Prediction of seasonal runoff in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 118

explanatory power. For example, hierarchical cluster
analysis (Ward

river sections using the random forest model (Snelder
et al., 2009 ). The predictive performance of the model
was highest when the study area was subdivided into only
a few individual regions.
Aschwanden et al.( 1986b ) proposed a method that is
based on Fourier analysis of seasonal runoff data. They
estimated Fourier coefficients using runoff data at several
gauged locations in the Swiss plateau to describe the
seasonal pattern and then developed regional regressions
between the Fourier coefficients and spatial positions of
the station. On the basis of this they were able to estimate
all Fourier coefficients, through interpolation, on to a 10
km × 10 km grid, and in this way constructed the seasonal
flow regime across the entire region, and also characterised
their regime types.

s method) of approximately 1000 small
Swiss catchments generated groups that, when visualised
through the Andrews curve, were found to have large
internal heterogeneity. That is, the resulting groups had
limited potential to describe similarities and differences
between catchments (Breinlinger, 1995 ).

'

6.3 Statistical methods of predicting seasonal
runoff in ungauged basins
6.3.1 Regression methods
Through regression methods, quantiles of monthly
runoff or parameters of the flow regime curve are trans-
ferred to the ungauged site based on their relationship
with catchment characteristics. Multiple regression

6.3.2 Index methods
Index methods associate a non-dimensional regime (i.e.,
Pardé coefficients PK i ) to an ungauged catchment by
(visual) mapping, interpolation or assignment to homo-
geneous regions. Monthly average runoff Q loc i for
month i at an ungauged location loc are computed by
multiplying the regionalised Pardé coefficients PK reg
i

approaches linear, log-linear, power-law or non-linear

Fourier coefficients

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can be adopted (Gan et al., 1991 ).
Different regression relationships may apply for different
times of year: for example, in a study of 26 US Geo-
logical Survey gauging stations on unregulated, rural
rivers in Maine with at least a 10-year record, the monthly
runoff during winter was found to be inversely propor-
tional to the distance between the coast and the drainage
basin centroid (Dudley, 2004 ). This relationship, how-
ever, reversed in May when higher runoff occurred in
basins further from the coast (which stored greater winter
snowpack and released it in the spring) (Kingston et al.,
2007 ). Monthly runoff during summer was positively
related to the areal fraction of the drainage basin underlain
by sand and gravel aquifers, which sustained streams
during low flow conditions in the summer and early fall.
Generalised least squares regression techniques were used
to derive the final coefficients and measures of uncer-
tainty for the regression equations. Stratification of catch-
ments may be necessary before applying regression
models: for example, improved results were obtained for
multivariate regressions when catchments were classified
into

by

the mean annual runoff Q loc
A

(regionalised as discussed in

Chapter 5 ):

Q loc
i

PK reg
i

Q loc
A

¼ ð 6 : 2 Þ

Several approaches to their use have been developed and
are outlined below.
The Pardé coefficients or other characteristics of the
seasonal runoff pattern are transferred from a representa-
tive station or group of stations to the ungauged catch-
ment. To perform this transfer, allocation methods are
developed. The

final allocation must be critically

reviewed based on the rainfall runoff processes operating

in the study catchment. A straightforward example of an
index approach is based on the assumption that the Pardé
coefficients are uniform within a region. If the mean
annual runoff in the ungauged catchment is known ( Chap-
ter 5 ), then the monthly average runoff can be computed
by multiplying the Pardé coefficients by the mean annual
runoff.
Hydrological similarity can be defined either in geo-
graphical space or in attribute space, where similarity is
defined based on catchment characteristics. Similarity in
attribute space may perform better than spatial proximity
(see Mosley, 1981 ; Weingartner, 1999 ). Features of topog-
raphy, geology and vegetation can assist in discriminating
regional seasonal runoff patterns (Gottschalk et al., 1979 ).
For example, by combining observations of flow regime
type and catchment characteristics, a 0.5 grid of

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water sources. Thus, regionalisation and data pooling
may be highly beneficial for making predictions at
ungauged sites (Sanborn and Bledsoe, 2006 ). Formal
methods exist for joint pooling and regression optimisa-
tion, such as the classification and regression tree or
'

' snowmelt ' , ' rain ' , ' rain and snow ' and ' variable

model (Breiman et al., 1984 ). The random forest
model (Ho, 1995 ) extends the regression tree approach.
Random forests consist of many decision trees, and the
output for the random forest is given by the modal
response of all the individual decision trees. Application
of a random forest model to French flow regimes classi-
fied 157 hydrological indices, which were collapsed to
nine PCA axes, which were then assigned to individual

CART '