The Braiding Index 2.0: eBI

We present a new metric for braiding intensity to characterize multi-thread systems (e.g., braided and anastomosing rivers) called the Entropic Braiding Index, eBI . This metric is a generalization of the widely used Braiding Index ( BI ) which is simply the average count of intercepted channels per cross-section. The co-existence of diverse channels (widely different widths and discharges) within river cross-sections distorts the information conveyed by BI , since its value does not reflect the diversity and natural variability of the system. Moreover, the fact that BI is extremely sensitive to resolution ( BI increases at higher resolution as smaller scale channels can be resolved) challenges its applicability. eBI , addresses these main drawbacks of BI .

eBI is rooted in the concept of Shannon Entropy, and its value can be intuitively interpreted as the equivalent number of equally important (in terms of discharge) channels per cross-section. Thus, if the channels observed in a multi-thread system are all carrying the same amount of discharge, eBI has the same value of BI . On the other hand, if a very dominant channel in terms of discharge co-exists with much smaller channels, eBI would take a value slightly larger than 1 (note that the actual value would depend on the number of small channels and their relative size with respect to the dominant channel).

We present a comparative study of BI and eBI for different multi-thread rivers obtained from numerical simulations and remote-sensing data and for different discharge stages. We also provide evidence of the robustness of eBI in contrast to BI when a given river system is studied under different resolutions. Finally, we explore the potential of eBI as a metric to characterize different types of multi-thread systems and their stability.