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\begin{document}

\title{An improved triangular form-based multiple flow direction algorithm for
determining the nonuniform flow domain over grid networks}



\author[1]{Pengfei Wu}%
\author[1]{Jintao Liu}%
\author[1]{Xiaole Han}%
\author[1]{Meiyan Feng}%
\author[1]{Junyuan Fei}%
\affil[1]{Hohai University}%


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  \date{May 17, 2024}


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\begin{abstract}
The naturally-existing diffusive flow makes the multiple flow direction
(MFD) algorithm for digital elevation models with revisited values.
However, owing to a generally accepted hypothesis, i.e., flow over a
grid cell is uniformly distributed ignoring the micro-topography and the
inflow direction/position, nearly no existing MFD algorithms can
simultaneously force the flow along the exact dispersive path, and
provide highly accurate hydrological/geomorphological parameters. In
this study, an improvement Triangular Form-based Multiple Flow Algorithm
called iTFM is proposed to limit the arbitrary dispersion caused by the
conventional hypothesis through considering the nonuniform flow domain
within a cell. In the new algorithm, each facet flow and its inflow
direction/position are considered to route the flow along the local
aspect over partial areas to downstream facets or cells. Facets with or
without inflow can behave quite nonuniformly in contributing areas,
namely flow domains. This procedure is adopted to generalize the
nonuniformity and route the flow to the exact downstream facets.
Quantitative assessments using artificial terrains show that iTFM
suppresses the artificial dispersion effectively and extracts the flow
paths highly consistent with the exact ones. Compared with previous
algorithms, iTFM provides the most accurate total contributing areas. In
addition, vector split and area split strategies are compared for flow
split within a facet which is a necessary step in both TFM and iTFM, and
the results prove that area split is more efficient. Hence, it can be
concluded that the iTFM algorithm combined with the area split strategy
can better define the dispersion flow path.%
\end{abstract}%



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