Sunday 27 December 2015

Press, politicians and 100 year floods

This post covers basic probability theory.

The media and the politicians seem to be completely confused by the concept of flood frequency, particularly in the abuse of the concept of "a hundred year flood".

The use of that term creats the misguided idea that you get such a flood every hundred years, and that having had one a few years ago, you aren't going to see another one for nearly a century.

This is shows a complete misunderstanding of statistics and probability. Which for the people being evacuated from their houses you can partly understand —you can't expect them all to have studied maths to A-level or remembered the details. What is wrong is that the press keeps using the same term, along with "20 year flood", misleading the people. And the politicians, they are equally a bunch of Oxbridge PPE-graduates who don't have a single cartesian coordinate between them —but should at least have those science advisors to explain the basics. FFS, there is the whole "Royal Society" which is meant to explain science to royalty, and, given we still live in a feudal state, the crown's ministers, Cameron included.

A "hundred year flood" really means a "1% chance per year flood". Assuming that the effects of the previous year's weather has no bearing on its successors, the probability of having a 1% flood the year after a 1% flood is, wait for it: 1%. The probability of having one in the five years after is, wait for it: five percent. And in 15 years, it's 15%. So the fact that York is currently underwater for the first time since 2000, means that the the two-flood-in-15-year-event, which had ~15% probability, has occurred. Which is not impossible, even for a "hundred year event". In fact, when you start counting since, say, 1995, you are looking at the probability of two 1% floods happening in a 20 year period —which is actually 20%: 1 in 5.

For the curious, assuming that the flood events are entirely independent, it'd follow a Poisson Distribution

Except, certainly within a single winter, we know the events are not independent —if the ground is saturated from previous rainfall, the rivers bloated from previous storms, then the probability of another storm triggering a flood is higher. If the land is already full of water, then it only takes a little bit more to tip things over the edge.

That "hundred year flood" really means, then:

The meteorologists' model of rainfall over a single winter, of the volume and frequency of rainfall, predicts the probability of flood of a specific volume occurring at 1%.

The probability of  a 1% flood re-occuring may follow a poission distribution —and hence the likelihood of multiple floods happening within a few decades is actually quite high.

Floods do appear to be happening more often than even a Poission distribution would apply, so what does that mean?

Some hypotheses spring to mind
  1. The rainfall model is correct and we've simply had the misfortune to have a rare-but-not-impossible series of storms.
  2. The rainfall model is correct, but the estimates of probability of storms within a season are wrong —that is, bad historical data created optimistic estimates.
  3. Year-on-year flood events are not independent.
  4. Changes in the terrain: farming differences, the building of houses on flood plains, etc, changed the runoff of the system, so amplifying the effect of rain
  5. The rainfall model is in fact wrong due to failures such as the failure to consider the impact of global warming on the evaporation of water, the actions and position of the gulf stream, and/or the fact that with warmer air, it falls more as a a liquid ("rain"), than in a crystalline form ("snow" and "hail").
  6. There was a more pessimistic (i.e. accurate) estimate of rainfall, but managerial or political pressure discounted it in favour of one which played down the risks, reducing the requirements and cost of flood defences, and obviated the need to press for changes in the agriculture system within the catchment area
Note also that these hypotheses are not exclusionary. The model could have failed to consider global warming, been based on bad historical data, and not planned ahead for the conversion of flood plains into suburban housing estates —then been downplayed by politicians who disagreed with the answers.. Which, when you think about it, is entirely possible.

That's why the term "hundred year flood" is so bogus. More accurate is "a 1% flood based on a broken or pre-global warming model with incomplete data without considering urban sprawl, and probably downplayed for political reasons". Using the term "100 year flood" does nothing but create unrealistic expectations that the floods aren't going to re-occur, year-on-year.

Someone in the press could look at the model, the data, the politics and determine what's actually happened, then try and explain it in a way which doesn't use terms like "hundred year flood". Because the science is there, the maths is there —and someone needs to hold the politicians and the scientists to account.

[These photos are all from Jan 4, 2014, showing the Avon fairly close to breaking its banks. Avon Crescent was actually underwater in winter 1990


Anonymous said...

There is also the detail that these are 1% probabilities for every single flood-prone area in England (I don't know how they are measured North of Hadrian's Wall). There will be no news articles about the places that haven't had any floods since 1995, and its pretty likely that somewhere will get a 1 in a hundred year flood every year (but not quite, because floods in different areas aren't actually independent events).

Bristol Traffic said...

now that is a good point!

if they were random, and you had 100 flood prone areas, then yes: you'd be expecting one century flood/year. (again, some poisson-distribution graph would cover the spread)

Unknown said...

Your maths is either wrong, or rounded up to make it appear wrong. Taking the probability of a 1% flood occurring in 5 years = 5%, and 15 years = 15%. Extrapolating this, the probability of a 1% flood occurring in 100 years would be 100%!

The correct probabilities are 4.95% and 14.85%. It may be you've rounded these up to get your values, but that does make it look like you've made the basic error of simply summing up the probabilities.

Bristol Traffic said...

correct: Basic math errors. Thank you for pointing out the incompetence of the maths team —they shall be roundly ridiculed