Timescales of Autogenic Noise in River Bedform Evolution and Stratigraphy

Bedform evolution and preserved cross strata are known to respond to floods. However, it is unclear if autogenic dynamics mask the flood signal in bedform evolution and cross strata. To address this, we characterize the temporal structure of autogenic noise in steady‐state bedform evolution in a physical experiment. Results reveal the existence of bedform groups—quasi‐stable collections of bedforms—that migrate at a similar speed as bedforms. We find that bedform and bedform‐group turnover timescales are the key autogenic timescales of bed evolution that set the transition time‐periods between different noise regimes in bedform evolution. Results suggest that bedform‐group turnover timescale sets the lower limit for detecting flood signals in bedform evolution, and floods with duration shorter than bedform turnover timescale can be severely degraded in bedform evolution and cross strata. Our work provides a new framework for interrogating fluvial cross strata for reconstruction of past floods.


Introduction
Sedimentary rocks archive past environmental changes.External environmental perturbations (e.g., base level, water and sediment supply) can change the pace and magnitude of river processes and cause architectural changes in fluvial stratigraphy.Reading preserved fluvial strata for past changes is, however, complicated by noise generated by autogenic dynamics (Ganti et al., 2014;Hajek & Straub, 2017;Jerolmack & Paola, 2010;Romans et al., 2016), which can buffer, distort or even obliterate the record of past environmental changes (Foreman & Straub, 2017;Straub et al., 2020).Previous work quantified the scales of environmental changes that can be influenced by noise in sediment transport systems (Foreman & Straub, 2017;Ganti et al., 2014;Jerolmack & Paola, 2010).However, these advances have primarily been tested using experimental delta evolution (Foreman & Straub, 2017;Griffin et al., 2023;Toby et al., 2019Toby et al., , 2022)), and it is currently unclear if similar environmental "signal shredding" effects complicate the interpretation of sedimentary processes and their deposits at other scales.
Bedforms are a common feature on riverbeds, and bedform size, celerity, and the magnitude of bed-material flux respond to variations in water discharge (Allen, 1976;Martin & Jerolmack, 2013).However, interactions within and between bedforms leads to variability in bedform evolution even under steady-state conditions (Hino, 1968;Nikora et al., 1997).For an external signal to be recognized in bedform evolution and cross strata, the imposed variations should be differentiated from noise in bedform evolution at base flow conditions.This issue of signal detectability is particularly applicable for cross strata, where preserved set thickness-deposit bound by • We show the existence of bedform groups, which are quasi-stable collections of bedforms, previously found in aeolian dune evolution models • Bedform and bedform group turnover timescales are key autogenic timescales that describe the temporal structure of noise in bed elevation • Floods of duration shorter than bedform turnover timescale are expected to be unrecognizable in bed elevation and preserved cross strata Supporting Information: Supporting Information may be found in the online version of this article.
successive erosional scours-is controlled by scour-depth variability (Paola & Borgman, 1991), and bed changes can often lag flow variations (Allen, 1976;Martin & Jerolmack, 2013).To assess how external variations are transformed in bedform evolution and cross strata, we need an understanding of the nature of autogenic noise in bedform evolution.
The structure and timescales of autogenic noise in sediment-transport systems are quantified using the power spectral density (PSD) of time series of a response variable (e.g., sediment efflux, bed elevation) under steadystate conditions, denoted as ϕ f (Griffin et al., 2023;Jerolmack & Paola, 2010).Using numerical simulations of 1D rice-pile evolution, Jerolmack and Paola (2010) show that the PSD of steady-state sediment efflux displays two distinct regimes, where ϕ f increases with time period, t, as ϕ f ∼ t α with α = 2 and subsequently transitions into a regime where ϕ f is constant.The first regime, referred to as the red noise, captures the temporal correlation at short timescales, and the second regime indicates no temporal correlation (white noise).Griffin et al. (2023) show that sediment efflux also displays a third regime of temporal anticorrelation (blue noise) beyond the white-noise regime (ϕ f ∼ t α ; α < 0).A higher α (>0) implies a higher temporal correlation, and systems that evolve toward a self-organized critical state have α = 1 (Bak et al., 1987).In this state, small perturbations can cause a large-scale change in the system (Bak et al., 1987;Griffin et al., 2023;Hwa & Kardar, 1992).The key autogenic timescales are marked by the transitions between different noise regimes, and our knowledge of the controls on these timescales in bedform evolution is incomplete.
The knowledge of autogenic noise in sediment-transport systems forms the basis for exploring environmental signal propagation in landscapes and strata (Griffin et al., 2023;Jerolmack & Paola, 2010).Using experimental rice-pile evolution data, Griffin et al. (2023) show that external signals with a duration shorter than T r (transition time period from red-to-white noise regime) are severely degraded; that is, the amplitude of the external perturbation is dampened in the response variable.Thus, T r provides a lower limit for environmental signal detectability.Griffin et al. (2023) also show that signals in the white-noise regime can be detected in the output variable, but the signal detectability is amplitude dependent.Signals in this duration range need to overcome the inherent variability at steady state for detection (Griffin et al., 2023).In contrast, external signals with a period in the blue-noise regime are faithfully represented in the output variable regardless of their amplitude.Moreover, regimes with high α are more efficient at signal degradation, when compared to regimes with low α, because it is difficult to perturb the system from its mean state when there is high temporal correlation.Therefore, identifying different noise regimes in bedform evolution can yield insight into the detectability of flood signals in bed topography and cross strata.
Previous work showed that bedform evolution is characterized by a red-noise regime at short timescales (Hino, 1968;Lee et al., 2021Lee et al., , 2022;;Nikora et al., 1997).However, the existence of different spectral regimes, potential controls on the transition between the regimes, and their relevance for preservation of floods in fluvial cross strata are yet to be explored.Here, we address this knowledge gap by quantifying the structure and timescales of noise in bed evolution, sediment efflux, and preserved cross strata of steady-state bedform evolution in a physical experiment.

