows that the effects of vegetation regime on meandering dynamics are independent of channel size (Fig. 2a–d).

Curvature-driven meander dynamics enhanced by riparian vegetation
To investigate variations in channel mobility while avoiding highly mobile rivers to systematically bias our data, we further normalized MR by dividing it by the average migration rate of the corresponding river reach (MR) (Fig. 4c). Importantly, this procedure also allows for filtering out spurious correlations due to inherent hydrological and sedimentological variability (e.g., flow intermittency and changes in bank erodibility) broadly related to site-specific climatic and environmental conditions.

For C≤0.3, the normalized width-adjusted migration rates m=MR/MR ([-]) increase linearly with curvature regardless of vegetation density and whether the 50th and 95th percentiles of m data are considered (Fig. 4c). Normalizing migration rates significantly reduces data scatter, especially for semi-vegetated rivers, and makes all linear relationships strong and statistically significant (p-value<0.001). Most importantly, the slope (β) of linear regression lines increases progressively from unvegetated to semi-vegetated and vegetated rivers, both when considering the median (βveg50=4.19±0.09; βsemiveg50=2.04±0.16; βunveg50=1.39±0.13) and 95th percentile of m data (βveg95=9.93±0.32; βsemiveg95=7.04±0.84; βunveg95=4.43±0.47). In contrast, the regression-line intercept (α) is larger in semi-vegetated and unvegetated rivers, suggesting relatively high rates of meander migration even at low curvatures (αveg50=0.78±0.01; αsemiveg50=1.04±0.02; αunveg50=1.15±0.02; αveg95=2.79±0.05; αsemiveg95=2.79±0.12; αunveg95=2.79±0.06). For C>0.3, a consistent plateauing in m values is observed for all three vegetation classes. The regression lines become nearly horizontal, indicating lack of correlation between migration rates and curvature, despite some regressions still being statistically significant (Fig. 4c). Whereas saturation of migration rates for C>0.3 appears unrelated to vegetation and is likely better explained by the complex flow structures that arise in sharp bends46,53,65–67, the observed differences in m for C≤0.3 can be attributed to the lack (or sparsity) of riparian vegetation. In particular, the diminished proportionality between migration rate and curvature, coupled with the relatively higher migration rates observed in semi-vegetated and non-vegetated rivers (as curvature approaches zero) underscore the impact of lack of vegetation on bank stability and sediment transport processes. The lack of vegetation enhances bank erosion through slump block collapse, which can occur even at low curvatures15. Additionally, it fosters hydrological connectivity between the river and its floodplain by limiting the formation of high-relief levees29. The reduced topographic prominence of levees facilitates sediment exchanges between channel and floodplain and the formation of erosional rills along the banks during waning flood stages, ultimately resulting in lateral channel infilling driven by return flows29. Consequently, pronounced sediment deposition is observed even at the outer (concave) banks of meanders, where larger water depths and sustained erosion should be expected if river banks were vegetated15,29. In addition, local perturbations of river morphology induced by widespread chute cutoffs in barren and poorly vegetated settings likely lead to accelerating migration and channel widening both locally and nonlocally68,69, thus further enhancing m data scatter at low curvature values that are typical of chute cutoffs. All of these processes are likely to reduce correlation between channel curvature and bank erosion (and related river migration) as the density of riparian vegetation decreases, thus explaining our observations.

Methods
The dataset analyzed in this study includes 54 meandering rivers encompassing different climate and geological regions, from polar to hyperarid, thereby ensuring representativeness for distinct hydrological regimes, sediment grain sizes, and, importantly, densities of riparian vegetation. These selected rivers also ensure an inclusive sampling strategy concerning geographical distribution (spanning most continents; Fig. 1a) and river size (covering three orders of magnitudes in width; Fig. 2a–d).

Extraction and analysis of meandering river planforms
To obtain planform morphometrics of individual meandering reaches, we first hand-digitized river bank lines in the QGIS environment based on freely available georeferenced aerial and satellite images. The latter includes several different products available through Google Earth Pro, SASPlanet, the U.S. Geological Survey Earth Explorer portal, and the QuickMapService QGIS plugin. Additionally, we included in our dataset the data collection provided by Sylvester et al.37 for vegetated meandering rivers in the Amazon basin (Fig. 1a).

In order to ensure data homogeneity among distinct fluvial settings, we only considered single-thread meandering river reaches that (i) contain at least 35 consecutive bends, such that a sufficiently long train of meanders can be analyzed; (ii) are found sufficiently far away from the coastline in order not to be affected by backwater and/or tidal effects; (iii) have not been significantly modified or engineered by humans.

Digitization of rivers in poorly vegetated settings includes also some abandoned (i.e., non-active) reaches for which planform morphometrics could be identified from aerial images. In the case of the Rio Colorado (Salar de Uyuni, Bolivia) and the Amargosa River (California, USA) (Fig. 1a), the analyzed reaches, though inactive, are still recent enough such that they cannot represent different riparian states, e.g., from past interglacials25,82. The dataset also includes the inactive Uzboy River in the Karakum Desert (Turkmenistan), which formed between the Upper Pliocene and the Preglacial Quaternary under an arid palaeoclimate21, although estimates of vegetation content during its active phase are still debated17,83.

To ensure a baseline of accuracy for all morphometric data collection, river banks were digitized using aerial scenes with a minimum ground resolution corresponding to approximately 5% of the average river width (e.g., images with 30 m ground resolution were used only for digitizing river larger than 600 m, whereas images with resolutions equal to or higher than 0.5 m were employed for 10-meter-wide rivers). For vegetated rivers, the bank line position was determined based on vegetation boundaries. In unvegetated and sparsely-vegetated rivers, the position of outer (concave) banks was typically clear as the cut banks are sharp and form an abrupt change of angle with the adjacent floodplain, whereas bank position along the gently-sloping meander inner (convex) side was identified by the accumulation of debris at the point-bar top, forming a line parallel to the channel path5,21 (Supplementary Fig. 6).

Freely available, high-resolution topographic data for the unvegetated Amargosa River (Death Valley, California, USA) and the semi-vegetated meandering systems developed in the Menindee and Panamaroo lakes (Darling River basin, New South Wales, Australia) were employed to test the accuracy of width measurements derived from aerial imageries (B*sat [m]) against bankfull width computed from topographic data (B*topo [m]). Results show a strong fit between the two width datasets (B*topo =1.01⋅B*sat; r2=0.98, p-value<0.001) measured at constant increments equal to 10 channel widths along the studied channel reaches (Supplementary Fig. 10).

Once river banks were digitized, we derived channel centerlines through a standard skeletonization procedure33. Channel centerlines were smoothed by means of a Savitzki-Golay low pass filter to avoid numerical discontinuities and then resampled using standard cubic spline-fit polylines with a spatial resolution approximately corresponding to one-tenth of the channel average width37. To isolate individual meander bends we used a semi-automated procedure based on the computation of local channel-axis curvature C* ([m−1]) (Supplementary Fig. 11). Specifically, for any given centerline point {x*(s*),y*(s*)}, we computed C*=dθ(s*)/ds*, where s*([m]) denotes the channel centerline curvilinear coordinate, {x*(s*),y*(s*)} represent the coordinates of an arbitrary axis point in a Cartesian reference system, and θ(s*) is the angle formed by the tangent to the channel axis and an arbitrarily fixed direction33,37. After computing C*, a Savitzky–Golay low-pass filter with a fixed polynomial order of 3 and a frame length of 21 centerline points was applied to further smooth noise in the original C* signal. Subsequently, half (full) meander bends were identified as the portion of the channel between two (three) consecutive inflection points (i.e., points where C*=0). Meander apexes were also identified as points corresponding to local curvature maxima between inflections (Fig. 1c and Supplementary Fig. 11). We note that the low-pass filtering of C* signal resulted in the automatic deletion of some “spurious” inflection points delimiting meander bends characterized by limited length and sinuosity, which are typical in double-headed meander bends featuring multiple local maxima in the C* signal (Supplementary Fig. 11).

Morphological features of individual meander bends were finally characterized based on several morphometric parameters (Fig. 2, Inset), namely: meander intrinsic wavelength (ℓ* [m]), which is the along-channel distance between inflection points; meander cartesian wavelength (L*[m]), defined as the planar distance between meander inflections; meander sinuosity χ=ℓ*/L* ([-]); meander amplitude (A* [m]), measured as the maximum point-line distance between any centerline point and the line connecting the two meander flexes; meander radius (R*[m]), defined as the radius of the best-fitting circle obtained by considering all meander centerline points50; and meander asymmetry index, computed as A=(ℓ*u -ℓ*d)/ℓ* ([-]) where ℓ*u and ℓ*d denote the distance between the meander apex and its upstream and downstream endpoints (Fig. 2, Inset), respectively, so that negative (positive) values of A indicate meanders skewed in the upstream (downstream) direction.

To directly compare rivers of different sizes, all the dimensional morphometric variables (i.e., those denoted with superscript asterisks) were normalized with the average channel width B*([m]) measured along individual meander bends (e.g., L=L*/B*; ℓ=ℓ*/B*; C=C*⋅B*; A=A*/B*; R=R*/B*).

Riparian vegetation density and aridity
To characterize riparian vegetation density, we utilized multi-annual statistics of the remotely-sensed Normalized Difference Vegetation Index (NDVI) computed through Landsat 7 Collection 1 Tier 1 8-Day NDVI composites with a ground-spatial resolution of 30 m, accessed through Google Earth Engine. The composites are derived from Tier 1 orthorectified scenes, using the computed top-of-atmosphere (TOA) reflectance, and are generated from all the scenes in each 8-day period beginning from the first day of the year and continuing to the 360th day of the year. As such, the final composite for a given year, starting from day 361, has a 3-day overlap with the initial composite of the subsequent year. Each composite includes all images from its respective 8-day period, with the most recent pixel serving as the composite value.

The NDVI is computed based on the Near-InfraRed (NIR) and Red bands of each scene as NDVI=(NIR-Red)/(NIR+Red) and ranges in value from −1.0 to +1.0. Snow filtering was also applied for rivers in continental and arctic climate zones based on a fixed normalized difference snow index (NDSI) threshold (NDSI=0.4), where NDSI represents the normalized difference between green spectral bands and the shortwave infrared.

For our analyses, we created a percentile composite of image collection wherein each pixel contains the 90th percentile of NDVI (NDVI90) values computed over a 20-year timespan (i.e., from 1999 to 2019) (Supplementary Fig. 12). Then, for each river in our dataset, we estimated the characteristic floodplain NDVI as the median of NDVI90 computed within an area obtained by buffering the river centerline with a buffer distance equal to 10 times the average river width (Supplementary Fig. 12). Finally, we categorized our rivers into three classes based on NDVI values: unvegetated (NDVI≤0.2), semi-vegetated (0.2<NDVI≤0.4), and vegetated (NDVI>0.4). For the meandering streams found in Lake Menindee and Lake Panamaroo (New South Wales, Australia), which were found to be flooded for most of the observation period, we assumed the same NDVI value calculated for the floodplain of the nearby Darling River, from which the lakes originate (Supplementary Fig. 13).

