Abstract. The accuracy of hydraulic models depends on the quality of the bathymetric data they are based on, whatever the scale at which they are applied (e.g., 2D or 3D reach-scale modeling for local flood studies or 1D modeling for network-scale flood routing). The along-stream (longitudinal) and cross-sectional geometry of natural rivers is known to vary at the scale of the hydrographic network (e.g., generally decreasing slope, increasing width, etc.), allowing parameterizations of main cross-sectional parameters with proxy such as drainage area or a reference discharge quantile (an approach coined downstream hydraulic geometry, DHG). However, higher-frequency morphological variability is known to occur for many stream types, associated with varying flow conditions along a given reach: alternate bars, pool-riffle sequences, meanders, etc. To better take this high-frequency variability in bedforms into account in hydraulic models, a first step is to design robust methods to characterize the scales at which it occurs. In this paper, we propose and benchmark several methods to identify bedform sequences in pool-riffle morphology, for six small French rivers: the first one called the index method, based on three morphological and hydraulic descriptors; the second one called wavelet ridge extraction, performed on the continuous wavelet transform (CWT) of bed elevation. Finally, these new methods are compared with the bedform differencing technique (BDT, O’Neill and Abrahams (1984)), compared by computing a score that gives a percentage of agreement along the total surveyed length and by calculating the number of bedforms and the pool spacings for each method. The three methods were found to give similar results on average for wavelength estimation, with agreement from 64% to 84% and a similar number of bedforms identified. The filter-like behavior of the wavelet ridge analysis tends to give more robust results for the estimation of mean bedform amplitude, which varies from 0.30 to 0.81 with an SNR (signal-to-noise ratio) from 2.68 to 7.91. Otherwise, BDT gives higher mean bedform amplitude but lower SNR values from 0.85 to 1.73.

Abstract. The accuracy of hydraulic models depends on the quality of the bathymetric data they are based on, whatever the scale at which they are applied. The along-stream (longitudinal) and cross-sectional geometry of natural rivers is known to vary at the scale of the hydrographic network (e.g., generally decreasing slope, increasing width in the downstream direction), allowing parameterizations of main cross-sectional parameters with large-scale proxies such as drainage area or bankfull discharge (an approach coined downstream hydraulic geometry, DHG). However, higher-frequency morphological variability (i.e., at river reach scale) is known to occur for many stream types, associated with varying flow conditions along a given reach, such as the alternate bars or the pool–riffle sequences and meanders. To consider this high-frequency variability of the geometry in the hydraulic models, a first step is to design robust methods to characterize the scales at which it occurs. In this paper, we introduce new wavelet analysis tools in the field of geomorphic analysis (namely, wavelet ridge extraction) to identify the pseudo-periodicity of alternating morphological units from a general point of view (focusing on pool–riffle sequences) for six small French rivers. This analysis can be performed on a single variable (univariate case) but also on multiple variables (multivariate case). In this study, we choose a set of four variables describing the flow degrees of freedom: velocity, hydraulic radius, bed shear stress, and a planform descriptor that quantifies the local deviation of the channel from its mean direction. Finally, this method is compared with the bedform differencing technique (BDT), by computing the mean, median, and standard deviation of their longitudinal spacings. The two methods show agreement in the estimation of the wavelength in all reaches except one. The method aims to extract a pseudo-periodicity of the alternating bedforms that allow objective identification of morphological units in a continuous approach with the maintenance of correlations between variables (i.e., at many station hydraulic geometry, AMHG) without the need to define a prior threshold for each variable to characterize the transition from one unit to another.

<p>River discharge is an essential component in the hydrological cycle. It is used to monitor rivers, the atmosphere, and the ocean through in-situ measurements, acquired on the surface, or from remote sensing to characterize natural disasters such as floods.</p><p>Estimating discharge in ungauged rivers with remote sensing data such as the Surface Water and Ocean Topography (SWOT) mission but without any prior in-situ information is difficult to solve, especially in the case of unknown bathymetry, friction, and lateral river flows. However, the current literature suggests that a better knowledge of bathymetry could considerably facilitate roughness and discharge inferring. SWOT observes water surface elevations, slopes, river widths for several overpasses. We propose an inverse method to estimate discharge in a non-uniform steady-state, maintaining longitudinal (alternating pool-riffle) and lateral (meanders) morphological variability of the river. The idea is to build a rating curve (water level - discharge relationship) at the reach scale using hydraulic signatures (quantities not related to a particular section of the reach, which characterize an aspect of the overall hydraulic behavior: e.g., flooded area as a function of Q, mean water level as a function of Q). The inverse approach requires building a model that produces rating curves that optimally correspond to the hydraulic signatures. It requires a direct hydraulic model and a geometric simplification to facilitate the resolution of the inverse problem.</p><p>The approach is based on the geomorphology of rivers. Indeed, the geometry of natural rivers presents high-frequency variability, characterized by alternating flow units: fast-flowing flow units in rectilinear and shallow areas (riffles), slow-flowing flow units in deeper areas (pools at alternating banks or inner side of meandering bends). This variability generates a variability of the hydraulic variables that covary at the reach scale. However, a simplification into a uniform geometry without spatial variability reappears as a bias in the frictional parameters, thus reducing the inversion's accuracy. For this, we propose a periodic approach that consists of representing the reach equivalent geometry by sinusoidal functions.</p><p>This direct periodic model is used to create a whole periodic geometry (curved based asymmetry sections, Kinoshita curves to model the meander planform) and then solve the Saint-Venant equations in the 2D Basilisk hydraulic model (http://basilisk.fr), which is based on finite volume methods with adaptive grid refinement.</p><p>This model does not require boundary conditions (use of periodic boundary conditions) and provides the ability to model floodplains and thus flood mapping. In the end, there are few parameters to adjust in the model (use of parameters covariances).</p>

Interactive comment on "Wavelet and index methods for the identification of pool-riffle sequences" by M. Mounir et al. M. Mounir et al.