# How to tell if a single day of weather is an anomaly or due to climate change?

I am interested in understanding how to tell if a single day of 'abnormal' weather is due to climate change or not.

From my understanding, you would compare this day's weather to historical weather. However, is a day-to-day comparison accurate? Or would you have to take a large sample, like week, month, or season?

It seems to me like it would be hard to compare one day to another historical weather average, because the day could just be an outlier not due to climate change...

In other words, how do you tell if a seasonal storm or really hot summer day is due to climate change?

• I feel uncomfortable linking climate change and individual weather events, since by definition they happen on such disparate time scales. Changes in the occurrences of weather patterns would be a much easier intellectual jump to make, but I'm not sure we have enough data from teleconnection indices over the years to actually attribute their variations to climate change. While I understand that it's easier to help the general public grasp what's going on with tangible things that happen in their backyard, I think it's actually very difficult to do what you're asking with simple statistics.
– Ian
Jun 12, 2015 at 18:10
• Although don't get me wrong, there have been successful efforts to do so with large outlier events such as Hurricane Sandy on the United States east coast. What I'm saying is that it's a lot harder to take a couple of weeks of moderate heat wave and argue for climate change as "the cause".
– Ian
Jun 12, 2015 at 18:18
• This question is more or less equivalent to saying "We have a (known) loaded die. We just threw a six. What is the chance that this is due to the loading?" - the answer is, who knows? A single datum is not enough. If you throw 20 times and get 10 sixes, then you can start making statements about how the loading is affecting the results (with appropriate uncertainty estimates). Jun 17, 2015 at 15:43

I am interested in understanding how to tell if a single day of 'abnormal' weather is due to climate change or not.

You can't. The day-to-day, locale-to-locale variations in weather are huge compared to the changes that occur from year-to-year and decade-to-decade, averaged over the surface of the Earth. Most of those climatological variations are periodic in nature (e.g., El Niño Southern Oscillation, North Atlantic Oscillation; note the "oscillation" in the names). Climate change is the small but steady secular change in climate.

Another way to look at it: Even the most pessimistic of projections is for a 4°C increase over the course of a hundred years. That corresponds to 0.04°C change per year. Weather can bring about a 4°C change over the course of a few minutes. Any one weather event can be attributed to the noisy, flukey nature of weather. Climate change begins to become apparent when one looks at weather events that occur all over the face of the Earth, and over the course of several decades.

• I feel compelled to share this link: www2.ametsoc.org/ams/index.cfm/publications/… . We can calculate probabilities that an event would not have occurred but for climate change.
– f.thorpe
Jun 1, 2015 at 22:19
• @farrenthorpe - The cited papers that did find a correlation did so for extreme, month-long heat waves. For other long-term extrema (e.g., California drought), the evidence that global warming is to blame is less clear. For single day extreme weather events, the evidence is even less clear. There's just too much natural variation in the weather during one day at a specific locale to be able to attribute that to global warming (so far). Jun 2, 2015 at 12:45
• David I completely agree!
– f.thorpe
Jun 2, 2015 at 14:52
• Right. It's called climate change, not weather change. Jun 4, 2015 at 20:39
• @David Hammen The mean alone seems to me to be a too limited definition of climate change. If the variance of conditions or the frequency of extreme events changes significantly, most people would consider this climate change. Good answer though (made me think.) Jun 11, 2015 at 2:06

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.

• In other words, can you reject the null hypothesis? In this case, the null hypothesis is that the variations are due to "just weather". Rejecting the null hypothesis for a single one day weather event at a specific locale today is highly problematic. Global warming hasn't done that much to change the weather yet. By 2050, rejecting the null hypothesis for a season, maybe a few weeks will not be a problem. By 2100, even isolated events will most likely be attributable to global warming. Jun 9, 2015 at 13:06
• @DavidHammen the frequentists' null-hypothesis testing isn't really used much within the Bayesian paradigm: although it was a fashionable method in the second half of the twentieth century, it's increasingly hard to defend, both in theory and in practice. Jun 9, 2015 at 14:58
• @DavidHammen If observations result in a likelihood <1, posterior probability < prior. There is no fundamental “null-hypothesis” with special significance. You could construct a “just weather” hypothesis and base your model on stochastic process you assumed had a Normal Distribution, but you would still need to explain variance based on either “weather physics” or a principle (e.g. maximum likelihood fit to data.) I expect in that case the frequentist approach would be more direct. Bayes is useful when you have other prior information (hopefully based in fact) that needs to be included. Jun 10, 2015 at 0:57

The answers to such questions come down to statistical analysis; particularly statistical significance and statistical hypothesis testing.

When conduction such tests, care must be taken in choosing the data for the analysis: don't compare summer temperatures with winter temperatures. Also, the amount of data used needs to be large enough for the result to be significant. Don't compare the recent apparently anomalous temperature with temperatures for the past 2 or 5 years.

The other thing is seasons don't always start and finish according to human timetables. They vary, sometimes they start early or late so you need to have some leeway when choosing to data to analyze.

Initially you'd get the day of the month of the anomalous data, to account for seasonal variability over the years, you'd then decide how far either side of that date you wanted to compare data: maybe a week or two, possibly three or four.