We used an approach akin to the method used for calculating NDVI to calculate the Aridity Index for the examined river reaches. The median Aridity Index (AI) was computed, within the same buffer area employed to derive NDVI statistics, based on the freely available “Global Aridity Index and Potential Evapo-Transpiration (ET0) Database v3” provided as high-resolution (30 arc-seconds) global raster data for the 1970–2000 period84.

Channel migration rate
Meander lateral migration was analyzed for a subset of rivers for which active migration was detected based on pairs of images available at adequate resolution. Lateral migration was measured at fixed increments Δx* no larger than the average river width along the channel centerline using a dynamic time-warping algorithm (DTW) implemented in R (ref. 85) and performed through the QGIS software (v.3.6.3) processing tool (Supplementary Fig. 11). Originally developed to correlate time series, DTW represents a state-of-the-art method to compute channel lateral migration in dynamic single-thread meandering systems thanks to improved estimates of bank migration trajectories compared to typical proximity algorithms such as nearest neighbor and inverse-distance weighted37,86. The DTW algorithm employs a cost matrix to minimize the sum of distances, rather than individual distances, between two consecutive river centerlines. Specifically, DTW alignment of two consecutive river centerlines is performed through a Euclidean distance matrix for corresponding centerline points, augmented with the third dimension of curvature at those same points. That is, for each pair of i and j point along the original and final river centerline, the matrix of following distance is computed:
d*i,j= sqrt((x*i - x*j)^2 + (y*i - y*j)^2 + λ^2(C*i - C*j)^2) (1)
where λ is a multiplier weighting parameter for curvature values. In this way, the sum of distance is weighted by both the spatial distance and the similarity in local channel curvature, so that the algorithm can effectively monitor changes in both channel centerline position and curvature26,37,38,44 (Supplementary Fig. 11). While this approach is similar to a simple nearest neighbor search in principle, its results differ from the latter as DTW effectively avoids large gaps between correlated centerline points (see example in Supplementary Fig. 11).

