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2. Accordingly, determine the proportional flow distribution among the neighbours (maximum 
two). 
3. In some circumstances, allow more flexible flow distribution such as flow diversion, i.e. split 
flow into two or more, non-adjacent neighbours. 
4. Compute flow accumulation based on the proportionally distributed flow directions. 
An algorithm based on the above mentioned steps will be presented in this paper. However, if we 
assume that the water flow is diverging over convex surfaces and converging over concave surface these 
models do not fit. 
To deal with this fact, a number of assumptions has to be made 
1. From any point in the terrain, the water flows in the steepest direction (perpendicular to the iso 
lines. 
2. The flow from a grid cell to one of its neighbours is proportional to the area of the centre grid cell 
giving water in that direction. 
3. Water is evenly distributed over a grid cell. 
4. Every cell in a regularly grided DEM (except sinks) has drainage distribution to its 
neighbourhood. 
The assumption of convex/concave flow distribution is presented in 
Figure 2. To adequately implement a ; form based’ flow direction algorithm 
for estimation of flow accumulation, several problems have to be resolved, 
namely: 
1. Given a 3 x 3 window, determine the topographic form 
(concavities/convexities) of the neighbourhood. 
12 
10 
12 
15 
15 
15 
17 
17 
17 
2. Determine the proportional flow distribution among the neighbours 
according to the assumptions mentioned above. 3 4 5 
3. Under some circumstances, allow more flexible flow distribution 
such as flow diversion, i.e. split flow into two or more, non- 
adjacent neighbours. 
4. Estimate flow directions over flat areas. 
Figure 2. Water will only 
flow to the grid cell above 
the centre cell because of 
the concave form. The 
numbers represent 
elevation. 
5. Compute flow accumulation based on the formed based flow directions.