A Tail of Two Models: Estimating the Annual Exceedance Probability
of Probable Maximum Precipitation
Rory Nathan
Assoc Professor, University of Melbourne; Technical Director, Jacobs, Melbourne
E-mail: [email protected]
Matthew Scorah
Hydrologist, Hydrology and Risk Consulting, Melbourne, Australia
E-mail: [email protected]
Phillip Jordan
Senior Hydrologist, Jacobs, Melbourne, Australia
E-mail: [email protected]
Simon Lang
Hydrologist, Hydrology and Risk Consulting, Melbourne, Australia
E-mail: [email protected]
George Kuczera
Professor, School of Engineering, University of Newcastle, Newcastle, Australia
E-mail: [email protected]
Melvin G. Schaefer
Principal, MGS. Engineering Consultants, Seattle, U.S.A.
E-mail: [email protected]
Erwin Weinmann
Private Consultant, Ruffy, Australia
E-mail: [email protected]
Abstract
This paper describes the development and application of two largely independent methods to estimate
the annual exceedance probability (AEP) of Probable Maximum Precipitation (PMP). One method is
based on the Stochastic Storm Transposition (SST) approach, which combines the “arrival” and
“transposition” probabilities of an extreme storm using the total probability theorem. The second
method – termed “Stochastic Storm Regression” – combines frequency curves of point rainfalls with
regression estimates of areal rainfalls; the regression relationship is derived using local and
transposed storms, and the final exceedance probabilities are derived using the total probability
theorem. The methods are applied to two large catchments (with areas of 3550 km2 and 15280 km2)
located in inland southern Australia. In addition, the SST approach is used to derive regional estimates
for standardised catchments within the Inland GSAM region. Careful attention is given to the
uncertainty and sensitivity of the estimates to underlying assumptions, and the results are used to help
formulate draft ARR recommendations.
1. INTRODUCTION
In Australia, current procedures for estimating extreme flood events are based on the use of a flood
event model in conjunction with design rainfall inputs. The largest flood that can be derived with an
estimated probability of exceedance using these procedures is termed the Probable Maximum
Precipitation Design Flood (PMPDF). The magnitude of this event should be derived using estimates
of the Probable Maximum Precipitation (PMP) provided by the Bureau of Meteorology (Minty et al,
1996; Walland et al 2003; Bureau of Meteorology, 2003). The annual exceedance probability of the
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PMP is currently obtained from recommendations developed by Laurenson and Kuczera (1999), as
adopted in Book VI of Australian Rainfall and Runoff (ARR; Nathan and Weinmann, 2000).
Book VI recommends that estimates of flood magnitudes between the 1 in 2000 AEP event and the
PMP should be derived by an interpolation technique based on design rainfalls. The assignment of an
AEP to the PMP is an essential requirement of this interpolation procedure and thus influences the
shape and position of the flood frequency curve for all floods rarer than 1 in 2000 AEP (see Figure 1).
Differences in estimates of the AEP of PMP can have a considerable impact on the risk assessment
process used in the design and evaluation of major civil infrastructure. Changes in the AEP of the
PMP by an order of magnitude or more can markedly alter the estimated risk of infrastructure failure
due to flood loading; in some cases differences of this magnitude may alter the decision on whether or
not to undertake expensive upgrading works.
The first means to provide an estimate of
the AEP of PMP for Australian design
practice was provided by Kennedy and
Hart (1984), and this was supplemented
by Rowbottom et al (1986), who
proposed a method of assigning an AEP
to the probable maximum event; both
these recommendations were included
in the 1987 edition of ARR.
Laurenson and Kuczera were then
commissioned
to
provide
recommendations on the AEP of the
PMP to assist the partial revision of ARR
that was released as Book VI (Nathan
and Weinmann, 2000). Laurenson and
Kuczera (1999) estimated the AEP of
the PMP to vary linearly in the
Figure 1 Influence of AEP of PMP on estimates of
logarithmic domain between 10-7 for
rainfalls and floods rarer than 1 in 2000 AEP.
small catchments with areas less than or
equal to 100 km2, and 10-4 for large
catchments with an area of 100,000 km2. These estimates are regionally applicable and not
catchment-specific.
