Geoscience Reference
In-Depth Information
determined by multiple linear regression, takes the form:
1
c
=
7
.
7
UPLAND
+
12
.
9
DECID
+
7
.
4
TILLED
+
9
.
0
URBAN
+
7
.
3
OTHER
−
0
.
4
CLASSB
−
0
.
8
REHPMN
(10.1)
where
c
is the proportion of rainfall contributing to catchment storage;
UPLAND
is the % area of
heath, moor and bracken land use types;
DECID
is the % area of deciduous and mixed forest land
use types;
TILLED
is the % area of arable crops;
OTHER
is the % area of the remaining three land
use types;
CLASSB
is the % area of semi-permeable mineral soils (no groundwater) and
REHPMN
is
the mean relative humidity averaged over the period 1961-1991. The relationship was developed from
calibrating the model to 60 different catchments in England and Wales. The correlation coefficient for
this relationship was 0.61, implying significant uncertainty in estimating the value of
for any individual
catchment. Similar equations for other parameters of the model had better and worse fits to the data and
two of the parameters showed a strong correlation across the 60 gauged catchments.
The independent variables in Equation (10.1) were chosen from a list of 10 morphometric variables,
five soil descriptors, eight land use types and seven climate variables. The statistical fitting techniques
allow the identification of independent variables that add a significant contribution to the explanation
of the observed variations in the dependent variables. Any variables that do not provide a significant
contribution are not included in the equation. The technique used to derive this type of equation is
a linear regression analysis. Any nonlinear relationships must be achieved by transforming either the
dependent or the independent variables. In one of the other predictive equations in the Sefton and
Howarth paper, log transforms on all the variables were used before performing the analysis. This type
of analysis is used widely in the estimation of model parameters or discharge characteristics within a
region for ungauged catchments. What is often not recorded is what other transforms or independent
variables were tried and rejected in favour of the final published equation. Variants on this approach
include the identification of predictive equations for model parameters by optimisation over the full
set of gauged catchments, rather than for individual catchments (Fernandez
et al.
, 2000; Hundecha and
Bardossy, 2004; Gotzinger and Bardossy, 2007; Samaniego
et al.
, 2010); the use of geostatistics to
take account of spatial correlation in parameter values (Merz and Bl oschl, 2004; Parajka
et al.
, 2005;
Viviroli
et al.
, 2009); and the use of clustering methods or self-organising maps rather than regression
for relating catchment characteristics to model parameters (Szolgay
et al.
, 2003; Rao and Srinivas, 2006;
Di Prinzio
et al.
, 2011).
It would be nice if such relationships always made good hydrological sense. This is sometimes hard
to extract from this type of regression equation. In Equation (10.1), one wonders what processes an
additive linear function of the mean relative humidity variable is acting as a surrogate for? Although
this is a widely used approach to regionalisation, we do not consider it further here. The PUB initiative
was, at least in part, a recognition of the limitations of this approach. We make just one final comment
which is to note that since these regression relationships are statistical in nature, then it should be
possible to derive a standard error of estimate for each parameter value estimated (even if the covariance
structure cannot be estimated if the regressions for each parameter are treated independently). Thus,
at least the uncertainty in the estimates for the ungauged site arising from the regression could be
assessed in the model predictions. This is rarely done (but see the work of Lamb and Kay (2004),
Wagener and Wheater (2006), Kay
et al.
(2007) and Calver
et al.
(2009) for exceptions). It also does
not account completely for different sources of uncertainty in the regionalisation process (see Jones and
Kay (2007) for a more complete statistical treatment of the parameter generalisation problem) but it is
at least a start when any decision depending on the modelling of the ungauged site might be sensitive
to uncertainty.
1
c