Experimental Setup and Data Acquisition
We conducted a steady-state experiment of bedform evolution in a 15-m-long, 2-m-wide, 1-m-deep flume in the Experimental Sedimentology Laboratory at the University of California Santa Barbara (Figure 1).We filled the flume with ∼0.3 m deep layer of quartz sand with median grain size of 0.35 mm.We recirculated water and sediment in a closed loop; the downstream water surface elevation was held constant using a standpipe.The experiment had a constant water discharge of 0.28 m 3 /s, and the bed was primed at this discharge for >5 days to ensure steady-state bedform evolution.The water surface slope, measured using an ultrasound distance meter (Massa) with a vertical accuracy of 1 mm, was constant and equal to 1.2 × 10 3 .We used a 7-m-long test section for the analysis of bedform characteristics; the flow depth over this section decreased from 0.35 to 0.3 m.The crosssection averaged flow velocity, Froude number, and Reynolds number were 0.43 m/s, 0.24, and 1.4 × 10 5 , respectively.The bed shear stress, computed as the depth-slope product, ranged from 3.5 to 4.1 Pa, which translated to a transport stage of 14-17, consistent with mixed-load transport conditions observed during the experiment.We collected high-resolution time series of sediment efflux and bedform evolution.The flume has four identical weigh pans (each 0.5 m wide) at the downstream end (Figure 1), which measured bedload transport rates.As bedforms migrated, sediment accumulated into the weigh pans, and automatically returned to the recirculation system once the pans reached 1.8 kg.Sediment weight accumulating in weigh pans was continuously monitored every 2 s for approximately 65 hr (Figure 1e).We normalized the detrended weigh pan measurements with duration and weigh-pan width to estimate unit mass flux (W s ; Figure S4 in Supporting Information S1).We then denoised W s by removing negative values and outliers and smoothed the data using a window size of 12 s (to match bed elevation data resolution).Finally, we converted the average W s , estimated across the four pans, into unit volume flux as: q s = W s /(ρ s ρ w ) (1 p), where p = 0.3 is the porosity, ρ s = 2,600 kg/m 3 and ρ w = 1,000 kg/ m 3 are the density of sediment and water, respectively (Figure 1e; Text S2 in Supporting Information S1).
We collected high-resolution bathymetric data using a laser scanning device, consisting an enclosed laser generator and camera (Figure 1).The apparatus is mounted on a computer-controlled data acquisition carriage, which can be automatically positioned within the flume coordinate system at submillimeter accuracy.We submerged the apparatus below the water surface, and projected a 1-mm-thick laser line in the spanwise direction (y).The camera captured the laser line while the instrument cart moved in the streamwise direction (x; x = 0 is 2.3 m downstream of the inlet), and the bed elevation (z) was measured at a submillimeter vertical precision.
We collected two sets of bathymetric data to balance the temporal and spatial resolution needs for spectral and bedform-tracking analysis.The spanwise extent of these data sets was centered along the flume centerline.First, for the spectral analysis, we monitored a 32 mm-by-251 mm patch of bed, located at x = 10 m, at a spatial and temporal resolution of 1 mm and 12 s, respectively, for 65 hr (Figure 1b).Second, for bedform tracking, we monitored a 7 m-by-251 mm patch, starting at x = 5 m, at a spatial and temporal resolution of 1 mm and 5 min, respectively, for 14 hr (Figure 1c).
We also quantified the temporal structure of preserved deposition rates (Figure 1g).We built synthetic stratigraphy from the 65-hr-long bed elevation data by clipping portions of the record that were subsequently eroded by bedform reworking (Ganti et al., 2013).We then quantified the preserved deposition rate from synthetic stratigraphy.We differenced the stratigraphic height between successive time steps and divided this difference by 12 s.We computed the preserved deposition rate time series for all points within the 32 by 251 mm patch.

