FLOOD01798

• County: Statewide
• Title: Australian Rainfall and Runoff 1998, Revision of Book VI - Estimation of Large to Extreme Floods
• Date: 11/28/1998
• Prepared By: Rory Nathan, Sinclair Knight Merz
• Floodplain - Doc Type: Educational/Technical/Reference Information

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3.6 Rainfalls Between the Credible Limit of
Extrapolation and the PMP

(a) Background

The foregoing sections provide recommendations on
deriving rainfall estimates to the credible limit of
extrapolation and the PMP. In order to derive a complete
rainfall frequency curve it is necessary to interpolate
between these two limits. The interpolation is necessarily
pragmatic as it attempts 10 link estimates based on
conceptually different methods and different data sets; it
cannot be supported by scientific reasoning. Similarly, any
testing can only be in terms of the procedure producing
plausible and consistent estimates, as there are no
independently estimated design rainfalls for this range of
AEP.
The interpolation technique recommended in the 1987
edition of ARR involved a high degree of uncertainty and,
when applied to rainfall frequency curves, provided
intentionally conservative estimates. The availability of Rare
rainfall estimates based on regional procedures and the
acceptance that the operational estimate of the PMP can
be exceeded provide an opportunity for a less conservative
interpolation procedure. Siriwardena and Weinmann (1998)
have developed a procedure suited to the interpolation over
'gaps' of different ranges corresponding to differences in
both the AEP of the credible limit of extrapolation and to the
assigned AEP of the PMP. The procedure is suited to those
situations in which regional design information (e.g. CRC-
FORGE) is available for some durations. The interpoiation
procedure is based on the form of function proposed by
Lowing and Law (1995) and involves the fitting of a simple
2-parameter parabolic function to satisfy the requirements
at either end of the interpolated curve.

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(b) Overview of design situations

Different interpolation recommendations are provided to
account for whether or not regional estimates are available
for Large to Rare rainfall events. Specifically, guidance is
provided for the follDwing three design situations:

(i) no regional design information is available for the
estimation of Large to Rare rainfall events and the
credible limit of extrapolation is 1 in 100 AEP (Section
3.6.1);

(ii) regional design estimates are available for all
durations of interest, and the credible limit of
extrapolation is considerably rarer than 1 in 100 AEP
(Section 3.6.2);

(iii) regional design estimates are available for some but
not all required durations, thus for some durations the
credible Umil of extrapolation is considerably rarer
than 1 in 100 AEP, whereas for other durations the
limit is 1 in 100 AEP (Section 3.6.3).

The procedures recommended for case (i) should be
regarded as prescriptive as in the absence of regional
design information there is no strong rational basis for
allemative estimates. The procedures described for the
remaining two cases represent recommended design
practice for those regions where regional design estimates
based on CRG-FORGE are available. These procedures
are provided for general guidance only as it is possible that
alternative procedures may be developed to suit the
characteristics Of other sources of regional design
information.

The nature of <he interpoiation procedure for the above
three design situations is sllmmarised in the different
columns of Table 6; the rows of the table summa rise the
distinguishing features of each method. The examples

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provided concerning the limits of duration and extrapolation
are relevant to Victorian CRC-FORGE estimates as
described by Siriwardena and Weinmann (1998), and it is
likely that different limits will be applicable for other regions
and/or procedures.

The following sub-sections detail the
computational steps and range of application
recommended procedures for the above three
situations.

basis,
of the
design

3.6.1 Interpolation Between 1 in 100 AEP and
the PMP When No Rare Regional
Estimates are Available for any Durations

(a) Basis of procedure

The recommended procedure for deriving Rare rainfall
depths in the absence of regional design estimates for any
durations is based on the shape factor approach used in
the 1987 edition of ARR Consistent with the terminology
used there, Xso, X100, Xy and XPMP represent respectively the
design rainfall values at AEPs of 1 in 50, 1 in 100, 1 in Y
and the PMP.
The use of this procedure in favour of the one detailed
in Section 3.6.2 is justified by the high degree of uncertainty
of rainfall estimates when interpolating over such a wide
range. The tendency of this procedure to produce
conservatively high estimates is considered to be a
desirable feature in this situation.

(b) Detailed steps in procedure

The steps involved in determining the shape of the
frequency curve and design rainfall values Xy at
intermediate AEPs 1 in Yare:

1. Determine the value of the ratio [log(x"MP/X,oo)/
10g(XlOoIXso)]

2. Round the assigned AEP of the PMP to the nearest
order of magnitude.

3. Read the values of the ratio
[log(Xy/XlOo)/IDg(x...p/X,oo)] from Table 7 for the two
intermediate points at AEPs 1 in y, and 1 in Y, for the
relevant AEP of the PMP.

4. Solve this ratio for the value of X at the two
intermediate AEPs.

5. Plot on log-Normal probability paper these two values
at their relevant intermediate AEPs, the PMP at its
assigned AEP, and the 1 in 100 AEP and 1 in 50 AEP
events (or the 1 in 100 AEP event and the slope of the
frequency curve at this point).

6. Draw in the complete frequency curve passing
through these points, being tangent to a line joining
the 1 in 50 AEP and 1 in 100 AEP events at the latter
point, and through the PMP at a slope consistent with
the shape of the lower portion of the frequency curve.

7. Read off the design rainfall for any desired AEP.

The rounding of the AEP of PMP specified in step 2
should be in the standardised probability domain, that is,
the AEP Df the PMP should be rounded to the order of
magnitude that lies closest to it when plotted on log-Normal
probability papeL For example, 1 in 3.1x10' AEP should be
rounded to 1 in 10' AEP, whereas 1 in 3.2x10' AEP should
be rounded to 1 in 10' AEP. (This is because the standard
normal deviate of the point midway between 1 in 10' and 1
'in 1 a' is equal to 4.509, and the standard normal deviates
of 1 in 3.1x10' and 1 in 3.2x10' are respectively 4.513 and
4.507; Abramowitz and Stagun, 1964, 1974). ~or some
intermediate probabilities, the event magnitude is given
directly by step 4. The complete frequency curve should