The observation of even a few exceptional storms can provide quantitative evidence for climate change. Doing so however requires observing and learning as much as possible about how storms work, and not merely counting storms. With some understanding of how atmospheric systems and storms operate, we have other observational information from physics, chemistry, and planetary science that we can also apply to the question. We should use all the information available.
Bayes rule can help us do this objectively. Here, P(A|B) can be the posterior probability that the climate has changed (A), given the observation of the exceptional storm (B). P(A) is the prior probability for climate-change. P(B|A) is the likelihood that storm B occurs given a changed climate (e.g. warmer). k1 and k2 are constants of proportionality. Let (!A) represent no change of climate. Then we can write two equations for Bayes Rule.
P(A|B) = k1 P(A) P(B|A)
P(!A|B) = k2 P(!A) P(B|!A)
The prior odds for a change in climate is P(A):P(!A), and let's assume the prior odds for and against climate change are even, 1:1.
Now if we use all the available information we have about atmosphere physics and chemistry, and we observe storm B in detail, we can make an informed estimate of the ratio of likelihoods P(B|A):P(B|!A). Let's assume that B is an exceptional storm and ten times more likely to occur when the atmosphere is warmer.
If a storm of type B is observed in actuality, the posterior odds can be applied, and the odds should be updated in favor of climate change to 10:1.
What this means is that the observation of exceptional (extreme) events should inform our opinion on climate change. This approach is most successful however when we have many, and many types, of information on how the atmosphere and climate works.
Measurements taken on a day during extreme weather will of course be outliers, but could also provide important information about how In a Warming World, Storms May Be Fewer but Stronger. We should not assume outliers always represent 'noise' that needs to be averaged away.
It does not seem unreasonable to ask the question whether or not we are seeing effects of climate change in the weather. Thursday morning I read the following on the US National Weather Service forecast discussion page:
CLIMATE...THERE IS A SMALL CHANCE THAT SEATTLE WILL GET TO 90
DEGREES ON SUNDAY WHICH WOULD TIE THE RECORD FOR THE DAY. SINCE
RECORDS STARTED IN SEATTLE AT THE FEDERAL BUILDING DOWNTOWN IN 1891
THERE HAVE BEEN ONLY SIX DAYS IN THE FIRST WEEK OF JUNE WITH A HIGH
TEMPERATURE OF 90 DEGREES OR MORE. THE LAST TIME IT HAPPENED WAS
JUNE 4 2009 WITH A HIGH OF 91 DEGREES. FELTON
Whether or not the temperature exceeds 90 degrees next Sunday, I wouldn't dismiss the question of what mechanisms might be operating out-of-hand. We should try to estimate how much what happens supports (or not) hypotheses based upon physical processes.
For example, use Bayes rule reasoning to estimate the change in posterior odds for a mechanism A that increases the likelihood of P(B|A) and P(!B|!A) by 15%, and decreases the likelihood of P(!B|A) and P(B|!A) by 15%.
$$\delta = 0.15$$
Then the likelihood is given by the following, where the record is exceeded for a years and not exceeded for b years.
$$
k \times\left[ \frac{P(B \parallel A)}{P(B \parallel !A)} \right] ^{a}\times \left[ \frac{P(!B \parallel A)}{P(!B \parallel !A)} \right] ^{b}
$$
$$
k \times\left[ \frac{1 + \delta}{1 - \delta} \right] ^{a-b}
$$
Let's also look at the support if the record is also exceeded in 2016 and 2017.
Change in posterior odds in favor of A(0.15)
(a) Record Not Exceeded 2015 - Posterior odds decrease from prior odds by 35%. By this method it is possible that additional observations eventually discredit the hypothesis.
(b) Record Exceeded in 2015 - Posterior odds increase by 35%.
(c) Record Exceeded in 2015 & 2016 - Posterior odds increase by 83%.
(d) Record Exceeded in 2015 & 2016 & 2017 - Odds increased by 148%.
Finally, the advantages of using this approach, rather than a frequentist approach, can be more easily understood by considering how it could be applied in practice. For example, how a Penn Cove shellfish business might use these calculated changes of climate-change probability to self-insure their farm. The owner of a shellfish farm may understand that climate change poses a risk to her business, and has hedged for the cost of the odd bad year due to this by putting an extra 100 dollars into an account each month. She has found this has worked well in the past, with the account growing to be large enough to cover costs in bad years, without ballooning too large.
How might she use the information that Seattle is breaking temperature records (and the probability of A may be changing) to adjust this amount? If the temperature record is exceeded in 2015, she may decide to increase the amount to 135 dollars per month, and if the record is exceeded again in 2016 she may decide to increase it to 183 dollars, and if it is exceeded again in 2017 increase it to 248 dollars. The advantage is the Bayes method helps her make a decision to act sooner than by using a frequentist approach. This way she may be able to prepare for future costs.