Prediction of floods in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 196

presence of hydraulic structures and other water resources
activities relevant to floods in the catchment area. Third,
the flood peak reduction mainly depends on the free
volume of the reservoir relative to the flood volume
(Fitzhugh and Vogel, 2010 ), so during extreme floods
the free reservoir capacity may be exhausted, leading to
very little peak reduction and unexpectedly large floods
downstream of the reservoir (Blöschl, 2008 ; Salazar
et al., 2012 ).

parameters of the flood frequency distribution (Merz and
Böschl, 2009b ). The coefficient of variation (CV) of the
flood peaks reflects the steepness of the growth curve. The
CV has been the most commonly used similarity measure
in regional flood frequency analysis. For example, the
index flood method (see Section 9.3.2 ) works on the
assumption of constant CV within a homogeneous region.
The coefficient of skewness is the third-order moment and
reflects the curvature of the flood frequency curve. It can
be used to define higher order measures of similarity,
which become important to capture more complex flood
frequency distributions. A number of studies have shown
evidence that the CV is actually scale dependent and relate
it to a number of factors, depending on the particular
hydrological context of the region analysed. For example,
Smith ( 1992 ) presented the scale dependence of CV in the
Appalachian region of north-eastern USA, which showed
an apparent increase of CV up to about 100 km 2 , and a
decrease subsequently. Smith proposed alternative explan-
ations: errors in stream gauging vs. spatial organisation of
extreme precipitation and the downstream changes in the
channel/floodplain system. Gupta and Dawdy ( 1995 ) sug-
gested an alternative explanation; in small catchments CV
may be governed by catchment response and at large scales
by the spatial scaling of precipitation. Robinson and Siva-
palan ( 1997b ) attributed the scaling of CV to the combined
effects of the interactions between precipitation duration
and catchment response time (which dominates at small
scales), and to the scaling of precipitation with catchment
size (which dominates at large scales). Blöschl and Siva-
palan ( 1997 ), using extensive flood frequency data in
Austria, showed that the scale dependence confirmed the
role of the time-scale interactions, but showed that scale
dependence is a combined result of several factors.
An important similarity measure that has received sig-
nificant attention in recent years is the seasonality of the
floods (Merz et al., 1999 ; Jain and Lall, 2000 ; Petrow
et al., 2007 ). The average period within the year that floods
occur and how variable that period is can be quantified by
circular statistics (Mardia, 1972 ; Burn, 1997 ). These are
the parameters shown in Figure 9.2 . This seasonality index
has been used to identify flood similarity at the regional
scale and to group catchments into regions with similar
flood processes (Piock-Ellena et al., 1999 ; Castellarin
et al., 2001 ; Sivapalan et al., 2005 ; Parajka et al., 2010a ).
Seasonality is also used as a diagnostic in the UK Flood
estimation handbook (IH, 1999 ). It is also interesting to see
whether the flood seasonality changes with the magnitudes
of the events ( Figure 9.4 ) and with time. Both dependen-
cies may shed light on the flood driving processes and
assist in regionalisation. For example, Parajka et al.
( 2009a ) found a trend towards an increase in winter floods
due to a warmer climate in parts of Central Europe. This

9.2.2 Similarity measures
Regionalisation of flood frequency behaviour from gauged
to ungauged catchments critically depends on the notion of
similarity. With respect to flood frequency, two catchments
can be deemed to be similar if their flood frequency curves
are similar in some respect arising from the similarity in the
flood generating processes. The most basic approach to
similarity is spatial proximity, i.e., assuming that catch-
ments that are close to each other behave in a hydrologic-
ally similar way (Merz and Blöschl, 2005 ). The rationale
for this concept is that the controls on the rainfall

runoff
relationship are likely to vary smoothly in space, or are
uniform in predefined regions. Merz and Blöschl ( 2005 )
showed, in a comparative study in Austria, that spatial
proximity is a significantly better predictor of regional
flood frequencies than any other catchment characteristic.
Bates et al.( 1998 ), in an Australian study, showed that super-
groups, consisting of sites within aggregated homogeneous
regions that have reasonably similar flood responses, show
some degree of spatial coherence. In the UK, Kjeldsen and
Jones ( 2009 , 2010 ) found geographical proximity of catch-
ments to be a useful surrogate to compensate for the inability
of lumped catchment characteristics to explain between-
basin differences in the observed index flood. There are
elaborate similarity measures that are adopted in practice
that account in a more detailed way for the flood generating
processes and the characteristics of flood runoff.

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Runoff similarity
Due to different catchment sizes, two catchments can be
hydrologically similar and still have different flood fre-
quency curves. The flood frequency curves may perhaps
be similar in terms of their shape but not in terms of their
magnitudes. One way of measuring similarity in regional
flood frequency analysis that accounts for these differences
is to scale the flood frequency curve by an index flood,
which is usually taken as the mean or median of the annual
maximum flood peaks. If the scaled flood frequency curves
(also called the growth curves) are similar, then the catch-
ments are deemed to be similar.
Instead of the growth curve (non-parametrically), one
can also assess similarity by comparing the moments or