Power Spectral Analysis
We generated discrete time-power spectral densities for bathymetric evolution (12 s interval data), sediment efflux (q s ), and preserved deposition rates using a multi-taper method (Griffin et al., 2023;Huybers & Curry, 2006).For bathymetry and preserved deposition rates, we computed ϕ f at each location in the 32 mm-by-251 mm patch, and then evaluated median, 5th and 95th percentiles of ϕ f for each time period, t.For sediment efflux, we computed the mean and 95% confidence intervals on ϕ f (Huybers & Curry, 2006).To identify the key autogenic timescales in bedform evolution, we analyzed ϕ f in log-log space and quantified the time period of gradient breaks in ϕ f using the "findchangepts" function in MATLAB (Griffin et al., 2023).We performed sensitivity analysis on ϕ f by varying the time bandwidth product in the multi-taper method.We report mean and standard deviation of transition time periods and α for each noise regime, estimated using ϕ f computed with different time bandwidth product (Text S2 in Supporting Information S1).

Quantifying Multi-Scale Bedform Geometry and Kinematics
We quantified multi-scale bedform characteristics from bed elevation data, collected at 5 min interval, using an algorithm developed by Lee et al. (2021).We detrended the data by removing a plane fit to the bathymetry averaged in the spanwise direction and in time (Figure 1c).We directly analyzed the raw detrended data and decomposed the detrended data into low-pass topography and high-pass topography using a discrete fast fourier transformation with a user-defined cutoff length scale (Text S1 in Supporting Information S1).We analyzed the low-pass and high-pass topography separately by varying the cutoff length scale between 0.5 and 1.25 m (Text S1 in Supporting Information S1).We quantified the bedform height (h d ), length (λ), and celerity (c) from raw data and low-pass and high-pass topography.We use a subscript of L or H (e.g., λ L or λ H ) to denote bedform geometry and kinematics of the low-pass and high-pass topography, respectively.
We characterized the bedform turnover timescale as (e.g., Allen & Friend, 1976;Myrow et al., 2018): where A is the bedform cross-sectional area, β is a shape factor (∼0.5 for the approximation of bedforms as a triangle and 1 for trapezoidal shapes) and q s is the average volumetric unit sediment flux measured from the weigh pans.Hydrodynamic changes occur instantaneously; however, bedform changes require the redistribution of mass, and T t quantifies the time required to displace a characteristic bedform volume under prevailing flow and sediment transport conditions (Myrow et al., 2018).We computed Equation 1 for raw data and reported the median and interquartile range (IQR) of T t .Similarly, we also defined the turnover timescale for features identified in the lowpass and high-pass topography, denoted as T t,L and T t,H , respectively.We compared these timescales to time periods of gradient breaks in PSDs of bed elevation, sediment efflux, and preserved deposition rate time series.

