Guest Post by Willis Eschenbach

I wrote before of my investigations into the surface air temperature records of the TAO/TRITON buoys in the Pacific Ocean. To refresh your memory, here are the locations of the TAO/TRITON buoys.

Figure 1. Locations of the TAO/TRITON buoys (pink squares). Each buoy is equipped with a sensor array measuring air and sea temperatures and other meteorological variables.

I have hypothesized that there is a thermostatic mechanism involving clouds and thunderstorms that maintains tropical temperature within a certain range. To investigate this mechanism, I decided to look at what happens at a given buoy on days when dawn temperatures are warmer than average, versus what happens at the same buoy on days when dawn temperatures are cooler than average.

My speculation was that when it was warmer at dawn, there would be more cloud and thunderstorm activity during that day. This would tend to drive the temperature down. On the other hand, when it was cooler at dawn, there would be less or no clouds or thunderstorms during that day. As a result, this would tend to drive the temperature upwards. And while I did find this, I was still surprised by the exact patterns.

To begin with, I compared the overall average of all days for each station with the overall average of the warmer days for each station, and the overall average of the cooler days for each station. Here are those results:

Figure 2. Average of all buoy records (heavy black line), as well as averages of the same data divided into days when dawn is warmer than average (heavy red line), and days when dawn is cooler than average (heavy blue line) for each buoy. Light lines show the difference between the previous and the following 1:00 AM temperatures.

First, the black line, showing the average day’s cycle. The onset of cumulus is complete by about 10:00. The afternoon is warmer than the morning. As you would expect with an average, the 1 AM temperatures are equal (thin black line).

The days when the dawn is warmer (red line) show a different pattern. There is less cooling from 1AM to dawn. Cumulus development is stronger when it occurs, driving the temperature down further than on average. In addition, afternoon thunderstorms not only keep the afternoon temperatures down, they also drive evening and night cooling. As a result, when the day is warmer at dawn, the following morning is cooler.

In general, the reverse occurs on the cooler days (blue line). Cooling from 1 AM until dawn is strong. Warming is equally strong. Morning cumulus formation is weak, as is the afternoon thunderstorm foundation. As a result, when the dawn is cooler, temperatures continue to climb during the day, and the following 1AM is warmer than the preceding 1 AM.

So this is the result that we would expect with a thermostat operating on a daily basis. If the dawn is warm, clouds and thunderstorms ensure that the following day starts out cooler. And when the dawn is cool, extra sun and few clouds and thunderstorms warm the day up, with the warmth lasting into the night.

Now … is this just a statistical oddity? One way to determine if we’re looking at a real phenomenon is the “dosage effect”. That is to say, the response should be proportional to the dosage. In this case, the “dosage” is the overall average temperature for that particular buoy. My hypothesis says that the effect seen above in Figure 2 should be greater in those buoys where the average air temperature is warmer, and less in those buoys where the air temperature is lower. And indeed, that proved to be the case, as is shown in Figure 3. This shows the buoys divided into four quarters (quartiles) on the basis of annual average temperature.

Figure 3. Differences between warm days (red line) and cool days (blue line) for the TAO/TRITON buoys divided into quartiles by temperature. Black line is average for all days.

Note that the response systematically grows larger and more exaggerated as we go from the first quartile (the coolest quarter of the buoys) sequentially to the fourth, warmest quarter of the buoys.

I hold these results out as strong support for my hypothesis that the temperature of the tropics is regulated by the combined action of clouds and thunderstorms. The difference in the temperature response of the warm and cool days shows the homeostatic mechanism in action, with warm mornings having cooler afternoons, and vice versa. All of this shows the clouds and thunderstorms at work.

I will ask again that if you disagree with something I’ve said, please quote it so that we both know what we’re discussing.

All the best,


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Bloke down the pub
August 25, 2011 3:58 am

Hi Willis, this all seems very sensible and reasonable. Just thinking out loud so be gentle with me but why on a graph of averages is the spread of temperature anomalies so much bigger at the end of the day than at the beginning. Surely the end temperature of one day is the start temperature for the next?

