Systematic identification and characterization of bedforms from bathymetric data are crucial in many studies of fluvial processes. Automated and accurate processing of bed elevation data is challenging where dune fields are complex or irregular and (especially) where multiple scales co-exist. Here, we introduce a new tool to quantify dune properties from bathymetric data representing large primary and smaller superimposed secondary dunes. A first step in the procedure is to decompose the bathymetric data using a LOESS algorithm. Steep lee-side slopes of primary dunes are preserved by implementing objective breaks in the algorithm, accounting for discontinuities in the bed elevation profiles at the toe of the lee-side slope. The steep lee slopes are then approximated by fitting a sigmoid function. Following the decomposition of the bathymetric data, bedforms are identified based on a zero crossing, and morphological properties are calculated. The approach to bedform decomposition presented herein is particularly applicable where secondary dunes are large and filtering using conventional continuously differentiable functions could thus easily lead to undesired smoothing of the primary morphology. Application of the tool to two bathymetric maps demonstrates that it successfully decomposes bathymetric data, identifies primary and secondary dunes, and preserves steeper lee-side slopes of primary dunes.

Dunes are rhythmic features that develop at the interface of a flow field and a mobile bed. In fluvial environments, dunes play an important role in various flow and transport processes on multiple scales. Flow separation downstream of steep dunes opposes the mean flow, increasing hydraulic roughness

Systematic identification and characterization of dunes from bed elevation scans greatly aid these research efforts. Examples are field and flume studies that investigate the development of dunes under a range of conditions

In fluvial systems, two scales of dunes often co-exist: larger, primary dunes and small, secondary dunes that are superimposed on the primary dunes. The secondary bedforms have long been considered an attribute of primary dunes, converting simple dunes into compound dunes

Various methods to quantify dune morphology have been developed

In this study we develop a new tool to quantify bedform characteristics from bathymetric data representing multiple scales. The initial bedform identification is based on a zero crossing after decomposition of the bathymetric data. A LOESS (locally estimated scatter plot smoothing) algorithm is used to fit the irregular larger-scale morphology, including the primary dunes. LOESS regression is a nonparametric technique that uses local weighted regression to fit a smooth curve through points in a scatter plot. The approach differs from previous methods

The first step in the procedure is to decompose bed elevation profiles (BEPs) into a signal representing secondary bedforms and the remainder, which includes the primary dunes. This step builds on the previously described method to decompose bed elevation profiles by

A LOESS curve is fitted to the data to separate the secondary bedforms from the underlying morphology

By fitting the LOESS curve, each optimized value is given by a weighted quadratic least-squares regression to a local subset of the data. Thus, for each grid point in a bed elevation profile (

The sigmoid function that is fitted to dune lee sides is defined as

Schematic overview of the tool.

The bed elevation data series is decomposed based on both the LOESS curve and fitting of the steep primary lee sides with a sigmoid function fit. Data are input as (curvilinear) grids. The methodology is applied per bed elevation profile (BEP). The subsequent steps are as follows.

An initial LOESS curve is fitted to the BEP (Fig.

Based on the initial LOESS curve, crest and trough locations of primary dunes are identified. If the maximum lee-side slope in the LOESS curve is larger than a specified value (default: 0.03 m m

If there are breaks in a BEP, the exact locations of these breaks are updated in the following steps. First, the local minimum of the bed elevation data is found within a specified window upstream of the previous breakpoint. Subsequently, the breakpoint location is updated if the slope to an upstream location within the window is lower than the cutoff slope (Fig.

A LOESS curve is fitted up to the first break. Following this, the sigmoid function is fitted at the primary lee side upstream of the break, with initial values of

A short LOESS curve is fitted to the data between the previous LOESS curve and the sigmoid function fit. The fit is forced to connect to the LOESS curve and sigmoid fit by artificially adding data points (Fig.

Steps 4 and 5 are then repeated (Fig.

The identification of both primary and secondary bedforms is based on the decomposed bed elevation signals. The characterization of bedforms includes the following properties: height, length, depth, trough and crest locations, lee-side slope, maximum lee-side slope, stoss-side slope, and aspect ratio.

Secondary bedform identification is based on a zero crossing applied to the decomposed bed elevation signal (

The identification and characterization of primary bedforms is similar to that of secondary bedforms. A zero crossing is based on the decomposed signal, excluding secondary bedforms, and a base level. The latter can be computed as a moving average (4 to 5 times the dune length), a smoothed LOESS curve, or a time average of the local riverbed, depending on data availability. Here, we compute the base level as a moving average. Primary dunes are identified, iterating once. If a primary dune height is smaller than 0.25 m, corresponding up and down crossings are removed and new minima and maxima are found. Properties are subsequently determined similar to secondary bedforms. The maximum lee slope is defined as the maximum slope of a grid cell between the crest and the downstream trough. If the primary lee side is fitted using the sigmoid function, the maximum slope is determined based on values corresponding to the fitted function only.

