Prediction of runoff hydrographs in ungauged basins - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 255

means, instead of the two-step procedure above of first
estimating model parameters at each site and then relating
them to catchment characteristics, these two steps are
implemented concurrently. The main motivation for doing
this is to find more reliable parameters than is possible by
calibrating the model parameters themselves and to make
use of the spatial information contained in the catchment
characteristics. There are two variants of this approach (see
Figure 10.8 ). (i) In regional calibration, typically, a lumped
rainfall

from seven catchments, as in the Saone catchment in
France. They accounted for parameter uncertainty in the
procedure and, based on validation, they concluded that
this uncertainty cannot explain all the simulation errors,
i.e., structural errors in the model are more important than
parameter uncertainties (see also Engeland and Gottschalk,
2002 ). In a much larger area, Parajka et al.( 2007a , b )
calibrated all model parameters simultaneously in 320
catchments and used local (proxy) information on the run-
off processes, such as snow cover data, to improve the
parameter estimates over those that are only based on
runoff.
When using lumped models the regional calibration
increases the number of calibration coefficients as com-
pared to individual calibration of parameters themselves,
e.g., from four parameters to eight regression coefficients
in a study by Fernandez et al. (2000). However, there is
also an increase in the amount of runoff information that is
available for calibration as multiple stream gauges are
used. The important issue is, of course, whether regional
calibration actually improves runoff predictions in
ungauged basins as compared to other approaches (e.g.,
regression, a-priori parameters). Studies by Fernandez
et al.( 2000 ) and Szolgay et al. (2003) indicate that
regional calibration improved the relationships between
model parameters and catchment characteristics but did
not improve the runoff simulations at ungauged sites.
Cross-validation analyses by Parajka et al.( 2007a ) showed
a slight improvement in runoff predictions in ungauged
catchments over other regionalisation approaches. This
suggests that the main value in the approach lies in
obtaining more realistic parameter values, which may be
very useful when extrapolating the models to conditions of
environmental change.

runoff model is applied to a number of gauged
catchments in a region and the coefficients of the relation-
ships between (lumped) model parameters and (average)
catchment characteristics are calibrated (e.g., Fernandez
et al., 2000 ). (ii) In the downscaling approach, a distributed
rainfall

-

runoff model is applied to one or more gauged
catchments in a region and the coefficients of the relation-
ships between model parameters and catchment character-
istics at the grid (or subcatchment) scale are calibrated
(e.g., Bandaragoda et al., 2004 ). While the model discreti-
sation and the number of stream gauges differs between the
two methods, the overall idea of relating model parameters
to catchment characteristics as part of the calibration
remains the same.

-

Regional calibration Fernandez et al.( 2000 ) calibrated
a monthly water balance model concurrently with regres-
sions between model parameters and catchment character-
istics in 33 catchments by optimising a compound
objective function involving runoff simulation efficiency
and goodness-of-fit of the regressions. Hlav ová et al.

(2000 ) and Szolgay et al. (2003) identified groups of
catchments by cluster analysis based on catchment charac-
teristics and then assumed uniform model parameters in
each group. In a similar study, Drogue et al. (2002)
assumed two parameters of an hourly conceptual catch-
ment model to be uniform in a region and stratified two
other parameters by lithological groups. Lamb et al.
(2000) , Kay et al. (2006) and Wagener and Wheater
( 2006 ) first estimated those parameters that could be iden-
tified with the least uncertainty from local calibration in a
region and related them to catchment characteristics, esti-
mated the parameter from the regression for each catch-
ment and fixed this parameter value for the remainder of
the analysis. In a second step they re-calibrated the model
to all catchments (without changing the values of the
previously identified parameter) and identified the next
parameter that could be estimated with least uncertainty.
They then proceeded to obtain regressions with catchment
characteristics for all parameters. Engeland et al. (2006 ),
on the other hand, used a multi-objective method to cali-
brate simultaneously regional parameter sets for

č

Downscaling method One starting point for the down-
scaling method is a-priori model parameters (see Section
10.4.3 ). Bandaragoda et al. (2004) applied a distributed
model to each sub-basin of the Illinois River. They esti-
mated Green and Ampt soil parameters a priori from
STATSGO soil texture using the Clapp and Hornberger
( 1978 ) relationship, and estimated the vegetation param-
eters from satellite data. They calibrated one (spatially
constant) multiplier for each parameter to adjust the
a-priori parameters while retaining the relative spatial pat-
tern obtained from the soils and vegetation data. In a
similar study Pokhrel et al.( 2008 ) used a relationship with
three coefficients to relate calibrated model parameters to
the a-priori parameters. Alternatively, the concept of
HRUs (see Section 10.2.2 ; Arheimer, 2006 ; Arheimer
et al., 2011 ) lends itself particularly well to the downscal-
ing of parameters of distributed hydrological models from
landscape characteristics. A typical case study is presented

the

regional Ecomag rainfall - runoff model to stream ow data