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\begin{document}

\title{The Braiding Index 2.0: eBI}



\author[1]{Alejandro Tejedor}%
\author[2]{Jon Schwenk}%
\author[3]{Maarten Kleinhans}%
\author[4]{Paul Carling}%
\author[5]{Efi Foufoula-Georgiou}%
\affil[1]{Max Planck Institute for the Physics of Complex Systems}%
\affil[2]{Los Alamos National Laboratory}%
\affil[3]{Utrecht University}%
\affil[4]{University of Southampton}%
\affil[5]{University of California Irvine}%


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  \date{June 18, 2024}


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\begin{abstract}
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.%
\end{abstract}%



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