The Laurenson and Kuczera (1999) recommendations were based on the review of a number of
theoretical and practical studies. They concluded that the most promising avenues of research were
based on total probability approaches developed and applied by National Research Council (1988),
Fontaine and Potter (1989) and Wilson and Foufoula-Georgiou (1990). Another promising approach
was demonstrated by Klemes (1992) who developed a combinatorial approach that considered the
joint distributions of the independent components that combined to produce PMP, and this was
extended to estimate the AEP of the Probable Maximum Flood (PMF) by Neudorf (1994).
Laurenson and Kuczera also considered estimates derived specifically for Australia. Pearce (1994)
further extended the concepts developed by Kennedy and Hart (1984) to derive an estimate of the
AEP of PMP that was independent of catchment area, but Laurenson and Kuczera concluded that the
assumptions inherent in the approach were incorrect. Pearse and Laurenson (1997) developed a
combinatorial approach similar to Klemes that was tailored to the method used by the Bureau of
Meteorology to estimate the magnitude of the PMP; their estimation of a probability distribution of
storm efficiency was based on the substitution of space for time using data for a given storm area
within the 250000 km 2 coastal zone of south-east Australia. Nathan et al (1999) adapted a
regionalisation approach proposed by Schaefer (1994) and derived estimates for the inland and
coastal regions of south-east Australia using the storm database prepared for generalised estimation
of PMP depths (GSAM; Meighen and Kennedy, 1995). Whilst this work provided a useful means of
characterising the extreme frequencies for storms occurring within the GSAM region, their estimation
of the transposition component was based on a formula proposed by Alexander (1963) which was
considered overly simplistic.
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The Laurenson and Kuczera (1999) recommendations have been used in design practice for the past
fifteen years. While these recommendations have provided a consistent basis for risk-based design
across Australia, Laurenson and Kuczera stressed at the time “that there is considerable uncertainty
surrounding these recommendations as they are for events beyond the realm of experience and are
based on methods whose conceptual foundations are unclear”. The estimates relevant to large
catchments are particularly problematic as they yield AEPs that are not low enough to satisfy the
(very) low tolerable risk criteria relevant to critical infrastructure. For example, the risk-based criteria
relevant to a dam which might cause high loss of life in the event of failure would be based on an AEP
of around 10-6 or less, but the lowest AEP that can be assigned to a flood for a 10,000 km 2 catchment
is 10-5. It is for these reasons, namely the inherent uncertainty in the current (regional) estimates and
the high range of AEPs relevant to large catchments, that the Murray Darling Basin Authority (MDBA)
commissioned a study to derive estimates of the AEP of PMP for two catchments relevant to their
responsibilities. This paper describes the development and catchment-specific application of two
largely independent methods to estimate the AEP of the PMP as part of the study undertaken for the
MDBA, and also presents the results for application of one of the methods to the derivation of a
regional relationship between catchment area and the AEP of PMP.
2. OVERVIEW OF APPROACH
Two methods were developed and applied to estimate the exceedance probability of rare design
rainfalls approaching, and up to, the magnitude of the PMP. While the two methods share some
common assumptions and conceptual elements, the application of each involved the analysis of
largely different data sets and procedures. The implementation of both methods relied heavily on
storm-specific and gridded rainfall products developed by the Bureau of Meteorology. Both methods
assume that an adjustment for site specific factors renders the GSAM Inland zone a homogeneous
region for transposition of storms.