You would then calculate the required statistical parameters, such a mean, standard deviation, standard error of the data, without the anomalous reading.

You then decide what confidence level you need for your analysis: 95%, 99.9% or higher. Then you do the hypothesis testing. One such test would be to test the anomalous reading with the mean of the historical data.

If the result of the hypothesis testing is that the anomalous reading is within the variability of the historical data then it's not due to climate change. If however, the anomalous reading falls outside the range of normal variability for the historical data then you start to look for reason why, of which climate change can be one of many reasons.

• Good answer, may I add...every 11.1 years (on average), the magnetic polarity of the sun reverses. Therefor comparisons of temperatures within 22.2 years of each other also lie outside of the apples to apples realm. Jun 7, 2015 at 19:10

Individual days weather variations can only be considered anomalies, since the theory of global climate change/global warming/anthropogenic CO2 related greenhouse effect acceleration only is theorized and described as affecting the planet over the course of decades and/or centuries and globally, not individual days or individual locations.

With that said

The weather variations in history have been far greater than any that have occurred during man's brief history of recording the weather, and far greater than any that have occurred during mans use of fossil fuels:

Answer: Weather is weather. Climate change is a "theory", not a "premise". Therefor with the question depends on the factual existence of climate change, which I believe is incorrect since the foundation knowledge doesn't support the extrapolation of measurement and observation to the extent some people have taken it.

Please consider that between quantum theory and the standard model, there is a reconciliation that has not been found. The balance point between that which is miniscule, and that which is massive has NOT been found. Our knowledge of physics is incomplete.

Example: Quantum theory vs Standard model (which dictates an origin where the entire universe existed momentarily in a singluarity smaller than a grain of sand that then expanded to create the universe)... No Big Bang? Quantum equation predicts universe has no beginning

So where we have observed and believe we understand what we perceive as "matter", we actually only understand the nature of 5% of what exists. The remainder, dark matter and dark energy fill the void between electrons and nuclei. Similarly between stars and planets. This is NASA's web site where the approximate quantification of Dark Matter and Dark Energy is published material:

NASA Quantification of Dark Energ - Dark Matter

By fitting a theoretical model of the composition of the Universe to the combined set of cosmological observations, scientists have come up with the composition that we described above, ~68% dark energy, ~27% dark matter, ~5% normal matter.

Without an understanding of the nature of the balancing act that lies in the middle between tiny and huge, believing we understand energy retention, energy dissipation, and the triggers involved to the point that we can properly determine the way the planetary energy system works is ludicrous. Physics in it's current state of development does NOT support our belief in CO2 based global warming.

With the researchers at CERN currently considering and looking for a FIFTH fundamental force, HOW can we believe we know how our planet actually works.CERN Looking for FIFTH fundamental Force

Engineers have spent more than a year upgrading the LHC's systems. The hope is that this will allow a new realm of physics to be opened up!!

And when it comes to choosing the mathematical model that best fits our observations, we are still waffling between String Theory 11D, String Theory 12D. And we are attempting to determine if said strings even exist?!?! Discussion of the number of dimensions that exist

which posits that there are 10 or 11 dimensions in our universe.

So with our very OBVIOUS failure to understand physics, 95% of it being a dark mystery, and waffling over the number of fundamental forces, whether the origin of the universe was a big bang, how many dimensions there are, etc....HOW is it, we can ask ourselves questions like, is daily weather indicative of climate change, when we should be asking, is it viable to believe we have mastered knowledge of the physics of our existence, to the point necessary to be sure that climate change exists.

We cannot.

• Dark matter and dark energy don't prove that the standard model is wrong, only that it's perhaps incomplete. That's like saying radioactivity proves chemistry wrong - which it doesn't. Chemistry is correct science for electron orbitals and bonds, it just doesn't cover nuclear bonds or the strong or weak force. And neither has anything to do with climate change, which is simple in principal, but with all the moving parts of the earth's atmosphere and oceans, it's enormously complex mathematically. Your argument is unrelated to the subject at hand. Jun 6, 2015 at 7:30
• That doesn't actually answer the question posted by the OP... In addition to all of the other problems in this answer Jun 7, 2015 at 3:51
• Thank you userLTK I agree.... it's enormously complex math. We haven't gotten the math of any single part of the universe nailed down mathematically. How we then think we can figure out the planet based on 50 - 60 years of dubiously adjusted record keeping is beyond common sense. Jun 7, 2015 at 19:07
• @AlistairRiddoch We cannot figure out the exact climate in 60 years with small uncertainties. Nobody seriously claim we can. We get lots of details wrong. But the big picture, that it's getting warmer with added CO₂, is pretty clear. Where, how, and when precipitation patterns will change is a much more difficult story.
– gerrit
Jun 9, 2015 at 10:26
• @AlistairRiddoch - this feels like it's approaching one of those political debates which is counter productive but the "dubiously adjusted" record keeping statement you made isn't correct. Records aren't being adjusted, estimates based on those records are, and that's fine, Trying to reconstruct an estimated global average temperature based on daily highs and lows and precipitation and not much else isn't exact science. Reconstructing annual estimates from years past is one of those things that SHOULD be open to adjustment. It' not "dubious" at all. Jun 10, 2015 at 5:12