https://i.ibb.co/gD01GqN/temp-By-Pres2019.png ]]>

I just realized that 3/4 Democrat outliers can be “explained” due to serving a partial term. These are also the only presidents running as Democrat to serve a partial term during the period we have temperature data for:

Truman: Succeeded when FDR died

Kennedy: Died in office

Johnson: Succeeded over when Kennedy died

That leaves only one exception:

Wilson: Two full terms

Ben:

“Theory predicts more support for Democrats when the rooms are lower in temperature,” but if we saw the opposite pattern, or any interaction whatsoever, that would be consistent with the theory too!

]]>Measure perceived warmth on a scale of 1 to 10 and divide the sample into bins based on various cutoffs.

See which cutoffs best fit the data. Test 1 to five different cutoffs.

Ask about political alignment using a lef/right scale from 1 to 100. Bin the sample by cutoffs using a similar technique to determine the best cutoffs.

You increase power when you try more cutoffs because you will identify the most powerful cutoffs.

]]>Thanks. I’m tempted to write this up and shop it around :)

]]>Fantastic! We can do a between subjects design where the undergrads are placed into different temperature rooms, then they watch a mock political debate between a Democrat and a Republican and identify which they like better. Theory predicts more support for Democrats when the rooms are lower in temperature. We can double our sample size by combining students from both psychology and political science courses.

But, we should also test to see if the perceived warmth or coolness of the debate host has an affect on the significance of the temperature effect. Implicit social cognition theory predicts that we might have a moderator named “moderator”.

]]>Yes, global effective radiative temperature means something totally different than global time averaged mean thermometer reading. I believe most climate data is thermometer readings but that the published global temperatures are estimates of the effective radiative temps calculated from a model incorporating a wide variety of data including thermometer readings, but this means the timeseries you are using is *nothing like* a direct measurement it’s the output of a model with tons of assumptions built in.

]]>What matters here is radiation and energy balance. If you can compute it with a huge array of thermal cameras in space without ever taking a ground level thermometer reading then that’s a good thing.

I agree, but that isn’t where this data comes from. They actually want to be measuring total energy content.

Anyway “global temperature” seems to have (at least) two different meanings then, or the current instrumental record measures something different with the same units. Was this your original point in asking what it means?

]]>RE size if object, in this model it cancels. The size of the object could matter in other models.

Re what’s meaningful. The radiative equivalent temperature tells us about the process of interest, the thermometer readings are indirect measurements that can inform estimates of the quantity of interest, but people often make the mistake of focusing on the measurements as if they were the actual thing of interest. This is in no little part due to Frequentist concepts of measurement as RNG output. What matters here is radiation and energy balance. If you can compute it with a huge array of thermal cameras in space without ever taking a ground level thermometer reading then that’s a good thing.

]]>Democrats are perceived as warm and tend to favor change. Republicans are perceived as cold and tend to favor stability. Thus, after a period of cooling or stable temperatures, the voters are eager for warmth and choose Democrats. After a period of noticeable increases in temperature, the voters are eager for a return to stability and a cooling down, and vote Republican.

This is too perfect.

]]>Ben:

Do an experiment on some undergraduates and Mechanical Turk participants, and you got yourself a Psychological Science paper. Put in some differential equations and a power law, and you’re ready for Phys Rev E, or Science/Nature/PNAS, or, failing that, Arxiv and publicity in Technology Review.

“A possible theoretical explanation for political instability”! Damn, that title’s already taken.

]]>Democrats are perceived as warm and tend to favor change. Republicans are perceived as cold and tend to favor stability. Thus, after a period of cooling or stable temperatures, the voters are eager for warmth and choose Democrats. After a period of noticeable increases in temperature, the voters are eager for a return to stability and a cooling down, and vote Republican.

Who wants to be my co-author?

]]>What model of reality provides a mechanism by which Democratic presidential administrations in the USA make volcanoes erupt?

I suppose one could imagine a way in which El Nino tilts the election toward Democrats? Maybe we should postulate a reverse causal relationship: flat temperatures benefit Democrats in elections, and rising temperatures benefit Republicans!

]]>Thanks for the correction. I was going from memory.

But the hypothesis is so great that being 180 degrees wrong is no problem. Just reverse that sign and another sign somewhere else and we are good to go!

The hypothesis is so great that it produces truth no matter what the facts are. Garbage In, Truth Out! GITO!

