Prediction of low flows in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 170

( Section 8.3.3 ); (ii) in record augmentation methods where
closeby gauges are typically used as donor sites ( Section
8.3.4 ); and (iii) in the index methods and the region of
influence approach where proximity is directly used to
identify similar sites in a given region ( Section 8.3.2 ).
Proximity may be measured based on distance in Euclid-
ean space in the landscape or, preferably, along the stream
network in order to account for stream network topology
( Sections 8.3.3 and 8.3.4 ).

annual precipitation, mean catchment elevation, slope of
the longest drainage path and proportion of crop and grass-
lands). They then manually delineated four regions, as
shown in Figure 8.6b , based on the spatial pattern of the
residuals. Due to the manual generalisation, the regions
can be made contiguous, but the method is subjective and
may be inappropriate if the initial model is far from perfect.

Regression trees
Regression trees (Breiman et al., 1984 ; Laaha and Blöschl,
2006a ) aim to divide a heterogeneous domain into a
number of homogeneous groups by maximising the homo-
geneity of low flows and catchment characteristics within
each group simultaneously. The homogeneity of groups is
commonly assessed by the spatial variance of low flows.
For the regression tree model, the optimum number of
groups can be determined by a cross-validation approach.
Regression trees yield groups that are often non-
contiguous in space. Vezza et al.( 2010 ) use the regression
tree to divide the study domain into three regions, as
represented in Figure 8.6c . The method shows that the
percentage cover with forest or bare rock were relevant
parameters with which to differentiate groups. Forested
areas (Group 1) are located in the Apennine hilly zones
and piedmont areas. These catchments are characterised by
a low flow regime with a strong drought period occurring
during summer. Group 2 (Alpine region) has low flows
occurring during winter and is affected by snow cover
and freezing soils. Group 3 is composed of highlands and
rock areas. These catchments are located in the upper part
of the Alps and have a winter low flow regime. Once the
regression tree is fitted to the data, it can be used to allocate
ungauged catchments to the groups obtained by the regres-
sion tree, and to estimate the low flow characteristic at the
site of interest (Laaha and Blöschl, 2006a ). Regression
trees are able to account for non-linearity otherwise not
easily accommodated in linear regressions. Also, catch-
ment classification allows one to implicitly take into
account factors affecting low flows that cannot be easily
included in the regression models, such as unknown con-
trols that do not change within the region but across the
regions, and differences in the sign of the regression coef-
ficients within a region. For example, catchment elevation
may be negatively correlated to winter low flows but
positively correlated to summer low flows.

8.2.3 Catchment grouping
Methods for estimating low flows in ungauged basins
usually require that the region is homogeneous with
respect to low flow processes. This is because they assume
that there is a unique relationship between low flow char-
acteristics and catchment/climate characteristics in a
region. Heterogeneous regions therefore need to be divided
into sub-regions that can be considered homogeneous.
A number of methods for subdividing regions into sub-
regions or catchment groups are typically used for low
flow regionalisation.

Cluster analysis based on catchment/climate
characteristics
In this method similarity is defined in terms of the similar-
ity of the catchment/climate characteristics. Hence the
selection and weighting of these characteristics is crucial
for obtaining classifications that are relevant for low flow
regionalisation (Nathan and McMahon, 1990 ). In a region-
alisation study for Q 95 in north-western Italy, Vezza et al.
( 2010 ) selected mean annual precipitation, mean catch-
ment elevation, slope of the longest drainage path and
proportion of crops and grasslands, and obtained the
grouping shown in Figure 8.6a . Andrews curves (see
Chapter 6 ) were used to examine the homogeneity of each
group visually. The regions were not contiguous in space,
even though they show a similar spatial organisation.

Residual pattern approach based on runoff and catchment/
climate characteristics
This method (e.g., Hayes, 1992 ) first fits a regression
model between the low flow index and catchment/climate
characteristics for the entire domain, and then maps the
differences between the regression estimates and the low
flow data, to be analysed for typical patterns in the sign and
magnitude of the differences. The approach assumes that
residual patterns arise from regional heterogeneity not
captured by a global regression model, and a manual
subdivision of the study area will improve the performance
of the model. An example is presented in Figure 8.6b ,
taken from Vezza et al.( 2010 ), who fitted a regression
model to all data (an additive regression of Q 95 with mean

Seasonality approach
An alternative to the above methods is to explicitly take the
seasonality of low flows into account (Young et al., 2000c ;
Laaha and Blöschl, 2006b ). The approach builds on the
notion that differences in the occurrence of low flows
within a year are a reflection of differences in the hydro-
logical processes and are therefore likely to be useful for