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the landscape (eg. concavities and convexities) also restricts the flow directions. This approach, 
compared to the traditional one. forms a more accurate and reliable basis to more realistically model the 
flow accumulation on land surface. The results of the methods can provide more useful information for 
studies requiring accurate hydrological information such as flood prediction, soil erosion, soil moisture 
and geomorphological processes. 
2.0 BACKGROUND 
The topographical characteristics of a point on a three dimensional land surface are commonly 
required in soil erosion modelling, hydrological applications, ecological models and management of 
natural resources (Morris and Heerdegen, 1988; Skidmore, 1989; Eklundh and Pilesjo. 1990; Zhou, 1990: 
Pilesjo, 1992). A number of methods for calculating important characteristics, such as gradient, aspect, 
slope length, size and shape of drainage basins and relief indices, from a regularly grided Digital 
Elevation Model (DEM), have been proposed by various authors (e.g. Evans, 1980; Zevenbergen, 198": 
Martz and De Jong, 1988; Zhou, 1989; Lee et al., 1992; Zhou, 1992). 
Many of the methods of calculating topographical characteristics reveal problems with deriving 
drainage directions and. at a later stage, flow accumulation. The drainage directions are normally 
estimated by rounding the calculated aspect value into one of the eight cardinal points of the compass 
(Horn, 1981; ESRI, 1991). However, this procedure causes problems in some ‘complicated' terrain. The 
problems are especially notable in flat regions, where no aspect can be reliably defined. Pilesjo (1994) 
presented a new algorithm that solves the above problem. In this algorithm, all cells in the DEM get one 
of the eight possible drainage directions. 
Even though the above problem can be solved, it is not totally satisfactory' as problems exist tor 
only letting the drainage direction to be one of the eight cardinal points. In reality', water does not only 
drain into eight directions. Hence, drainage directions, or drainage distribution from a given cell, should 
be modelled based on a continuous, 'aspect like', mean slope direction. In other words, the improvement 
can be made to allow distributing water flow from a given cell into more than one neighbouring cell in a 
Figure 1. 'Aspect like', mean slope direction 
versus one-to-one flow distribution. 
on the aspect values for the individual grid cell 
resolved, namelv: 
three by three cell window, while most existing 
algorithms only allow one-to-one flow distribution 
from the central cell to one of the eight neighbours 
(Figure 1). 
Attempts to solve the problem have led to 
several proposed 'multiple flow direction algorithms' 
(Freedman, 1991; Quinn et al., 1991: Holmgren. 1994: 
Quinn et al.. 1995: Wolock & McCabe, 1995). These 
algorithms estimate the flow distribution values 
proportionally to the slope gradient, or rised slope 
gradient, in each direction. An alternative way to 
implement the continuous flow direction can be based 
However, to do this a number of problems have to be 
1. Given a 3 x 3 window, determine the flow direction in a compass range of 0 to 360 degrees.