Prediction of floods in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 210

Flood estimates Uncertainty

Top-
kriging

Top-
kriging

0.30
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.80
1.00
2.00

0.0

0.1
0.2
0.3
0.4
0.5
0.6
0.8
1.0
2.0
3.0

Ordinary
kriging

Ordinary
kriging

Figure 9.16. Normalised speci c 100-year flood ((m 3 /s)/km 2 ) and uncertainties expressed as coefficient of variation estimated by top-kriging
(top) and ordinary kriging (bottom) colour-coded on the stream network of the Mur region, Austria. The main stream flows from bottom left to
top right. The measurements and their uncertainties are shown as circles at the location of the stream gauges. From Skøien et al.( 2006 ) .

ungauged catchments in that data from many sites in a
region are pooled to estimate the growth curve, which is
assumed constant in the homogeneous region. Local data
are used to estimate the index flood (mean or median
annual flood peak) (e.g., NERC, 1975 ; Hebson and Cun-
nane, 1987 ). Similarly, most other regional estimation
methods discussed previously can be combined with local
runoff data from short records. Madsen and Rosbjerg
( 1997 ) tested the performance of the regional method for
regional heterogeneity and intersite dependence. For small
to moderate sample sizes, the regional estimator was found
to be superior to the at-site estimator even in extremely
heterogeneous regions, as the relative performance of the
regional estimator was better in regions with a negative
shape parameter. When the record length increases, the
relative performance of the regional estimator decreases,
but it is still preferable to at-site estimation in moderately
heterogeneous and homogeneous regions for large sample
sizes (Hosking and Wallis, 1988 ).
Envelope curves are based on the same idea of homoge-
neous regions and exploit short records. An envelope curve
is a curve drawn to envelop maximum observed flood

peaks experienced in a region as a function of drainage
area. They are often used in practice as a first guess against
which to compare flood frequency estimates, in particular
for large return periods. Figure 9.17 presents envelope
curves for major flash floods in Europe (Gaume et al.,
2009 ; Marchi et al., 2010 ; Borga et al., 2011 ). The envel-
ope curve shown in the figure was obtained from another
data set by Gaume et al.( 2009 ) and was found to be
consistent. The highest unit peak runoff values correspond
to events from the Mediterranean region. For small basin
areas, the flash floods observed under a continental cli-
mate, namely in Slovakia, also attain high values of unit
runoff, even though the peaks of these unit runoff values
seem to decrease upstream at a faster rate than for events in
the Mediterranean region. This behaviour highlights the
different spatial and temporal scales of the runoff-

generating storm events.
On the basis of simplifying assumptions, recent papers
have introduced a probabilistic interpretation of regional
envelope curves and formulated an empirical estimator of
their associated return period (see Castellarin et al., 2005 ,
2009 ; Vogel et al., 2007a ; Viglione et al., 2012 ).