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Fig. 3 Comparison of each flow direction concepts (Tarboton 1997 ). a Theoretical flow
direction. b and c Example of SFD model results. d Theory of MFD. e and f Example of MFD
model results
phenomenon upon real water flow concept. Apart from that, even if there is
stagnant water on the earth surface, it will attempt to flow to the lower places due
to the earth gravitational force except surrounded by the higher solid object or
material such as in Fig. 2 . For instance, the water at upstream river will flow
naturally toward the downstream river and then go to the sea as it final destination.
To describe this natural phenomenon, most of the researchers in related fields of
study agreed that the best method or model to describe water flow direction
concept is represented by eight directions such as D8, Rho8, FD8, and FRho8
algorithms in SFD model. Eight directions are the result of the only eight sur-
rounded pixel that directly touch the pixel except the outer pixel (row and column)
of any input raster dataset. The concepts of flow direction and model, examples of
expected output results from several algorithms in SFD and MFD are shown in the
Fig. 3 a-f. The black pixels show the potential flow direction of that particular
point.
2 Current SFD and MFD Algorithms
2.1 Single Flow Direction
Single Flow Direction (SFD) is the simplest and very essential model to describe
the flow direction either in GIS field or others based on height difference such as in
Fig. 4 . The formula is based on difference in height (steepest slope) between a
certain point to its neighbours.
The D8 algorithm is proposed by O'Callaghan and Mark ( 1984 ) and now is
widely used in SFD model in various open source and commercial software. This
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