Autogenic Noise in Sediment Efflux, Bedform Evolution and Fluvial Cross Strata
We observed multiple noise regimes in the sediment efflux data (Figure 2a).In the first regime, we find that ϕ f ∼ t 1.39 for time periods ranging from the highest resolution to T r = 0.063 hr.In the second regime, ϕ f ∼ t 0.31 from 0.063 hr to 1.7 ± 0.3 hr, indicating temporal anticorrelation (i.e., blue noise).Beyond the blue noise regime, ϕ f rapidly increased and subsequently transitioned into a white noise regime, which is characterized by a constant ϕ f (Figure 2a).
The bed elevation displayed three distinct noise regimes (Figure 2b).In the first regime, we find that ϕ f ∼ t 2.4 up to a time period of T r = 0.22 ± 0.01 hr.
Interestingly, preserved deposition rates displayed only two noise regimes (Figure 2c).The first regime, with α = 1.32 ± 0.03, persisted up to 0.11 ± 0.01 hr.For t > 0.11 hr, preserved deposition rates exhibit a spectral gradient of α = 0.21 ± 0.01, indicating weak temporal correlation.Notably, we observed that, for similar time periods, the spectral gradient in preserved deposition rates is consistently smaller than that of bed elevation (Figure 2).

Characteristics of Multi-Scale Bedform Geometry and Kinematics
Bedform characteristics were temporally consistent during the experiment.
The bedform tracking tool revealed the existence of multiple scales of topography (Figure S1 in Supporting Information S1).In the high-pass filter topography, h d,H is 17.8 mm (overbar denotes median value), with an IQR of 12.9 mm, and λ H is 181 mm (IQR of 100 mm; Figure 3a).We found that h d,L was similar to h d,H (Figure 3a), and the statistics of bedform heights in the lowpass topography did not vary with cutoff length scales (Figure S3 in Supporting Information S1).The estimated λ L is significantly different from λ H (Figure 3b), and it showed a dependence on the cutoff length scale (Figure S3 in Supporting Information S1).The aspect ratio of bedforms in the high-pass filter topography had a median and IQR of 0.1 and 0.04, respectively, similar to previous observations of bedforms in shallow flows with similar transport stage (Bradley & Venditti, 2017).However, the aspect ratio of bedforms in the low-pass filter topography was significantly different from that of high-pass filter topography for all cutoff length scales (Figure S3 in Supporting Information S1).
We interpret the low-pass filter topography to represent bedform groupsquasi-stable groups of bedforms that result from self-organization of bedforms, as reported in numerical models of aeolian dune evolution (Swanson et al., 2019).The celerity of bedforms and bedform groups is similar, with c H and c L equal to 0.15 and 0.14 mm/s, respectively (Figure 3c; Figure S3 in Supporting Information S1).This observation contrasts with the coevolution of host and superimposed bedforms, where host bedforms often migrate slower than the superimposed bedforms (Lee et al., 2021(Lee et al., , 2022)).The  estimated T t,H is 0.24 hr (IQR = 0.33 hr; β = 0.5 in Equation 1), and it did not change with cutoff length scale and was similar to T t of the raw data (Figure 3d; Figure S3 in Supporting Information S1).We estimated T t,L using β = 1 in Equation 1 as bedform groups had a shape that was more consistent with a trapezium rather than a triangle (Figures S1 and S2 in Supporting Information S1).Estimated T t,L varied with the cutoff length scale and ranged from 2.11 hr (IQR = 2.51 hr) at 0.5 m cutoff length scale to 4.92 hr (IQR = 4.28 hr) at 1.25 m cutoff length scale (Figure 3d; Figure S3 in Supporting Information S1).

Controls on Timescales of Autogenic Noise in Bedform Evolution and Cross Strata
Our results demonstrate that turnover timescales of bedforms and bedform groups serve as critical factors influencing the dynamics of bedform evolution (Figures 2b and 3d).We observe that T r of bed evolution aligns with T t,H (Figure 2b).Furthermore, the second noise regime with α = 1.1 persists for time periods longer than the bedform turnover timescale but shorter than the bedform-group turnover timescale (Figure 2b).The white noise regime in bed evolution persists only for time periods longer than the bedform-group turnover timescale (Figure 2b).
While the spectral gradients in PSD of preserved deposition rates were different from that of bed elevation, we find that T t,H aligns with T r of preserved deposition rates (Figure 2c).However, we do not observe a gradient break corresponding to the bedform-group turnover timescale in the preserved deposition rates (Figure 2c).Finally, bedform turnover timescale is significantly longer than the estimated T r of sediment efflux (Figure 2a), and the bedform-group turnover timescale sets the upper limit on the blue noise regime (Figure 2a).We find that the sediment efflux data show temporal correlation on time periods that correspond to the estimated bedform group turnover timescales (Figure 2a).