The approach that has required the most effort on development and application is here termed the
“Stochastic Storm Regression” (SSR) method. The conceptual basis of this approach was developed
by Schaefer over a number of years in the process of deriving extreme hazard estimates for dam
owners in north America (eg MGS Engineering and Applied Climate Services, 2014). The main
elements of the approach involved:
 the derivation of frequency curves of point rainfalls for a small number of “key sites” located
within the catchment, which were extrapolated out to an annual exceedance probability (AEP)
of around 1 in 106;
 the development of “space-time” patterns of storm behaviour (based on events between 20%
and 60% of PMP depths) using locally observed data as well as storms transposed from the
whole of inland south-east Australia;
 the development of a regression equation to estimate catchment rainfalls from point rainfalls at
the key sites;
 use of the foregoing relationships to simulate many thousands of synthetic storms in a manner
that accounts for the natural variability (and uncertainty) in the governing processes; and,
 statistical analysis of the simulated rainfalls to derive a frequency curve of areal rainfalls
specific to the catchments of interest.
Though based on existing concepts, the approach was developed to suit the nature of data sets
available in Australia and adapted to suit the large size of the catchments involved.
The other approach used is the Stochastic Storm Transposition (SST) method; this method was
recommended by Laurenson and Kuczera (1999) and then modified for use with non-dimensional
rainfalls by Agho et al (2000). The basis of this approach is to compute the probabilities of extreme
rainfalls by the separate consideration of the “arrival” and “transposition” probabilities, where:
 the arrival probability of an extreme storm is the probability that a storm exceeding a given
non-dimensionalised average depth occurs anywhere in inland south-east Australia, and
 the transposition probability is the likelihood that, once the storm has arrived in south-east
Australia, it produces at least that average rainfall depth over the catchment of interest.
Computation of the second component involved the simulation of many thousands of synthetic storms
in a manner that accounted for the variation of rainfall depth with storm area.
These above two methods were used to estimate the frequency of extreme rainfalls for the
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catchments above Dartmouth and Hume dams, which have areas of 3,550 km 2 and 15,280 km2,
respectively.
3. DATA AND STORM SELECTION
Four primary datasets were used in the analyses, namely: (i) the catalogue of significant rainfall
events used to develop the Generalised South-east Australia Method (GSAM) of PMP estimation
(Meighen and Kennedy, 1995), (ii) the Australian Water Availability Project (AWAP) gridded daily
rainfall dataset (Jones et al, 2009), (iii) the new intensity-frequency-duration design rainfalls developed
by the Bureau of Meteorology (Green et al, 2012), and (iv) gauged records of daily rainfalls within the
Hume catchment and surrounding region.
The GSAM data was used to identify major historical storms that have occurred over the wider inland
region of south-east Australia. Importantly, this quality controlled data were also used to correct for the
bias in the AWAP gridded daily rainfall estimates for major historical storms. The advantage of the
AWAP data set is that it provides daily (9 am to 9 am) rainfall estimates from January 1900 onwards at
a resolution of 0.05⁰ x 0.05⁰ (approximately 5 km by 5 km) for the whole of Australia. However, the
limitations of the data are that:
 the number of rain days are over-estimated and the depth of large rainfalls is under-estimated;
 the absolute errors tend to increase with increasing observed rainfall and with decreasing
area;
 the accuracy of the AWAP data is limited in regions where the rainfall gauge network is
sparse;
 the number of rain gauges used to generate the gridded rainfall estimates on any one day
varies; &
 errors increase where climate gradients are steep, for example in coastal areas when high
rainfall is recorded on land but there is no measurement of rainfall over the sea.
Figure 2 Comparison of (a) uncorrected and (b) bias corrected
data with GSAM estimates.
Accordingly, considerable effort
was expended on deriving a
bias-correction equation that
rectified the errors of underestimation at high rainfalls in a
manner
that
progressively
reduced
with
increasing
catchment area (Figure 2).
There
remains
some
uncertainty about the efficacy of
the bias correction and its
reconciliation with estimates
obtained using other methods,
but the adopted approach was
considered reasonably fit for the
purpose of this study.
