Temperature causes
Here is an atmospheric monthly average temperature series: T = (61, 69, 69, 70, 72, 65, 63) (all F). What caused the temperature to take the value T1 = 61?
Well, the sun, the amount of moisture in the air, especially in the form of clouds, the characteristics of the land around the measurement device, and things of that nature. Not just one cause, but many contributing causes. The temperature, after all, is a bunch of air molecules (you know what I mean) jostling around the surface of a thermometer. And every air molecule didn’t get pushed in precisely the same way.
And since these are monthly averages of daily averages, which themselves are averages of hourly measurements, it is difficult to identify clearly all the causes that went into that 61. Regardless of our ignorance, it has some cause or causes.
So what caused the temperature to take the value T2 = 69? Was it T1?
Before answering, consider that you took two air temperature measurements one second apart, with values, say, 68 and 68. Did the first 68 cause the second 68? How much can change in a second? Air can “entrain” in, a fancy way of saying the wind can blow new air onto your thermometer. Solar radiation, mediated by clouds, can change that quickly, but maybe not enough to cause the air to change by more than 1 degree.
But since it is tiny air molecules that make temperature, and several things can and do change those molecules, which are moving at enormous speeds, the first 68 did not cause the second 68. Instead, the air molecules and the forces acting on them are the cause of both temperatures. It then becomes clear that in our monthly series T2 was not caused by T1.
Enter Statistics
What if I were to suggest that the series was caused by some mechanism or mechanisms that actually first made each monthly temperature 67 and then pushed it upwards or downwards from there? Thus the “real” series is T = 67 + (-6, 2, 2, 3, 5, -2, -4). This could happen. It might be that some physical force loves the number 67 so much that it returns all values there before moving them on to other pastures. Nothing we know of physics gives any support for this curious view, however; indeed, it is rather silly.
If the values of T are similar, it’s much more likely that the causes of the temperatures haven’t themselves varied much and are operating along more-and-less understood pathways (such as a bent earth swirling around the sun once each anno Domini).
Our series is only 7 members long. What if we wanted to guess T8? On the theory that the series starts low, comes up a bit, then descends, we might say, given only this information, the chances that T8 is 62 or lower are fair. And that’s about as good as we can do.
Notice very, very carefully that the information we’re conditioning our guess on tacitly includes facts about seasonality and such like. When we say the chance is “fair”, we’re not saying anything directly about the cause; instead, we’re giving a measure of our uncertainty of T8 based on effects possibly and hopefully related to its causes and not its causes themselves. If we knew the cause(s), we would know what T8 would be and we wouldn’t need our crude statistical model.
Sophistication
Since our word-model—and it is a statistical model—is crude, it’s unlikely to meet peer review. Why not something better? How about fitting a sine wave to account for seasonality, which we suspect on physical ground is associated with the cause of changing solar irradiance? Slicker yet, a generalized autoregressive conditional heteroscedastic time series beauty, complete with a built-in trend parameters? Or if we want to be cute, we can go with a machine learning or neural net algorithm which “learns” from the data.
Doesn’t matter. Pick any model you like, and call it M. Unless M incorporates every cause of T, it will be probabilistic and not physical, even though it may contains portions of causes; say, radiative transfer at the molecular level, or fluid flow dynamics; even our word-model was partly physical. M is thus no different in essence than our crude word-model, except that M will likely be able to better quantify the probability T8 takes some value.
We know from observation that T6 = 65 and T7 = 63. Given these observations, what is the probability of two months equal to or under 65? Well, it’s 1, or 100% because, I feel I must emphasize, we saw two months equal to or under 65.
Now this is a separate, entirely different probability to this separate, entirely different question: given M, what is the probability that T8 and T9 are less than or equal to 65? And that is separate, entirely different question than, given M, what is the probability that two months out of the next N are less than or equal to 65?
If we want to know what happened, we just look. (Repeat that thrice.) If we want to know what’s going to happen, or, at least, if we want to quantify our uncertainty in what will happen, we need M. Conversely, we do not need M to give probabilities of anything that already occurred. That would be silly.
