Micevski, T., A. Hackelbusch, K. Haddad, G. Kuczera and A. Rahman (2014). “Regionalisation of the parameters of the log-Pearson 3 distribution: a case study for New South Wales, Australia.” Hydrological Processes. DOI: 10.1002/hyp.10147 DOI: 10.1002/hyp.10147

Micevski et al develop a regional flood frequency analysis approach for the eastern part of NSW. In this post I present an example based on the simplest outputs and interpretation of their paper. Please refer to their paper for all the details and if you are interested in the sophisticated method they propose.

Micevski et al suggest that, when considering this area of NSW as a whole, it is possible to estimate the three parameters of the Log Pearson 3 (LPIII) distribution of flood magnitudes i.e. the mean, standard deviation and skewness. In fact, the standard deviation and skewness are constant. Standard deviation is 1.2318 and skewness is -0.3567 (see table 3 of the paper).

From table 3 in the paper, an equation can be developed for the mean of the LPIII distribution.

Where, *A* = area in km^{2} and *I*_{12,50} is the rainfall intensity for a 12 hour, 50 year ARI rain storm.

We can use this relationship to estimate flood magnitudes anywhere in eastern NSW.

### Example

Estimating the 100-year flood for Gillamatong Creek near Braidwood.

A flood study for creeks near Braidwood was undertaken by Cardo Willing in 2005 (link to report). They estimated the 100-year flood for Gillamatong Creek as 518 m^{3}/s.

Lets make a similar estimate using the approach suggested in Micevski et al. (2014).

area = 77 km^{2}

Lat = -35.45^{o}

Lon = 149.8^{o}

Looking at the 1987 IFD values from the BoM website *I*_{12,50}= 12.4 mm/h

We will undertake the analysis for a 100-year flood. Parameters can be defined and the mean flood estimated as follows.

`area <- 77 I12.50 <- 12.4 flood.skew <- -0.3567 flood.sd <- 1.2318 flood.aep <- 1/100 flood.mean <- 0.3326 + 1.322 * log10(area) + 4.7182 * log10(I12.50) flood.mean`

`## [1] 7.986`

To calculate the 100 year flood, we use the standard frequency factor approach for the LPIII distribution – however this is the tricky part of the Micevski et al.’s paper; they use natural logs for flood magnitudes and base 10 logs for catchment attributes. Also the flow units are ML/d not cumec. Therefore, the equation we need is:

Where *K* is the frequency factor.

The frequency factor for the 100 year flood can be estimated in R using using the quape3 function from the lmom package. Frequency factors can also be looked up in Australian Rainfall and Runoff (Book IV, Table 2.2). Calculations for the 100 year flood are:

`library(lmom) flood.K <- quape3(1 - flood.aep, para = c(0, 1, flood.skew)) flood.K`

`## [1] 2.062`

So our log_{e}(Q_{100}) will be:

`flood.mean + flood.sd * flood.K`

`## [1] 10.53`

Therefore Q_{100} = 3.72 × 10^{4} ML/d or 431 cumec.

So the estimate is smaller than that of Cardo and Willing but in the same ballpark and reasonable for a quick approximate method.

A single snippet of code to calculate a flood estimate is as follows:

```
area <- 77
I12.50 <- 12.4
flood.skew <- -0.3567
flood.sd <- 1.2318
flood.aep <- 0.01
B0 <- 0.3326
B1 <- 1.3222
B2 <- 4.7182
Q100 <- exp(B0 + B1*log10(area) + B2*log10(I12.50) + flood.sd * quape3(1-flood.aep, para = c(0, 1, flood.skew)))
```

It’s generally good practice, when providing the estimate of some statistic, to also estimate the uncertainty. Micevski et al., list means and standard deviations of all their coefficients although not the covariances. Figure 5 in Micevski et al’s paper show uncertainties (posterior distributions) for a few stream gauges.