The largest historical storms to have occurred over the Hume and Dartmouth catchments were
identified using the AWAP data sets. A time series of catchment average rainfall for each day of the
113 years of available record was calculated for each catchment from the AWAP data. The top ten
storms with the highest average depth across each catchment were identified separately for the Hume
and Dartmouth catchments, and for 1 and 2 day durations. A total of 21 unique storms were identified.
The largest historical storms to have occurred over the inland GSAM region were identified from the
GSAM catalogue for the standard storm areas of 2,500 km 2 and 20,000 km2 (to encompass the extent
of the Dartmouth and Hume catchments. A total of 18 storms were identified for which the required
data could be obtained. Three of these were found to be poorly characterised by the AWAP data and
were excluded from transposition, and three were identified for translation (without rotation) away from
the centre of the parallelogram used by the Bureau of Meteorology to define the storm area.
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4. STOCHASTIC STORM REGRESSION
A schematic of the framework developed to apply the stochastic regression method is shown in Figure
3. The approach uses two distinct sampling schemes to characterise: (a) the aleatory uncertainty
associated with natural hydrologic variability, and (b) the epistemic uncertainty arising from errors
associated with fitting parameters to the limited data available. The steps involved in the first sampling
scheme are shown in green shaded boxes in Figure 3, and those used to characterise epistemic
uncertainty are shown in blue shading.
Figure 3 Schematic illustration of stochastic regression framework.
The stochastic regression approach utilises information at a small number of key sites in the
catchment. The two main analyses required are i) the derivation of frequency curves of point rainfalls
at key sites for estimation of events with AEPs of around 1 in10 6, and ii) the development of a
regression equation to estimate catchment rainfalls from point rainfalls at the key sites. The steps
involved in assessing the aleatory uncertainty were as follows (with reference to Figure 3):
A. Point rainfalls at the prime key site were stochastically generated between 1 in 2 AEP out to 1 in
106 AEP using a stratified sampling scheme. The stochastic sampling was undertaking using
frequency curves derived using the CRC-FORGE procedure with additional uncertainty analysis,
as illustrated in Figure 4a. Some additional analyses were also undertaken using an approach
based on regional L-Moments, and it was found that these estimates lay well within the derived
confidence limits (also shown in Figure 4a).
B. Correlated rainfalls were generated for the other key sites from the marginal distribution of
extreme point rainfalls relevant to each location; this was done in a manner that reflected the
natural variability of storms across the catchment, where four key sites were used for the Hume
catchment and two for Dartmouth.
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C.
Areal rainfalls were estimated for each stochastic combination of point rainfalls generated at the
key sites using an appropriate regression equation (Figure 4b shows the typical quality of fit of the
regression equation); this regression equation was based on the analysis of local rainfalls (red
diamond symbols) and the transposition of much larger storms that had occurred over the inland
GSAM region (blue diamond symbols).
D. The computation of expected probability quantiles from the Total Probability Theorem, based on
1000 simulations generated within each of the twenty intervals used to discretise the probability
domain (ie 20000 simulations).
The above four steps yield the expected probabilities of areal rainfalls for the catchment of interest.
These expected probabilities are derived using three functional relationships, namely i) the frequency
distributions of point rainfalls at each key site, (ii) correlations between point rainfalls at the prime and
secondary key sites, and (iii) a regression equation that estimates areal rainfalls from point rainfalls at
key sites. The parameters of each of these relationships are subject to the epistemic uncertainty
arising from the finite nature of the available data. Accordingly, a parametric bootstrap procedure was
used to construct 90% confidence intervals. The relationships used to characterise hydrologic
variability are themselves stochastically sampled to reflect the uncertainty involved in their
parameterisation. This uncertainty is explicitly represented by generating (again, with reference to
Figure 3):
E. frequency distributions of point rainfalls for key sites with correlated parameter sets that reflect
the uncertainty in the parameters of the marginal distributions
F. correlations between key site point rainfalls based on the standard error computed from the
sample size
G. regression equations with slope and intercept terms that vary in accordance with sample
uncertainty
A total of 1,000 different sets of functional relationships were generated to capture the above
uncertainty, and expected probability quantiles were derived for each set of distributions using the
Total Probability Theorem. Overall, the total number of simulations used to capture both aleatory and
epistemic uncertainty was 20x106.
