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====== Efficient longest flow path algorithm ======
[[Efficient longest flow path algorithm:start|Workspace]]

{{:r_lfp_nc_example_single_warning.png?400|}}

\[
\def\LFP{\overrightarrow{\text{LFP}}}
\def\FP{\overrightarrow{\text{FP}}}
\def\FL{\text{FL}}
\def\DFL{\text{DFL}}
\def\UFL{\text{UFL}}
\def\LFL{\text{LFL}}
\]

A flow path $\FP_i$ is the watercourse between a pair of two points $i$ within the watershed and the longest flow path $\LFP$ is defined as

\[
  \LFP\in\left\{\FP_i\;:\;\left|\FP_i\right|\geq\left|\FP_j\right|\;\forall i\neq j\right\}.
\]

The longest flow path plays an important role in hydrologic modeling, but its computation requires multi-step raster calculations for each watershed. This research project aims to improve the current process and efficiency of computing the longest flow path for a lot of watersheds.

===== Performance comparisons =====

{{:fig-ga-ssd-elapsed-vs-subarea-archydropro.png?400|}}

{{:ga-elapsed-time-gwrc.png?400|}}

^ Method        ^  [[https://github.com/HuidaeCho/grass-lfp-deprecated/blob/master/lfp.sh|lfp.sh]]  ^  [[https://github.com/HuidaeCho/grass-lfp-deprecated/blob/master/lfp2.sh|lfp2.sh]]  ^  [[https://github.com/OSGeo/grass-addons/tree/master/grass7/raster/r.lfp|r.lfp]]  ^  [[https://github.com/OSGeo/grass-addons/tree/master/grass7/raster/r.accumulate|r.accumulate]] ^
^ Elapsed time  |  3h 48m                                                                           |  9h 8m                                                                              |  6h 46m                                                                           |  **56s**      |

===== References =====

  * Huidae Cho, July 2020 in Press. //__A recursive algorithm for calculating the longest flow path and its iterative implementation.__// [[https://www.journals.elsevier.com/environmental-modelling-and-software/|Environmental Modelling & Software]]. [[https://doi.org/10.1016/j.envsoft.2020.104774|10.1016/j.envsoft.2020.104774]]. SCIE, 2018 Impact Factor 4.552, [[https://idea.isnew.info/publications/A%20recursive%20algorithm%20for%20calculating%20the%20longest%20flow%20path%20and%20its%20iterative%20implementation.pdf|Author's Version]].
  * [[https://idea.isnew.info/how-to-calculate-the-longest-flow-path-in-grass-gis.html|How to calculate the longest flow path in GRASS GIS]]

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