How were the 2016 design rainfalls estimated?
Summary of methods
A number of steps were used to derive the 2016 design rainfalls from observed rainfall data for Australia. The methods and rainfall data selected for each probability range varied as outlined in the following table.
|Step||Very Frequent design rainfalls||IFDs||Rare design rainfalls|
|Number of rainfall stations||Daily read: 15364
|Daily read: 8074
|Daily read: 3955|
|Period of record||All available records up to 2012||All available records up to 2012||All available records up to 2012|
|Length of record||Daily read: > 5 years
Continuous: > 5 years
|Daily read: >= 30 years
Continuous: > 8 years
|Daily read: >= 60 years|
|Source of data||Many organisations collecting rainfall data across Australia||Many organisations collecting rainfall data across Australia||Bureau of Meteorology|
|Extreme value series||Partial Duration Series (PDS)||Annual Maximum Series (AMS)||Annual Maximum Series (AMS)|
|Frequency analysis||Generalised Pareto (GPA) distribution, fitted using L-moments||Generalised Extreme Value (GEV) distribution, fitted using L-moments||Generalised Extreme Value (GEV) distribution, fitted using LH(2)-moments|
|Regionalisation||Ratios based on 50% annual exceedance probability (AEP)||Region of Influence (500 station years)||Region of Influence (minimum 2000 station years)|
|Gridding||Regionalised at-site ratios, gridded using ANUSPLIN||Regionalised at-site distribution parameters, gridded using ANUSPLIN||Regionalised at-site distribution parameters, gridded using ANUSPLIN|
The approach adopted is outlined in Green et al (2015). These methods are summarised below, with links to key papers. Book 2, Chapter 3 of the 2016 edition of Australian Rainfall and Runoff ARR also contains more detailed information on the methods used to derive the 2016 design rainfalls, including the IFDs, Very Frequent and Rare design rainfalls.
Collation of the rainfall database
A database containing data from all available rainfall stations was created. The number of continuously recording (sub-daily) rainfall stations available was significantly greater than the number available for ARR87 due to the inclusion of data collected by other organisations, provided to the Bureau through the Water Regulations 2008 (Commonwealth).
|Type||Source||Length of record||ARR87||2016 IFDs|
|Daily||Bureau||>= 30 years||7500||8074|
|Continuous||Bureau||> 8 years||600||754|
|Continuous||Water Regulations data||> 8 years||n/a||1526|
Rainfall records for each station were put through automatic and manual quality control procedures, described in Green et al (2011) . Some types of errors identified and corrected include accumulations, time shifts, missing data, and gross errors. The location information (latitude, longitude and elevation) was also checked.
Undertaking frequency analysis
The Annual Maximum Series (AMS) was extracted from the quality controlled database for:
- all daily-read stations with at least 30 years of record
- all continuously-recording stations with more than 8 years of record
An AMS is a list of the highest rainfall total recorded at a station for a specific standard duration each calendar year. Factors were applied to the daily-read rainfalls to change restricted 24 hour rainfall totals (9 am to 9 am) to unrestricted 24 hour rainfalls so these two data types could be combined across Australia.
A Generalised Extreme Value (GEV) frequency distribution was fitted to each AMS, as this distribution best represents Australian rainfall data. The three L-moments (mean, coefficient of L-variation (L-CV) and L-skewness) were then used to summarise the statistical properties of each AMS (Hosking and Wallis, 1997; Green et al., 2012). To improve the spatial coverage of sub-daily rainfall data, a Bayesian Generalised Least Squares Regression (BGLSR) was applied to infer sub-daily L-moments from those at the daily-read stations (Johnson et al., 2012a)
Regionalisation of rainfall data
Regionalisation was undertaken, to reduce the sampling uncertainty introduced by stations with shorter periods of record, by combining L-moments from stations within a region of influence to give more weight to the stations with longer records. The regionalised L-CV and L-Skewness were combined with the at-site mean to estimate GEV distribution parameters (mean, shape and scale) and rainfall quantiles for all required exceedance probabilities at each station location. (Johnson et al., 2012b)
Preparation of final grids
To extend the regionalised GEV distribution parameters of mean, shape and scale to any point in Australia, the at-site values were translated to regular gridded rainfall estimates using thin plate smoothing splines using the ANUSPLIN algorithm. This enabled rainfall quantiles for the standard IFD annual exceedance probabilities to be estimated at any point in Australia. (The et al., 2014)
Very Frequent design rainfalls
Very Frequent design rainfalls are commonly used for stormwater quality purposes. The method adopted to estimate these was very similar to the IFDs outlined above; however the increased occurrence of these events meant that a different approach was required for the frequency analysis. A Partial Duration Series (PDS) was used to summarise the significant events for each rainfall station, after enforcing a minimum inter-event time (MIT) to ensure independence. A minimum length of record of five years was used, with a threshold defined to select an average of one event per month of record (Xuereb and Green, 2012). A Generalised Pareto (GPA) distribution was then fitted to the PDS using L-moments. Ratios of the at-site quantiles to the 50% AEP were extracted for each standard frequency and gridded using ANUSPLIN to form the Very Frequent design rainfall grids (The et al., 2015)
Rare design rainfalls
Estimating Rare design rainfalls required extrapolation outside of observed events, therefore, the minimum length of station record was set to 60 years. To place weight on the largest observed rainfall values in the AMS, a GEV distribution was fitted using LH moments. The GEV parameters were regionalised using a similar region of influence approach to the IFD method, but with an increased number of station years. To extend the regionalised GEV parameters to areas with no rain gauges, they were gridded using ANUSPLIN. To produce a continuous design rainfall frequency curve, the Rare design rainfalls were anchored to the more frequent design rainfalls at the 5% AEP (Green et al., 2016).