Geography Reference
In-Depth Information
to assist in the understanding of hydrological processes;
a)
b)
to transfer
information from gauged to ungauged
f 2
locations.
Understanding of hydrological processes: Once the
hydrological similarity or dissimilarity of catchments has
been identified (for a particular purpose) the catchments
can be grouped to reflect the similarity. These groups can
then be used for classifying catchments. The power of
classification can perhaps be best illustrated by the periodic
table of chemical elements credited to Dmitri Mendeleev.
Before Mendeleev
Cc =B
f 1
Cc =A
Figure 2.10. Map of an imaginary country where catchments
(indicated as points) are grouped into regions. (a) Grouping into
regions with similar catchment characteristics, Cc; (b) grouping into
regions where the regionalisation methods f 1 and f 2 (such as the
regression equations) are similar.
s classification, the reactions of chem-
ical elements must have appeared chaotic and confusing.
Mendeleev
'
s periodic table not only enabled him to better
understand the behaviour of various chemical elements
(e.g., on the basis of their atomic number) but he was also
able to
'
where the catchment characteristics within each of the two
regions are similar, but are different between the regions.
There is a trade-off between the number of groups and the
homogeneity within the group, the more groups one forms
the more homogeneous each of them will be, but a larger
number of groups entails a relatively smaller number
of catchments per group. There are numerous methods
available for identifying homogeneous groups,
including cluster analysis and other multivariate statistical
methods (see e.g., Cressie, 1991 ; Arabie et al., 1996 ).
This grouping step breaks up the landscape into a
mosaic of units that may or may not be contiguous. The
rationale is that, if the climate/catchment characteristics are
similar, the hydrological processes will also be similar. In a
second step, this grouping is then exploited for regional-
isation. For example, the grouping can be used to transfer
the flow duration curve scaled by the mean annual flow
from gauged to ungauged basins on the basis of the
assumption that these scaled curves will be identical in
the entire homogeneous region. Similarly, scaled flood
frequency curves (i.e., growth curves) can be transferred
from gauged to ungauged catchments based on similar
assumptions.
Sometimes, however, one is not interested in finding
groups of catchments that are most similar in terms of their
climate/catchment characteristics but in terms of their map-
ping functions, i.e., the models that estimate runoff from
climate and catchment characteristics. The mapping func-
tions can be regressions between catchment characteristics
(such as elevation) and runoff signatures (such as mean
annual runoff). The mapping functions can also be process-
based rainfall
characteristics of chemical elements that
were then unknown. In a similar fashion, classification can
be used in hydrology for organising catchments, simplify-
ing relationships and generalising findings. These may
help with process-based models, in particular to find out
what types of models to use. This type of classification/
grouping may also assist with assessing our predictive
ability, e.g., in what kind of catchment is our predictive
ability higher or lower. Ultimately this will assist with the
generalisation issue that has haunted hydrologists since the
science began.
'
predict
'
Transferring information from gauged to ungauged
locations
From a more practical point of view, similarity can be used
to transfer information from gauged to ungauged locations.
In a first step, catchments (or landscape units) are identi-
fied that are similar in terms of the climate and/or the
catchment characteristics chosen and are grouped together.
Usually some index is chosen that quantifies what makes
two catchments similar in terms of climate (such as similar
mean annual precipitation, P A ) and catchment characteris-
tics (such as mean catchment elevation, Z). A distance
measure then defines the similarity or dissimilarity
between two catchments. A typically used distance meas-
ure is the Euclidian distance. In the examples above, the
Euclidian distance is D²
Z j ) 2 (in
fact, the indices could be scaled to make P A and Z dimen-
sionless, and in this way give them equal power). The
important point here is that the distance D is small if the
catchments are similar with respect to their catchment/
climate characteristics. The catchments are then grouped
into similar regions on the basis of minimising the distance
measure D. The over-riding idea of grouping usually is that
within the group the catchments should be as similar as
possible, but the averages of the different groups should be
as different as possible. This is illustrated in Figure 2.10a
¼
(P A,i
P A,j )² + (Z i
runoff methods. The important difference
from the previous approach is that now we are not inter-
ested in finding regions that are homogeneous in terms of,
say, mean annual runoff, but in terms of the regionalisation
method, i.e., implying that the same, say, regression model
applies to all catchments within a region, but a different
model applies in different regions. This is illustrated in
-
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