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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6 WORKED EXAMPLES

6.1 The Design Problem

(a) General

In order to illustrate the application of some of the
procedures described in the previous sections, flood
frequency curves are derived for a hypothetical 439 km'
catchment located in south-eastern Australia. A reservoir is
located at the outlet of the catchment, and a streamflow
recording gauge is located just upstream of the reservoir.

Flood frequency curves are derived for both inflows to
the reservoir, as well as for reservoir outflows. As the
voiume of the reservoir is large compared to the volume of
runoff, and it is likely that the reservoir is drawn down below
full supply level, the derivation of the outflow frequency
curve requires consideration of the joint probabilities of both
inflows and storage volume. A tributary enters the
mainstream just below the reservoir, and estimates of
concurrent tributary flows are required for a range of AEPs
in order to help determine the component of incremental
damages that could be attributed to dam failure.

(b) Approach adopted and intent

The following worked examples illustrate application' of
the various procedures to different design situations. The
one hypothetical problem is used for convenience
throughout, though different amounts of information are
assumed to be available in order to illustrate the different
approaches required. For example, in Section 6.2.1 it is
assumed that regional design rainfall information is not
available, and that the credible limit of rainfall extrapolation
is only 1 in 100 AEP. In practice if design rainfalls with
AEPs rarer than 1 in 100 can be obtained (using for
example the CRC-FORGE procedure), then the procedures
illustrated in Section 6.2.2 should be used. As such, the
different procedures should not be regarded as providing
competing estimates for the one design problem, the
different examples merely illustrate the different
approaches to be adopted under different design situations.

While somewhat didactic, the examples are not meant
to provide detailed tutoriais on the implementation of best
practice, and thus some relevant experience will be
required to fully understand the context and nature of the
procedures. The examples illustrate application of the
procedures using (largely) "real-world" data.

Application of the different procedures to the one
problem also provides a useful illustration of the how the
availability of additional information decreases the degree
of conservatism provided by the guidelines. The
recommended procedures are biased towards providing
conservatively high estimates where there is a dearth of
design data, and the examples illustrate how the
successive incorporation of additional information reduces
the degree of conservatism.

(c) Nature of available data

The examples are in part based on data derived for a
specific catchment, though some changes Were introduced
to better illustrate application of the range of procedures
considered.

A summary of the data available for the catchment is as
follows:

. a set of calibration results obtained by fitting a RORB
model to several large observed floods;

. a series of annual instantaneous maximum flood peaks
at the stream gauge;

............" v. - ......",,"c'"',........... .......::&1....... ....^.......,.."". ..............

. a synthetic monthly time series of reservoir volume
obtained from a system simulation model;
. 1 in 50 and 1 in 100 AEP design point rainfalls obtained
using Book II procedures;

. CRC-FORGE estimates for 1 in 100 to 1 in 2000 AEP
design rainfall depths; and,

. GSAM estimates of the PMP for a range of standard
durations obtained from the Bureau of Meteorology.

(d) Note on accuracy offinal results

It should be noted that the number of significant figures
used to present the results of the worked examples are
generally higher than can be justified. In most cases the
accuracy of the final resulls is probably limited to only two
significant figures, but greater accuracy is adopted merely
to facilitate checking of the calculations.

6.2 Derivation of Rainfall Frequency Curves

Rainfall frequency curves are derived for two design
situations. Initially, it is assumed that the credible limit of
extrapolation is the 1 in 100 AEP design rainfall event. In
the second example, it is assumed that 1 in 2000 AEP
estimates are available from the CRC-FORGE procedure.
These two examples are presented in the following
sections. In addition, the derivation of preliminary PMP
estimates is undertaken to illustrate application of the
regional prediction equations.

6.2.1 Upper Limit of Extrapolation is
1 in 100 AEP

This example illustrates the interpolation procedure
described in Section 3.6.1.

The design point rainfalls for the 1 in 50 AEP and 1 in
100 AEP events are shown in the first three rows of Table
12 for a range of durations. These point rainfalls need to be
adjusted by areal reduction factors to represent areal
rainfalls, and the factors derived by Siriwardena and
Weinmann (1996) are used in preference to the values
presented in Book II, Section 1. For durations of 18 hours
and longer, Siriwardena and Weinmann provide an
equation for estimation of the Areal Reduction Factor (ARF)
as a function of rainfall duration (D, hrs), catchment area
(A, km'), and AEP as follows:

ARF = 1.00 - O.4(Ao.t4 - 0.710glOD)D..... +
0.0002(A)O4DO4' (0. 3+log,o(AEP))

For durations of less than 18 hours, Siriwardena and
Weinmann propose a relationship that is not dependent
upon AEP (see Grayson et aI., 1996):

ARF = 1.00-0.1(Ao.t4-0.879,l,
- 0.029(A)o. 33(1.255-109100)

The computed areal reduction factors for the 1 in 50
and 1 in 100 AEP events are shown in the 4'" and 5'" rows
of Table 12, and the corresponding areal rainfalls are
shown in the following two rows. The areal PMP values are
listed in the 7'" row.

For a catchment area of 439 km', the AEP of the PMP
is estimated from Figure 4 to be 1 in 2.28x1 0'. The
standardised normal variate (i.e. lheinverse of the standard
normal cumulative distribution) of this AEP is 4.912, which
is closer to the standardised normal variate of 1 in 10' AEP
(=4.753) than is 1 in 10' AEP (=5.199). Accordingly, the
AEP of the PMP adopted for interpolation purposes using
Table 7 is 1 in 10'.

The values of the primary look-up ratio
10g(XPMp!X,oo)JI09(XlOoIXso) are given in the 9" row, and the
values of 10g(Xy!X,oo)lIog(XPM"!x,oo) from linear interpolation