After DTW computations, we identified and masked meander bend cutoffs within each river reach to exclude them from subsequent analyses (Fig. 1d). Then, following the same procedure used for filtering C*, migration (M* [m]) data were smoothed using a low-pass Savitzky-Golay filter to reduce data noise (Supplementary Fig. 11), and migration rates were computed as MR* =M*/Δt ([m yr−1]), where Δt denotes the time difference, in years, between the dates when river centerlines were acquired. Finally, in order to account for the spatial lag between curvature and migration maxima (see Supplementary Method 2 for a thorough discussion), we shifted the MR* signal upstream by a length corresponding to the reach-averaged curvature-migration lag Δ*CM (Supplementary Method 2). In this way, the functional correlation between channel curvature and lateral migration can be studied in a physically sound fashion.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Specific comments:\nLine 24: The connotafion of “morphodynamic maturity” will likely not have meaning to the reader unfil it\nis defined.\nLine 28-29: It is unclear what is implied by “enhances the proporfionality between migrafion rate and\nchannel curvature”, i.e., a higher correlafion coefficient, a higher regression slope, or a higher intercept?\nIt is unlikely to be the lafter since the migrafion rate is lower according to the first clause of the sentence.\nLine 29: The antecedent “effect” is unclear for this sentence. Is it the reduced “rate of river lateral\nmigrafion”? Also, what is “obscured”? The rate of migrafion?\nLine 31: Eliminate “Hence,”, because this has not been demonstrated in the abstract. The sentence works\nwithout this.\nLines 44-46: The text leaves unresolved the quesfion of why heterolithic strata are uncommon prior to\nthe development of vascular plants, given that vegetafion is asserted to be not necessary for\nmeandering behavior. Is this issue addressed later in the paper?\nLine 62: It is unclear what would be implied by the inverse relafionship implied by “vice-versa”. Would\nmeandering somehow lead to development of vegetafion?\nLine 78 and lines 418-450: The present authors are probably not responsible for the misnomer\n“dynamic” in dynamic fime warping. Based on the descripfion, this methodology is at best “kinemafic”\nbecause it is not based on mechanisfic, determinisfic forward modeling.\nLine 88-89: Because “x” is a scaled variable in the equafion, it probably should be designated as “x*”.\nLine 91-92: “fairly constant” is not quanfifiably interpretable. Does it imply stafisfical equality of values?\nLine 96: Clarify what is meant by [-] .\nLine 102-103: “significant differences” should be “significant differences in morphometric relafionships”\nLine 132: The criteria for this downsizing is not specified. This is not a crucial issue, but could be\nmenfioned in the supplementary materials or methods.\nLine 146: Here again, “maturity” of bends is menfioned without precise definifion.\nLine 170: Is “impulsive” a well-recognized descriptor of sediment transport behavior?\nLines 183-186: I’m not sure why the effect of vegetafion on chute cutoffs is a “confounding” factor and\nmakes it challenging to infer causafion. Cutoffs are probably the dominant factor in explaining the lower\naverage sinuosity in arid-zone channels due to sparse floodplain vegetafion.\nLine 211: something is missing in the phrase “poinfing to a strong first-order control of C meandering\nriver morphodynamics”\nLine 217 and Supplementary Material 2: It is unclear what is meant by “correcfing migrafion rates by the\naverage spafial lag”. The effect of the lag is clear in Supplementary Figure 10. Is the lag used to “correct”\nthe data the average of the individual lags applied to the reach as a whole, or is the lag determined and\napplied to each bend individually? Parenthefically, the term “corrected” should probably be\n“normalized” or “adjusted”. In Supplementary Figure 13 all the lags are posifive, presumably implying a\nsub-resonant regime. Was this true for all rivers studied?\nMaterials and Methods: Extracfion and analysis of meandering river planforms: As is acknowledged in\nthe discussion care needs to be taken to remove “noise” related to the digifizing procedure in\ndetermining the generalized planform. The discussion is generally clear about the procedures, but some\ndetail is lacking due to reliance on previous studies. One of the most crifical steps in segmenfing natural\nchannels is defining the inflecfion points. The issue is illustrated in Supplementary Figure 10, where near\nthe north arrow there is a slight inward inflecfion of the adjacent long bend. If the plofted centerline\nbetween iv and v is correctly plofted there should be two intermediate inflecfion points and one half-\nbend that are not evident in part B of this figure. This issue only becomes important if including those\ninflecfion points would significantly affect the subsequent analyses. Have the authors, or previous\nstudies, evaluated the influence of planform generalizafion on resulfing morphometric parameters?\nGeneral comments:\nThe role of sediment supply characterisfics in meandering behavior is not discussed in this paper. In this\ncomment I rely on informal observafions that may not be universally applicable. Meandering in arid\nenvironments seems to occur only when the supplied sediment contains a high fracfion of mud relafive\nto sand and gravel. Sand or gravel-dominated channels tend to be braided (this also applies to glacially-\nfed channels). The “point bars” of these mud-dominated channels are also cohesive. The presence of\nvegetafion in more humid condifions allows stable meandering in sand and gravel-dominated seftings\nwhich would be braided in more arid environments. Thus the characterisfics of sediment supply may be\nan uncontrolled factor in the present analysis that is indirectly associated with vegetafion.\nThe high frequency of chute cutoffs in channels with low density of vegetafion may influence average\nmigrafion rates due to the perturbafion of the flow field, which generally results in rapid adjustments of\nthe planform and locally high migrafion rates. This is very evident in simulafions of meandering where\nneck cutoffs result in fast migrafion, somefimes with reverse direcfion of migrafion. This is largely\ncompensated for in the present study by considering in detail only the low-curvature bends, but could\nsfill have some influence on low-curvature bends.\nOverall evaluafion: This is an important and informafive evaluafion of the role of vegetafion on\nmeandering behavior. The methodology and analyses are largely clearly explained. Most of the detailed\ncomments can be easily addressed. The issues raised in the general comments are largely beyond the\nscope of the paper, but the authors should assess whether they have implicafions for interpretafions in\nthe paper", "reviewer_2": "This is a very fimely work that reveals the role of vegetafion in meandering river development. Mulfiple\ncontrols have been previously proposed for the long-standing debate about the necessary condifions for\nmeandering river development. Among these controls, vegetafion has sfirred up a lot of discussions\nrecently, but how specifically does vegetafion affect the morphology and dynamics of meandering river\nhave not been systemafically explored in sufficient details unfil this current manuscript. This work\ndocumented a list of key geometric aftributes of meandering river planform morphology across a wide\nrange of riparian vegetafion densifies. Stafisfical analyses of these aftributes reveal that the impact of\nvegetafion on meandering morphology and dynamics is subtle but significant. Moreover, the author\nfound the range of curvature that disfinct vegetafion control operates. These results have important\nimplicafions for the role of riverine environments in global carbon cycle and reconstrucfion of the\nmorphology and dynamics of ancient rivers on Earth and Mars.\nThere is one missing aspect of the dataset analyzed that could potenfially hinder the applicafion of the\nresults from this study. It seems that the rivers in the analyzed dataset collected by the authors are all\nsmall to intermediate-sized rivers, and most large lowland rivers are not included. This raises the\nquesfion whether the findings of the study apply to large lowland meandering rivers as well. I speculate\nthat the impact of vegetafion on large rivers is limited as the flow depth of these rivers extends far below\nthe roots of vegetafions. This does not negate the results of this study but suggests that there might be a\nriver size limitafion on the role of vegetafion on meandering river morphology and dynamics. In order to\nmaximize the applicafion of this work, I would suggest the author to consider the following:\n(1) Include some large rivers in the dataset. Whether the large lowland rivers follow the trends\ndemonstrated in this study will be useful informafion. If they do, then it supports that the impact of\nvegetafion is also important for large rivers. If not, there might be a river-size limit for vegetafion to\naffect the morphology and dynamics of meandering river. This is not to underrate the importance of\nsmall- to intermediate sized rivers, as they comprise a large porfion of global rivers.\n(2) Characterize the size of the rivers in the dataset in terms of slope and discharge and provide the\noverall range/distribufion of these metrics. This will help to put the size of the rivers in the dataset into a\nspectrum so that in case no large river will be included in the analysis, at least it shows the slope and\ndischarge range that the current results are applicable to.\nSome minor points for the author to consider:\nIs there a threshold curvature used for idenfifying cross-over point? For example, there seems to be\nlow curvature bends that are part of a compound bend but not considered as a bend defined by cross-over\npoint in figure 1C (e.g., upper secfion of Humboldt river below the 7th cross-over point, and mid-secfion\nof the Rio Horton river below the 13th cross-over point). It seems that the current method skips some of\nthe low curvature bends.\nSpecific comments:\nLine 71: what about different types of vegetafion, which may contribute to the spread of data in the\nanalysis1.\nLine 177 “low-gradient terminal fluvial fans…”\nCould you provide the actual slope range for the studied rivers.\nLine 212 “reaches (C<0.3)…”\nHow is this threshold value of curvature determined? Seems the curvature for peak adjusted migrafion\nrate for semi-vegetated and unnegated rivers is closer to 0.2 (Fig. 4B, C).\nLine 236 “morphodynamic feedbacks that arise…”\nWhat specific feedback this is referring to?\nLine 249 “…independent of channel size”\nAgain, what about large rivers.\nChenliang Wu\nPostdoc Researcher\nTulane University\nReferences\n1. Zhu, L., Chen, D., Hassan, M. A. & Vendifti, J. G. The Influence of Riparian Vegetafion on the Sinuosity\nand Lateral Stability of Meandering Channels. Geophysical Research Lefters 49, e2021GL096346 (2022).", "reviewer_3_and_4": "Review of Vegetafion Signature on River Meander Morphology and Dynamics by Finotello et al.\nsubmifted to Nature Communicafions\nFinotello et al. provide a comprehensive analysis to show how vegetafion influences river meandering.\nThe manuscript is well wriften and the authors should be applauded for their detailed science and\nvaluable data its created. The work is significant. The authors find that rivers with unvegetated and\nvegetated banks have different planform sinuosifies and bend asymmetries—suggesfing that bends\ndon’t reach maturity in unvegetated seftings. They also use a novel analysis and show that while rivers\nwith all types of bank vegetafion have consistent curvature vs. migrafion rate relafionships, unvegetated\nrivers have faster bank migrafion rates at low curvature. The methodology and data analyses are very\nsound, and the results are of broad interest to fluvial geomorphologists and geologists that keep up with\nthe debate on the role of vegetafion in river meandering. With that said, there are a few overarching\ndifficulfies I had with the present version of manuscript that include: 1) more discussion connecfing the\nmorphometric and migrafion rate analyses, 2) a need to befter jusfify methodological choices, and32)\nfigure simplificafion and readability.\nThere are two related, but separate analyses included in the manuscript. The first half of the arficle\nfocuses on a morphometric analysis of river planform. They ufilize and report on two different stafisfical\napproaches (populafion inference and PCA). The second half of the paper is a novel test of exisfing\nempiricism and theory that for the first fime in my knowledge, looks at curvature and meander migrafion\nfor both unvegetated and vegetated rivers. However, there is liftle structure connecfing these two\nanalyses. Some notes on this:\n• The “Other Impacts on Planform Morphology” secfion (L150) is indicafive of the difficulty the text had\nin bridging the two analyses. I found this secfion out of place as it was a discussion describing drivers of\nplanform morphology that aren’t explicitly vegetafion without a clear secfion devoted to discussing the\nrole of vegetafion itself on planform morphology.\n• Further, the opening of the “Meandering river dynamics” secfion (L189) is too generic and can use\nmore jusfificafion as to why were are looking at morphometrics and dynamics in the same analysis.\nInstead, the paragraph (L189-L203) spends valuable text comparing to previous literature, which while it\nis great to see that it lines up, could be used to fie the analyses together.\n• The primary connecfion between the two analysis is finally discussed in the implicafions secfion (L303).\nWhile I think this is a reasonable hypothesis, it would be strengthened by a more structured set-up\nconnecfing morphometrics and dynamics. The full discussion of the morphometrics could be included in\nthe implicafions. If the authors are making the argument that a lack of vegetafion and high low-curvature\nmigrafion rates leads to channel wandering and limited sinuosity, a side-by-side discussion of channel\ncutoffs (which can also be influenced by vegetafion) has to be included to make the argument\nconvincing.