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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(b)

Detailed steps in procedure

Application of the procedure is quite straightforward,
and design estimates over the interpolated range can be
easily computed, as described below.

With reference to Figure 5, the AEP Df 1 in y,
represents the starting point of the interpolation, and the
AEP of 1 in y, represents a lower value such that between
1 in Y, and 1 in Y, the frequency curve can be assumed to
be linear in the log-log domain. Xv, and Xv, represent the
design rainfalls with AEPs of 1 in Y, and 1 in Y,. The slope
of the frequency curve at the commencement of the
transition, S", is determined by the slope between the two
design values atAEPs of 1 in Y, and 1 in Y,.

The end point of the interpolation is the AEP of the
PMP. which is denoted 1 in Y PMP. For consistency of
nomenclature, the magnitude of the PMP is here denoted
as )(PMP.
A design rainfall estimate with an AEP of 1 in Y
(denoted Xv) can be estimated using:

Xy = '10RvlogIXV2l

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1
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1

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(1)
where Ry is defined by the parabola fitted between Xy, and
XPMP:

z
Ry = 1 + Sgc '" gy + (Sgap - Sgc)Zd gy (2)

'" = 10g(YpMP / Y2) (3)

log(Y/Y2) (4)
gy =
'"

log(Xy, f Xy2) (5)
5gc =
10g(Xd.log(Y, f Y2)

10g(XPMP) 1

Sgap = log(XY2) (6)
Zd

For Victoria. Siriwardena and Weinmann recommend
that the slope of the frequency curve at the commencement
of the transition should be defined by the 1 in 1000 AEP
and 1 in 2000 AEP events, I.e. Y, = 1000 and y, = 2000.
Thus the start point of interpolation is the credible limit of
extrapolation obtained using the eRe-FORGE method
(Nandakumaret aI., 1997).
An example describing the application of the above
interpolation procedure is provided in Section 6.2.2.

x,.

..
~
g

x, ......................-...

.
.
.
"
>
,
~
.
Q

"'.---- j

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'.

Xn ................

x"

1:Y, l:Yl l:Y l:Y....
Annual Exceedance Probabiity(log scale)

l'

~ t.

'-

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Figure 5 Schematic iUustration of interpolation
procedure.

.............., v. .........."'.a'''_''....., .......:1...,....................,...... ................

(c)

Range of application

Siriwardena and Weinmann (1998) have shown that the
procedure performs satisfactorily over a range of design
situations that specifically include:

o different starting points for interpolation (I.e. the AEP of
the credible limit of extrapolation can vary, though note
if no Rare rainfall information is available and the
credible limit of extrapolation is 1 in 100 AEP, then the
procedure described in Section 3.6.1 should be used);

- different AEPs assigned to the PMP (ranging from 10"
to 10.7, as discussed in Section 3.5); and,

o different 'shape parameters' defined by the ratio of the
slope of the upper end of the directly determined
frequency growth curve, S", and the slope between the
two end points of the 'gap', S,"" (the 'shape parameter'
S,JS,.. ranges between 0.25 to 2.0).

The above concepts are schematically illustrated in
Figure 5. and are summarised in Table 6. Siriwardena and
Weinmann (1998) have tested the above interpolation
procedure on 25 catchments ranging in size from 25 to
15000 km' with diverse characteristics. The resultant
frequency curves were shown to be plausible and well
behaved for all test catchments.

3.6.3 Extrapolation of Regional Design
Information to Other Durations

(a) Basis of procedure

Sites with daily rainfall records provide a considerably
denser spatial coverage and longer perioc of record than is
available from the pluviometer network. Accordingly, where
Large to Rare regional estimates are available, it is likely
they are only applicable to design storm durations of 24
hours and longer. Derivation of design rainfalls for shorter
durations is of particular importance for small catchments,
and accordingly it is desirable to apply an approximate
procedure to extend the Large to Rare regional estimates
to shorter durations. As discussed in Section 3.2. design
rainfall information available in Book II Section 1 is only
available up to a duration of 72 hours. and thus a
procedure is also required to extend Large rainfall
estimates to longer durations.
Siriwardena and Weinmann (1998) adapted the above
interpolation procedure to this situation, and tested the
approach using Victorian data. While alternative
approaches may be developed for other regions, the
procedure proposed by Siriwardena and Weinmann should
be applicable to most design situations.

(b) Detailed steps in procedure

The procedural steps involved are as follows (see
Figure 6):
1. Prepare a log-log plot of 1 in 50 AEP and 1 in 100
AEP point design rainfall depths (Dr intensities) versus
duration for all required durations using design
information presented in Book II Section 1.
2. Add to the plot established in step 1 the regional
design point rainfall depths/intensities for AEPs rarer
than 1 in 100 for all available durations (e.g. 24 hours
. and longer using the eRe-FORGE technique, as
described in Section 3.3.2). These pDints are
indicated by the filled symbols in Figure 6.
3. Fit a linear relationship in the log-log domain to the
storm durations and the Large to Rare regional rainfall
deplhsJirllensilles plotted in step 2.
4. Extrapolate the relationship from step 3 down to
durations fDr which the 1 in 50 AEP and 1 in 100 AEP