Australian Rainfall and Runoff (Book 8 Section 3.6.3) suggests a simple approach to estimate design rainfall depths for durations less than 24 hours and annual exceedance probabilities from 1 in 100 years to 1 in 2000 years. Growth factors, based on work by Jordan et al. (2005), are provided that relate very rare event rainfalls to the 1 in 100 year rainfall depth which can be obtained from the Bureau of Meteorology.

AEP (1 in Y years) |
Growth factor |
---|---|

100 | 1.00 |

200 | 1.140 |

500 | 1.344 |

1000 | 1.513 |

2000 | 1.698 |

**Example:**

The 1 in 100 year , 12 hour rainfall depth for Melbourne (-37.81, 144.96) is 100.8 mm (based on the Rainfall IFD Data System) Therefore, an estimate of the 1 in 2000 year 12 hour rainfall is 100.8 x 1.698 = 171.2 mm.

If we plot the annual exceedance probability as a z-score on the x-axis and log of the growth factor on the y-axis, the result is almost a straight line (Figure below). This provides a reasonable basis to interpolate between the points in the table.

An R function to interpolate between the provided points is below. I’ve implemented this in a web app here.

GFactor_interp <- function(ari){ if(ari < 100) stop('Value must be 100 years or greater') if(ari > 2000) stop('Value must be 2000 years or less') aep <- 1/ari ari.std <- c(100, 200, 500, 1000, 2000) growth.factor <- c(1, 1.140, 1.344, 1.513, 1.698) x <- qnorm(1 - 1/ari.std) y <- log(growth.factor) F_interp <- approxfun(x, y) exp(F_interp(qnorm(1 - aep))) } # test # Growth factor for a 1 in 1500 years storm GFactor_interp(1500) # [1] 1.619841

### References

Australian Rainfall and Runoff Book 8 Section 3.6.3 (see ARR web book)

Jordan, P., R. Nathan, L. Mittiga and B. Taylor (2005) Growth curves and temporal patterns of short duration design storms for extreme events. *Australian Journal of Water Resources ***9**(1): 69-80. link.

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