Right?
Probabilities can’t cause anything
Whatever question we have about the future, it should be blazingly obvious that the choice of M dictates these probabilities: different M’s will (probably) give different probabilities. M is not a cause of T, nor do its probabilities cause T, and nor are past values of T causes of future values. M is an encapsulation of our limited knowledge and nothing else.
Now suppose my M said that the probability of two months in a row less than or equal to 65 was very small; make it as small as you like as long as it isn’t 0. Of course, we saw two months in a row meeting this criterion. We’d thus be right to suspect that M wasn’t any great shakes as a model since it gave such a low probability to an event we saw. On the other hand, this is far from proof against M. It could be that this kind of event really is rare. It would, incidentally, be the grossest mistake to say these events cannot happen because, of course, we saw that they can.
It could be that our ignorance of the cause(s) of T is so great that any reasonable M we can think of would say the probability of two low months is small. But then, because we have a big tool bag, it usually isn’t difficult to find some model which would say streaks like this are common. So, given our observations, which M would you prefer? One that said the probability of streaks was small or another that said it was not?
Here’s the bad news. It’s impossible to know which non-causal model is best given just the observed data, especially considering the non-causal models were derived from the observed data. The only real way to know non-causal model quality is to use each M to predict never-before-seen data, and then to compare the predictions with what happened. Statements of how well your M “fit” the observed data are not interesting, especially considering that it is always possible (I won’t prove this here) to find an M which fits any observed data perfectly.
What are the Chances?
And now a practicum in the form of a peer-reviewed paper, “Warm Streaks in the US Temperature Record: What are the Chances?” by Peter Craigmile and a few others in JGR: Atmospheres. The authors examined NOAA’s National Climatic Data Center’s monthly contiguous US average monthly temperatures and discovered that temperatures for sixteen consecutive months were above some (arbitrary) threshold (this data’s upper tercile).
They wanted to know the probability this could happen. As above, given that we have seen it, the probability is 1. But Craigmile and friends, conditioning a couple of M, say it is low, and conditioning on a couple of other M, say it not low. Actually, because of mathematical considerations, they calculate the probability of streaks of 16 or more months in some hypothetical future of arbitrary length of time.
They use fancy M—only the best—and the probabilities were estimated by simulation, which surely sounds impressive. But these must, as we learned above, be the probabilities of events that have not yet happened. They cannot be of events that have already happened, because the probability of these events are 1. Here’s what they say:
Our resulting calculations imply that in the absence of a trend, the probability of a 16-month or greater streak is likely in the range of 0.02 to 0.04, which is small, but not so small as to make the event completely implausible. When a linear trend of the magnitude observed in the historical record is included, this probability increases to the range of 0.06 to 0.15. Even larger probabilities were obtained when nonlinear trend models were considered…
Overall, the paper shows that in the absence of trend, the probability of a streak of 16 consecutive top-tercile events is low enough that one could legitimately query its plausibility. When either a linear or non-linear trend is included, the probability increases to the point where such a result is not out of the ordinary.
A physical trend would be a systematic, uniform change in the causes which drive T. A statistical model trend is just a parameter in a model indicates change through time. The parameter is not a cause and could only be said to represent the real cause accidentally. Also, some of their M have a parametric trend and some don’t.
What the future holds
Which of these models is the best in judging the probability of the 16-month streak? None. The observations are enough to tell us all we need know about what already happened. But which model is best for future data? I have no idea. Nobody does. And we won’t know until we wait until each of the models makes predictions of future data, which can be used to check their predictions.
That won’t happen. Statisticians usually aren’t interested in actual, real-life model performance, preferring instead to make pseudo-statements about past data, such as implying model probabilities are for already-observed data. Most statistics is hit and run.
The elephant in the paper is global warming—please don’t say “climate change”—and the hints are that the 16-month streak was caused by it. Maybe so. But we learn zero about this theory from the non-causal statistical models used. Are the “trend” non-causal models really like the actual changes in physical causes (which are supposed to be linear) due to global warming? Who knows? The models themselves can’t tell you, nor can pseudo-probabilities about already observed data derived from them.
