The Entropic Braiding Index (eBI): A Robust Metric to Account for the Diversity of Channel Scales in Multi‐Thread Rivers. Issue 16 (22nd August 2022) - Tejedor, Alejandro; Schwenk, Jon; Kleinhans, Maarten; Limaye, Ajay B.; Vulis, Lawrence; Carling, Paul; Kantz, Holger; Foufoula‐Georgiou, Efi
Abstract: The Braiding Index ( BI ), defined as the average count of intercepted channels per cross‐section, is a widely used metric for characterizing multi‐thread river systems. However, it does not account for the diversity of channels (e.g., in terms of water discharge) within different cross‐sections, omitting important information related to system complexity. Here we present a modification of BI, the Entropic Braiding Index ( eBI ), which augments the information content in BI by using Shannon Entropy to encode the diversity of channels in each cross section. eBI is interpreted as the number of "effective channels" per cross‐section, allowing a direct comparison with the traditional BI . We demonstrate the potential of the ratio BI/eBI to quantify channel disparity, differentiate types of multi‐thread systems (braided vs. anastomosed), and assess the effect of discharge variability, such as seasonal flooding, on river cross‐section stability. Plain Language Summary: Multi‐thread rivers display astonishingly complex patterns with multiple channels splitting and joining to form intricate networks. Multi‐thread rivers are often highly dynamic, and seasonal flooding can trigger significant channel reorganization. Understanding multi‐thread systems and their dynamics relies on our capacity to characterize them. However, the most widely used metric to analyze multi‐thread systems—the Braiding Index ( BI )—is just the average count of channels per cross‐section. BI is blind to differences in channel scale (water discharge, width) and, thus, BI is very sensitive to observational resolution—higher resolution would reveal smaller channels, often orders of magnitude smaller than the largest channels. Here we propose a modification of the BI using concepts of entropy ‐ the entropic BI, eBI ‐ which encodes not only the channel count but also the heterogeneity of channels in terms of scale (flow, channel width, or any other relevant property) within cross‐sections. We demonstrate that eBI is a robust and suitable metric to characterize multi‐thread systems, differentiate between braided and anastomosed systems, and provide information about river cross‐section stability to forcing, for example, seasonal flooding. Key Points: We present an entropy‐based metric, Entropic Braiding Index ( eBI ), that quantifies braiding intensity by providing the effective number of channels per cross‐section eBI is more robust than previous metrics to changes in resolution by accounting for channel diversity in terms of scale (e.g., water discharge) eBI can differentiate between braided and anastomosed systems and assess river cross‐sectional stability in response to seasonal flooding