model to estimate

financial loss

**Return periods, also called recurrence intervals, are a way of talking about risk probabilities. In our case, return period indicates the average length of time between flood events of a given characteristic, such as severity or loss.**

We calculate a given event’s return period by dividing a time interval (such as one year) by the probability of an outcome (that event occurring) within that time. If the probability of a flood event which exceeds a given severity occurring in any one year is 0.01, the event has a return period of one hundred years (one divided by 0.01). In theory, a flood with the given event’s characteristics will occur, on average, once in every one hundred year period, but in reality similar magnitude events occur at much more variable intervals, including multiple events of a given characteristic in one year.

The table below shows the relationship between return periods, probability and the chance of occurrence of a flood event in a given time period.

The return period of a flood event can be measured in many ways when using a catastrophe model but is invariably based on either physical flood characteristics (such as the river flow, flood depth or the volume of rainfall) or upon financial losses. When estimating the return period of a given event by financial loss, one of the more common methods is to simply rank all of the observed events in a given time period by descending order of loss and then divide the time period by that given event’s rank. This method can result in unreliable estimations of return period.

We can better understand the drawbacks by using this worked example:

The summer 2007 floods in the UK resulted in a financial loss of £1.6 billion (Chatterton et al, 2010), the second largest loss in 70 years after the event of 1947 (Marsh et al, 2016). Using the method above, the return period would be calculated as followed:

*Time period = 70 years**Rank of summer 2007 UK flood event = 2 (second largest loss in 70 years)**Estimated return period = (70 / 2) = 35*

The ranking method estimates a loss return period of 35 years. However, relying on a short observed record is error-prone as there is not enough data to adequately estimate the probability or return period of larger and less frequent events that might fall outside of the observed record.

This potential volatility in the loss is demonstrated through Figure 1. We have taken 140 different continuous 70-year periods of modelled residential market losses generated using JBA’s UK Flood Model, which is derived from statistical analysis of precipitation and river flow data, and for each 70-year period, the loss is ranked and assigned a return period. Annual Exceedance Probability (AEP) curves for each of the 70-year periods are shown in Figure 1.

*Figure 1: AEP for 140 different continuous 70-year periods. The blue line indicates the £1.6 billion loss estimate from Chatterton et al, 2010.*

Figure 1 illustrates the problem of relying on a short record length to inform loss expectations and project future losses. For a loss of £1.6 billion, the return period can vary anywhere from 9.9 years to 70 years (the full length of the record).

The estimated return period varies depending on which 70-year record is used for context. For example, Figure 2 shows an example of a 70-year period with few flood events; there are no events that generate a loss of £1.6 billion or greater. Figure 3 shows a contrasting 70-year period with many flood events - in this case, there are 5 events generating a loss of £1.6 billion or greater. Using these two reference periods as context and using the ranking method discussed above, the return period for a £1.6 billion loss ranges from 14 years for the flood-rich period to > 70 years for the flood-poor period, solely due to the different events that are simulated in each 70-year period.

*Figure 2 (below): A flood poor 70-year period. The orange line indicates a loss of £1.6bn. Figure 3 (right): A flood rich 70-year period. The orange line indicates a loss of £1.6bn.*

If we could extend the observed record by a few thousand years we would be in a far better position to make simple calculations based on event ranking. Until then, we can use a catastrophe model to extend the record.

Flood modelling is an essential tool for effective risk management because it allows us to overcome the limitations of a fixed historical dataset by extrapolating based on scientifically-justified statistical and physical principles. Generating a long stochastic event set allows us to use simulated events to extend the observed record of flooding. By adding more data points, we gain a better understanding of how frequently large losses can occur.

We use our model and event set to help improve the precision of estimates of risk based on a long-term perspective, rather than relying solely on a short record of recent claims, enabling a better understanding of flood.

If you would like to find out more about our probabilistic catastrophe models or how we can help you to understand your flood risk, please get in touch.

**References**

*Chatterton J. B., Viavattene C., Morris J., Penning-Rowsell E. C., and Tapsell S. (2010). The costs of the summer 2007 floods in England. Project: SC070039/R1 Environment Agency, Bristol. Retrieved from: https://www.gov.uk/government/publications/the-costs-of-the-summer-2007-floods-in-england*

*Marsh, T., Kirby, C., Muchan, K., Barker, L., Henderson, E., & Hannaford, J. (2016). The winter floods of 2015/2016 in the UK-a review. NERC/Centre for Ecology & Hydrology*

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