After bedform identification and characterization, the secondary and primary bedforms are filtered to exclude bedforms that are deemed unrealistic, such as small fluctuations around the zero line. Secondary bedforms are filtered out if one or more of the following user-defined and site-specific conditions hold:

height is smaller than 0.05 m or larger than 0.75 m,

length is larger than 25 m or smaller than 0.5 m (5 times the resolution for data presented herein),

the aspect ratio is larger than 0.2 or smaller than 0.005,

the crest elevation in the unfiltered data is less than 0.01 m lower than the upstream or downstream trough,

the maximum lee-side slope is smaller than 0.03 m m

height is smaller than 0.25 m or larger than 4 m,

length is larger than 200 m or smaller than 25 m,

aspect ratio is larger than 0.2 or smaller than 0.005,

the maximum lee-side slope is smaller than 0.03 m m

The tool is applied to two data sets. Multibeam echo sounder (MBES) data were provided by the Dutch Ministry of Infrastructure and Environment (Rijkswaterstaat) for the Waal river, which is the main branch of the River Rhine. The used data set consists of 1 km of the river, from approximately 425 370, 154 178 to 426 252, 154 618 (EPSG:28992; in WGS 84, these coordinates are approximately (lat, long) 51.8175633

The bathymetric maps before and after decomposition:

The two data sets were decomposed with the following parameters: [

Four example BEPs. Each panel shows the bed elevation signal, the fitted line, and the crests and troughs of the primary (large, purple circles) and secondary dunes (small, orange circles).

Histograms of the height, length, and maximum lee-side slope of secondary and primary dunes.

Following the decomposition of the bed elevation data, bedforms have been identified based on zero crossing. For primary bedforms, the base level consists of a moving average of 400 m. Four BEPs are shown in Fig.

Histograms of the slope of downstream-facing cells with values larger than 0.03 m m

In the applied decomposition procedure, breaks were implemented to avoid smoothing of steep primary lee-side slopes. To investigate the effectiveness of the procedure, histograms of the slopes of downstream-facing cells with a value larger than 0.03 m m

The new tool presented herein serves two purposes: to isolate secondary bedforms from the underlying topography and to identify bedform properties for both the primary and secondary bedforms based on a zero crossing. Figures

Figure

In the application of this method, a user should be careful in choosing the parameters with which the tool is applied. The quality of the decomposition, and thus the bedform identification and characterization, depends to some extent on the initial parameters

For both primary and secondary dunes, a mean lee-side angle and a maximum lee-side angle are calculated. Usually, the lee-side slope is not straight, which is relevant for lee-side processes such as flow separation. For high-angle dunes, the steepest section of the lee slope is also referred to as the slip-face angle, which exerts a control over avalanching of sediment

The tool presented here is appropriate for data sets with multiple scales of bedforms, as long as these scales are sufficiently separated and the longitudinal resolution of the data is high enough relative to the length of the smallest bedform scale. In this study, the smallest bedform lengths are 5 times the longitudinal data resolution of 0.1 m.
The tool is appropriate for primary dunes with steep lee-side slopes. In this study, the tool is applied to a data set with subaqueous bedforms under unidirectional flow. We expect that this tool can be applied to data sets from different environments if the above-mentioned requirements hold and the primary dune lee sides are similarly shaped. In tidal environments, primary dunes can have both an ebb and flood steep face

A tool is presented to decompose bed elevation data representing multiple scales for the identification and characterization of larger primary and smaller superimposed secondary bedforms. A LOESS algorithm was used to isolate the secondary dunes from primary dunes in between breaks downstream of steep primary lee-side angles. The steep lee-side slopes of primary dunes are approximated with a sigmoid function, replacing the LOESS fit at the slope. The decomposed data series are used to identify both secondary and primary dunes through a zero crossing and to measure dune properties based on filtered and unfiltered bed elevation profiles. The results show that the tool is successful in separating scales for data sets with well-defined bedform scales.

The MATLAB code used in this study can be accessed through

Initiation and design of the study was a result of discussion between all co-authors. JYZ developed the tool, about which the co-authors were regularly consulted. JYZ analyzed the data and wrote the manuscript. The manuscript was reviewed and edited by all co-authors.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This study is part of the research program Rivers2Morrow, which is funded by the Dutch Ministry of Infrastructure and Water Management and its executive organization Rijkswaterstaat. We thank Rijkswaterstaat-CIV for providing the data used in this study. We thank Ray Kostaschuk and one anonymous reviewer for their helpful comments and suggestions.

This research has been supported by the Rijkswaterstaat (grant no. 31137987) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (grant no. 17062).

This paper was edited by Wolfgang Schwanghart and reviewed by Ray Kostaschuk and one anonymous referee.