\nWhile the depth of the analysis produces significant results, a few methodological choices can use befter\njusfificafion to strengthen the manuscript:\n• There is liftle explanafion as to how or why the data is/is not aggregated. The dataset includes 54\nrivers, but all the analyses are completed at the bend-scale. This means that dependent measurements\nat the bend-scale, are treated as independent measurements throughout all stafisfical tests (e.g.\ninferenfial stafisfics in the morphometry and the comparison of width-averaged migrafion rates). While\nbend-scale measurements have to be used for the curvature analysis, using bend-scale measurements\nfor the WRS and KS tests will lead to arfificially low p-values. This is a significant point because all the\nindividual bend-scale measurements are *not* independent measurements and some sort of\nbootstrapping is essenfial for correcfing for this inherent bias. The authors really have 54 independent\nrivers and not hundreds to thousands of independent measurements as the data plots make it out to be.\n• Why do the authors select the morphometric variables used in the analysis (L93)? There is a good deal\nof overlap between variables. For example, what is gained by including intrinsic wavelength, cartesian\nwavelength, and sinuosity?\n• What is the PCA analysis contribufing to help flesh out the results from inferenfial stafisfics? Is the\nmost significant takeaway that only sinuosity and skewness are important (L143)? The authors do include\nhigher order stafisfics of the variables, and these show up in the results, but are not discussed.\n• In the current text, it’s unclear whether the mean-normalizafion (L253) is producing a result that is\ndifferent than the width-normalizafion (L216). The authors include reporfing the curve-fits for the mean-\nnormalizafion (L262-L268), but not the width-normalizafion. It currently reads that the mean-\nnormalizafion simply reduces the noise in the semi-vegetated rivers. A related quesfion, is the correct\ninterpretafion for figure 4c (unvegetated) that the median migrafion rate for an unvegetated straight\nreach is faster than the average migrafion rate for the river?\nThe figures contain a wealth of informafion, but they are at fimes difficult to unpack. A couple of notes on the figures:\nFigure 2:\n• The “inset” is the last subplot on the figure, but cited first. This should be directly labeled.\n• The faint shading that is used in the figure makes it hard to read/interpret. This is most striking in A-D\nwhere only the axes appear to have 100% opacity.\n• Including all the box plots, probability density plots and exceedance probability plots is not necessary.\nThe overlap in spread between the bend-scale data can be seen in either the points from the box plots\nor the pdf plots. Depending on how the figure is revised, plofting some version of the river-aggregated\ndata could also be useful.\nFigure 3:\n• While Figure 3A would be nice to have in the supplement, the senfiment is covered well in the text\nalready (L135).\n• Because you minimize all components other than 1 in the text (L138), the plot between a2 and a3 is\nsuperfluous given that you include more PCA plots in the supplement that also don’t show vegetafion\ndifferences. You could move D/G into the supplement, which might allow you to have bigger symbols,\netc. There is an argument to be made that B and E are the only important subplots according to how it’s\ndiscussed in the text.\n• There is also overlap between table 1 and the list of variables included in the figure. The variable\nnames in the figure are faint and hard to read. They could be cut.\nFigure 4:\n• Subplot A is a bit misleading because the data is not aggregated or bootstrapped. The boxplots will be\naffected by including dependent bend-scale measurements. There could be an opportunity here to show\nthe river-aggregated data as well.\n• The kernel density plots are a great way to show the massive amount of bend-scale data. It’s too faint\nas is. The colors need to be more visible\nOverall, I thoroughly enjoyed reading the results and I do think they are noteworthy and significant. The\nanalysis between curvature and migrafion rates across different vegetafion is especially novel. With\nmajor revisions this will be an important contribufion. The major themes in revisions we suggest are to\nbefter jusfify the use of bank-aggregated data across all analysis, streamline the figures, and connect the\ntwo analyses within the same discussion and conceptual framework.\nOther specific notes:\nL74: What is “individual” in this context. This is only point in the paper that there is a discussion about\naggregafing at mulfiple scales. There needs to be more detailed descripfion about what each data point\nrepresents.\nL104-107: Does this mean that the differences between the unvegetated and semi-vegetated rivers are\nstafisfically similar? Or did you only test for differences with the vegetated rivers?\nL112: Provide a count of unvegetated and vegetated rivers that fall into these categories to back this up.\nThat way the reader doesn’t have to go into the tabulated data.\nL131: Is cross-correlafion the reason some variables were left out? Could swap this and the previous\nsentence to help clarity. Did the authors use any standardized method to determine which variables to\nuse, i.e., a threshold? Were things like average half sinuosity and half meander intrinsic length not\ncorrelated?\nL178: Wouldn’t this mean that the avulsion fimescale would have to approach bend-migrafion\nfimescales (the fime necessary to reach a “mature” bend).\nL189: Why are avulsions not a concern if they are menfioned as an important considerafion at the\nmigrafion fimescale in the previous secfion?\nL213: This is a fairly novel connecfion of ideas based on your Geology comment of Sylverster et al. 2019.\nIt may be useful to give just a sentence more detailed descripfion to strengthen this key point past\n“hydrodynamic nonlinearifies”."}, "author_response": "RESPONSE TO REVIEWERS ON\n\"Vegetation enhances curvature-driven dynamics in meandering rivers\" by Finotello et al.\n(Manuscript ID: NCOMMS-23-37093)\nPlease note that in this response, italics refer to the text of the reviewers’ comments, our detailed\nreplies are in black, and the new text of the revised version is in bold font. Line numbers in our\nreplies refer to the revised version of the manuscript.\nREVIEWER #1 (REMARKS TO THE AUTHOR):\nOverall evaluation: This is an important and informative evaluation of the role of vegetation on\nmeandering behavior. The methodology and analyses are largely clearly explained. Most of the\ndetailed comments can be easily addressed. The issues raised in the general comments are largely\nbeyond the scope of the paper, but the authors should assess whether they have implications for\ninterpretations in the paper.\nThank you for this supportive assessment of our work.\nGeneral comments:\nThe role of sediment supply characteristics in meandering behavior is not discussed in this paper.\nIn this comment I rely on informal observations that may not be universally applicable. Meandering\nin arid environments seems to occur only when the supplied sediment contains a high fraction of\nmud relative to sand and gravel. Sand or gravel-dominated channels tend to be braided (this also\napplies to glacially-fed channels). The “point bars” of these mud-dominated channels are also\ncohesive. The presence of vegetation in more humid conditions allows stable meandering in sand\nand gravel-dominated settings which would be braided in more arid environments. Thus the\ncharacteristics of sediment supply may be an uncontrolled factor in the present analysis that is\nindirectly associated with vegetation.\nWe fully agree with the reviewer that sedimentological differences between rivers in vegetated and\nnon-vegetated (or poorly vegetated) settings are undeniable. As discussed in the Introduction\nsection, it is precisely these sedimentological differences that allow the development of meanders in\nnon-vegetated landscapes in the first place, with single-thread meandering rivers only forming\nunder favorable conditions (i.e., where cohesive agents such as mud provide the necessary bank\nstrength). As stated by the reviewer, meandering rivers exist in a narrow range of bed material and\nbank strength (see, for instance, Candel et al., 2021 and references therein), and it is unclear\nwhether those conditions would be met in a world fully devoid of land plants. Thus, our analysis\nbest applies to the variety of landscapes – unvegetated to vegetated – found on the modern Earth.\nNotwithstanding, mudrock (of detrital origin) is common in the Precambrian record and on Mars,\nwhere plants never evolved, such that our analysis may also shed light onto fluvial dynamics in the\nabsence of vegetation (e.g., Ielpi et al., 2022; Lapôtre et al., 2019).\nThe high frequency of chute cutoffs in channels with low density of vegetation may influence\naverage migration rates due to the perturbation of the flow field, which generally results in rapid\nadjustments of the planform and locally high migration rates. This is very evident in simulations of\nmeandering where neck cutoffs result in fast migration, sometimes with reverse direction of\nmigration. This is largely compensated for in the present study by considering in detail only the\nlow-curvature bends, but could still have some influence on low-curvature bends.\nAgreed. We also notice here that neck cutoffs, which are incidentally more widespread in vegetated\nrivers for the reason discussed at l. 286-292, likely have a stronger influence on enhancing\nmigration rates because they produce higher river curvature than chute cutoffs, and migration rates\nare positively correlated with higher curvature values in the way we demonstrate. Notwithstanding,\nwe added the following sentence in the revised “Curvature-driven meander dynamics enhanced by\nriparian vegetation” section:\n“In addition, local perturbations of river morphology induced by widespread chute cutoffs in barren\n1\nand poorly vegetated settings likely lead to accelerating migration and channel widening both locally\nand nonlocally68,69, thus further contributing to enhancing and data scatter at low curvature\nvalues that are typical of chute cutoffs. All of these processes are likely to make bank erosion and\nrelated river migration less correlated with curvature as the density of riparian vegetation decreases,\nthus explaining our observations.”\nSpecific comments:\nLine 24: The connotation of “morphodynamic maturity” will likely not have meaning to the reader\nuntil it is defined.\nTo keep the abstract as simple as possible, we have revised the sentence that now reads:\n“We show that denser riparian vegetation correlates with enhanced meander sinuosity, skewness,\nand curvature.”\nLine 28-29: It is unclear what is implied by “enhances the proportionality between migration rate\nand channel curvature”, i.e., a higher correlation coefficient, a higher regression slope, or a higher\nintercept? It is unlikely to be the latter since the migration rate is lower according to the first clause\nof the sentence.\nWe meant regression slope (i.e., the coefficient of proportionality). We have revised the sentence as\nfollows:\n“Nevertheless, we find that vegetation demonstrably reduces the rate of river lateral migration, and\nenhances the coefficient of proportionality between migration rate and channel curvature”\nLine 29: The antecedent “effect” is unclear for this sentence. Is it the reduced “rate of river lateral\nmigration”? Also, what is “obscured”? The rate of migration?\nWe have rephrased the sentence entirely as follows:\n“This enhancement is most evident at relatively low curvature and wanes in curvier channels\nregardless of vegetation density”\nLine 31: Eliminate “Hence,”, because this has not been demonstrated in the abstract. The sentence\nworks without this.\nDone, thank you.\nLines 44-46: The text leaves unresolved the question of why heterolithic strata are uncommon prior\nto the development of vascular plants, given that vegetation is asserted to be not necessary for\nmeandering behavior. Is this issue addressed later in the paper?\nThis aspects, albeit important, is largely beyond the scope of the present work. Although there is an\napproximate alignment noted between the extended proliferation of land plants during the early to\nmiddle Palaeozoic era and the emergence of sedimentological markers associated with lateral\naccretion in modern meandering rivers, lateral accretion sets in modern meandering rivers in\nunvegetated landscapes are not heterolithic (Hasson et al., 2023). It is thus possible, if not likely,\nthat many deposits from pre-vegetation meandering streams have remained undetected to date.\nLine 62: It is unclear what would be implied by the inverse relationship implied by “vice-versa”.\nWould meandering somehow lead to development of vegetation?\nThat is precisely what we meant here. Indeed, Santos et al. (2017) posit that the abrupt and\nwidespread appearance of fluvial deposits, signalling the accumulation of meandering river systems\nduring the Middle Palaeozoic on Earth, was predominantly a consequence of prevailing\nenvironmental and tectonic conditions during this period, leading to a global rise in the prevalence\nof meandering rivers that, in turn, facilitated a conducive environment for the colonization of\ncontinents by land plants. This hypothesis has sparked a debate within the scientific community\n(Davies et al., 2017; Santos, Mountney, Peakall, et al., 2017), and therefore, we believe it is\nnecessary to mention these references in our introduction.\nsentence works without this.\nLine 78 and lines 418-450: The present authors are probably not responsible for the misnomer\n“dynamic” in dynamic time warping. Based on the description, this methodology is at best\n“kinematic” because it is not based on mechanistic, deterministic forward modeling.\nThe “dynamic” term in DTW refers to the fact that the warping or alignment of two data series is\nnot predetermined but is determined dynamically during the computation. Although we agree with\nthe reviewer that this might seem confusing when used in the context of morphodynamics, DTW is\na well-established technique used in the field of pattern recognition, time series analysis, and data\nmining, and using a different term than what is used broadly in the literature would be even more\nconfusing.\nLine 88-89: Because “x” is a scaled variable in the equation, it probably should be designated as\n“x*”.