Indeed, the authors, all smart, well-employed statisticians, are too clever to outright claim that it is global warming which caused the observed streak. But they’re just political enough to leave the implication that it did hanging in the air.
Haven’t used the term “climate change” since certain malcontents went after Fox News for using “global warming”. I decided to go with “global warming” everywhere. It was interesting that when I one time explained that climate change, as used, is absolutely global warming because without the warming, there would not be the climate change if you believe the model. One guy said it was good I knew the difference and completely missed that if you are claiming climate change is due to humans, you ARE claiming global warming is happening. Sigh….
About not using past data: I understand that just because something happened in the past does not mean it will in the future. However, can data from the past be put into the model to see if it correctly predicts the outcome of a series, provided the data is chosed from a random section of the temperature record? Does the ability to backcast have any effect on the ability to psychic—oops, no statistically model the future. I do understand that the accuracy of the prediction can only be verified at the completion of the time period included in the predicition (requiring that global warming scientists grandchildren come up with excuses in 2100 for why the predicitions failed, assuming we don’t keep pushing the predictions further and further into the future, kind of like Obamacare!)
Your enemies strike again. “say it is low, and conditioning on a couple of other M, say it not low.”
If you take a thermodynamics course you will learn that temperature is an intensive parameter and does not scale. Average temperature is physically meaningless.
I think “backcasting” is just a fancy word for predicting the training data with the model. A model that doesn’t do well on the training data is likely a poor one but conversely a model that does well on the training data is likely an overfit that will not do well on future (unseen) data hence “Statements of how well your M ‘fit’ the observed data are not interesting”.
Average temperature is physically meaningless
But the number you get from a thermometer is an average temperature. When you say the room in 72F what do you mean other than it averages to that value?
You have ruined me. Today, I understood every word of what you wrote, whereas five years ago, I wouldn’t have understood much, if anything, of the same piece.
I can still vaguely remember the long, hard slough towards having remarks like “the probability is 1” sink in. Which meant that a lot of what I previously ‘knew’ had to change before I could actively grasp its meaning.
And so nowadays I get annoyed when I see drafts of papers that say the equivalent of this: “The observed mean difference between Group A (15) and Group B (20) was statistically significant (p < 0.05)."
It now makes me crazy that I can't do anything about such language in such papers; that, if I took it out in edit, somebody else would just put it right back in. And it would stay in.
Nowadays, fewer of the words in scientific journals make sense to me.
In my youth, I thought the trend was going to be the opposite of that.
I have a point of contention, but first let me say that I agree with everything you say about models and prediction. It’s too easy to make a model that “fits” the data. In many cases, I don’t see statistical modeling as much more than mathematical question begging.
My contention is how you treat their questions of probabilities of outcomes (in this article and others you write).
You say:
“They wanted to know the probability this could happen. As above, given that we have seen it, the probability is 1.”
I think that misrepresents what the authors were really doing. I have only recently become aware of your site, and have been greatly enjoying it as I go through the classic posts. It has taught me a lot (and I thank you for that)! I bring this up because I see you make these kinds of statements about the mindsets of authors of papers fairly regularly, and I find them disingenuous. I do not mean to imply malice or ill intent in saying so. In fact, I completely understand how frustrating it is to see people speak that way, because it indicates a poor mindset about statistics and probability.
I myself have gone from Frequentist to Bayesian thinking, and I remember when I would make statements like the above. However, I know with certainty that I never meant them in the literal manner that you seem to imply. I believe that this applies to most people as well. I will start with the paper in question here, then make some general statements to illustrate this.
Given what was done in the paper you discuss, their (the authors) question appears to actually be “From a set of M’s, which M is more likely to produce the observations we have?” Then they make some statements about the M’s and what they might imply. It does not look like they were asking such a basic question as “did we see the data we saw?”. Of course they saw that data, and they admit as much.
