Prediction of floods in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 203

The grouping methods discussed above are sometimes
used as black box or optimisation procedures to get the best
statistical performance of the regionalisation methods in a
region. However, the hydrological interpretation of the
location of the groups in the landscape is a necessary step
for building confidence in the groups, to ensure that the
groups reflect real hydrological processes and are not an
artefact of the data and the methods used (Merz and Blöschl,
2008a , b ). It is important to justify by hydrological
reasoning why catchments are grouped together, beyond
stating that a similarity measure was minimised. The hydro-
logical interpretation needs to give an account of the flood-
producing processes and to explain why the hydrologist
thinks they are similar in the group. The hydrological inter-
pretation can be guided by process indicators at the regional
scale, such as the seasonality of the floods and the rainfall
regime (e.g., Castellarin et al., 2001 ; Parajka et al., 2010a ),
the flood types in a region (House and Hirschboeck, 1997 ;
Merz and Blöschl, 2003 ) , and the runoff generation pro-
cesses as simulated by regional runoff models (e.g., Sama-
niego et al., 2010b ). While such an interpretation involves
more effort than an optimisation method, it will enhance the
credibility of flood predictions in ungauged basins with
both statistical and process-based methods.

Stedinger, 2007 ). For example, in regional estimation of
flood quantiles, this corresponds to a power law relation-
ship such as

A αð T Þ P βð T Þ S γð T Þ ::: Q T ¼ k ð T Þ ð 9 : 1 Þ

where k, are the parameters of the regression

model and A, P and S are catchment/climate characteris-
tics. Analogous relationships can be developed for param-
eters of the flood frequency curves as well. The parameters
represent the flood generation processes in a simplified
way. These processes may vary within a region. Instead
of applying a global regression within the study area, the
area is sometimes subdivided into regions. These are not
necessarily homogeneous regions with respect to the flood
frequency curve (Figure 2.10a) but are homogeneous with
respect to the parameters of the regression model (Figure
2.10b). For example, Thomas and Benson ( 1970 ) used
multiple least squares regression to predict flood quantiles
for four different regions in the USA. Subsequently, Tas-
ker et al.( 1996 ) found that subdivision into smaller geo-
graphically based sub-regions led to more accurate results.
Haddad et al.( 2011b ) used a variable group of catchments
specific to the ungauged basins of interest, whose member-
ship was selected to minimise the regression model error
instead of the heterogeneity in the catchment characteris-
tics. This approach therefore formally minimised the
unaccounted-for heterogeneity in the regression model. In
all instances, the parameters of the regression model need
to be estimated in some way. There are a number of
options by which this can be conducted, which are dis-
cussed below.

α , β and γ

9.3 Statistical methods of predicting floods
in ungauged basins
Once a group of catchments has been identified that are
hydrologically similar to the ungauged basin of interest,
the flood peak data in those catchments can be analysed to
transfer them, in some way, to the ungauged basin. There
are various methods for doing this that differ in several
ways: (i) in the way they formulate the model between
flood peak data and catchment/climate characteristics;
(ii) in the way they estimate the parameters of that model;
(iii) in the way they apply the grouping; and (iv) in the
way they account for the correlations among the variables
(e.g., Cunnane, 1988 ).

Ordinary least squares, weighted least squares The
simplest method is ordinary least squares (OLS). While it
produces unbiased estimates, it lumps sampling and model
errors into a single error term, assuming it has zero mean
and constant variance, and the errors are uncorrelated. This
leads to an overestimate of predictive error and ineffi-
ciency when sampling errors vary from site to site (i.e.,
larger sampling errors where short flood peak records are
available). The weighted least squares (WLS) procedure
(Tasker, 1980 ) accounts for the sampling error introduced
by unequal record lengths.

9.3.1 Regression methods
The regression approach assumes that there is a relation-
ship between a flood peak runoff of a given return period
(i.e., quantile Q T ) and catchment/climate characteristic, or
there is a relationship between the parameters of the distri-
bution function of flood peaks and catchment/climate char-
acteristics (Thomas and Benson, 1970 ). In general, this
relationship is non-linear, but often the relationship is
approximated by a linear model with transformed vari-
ables, e.g., by a logarithmic transform (see e.g., Thomas
and Benson, 1970 ; Pandey and Nguyen, 1999 ; Griffis and

Generalised least squares Sampling errors are often
correlated in neighbouring catchments, being impacted
typically by the same storms, unless small-scale convective
storms are dominant. Generalised least squares (GLS)
regression is an extension of WLS that also accounts for
cross-correlation of flood peaks between sites (Stedinger
and Tasker, 1985 ). Rosbjerg ( 2007 ) demonstrates the