Figure 4 Example illustration of (a) a frequency curve fitted to local and regional annual
maximum point rainfalls at a key site, and (b) quality of regression fit between point rainfalls at
key sites and areal catchment rainfalls based on local and transposed storms.
5. STOCHASTIC STORM TRANSPOSITION
The algorithm adopted for the stochastic storm transposition approach was based directly upon the
approach described by Agho et al (2000), though a number of minor improvements were implemented
to improve simulation performance and to allow additional frequency distributions and irregular-shaped
catchments to be considered. The total probability theorem was used to combine the probabilities of
extreme storms occurring in the transposition region (the “arrival probability”) with the likelihood that
they were positioned in a manner that would equal or exceed the estimated target depth on the
catchment for the specified duration (the “transposition probability”).
The arrival distributions were derived using areal rainfall maxima obtained from the analysis of 113
years of gridded historical AWAP rainfalls prepared by the Bureau of Meteorology. The rainfalls were
bias-adjusted and transformed to represent non-dimensional depths as a proportion of a gridded index
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variable based on estimates of 1 in 50 AEP areal rainfalls, where the latter were derived by fitting a
GEV distribution to the AWAP maxima for each individual grid cell across the whole of the GSAM
region. A test was undertaken to assess the homogeneity of the non-dimensional rainfall maxima over
the transposition region and this assumption was found to be reasonably satisfied. Some attention
was given to the selection and fitting of a suitable distribution to the non-dimensional rainfall maxima.
The rainfall maxima used to fit the arrival distributions were censored to consider only the top 20% of
events, though this proportion was increased (with increasing storm duration and storm size) to
around the top 70%. The approach to censoring required some subjective judgement but its
defensibility rests on hydrometeorological reasoning: the degree of censoring broadly reflects the
relative frequency of the two dominant storm types in the region, namely common storms of low
intensity that are associated with cold fronts, and the far less common but more severe rainfalls that
are spawned by monsoonal troughs. It was not practically feasible to censor on the basis of detailed
storm typing given the large number of storms involved, and hence the censoring was based on
seasonality as this was assumed to capture the arrival of monsoonal troughs that occur in summer
months (see inset panel in Figure 5a). A Kappa distribution (with second shape parameter fixed to
0.25) was then fitted to the rainfall maxima (Figure 5a), where the sample L-Moments derived from the
different data sets were regularised for consistency across storm area and duration.
The transposition probability was determined by calculating all the different combinations of storm
area, location and depth that yield catchment rainfalls of the required depths (under varying
assumptions of storm orientation and shape). A relationship between storm depth and area was
derived from an analysis of the arrival distributions based on AWAP data. The western region of the
inland zone is poorly gauged and thus the sampling probabilities were also adjusted to account for the
reduced sampling area adopted (Figure 5b).
Figure 5 (a) Example frequency curve fitted to standardised areal maxima within the inland
GSAM zone showing seasonality of the storm maxima, and (b) the location of storm maxima
within the sampling region used to fit the arrival distribution.
6. CATCHMENT-SPECIFIC RESULTS AND DISCUSSION
Results were derived for the Hume and Dartmouth catchments using both methods, and the derived
frequency curves for the Hume catchment are shown in Figure 6. It was found that there is good
agreement between the stochastic regression and storm transposition estimates for the Hume 24-hour
rainfall and Dartmouth 48-hour rainfall curves for AEPs of 1 in 104 and rarer. For the Hume Dam 48hour rainfall and Dartmouth Dam 24-hour rainfall there is an appreciable level of difference between
the stochastic regression and storm transposition estimates, though the average of these estimates
corresponds to the results obtained for the other durations. It was also found that the level of
agreement between the design rainfall estimates (based on new IFDs and CRC-FORGE methods
using areal reduction factors based on Jordan et al (2013)) and the stochastic storm transposition
method was better than the level of corresponding agreement obtained using the stochastic storm
regression method.