Carl Chapman
August 25, 2011 4:00 am

If days that start warmer end cooler, and days that start cooler end warmer, then negative is so strong that the only way there isn’t stasis is because of the delay in the feedback.
The strong negative feedback combined with the delay, producing more than 100% feedback after 24 hours, means there should be oscillation.
Can you do an analysis looking for an oscillation with a period of 24 hours? If what you say is correct, there has to be an oscillation, probably with a period of 24 hours, superimposed on the random changes.

richard verney
August 25, 2011 4:13 am

The way to go. Check observation and analyse and since there is not a computer model in sight, this will reveal much more about what is going on in the real world, rather than imaginations in the realm of cyber space.

August 25, 2011 4:13 am

Thanks Willis, I think this is a great analysis, and good support for your thermostat hypothesis.
It’s noticeable that for all buoys, the amount cooler the following dawn is after a warm start, is smaller compared to the amount warmer the following dawn is after a cool start.
Is that due to an overall trend in the data for the period of study?

August 25, 2011 4:29 am

Or two other inferences in a general sense from this–the warmer the earth’s oceans are, the more cooling takes place; the mechanism just happens to be cloud and precipitation formation (and the converse is true–when the earth is cool, it tends to get warmer since the cooling mechanisms don’t form). These relationships and mechanisms aren’t included in any of the computer models, are they?

Dave in Delaware
August 25, 2011 4:29 am

Very interesting results, and certainly the pattern is consistent with the Thunderstorm Thermostat speculation.
I wonder if the data would show a 48 hour cycle? A ‘red-line’ day starts warmer, ends cooler – would that then engender a ‘blue-line’ day? Is there some other cyclic pattern of X ‘red-line’ days followed by X or Y ‘blue-line’ days?
I am not aware of that sort of cycle pattern so would not necessarily expect a 48 hour cycle, but odd things sometimes appear out of a good analysis.
Wax on Wax off.

August 25, 2011 4:48 am

First, the black line, showing the average day’s cycle. The onset of cumulus is complete by about 10:00.
Please give me a link or blog where you have written of the ‘onset of cumulus is complete…’.
I wish to re-read your work. Thank you

slow to follow
August 25, 2011 4:57 am

Willis – I like the fact you are working in small steps on hour by hour data.
Please can you give some details on the total length of data set you are working with? From this page I’m guessing that you are using the total records from 1994 onwards – is this correct?:
I’d also like to know about the geographical clustering/distribution of the quartiles you have identified.
Thank you.

August 25, 2011 5:02 am

You wrote “I was still surprised by the exact patterns.” Yet it seems that the data analysis bears out your expectations. So what part of it did you find surprising?
What surprises me is that the end-of-day temperature seems to deviate further from the average than the start-of-day temperature. [In the opposite direction.] Naively, this would suggest an unstable cycle, which is patently incorrect. Can you comment on that?

Dave in Delaware
August 25, 2011 5:16 am

Predator – Prey in clouds
As posted at WUWT in July 2011, these guys were focused on aerosols, but certainly their predator-prey discussion would fit with a pattern of ‘red line’ days following (chasing? ::chuckle::) ‘blue line’ days. Perhaps their observed pattern is due to Thunderstorm Thermostat rather than aerosol cycles.
Koren and Feingold “found that equations for modeling prey-predator cycles in the animal world were a handy analogy for cloud-rain cycles: Just as respective predator and prey populations expand and contract at the expense of one another, so too rain depletes clouds, which grow again once the rain runs out. And just as the availability of grass affects herd size, the relative abundance of aerosols – which “feed” the clouds as droplets condense around them – affects the shapes of those clouds. ”

John S.
August 25, 2011 5:23 am

Carl Chapman said:
“The strong negative feedback combined with the delay, producing more than 100% feedback after 24 hours, means there should be oscillation.”
Yes, I’d like to see similar graphs done on a 48 hour time scale instead of 24.

August 25, 2011 5:50 am

If one is averaging the diurnal cycles throughout a year, which I believe you are doing but correct me if I am wrong, one needs to center the records on something like sunrise or sunset for each day, because the time of each varies through the year.

August 25, 2011 6:21 am

This is important work. Modelers need to recognize that the tropics are in an unstable zone and in which thunderstorm activity limits temperatures. If enough data are available, you could also plot a time series of lifted index and CAPE (convective available potential energy) to show how the tropical atmosphere bumps against the unstable regions.

Steve Keohane
August 25, 2011 6:37 am

Nice Willis, Thanks for your clear-headed work.

Steve Richards
August 25, 2011 6:44 am

Can this work be translated to land based measurements?
Monitoring stations measuring ground temperature, air temperature and cloud cover?
Checking the difference between arable/forest/city curves to see if similar effects can be discovered?

