Model accuracy and sensitivity to fuzzy parameters and climatic inputs

The fuzzy climatic input variables introduce much less uncertainty than the eight fuzzy model parameters. This is demonstrated in Figure 10.8(a-d), which presents the simulated fuzzy discharge generated using fuzzy input data (precipitation and temperature) but crisp (defuzzified) estimates of parameter values. This suggests that bigger contribution to uncertainty in the predictions of the water balance model comes from fuzziness of the model parameters than from fuzziness of the meteorological inputs.

We next turn to a possible ranking of the various parameters in terms of their individual contributions to

(a) Inter-annual variability of annual yield (b) Annual streamflow hydrograph

Exceedance probability (1)

Exceedance probability (1)

50 0

50 0

10 15 20 (Year)

(c) Intra-annual yield: Flow regime 20

J FMAMJJ ASOND A (Month)

J FMAMJJ ASOND A (Month)

(d) Monthly streamflow hydrograph 30

(d) Monthly streamflow hydrograph 30

12 32 52

1975-1979 Time clip (Month)

Fuzzy results _p : Interval of confidence for m = 0.8 [P] '

12 32 52

1975-1979 Time clip (Month)

Figure 10.7 Annual and monthly simulated versus observed discharge: Intervals of confidence at the level of presumption of 0.8 generated with the basic water balance model accounting for saturation excess runoff, inter flow and base flow with fuzzy values for climatic input variables and parameters the overall uncertainty of simulated model results. This was achieved by repeatedly running the model with each parameter held constant (crisp), while letting all other parameters to remain fuzzy and estimating overall, bulk measures of uncertainty. The following ranking of parameters and climatic input variables, ranging from high to low contributions to total uncertainty of the simulated discharge, was consequently arrived at: Cfc, fc-in, ?c-bf ; T, p, T crit, m f, C tp.

Table 10.3 lists all parameters and input variables with their potential to overall model uncertainty. Here, the fuzziness of model predictions is evaluated through two criteria, the mean (hh), and mean squared (hh2) of the absolute magnitude of the interval of confidence of simulated daily discharge at the level of presumption of 0.8. If a parameter or input variable is set to a crisp value and both evaluation criteria show high

Table 10.3 Mean absolute (hh) and mean squared magnitude of the intervals of confidence (hh2) of simulated daily discharge

-=&- at a selected level of presumption /i of 0.80 that is dependent on fuzzy input data and parameters for the 1972-1993 period

Table 10.3 Mean absolute (hh) and mean squared magnitude of the intervals of confidence (hh2) of simulated daily discharge

-=&- at a selected level of presumption /i of 0.80 that is dependent on fuzzy input data and parameters for the 1972-1993 period

Estimation of climatic

HH2

input and parameter

[1]

[1]

values: crisp or fuzzy

All fuzzy

0.956

0.076

All fuzzy except P

0.720

0.043

All fuzzy except T

0.716

0.043

All fuzzy except Ctp

0.743

0.046

All fuzzy except Cfc

0.577

0.028

All fuzzy except ic_;n

0.603

0.030

All fuzzy except ic_bf

0.652

0.035

All fuzzy except m f

0.752

0.047

All fuzzy except Tcrit

0.737

0.045

(a) Inter-annual variability of annual yield (b) Annual streamflow hydrograph

100

[10-2]

50

[Q]

[P ]

0

Exceedance probability (1)

Exceedance probability (1)

50 0

50 0

0 5 10 15 20 (Year)

(c) Intra-annual yield: Flow regime (d) Monthly streamflow hydrograph

JFMAMJJASOND (Month)

12 32 52

1975-1979 Time clip (Month)

JFMAMJJASOND (Month)

12 32 52

1975-1979 Time clip (Month)

Fuzzy results : Interval of confidence for m = 0.8

Qo rl

0 0

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