ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
ISPRS, V 
40 
algorithms use different weights for the diagonal neighbors. 
This study used a modified version of Sharpnack and Akin’s 
method using unequal weights for the closer elevation values 
(Horn, 1980) as follows, 
e 5 
e 2 
e 6 
ei 
e 
e 3 
e 8 
e 4 
e 7 
Fig. 2 Slope calculation from three by three window with 
elevation values 
Slope m = 
(e 7 + 2e A + g 8 ) - (e 6 + 2e 2 + e 5 ) 
8 xcell size 
the DEM, do not drain. These are rare in natural topography 
and generally assumed to be artifacts arising due to the 
discrete nature and data errors in the preparation of the DEM. 
They were eliminated here using a ‘flooding’ approach. This 
raised the elevation of each pit grid cell within the DEM to the 
elevation of the lowest pour point on the perimeter of the pit 
(Jenson and Domingue, 1988). 
In most cases, the existence of pits in the DEM is explained by 
numerical errors introduced in the process of interpolation of 
observed values to estimate values for each grid cell. Filling the 
DEM pits consists of increasing the value of the pit cells to the 
level of the surrounding terrain, so that water is able to flow out 
of the area. Once the pits have been filled and the flow 
directions are known, the drainage area (in units of cells) is 
calculated counting the number of cells located upstream of 
each cell (the cell itself is not included) and, if multiplied by the 
cell area, equals the drainage area. 
• Contributing Area 
Slope we 
(g 8 +2e, +e 5 )~ (e 7 + 2e 3 + e 6 ) 
8 x cell size 
• Flow direction 
Topographic analysis required to define the hydrologic system 
is based on the DEM. According to the process showed in Fig. 3, 
a single downstream cell - in the direction of the steepest 
descent -- was defined for each terrain cell, so that a unique 
path from each cell to the basin outlet is determined. This 
process produced a cell-network, with the shape of a spanning 
tree, which represents the paths of the watershed flow system. 
However, because a flow direction can not be determined for 
cells that are lower than their surrounding neighbor cells, a 
process of filling the spurious terrain pits is necessary before 
the flow direction determination. 
Fig. 3 Grid functions for terrain analysis for hydrologic 
purposes (Francisco and David, 1999) 
Pits in digital elevation data are defined as grid elements or sets 
of grid elements surrounded by higher terrain that, in terms of 
Upslope area (counted in terms of the number of grid cells) was 
calculated for both single and multiple flow directions using a 
recursive procedure that is an extension of the very efficient 
recursive algorithm for single directions (Mark, 1988). The 
upslope area of each grid cell is taken as its own area (one) plus 
the area from upslope neighbors that have some fraction 
draining to it. The flow from each cell either all drains to one 
neighbor, if the angle falls along a cardinal (0, tt/2, tt, 3tt/2) 
direction or diagonal (tt/4, 3tt/4, 5rr/4, 7tt/4) direction, or is on 
an angle falling between the direct angle to two adjacent 
neighbors. In the latter case the flow is proportioned between 
these two neighbor pixels according to how close the flow 
direction angle is to the direct angle to those pixels, as 
illustrated in Fig. 4. Specific catchment area, is then upslope 
area per unit contour length, taken here as the number of cells 
times grid cell size (cell area divided by cell size). This assumes 
that grid cell size is the effective contour length, in the definition 
of specific catchment area (Fig. 4) and does not distinguish any 
difference in contour length dependent upon the flow direction. 
For shallow lateral subsurface flow follows topographic 
gradients, this implies that the contributing area to flow at any 
point is given by the specific catchment area defined from the 
surface topography. 
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