Discrimination of bed form scales using robust spline filters and wavelet transforms: Methods and application to synthetic signals and bed forms of the Río Paraná, Argentina

Abstract

[1] There is no standard nomenclature and procedure to systematically identify the scale and magnitude of bed forms such as bars, dunes, and ripples that are commonly present in many sedimentary environments. This paper proposes a standardization of the nomenclature and symbolic representation of bed forms and details the combined application of robust spline filters and continuous wavelet transforms to discriminate these morphodynamic features, allowing the quantitative recognition of bed form hierarchies. Herein the proposed methodology for bed form discrimination is first applied to synthetic bed form profiles, which are sampled at a Nyquist ratio interval of 2.5-50 and a signal-to-noise ratio interval of 1-20 and subsequently applied to a detailed 3-D bed topography from the Río Paraná, Argentina, which exhibits large-scale dunes with superimposed, smaller bed forms. After discriminating the synthetic bed form signals into three-bed form hierarchies that represent bars, dunes, and ripples, the accuracy of the methodology is quantified by estimating the reproducibility, the cross correlation, and the standard deviation ratio of the actual and retrieved signals. For the case of the field measurements, the proposed method is used to discriminate small and large dunes and subsequently obtain and statistically analyze the common morphological descriptors such as wavelength, slope, and amplitude of both stoss and lee sides of these different size bed forms. Analysis of the synthetic signals demonstrates that the Morlet wavelet function is the most efficient in retrieving smaller periodicities such as ripples and smaller dunes and that the proposed methodology effectively discriminates waves of different periods for Nyquist ratios higher than 25 and signal-to-noise ratios higher than 5. The analysis of bed forms in the Río Paraná reveals that, in most cases, a Gamma probability distribution, with a positive skewness, best describes the dimensionless wavelength and amplitude for both the lee and stoss sides of large dunes. For the case of smaller superimposed dunes, the dimensionless wavelength shows a discrete behavior that is governed by the sampling frequency of the data, and the dimensionless amplitude better fits the Gamma probability distribution, again with a positive skewness. This paper thus provides a robust methodology for systematically identifying the scales and magnitudes of bed forms in a range of environments.

Three‐Dimensional Flow Above River Bedforms: Insights From Numerical Modeling of a Natural Dune Field (Río Paraná, Argentina)

“…As also visually recognized on Figure b, the slip faces are mainly situated close to the trough and away from the crest, having an average normalized beginning and end at 0.67 to 0.76 between crest and trough (Figure e and Table ). This shows the presence of a well‐developed crestal platform already identified by Parsons et al () and Gutierrez et al ().…”

“…Gutierrez et al () further analyzed the bathymetry collected by Parsons et al () using robust spline filters and wavelet transforms to discriminate bedform scales. Using this method, the bed morphology was separated in three units: small dunes or ripples, medium to large dunes, and bar.…”

“…Two other noticeable features were recognized at the study area ( Figure 5): a bedrock that protrudes around 2 m above the bed and channel deepening toward the SSW corner of the survey area due to the presence of a large bar upstream of the study site. Gutierrez et al (2013) further analyzed the bathymetry collected by Parsons et al (2005) using robust spline filters and wavelet transforms to discriminate bedform scales. Using this method, the bed morphology was separated in three units: small dunes or ripples, medium to large dunes, and bar.…”

Spectral behavior of gravel dunes

“…Singh et al (2011) used a symmetrical wavelet, the 'Mexican hat' wavelet, for the decomposition of time series; while an asymmetrical wavelet, the Daubechies 4 tap wavelet, is used in this study. Because of the asymmetrical form of gravel dunes, using an asymmetrical wavelet can improve the decomposition effect significantly, especially within the time domain (Gutierrez et al, 2013).…”

Modulation of the flow structure by progressive bedforms in the Kinoshita meandering channel

“…Even though the averaged bed morphology is the result of averaging several stages in a cycle, some local bed perturbations remain. To completely filter out the perturbations in future studies will require taking the average over the higher number of instantaneous bed measurements or by separating the large and small scales from the bed morphology signature, such that a purely smooth time-averaged pattern can be obtained (Gutierrez et al, 2013). In general, the maximum velocity regions are found when the crest of a dune is passing through a given control section, thus manifesting the variation on the depth-averaged velocity magnitude, which is a flow parameter widely used to predict meandering migration (Ikeda et al, 1981).…”