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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signiflcant impact on the outcome of the study than the
selection of runoff-routing parameter values.

One design objective of general importance is the
derivation of floods of specifled AEP. Satisfying this
objective generally requires the adoption of AEP-neutral
inputs i.e., the selection and/or treatment of design inputs
to ensure that any bias in the AEP of the transformation
between rainfall and runoff is minimised. The issues
considered in this section are generally aimed at the better
treatment of the joint probabilities involved in the selection
of design inputs. However, as discussed in Section 2.2, it
should be recognised that it is not possible to assure the
achievement of the AEP-neutral objective beyond the
credible limit of flood extrapolation.

The appropriate level of complexity to be adopted is
dependent upon the sensitivity of the design outcome to the
input. Accordingly it is not possible to provide
recommendations that are applicable to all design
situations. The procedures recommended here are relevant
to many situations, but they should be regarded as
providing only a general guide to recommended practice.
The practitioner is thus encouraged to adopt different
procedures if they have a sound theoretical basis.

5.2 Derivation of Reservoir Outflow

Frequency Curves

5.2.1 Importance of Reservoir Storage and Initial
Drawdown

The attenuation of an inflow hydrograph as it passes
through a reservoir or another natural or artificial storage
depends mainly on the available storage volume relative to
the flood volume, and to a lesser degree on the spillway
capacity and the degree of regulation of outflows by
spillway gates or other outflow control structures. More
speciflcally, the total storage available to mitigate floods
can be divided into two parts: the storage above the normal
full supply level (flood storage) and the drawdown below full
supply level at the onset of a flood (initial drawdown, or air-
space). The flood storage for a given inflow hydrograph is a
fixed system characteristic determined by the adopted
spiltway and freeboard characteristics of the storage, but
the initial drawdown or initial reservoir level is a stochastic
variable.

The selection of an appropriate initial reservoir level is
of considerable importance in determination of spillway
adequacy. In particular, it is an important consideration in
the determination of criteria related to the flood capacity of
the dam, such as the Dam Crest Flood and the Imminent
Failure Flood (ANCOLD, 1998). In many cases it may be
appropriate to adopt a full reservoir level, but if there Is a
reasonable chance that the reservoir may be drawn down,
and if the volume of drawdown is significant compared to
the volume of the inflow floods of interest, then it will be
desirable to analyse in more detail the effect on estimates
of the frequencies of a particular peak outflow of the
variation in storage volume. Where there is a strongly
seasonal variation of storage volume, it may be necessary
to undertake a seasonal analysis of storage impacts on
outflow floods.

5,2.2 Approximate Methods - Representative
Initial Storage Volume

For preliminary analyses it may be sufficient to adopt a
mean or median- storage volume, or else compute the
mean or median storage volume associated with, say, the
top 10% of inflow floods. In general, adoption of a mean or
median value will not provide an AEP-neutral

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t\lOOK VI - t::.Stlmauon aT Large to t:Xl:reme t'"looas

transformation as the relationship between inflow and
outflow floods is highly non-linear. Accordingly, for detailed
design estimates, it is prudent to determine the probability
of the outflow hydrograph by the joint probabilities of the
inflow and initial storage volume, and by the deterministic
relationship that governs the conversion of an inflow
hydrograph of given duration and magnitude into an outflow
hydrograph for different storage volumes.

5.2.3 Joint Probability Analysis of Inflow and
Initial Storage Volume

(aJ Background

Laurenson (1974) developed a method for the analysis
of systems which incorporate both stochastic and
deterministic components (in this context, the joint
probabilities of the inflow and initial storage volume
represent the stochastic component, and the relationship
between the magnitudes of inflow and outflow floods
represent the deterministic component). Other methods are
available (e.g. Hill and Daniell, 1994; Loh et aI., 1997) and c>~
the practitioner is encouraged to adopt a method most
suited to the problem at hand. The LaureQson method is
suited to a wide variety of problems and provides
information on the complete probability distribution of
outflows. Application of this method is straightforward as
long as the probabilities of all the inputs can be
appropriately defined; this may pose some practical
difficulties, though in most situations where it is worthwhile
undertaking the analysis the required information can
usually be derived.

The analytical solution proposed by Laurenson involves
the convolution of the conditional probability distribution of
outflows with the distribution of the conditioning event. In
principle, the conditioning event may be either the reservoir
inflow or the initial storage volume, but reservoir inflow is
adopted in most applications.

In practice the convolution is achieved by approximate
numerical methods, based on discrete approximations to
the continuous probabilily distributions of the inflows and
the outflows. To this end, the total range of inflows and
outflows has to be divided into a finite number of class
intervals.

(b) Representation of probability distributions

The selection of class intervals for the approximate
representation of continuous probability distributions by
discrete ones represents a compromise between efficiency
and accuracy of computations. A total of 10 to 20. class
intervals is generally sufficient, but they need to be well
distributed over the range of possible variate values to
ensure accuracy in the most important part of the range.
Each interval is then represented by the variate value at the
mid-point of the interval and by the width of the interval on
the probability scale. The total probability of all the intervals
must add up to unily. It is worth considering the following
issues when discretising the distributions:

. Discrete probability distribution ofinflows: Il is desirable
to discretise the probability distribution of inflows
(Section 4.5) so as to have most of the classes
representing Rare and Extreme floods; classes do not
need to cover equal probability or flow ranges. One
pragmatic approach is to discretise on the basis of
equal logarithmic-transformed inflow intervals, though it
may be more appropriate to experiment with different
definitions of classes to explore the stability of the
resulle. UAequ&f class intervals are flI'eferred as iRtlows
are approximately log-Normally distributed, and
intervals of equal probability would lead to the selection
of most of the classes encompassing flows of little