# The distribution of pre-burst rainfall

Pre-burst rainfall is storm rainfall that occurs before the main rainfall burst.  In design, we get information on bursts from IFD tables and sometimes need to take account of pre-burst rainfall to construct complete storms or determine the correct initial loss values to use in modelling.

Pre-burst rainfall is characterised, regionalised and mapped in Australian Rainfall and Runoff (ARR) (Book 2, Chapter 5.2.1).  Information on the analysis that supports this work is  available as conference paper (Loveridge et al. 2015a) and there is also a detailed report (Loveridge et al., 2015b).

Pre-burst depth  throughout Australia is provided on Figure 2.5.10 in ARR; reproduced as Figure 1 below.  Note the figure caption is ARR is incorrect.

Looking at the values for Victoria, the pre-burst depths are reasonably small (0 – 15 mm) but are of similar magnitude to initial loss so need to be considered in design and modelling particularly in urban areas where initial losses are low.

Figure 1: Pre-burst depth (Source: Figure 2.5.10 of Australian Rainfall and Runoff)

Specific information on pre-burst rainfall for locations throughout Australia is available from the ARR data hub:

• pre-burst depths
• pre-burst to burst ratios.

There is some information on the variability of these values with estimates available for a range of percentiles (10, 25, 50 (median), 75, 90).

Consider Toomuc Creek (-38.064520N, 145.463277E) as an example.  The pre-burst depths and pre-burst to burst ratios for a 1% AEP, 2 hour event, available from the data hub are shown in Table 1.

We can also estimate the pre-burst depths independently by multiplying the burst depth by the pre-burst to burst ratios.  The 1% AEP, 2 hour burst depth is 52 mm (available from the IFD page at the Bureau).  So the  90th percentile pre-burst depth will be 52 x 0.739 = 38.4 mm.  The value of  0.739 is from Table 1, bottom value in column 3.

Table 1: Pre-burst information for Toomuc Ck, sourced from the data hub
Percentile Depth Ratio
10 0 0
25 0 0
50 1.5 0.029
75 13.3 0.256
90 38.4 0.739

For Monte Carlo analysis, the data in Table 1 can be treated as an empirical distribution so that pre-burst depths and ratios can be randomly generated using the methods in the ARR supporting document, Monte Carlo Simulation Techniques (See Section 7.2).  Here, I’ve linearly interpolated between the given percentiles, and linearly extrapolated beyond 90% and between 0 and 10% (Figure 2).

Figure 2: Empirical distribution of pre-burst rainfall depth for Toomuc Creek (2 hour 1% AEP), data are from Table 1

Histograms of 10,000 randomly generated pre-burst depths and ratios are show in Figures 3 and 4.  The data are highly skewed with many values near zero. The median pre-burst depth is 1.5 mm and the mean is 10.66.  For the ratios, the median is 0.029 and the mean is 0.21.  As expected, the median values are equal to those shown in Table 1.

Also note that some of the time, pre-burst is quite large.  The depth is greater than 20 mm for 21% of values.  This is comparable with the median initial loss in rural catchments (there is a summary of initial loss values here).  This suggests that in a wet catchment, the pre-burst could be larger than the initial loss and runoff could have started before the main burst arrives.

Figure 3: Histogram of randomly generated pre-burst depths

Figure 4: Histogram of randomly generated pre-burst ratios

Code to reproduce the figures and calculations are available as a gist.

### References

Loveridge, M., Babister, M., Stensmyr, P., and Adam, M. (2015a) Estimation of pre-burst rainfall for design flood estimation in Australia.  36th Hydrology and Water Resources Symposium.  Engineers, Australia. (link to paper)

Loveridge, M.,  Stensmyr, P., Babister, M., (2015) Project 3: Temporal Patterns of rainfall, Part 2 – pre-burst rainfall. Australian Rainfall and Runoff.  Engineers, Australia. (link to report)