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will not be eliminated then the catchment of W, should
be merged with C,
> find C, for which Upstr[C,, Cj] = 1
if D £s
and thôre-is.no D, € S with Upsic,, C1 1
then
> AGGR(D;,D,) = Di
> AGGRIC;, Chi) = Chi
The notation D, means that D; and D, have been merged
and Ci. Means that C; and C,; have been merged. When
these steps have been done for each element D, € S, then
new Strahler numbers can be assigned to the remaining
elements according to their new position in the network.
Then the selection procedure can be repeated and so on
until no more elements are eliminated.
A Test Case
The drainage system represented in figure 9.a will be used
as an example to demonstrate the generalization process.
This figure is a schematic representation of the Romani
Drainage system in the Anoia-Penedes Area in NE-Spain
(Martinez Casasnovas 1994). The total area of this drain-
age system is 28.53 km?, at a 1:50.000 scale it has 37
mappable drainage elements. The figure only shows the
water lines W; with their catchments, the drainage element
D; are not shown here.
fig. 9: a) The drainage system at 1:50.000 scale
representation
b) The drainage sustem at 1:100.000 scale
representation
The transition from the original scale to the scale
1:100.000 will be done through the generalization
procedure explained before. So first the drainage elements
with Strahler number — 1 and width « 75m are elimin-
ated, their catchments are aggregated with their down-
stream catchments. Thenthe remaining drainage elements
arereclassified and the procedure is repeated until no more
elements are eliminated.
The result of this procedure is shown in figure 9.b. The
drainage system represented at 1:100.000 scale has only
nine mappable drainage elements. Their catchments are
aggregates of the catchments shown at the 1:50.000
scale. The fact that they are considered to be aggregated
catchments implies that the information carried by the
original catchments is now transferred to these aggre-
gates.
The Romani drainage system has been mapped for an
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
erosion survey. Erosion classes are estimated per catchment
from the information contained in the attributes of the
drainage elements. These are used to compute per
catchment the drainage density in km/km? and the
crenellation ratio in km/km? These data combined with the
depth and the activity class of the drainage elements
determine the erosion class of each catchment. When the
area of the catchments are summed per erosion class we
find in the original situation at 1:50.000 scale that 6896
of the area is slightly eroded, 3096 is moderately eroded
and about 2% shows severe erosion, see figure 10.a.
After generalization aggregated catchments are formed
for which the erosion classes have to be estimated.
Although a large number of drainage elements have not
been represented any more at the reduced scale, the
[1 sightly eroded
moderately eroded
severely eroded
fig. 10: a) Erosion classes estimated in 1:50.000
scale representation
b) Erosion classes estimated in 1:100.000
scale representation
information they carry has been transferred to the aggre-
gated catchments. With these data we find now for the
erosion classes that 79,5% of the area is slightly eroded,
20% is moderately eroded and 0.5% is severely eroded,
see figure 10.b. These numbers deviate significantly from
the original values, furthermore the spatial distribution of
the occurrence ofthe erosion classesis quite different from
the original distribution. The case is even worse if we had
completely ignored the information carried by the eliminated
drainage elements. Then the values would be respectively
99.5%, 0% and 0.5%.
The structural generalization of the drainage system kept
considered its constituting entities as hydrologic units. This
had the effect that the computation of hydrologic processes
is invariant after the generalization. The generalized network
could, however, not be used to formulate reliable
statements about the erosion classes of the areas in the
system. That would require another generalization process
where we have to specify what statements about erosion
should be invariant after transformation. A class driven
or ageometry driven strategy might have been more useful
in this case.
4. OBJECT GENERALIZATION AND LEVELS OF
SPATIAL COMPLEXITY
Chapter 3. discussed several strategies for the generaliz-
ation of spatial databases. These strategies were based
on the concept of spatial object aggregation in combination
