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predictions within the limits specified for all time steps in the calibration period. Indeed, of the 50 000
model runs made, not one model was always within the limits. Since no explicit account had been taken
of input error in setting the limits, the rejection criterion was relaxed to allow models that were within the
limits 95% of the time to be considered behavioural (by analogy with the confidence limits of a statistical
evaluation). There is some danger in doing this because, given that the deviations are not random, the
remaining 5% could conceivably be the periods of greatest interest (e.g. around the peaks). This is also
sometimes seen in the results of statistical error models, giving further support to the idea that random
error assumptions may not hold in practice. In the GLUE limits of acceptability approach, no random
error assumptions are made, but there is still a potential impact of errors that have not been accounted
for in setting the limits.
Under this relaxed rejection criterion, some 413 models were retained as behavioural. An attempt was
also made in this study to see whether there was any structure in the residuals that could lead to improved
predictions by correcting for bias in the simulations of individual behavioural models. Since this was
expected to be nonstationary, the model outputs were classified for different parts of the hydrograph.
Five classes were used (rising limbs, peaks, falling limbs, baseflows and troughs). The standardised
scores for each of these periods for each behavioural model were examined for consistent deviations
with a view to reconstructing the observations in a way that could then be used in prediction. Only in the
baseflow periods were consistent deviations found. For the other periods, applying the distributions of
scores made little difference to the final uncertainty bounds; in the baseflow periods some improvement
in predicting the observations could be found. The resulting uncertainty in the simulated hydrographs
for a prediction period (not used in the choice of behavioural models and reconstruction) is shown in
Figure 7.15.
Figure 7.15
A comparison of reconstructed model flow and observed flow for the validation period,
18-28 November 1996: the reconstructed flow is shown by the middle dotted line and was created by
taking the median value of the reconstructed flows from all of the behavioural models at each time step; the
outer dotted lines show the 5th and 95th percentiles of the reconstructed model flow; the dashed lines show
the 5th and 95th percentiles of the unreconstructed behavioural models; the continuous line is the observed
flow; the shaded grey area shows the limits of acceptability applied to the observed discharges for this period
(calculations by Philip Younger).