\nCorrect. To avoid confusion with x*(s*) (mentioned in methods as the Easting coordinate of\nchannel axis centerline), we have changed x to z*. Thank you for noting this.\nLine 91-92: “fairly constant” is not quantifiably interpretable. Does it imply statistical equality of\nvalues?\nTo avoid misinterpretation, we have rephrased the sentence as follows:\n“Notably, whereas power-law prefactors ( ) differ slightly among distinct vegetation classes, power-\nlaw exponents ( ) range between 0.98 and 1.01 and are all sub-equal to 1, implying a linear scaling\nrelationship between and all analyzed morphometric descriptors.”\nLine 96: Clarify what is meant by [-] .\n“[-]” denotes dimensionless variables. For consistency with other dimensionless variables\nmentioned in the text, we have removed it.\nLine 102-103: “significant differences” should be “significant differences in morphometric\nrelationships”.\nWe have revised the sentence as suggested.\nLine 132: The criteria for this downsizing is not specified. This is not a crucial issue, but could be\nmentioned in the supplementary materials or methods.\nThe reason for this downsizing is that some variables are strongly cross-correlated, which is\nimplicitly mentioned in the previous sentence. Therefore, retaining the entire set of variables results\nin two (or more) of them having the same effect in terms of data separation in the PC space. This is\nclear from Supplementary Figure 1, which shows PCA results utilizing the entire set of\nmorphometric variables.\nIn the main text, we have added a brief explanation regarding the downsizing (following also\nsuggestions from toher reviewers) that reads:\n“Whereas the resulting dataset consists of 28 variables overall, we performed PCA on a subset of 17\nvariables (Fig. 3) that succinctly captures the variation in the original data while avoiding redundancy\nfrom cross-correlations.”\nLine 146: Here again, “maturity” of bends is mentioned without precise definition.\nWe rephrased the sentence as follows:\n“Higher , larger , and lower values are typically associated with late-stage meander\ngrowth40,41, suggesting that denser riparian vegetation correlates with the continued growth of\nmeanders until they reach morphodynamic maturity. At this stage, bends become highly sinuous and\nare more likely to shortcut themselves through neck cutoff40, representing the breaching of the\n3\nnarrow floodplain limb separating two adjacent bends that marks the endpoint of meander evolution\n(Fig. 1D).”\nLine 170: Is “impulsive” a well-recognized descriptor of sediment transport behavior?\nTo avoid confusion, we have changed the sentence as follows:\n“Flashier hydrological and sediment-transport regimes in arid and semi-arid settings may also\nfurther facilitate meander chute cutoffs, compounding the priming effect of reduced riparian\nvegetation density.”\nLines 183-186: I’m not sure why the effect of vegetation on chute cutoffs is a “confounding” factor\nand makes it challenging to infer causation. Cutoffs are probably the dominant factor in explaining\nthe lower average sinuosity in arid-zone channels due to sparse floodplain vegetation.\nWe do not fully understand this comment. Lines 183-186 in the original manuscript read: “(…)\nmore frequent avulsions in modern unvegetated and sparsely vegetated settings are a confounding\nfactor that makes it challenging to infer causation between vegetation and meandering river\nplanforms.” We believe this is correct because avulsion (not cutoff) is implied here as a\nconfounding factor. The reviewer is correct in stating that meander cutoff can be a dominant factor\nin explaining the lower sinuosity of unvegetated meandering rivers. However, the significant\ndisparity in avulsion regimes between modern unvegetated and vegetated meandering rivers makes\nit impossible to ascribe lower sinuosity to a higher chute cutoff frequency alone. This is because\navulsion effectively limits the development of meander sinuosity by shifting the river course and\ncausing the sinuosity development process to begin anew.\nLine 211: something is missing in the phrase “pointing to a strong first-order control of C\nmeandering river morphodynamics”\nYes, thank you for noting that. The correct sentence is:\n“(…) pointing to a strong first-order control of on meandering river morphodynamics.”\nLine 217 and Supplementary Material 2: It is unclear what is meant by “correcting migration rates\nby the average spatial lag”. The effect of the lag is clear in Supplementary Figure 10. Is the lag\nused to “correct” the data the average of the individual lags applied to the reach as a whole, or is\nthe lag determined and applied to each bend individually? Parenthetically, the term “corrected”\nshould probably be “normalized” or “adjusted”.\nAt line 217, we rephrased the sentence using 'adjusts' instead of 'correct' and specified that the\nspatial lag is taken as the reach-average value. This is in agreement with previous studies (Sylvester\net al., 2019b) that demonstrated this procedure to be appropriate since the lag exhibits limited\nvariability along any given river reach. The revised version of the sentence reads as follows:\n“In order to explore the effect of vegetation on curvature-driven meander dynamics, we derived the\nrelationship between dimensionless curvature ( ) and width-adjusted migration rate ( ) for each\nriver in our dataset, further adjusting migration rates by the reach-average spatial lag ( [m])\nbetween local maxima in channel curvature and migration rate37,44,51 (Supplementary Method 2).”\nIn the revised version of “Supplementary Method 2” we also better specify the above point. The\nrevised Supplementary text reads:\n“Hence, the curvature-migration lag is not necessarily constant but rather a function of the local\nmorphodynamic regime and related meander features2. Moreover, the lagis likely to vary between\ndifferent river systems depending on a range of factors (e.g., underlying geology, sediment\ncharacteristics, and environmental conditions). This notwithstanding, previous analyses suggested\nthat the along-channel distance between peak curvatures and migrations is fairly consistent across a\nwide range of climates and geological settings, typically attaining values ranging between 2 to 3\nchannel widths33,39,40,92. Our data confirm the above. It is clear from measurements of local migration\nrates in time-lapse satellite images that the pattern of river migration rate closely follows that of the\nlocal curvature, with a roughly constant phase lag between the two (see an example from the actively\nmigrating Rio Horton in Supplementary Fig. 11). Moreover, as illustrated by Supplementary Fig. 14,\nthe reach-averaged curvature-migration lag ( [-]) consistently scales with river width across a\n4\nwide range of environmental and climatic settings (as typified by distinct riparian vegetation density),\nwith values just slightly larger than two channel widths. Thus, in order to account for the spatial lag\nbetween curvature and migration maxima, in our analyses we first computed and separately\n(see Materials and Methods in the Main Text), and then shifted the signal upstream by a length\n, so that we could study the vs. functional relationship in a physically sound fashion.”\nIn Supplementary Figure 13 all the lags are positive, presumably implying a sub-resonant regime.\nWas this true for all rivers studied?\nThe dominant morphodynamic regime can be observed based on the distribution of meander\nasymmetry, as reported in Figure 2J. In the revised version of Fig.2, we have also included data\npoints related to individual meandering river reaches on top of the data concerning individual\nmeander bends (which were already reported in the early version of the manuscript). It is\nimmediately apparent that asymmetry index values are consistently negative on average, both when\nconsidering individual river reaches and the distribution of individual meander data, regardless of\nthe presence or absence of riparian vegetation. This indeed points to a sub-resonant morphodynamic\nregime in all analyzed rivers, although the presence of individual, downstream-skewed bends\nindicative of local super-resonant dominance is also observed. This comes as no surprise since most\nmeandering rivers are known to fall within the sub-resonant domain.\nMaterials and Methods: Extraction and analysis of meandering river planforms: As is\nacknowledged in the discussion care needs to be taken to remove “noise” related to the digitizing\nprocedure in determining the generalized planform. The discussion is generally clear about the\nprocedures, but some detail is lacking due to reliance on previous studies. One of the most critical\nsteps in segmenting natural channels is defining the inflection points. The issue is illustrated in\nSupplementary Figure 10, where near the north arrow there is a slight inward inflection of the\nadjacent long bend. If the plotted centerline between iv and v is correctly plotted there should be\ntwo intermediate inflection points and one half-bend that are not evident in part B of this figure.\nThis issue only becomes important if including those inflection points would significantly affect the\nsubsequent analyses. Have the authors, or previous studies, evaluated the influence of planform\ngeneralization on resulting morphometric parameters?\nThe absence of an inflection point (two, in fact, since a complete yet short meander bend is defined)\nbetween inflections 'iv' and 'v' in SI Fig. 10 is attributed to the low-pass filtering of the curvature\nsignal, a point that we agree was not sufficiently emphasized in the original manuscript. This\nfiltering, which compounds the filter and smoothing procedure (via cubic spline) applied to river\ncenterlines, is necessary to eliminate remaining noise in the curvature signal and prevent the\nidentification of spurious inflection points, as correctly anticipated by the reviewers based on SI\nFig. 10. Note that in this context, we use the term 'spurious inflections' to refer to zero-crossing\npoints in curvature signal describing short meander bends with extremely low sinuosity values.\nThese spurious infections are extremely common in double-headed meander bends characterized by\ntwo local maxima of curvature; multiple examples can be found in SI Fig. 10. Specifically, the river\nplanform geometry shown in Fig. 10 was characterized by the presence of two zero-crossing points\nin the curvature signal between inflections 'iv' and 'v.' These zero crossings in the original curvature\nsignal, which described a pseudo-meander with an intrinsic length approximately equal to 1 channel\nwidth and a sinuosity <1.01 (which is why we call it a “pseudo-meander”), were automatically\nsmoothed away by our filtering procedure. It is important to note here that no custom-user\ncorrection was applied, ensuring homogeneity in data analyses for all the river centerlines in our\ndataset. Since river centerlines were resampled at a standard resolution of one-tenth of the channel\naverage width, our filtering procedure remains consistent across channel sizes and does not affect\nour results (as spurious inflections are discarded or retained based on an automatic size-independent\nprocedure). This consistency effectively filters out size-dependent oscillation in meander\nmorphometrics, a long-known issue that has been recently addressed by Stanislawski et al., (2023)\nwith respect to meander sinuosity, for example. We also emphasize that double-headed meander\n5\nbends are the exception rather than the norm along a given meandering river reach and are not\nexpected to critically impact the results reported in our study.\nTo better clarify this point, we have updated the “Extraction and Analysis of Meandering River\nPlanforms” section in Material and Methods (main text) as follows:\n“To isolate individual meander bends we used a semi-automated procedure based on the\ncomputation of local channel-axis curvature ([m-1]) (Supplementary Fig. 11). Specifically, for any\ngiven centerline point , we computed = , where ([m]) denotes the\nchannel centerline curvilinear coordinate, represent the coordinates of an arbitrary\naxis point in a Cartesian reference system, and is the angle formed by the tangent to the\nchannel axis and an arbitrarily fixed direction33,37. After computing , a Savitzky–Golay low-pass\nfilter with a fixed polynomial order of 3 and a frame length of 21 centerline points was applied to\nfurther smooth noise in the original signal. Subsequently, half (full) meander bends were\nidentified as the portion of the channel between two (three) consecutive inflection points (i.e., points\nwhere =0). Meander apexes were also identified as points corresponding to local curvature\nmaxima (Fig. 1C and Supplementary Fig. 11). We note that the low-pass filtering of signal resulted\nin the automatic deletion of some “spurious” inflection points delimiting meander bends\ncharacterized by limited length and sinuosity, which are typical in double-headed meander bends\nfeaturing multiple local maxima in the signal (Supplementary Fig. 11).”\nThis is a very timely work that reveals the role of vegetation in meandering river development.\nMultiple controls have been previously proposed for the long-standing debate about the necessary\nconditions for meandering river development. Among these controls, vegetation has stirred up a lot\nof discussions recently, but how specifically does vegetation affect the morphology and dynamics of\nmeandering river have not been systematically explored in sufficient details until this current\nmanuscript. This work documented a list of key geometric attributes of meandering river planform\nmorphology across a wide range of riparian vegetation densities. Statistical analyses of these\nattributes reveal that the impact of vegetation on meandering morphology and dynamics is subtle\nbut significant. Moreover, the author found the range of curvature that distinct vegetation control\noperates. These results have important implications for the role of riverine environments in global\ncarbon cycle and reconstruction of the morphology and dynamics of ancient rivers on Earth and\nMars.\nThank you for this supportive assessment of our work.