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In-Depth Information
hydrological characteristics of a catchment directly. If model predictions are still required (as they often
are) the estimates of the hydrological response characteristics can then be used to constrain suitable
model parameters (see Section 10.8).
There is another approach to defining model parameters for an ungauged catchment within such a
learning process. If an application justifies the cost, then it might be possible to provide some point
discharge or other response measurements, or a short period of measurements, to improve the prior
estimates of the hydrological response (see Section 10.10). This is consistent with the PUB approach of
using any information available to constrain uncertainty in the predictions of the site of interest.
10.6 Regression of Model Parameters Against Catchment
Characteristics
The basis for any regionalisation method based on direct estimation of model parameters is a sample
of parameter values of interest determined for gauged catchments. Most regionalisation strategies then
use a method of relating those parameter values to the physical characteristics of the gauged catchments.
The methods are tested against other gauged catchments, treated as if they were ungauged. In the past,
parameter values were generally fitted to the observations from the gauged catchments by optimisation.
Thus, each gauged catchment would be associated with only one value of a particular parameter. This
allowed the prediction problem to be set up as a statistical regression, with the parameter values treated
as dependent variables and one or more catchment characteristic measures as independent variables.
Generally, a form of multiple regression is used in which many different independent variables are tried
and only those that make a significant contribution to explaining the variance of the dependent variable are
retained. There are statistical tests that allow the significance of the contribution to be assessed, generally
under an assumption that the residuals in fitting the dependent variable are independent and distributed
as a normal random variate.
In the UK, this was the approach taken by the
Flood Studies Report
(NERC, 1975) and its later
revision as the
Flood Estimation Handbook
(IH, 1999). Both these reports provided regression equa-
tions for flood frequency distributions and for rainfall-runoff model parameters (a model based on unit
hydrograph concepts was used in both, see Kjeldsen, 2007). This type of regression method can also
be used to estimate the parameters of rainfall-runoff models directly. This approach was first used in
the UK with a unit hydrograph model by Eamonn Nash (1960), who was later involved in producing
the
Flood Studies Report
. More recent studies of this type have been used in the USA (Abdulla and
Lettenmaier, 1997a; Fernandez
et al.
, 2000); in Australia (Boughton and Chiew, 2007); in France (Oudin
et al.
, 2008); in Belgium (Heuvelmans
et al.
, 2006); in Germany (Hundecha
et al.
, 2008); in Austria
(Merz and Bl oschl, 2004); in Sweden (Seibert, 1999; Xu 1999); in South Africa (Kapangaziwiri and
Hughes, 2008); in China (Xie
et al.
, 2007) and elsewhere for both flood frequency and hydrograph
model parameters.
There are a number of problems with this approach. The first is the problem of optimisation of the
model parameters at the gauged sites. As we have seen in Chapter 7, the optimised values of the param-
eters may not be robust to uncertainty in the calibration data, calibration period, performance measures,
optimisation method or interactions between the parameters. The possibility of parameter interactions
within a model structure is often ignored in this approach, with regressions against catchment character-
istics being carried out independently for different parameters, without any allowance for uncertainty in
the estimation of those parameters. Finally, although it is possible to use some hydrological reasoning in
deciding which catchment characteristics might be related to different parameters, the regression method
is purely statistical. As an example, Sefton and Howarth (1998) produced regression relationships for
the parameters of the IHACRES model for catchments in England and Wales. One such relationship,
