Geoscience Reference
In-Depth Information
The results shown in Figures 5.10 through 5.12 are for ! -cut levels 0 and 1 only. To
construct a complete membership function (MF) of the output, the computation needs to
be carried out at different level ! -cuts. Three more ! -cuts at ! =0.25, 0.5, and 0.75 were
selected. The MFs obtained for the forecasts at 81, 84 and 87 hours with reconstructed
and uniform precipitations are shown in Figures 5.13(a) through (c). These figures
further illustrate that the uncertainty due to the unknown temporal distribution
is dominant over the uncertainty in the magnitude of precipitation.
Also of significance are the shapes of the MFs. The shapes of the MFs with uniform
precipitation are fairly triangular showing that triangular MFs of inputs (precipitation) result in a
triangular MF of output (discharge). However, with reconstructed precipitation the shapes
are rather uniform, suggesting that more or less the same amount of uncertainty is
added due to the uncertainty in the temporal distributions irrespective of the ! -cut level.
Figure 5.12. Uncertainty range in forecasted discharges (Q UB -Q LB ): (a) for
! -cut level 0, and (b) for ! -cut level 1. There are no upper and lower
bounds for ! -cut level 1 in the case of uniform precipitation.
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