Investigating uncertainty and parameter sensitivity in bedform analysis by using a Monte Carlo approach

Precise and reliable information about bedforms regarding geometry and dynamics is relevant for many applications - such as ensuring safe conditions for navigation along the waterways, parameterizing the roughness of the riverbed in numerical models, or improving bedload measurement and monitoring techniques. There are many bedform analysis tools to extract this information from bathymetrical data. However, most of these tools require the setting of various input parameters, for which specific values have to be selected. How these settings influence the resulting bedform characteristics has not yet been comprehensively investigated. We therefore developed a workflow to quantify this influence by performing a Monte Carlo simulation. By repeating the calculations many times with varying input parameter settings, the possible range of results is revealed, and thus the procedure-specific uncertainties can be quantified. We implemented a combination of the widely used zero-crossing procedure to determine bedform geometries and a cross-correlation analysis to determine bedform dynamics. Both methods are well known and established, which ensures the transferability and value of the findings. In order to increase the robustness of the workflow, we implemented a wavelet analysis based on Bedforms-ATM (Guitierrez et al., 2018), which is carried out before the zero-crossing procedure. This provides further orientation and accuracy by identifying predominant bedform lengths in a given bed elevation profile. The workflow has a high degree of automation, which allows the processing of large amounts of data. We applied the workflow to a test dataset from the Lower Rhine in Germany that was collected by the German Federal Waterways and Shipping Administration in February 2020. We found that bedform parameters reacted with different sensitivity to varying input parameter settings. Uncertainties of up to 35 % and up to 50 % were identified for bedform heights and bedform lengths, respectively. The setting of a window size in the zero-crossing procedure (especially for the superimposed small-scale bedforms in cases where they are present) was identified to be the most decisive input parameter. Here, however, the wavelet analysis offers orientation by providing a range of plausible input window sizes, and it thus allows for a reduction in uncertainty. Concurrently, the time difference between two successive measurements has been proven to have a significant influence on the determination of bedform dynamics. For the test dataset, the faster-migrating small-scale bedforms were no longer traceable for intervals longer than 2 h. At the same time, they contributed to up to 90 % of the total bedload transport, highlighting the need for measurements at high temporal resolution in order to avoid a severe underestimation.