You also say: “Conversely, we do not need M to give probabilities of anything that already occurred. That would be silly.”
It would be very silly! Again, I think you’re treating their work as operating in one direction, whereas I think it’s fair to say that they are operating in a different direction. They are, as it appears to me, using the observations to give the probabilities of the models.
We might even be able to say that they are implicitly using a proportional form of Bayes’ Theorem where: P(data|model) ~= P(model|data), with P(data) = 1 (since we saw it), and the proportionality because you really can’t quantify P(model). What is left is a fuzzier comparison of P(data|model) to represent P(model|data). This formulation matches the steps they took, as well as their discussion of the conclusions. There are certainly issues with using the procedure I described, but I think that they implicitly used that procedure.
It is my general experience that no one really means to ask “what is the probability that X could happen (after I saw X)?”. To ask that literally is to start to fundamentally distrust observation! Rather, it’s generally a figurative shorthand that is searching for models and relationships that can repeat the observations (which I described in the particular case of your critique of the article). In other cases, it’s also used as a shorthand to ask about what existing models have to say about the outcomes seen (especially in terms of things related to gambling/die/coin flips).
Your writing is helpful in showing how silly the literal question is, and it is valuable for helping people (such as myself) really understand the distinction at play here, but I do think it disingenuous to make statements that people might mean it literally.
When I dip back into my experience I realize what the question I was asking was really trying to ask, and I know how I can phrase it better. The authors of this paper (and authors everywhere using probability and statistics) need to phrase it better. The whole pedagogy needs to be better about it!
To summarize, I think that when you say “They wanted to know the probability this could happen”, what should really be said is “They said they wanted to know the probability this could happen, but their actions show that they are really searching for the probability of the models being correct. This is a common problem with statistical shorthand language.” The rest of the article is pretty much the exact same after that!
If I have committed the error I have accused you of (of misinterpreting a statement without applying a reasonable benefit of the doubt), then I do apologize. Even if that has occurred, I hope that what I wrote is at least useful for the future in categorizing what people are really looking for in their papers.
TL;DR:
It is problematic to assume that when people appear to ask for P(data), that they mean it literally. They are probably really asking for P(data|some model) [such as what a fair coin flip model has to say about some outcomes we just saw], or P(model|data) [in order to focus further learning, detect trends/patters, etc.]. This is borne out by the steps people take after asking the apparent P(data) question.
Overall, solving this problem requires improved pedagogy, but we should give people the benefit of the doubt and try to lead them to a better understanding of the distinction between what they say and what they mean.
I notice that DAV has a very short version of what I was trying to say. The overfit/underfit problem is one that complicates the relationship between P(data|model) ~= P(model|data), and great care must be taken to avoid over-fitting, maintain validation data vs training data, and to also have prediction data set aside.
DAV: When I say the temperature of a room is 72 degrees, I mean it’s 72 degrees where the thermostat sits. I have half a dozen thermometers throughout my house and they rarely all match.
What I mean by “backcasting” may not be what the term actually means. What I am asking is not exactly “training data”, but rather say 30 year temperature sets, chosen at random by a nameless, faceless undergraduate who has no idea what they are being asked to provide, fed back into the model and then another nameless, faceless undergrad says “Yes you succeeded” or “No, revise the model—without the additional data, so you are not modeling to the data instead of the reverse—and try again.” Kind of like a double blind taste test. This would force the modeler to re-evaluate his model and look for factors he may have missed, rather than modeling to the data.
These kinds of studies are incestuous, with all parties having carnal knowledge of input and desired output. A scrupulous, virtuous, ideal, double-blind, very unlikely study would:
1. Collect historical data set and call it the ‘target set’.
2. Develop theories of causative factors.
3. Collect historical data of causative factors and call it the ‘causative set’.
4. Submit theories and, say, half the ‘causative set’ to second party for development of a mathematical model. This party is kept completely ignorant of the ‘target set’. However they must have good knowledge of the interaction between the causative factors.
