Geoscience Reference
In-Depth Information
10.7 Donor Catchment and Pooling Group Methods
While the regression equation approach to estimating catchment scale parameters has been widely used,
the UK
Flood Estimation Handbook
(FEH) did not recommend it as the technique for regionalisation
for most cases. This was a recognition of the high uncertainties (and occasional inaccuracies) associated
with the regression estimates. Instead, where no nearby gauging station is available, an approach based
on a
pooling group
of gauged catchments was preferred. The pooling group is chosen on the basis of
proximity to the ungauged catchment of interest of potential donor gauged catchments. The concept
is hydrological rather than simply statistical: catchments that are similar in their characteristics should
be similar in their hydrological responses. The problem, of course, is that catchments can vary in so
many ways that defining similarity is always going to be difficult and there are many different similarity
measures that could be used. The FEH uses a database of physical characteristics of catchments (actually
the same variables as used in the statistical regression approach) to define similarity as proximity in terms
of a Euclidean distance measure in the space of these physical characteristics. A Euclidean distance in a
k
dimensional space between points
i
and
j
is defined as:
x
j,k
−
x
i,k
2
E
=
(10.2)
k
The Euclidean distance is often normalised by dividing the contribution on each dimension by the
variance of the values
x
on that dimension. Other distance measures have also been used, such as the
Mahalanobis distance which allows for the full covariance of values on different dimensions (Cunderlik
and Burn, 2006). Some catchments are more similar than others, of course, and it is a somewhat subjective
decision as to which catchments are included in the pooling group. It is often the case that catchments that
are in the same physioclimatic region are closest to the study site but there may also be distant catchments
that have similar characteristics and (we would expect) hydrological responses. The contribution of each
donor catchment to the estimation of the parameters for the study site can be weighted, depending on the
degree of similarity identified from the catchment characteristics.
This approach raises two major issues. The first is what sort of similarity measure to use; the second
how to allow for uncertainty in the transfer of information from gauged donor sites to the study site.
There are a variety of similarity and dissimilarity measures that have been used in the past (see review
by Wagener
et al.
, 2007) but there is, as yet, no common agreement on what catchment characteristics
should be used in defining similarity and what measures should be used. In fact, Oudin
et al.
(2010)
question the basis for this approach, which depends on an assumption that hydrological similarity is
equivalent to physical similarity (at least if the right physical characteristics are included in the analysis).
They assessed hydrological similarity in terms of model parameters and physical similarity in terms
of catchment characteristics and showed that there was only overlap between the two definitions for
60% of the 900 catchments in France and England included in the analysis. For the other catchments,
the subsurface properties of the catchment, not well represented by the set of physical measures in the
analysis, were a major control on the hydrological response. Reichl
et al.
(2009) also tried to optimise the
weights on different physical characteristics in defining a distance measure. This gave some improvement
over standard distance measures but did not give good predictions for all the test catchments, and they
suggested that the weights were dependent on the sample of catchments used.
One response to this is to try to define groups of catchments or regions that might be considered
to be hydrologically similar before carrying out a regionalisation exercise. This necessarily cuts down
the number of potential donor catchments in each grouping but can mitigate the problem of including
catchments with quite different rainfall regimes or geology and baseflows within the same regionalisation
exercise. There has been quite a lot of research on trying to define homogeneous groups or regions of
catchments, but the donor catchment or pooling group approaches to regionalisation centre this on the