The final set of curves was adopted giving equal weight to the estimates from the two methods. For
Hume catchment both methods yielded the same estimate for the AEP of the 24-hour PMP event,
namely 1 in 106; since the average of the two estimates for the 48-hour event is also 1 in 106, this
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value was used to anchor the top end of the frequency curve. A similar situation exists for Dartmouth
catchment, though here the two methods both indicate that the AEP of the 48-hour PMP is 1 in 107,
which is similar to the average of the two estimates for the 24-hour event.
The Stochastic Storm Regression method is attractive in that it makes use of the detailed analysis of a
number of large events that have occurred in a meteorologically homogeneous region, as used to
derive the PMP events of interest; its weakness, however, is that it relies on the estimation of point
rainfalls by extrapolation to exceedance probabilities beyond 1 in 10 6, and its implementation requires
the undertaking of complex statistical analysis to correctly account for the correlations between point
and areal rainfalls.
The Stochastic Storm Transposition approach is attractive in that it requires few inputs, is based on a
rigorous statistical framework that takes good advantage of regionalised inputs, and requires an
extrapolation of the arrival distribution only to an AEP that is one to two orders of magnitude less than
the computed frequency of rainfall exceedances over the target catchment; its weakness, however, is
that it relies heavily on the defensibility of the arrival distribution of areal rainfalls, which is difficult to
identify robustly from the available data.
Figure 6 Derived frequency curves of areal rainfall for the Hume catchment for the (a) 24-hour
and (b) 48-hour rainfall events.
7. REGIONAL APPLICATION AND DISCUSSION
The SST procedure was also used to derive
estimates of the AEP of the PMP for a
sample of locations within the inland GSAM
region (see Figure 7). The storm locations
coincided with historic events used in
development of the GSAM procedure
(Meighen & Kennedy, 1995), where the
corresponding PMP estimates were derived
by Nathan et al (1999). For this study these
estimates required factoring to allow for the
influence of topography, and this was done
in a manner consistent with (but not identical
to) the approach used by the Bureau of
Meteorology (Minty et al, 1996).
Figure 7. Location of storm centres used to derive
the regional relationship between AEP of PMP and
area using the SST method.
The AEP of PMP estimates were plotted
against storm area separately for each
duration, as well as combined across all four
durations. It was found in all cases that the
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relationship was most linear when a logarithmic scale was adopted for both area and the AEP of the
PMP. Regressions between log10(Area) and log10(AEP of PMP) were constructed separately for
each duration, as well as for all durations.
It was found that the spread in AEP of the PMP is larger for the one day dataset than the two, three
and four-day durations. This can be attributed to the relatively shallow arrival distributions for one day
storms which lead to a much larger change in arrival probability for a given change in PMP fraction
(compared with the other durations). Additionally, the depth-area curve for one day events has slightly
greater curvature than the other durations, and thus the spread of the one-day AEP estimates
decreases slightly with increasing catchment area.
A single regression equation was derived for all four durations. Given the significant spread in the one
day results for the individual catchments, a further regression was undertaken using the two to fourday datasets only (Figure 8a). It should be noted that the spread in results for individual catchments
reflects the “site-specific” nature of several factors involving: a) the index variable used to scale the
non-dimensional arrival distribution, b) the topographic enhancement factor used to estimate the
topographic component of the PMP estimate, and c) the moisture adjustment factor used in PMP
estimation that accounts for variation in extreme precipitable water at the catchment site; across storm
area for a given duration, there is additional variability associated with d) differences in the severity of
the storms used to construct the (region-wide) standardised convergence component of the deptharea curves. With the one day data set excluded, the span of the confidence limits is approximately
one order of magnitude smaller. Regressions including the one day dataset return rarer AEP of the
PMP values than regressions based on other durations.
Figure 8 AEP of the PMP as a function area showing (a) influence of site-specific factors on
derived regional relationship and (b) comparison with Laurenson and Kuczera (1999)
recommendations.