5. Give a third party the model and the second half of the ‘causative set’ to generate an ‘output set’.
6. Give the ‘target set’ and ‘output set’ to statisticians for analysis. They will get two sets of numbers, and will not know what the numbers represent, nor will they know which set is which. (Perhaps it could be you, and you could charge big bucks to simply look at the data for 10 minutes to determine if there might be some correlation or not. )
7. Repeat steps 2-6 with new theories and new ‘causative set’ data until either the money runs out; or they run out of impartial second and third parties; or the heat-death of the universe results in a very, very linear ‘target set’, and so a very, very simple mathematical model.
8. Profit!
When I say the temperature of a room is 72 degrees, I mean it’s 72 degrees where the thermostat sits.
Yes, of course but its the number is really the average temperature within the thermometer — just a smaller volume than the room. No average (I could be wrong here) is “physically meaningful”. Doesn’t make it useless.
What I mean by “backcasting†may not be what the term actually means.
What you are describing is a Leave N Out approach. I don’t think this is what is meant when a climate model is backcasted. I asked Gavin directly once if the models were tested by this approach but he never answered the question.
If the held out data are used for model selection then effectively the held out data become part of the training set even when perhaps not directly used to set the parameters. Another approach is to have two hold out sets. One for validation and the other for testing.
The hold-out approach is likely the best one can ever do. It is as close to collecting more data as one can get. It won’t overcome bias generated during collection but then neither will waiting for more data if the collection process is faulty. If the process is biased you will never know until you find something that doesn’t fit — which could take a very long time.
DAV: I don’t think it’s an average. I think that it is measured at one point, or at best several very, very nearby. They measure changes in the expansion of the air which I suppose you can call it an average if you use a tiny sample just around the thermometer. Maybe. (I don’t know if every average is not physically meaningful, but it seems the majority are. Unless the data is very similar, and even then I’m not even sure an average is useful. (I dislike averages. They are too useful for hiding data and making improper leaps of logic and prediction.)
Noted: “Leave N out”. Thank you. I would bet climate science does not use this. The “held-out” method is probably better than nothing, but with the track record of global warming, it’s hard to believe any validation is actually being undertaken.
Briggs:
Time series are useful when events take place over time. But events that take place over time don’t necessarily have to be plotted against time to discover relationships.
If you have a hypothesis that some change in X causes some change in Y, do a scatter plot of X against Y. And as you often say, just look at the !@#$!#-ing thing and let your eyes tell you something about what might be going on.
From first principles, the theory of anthropogenic global warming is:
1) Any physical body which absorbs energy from another source rises in temperature.
2) The body’s temperature will continue to rise until it is dissipating energy at the same rate as it is being absorbed from the source.
3) Temperature cannot rise above, or remain higher, than the point at which it is dissipating energy at a faster rate than it is absorbing.
4) If the energy received increases or decreases, the temperature of the body will rise or descend respectively until the body is again dissipating energy at the same rate it is recieved.
5) All else being equal, a more massive body will change temperature more slowly than a less massive one.
6) Given a constant rate of energy absorption, anything which decreases the rate at which the body can dissipate energy will cause the body to rise in temperature until it is again dissipating energy at the same rate it is absorbing energy.
7) The sun transfers heat to the earth via electromagnetic radiation, where it is then absorbed.
8) The earth can only dissipate absorbed solar energy by emitting electromagnetic radiation back out to empty space.
9) The net rates at which the earth can absorb then emit electromagnetic radiation determines its equilibrium temperature.
10) Solar output varies, therefore affecting earth’s equilibrium temperature independely of any changes to earth.
11) Changes to the earths rate of absorption and/or rate of emission change earth’s equilibrium temperature independently of any changes to solar output.
12) 10 and 11 combime in net to determine the earth’s equilibrium temperature.
13) The earth is massive enough to cause “inertia” in reaching its equilibrium temperature.
14) Earth’s emissivity/absorbtivity properties change over time chaotically in response to orbital parameters, continent and sea surface location and albedo, atmospheric conditions, etc.
