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assigning the label to all neighbours with flow directions 
to already labelled points. Here, a slightly different 
algorithm is used utilising the existence of a sorted 
indexing array. Work takes place upwards. To each 
grid-cell all deeper neighbours (in 4-connectivity) are 
examined. The following conditions may occur: 
1) No deeper neighbours exist. 
a) The cell lies at the edge of the region: A new 
"global basin" starts. 
b) The cell lies within the region (this is impossible 
in a depressionless DEM): A new depression with 
a "pit-basin" starts. 
2) All deeper neighbours belong to the same basin: The 
cell is assigned to this basin. 
3) Deeper neighbours belong to different basins: The 
cell is marked as a border cell. 
4) All deeper neighbours are border cells: The cell is 
marked as a border cell, too. 
Criterion 1) b) has been inserted for use of this algo- 
rithm in the elimination of pits: If a cell meets this crite- 
rion, a new entry in the pit-table is created (compare to 
chapter 3.2). Following, whenever a cell has deeper 
neighbours partly belonging to a pit-basin and a global 
basin, this cell becomes outflow point of the participat- 
ing pit-basin. It is recorded in the respective entry in the 
pit-table and the pit-basin is assigned to the participat- 
ing global basin to prevent from creating further outflow 
points for this pit-basin. 
Criteria 2) and 3) do not change, if there are also border 
cells involved. Picture 8 shows the result of this label- 
ling procedure on part of the model of picture 4 with all 
catchment areas shown in different gray values and the 
borderlines in black. 
e: » 
     
‚N 
Fig. 8: Catchment areas and borderlines in a part of the 
model of fig. 4. a) Coded areas; b) border lines on ter- 
rain. 
  
Obviously, there are some dependencies on the grid 
direction, and some borderlines are too broad. Therefore 
the concept of the DOVs is adapted as the "catchment 
affiliation values" (CAVs): 
The base-cell of a catchment area is assigned a CAV of 
1. The same is true for all cells along the marked river 
sections, which means, that all these cells completely 
belong to the catchment area. For processing reasons, 
the label is constructed as follows (cnr be the label 
number of the catchment area, cav the CAV in the 
respective cell, and /abe/ the value finally assigned): 
cnr for cav=1 (3) 
label = 
cnr * cay for cav «1 
The CAV furthermore is limited to a range of about 
0.0001 through 0.9999 to avoid numeric zero for very 
small values (which would falsely be interpreted as a 
647 
CAV of 1.0000) and numeric 1.0000 (which would 
falsely be interpreted as the catchment area with the 
next higher code-number, cnr+ 1). Each cell / is as- 
signed a CAV from all deeper neighbours j of the same 
catchment area k as follows: 
4 
gay = gay: da, (4) 
j=1 
dqv is the drainage quota value as defined in equation 
(2). The affiliation values are now obtained by working 
from bottom to top of the DEM. Each cell's CAV is 
calculated from all its deeper neighbours, thus the pro- 
cess can be finished in one step just like the ordered 
calculation of the drainage accumulation values. 
Within the catchment area all points have CAVs of 
exactly 1.0, while in the border regions the CAV will be 
lower than 1. In the last case, the cell belongs to more 
than one catchment area. Since only one value is pro- 
vided, the cell is assigned to the catchment area with 
the highest affiliation value of all participating basins. 
For better results the complement of Càv; is adjoined as 
the CAV to the other participating catchment areas as 
(1-cav;)/n in the neighbour / to point /, if cell / has n 
neighbours belonging to other catchment areas. Picture 
9a) shows the CAVs for a part of the DEM of picture 4. 
Picture 9b) shows the zones with CAVs lower than 1 in 
dark gray as an overlay on the terrain. 
  
   
     
  
  
Fig. 9: a) Catchment affiliation values (CAVs) in a part 
of the terrain of fig. 4. White: CAV =1, black: CAV =0, 
gray: 0.5 x CAV « 1. b) Zones with CAV « 1 in dark gray 
on the terrain. 
  
Borderlines are found by examining all cells with neigh- 
bours belonging to other basins. The respective cells 
with the highest height value and the lowest CAV are 
marked as border cells. Picture 10 shows the final re- 
sults, river-courses and catchment borders on the whole 
terrain of picture 4. 
LS E ORE AE: ü E 
Fig. 10: Terrain of picture 4 with river courses (black) 
and catchment areas (borderlines in white) 
The same algorithm can be used for marking the out- 
flow points of depressions, as mentioned. Within de-