The regressions are compared to the recommendations from Laurenson and Kuczera (1999), as
shown in Figure 8b. It is seen that the two to four-day regression fits are very similar to the Laurenson
and Kuczera recommendations. The slope of the one day regression is also approximately parallel to
the Laurenson and Kuczera curves, though the regression fit to the two day storms exhibit a
comparatively lower slope.
The notional confidence limits (computed simply from the sample exceedances) for the regression
estimates are generally similar to limits recommended by Laurenson and Kuczera, though those for
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the “one day” and “one to four-day” duration samples are wider. The slightly wider 75% confidence
interval for both the “one day” and “one to four-day” duration regressions are mainly the result of the
spread in the one day estimates. The width of the 100% confidence interval for the “all durations”
sample is slightly larger than two orders of magnitude. Variation in the AEP of the PMP for individual
catchments can be driven by site specific characteristics such as described above and differences in
the severity of storms that influence the envelope curve most relevant to the combination of storm
area and duration. This highlights the fact that while the “best estimate” curve might provide useful
information as an initial regional estimate of the AEP of the PMP, site-specific analyses would help to
reduce the uncertainties involved.
8. CONCLUSIONS
On the basis of the results obtained, it was concluded that:
 both the Stochastic Storm Regression and Stochastic Storm Transposition methods provide
similar estimates of the frequency of extreme areal rainfalls;
 the best estimates of annual exceedance probability (AEP) of Probable Maximum Precipitation
(PMP) events over the Hume and Dartmouth catchment are 1 in 106 and 1 in 107, respectively,
around one order of magnitude rarer than suggested by the current guidelines;
 the derived regional estimates of the AEP of PMP for catchments located in the inland GSAM
zone are nearly one order of magnitude rarer than the best estimate of the current
(Laurenson-Kuczera) recommendations, however this difference is largely due to the influence
of the one-day results; when two- to four-day results are considered, the differences between
the two sets of estimates is a little less than half an order of magnitude, which is not
statistically significant given the width of the notional uncertainty limits.
 in view of the closeness of the derived regional estimates to the original Laurenson-Kuczera
curves, it is not proposed to change the current ARR recommendations except to include
advice for the provision of site-specific estimates for the small number of design cases where
the required effort may be warranted; and,
 the site-specific estimates are expected to have smaller uncertainties than the (regional)
Laurenson-Kuczera recommendations, and thus they have been recommended for adoption
for these catchments.
Both methods have their strengths and limitations and the study has yielded catchment-specific
estimates that are more defensible than the current regional recommendations. However, the
uncertainty of all these estimates is still appreciable and spans around one to two orders of
magnitude. The study raises a number of issues that would benefit from longer-term research; these
are primarily associated with factors involved in the estimation of the arrival distribution, the scaling
variables used for transposition, and reconciliation of more frequent rainfall estimates with other
available information.
9. ACKNOWLEDGMENTS
All rainfall data used in the project was sourced from the Bureau of Meteorology, with the assistance
of Janice Green and Karin Xuereb. Some information was sourced via Mark Babister, Chair of the
ARR Revision Committee, under the auspices of Engineers Australia. Dr Nanda Nandakumar
(Water NSW) provided processed information on CRC-FORGE fits to the local rainfall gauges, and he
also contributed to a workshop held to review progress and methodology. The conduct of the project
required some considerable changes to focus and scope, and the project team greatly benefited from
the informed support and guidance provided by MDBA staff (Robert Wilson, Andrew Reynolds, and
David Dreverman). The funding and support provided by Engineers Australia for the regional analyses
undertaken is greatly appreciated.
10. REFERENCES
Agho, K.E., Kuczera, G., Green, J., Weinmann, E. and Laurenson, E. (2000). Estimation of extreme
rainfall exceedance probabilities: Nondimensional stochastic storm transposition, Proceedings of the
2000 Hydrology and Water Resources Symposium, Perth.
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