]]>Yes, the main physically meaningful number here is the SBlaw(mean(Irrad)), That’s the one that tells you what temperature the uniform black-body radiator the size of the earth needs to be at in order to radiate the same amount as the actual radiation.

I don’t think the size of the object matters.

The other mean(SBlaw(Irrad)) tells you what numbers the individual local thermometers average around

It seems to me this is what is actually being measured by the various weather stations, so therefore that is the “physically meaningful number”. If we want our theoretical “global average temperature” to match with what we are measuring, we need to calculate the same thing.

]]>Terry:

Silly they may sound, but link them up with Gladwell, NPR, Ted, PNAS, etc., and they can get lots of publicity and influence.

]]>Terry wrote, “Volcanic eruptions increase global temperatures (this has the advantage of actually being true).”

No, it is actually false. The big volcanic eruptions (Pinatubo 1991, cooling trend 1992) produce a short-term global cooling trend due to injection of sulfate aerosols into the stratosphere. These aersols reflect more sunlight back to space rather than being absorbed at the surface for warming. Fact: The climate computers modellers have to tweak-in higher than observed sulfate aerosols to cool their model runs when studying the past.

]]>I agree. It is easy to make up silly hypotheses, and I don’t think any of these rise above the silly level. That is my point. Making up silly hypotheses doesn’t move us forward. Indeed, the more you think about them the sillier they sound.

]]>One of the real advantages of doing this more explicit smaller scale model is that you can actually run Bayesian posterior distributions over the 5 or 10 parameters, and see how the various effects work relative to each other in terms of contributing to the uncertainty in climate response.

]]>Yes, the main physically meaningful number here is the SBlaw(mean(Irrad)), That’s the one that tells you what temperature the uniform black-body radiator the size of the earth needs to be at in order to radiate the same amount as the actual radiation.

The other mean(SBlaw(Irrad)) tells you what numbers the individual local thermometers average around, but the hotter ones obviously radiate a lot more and the cooler ones radiate a lot less due to the T^4 law which is why these numbers are so different (144 vs 260 K)

The other bit is that we really want not what is the surface radiation, but rather what is the radiation to space, so for example you could look at the earth from the moon, and measure its radiative brightness like by taking an IR photograph of it… and do this from many angles, and at each point above the surface of the earth, discover what the radiative quantity is there…

the difference in the radiation as seen from the moon and the radiation as measured at the surface is in essence the “greenhouse effect” as some surface radiation is absorbed and converted to kinetic energy in the gas, and some re-reflected back to the earth, etc.

So with all that said, ElNino probably does change the temperature of the gas, and surface, and hence is somewhat of a signal, but *it also violates the equilibrium assumption* as now you could be radiating *more* heat than the solar influx (since you’re basically bringing heat out of the deep ocean) and during LaNina you violate the equilibrium assumption as well because you’re storing heat in the ocean.

So one way to think about this is as modeling error: your assumption is on a relatively short timescale, like a month or so, there is zero net energy put into or taken out of the earth. That’s *how you define your effective temperature* and then, you try to use this equilibrium model to discuss a situation in which you’re explicitly violating that assumption by having heat storage over time scales from decades to millenia (in the ocean, ice pack, etc).

In the past I’ve said that I’m not in favor of the current fad for Global Circulation Models, and would prefer people spend more time on this kind of model, adding 5 or 10 known important effects and estimating coefficients for those, and try to describe the climate with just these 5 or 10 unknowns instead of a GCM which might literally have a million.

]]>Well, the *observations* aren’t affected by nearby observations, but the *estimates* / (or output of the “predict” function) are. However in the basis expansion method we’re choosing the function that *globally* minimizes squared error (at least when we do least squares, in a Bayesian analysis you get a distribution over possible functions). What happens is by limiting the number of coefficients we limit the degree of “detail” that can be in the function’s we’re considering. In a Bayesian analysis we can put strong priors on the magnitude of the higher order terms thereby getting a more continuous version.

So yes, it uses global information to estimate each value, that’s why it’s so powerful, but no, it doesn’t shift the information forward or backward in time, like you would with say an exponential weighted moving average of the past (which shifts your estimates backwards in time)

]]>This seems like it side-steps the issue. I would want to know why the “experts” are ranking/voting the way they did. What principles are being used to determine what looks interesting?

]]>The hardest part for me is believing that the stance of the two parties has been consistent enough on the relevant position since 1880 for any of these explanations to really work (including my “farmers voting for subsidies” one). Maybe I underestimate how consistent the positions have been on certain tariffs/subsidies/whatever though.

