# Growth factors for sub-daily design rainfalls

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.

Growth factor as a function of Annual Exceedance Probability

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.