risk assessment – Cabot Institute for the Environment blog

This is the first in an irregular sequence of snippets about some of the slightly more technical aspects of uncertainty and risk assessment. If you have a slightly more technical question, then please email me and I will try to answer it with a snippet.

Suppose that an event has a probability of 0.015 (or 1.5%) of happening at least once in the next five years. Then the probability of the event happening at least once in the next year is 0.015 / 5 = 0.003 (or 0.3%), and the probability of it happening at least once in the next 20 years is 0.015 * 4 = 0.06 (or 6%).

Here is the rule for scaling probabilities to different time intervals: if both probabilities (the original one and the new one) are no larger than 0.1 (or 10%), then simply multiply the original probability by the ratio of the new time-interval to the original time-interval, to find the new probability.

This rule is an approximation which breaks down if either of the probabilities is greater than 0.1. For example, to scale a probability of 0.04 in the next 5 years up to 20 years we cannot simply multiply by 4, because the result, 0.16 (or 16%), is larger than 0.1. In this case we have to use the proper rule, which is

p_new = 1 – (1 – p_orig)^(int_new / int_orig)

where ‘^’ reads ‘to the power of’. The example above becomes

p_new = 1 – (1 – 0.04)^(20 / 5) = 0.15 (or 15%).

So the approximation would have been 1 percentage point out in this case. The highlighted text in yellow can be pasted directly into a spreadsheet cell (the answer is 0.1507).

Of course it is unlikely to matter in practice whether the probability is 0.15 or 0.16. But the difference gets bigger as the probabilities get bigger. For example, it would definitely be a mistake to multiply a 0.25 one-year probability by 5 to find the five-year probability, because the result would be greater than 1. Using the formula, the correct answer is a five-year probability of 0.76.

Blog post by Prof. Jonathan Rougier, Professor of Statistical Science.

Second blog in series here.
Third blog in series here.

Image: By Hovik Avetisyan [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons

The “Statement of Principles” on flood insurance agreed by the UK Government and the Association of British Insurers as a temporary measure in the year 2000 is due to expire on 31st July 2013. At the heart of this document is an undertaking by insurers to continue to provide cover for domestic property and small business customers as long the Government continues to manage the risk adequately.

Specifically the agreement says that cover will be provided for properties built before 2009 either if the risk is low or there is a commitment by the Environment Agency to reduce it to low within 5 years. ‘Low’ risk is arbitrarily defined as a property having a less than 1.3% annual chance of flooding, of which there are believed to be ~200,000 in England and Wales. In other words properties need to be protected against the 1 in 75 year event.

Premiums can still vary with risk and the Statement makes no explicit provision for affordability, but the agreement does allow owners of some at risk properties to continue to obtain cover (and hence for buyers of these properties to obtain mortgages). An implicit assumption is that for properties built after 2009 the planning system has been operating effectively and has only allowed development in low risk zones.

Negotiations over a replacement were clearly going to the wire but today a Memorandum of Understanding was agreed between the ABI and the Government. This involves the setting up of a flood insurance pool known as ‘Flood Re’ for the ~200,000 ‘high risk’ properties. Premiums for the ‘high risk’ properties will be set based on council tax band. Flood Re will charge member firms an annual charge of £180 million which equates to a levy of £10.50 on annual household premiums.

This represents the estimated level of cross-subsidy that already exists between lower and high flood risk premiums. The scheme will be up and running by summer 2015 and in the meantime, ABI members will continue to meet their commitments to existing customers under the old Statement of Principles agreement.

Clearly the questions most commentators have fixated on are “who pays?” and “how much?”. However, as a flood scientist a far more interesting question is “how will we know?” and this applies as much to the existing Statement as to any new agreement. To put this another way: are we confident that we can determine to reasonable accuracy which properties are ‘at risk’? You might think this is typical academic hand wringing, but actually answering this question is, in my view, critical to running an effective flood insurance business.

For any given site the 1.3% annual chance flood will not have been observed and the Environment Agency and insurers use computer models that simulate flooding to calculate what such events look like. To use these you need to know how big the 1.3% annual probability flow is and to have a detailed 3D map of the terrain. The model then uses more or less complex variations on Newtonian physics to determine how this volume of water moves over the land surface.

At particular places such models can be great, but all predictions have error and because of uncertainties in both data and models this is certainly the case with flooding. How big can these errors be? Well, in a recent study we found the plausible range for the current 1% annual probability flow for the River Avon in Warwickshire to be between 310 and 425 m³s^-1: enough to make a significant difference to the area predicted as inundated. Ok, this isn’t the 1.3% level exactly, but you get the idea. Models also get worse as you zoom out because to be computationally tractable at regional to national scales they have to simplify the representation of terrain and flow which introduces errors.

Irrespective of what the ABI and the Government do in the future, this situation doesn’t change. The question of how good national scale flood risk assessments need to be to confidently manage risk and set insurance premiums is still unanswered.

This blog is taken from WillisWire and written by Cabot Institute Director Professor Paul Bates, University of Bristol and Willis Research Network (WRN) Senior Academic. Edits by Tim Fewtrell, Chief Hydrologist at the WRN

Professor Paul Bates, Cabot Institute Director

Tag: risk assessment

Converting probabilities between time-intervals

Brinkmanship, flood insurance and science