15) Time scales for 10-14 range from very long to relatively short periods of time.
Some of these things are time-dependent. It takes time for the tea kettle to boil. If you turn up the burner, the kettle will whistle sooner than if you had left well enough alone. If you turn down the burner a smidge, it won’t boil as quickly. There is some point at which a given burner setting will not boil the water.
If you turn the burner completely off, the temperature of the water will fall until it reaches the ambient temperature of its surroundings. As well, the burner heat and the heat of the water in the kettle will also affect the temperature of the air in the room. More so in a smaller room that is sealed off from the rest of the house, less so if the stove and kettle are sitting in a blimp hangar.
The sun is not in the same room as us. There is no air in space to conduct or convect energy from the sun to us, nor from us to anywhere. Radiative transfers are it.
All these parameters change over time. Temperature goes up and down. Climate does change. But we can’t turn down the burner if things get too hot for our liking.
If there is something, anything “happening” — natural or not — that affects the average rate at which the earth is able to radiate energy, the earth has to, must, by all the laws of known physics either heat or cool to meet that new equilibrium point.
Pick any 10 years of global temperature data, make that the Y axis. For the same 10 year period, pick any other measurement of anything you like — OTHER THAN TIME ITSELF — and use that as the independent variable on the X axis.
Look at it.
Do a least squares linear regression if you’d like. Calculate the Reynolds coefficent of correlation if you’re curious. Wave a dead chicken over it and mutter whatever Baysian or Frequentist incantations you’d like. All of the above if you have time.
Whatever you do, for the next step of this experiment, don’t change anything from the first step except what you choose for X.
Then move time periods around. Pick one or two years prior to or after the first time period you chose, but plot all the same Xs against temperature Y as before.
Then vary the time scale. Do 10, 25, 50, 100 years. Shift those around from decade to decade.
I myself has gone back 400,000 years with every chunk of data I could get my grubby paws on. Time-series plots and scatter plots both. So that I would know that I had looked at everything I could think of to look at within the limits of my knowedge of statistics. Which is meager.
Which is why I love you when you say, “Just look at the graph.”
In summary, it would seem that Craigmile et al. are comparing a null hypothesis “average temperature (whatever that is) not changing” with an alternative hypothesis “[upward] temperature trend” finding that the data likelihoods disfavor the null hypothesis. This is not a good argument in favor of an upward trend, since other alternatives — baseline shift, square-wave type variation, or long-period sinusoidal variation, for example — work as well or better. Without some concrete reason (more than hints) motivating the need to explain the 16-month streak in any terms other than “s**t happens,” this straw-man comparison is sophistry.
An “average temperature” or “mean temperature anomaly” as seen in “climate science” is unphysical but does not have to be physical in order to be useful — it is just an index number hoked up from physical measurements, and it could be studied and commented on just as meaningfully as, say, a stock price index. The problem is that (unlike a stock price index) the basis for calculating the temperature index varies from author to author and year to year, so it is hard to take it seriously.
I found a graph of temperature anomalies versus time that was labelled on the x-axis:
“temperature variation from arbitrary baseline”.
It was produced by the national space science and technology center. That was probably the most honest labelling I have seen.
Sheri: “I found a graph of temperature anomalies versus time that was labelled on the x-axis: ‘temperature variation from arbitrary baseline’. It was produced by the national space science and technology center. That was probably the most honest labelling I have seen.”
Amazingly enough it does happen from time to time. That’s why I look at what the data are telling me instead of what the language is saying.
Speaking of data, what was the Y axis measuring?
Brandon Gates has made a point, if I understand his comment correctly, and as Briggs implied in his opening paragraph. Without solar radiation data, all the other physical data, solutions of the non-linear differential equations governing heat transfer, etc., etc.,all any predictions are nonsense (see what Richard Lindzen, who holds an endowed chair of Meteorology at MIT has to say about all the global warming foolishness).
