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

I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

I
I

utv\r- I U

100%

Storage
Content

~
c;:
-
::l
o
.x:
'"
Gl
ll.

Outflow interval, Qj

._t_,_._._._.___,__
.-t-.-.-.-,-.-.-.-

I Peak Inflow

~
:c
'"
.a
e
ll.
'"
o
c
'"
..,
Gl
Gl
o
al

!+-
I

Inflow interval, I,
-.:.
I

Inflow
probability I
I interval, P[IJ
.Y.-.-.-.-.-.-.-.-.-

't.-.-.-.-.-.-.-.-.-,-.

..........." VI - ....:HIII IClUV', v, ....c.I,::II.......... ....^......,..... .............

C
Gl
-
C
o
l)
Gl
Ol
~
o
i'i3

Storage content
probability interval
~ ;.- P[QjllJ

% Time Level Exceeded

Figure 9 Schematic illustration of the determination of the probability interval of storage volume as a function of
inflow and outflow,

issue of concurrent floods is of minor importance, and as
such it may be appropriate to adopt a simpler, more
approximate procedure.

5.3.2 Approximate Procedures

It would be possible to derive a range of approximate
procedures for the assessment of concurrent flows. The
following method is just one procedure, and practitioners
are encouraged to seek alternative approaches where
appropriate.

(a) Bivariate log-Normal distribution

One simpler approach that can be used when the
concurrent flow of interest is small compared to the design
flow of interest has been proposed by Nathan (1996). The
basis of the approach is to assume that the joint distribution
ofthe concurrent flows at two sites can be characterised by
a bivariate log-Normal distribution. The magnitude of the

average concurrent flow in one tributary (mYlx), given a flow
of magnitude x in the other, can be approximated by:

mYlx ::: my

Sy
+ p- (x-m )
s x
x

where m and s signify the mean and standard deviation of
the marginal distributions, p is the correlation between the
two variates, and x and y represent design flows at the two
sites; note that aIf flows need to be transformed into the
logarithmic domain.

The correlation p can be obtained from an analysis of
large historic events, and the other parameter values can

(9)

be found by fitting log-Normal distributions to both the
mainstream and tributary streamflow data. The mean and
standard deviation can be determined by fltting a line of
best fit (either graphically or analytically) through the
available design flood estimates in the log-Normal domain.
Usually a number of design flood estimates will be available
for the mainstream flows as a complete frequency curve will
have been derived (Section 4.5), but design flood estimates
for the tributary flow may be derived using the approximate
procedures provided in Section 4.7.1.

Given the uncertainty of the correlation structure over
the range of magnitudes of interest, it is considered that the
above approximations are appropriate for those design
situations in which the magnitude of the tributary flows are
minor compared to the mainstream flows, and the
correlation between the two flows is small or modest. It is
worth noting that the magnitudes of the tributary floods are
very sensitive to the strength of the correlation, and thus
careful attention should be given to the nature and
selection of the events used to derive the correlation value.
It is also perhaps worth noting that the tributary distribution
of interest is the flow value coinciding with the peak flows in
the mainstream; the use of the peak flow distribution for the
tributaries is an additional approximation.

A worked example illustrating some of the above
concepts is presented in Section 6.5.

(b) Correlation estimated from rainfall data

If streamflow records in adjacent clItchments are not
available, one approach to the estimation of concurrent
flooding is to assume that the correlation between