Discussion
Our results indicate that bedform groups, which emerge from the self-organization of bedforms, can exist within the fluvial morphodynamic hierarchy.In numerical models of aeolian dunes, bedform groups emerge under a range of conditions (Swanson et al., 2019); bedform groups initiate because bedform troughs descend significantly below mean bed elevation causing low local bed shear stress, and spatial variability in scour depths.
Bedform groups are then bound on the upstream and downstream end by deep scours, where bedforms in the upstream part of the group ascend in elevation causing an increase in bed shear stress, and more scouring (Swanson et al., 2019).This excess sediment is routed downstream into the lee side of the bedform group, and the bedforms in the downstream part of the group progressively receive more sediment than they can transport (Swanson et al., 2019).Our data show that bedform groups are quasi-stable features; bedform celerity across scales is similar (Figure 3c), which is in contrast to the dynamics of large dunes with superimposed smaller dunes (Lee et al., 2021(Lee et al., , 2022)).Moreover, bed elevation displays characteristics of a self-organized critical state on timescales between bedform and bedform-group turnover timescales (Figure 2b).Previous numerical sandpile models demonstrate that red noise in sediment-transport systems can emerge from interactions within avalanches and ϕ f ∼ t regime emerges from the interaction of avalanches (Hwa & Kardar, 1992).Similarly, bed elevation shows a red-noise regime for timescales less than the bedform turnover timescale and suggests that the correlated ϕ f ∼ t 1.1 regime in bed elevation is a manifestation of bedform interactions (Figure 2b).
The existence of bedform groups may have implications for reading fluvial cross strata (Cardenas et al., 2019;Swanson et al., 2019).Numerical models indicate that bedform movement within groups can create and truncate co-sets of cross strata (Swanson et al., 2019).The passage of deep scours associated with groups can lead to extensive reworking of bedform deposits, and cause deviations of the preserved set thickness from the variabilitydominated preservation model of Paola and Borgman (1991), which assumes a random distribution of scour depths in time.This recognition provides an alternative hypothesis for the deviation of fluvial cross strata in the field from the expectations of the variability-dominated preservation model.This deviation is typically attributed to the influence of unsteady flow on bedform evolution (Leary & Ganti, 2020;Lyster et al., 2022) or the presence of a morphodynamic hierarchy (Cardenas et al., 2020;Ganti et al., 2020;Reesink et al., 2015).Future work should focus on how bedforms, bedform groups, and bars coevolve and control the preservation of bedform evolution in cross strata.

Geophysical Research Letters
10.1029/2024GL108965 Our results reveal that bedform and bedform-group turnover timescales are the key timescales of autogenic noise in bedform evolution (Figure 2b).These findings have important implications for the degradation and detection of flood signals in bedform evolution and cross strata.Following Griffin et al. (2023), we suggest that bedform-group turnover timescale, which is significantly longer than bedform turnover timescale (Figure 3d), sets the lower limit on flood durations (T f ) that are detectable in bedform evolution (Figure 2b).Previous bedform experiments found that flow variations are accompanied by instantaneous adjustment in bedform celerity but bed elevation changes only occurred on timescales that were at least five times the bedform turnover timescale at base flow conditions (Martin & Jerolmack, 2013).This observation is consistent with the PSD of bed elevation (Figure 2b), and also with the temporal structure of sediment efflux-a combination of bedform dimensions and celerity (Simons et al., 1965)that displayed a blue noise regime on time periods ranging from approximately 0.2T t,H to T t,L (Figure 2a).Thus, a wider range of T f values are detectable in sediment efflux when compared to bed elevation (Figure 2).
Our results indicate that noise in bedform evolution can degrade the signal of floods with a duration less than the bedform-group turnover timescale to varying degrees (i.e., T f < T t,L ).Floods with T f < T t,H (signals in red noise regime) are unlikely to induce detectable changes in bed elevation, unless the flood magnitude is substantial (Griffin et al., 2023;Jerolmack & Paola, 2010).Several large, lowland rivers can have T f < T t,H (Leary & Ganti, 2020), indicating that flood signals may be shredded in their preserved cross strata.
However, for T t,H < T f < T t,L (i.e., the regime with ϕ f ∼ t 1.1 ), bed elevation exhibits characteristics of a selforganized critical state (Bak et al., 1987;Hwa & Kardar, 1992), and erratic behavior around the mean state can be induced with small external perturbations (Hwa & Kardar, 1992).This suggests that floods with T t,H < T f < T t,L can cause a complex response in bed elevation with potential for smearing of the flood signal.We also find that α is consistently low for preserved deposition rates compared to bed elevation for time periods less than T t,L (Figures 3b  and 3c), and preserved deposition rates do not transition to a white noise regime, even beyond T t,L .We anticipate this prolonged transition to the white-noise regime in preserved deposition rates because scours bracketing bedform groups can cause hiatuses in the preserved record, spanning multiple bedform-group turnover timescales.Together, these results provide a mechanistic basis for the findings of Colombera et al. (2024), who, in their meta-analysis of modern river deposits, identified a lack of correlation between T f normalized by T t,H and preserved set thickness.This lack of correlation can be indicative of varying degrees of flood signal degradation, where floods with T t,H < T f < T t,L have a lower degradation potential than T f < T t,H , and only floods with T f > T t,L are expected to be minimally degraded (Figure 2).Finally, our analysis highlights a need to revise the framework for reconstructing T f from cross strata.Leary and Ganti (2020) suggested that the coefficient of variation of preserved set thickness may reflect the ratio of formative T f and bedform turnover timescale-a result subsequently used to reconstruct T f from fluvial strata (Lyster et al., 2022;McLeod et al., 2023).However, Leary and Ganti (2020) used a bed adjustment timescale, which was significantly longer than T t,H of baseflow-equilibrated bedforms, in their analysis.We find that the two floods they analyzed had T f of 3 and 12 times the estimated T t,H at base flow conditions (Ganti et al., 2013), indicating that the floods were likely in the bed elevation noise regime with ϕ f ∼ t 1.1 or constant ϕ f .Future research should explore preservation in a range of flood durations that systematically cover the different noise regimes of bed elevation to assess the magnitude-duration space for flood signal detection and degradation in fluvial cross strata.