\nThere is one missing aspect of the dataset analyzed that could potentially hinder the application of\nthe results from this study. It seems that the rivers in the analyzed dataset collected by the authors\nare all small to intermediate-sized rivers, and most large lowland rivers are not included. This\nraises the question whether the findings of the study apply to large lowland meandering rivers as\nwell. I speculate that the impact of vegetation on large rivers is limited as the flow depth of these\nrivers extends far below the roots of vegetations. This does not negate the results of this study but\nsuggests that there might be a river size limitation on the role of vegetation on meandering river\nmorphology and dynamics. In order to maximize the application of this work, I would suggest the\nauthor to consider the following:\n(1) Include some large rivers in the dataset. Whether the large lowland rivers follow the trends\ndemonstrated in this study will be useful information. If they do, then it supports that the impact of\nvegetation is also important for large rivers. If not, there might be a river-size limit for vegetation\nto affect the morphology and dynamics of meandering river. This is not to underrate the importance\nof small- to intermediate sized rivers, as they comprise a large portion of global rivers.\n(2) Characterize the size of the rivers in the dataset in terms of slope and discharge and provide the\noverall range/distribution of these metrics. This will help to put the size of the rivers in the dataset\ninto a spectrum so that in case no large river will be included in the analysis, at least it shows the\nslope and discharge range that the current results are applicable to.\nWe thank the reviewer for this important comment, which highlights the need for a deeper\ndiscussion of our selection criteria. The present dataset includes vegetated meandering rivers that\nare up to ~1 km wide; while we’d certainly like to include more, larger rivers are inherently few.\nFurthermore, we only consider (1) single-thread meandering rivers that are (2) not significantly\naffected by human activity, and (3) are sufficiently far away from the coastline in order not to be\naffected by backwater and/or tidal effects. These criteria significantly restrict the pool of case\nstudies that are suitable for expanding our dataset. Finally, we only consider reaches containing at\nleast 35 consecutive bends, so that a sufficiently long train of meanders can be analyzed to ensure\ndata homogeneity among distinct fluvial settings. We could thus not include stretches of >1 km\nwide meandering rivers comprising fewer than 35 meander bends in our analyses. Together, we\nbelieve that these criteria leave the pool of available candidate rivers to exactly zero. To check this,\nwe used the global dataset provided by Frasson et al. (2019), filtering out river stretches that i) are\nnarrower than 1050 meters; ii) belongs to lake/reservoirs; iii) have an overall sinuosity lower than\n1.2 (the filtered Frasson et al.’s database can be accessed, for the reviewer benefit, at the following\nlink:\nhttps://drive.google.com/drive/folders/1yKThmeFQT37QE-hfHp7leUAeNvNi1ALB?usp=sharing).\nIt clearly emerges that the only handful of large rivers that meet our selection criteria are not free\nfrom human influences (e.g., the lower stretch of the highly engineered Mississippi River), and\ntherefore cannot be included in our dataset. In summary, our dataset includes the largest single-\n7\nthread, sufficiently long, undisturbed vegetated river stretches we are aware of. In the revised\nversion of our manuscript, we now discuss those selection criteria in more detail. Specifically, the\nrevised “Material and Methods - Extraction and Analysis of Meandering River Planforms” section\nnow includes:\n“To obtain planform morphometrics of individual meandering reaches, we first hand-digitized\nriverbank lines in the QGIS environment based on freely available georeferenced aerial and satellite\nimages. The latter include several different products available through Google Earth Pro, SASPlanet,\nthe U.S. Geological Survey Earth Explorer portal, and the QuickMapService QGIS plugin.\nAdditionally, we included the data collection provided by Sylvester et al.37 for vegetated meandering\nrivers in the Amazon basin in our dataset (Fig. 1A).\nIn order to ensure data homogeneity among distinct fluvial settings, we only considered single-\nthread meandering river reaches that i) contain at least 35 consecutive bends, such that a sufficiently\nlong train of meanders can be analyzed; ii) are found sufficiently far away from the coastline in order\nnot to be affected by backwater and/or tidal effects; iii) have not been significantly modified or\nengineered by humans.“\nAs a side note, we emphasize that the lack of large unvegetated streams on modern Earth cannot be\nused to infer that vegetation enables larger meandering systems because vegetation is everywhere in\npresent-day Earth except for small arid endorheic basins draining relatively small catchments.\nIn terms of bed slope and flow discharge, the other two parameters requested by the reviewer, we\nnote that:\n• Not all the analyzed rivers are gauged (most are not, in fact, especially smaller and poorly\nvegetated ones); since river width (W) is known to scale with formative discharge (Q), we\ncould use known global relationships to derive Q from W, but this would add nothing to the\nproposed analyses currently carried out based on W.\n• Slope is perhaps the easiest parameter to estimate, which can be done, for example, based on\nremotely sensed SRTM data. However, critical changes in river size (with W spanning 4\norders of magnitude in our dataset) combined with the fixed resolution of SRTM data would\nresult in biased estimates of slope depending on river size. Furthermore, we note that slope\n(like discharge) would be somewhat redundant with width (for given bed and bank\nmaterials) as we only consider self-formed, alluvial rivers.\nSome minor points for the author to consider:\nIs there a threshold curvature used for identifying cross-over point? For example, there seems to be\nlow curvature bends that are part of a compound bend but not considered as a bend defined by\ncross-over point in figure 1C (e.g., upper section of Humboldt river below the 7th cross-over point,\nand mid-section of the Rio Horton river below the 13th cross-over point). It seems that the current\nmethod skips some of the low curvature bends.\nNo, there is no pre-defined curvature threshold used for identifying cross-over (i.e., inflection)\npoints. However, a low-pass filter is applied to the curvature signal that automatically filters out\nsome “spurious” inflections as discussed above in our response to Reviewer 1’s last comment.\nSpecific comments:\nLine 71: what about different types of vegetation, which may contribute to the spread of data in the\nanalysis?\nDifferent types of vegetation could clearly have different impacts on river morphodynamics, due to,\nfor instance, varying rooting depths. However, rooting depth is not just a function of vegetation\nspecies but also depends on local factors such as the elevation of the water table and soil properties,\nfor example. Assessing the specific types of vegetation species is impractical based on remotely\nsensed NDVI data alone (multispectral data at proper resolution would be needed, together with\nground thrusting surveys). In addition, different vegetation species suited to distinct climate settings\n8\nmight have similar rooting depths, which further complicates possible detailed analyses. The latter\naspect is beyond the scope of the present work. Notwithstanding, we agree with the reviewer that\nnot only riparian vegetation density but also the type of vegetation can affect both river morphology\nand dynamics. However, we shall also note that denser riparian vegetation typically (i.e., higher\nNDVI values, say NDVI > 0.4) consists of trees and arborescent shrub species, with poorly\nvegetated settings (0.2 < NDVI < 0.4) featuring mostly shrubs and ground covers. In this way, a\ntransition from high to low NDVI values also denotes broad changes in plant taxonomy. A\ndiscussion on possible effects related to river size and vegetation type, not necessarily exhaustive, is\nreported in the text:\n“Plant density, as well as channel width and depth relative to plant stem diameter and rooting\ndepth14,25,61–63, have been shown to influence channel dynamics. In sparsely vegetated landscapes,\nshrubby arborescent, drought-resilient plants will encroach into the moister and nutrient-rich\nthalweg zone of ephemeral channels, where groundwater is more accessible17,25. Especially in rivers\nnarrower than 10 m, such clusters of in-channel vegetation can enhance local scour and bank\nerosion, disrupt curvature-induced helical flow that is necessary to sustain lateral migration, and\nlimit meander growth by facilitating braiding and meander chute cutoffs25,62 (formed when the river\ncuts a new bypass channel through its own point bar64; see Supplementary Fig. 6). In contrast, deep-\nrooted trees can sustain large single-thread meandering channels (width>102 m)25,63 in densely\nforested floodplains, aiding flow confinement through enhanced bank-erosion resistance and\nfacilitating the continued development of highly sinuous meander bends until neck cutoff. On\naverage, larger rivers are associated with higher NDVI values (Supplementary Fig. 7), but our\nanalysis of normalized morphometric characteristics shows that the effects of vegetation regime on\nmeandering dynamics are independent of channel size (Fig. 2A-D).”\nLine 177 “low-gradient terminal fluvial fans…”\nCould you provide the actual slope range for the studied rivers.\nWe have revised the sentence as follows:\n“Besides, meandering streams in modern barren environments are found almost exclusively along\nlow-gradient (slope ~ 10-5-10-4) terminal fluvial fans where relatively high rates of vertical aggradation\nincrease the frequency of river avulsions5,21,25,80”\n(see also our detailed response to a previous comment).\nLine 212 “reaches (C<0.3)…” How is this threshold value of curvature determined? Seems the\ncurvature for peak adjusted migration rate for semi-vegetated and unnegated rivers is closer to 0.2\n(Fig. 4B, C).\nThe threshold value of curvature we used is based on both the results we present in our manuscript\nand earlier literature. Specifically, beginning with the seminal work of Edward Hickin and Gerald\nNanson on the Beatton River (British Columbia, Canada) (Hickin & Nanson, 1975), it has been\nrecognized that migration rate maxima occur for a value of bend radius over width 2.5<R*/W*<4\n(see also Blanckaert, 2011 and Hooke, 2013, among others). Such a range of bend radii, which\ncorresponds to a normalized channel curvature 0.25<C*·W*<0.4, is not incidental, as it depends on\nstrong hydrodynamic nonlinearities arising in sharp bends (e.g., Blanckaert, 2009, 2010; Blanckaert\n& de Vriend, 2005; Finotello et al., 2019; Ottevanger et al., 2012). In summary, although there isn't\na specific curvature value associated with the growth of such nonlinearities and the related\nsaturation of migration rates, we used C=0.3 as a typical value to avoid constantly referring to a\nrange of critical C*·W* values.\nWe have also specified this in the revised manuscript:\n“This proportionality typically only holds for mildly curved channel reaches (i.e., for width-adjusted\ncurvature values smaller than 0.25-0.5, taken here as <0.3 for convenience) and breaks down at\nhigh curvatures ( >0.3) where saturate due to the growth of hydrodynamic nonlinearities that\neffectively limit bank erosion, such as saturation of centrifugally driven secondary flows, enhanced\nsecondary outer bank cells, and flow separation at the outer bank1,38,46,53,54 (Supplementary Method\n2).”\nLine 236 “morphodynamic feedbacks that arise…”\nWhat specific feedback this is referring to?\nThis is explained in the next paragraph:\n“Plant density, as well as channel width and depth relative to plant stem diameter and rooting\ndepth14,25,61–63, have been shown to influence channel dynamics. In sparsely vegetated landscapes,\nshrubby arborescent, drought-resilient plants will encroach into the moister and nutrient-rich\nthalweg zone of ephemeral channels, where groundwater is more accessible17,25. Especially in rivers\nnarrower than 10 m, such clusters of in-channel vegetation can enhance local scour and bank\nerosion, disrupt curvature-induced helical flow that is necessary to sustain lateral migration, and\nlimit meander growth by facilitating braiding and meander chute cutoffs25,62 (formed when the river\ncuts a new bypass channel through its own point bar64; see Supplementary Fig. 6). In contrast, deep-\nrooted trees can sustain large single-thread meandering channels (width>102 m)25,63 in densely\nforested floodplains, aiding flow confinement through enhanced bank-erosion resistance and\nfacilitating the continued development of highly sinuous meander bends until neck cutoff. On\naverage, larger rivers are associated with higher NDVI values (Supplementary Fig. 7), but our\nanalysis of normalized morphometric characteristics shows that the effects of vegetation regime on\nmeandering dynamics are independent of channel size (Fig. 2A-D).”\nLine 249 “…independent of channel size”\nAgain, what about large rivers.\nPlease refer to our detailed response to a previous comment.\nChenliang Wu\nPostdoc Researcher\nTulane University\nReferences\n1. Zhu, L., Chen, D., Hassan, M. A. & Venditti, J. G. The Influence of Riparian Vegetation on the\nSinuosity and Lateral Stability of Meandering Channels. Geophysical Research Letters 49,\ne2021GL096346 (2022).\nReview of Vegetation Signature on River Meander Morphology and Dynamics by Finotello et al.\nsubmitted to Nature Communications\nFinotello et al. provide a comprehensive analysis to show how vegetation influences river\nmeandering. The manuscript is well written and the authors should be applauded for their detailed\nscience and valuable data its created. The work is significant. The authors find that rivers with\nunvegetated and vegetated banks have different planform sinuosities and bend asymmetries\nsuggesting that bends don’t reach maturity in unvegetated settings. They also use a novel analysis\nand show that while rivers with all types of bank vegetation have consistent curvature vs. migration\nrate relationships, unvegetated rivers have faster bank migration rates at low curvature. The\nmethodology and data analyses are very sound, and the results are of broad interest to fluvial\ngeomorphologists and geologists that keep up with the debate on the role of vegetation in river\nmeandering.