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2009 , in Norway; and Aschwanden and Kan, 1999 ,in
Switzerland). Their findings regarding the best grouping
methods to be used for regional regressions differ. This is
partly because of the different techniques that have been
evaluated, but also because of the different settings of the
studies. The Australian study, for instance, found that a
weighted cluster analysis based on catchment characteris-
tics that were weighted according to the coefficients of a
global regression model was better suited than ordinary
cluster analysis and a global regression model. This was
also found in the Austrian study, though alternative catch-
ment classifications based on seasonality analysis and the
regression tree performed better. Regression trees were
found to be more suitable than cluster analysis in the
Austrian and north-west Italian study. For highly seasonal
regimes, seasonality measures contain essential informa-
tion about dominant processes, which can be profitably
used in catchment classification as indicated in the Aus-
trian, Norwegian and north-west Italian studies.
8.3 Statistical methods of predicting low flows
in ungauged basins
On the basis of the grouping methods discussed above, low
flows in ungauged basins can be estimated by transferring
information from one or more nearby gauged basins.
The simplest methods are specific runoff techniques,
where runoff per unit area is assumed to be spatially
uniform (Dyck, 1976 ). However, this is not always appro-
priat e, so more sophisticated statistical methods have been
developed, which exploit either correlations between low
flows and catchment/climate characteristics or correlations
between low flows across space. Both kinds of approaches
involve hydrological similarity measures, in the latter case,
on the basis of spatial proximity.
Figure 8.7. Low flows in the Kander catchment, Switzerland. Big
bold numbers are Q 95 low flows (l/s), Small numbers are catchment
indices. Triangles indicate stream gauges from which low flows have
been estimated (red: period 1984
93; purple: other period; grey: not
used for regionalisation). Points indicate cross-sections where low
flows have been estimated by regression. Map is 25 km across. From
Aschwanden and Kan ( 1999 ).
-
(Gustard et al., 1989 ; 1992 ; Demuth, 1993 ; Laaha and
Blöschl, 2007 ; Engeland and Hisdal, 2009 ), Australia
(Nathan and McMahon, 1992 ) and the USA (Thomas and
Benson, 1970 ; Kroll et al., 2004 ). If the study domain is
large or very heterogeneous in terms of the low flow
processes it is useful to split the region into groups by
methods such as those discussed above. For each of the
regions a regression model is then fitted independently.
This is termed the regional regression approach, as
opposed to the global regression approach where only
one regression model is used for the entire domain.
A typical example of a regional regression is shown in
Figure 8.7 . Aschwanden and Kan ( 1999 ) grouped Switzer-
land into six regions based on the residual patterns of a
global regression model. For each of the regions they fitted
a regression model independently between specific low
flows and catchment characteristics and cross-validated it.
In the final presentation ( Figure 8.7 ) they combined the
estimates from a 10-year standard period with estimates
from shorter records, as available, to best exploit the infor-
mation in the runoff data they had. An important part of
8.3.1 Regression methods
Multiple regression is a frequently used method to develop a
relationship between the low runoff statistic of interest, such
as Q 95 , and catchment/climate characteristics (see also syn-
thesis in Section 8.5 ). Additive and multiplicative regression
models are commonly used, and the choice between the two
forms is generally guided by an analysis of the residual
structure (e.g., Draper and Smith, 1998 ). Vogel and Kroll
( 1992 ) showed the multiplicative form to be consistent with a
theoretically based low flow model derived from hillslope
runoff models, and suggested that it may be a natural choice,
while Laaha and Blöschl ( 2006a ) found their data to be better
represented by the additive form.
Low flow regression models have been developed for
many regions throughout
the world,
including Europe
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