Prediction of floods in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 208

for and, accordingly, the estimation uncertainty is realistic-
ally assessed. Madsen and Rosbjerg ( 1997 ) applied the
method in a regional study of 48 New Zealand catchments
using regional data as prior information.
An adjustment procedure was introduced in the Flood
Estimation Handbook (IH, 1999 ), where a regression-based
estimate of the index flood at an ungauged location is adjusted
by scaling it with the ratio of predicted to observed floods at a
nearby gauged site. The Flood Estimation Handbook (IH,
1999 ) suggests that the gauged catchment should ideally be
located just upstream or downstream of the subject site. If no
such data are available, alternative data might be sought
within the same catchment, or froma nearby or hydrologically
similar catchment, where hydrological similarity is defined as
a combination of catchment area, mean annual precipitation
and soil type. A modified version of the adjustment procedure
was presented by Kjeldsen and Jones ( 2007 ), who found that
discounting the adjustment according to geographical dis-
tance improved the performance of the method.

the stream gauges on the stream network. Geostatistical
methods developed for hydrological applications explicitly
account for the spatial correlations along the stream net-
work. The top-kriging, or topological kriging, method of
Skøien et al.( 2006 ) is based on integrating a point vario-
gram of runoff generation over nested catchments, which
maps on the correlations along the stream network. Figure
9.16 (top left) presents an example of their approach for
estimating the 100-year flood on the stream network, on
the basis of regionalising the flood moments. To highlight
the spatial patterns, the 100-year flood was scaled by
catchment area A 0.33 (where A is catchment area), which,
for the region they studied, minimises the scale depend-
ence. For comparison, Figure 9.16 (bottom left) shows the
estimates from ordinary kriging (Merz and Blöschl, 2005 ).
The measurements are shown as circles in both figures
with the same colour-coding. For both methods, the esti-
mates next to the stream gauges are almost equal to the
measurements of the stream gauge itself. Along the
streams, on the other hand, the ordinary kriging estimates
differ substantially from the top-kriging estimates, the
main difference being that ordinary kriging uses Euclidean
distance in space. For top-kriging the specific floods are
around 0.65 (m³/s)/km² for the main stream in the centre of
the region shown, lower to the north of it and larger to the
south of it, as suggested by the stream gauges. In contrast,
ordinary kriging does not account for the stream network
structure, so the flood data on the main stream and the
tributaries are dealt with in the same way. The panels on
the left of Figure 9.16 show the uncertainties expressed as
the coefficient of variation of the estimates. Both methods
estimate the lowest uncertainties close to the measure-
ments. Top-kriging gives relatively small uncertainties on
the main river while the uncertainties of some of the
tributaries are considerably larger: the uncertainties are
small for those tributaries where measurements are avail-
able, but rather large for tributaries without any measure-
ments. It is interesting that the uncertainty increases
substantially with decreasing catchment area. The uncer-
tainties estimated by ordinary kriging ( Figure 9.16 bottom
right) do not reflect this expected pattern.

Hydrological interpretation
Index flood studies have been interpreted in a broader
context by Meigh et al.( 1997 ) for numerous countries
around the world. Figure 9.15 shows mean annual flood
peaks and the 500-year flood scaled by the mean annual
flood from their study plotted against the median annual
precipitation. The scaled 500-year flood is an indication
of the steepness of the growth curve. For humid, high
rainfall regions the average flood is relatively large, but
the flood frequency curve is not very steep; rare floods
(occurring once in every 100 to 1000 years) are not very
much larger than the average flood. Conversely, in arid
regions, the average flood is small, but rare floods can be
extremely large multiples of the average. Clearly, this is
related to differences in the flood generating processes.
The rainfall regime may be more variable in arid than in
humid regions, with a small number of extraordinary
events (Wheater et al., 2007 ). Also, the runoff generation
process will be different where the abstraction in arid
regions tends to be large, making the rainfall runoff pro-

cess more non-linear than in humid regions ( Chapter 4 ).
The combined effect of the differences in the rainfall
regime and runoff generation then leads to enormous
differences in the growth curves. Similar comparative
interpretations are possible for smaller regions where the
differences in the flood frequency curves are more subtle.

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Geostatistics combined with catchment characteristics
Geostatistical methods can be extended in a number of
ways to account for differences in the catchment and
climate characteristics in the landscape. Chokmani and
Ouarda ( 2004 ) used kriging in physiographic space to
estimate quantiles for ungauged catchments. They used
both canonical correlation analysis (CCA) and principal
component analysis to define the multivariate space in
which kriging was applied. A similar approach was used
by Ouarda et al.( 2008 ) in a comparison of regionalisation
techniques in Mexico. CCA has also been used in

9.3.3 Geostatistical methods
Top-kriging
While the regression approach with generalised least
squares accounts for inter-site correlations of the flood
events, it does so without accounting for the location of