\nThank you for this supportive assessment of our work.\nWith that said, there are a few overarching difficulties I had with the present version of manuscript\nthat include:\n1) more discussion connecting the morphometric and migration rate analyses;\n2) a need to better justify methodological choices;\nand 3) figure simplification and readability.\nWe are thankful for the constructive review from the present reviewers. We addressed all\nsuggestions in full, as detailed below.\nThere are two related, but separate analyses included in the manuscript. The first half of the article\nfocuses on a morphometric analysis of river planform. They utilize and report on two different\nstatistical approaches (population inference and PCA). The second half of the paper is a novel test\nof existing empiricism and theory that for the first time in my knowledge, looks at curvature and\nmeander migration for both unvegetated and vegetated rivers. However, there is little structure\nconnecting these two analyses.\nSome notes on this:\n• the “Other Impacts on Planform Morphology” section (L150) is indicative of the difficulty the text\nhad in bridging the two analyses. I found this section out of place as it was a discussion describing\ndrivers of planform morphology that aren’t explicitly vegetation without a clear section devoted to\ndiscussing the role of vegetation itself on planform morphology.\n• further, the opening of the “Meandering river dynamics” section (L189) is too generic and can\nuse more justification as to why were are looking at morphometrics and dynamics in the same\nanalysis. Instead, the paragraph (L189-L203) spends valuable text comparing to previous\nliterature, which while it is great to see that it lines up, could be used to tie the analyses together.\n• the primary connection between the two analysis is finally discussed in the implications section\n(L303). While I think this is a reasonable hypothesis, it would be strengthened by a more structured\nset-up connecting morphometrics and dynamics. The full discussion of the morphometrics could be\nincluded in the implications. If the authors are making the argument that a lack of vegetation and\nhigh low-curvature migration rates leads to channel wandering and limited sinuosity, a side-by-side\ndiscussion of channel cutoffs (which can also be influenced by vegetation) has to be included to\nmake the argument convincing.\nIn hindsight, we realize that the connection between morphometrics and dynamics was not as\ncompelling as we wish it were. To strengthen that connection, we restructured the manuscript\nsignificantly; notably, through a discussion of results from both morphometric and dynamic\nanalyses, followed by a discussion of their joint implications in the 'Discussion and Implications'.\nbetter justification to strengthen the manuscript:\n• There is little explanation as to how or why the data is/is not aggregated. The dataset includes 54\nrivers, but all the analyses are completed at the bend-scale. This means that dependent\nmeasurements at the bend-scale, are treated as independent measurements throughout all statistical\ntests (e.g. inferential statistics in the morphometry and the comparison of width-averaged migration\nrates). While bend-scale measurements have to be used for the curvature analysis, using bend-scale\nmeasurements for the WRS and KS tests will lead to artificially low p-values. This is a significant\npoint because all the individual bend-scale measurements are *not* independent measurements and\nsome sort of bootstrapping is essential for correcting for this inherent bias. The authors really have\n54 independent rivers and not hundreds to thousands of independent measurements as the data\nplots make it out to be.\nThis is a good point. We first note that not all analyses were conducted at the bend scale.\nSpecifically, morphometric variables are reported both as reach-averaged and bend-scale values.\nFor instance, in Fig. 2, boxplots represent bend-scale morphometrics, while exceedance probability\nplots denote reach-scale distributions of morphometric variables (i.e., we had indeed 54 individual\nplots, one for each river in our dataset). Accordingly, whereas WRS tests were performed with\nreference to bend-scale data, KS tests referred to probability distributions of reach-scale\nmorphometrics. In this way, we demonstrate that reported differences are statistically significant\nboth with reference to individual bends and river-aggregate planform characteristics of meander\nbends. However, it is clear from the reviewer’s comment that this distinction was not clear in the\noriginal version of the manuscript. To address this issue, we now included, in panels A-D of Fig. 2\nand in each boxplot within the same figure, data points of reach-averaged morphometric values for\nevery river in our dataset, in addition to bend-scale data. Furthermore, we now also perform WRS\ntests considering aggregate river data instead of bend-scale data. The updated results of these tests\nare now included in both the text and the table. It is important to highlight that considering\naggregate data yields minimal differences compared to the previously reported results; specifically,\nno statistically significant changes are observed in terms of differences among the considered\nmorphometric variables (i.e., aggregating data does not significantly impact our result). The revised\nversion of the text reporting the results of statistical tests now reads:\n“Two-sample Wilcoxon Rank Sum (WRS) and Kolmogorov-Smirnov (KS) tests, performed at a\nstandard 5% significance level on river-aggregated data, highlight statistically significant differences\nin morphometric relationships between vegetated rivers (used as the control group) and both\nunvegetated and semi-vegetated rivers. The KS tests all reject the null hypothesis that the\nmorphometries of unvegetated and semi-vegetated rivers come from the same distribution as those\nof vegetated rivers. Additionally, the WRS tests reject the null hypothesis that the morphometric\nparameters of both unvegetated and semi-vegetated rivers have the same median as vegetated rivers\nin all cases except for the meander amplitude in unvegetated rivers and meander wavelengths and\ncurvature in semi-vegetated rivers.\nCompared to their vegetated counterparts, rivers in unvegetated settings typically feature longer\nmeander wavelengths and larger radii of curvature relative to channel width, with lower meander\nsinuosity and width-adjusted curvature (Fig. 2E,F,H,I,K). Specifically, while in vegetated rivers 26% of\nmeanders have a sinuosity >2 and 13% have a curvature >0.3, these percentages decrease to 7%\nand 5%, respectively, for unvegetated rivers. Vegetation also appears to correlate with bend\nasymmetry: meanders in vegetated and semi-vegetated rivers are more strongly upstream-skewed\n(i.e., lower values of ) whereas unvegetated rivers host more symmetric bends on average (Fig.\n2J). Whereas these differences emerge when data are treated as ensemble averages (i.e., binned\nover the entire data set), distributions associated with individual rivers display a wide dispersion\n(Fig. 2E-K). Thus, meander morphologies overlap considerably among different vegetation classes.”\nIn addition, we eliminated histogram plots of morphometric parameter distributions (previously\nreported in the form of aggregated plots for each vegetation class) and changed colors to reduce\nexcessive fainting.\n12\n• Why do the authors select the morphometric variables used in the analysis (L93)? There is a good\ndeal of overlap between variables. For example, what is gained by including intrinsic wavelength,\ncartesian wavelength, and sinuosity?\nThe reviewer is correct that not all variables are fully independent. However, as suggested by\nprevious studies (e.g., Finotello et al., 2020; Frascati & Lanzoni, 2009; Howard & Hemberger,\n1991), the functional relationships between some of these variables are nontrivial such that no\nindividual variable alone suffices to completely characterize meander bend geometry or, more\nimportantly, to discern any morphometric differences in meander bend subgroups. For other\nvariables, that functional relationship is linear and simple (e.g., wavelength and sinuosity).\nHowever, including both greatly facilitates the discussion of our results, as well as allows us to\nexplicitly define the meander size (relative to channel width) producing a given sinuosity value.\nFurthermore, including all possible morphometric variables enables a direct comparison with\npreviously published literature, broadening the relevance of our work in the context of meandering\nriver research.\nL131: Is cross-correlation the reason some variables were left out? Could swap this and the\nprevious sentence to help clarity. Did the authors use any standardized method to determine which\nvariables to use, i.e., a threshold? Were things like average half sinuosity and half meander\nintrinsic length not correlated?\nWhat is the PCA analysis contributing to help flesh out the results from inferential statistics? Is the\nmost significant takeaway that only sinuosity and skewness are important (L143)? The authors do\ninclude higher order statistics of the variables, and these show up in the results, but are not\ndiscussed.\nAs noted in our previous response, many variables are indeed cross-correlated to some extent for\npurely geometric reasons (and so are most of the variables we retain for the analyses presented in\nFig. 3 as well as in SI). This is overall consistent with the use of PCA, which is typically used for\ndimensionality reduction and summarizing data. Again, we note that this is a standard procedure in\nthe river meander literature, both in terms of methodology and considered morphometric variables\n(Bogoni et al., 2017; Finotello et al., 2020; Frascati & Lanzoni, 2009; Howard & Hemberger,\n1991). The use of PCA not only allowed us to derive critical information regarding differences in\nmeandering river planforms as a function of vegetation (impractical using univariate statistics alone,\nas we demonstrate), but also aligns our study with previous research wherein it was shown that\nmorphological variations between freely meandering streams can be resolved by morphometric\nparameters related to wavelength, skewness, sinuosity, and curvature of meander axis (Howard &\nHemberger, 1991 being the seminal work in this respect).\nConsidering that PCA performed on ensembles of morphometrics different from those reported in\nthe main text (SI Fig. S1 and S2) holds similar results, we can conclude that data separation is\npredominantly driven by higher meander sinuosity, curvature, and degree of upstream skewness in\nvegetated rivers. This however doesn’t mean that only sinuosity and skewness are important, but it\nrather indicates that these are the variables that explain most of the variance in the dataset.\nWe shall also notice here that higher-order statistics are included because i) they can be relevant in\ndriving data separation at times and ii) including them is standard practice in the literature (see refs.\ncited above and also Appels et al., 2008). However, discussing high-order statistics would add little\nto the reported results in the text at the cost of unnecessarily complicating the reading (besides the\nfact that the meaning of high-order statistics is debatable per se; see for instance Balanda &\nMacgillivray, 1988; Darlington, 1970; Moors, 1986; Ruppert, 1987; Zhiqiang et al., 2008). Hence,\nwe prefer not to discuss their implications in detail, especially considering that a clear separation of\ndata as a function of vegetation class does not exist (rather, there is a continuous transition as we\ndemonstrate) and that, even if there was a separation, the discrepancy in river avulsion tendency as\na function of vegetation would confound it anyway.\nFollowing the reviewer’s suggestion, we have modified the sentence in L.131 of the original\nmanuscript as:\n13\n“Following a standard approach in river morphodynamics33–35,39, we applied Principal Component\nAnalysis (PCA) (Supplementary Method 1) to a set of distinct morphometric variables derived from\nriver-aggregated distributions of meander planform features (Table 1 and Material and Methods). As\ndemonstrated by Howard and Hemberger35, morphological variations among freely meandering\nstreams can be resolved by morphometric parameters related to meander wavelength, skewness,\nsinuosity, and curvature. Hence, we considered the first- to fourth-order statistics of the probability\ndistributions of meander sinuosity ( ), asymmetry ( ), and both width-adjusted curvature ( ) and\nintrinsic wavelength ( ).\nAll variables were computed for both half and full meander bends (Table 1 and see Material and\nMethods), except for , for which we considered the reach-averaged values. Whereas the resulting\ndataset consists of 28 variables overall, we performed PCA on a subset of 17 variables (Fig. 3) that\nsuccinctly captures the variation in the original data while avoiding redundancy from cross-\ncorrelations.”\n• In the current text, it’s unclear whether the mean-normalization (L253) is producing a result that\nis different than the width-normalization (L216).\nThe authors include reporting the curve-fits for the mean-normalization (L262-L268), but not the\nwidth-normalization.\nIt currently reads that the mean-normalization simply reduces the noise in the semi-vegetated\nrivers.\nThe main effects of mean-normalization are twofold: i) it reduces noise in the semi-vegetated data;\nand ii) it better highlights the plateau in migration rates for vegetated rivers beyond the C=0.3\nthreshold. Aside from the above, mean normalization has limited impact on reported C vs. M\nrelations. Still, we deem mean-normalization to be necessary to avoid systematic data bias toward\nhighly mobile river reaches. This latter point was not well conveyed in the original manuscript. The\nrevised version of the “Curvature-driven meander dynamics enhanced by riparian vegetation”\nparagraph now reads:\n“To investigate variations in channel mobility while avoiding highly mobile rivers to systematically\nbias our data, we further normalized by dividing it by the average migration rate of the\ncorresponding river reach ( ) (Fig. 4C). Importantly, this procedure also allows for filtering out\nspurious correlations due to inherent hydrological and sedimentological variability (e.g., flow\nintermittency and changes in bank erodibility) broadly related to site-specific climatic and\nenvironmental conditions.”