# Initial loss: storm v burst

This post is about choosing a value of initial loss, as an input to a flood event model, to match the choice of design rainfall; either a design burst, or a complete design storm.

Design rainfall values are available for any location in Australia for a range of durations (6 min to 7 days) and frequencies (1 event per year up to an annual exceedance probability of 1%).  These design rainfall values are usually bursts rather than complete storms.  A burst is the most intense part of a storm (Figure 1).

Figure 1: Distinction between storm and burst initial loss (source: ARR Book 5, Figure 5.3.5)

For real runoff events there is some initial loss of rainfall and then flow will begin to increase i.e. the hydrograph will start to rise (Figure 1).    The initial loss for a storm can range from zero – when streamflow increases as soon as rain starts – up to the total storm rainfall i.e. all the rain is lost and the storm does not result in any increase in streamflow.

The initial loss for a burst $I\!L_b$ can range from some negative value (when the hydrograph commences to rise before the start of the burst), up to the storm initial loss, $I\!L_s$ (when the start of the burst coincides with the start of the complete storm).  Consequently, burst initial loss will often be less than storm initial loss.

When using ‘design’ rainfall in modelling, we need a suitable ‘design’ value for initial loss.  The problem is that initial losses derived from real events are based on complete storms, not bursts.  For example, all the initial loss values in Australian Rainfall and Runoff Book 5 are based on complete storms.

In summary:

So, in flood modelling, we either need to factor up the design rainfalls to convert them from bursts to storms, or reduce the initial loss values so they are suitable for bursts.

ARR recommends that burst initial loss is calculated as:

ILb =  ILs – Preburst rainfall.

(See Book 2, Chapter 5.9.9).

Values of storm initial loss and pre-burst rainfall are available from the data hub.

This can work well but occasionally, the pre-burst rainfall is large compared to the storm initial loss which means the burst initial loss will be very low or even negative.  This is acknowleged in ARR (Book 2, Chapter 5.9.9).

As an alternative, there are studies that have looked at the issue of the relationship between burst and storm initial losses and two empirical equations have been developed.

Hill et al. (1996; 1998) developed the following relationship.

$I\!L_b = I\!L_s \left( 1 - \frac{1}{1+142\frac{\sqrt{d_b}}{MAR}} \right)$

Where:

• $I\!L_b$ is the burst initial loss (mm)
• $I\!L_s$ is the storm initial loss (mm)
• $MAR$ is the mean annual rainfall (mm)
• $d_b$ is the burst duration (hour)

Rahman et al. (2002) suggested an equation based on 11 Victorian catchments.

$I\!L_b =I\!L_s (0.5 + 0.25 \log_{10}(d_b))$

$I\!L_s$  – initial loss for a complete storm (mm)

$I\!L_b$ – initial loss for the burst (mm)

This gives  ILb = 0.5ILs at db = 1 h and ILb = ILs at db = 100 h

Plotting the Rahman equation shows  asymptotic behaviour (Figure 2).   The burst initial loss approaches the storm initial loss as the duration of the design rainfall increases.

Figure 2: Rahman equation relating burst and storm initial loss

A comparison with Hill equation is shown in Figure 3 for mean annual rainfall (MAR) ranging from 400 mm to 1000 mm.  In this figure duration is plotted on a log scale. Using the Hill equation, the burst initial loss is always substantially less than the storm initial loss even for long duration storms.   The higher the MAR, the smaller the ratio of burst to storm loss.

Figure 3: Comparison and Rahman and Hill equations relating burst and storm initial loss.  Note that duration is on a log scale.

This suggests that when modelling floods, if the initial loss values from ARR Book 5 are combined with the design rainfalls from the BoM, the resulting flood estimates will be too small.  Too much of the rain will be lost.  This is a particular issue for short duration design storms which are most important in small catchments.

Code to create the graphs is available as a gist.

### References

Hill, P. I., Maheepala, U. K., Mein, R. G. and Weinmann, P. E. (1996) Empirical analysis of data to derive losses for design flood estimation in south-eastern Australia.  Cooperative Research Centre for Catchment Hydrology.  Report 96/5 (link).

Hill, P., Mein, R. and Siriwardena, L (1998) How much rainfall becomes runoff? Loss modelling for flood estimation.  Industry report 98/5.  Cooperative Research Centre for Catchment Hydrology (link).

Rahman, A., Weinmann, P. E., Hoang, T. M. T. and Laurenson, E. M. (2002) Monte Carlo simulation of flood frequency curves from rainfall.  Journal of Hydrology 256:196-210 (link)