But anyway, I definitely do not feel inspired to go dig up info on all these putative intermediate mechanisms to see which would survive. However, I still don’t get exactly what rule I am using that makes me act/think/feel that way about this correlation.

]]>unfortunately, it being a nonlinear equation, you can’t get the effective temperature by averaging the effective temperature of each piece of the earth… You need to integrate the total radiation over the earth, and then take the fourth root of that…

I think ideally they would have stations uniformly sampled over the surface, using the R geosphere and rworldmap packages I checked what 100 stations would look like: https://i.ibb.co/cCvtZJ0/Station-Map.png

Each station never moves over the course of the observations and the instruments are always perfectly calibrated. All the “adjustments” to the data are attempting to make it more like that.

Then the mean and equilibrium/effective temperatures would be calculated like this: https://pastebin.com/b1YJFxJ6

> # Mean Temperature (K)

> mean(SBlaw(Irrad))

[1] 143.9252

>

> # Equilibrium Temperature (K)

> SBlaw(mean(Irrad))

[1] 260.0704

The “mean” temperature is what we would expect to *measure* “without an atmosphere”, and of course at any one time the blackbody temperature will be zero over half the globe unless we give the surface a heat capacity.

I don’t see an overall mean temperature measured for the moon but this paper reports averages 215.5 K at the equator and 104 K at the poles, so it must be between those values. So I think this value is ok:

The mean temperature at the equator (◇) is 215.5 K with an average maximum of 392.3 K and average minimum of 94.3 K (arrows show range between average maximum and minimum Tbol). The mean temperature of the polar regions poleward of 85° (○) is 104 K with an average maximum of 202 K and average minimum of 50 K

https://www.sciencedirect.com/science/article/pii/S0019103516304869

The temperature of the earth based on the measurements is obviously more like 288 K, meaning surface and atmosphere effects account for ~150 K worth of “greenhouse effect” and need to be added to the model. Obviously the night side doesn’t cool to zero as soon as it is out of the sun, etc. Once we have defined that model then we know exactly what the “global temperature” actually refers to.

]]>Thanks for the correction.

On a more general level, though, does this transform mean that an observation at time t is affected or transformed or altered in some way by nearby observations? Do we know that such a transformation doesn’t subtly affect a time series analysis?

]]>Basically in an asymptotic analysis we can drop the Absorption because we can make the whole thing dimensionless by dividing by Influx, and then Absorption/Influx is small, this gives a good way to estimate the approximate size of Radiation(T_e) and therefore T_e but it is very slightly off. However you can perhaps put some kind of bounds on the rate of absorption, so that Absorption/Influx is known to be less than some number, just throwing a random number out there let’s say it’s 0.002 then you’re going to find that the bias caused by ignoring absorption is quite small. so for the moment we’ll leave it at that.

Additionally there’s an error in the typesetting of the equation, equation (1) should have T^4 which is where the T = (…)^(1/4) comes from.

unfortunately, it being a nonlinear equation, you can’t get the effective temperature by averaging the effective temperature of each piece of the earth… You need to integrate the total radiation over the earth, and then take the fourth root of that…

The physicists working on these issues know this stuff, but it’s not always obvious what’s going on “under the blankets” when you get some time-series from a website.

]]>So it’s “effective radiating temperature” in other words (I think) the temperature of a black body the size of the earth (say sea level radius) that radiates the same total energy to space as the earth does.

I have one problem with their assumption there which is that “determined by the need for infrared emission from the planet to balance absorbed solar radiation”

In the bulk it must, or we’d have RAPID rise in temperature. But to second order we’re talking about trapping energy from the sun and warming the planet, so it should be modified so that the solar influx balances the radiation + absorption.

Influx = Radiation(T_e) + Absorption

Unfortunately, the Absorption is itself the thing we’re most interested in, and it’s not directly measurable, and neither is the effective radiating temperature, so the problem is inherently unidentified as the right hand side of the equation is the sum of two Bayesian parameters.

We can partially solve this by finding ways to estimate absorption and estimate radiation, and thereby come up with tighter posterior intervals, but we’re not going to eliminate this entirely.

]]>No, this isn’t a moving average, this is a basis function expansion of the time series. In the fourier case, the high frequency terms are truncated to zero, but there is no phase shift. In the Chebyshev example it’s slightly different, a Chebyshev polynomial *is* a Fourier expansion of a transformed version of the problem. But it still is an orthogonal basis, so truncating the higher order terms doesn’t really affect the values of the coefficients of the lower terms.

