Rethinking infrastructure in flood prone areas

[sophiecentaur]

Insurers are going to have to adjust premiums to reflect better understanding of actual risks.

They have a much more powerful way of reducing their risk because they can just refuse to sell insurance in high risk areas. They realise that weather is not a memoryless process, meaning that. flood today can be followed by another flood next week. It's just not worth their while to insure bad risks.

So then the government has to support the unfortunate uninsured victims. The recent US and UK elections were won with 'manifestos' which promise low / no taxes.

 

[Flyboy]

A similar flood happened in 1916.

A "1000 year storm" is one that has a 1 in 1000 chance of happening any given year, not one that can only happen every thousand years or so. Meaning you could, in theory, get two thousand year storms in under a month. Highly unlikely, but not impossible.

 

[sophiecentaur]

Highly unlikely, but not impossible.

If only people appreciated what statistics really tells them, they would never play the lottery or roulette. Poker, on the other hand allows good players to make a fortune; they rely on the first sentence of this post. Open season.

 

[Dale]

A "1000 year storm" is one that has a 1 in 1000 chance of happening any given year, not one that can only happen every thousand years or so. Meaning you could, in theory, get two thousand year storms in under a month. Highly unlikely, but not impossible.

I understand. But the fact that such a storm happened in 1916 and 2024 indicates that the hypothesis that it is a 1000 year storm is probably not correct.

In fact, with 173 years on record and with two such observations, the probability that it was a 1000 year (or more) event is only 0.00076. The 95% credible interval is a 24 to 280 year storm. (Bernoulli likelihood with a uniform prior)

 

[gmax137]

In fact, with 173 years on record and with two such observations, the probability that it was a 1000 year (or more) event is only 0.00076. The 95% credible interval is a 24 to 280 year storm. (Bernoulli likelihood with a uniform prior)

Hi @Dale can you outline the method for making such determinations? Thanks.

 

[Flyboy]

I understand. But the fact that such a storm happened in 1916 and 2024 indicates that the hypothesis that it is a 1000 year storm is probably not correct.

In fact, with 173 years on record and with two such observations, the probability that it was a 1000 year (or more) event is only 0.00076. The 95% credible interval is a 24 to 280 year storm. (Bernoulli likelihood with a uniform prior)

A valid point, and one I'm sure that the people who make those assessments are looking into as we discuss this.

Most of those assessments of storm frequency are model-based, not empirically based over a representative timespan. But for the purposes of planning, they have been largely sufficient.

 

[Dale]

Hi @Dale can you outline the method for making such determinations? Thanks.

This is a Bayesian method using the simplest model that the likelihood of such a storm occurring in a given year is Bernoulli distributed with some probability $\lambda$ (independent fixed probability). A 1000 year storm is one where the annual probability is $\lambda=0.001$.

In Bayesian methods, you start with a model and some prior belief, and then Bayes' theorem tells you how to update your belief based on the data you observe. Bernoulli models are particularly convenient because if the prior is beta distributed $\lambda \sim \beta(a,b)$ then the posterior is also beta distributed $\lambda \sim \beta(a+m,b+n)$ after observing $m$ "successes" and $n$ "failures".

So here, if we start with a uniform prior that is $\lambda \sim \beta(1,1)$. Then we observe 171 years without such a strong storm and 2 years with such a strong storm. Applying Bayes' theorem then says our updated belief is $\lambda \sim \beta(3,172)$.

With this we can simply evaluate the PDF and the CDF to get probabilities of interest. For example $P(\lambda < \frac{1}{1000}) = 0.00076$ and $P(\frac{1}{280}<\lambda<\frac{1}{24})=0.95$