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by Beven (2006a). Each model realisation was compared against 114 different limits of acceptability. The
evaluation of discharge predictions included both peak frequency quantiles (up to an annual exceedance
probability of 0.1 to be robust in the estimation from relatively short periods of observations) and quantiles
of the flow duration curve for each site, taking account of the observational errors in discharges derived
from rating curve interpolation and extrapolation using fuzzy regression. Other limits were set for the
distribution of maximum winter snow accumulation in each accumulation area, estimated by fuzzy
regression from the four observation sites. For the rainfall model, limits of acceptability were defined by
putting bounds on the subcatchment hourly and daily rainfall frequency information estimated from the
point raingauge sites by bootstrapping from the distributions of estimates of the average subcatchment
rainfalls from the point measurements. Excluding one measurement point at a time and reestimating the
subcatchment rainfalls allows a range of possible subcatchment rainfalls to be defined directly from the
measurements. A final limit of acceptability was imposed for the proportion of floods occurring in the
winter season. This was not a strong constraint, but was set because in early runs too many floods were
found to be generated in summer.
Within this version of GLUE, all models that survive the multicriteria tests of acceptability are then
used in prediction of the frequency characteristics for the catchment, weighted by a likelihood measure
that depends on performance of the model within the limits of acceptability, represented as a standardised
score (see Figure B7.1.2). For each criterion, the likelihood measure was defined as a trapezoidal fuzzy
measure around each observation, reducing to zero at the limits of acceptability (see Figure B7.1.3). The
full model had 46 parameters that could be varied and, as noted above, whether a particular model run
matches the limits of acceptability derived from the observations might depend on the particular realisa-
tion of the inputs. In fact out of 610 000 model runs of 67 years duration, only 39 were found to satisfy all
114 limits. These were run to generate flood frequency curves for the Cheb validation site (see Figure 8.5).
Figure 8.5
Flood frequency curve at the Cheb gauging station: circles are the observed annual flood peaks
(1887-1959); grey lines are the 4192 simulations, each of 10 000 years of hourly data, with scores on all
criteria
1.48; dashed lines are the 5% and 95% possibility bounds from the trapezoidal weighting; thin
black lines are the behavioral simulations with scores on all criteria
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1 for the initial 67-year simulations (after
Blazkova and Beven, 2009, with kind permission of the American Geophysical Union).
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