160 
w„ = 
and 
= 
a + c 
a + c 
(9) 
Similar calculations can be carried out for drainage vectors between 45° 
and 90°, 90° and 135°, 135° and 180°, 180° and 225°, 225° and 270°, 270° and 
315°, and 315° and 360°. 
The estimation of drainage distribution presented above often results in 
drainage to cells with higher elevation than the centre cell. For example, as 
shown in Figure 4, the calculated drainage vector was 27°, therefore the 
resulting drainage distribution is calculated as 41% to the ‘up’ cell (which is 
higher) and 59% to the ‘upright’ cell. 
13 
,3. 
/ 
1 ii 
15 
/ 
12 
13 
14 
14 
16 
10 *\ 
15 
x° 
12 
\ / 
12 
12 
16 
16 
16 
Figure 4. An example 
where the calculated 
drainage vector results 
in flowing to a cell with 
higher elevation than the 
centre cell. 
Figure 5. An example 
where the calculated 
drainage vector results 
in drainage distribution 
to two, not adjacent 
cells. 
Drainage to cells with higher elevations than 
the centre cell is not always illogical. The elevation 
value of a cell is only an estimation of the mean 
elevation in that area (or spot height at the centre of 
the cell), and it is quite possible that a part of a cell 
is considerably lower in elevation than the rest. However, for special 
instances, the algorithm also offers an option to disallow drainage (partly or 
totally) to cells with higher elevation. 
In some cases the drainage vector may be split to allow water flowing 
into two, not adjacent cells. Figure 5 describes a case like this where the cell 
above the centre cell can be regarded as saddle, or peak, cell. In this case, the 
drainage distribution will be 50% to the upper left cell, and 50% to the upper 
riaht cell. 
If the terrain is too ‘complicated’, for 
example the drainage vector sometimes point at a 
‘wall’ of cells with higher elevations than the centre cell. In these cases, such 
as in Figure 6, the user has to decide the drainage distribution manually. 
3.1.3 Removal of contradictive drainage directions 
If the digital elevation model contains multiple (more than one cell) flat 
(same elevation values) sinks, the presented algorithm may produce 
contradictive drainage directions (i.e. two cells having drainage flow to each 
other). Since these may cause difficulties for calculating flow accumulation 
and other topographic measurements, the contradictive drainage directions 
should be removed. This is done by letting the larger contradictive vector 
stand as it is, and distribute the smaller contradictive vector flow to the other 
drainage direction(s) for a given cell. 
10 
10 
f 
10 
08 
/ 
08- 
>07 
12 
12 
12 
Figure 6. An example 
where the user has to 
decide the drainage 
distribution. The 
drainage vector is 
calculated to 14°, while 
the user-defined 
direction is 90°.