161 
3.2 THE FORM BASED ALGORITHM 
This algorithm is best described by explaining the flow for different cases. The following 
paragraphs describe how the drainage pattern is estimated from a centre cell in a three by three window. 
Case 1: All neighbour cells higher than the centre cell. 
In this case (see Figure 7), the water cannot flow to any of the eight 
neighbour cells. The centre cell represents a single sink, and the water 
distribution is set to zero. However, if it's assumed that the single sinks in the 
DEM are created due to errors in the interpolation algorithm, it's easy to 
change the value of the centre cell to the value of its lowest neighbour. 
It should be noted that the sinks, and possible no data values, are the only 
grid cells in the DEM that will not get a defined flow direction. If the value of 
the centre cell in Figure 7 will be changed to 17, it still will get a defined flow 
direction according to the special treatment of flat areas (see Pilesjo, 1994 and 
below). 
17 
17 
17 ! 
! 17 
15 
17 
. 17 
i 
17 
17 
Figure 7. All neighbour 
cells higher than the 
centre cell. 
Case 2: At least one neighbour cell equal to the centre cell, and the rest higher. 
In this case the drainage distribution is initially set to zero. This is done because the down slope 
gradient is considered to be more important than the up slope gradient. In the presented example (Figure 
8) the main drainage direction is intuitively supposed to be right/up right. If we had used up slope 
gradients (either proportionally or by dividing the aspect vector) it would be estimated to up right. 
Due to the importance of the down slope, the drainage distribution is 
later estimated by vector addition of neighbouring flow directions. In order to 
describe the drainage distribution to the cells around the centre cell, the 
summed drainage vector of the neighbour cells has to be split. This is done 
according to the method described in chapter 3.1.2. 
The estimation of flow directions over a flat area always starts at the 
outflow point, and is begins with cells with as many cells with a defined flow 
direction as possible. This is done to guaranty the outflow from the flat area. 
Case 3: Only one neighbour cell lower than the centre cell, and the other equal 
or higher 
This case always represents a ‘concave situation’, and 100% of the water 
will drain into the lower cell. 
1 17 
15 
15 
Ì 17 
15 
15 
I 17 
17 
17 
Figure 8. At least one 
neighbour cell equal to 
the centre cell, and the 
rest higher. 
Case 4: Two neighbour cells lower than the centre cell, and the other equal or higher 
This distribution of elevation values either represents a convex, a concave, or a ‘double concave' 
topographical form (see Figures 9-11).