]]>I can’t resist telling the joke my lawyer cousin once told:

Question: Why didn’t the shark eat the lawyer?

Answer: Professional courtesy.

]]>The downside of smoothing is you are screwing up the timing of the data and timing is critical here.

If you impose a 10-year moving average, what year do you assign that average to? Your choice could easily reverse the results. Your choice could shift some of the temperature data up to 10 years. You could easily introduce spurious ESP into the sample where you include temperatures from year t+9 in your calculated temperature at time t.

]]>+1

]]>Hypothesis number 5:

Volcanos! (Volcanoes?)

Volcanic eruptions increase global temperatures (this has the advantage of actually being true).

Voters vote for Democratic presidents following volcanic eruptions because … reasons!

]]>Hypothesis number 4:

Republicans are good for the economy and Democrats are bad for the economy. (Not empirically true, but that hasn’t stopped us so far.) The economy revs up under Republicans and energy usage increase causing a increase in greenhouse gasses and an increase in temperature. But the increase is lagged so the increase in temperature occurs during the next administration and voters get tired of having one party in power so they like to switch parties from election to election.

]]>Hypothesis number 3:

When temperatures drop, crop yields and farm profits fall and the economy slows down. Voters tend to hold Republicans responsible for the economy but not Democrats. Temperatures are mean reverting to the trend. So when temperatures temporarily drop below trend, Republicans are replaced by Democrats and the rebound occurs during a Democratic administration. The same does not happen to Democrats because … reasons.

]]>Hypothesis number 2:

Changes in budgetary priorities means less money is spent on maintaining weather instruments in Democrat administrations and so the instruments read higher than they should (dirty housings are darker and so increase internal temperatures). During Republican administrations, the instruments are cleaned better and so temperature readings drop. Need to make up a reason why Democrats want to spend less on instrument maintenance than Republicans do … shouldn’t be hard.

]]>“What is number 1?”

Good challenge.

How about the data is manipulated where a Democratic administration, at least implicity, pressured record-keepers to report higher temperatures. Someone else proposed this, or something very like it elsewhere. Or the inverse that a Republican administration pressures record-keepers to depress temperature readings and temperatures rebound after a change in administration.

]]>I think what they *want measure is defined here: *

Climate Impact of Increasing Atmospheric Carbon Dioxide. J. Hansen1, D. Johnson1, A. Lacis1, S. Lebedeff1, P. Lee1, D. Rind1, G. Russell. Science 28 Aug 1981: Vol. 213, Issue 4511, pp. 957-966 DOI: 10.1126/science.213.4511.957

https://climate-dynamics.org/wp-content/uploads/2016/06/hansen81a.pdf

T_e = [S_0(1 – A)/4*sigma]^0.25 + gamma*H

S_0 = Mean solar insolation = 1367 W/m^2

A = Mean proportion of solar radiation reflected back to space = 0.3

sigma = The Stefan-Boltzmann constant = 5.670367(13)e-8 W/(m^2⋅K^4)

gamma = Mean lapse rate of the atmosphere = 5.5 C/km

H = Mean distance from sea level to the tropopause = 6 km

All averages are over the course of a year and the entire surface.

]]>Sure, maybe. If someone can tell me what the actual physical quantity that “Global Temperature” is supposed to approximate, then I’d have an idea of whether El Nino is a “real” signal *in the Global Temperature* data or is in fact noise.

Like for example, suppose “Global Temperature” is C/N * sum(K[i],i,1,N) where K is the kinetic energy of all molecules not currently residing in a solid substance at altitudes greater than 10 meters above mean sea level

Then is ElNino signal or noise? Reading the wikipedia article it looks like ElNino would be signal caused by energy transfer out of the deep ocean into the surface layer of ocean and then the atmosphere.

But if you defined Global Temperature in terms of the sum of kinetic energies of all molecules in the ocean + atmosphere, you’d have to call it measurement noise because heat coming into the atmosphere is coming out of the ocean.

So, at its heart, we have a measurement issue first. Tell me what “global temperature” means.

]]>Wins thread.

]]>THAT’S IT!! because there are no longer any Republican scientists, Global Temp is on the rise!

]]>No, I think this was just a politically charged topic. Suppose instead of global temperature it had been global Coffee Bean yield? No one would be getting their undies in a twist and would instead be discussing the question of how you can determine if something is “real” vs a spurious correlation.

