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\begin{document}

\title{Emergence of efficient channel networks in fluvial landscapes}



\author[1]{Dnyanesh Vijay Borse}%
\author[1]{Basudev Biswal}%
\affil[1]{Department of Civil Engineering, Indian Institute of Technology Bombay}%


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  \date{June 09, 2024}


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\begin{abstract}
Channel networks across fluvial landscapes are believed to have evolved
to minimize energy expenditure{[}1--3{]}, as evidenced by the
similarities between computer-generated optimal channel networks (OCNs)
and real networks{[}4,5{]}. However, the specific mechanisms driving
energy minimization in fluvial landscapes remain largely elusive{[}6{]}.
Here we propose that randomness has a profound role in landscape
evolution{[}7{]} and that efficient channel networks emerge when the
probability of a channel pixel changing its flow direction decreases
with drainage area. The proposed probabilistic growth model then employs
a power function to simulate channel-network evolution, with positive
exponent (?) values leading to asymptotic decrease of energy
expenditure. An interpretation of this result is energy minimization
tendency of river networks is a result of landscape evolution following
specific adaptive rules rather than being the cause of landscape
evolution itself. A greater ? ensures a greater restriction on the role
of randomness and thus results in a more stable channel network
configuration, and vice versa. Interestingly, the most efficient
networks are observed to emerge always at ? =0.5, suggesting that
randomness plays an important but limited role in the emergence of
efficient channel networks. The proposed framework holds promise for
explaining the evolution of other tree-like networks in nature and for
developing more efficient optimization methods for practical
applications.%
\end{abstract}%



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