Conclusions
We determined the structure and timescales of autogenic noise in bed elevation, sediment efflux, and preserved deposition rates during steady-state bedform evolution, utilizing high spatiotemporal resolution data from a physical experiment (Figure 1).We find that the: 1. Bedforms self-organize into bedform groups, which are quasi-stable collections of bedforms (Figures 2b  and 3); 2. Bedform and bedform-group turnover timescales are key timescales of autogenic noise in bed evolution, where bed elevation shows three noise regimes: ϕ f ∼ t 2.4 for t < T t,H , ϕ f ∼ t 1.1 for T t,H < t < T t,L , and ϕ f ∼ t 0 for t > T t,L (Figure 2b); 3. Bedform-group turnover timescale may set the lower limit on the flood duration that is detectable in bed elevation, and floods with a duration less than bedform turnover timescale can be severely degraded in bed elevation and cross strata (Figures 2b and 2c).
These insights provide a new framework for the systematic investigation of flood signal propagation into bedform evolution and fluvial cross strata.

Figure 1 .
Figure 1.(a) Schematic of the flume in Experimental Sedimentology Laboratory at the University of California Santa Barbara.Space-time plot of sequential (b) 0.25-m cross-stream profiles (12 s resolution) and (c) 7-m-longitudinal profiles (5 min resolution).(d) Example of the 65-hr-long time series of bed elevation (dashed line in panel b).(e) Time series of the volumetric unit sediment flux measured using sediment weigh pans.(f) Example longitudinal bed (black line; dashed line in c) and water surface elevation (blue line) profiles, where the dashed blue line indicates the best-fitting line to the water surface elevation.(g) Time series of preserved deposition rates for bed elevation data in panel (d).

Figure 2 .
Figure 2. Power spectral densities of (a) sediment efflux, (b) bed elevation, and (c) preserved deposition rate time series.The dashed lines/rectangles are transition time periods between noise regimes.Blue bar indicates the interquartile range of estimated bedform turnover timescale, and the orange bar denotes the median range of bedform-group turnover timescales computed across cutoff length scales varying from 0.5 to 1.25 m.In panel (a), gray markers and shaded area are the estimated spectral power and the 95% confidence interval, respectively.The vertical gray line denotes the tipping period of sediment weigh pans.In panels (b) and (c), the gray markers and shaded area are the median and the extent of 5th and 95th percentiles of the estimated spectral power computed on all 8032 realizations of the bed elevation and preserved deposition rate time series.

Figure 3 .
Figure 3. Violin plots of estimated (a) height, (b) length, (c) celerity, and (d) turnover timescale from the low-pass (orange; cutoff length scale of 1 m) and high-pass filter (blue) topography.The insets in the violin plots show the box plots where the white marker shows the median and the edges of the box show the first and third quartiles.