]]>IID normal noise has Fourier spectrum that’s flat out to the full Nyquist bandwidth. The smoothed data has Fourier spectrum that rolls off at some intermediate frequency. If the underlying data doesn’t have “real” variation above some frequency, then the smoothed version will be eliminating mostly the IID noise.

So, there are situations where smoothed data should be expected to better represent reality, when your measurements literally have algorithmic and measurement error that dominates the high frequency components.

Interesting, thanks. Thinking of how to tell if this applies to the current problem I realized that other people in the thread can apparently see the effects of short term volcanic eruptions and El Nino events (e.g, https://en.wikipedia.org/wiki/1997%E2%80%9398_El_Ni%C3%B1o_event) in this data.

So if the smoothing process removes/alters the signal from these “known” influences then it would be a step backwards right? I mean it may also remove “real” noise but if it is also removing signal that is bad.

]]>Is this getting dangerously close to admitting the correlation is probably spurious?

As mentioned in the OP, a “spurious” correlation can still be “real”, it is just that a third factor C explains the relationship and there is no causal connection between A and B. That is different from: “if you look at enough data you will eventually find a correlation and even if you personally didn’t look someone else looked so we need to adjust our p-value for that”. Multiple comparisons adjustments never made sense to me for exactly this reason.

So what does making up goofy ad hoc hypotheses accomplish?

Please see my comment here for the role I give this type of activity in the scientific method.

I’m beginning to think we are being trolled. A very subtle and imaginative trolling of the highest order, I’ll grant you.

The only way I could be trolling is if I actually did data mine this correlation, which I didn’t (if I had it would have held zero interest to me). I can’t prove I didn’t, so there’s that. I could have (but declined to) easily had a career producing medical “discoveries” like that though if I wanted.

There are a thousand other ad hoc hypotheses we could have created, and this farmer hypothesis doesn’t strike me as being even in the top 20.

It took me awhile to come up with that one. What is number 1?

]]>“So if Anoneuoid wants to chase this down to his (her?) satisfaction”

Did you just assume Anoneuoid is binary? I can’t believe people are still doing this in 2019. That is so 2016.

]]>Is this getting dangerously close to admitting the correlation is probably spurious?

If you need a hypothesis as convoluted and tenuous as this, doesn’t that suggest there isn’t really something there and we are just making things up? The most direct causation model is the one everyone assumed (that’s why they assumed it). There are a thousand other ad hoc hypotheses we could have created, and this farmer hypothesis doesn’t strike me as being even in the top 20.

So what does making up goofy ad hoc hypotheses accomplish?

BTW, it hasn’t even been shown that there is anything statistically significant here. The temperature data is a complicated time-series with time-varying properties. The presidential data also has patterns. This seems like fertile breeding grounds for a spurious correlation. All you need is for one of the patterns in the temperature data to line up with one of the patterns in the presidential data. To take an extreme example, imagine that all the presidents in the first half were Republicans while all of them were Democrats in the second half. Since the temperature data is flat in the first half, it would generate a spurious correlation. All this needs to be statistically modeled … a very tall task.

I’m beginning to think we are being trolled. A very subtle and imaginative trolling of the highest order, I’ll grant you.

]]>I don’t know if adding smoothing represents reality better or not. But I imagine it should under certain circumstances. Specifically suppose that there exists a meaningful “true” global mean temperature. Suppose that we have an estimating algorithm for this quantity and it uses only measurements of various types from the year in question to get the value for the year in question. Now suppose that there is algorithmic error involved in the estimate that we can model as IID normal(0,s) for some scale s and that the underlying true temperature changes no faster than some rate R from year to year. Then the calculated rate of change:

t(n)-t(n-1) = a*R + normal(0,sqrt(2)*s)

for a in [-1,1]

whereas the smoothed version will be much closer to a*R

Try it out. Take the smoothed version you calculated with say 25 terms…. add normal noise to it of scale say 0.1 degrees C. Fit a *new* smoothing function to the noisy smoothed version. Compare the adjacent differences with noise and the adjacent differences in the re-smoothed data, to the actual underlying thing (the smoothed with 25 terms data).

IID normal noise has Fourier spectrum that’s flat out to the full Nyquist bandwidth. The smoothed data has Fourier spectrum that rolls off at some intermediate frequency. If the underlying data doesn’t have “real” variation above some frequency, then the smoothed version will be eliminating mostly the IID noise.

So, there are situations where smoothed data should be expected to better represent reality, when your measurements literally have algorithmic and measurement error that dominates the high frequency components.

]]>