and at *Y*l = 12.33 is

uncertainty distribution. The resulting confidence

limits at plus or minus one and two standard

deviations associated with the uncertainty calculation

0.333 & 0.238

(13)

' 0.0498

are shown in Figure 3 for the entire frequency curve.

22.11 & 20.52

Statistics of Uncertainty

Frequency Curve

from Incomplete Beta

Quantile

Mean

Std Dev

0.905

8.45

9.15

1.52

0.857

9.10

10.13

1.96

0.810

10.80

11.26

2.26

Beginning of data used in interpolation

0.762

12.33

12.39

2.35

0.714

13.53

13.47

2.31

0.667

14.73

14.48

2.16

0.619

15.52

15.40

1.98

0.571

16.32

16.21

1.87

0.524

17.07

16.98

1.75

0.476

17.80

17.71

1.66

0.429

18.53

18.40

1.60

0.381

19.20

19.07

1.53

0.333

19.90

19.76

1.52

0.286

20.52

20.46

1.53

0.238

21.29

21.18

1.54

End of data used in interpolation

0.190

22.11

21.93

1.53

0.143

23.00

22.67

1.48

0.095

24.13

23.48

1.38

The equivalent record lengths are obtained using *S*m

(1) The estimated uncertainty distribution for a

= 1.54 and *p *= 0.286 in Equation 8

regulated frequency curve on the Savannah River was

calculated, resulting in the confidence limits shown in

Figure 4. The frequency curve was based on informa-

tion from a long inflow series, historic information,

0.286 ( 1 & 0.286 )

- 35

(14)

observed regulated flows, and model simulations. The

2

2

( 1.53 ) ( 0.0498 )

equivalent record length from this information was

believed to be about 190 years.

and *S*l = 2.35 and *p *= 0.762 in Equation 9

(2) The interesting aspect of this example is that

the uncertainty about the frequency curve is negligible

0.762 (1 & 0.762 )

- 27

as the frequency curve flattens near the 50 percent

(15)

2

2

2.35 ( 0.035 )

chance exceedance probability event. This is indicated

by the convergence of the confidence limits in

A straightforward application of the normal

Figure 4.

distribution can now be used to extrapolate the

9

Integrated Publishing, Inc. |