5 THE GLUE PROCEDURE The GLUE procedure
9
comprises several steps between generation of the likelihood surface over the parameter
space and producing estimates of uncertainties in the pre- dicted model responses. These steps are outlined in the next
few sections, in which those figures associated with the statistical calibration and the fuzzy-rule-based calibration
are labelled A and B respectively.
5.1 Selection of the parameter ranges The first step of the GLUE procedure is to decide upon the
range of the parameter space to be examined, which relies upon ‘expert knowledge’ of the system. The two physical
parameters to be calibrated in this study are the Manning coefficients, one to represent the roughness of the flood
plain region and the other to represent the river bed. Clearly, such a simple model structure does not reflect the true
distributed roughness in the basin, and it becomes less imperative to find an optimum fit, as discussed earlier.
However, the initial decision as to the range of parameter space to be examined can exert an influence on the decisions
to be made later, on the basis of the predicted uncertainties. For instance, having generated uncertainty bounds for the
model predictions on the basis of a truncated range of rough- ness coefficients, caution must be taken when using these to
disregard certain outlying predictions or to disregard obser- vations the modeller might wish to use a truncated range of
parameter values in order to assert some a priori knowledge about the physical situation in the field. It is considered that
this problem can be largely overcome by initially using ranges of parameters which cover the extremes of feasible
values, for example, in this study, Manning coefficients corresponding to bare soil, all the way to values correspond-
ing to a highly rough floodplain were used
10
. This resulted
Fig. 9. B Likelihood measures for fuzzy-rule-based calibration, user discharge information only. G is the stringency parameter defined in
eqn 24.
360 G. Aronica et al.
in a range of roughness coefficients for c of 0.025 m
¹ 13
s
¹ 1
and 0.2 m
¹ 13
s
¹ 1
to be used, with the restriction that the roughness of the river could not exceed the roughness of
the floodplain, hence, the triangular parameter domain on the possibility measure plots. Bates et al.
7
used Manning values for the channel ranging between n
c
¼ 0.01 m
¹ 13
s
¹ 1
corresponds to
a concrete
lined channel
to n
c
¼ 0:05 m
¹ 1=3
s
¹ 1
corresponds to
a mountainous
stream with a rocky bed and for the floodplain, they used n
f
¼ 3n
c
þ 0.01. The 1000 different combinations of the
Manning coefficients
within the
triangular domain
described before were used to generate the likelihoods or relative possibility measures.
5.2 Generation of likelihood surfaces