\nPlease note that curve fits were reported only for mean-normalized data and only for the C < 0.3\ndata range. We feel this is a sensible decision to avoid excessively lengthening the text, especially\nsince all fits are reported (along with p-values and R-squared coefficients) in Figure 4B,C.\nA related question, is the correct interpretation for figure 4c (unvegetated) that the median\nmigration rate for an unvegetated straight reach is faster than the average migration rate for the\nriver?\nAssuming that 'straight' corresponds to C < 0.3 (although we note that C = 0.3 already represents a\nsignificant curvature), we obtain, for the unvegetated river considering ensemble data (i.e., all\nreaches on record), an overall width- and mean-normalized average migration rate of m = 1.2980.\navg\nHowever, the median migration rate, considering only data with C < 0.3, is equal to m t =\nstraigh\n0.9902 (hence smaller than m ). Even if we restrict our analysis to include only quasi-straight\navg\nreaches, defined as reaches where C < 0.001, we obtain m = 0.9805, which is still slower than\nstraight\nthe average migration rate for the river.\nThe figures contain a wealth of information, but they are at times difficult to unpack. A couple of\nnotes on the figures:\nFigure 2:\n• The “inset” is the last subplot on the figure, but cited first. This should be directly labeled.\n• The faint shading that is used in the figure makes it hard to read/interpret. This is most striking in\nA-D where only the axes appear to have 100% opacity.\n• Including all the box plots, probability density plots and exceedance probability plots is not\nnecessary. The overlap in spread between the bend-scale data can be seen in either the points from\nthe box plots or the pdf plots. Depending on how the figure is revised, plotting some version of the\nriver-aggregated data could also be useful.\nWe modified Figure 2 as shown above in our reply to a previous comment. Regarding the inset, we\nbelieve it is appropriate to leave it as it is (unlabelled) precisely because, for graphic reasons, it\nneeds to be placed in the bottom right corner and at the same time, it is the first one mentioned in\nthe text\nFigure 3:\n• While Figure 3A would be nice to have in the supplement, the sentiment is covered well in the text\nalready (L135).\n• Because you minimize all components other than 1 in the text (L138), the plot between a2 and a3\nis superfluous given that you include more PCA plots in the supplement that also don’t show\nvegetation differences. You could move D/G into the supplement, which might allow you to have\nbigger symbols, etc. There is an argument to be made that B and E are the only important subplots\naccording to how it’s discussed in the text.\n• There is also overlap between table 1 and the list of variables included in the figure. The variable\nnames in the figure are faint and hard to read. They could be cut.\nPanel A has been moved to the Supplementary Information (SI), and the list of variables has been\nremoved from Fig. 3 as suggested. We agree that panels B and E are the most important ones.\nHowever, we prefer to keep D/G in place because it better conveys the message that PC > 3 are not\nimportant (especially now that we moved the eigenspectrum to SI). Additionally, this is standard\npractice in recent literature (Bogoni et al., 2017). Note that, having moved Panel A to the\nSupplementary Information and removed the inset, we have also enlarged the remaining panels to\nimprove readability as requested.\nWe also modified the colors and shading of panel A-C for consistency with the revised Fig. 2.\nFigure 4:\n• Subplot A is a bit misleading because the data is not aggregated or bootstrapped. The boxplots\nwill be affected by including dependent bend-scale measurements. There could be an opportunity\nhere to show the river-aggregated data as well.\n• The kernel density plots are a great way to show the massive amount of bend-scale data. It’s too\nfaint as is. The colors need to be more visible\nWe modified Fig. 4 as suggested, updating the boxplots using individual-river data (plotted on top\nof bend-scale data), changing colours for consistency with other figures, and reducing faint shading\nin KDE plots to make colours more visible.\nOverall, I thoroughly enjoyed reading the results and I do think they are noteworthy and\nsignificant. The analysis between curvature and migration rates across different vegetation is\nespecially novel. With major revisions this will be an important contribution. The major themes in\nrevisions we suggest are to better justify the use of bank-aggregated data across all analysis,\nstreamline the figures, and connect the two analyses within the same discussion and conceptual\nframework.\nWe are thankful for these important suggestions which greatly helped us clarify and streamline our\nmanuscript.\nOther specific notes:\nL74: What is “individual” in this context. This is only point in the paper that there is a discussion\nabout aggregating at multiple scales. There needs to be more detailed description about what each\ndata point represents.\nAgreed, and we have done that throughout the manuscript (as well as in Figures) as suggested.\nConcerning l.74 in the original manuscript specifically, we have modified the phrasing as follows to\navoid any confusion:\n15\n“For each class, we analyzed the width-adjusted morphometric properties of meander planforms at\nboth the scale of single bends and individual river reaches, using classical uni- and multivariate\nstatistical methods in the river-meander literature”.\nL104-107: Does this mean that the differences between the unvegetated and semi-vegetated rivers\nare statistically similar? Or did you only test for differences with the vegetated rivers?\nWe did only test for differences with vegetated rivers (used as the control group).\nL112: Provide a count of unvegetated and vegetated rivers that fall into these categories to back\nthis up. That way the reader doesn’t have to go into the tabulated data.\nThe sentence has been revised as follows:\n“Specifically, while in vegetated rivers 26% of meanders have a sinuosity >2 and 13% have a\ncurvature >0.3, these percentages decrease to 7% and 5%, respectively, for unvegetated rivers.”\nL178: Wouldn’t this mean that the avulsion timescale would have to approach bend-migration\ntimescales (the time necessary to reach a “mature” bend).\nNot precisely. The avulsion timescale T is defined (sensu Jerolmack & Mohrig, 2007) as the time\nA\nrequired for the river to aggrade one (or a fraction of) channel depth vertically, whereas the\nmigration timescale T is the time required for the river to migrate one channel width laterally. In\nM\nthis sense, to have mature bends, it is required that T is sufficiently small compared to T . We note\nM A\nhere that to have single-thread meandering rivers (rather than anabranching ones), the ratio M= T /\nA\nT needs to be >>1 (see again Jerolmack & Mohrig 2007). All rivers in our dataset fall in this\nM\nregime, being all single-threaded, and yet the disparity in T might still be able to drive critical\nA\nmorphodynamic differences in the way we illustrate.\nL189: Why are avulsions not a concern if they are mentioned as an important consideration at the\nmigration timescale in the previous section?\nThis is because we are now focusing on meander dynamics in between avulsions, which depends on\ncurvature (both local and upstream-aggregated) rather than on meander planform more broadly\ndefined. Specifically, since the M= T / T ratio (see previous comment) is still large enough even\nA M\nin the unvegetated class to allow for developing single-thread rivers, the migration dynamics (i.e.,\nrate of lateral migration and the relation between migration and curvature) can be studied in details\nas long as no avulsion occurs during the timeframe used for analysis.\nL213: This is a fairly novel connection of ideas based on your Geology comment of Sylverster et al.\n2019. It may be useful to give just a sentence more detailed description to strengthen this key point\npast “hydrodynamic nonlinearities”.\nWe have modified the sentence as follows:\n“This proportionality typically only holds for mildly curved channel reaches (i.e., for width-adjusted\ncurvature values smaller than 0.25-0.5, taken here as <0.3 for convenience) and breaks down at\nhigh curvatures ( >0.3) where saturate due to the growth of hydrodynamic nonlinearities that\neffectively limit bank erosion, such as saturation of centrifugally driven secondary flows, enhanced\nsecondary outer bank cells, and flow separation at the outer bank1,38,46,53,54 (Supplementary Method\n2).”\nAppels, W. M., Hoitink, A. J. F., & Hoekman, D. H. (2008). Planform geometry of peat meanders.\nRiver, Coastal and Estuarine Morphodynamics: RCEM 2007 - Proceedings of the 5th IAHR\nSymposium on River, Coastal and Estuarine Morphodynamics, 1, 271–277.\nhttps://doi.org/10.1201/noe0415453639-c34\nBalanda, K. 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Dynamic single-thread channels maintained by the interaction of flow\nand vegetation. Geology, 35(4), 347–350. https://doi.org/10.1130/G23260A.1\nTörök, G. T., & Parker, G. (2022). The influence of riparian woody vegetation on bankfull alluvial\nriver morphodynamics. Scientific Reports, 12(1), 1–15. https://doi.org/10.1038/s41598-022-\n22846-1\nZhiqiang, L., Jianming, W., Junyu, Z., Haitao, L., Baoqing, L., Jie, S., & Chunlei, Z. (2008). The\nstatistical meaning of kurtosis and its new application to identification of persons based on\nseismic signals. Sensors, 8(8), 5106–5119. https://doi.org/10.3390/s8085106\nReviewer #2 (Remarks to the Author):\nThe authors have addressed all the issues I raised with sufficient detail. Thank you for taking the fime to\nrespond to all the comments.\nReviewers #3 and #4 – Co-Review (Remarks to the Author):\nWe enjoyed re-reading the revised manuscript. In short, the authors have done a commendable job at\naddressing the reviewers’ comments and we believe that the manuscript will be a broadly-read\ncontribufion. The authors restructured the paper, to present all the results before going into an\nexpanded discussion on the morphometrics and dynamics side-by-side (in the Discussion and\nImplicafions) secfion. The current structure works well, and is a marked improvement from the previous\nversion. We especially liked the combined nuance discussion on the complex connecfions between\ncutoffs, avulsions, and bend maturity, and its relafion to migrafion pafterns. The authors befter address\ndata aggregafion in the main text and the figures, and the color contrast significantly help figure\nreadability in all cases.\nOne last comment on lines 158-161 in revised manuscript – are the authors referring to the stafisfical\ndifference in migrafion rates shown in figure 4a? If so, it seems like the P value might be reported for the\nbend-scale data as opposed to reach-scale data. It seems like the reach-scale data show significant\noverlap. Could the authors double check this in the final version? Visually, the data do not seem so far off\nfrom each other to yield the small P value reported unless the differences are being swamped by the log\nscale.\nIn summary, we believe that our concerns have been addressed in the revisions and we look forward to\nthe manuscript in publicafion. This manuscript was co-reviewed as part of the Nature Communicafions\ninifiafive to facilitate training in peer review and to provide appropriate recognifion for Early Career\nResearchers.\nRESPONSE TO REVIEWERS ON\n\"Vegetation enhances curvature-driven dynamics in meandering rivers\" by Finotello et al.\n(Manuscript ID: NCOMMS-23-37093A)\nPlease note that in this response, italics refer to the text of the reviewers’ comments, our detailed\nreplies are in black, and the new text of the revised version is in bold font. Line numbers in our\nreplies refer to the revised version of the manuscript.\nREVIEWER #2 (REMARKS TO THE AUTHOR):\nThe authors have addressed all the issues I raised with sufficient detail. Thank you for taking the\ntime to respond to all the comments.\nThank you for this supportive assessment of our work.\nREVIEWER #3 AND #4 - CO-REVIEW (REMARKS TO THE AUTHOR):\nWe enjoyed re-reading the revised manuscript. In short, the authors have done a commendable job\nat addressing the reviewers’ comments and we believe that the manuscript will be a broadly-read\ncontribution. The authors restructured the paper, to present all the results before going into an\nexpanded discussion on the morphometrics and dynamics side-by-side (in the Discussion and\nImplications) section. The current structure works well, and is a marked improvement from the\nprevious version. We especially liked the combined nuance discussion on the complex connections\nbetween cutoffs, avulsions, and bend maturity, and its relation to migration patterns. The authors\nbetter address data aggregation in the main text and the figures, and the color contrast significantly\nhelp figure readability in all cases.\nOne last comment on lines 158-161 in revised manuscript – are the authors referring to the\nstatistical difference in migration rates shown in figure 4a? If so, it seems like the P value might be\nreported for the bend-scale data as opposed to reach-scale data. It seems like the reach-scale data\nshow significant overlap. Could the authors double check this in the final version? Visually, the\ndata do not seem so far off from each other to yield the small P value reported unless the\ndifferences are being swamped by the log scale.\nIn summary, we believe that our concerns have been addressed in the revisions and we look\nforward to the manuscript in publication. This manuscript was co-reviewed as part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate\nrecognition for Early Career Researchers.\nThank you for this supportive assessment of our work.\nRegarding data reported in Figure 4a, we have double-checked them and can confirm the accuracy\nof the reported values, with the logscale helping to minimize visual differences between the three\nsets of data.\n1"}]

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