Bob: You understand me correctly, though it wasn’t my main point. It is true that without the physical data, a lot of it, plus a bunch of calc, we’d have a snowball’s chance in 2500 of understanding what really might happen until we got there. All that data and math mean diddly squat without underlying principles to help us understand what the output of our data gobbling algorithms mean.
I do know what I think is going to happen. My little screed is nothing more than an experimental protocol that roughly summarizes how I got there. I don’t have the math Briggs does, though, so this is me asking him to make some plots in the way that I’m used to looking at them when I’m doing my own research, and apply his statistical knowledge to it.
But I don’t want bias him, or anyone, any more than I already have. So I’ve not drawn any conclusions about what he, you, or anyone else will find. Only my understanding of underlying theory, and a suggested process for playing with whatever data they can dredge up.
I insist on no time series plots for this experiment. Just once I want to see a scattergram. Gracias.
I spent a way to much time trying to explain to a warmish that no model can predict the future and anyone claims it possible was a fraudster. I got back a nice lecture about how weather is not climate you cannot predict weather but you can climate after all Gavin said it possible. I just wish when I tell someone the financial firms tried to model the stock market they gave up because it a waste of money, why cannot these morons understand the stock market is just like climate. Every time a finical company give figure on one of it funds they are required either by law or their legal team to put in the disclosure past performance may not reflect future performance. To bad the climatologist aren’t require to disclose the same thing. Oh I all ready know the reason if they did they would not be able to continue wasting taxpayers money.
Brandon: The years 1979 to 2010.
Bob: Lizden may make sense, but internet courses from MIT on climate change are sadly lacking in such skepticism and a lot of other things.
Mark: The reason we can’t predict weather but we can climate is all the nifty math and physics. See weather is just such a short period we can’t introduce radiative balance, how the earth absorbs radiation based on the area of a circle, but emits over the surface of sphere, we can’t average, run multiple statistical analysis, throw out the data we don’t like or alter it slowly over time to make the past look colder, we can’t throw out the Medieval Warming Period or the Little Ice Age. Weather consists of forecasting a week at best, and can be immediately shown to be right or wrong. There is a misconception that the reason climate can be predicted is more data yields better results. Or that’s what the warmists say. So not true. (Note than in the case of your financial company, results are quite immediate. What really determines the certainty of a forecast is if the persons making the predictions will be around when the prediction is due to happen and whether said persons can be held accountable. In finances, Bernie Madoff managed to fudge data and make millions, but sadly could be held accountable and went to jail (sad for Bernie). Maybe that’s why periodically you read of the IPCC and climatologists trying to get immunity from prosecution concerning their prognostications.)
Sheri: “The years 1979 to 2010.”
I apologize, my original question was due to a reading comprehension fail. I understand that the graph is a timeseries of temperature.
Choosing a baseline period is inherently arbitrary, except when it is not. When not arbitrary, it is not necessarily nefarious. That doesn’t mean it isn’t.
We agree that stock markets are not predictable. At all. I understand the analogy, but I it doesn’t necessarily follow that one must be like the other.
Brandon: They appear to have been using the 30 year period immediately preceeding the graphing of the data. The thirty year period is common, but not always used. As noted, it is arbitrary, except when it’s not. Personally, I find 30 years to be a very short period.
While it may not necessarily follow that predicting the stock market is not like climate science, there are similarities. Both depend on using past performance to predict future behaviour, though the stock market uses a legal disclaimer saying that the past performance does not assure future predictions, which global warming does not. Both involve trying to predict the future. Neither succeeds very often.
No average (I could be wrong here) is “physically meaningfulâ€.
Yes you are.
Ironically the temperature is precisely defined as being the average of the energy distribution of molecules in a small volume dV. An average as physically meaningful as you can get.
However as far as (all) equations of dynamics go ( f.ex M.d²x/dt² = F) there are never any averages that appear. Here M, x and F are all local instantaneous variables which have all a physical meaning.
Obviously solving for x(t) in this example, one can later compute all kind of averages which may have interesting properties.
But properties of averages are always derived from the local and instantaneous natural laws they don’t belong to first principles.