Geography Reference
In-Depth Information
1999 ). Seasonality has also been used for classification to
identify low flows and floods (see e.g., Young et al.,
2003 ; Laaha and Blöschl, 2006b ), based on the assump-
tion that differences in the occurrence of low flows or
floods within a year are a reflection of differences in
hydrological processes and can thus be used to define
homogeneous regions. Homogeneous groups can be
delineated manually on a map, or by means of statistical
grouping techniques.
More complex multivariate analyses include additional
independent variables, e.g., hydroclimate, area, elevation
and land cover. Hawley and McCuen ( 1982 ) discuss
numerous advantages of multivariate regional regression
analysis to estimate mean annual runoff. Water yield
estimates from regression methods are objectively repro-
ducible, their bias is minimised by the method, and uncer-
tainty associated with them can be quantified under
explicit assumptions. A less evident advantage is that
regression methods may capture relationships that are
evident in the data, but for which no theoretical explan-
ation is available, for example due to the co-evolution of
vegetation, landscape and hydrological response. In
regression models, mean annual runoff is related typically
to geomorphic and climate characteristics. Examples for
the USA include Lull and Sopper ( 1966 ) and Johnson
( 1970 ) for New England, Thomas and Benson ( 1970 ) for
regions in the western, central and southern USA, Majte-
nyi ( 1972 ) for areas of South Dakota, Hawley and
McCuen ( 1982 ) for the western USA, and Vogel et al.
( 1997 ) for the north-eastern USA. Vogel et al.( 1999 )
developed regional multivariate models to estimate mean
and variances of annual runoff across 18 regions in the
USA. The results of Vogel et al.( 1999 ) are discussed
further in Section 5.5.1 . Figure 5.12 presents one case
study in north-western Italy (Viglione et al., 2007a ). The
mean annual runoff was obtained by a non-linear regres-
sion with the mean annual precipitation and the catchment
average elevation. Elevation provides a surrogate for tem-
perature (and therefore energy, vegetation type, snow
processes and their seasonal variation). Cross-validation
results are shown, along with the 90% prediction intervals
for the regression in Figure 5.12b .
Duan et al.( 2010 ) used principal component analysis to
relate 51 years of annual runoff data for 11 stream gauging
stations in north-west China to annual precipitation, evap-
oration and catchment characteristics. The regional regres-
sion model accounted for 87% of the variance in the runoff
estimates. The eight variables included in the model are
annual precipitation, annual surface water evaporation,
sub-basin centroid coordinates, sub-basin centroid eleva-
tion, sub-basin area, sub-basin wetland area and sub-basin
shape factor.
5.3 Statistical methods of predicting annual
runoff in ungauged basins
To predict runoff signatures in ungauged catchments,
transfer mechanisms are needed to link information from
other catchments to the catchment of interest. Regional
statistical techniques have been a topic of intensive explor-
ation in this area. These techniques treat the prediction of a
target variable as the problem of estimating a random
variable, while explaining the maximum amount of the
spatial variance. Similar statistical assumptions and struc-
tures are used for many different predicted runoff signa-
tures. In Chapters 5 to 10 these methods are reviewed,
under the topics of:
regression methods, where specific runoff signatures are
transferred based on their relationship with catchment
and climatic attributes via some analytical expression;
index methods, which assume that a known, quantitative
runoff, catchment or climatic signature is constant
within a defined homogeneous region, except for a
locally varying scaling index;
geostatistical and proximity methods, which exploit
spatial smoothness of the runoff signature. Here
'
may refer to either geographic space or a parameter
space defined by catchment attributes;
'
spatial
runoff estimation from short-records, which exploits the
relationship between moments of short runoff records
and runoff in neighbouring catchments.
5.3.1 Regression methods
Mean annual runoff
Regressions are one of the simplest statistical methods
used to estimate mean annual runoff. The relationships
often exploit independent variables that are prime drivers
in runoff generation, for example, mean annual precipita-
tion, or that are clearly related to runoff volume, such as
catchment area. An early application of regional modelling
of annual runoff was by Langbein (1949) , who developed
graphical relationships between mean annual runoff, pre-
cipitation and temperature in the USA.
Inter-annual variability
Kalinin ( 1971 ) was probably the first researcher to develop
an empirical relationship to estimate the coefficient of
variation of annual runoff (CV). The CV was related to
the catchment area through a two-parameter, decreasing,
non-linear relationship. The decrease of the CV of annual
runoff with area is to be expected, as a result of space
time
averaging. McMahon et al.( 1992 ) related the CV to the
mean annual runoff with a power-law relationship, which
-
 
Search WWH ::




Custom Search