August 25, 2011 7:05 am

I think my Process Excellence (Allied Signal version) trainers would be pleased with your way of looking at processes- I know I am! I have found your use of Systems Theory concepts (“It is a self-organized emergent phenomenon. It is threshold-based, meaning that it emerges spontaneously when a certain threshold is passed.” with the nity gritty way of looking at the data to be enlightening.

August 25, 2011 7:11 am

I’ve just been looking at time-lapse satellite images of the western tropical Pacific for the past 24 hours (Aust BOM site). From what I could see there appears to be waves or clusters of cloud that migrate westerly, this may be evidence of the hot / cooler days seen in the graphs? As far as a general diurnal cloud cycle, there seems to be little evidence of it over the ocean from just eyeballing the images. I have certainly seen this cycle over land areas in the past but I’m somewhat sceptical whether it happens to any great degree over the ocean.
Willis, just wondering about the characteristic shape of your temperature graphs, particularly the shoulders on the ones over cooler waters. Have you considered the influence of atmospheric tides? In tropical areas there is a daily 2-3 mb increase in pressure between 4am -10am and about the same from 4pm to 10pm.

Craig Moore
August 25, 2011 7:23 am

Willis, always enjoy your posts from the viewpoint of a cowboy fisherman. Have you considered that the push-and-pull, yin-and yang of your hypothesis could be studied through fractal modeling?

August 25, 2011 7:27 am

Timetochooseagain says “… one needs to center the records on something like sunrise or sunset for each day, because the time of each varies through the year.”
This is quite true, but near the equator — and these buoys are within ten degrees — the length of day varies much less than it does in more temperate climes. Your suggestion would be most valuable in a refined, second-stage analysis.

August 25, 2011 8:06 am

Willis, these are some pretty remarkable findings. Certainly far more interesting than almost all of the usual climate “papers” found in the literature. I’d suggest you’d get it published, but that’s like pulling teeth. The legit climate scientists need to study this, tho.
One would think this mechanism would negate any few W/m CO2 warming, at least in the tropics.

August 25, 2011 8:52 am

So far, so beautiful, at least from my rudimentary perspective. And, therefore, I’m still waiting for some CO2 = AGW physicist to explain to me why, within the actual atmospheric system present, the “ghg physics” of CO2 would “make” water vapor do something – such as produce an extra net heating effect, perhaps even up to a “runaway” – which it was either already able to do, or else was already unable to do – because of some countervailing process – completely on the basis of its own “ghg potential”, or at least including its “ghg potential”, that is, without any CO2 even being present.
That “process” which governs water vapor’s naked ‘ghg potential’ and drastically lessens its alleged relevance seems to be Willis’ thermostat mechanism, in which water vapor itself is only[?] a vehicle for heat energy transport and then a substrate for cloud formation and rain.
Therefore, given the presence and working of the thermostat mechanism, I don’t see why CO2 would “set” the surface temperature any higher than the temperature already could have been set according to AGW “ghg physics”, that is, when increased water vapor due to increased temperature, in an upward cycle ending at some point, could have already done the same thing, according to AGW’s “ghg physics” – since both CO2 and water vapor “are ghg gases”, and given the essentially infinite availability of a water vapor source, or at least enough of an availability compared to the availability of the right kind of electromagnetic radiation.
What the AGW proponents I’ve seen around here do in order to try to avoid this inconvenient, imo, problem, is to claim that water vapor both is and is not “a ghg gas”. It’s not a ghg when they say, “the concentration of water vapor is determined solely by atmospheric temperature”; but it is a ghg when CO2 needs it to be in order to further increase the atmospheric temperature!
So why wasn’t water vapor alone already increasing atmopheric temperature, and then what stopped it?

August 25, 2011 9:03 am

naively speaking, it would even suggest that a few W/m^2 CO2 “warming” would stimulate an overshoot, resulting in net cooling!

Louis Hooffstetter
August 25, 2011 9:12 am

Thank you Willis for your clear, concise, and unambiguous presentation. This article is everything that Climate Science research is not, but should be. You should consider trying to publish this in a mainstream Science journal. We know your chances would be less than those of a snowflake surviving a forest fire in the Amazon in mid summer, but reading the details of the peer review and editorial shenanigans here on WUWT would be highly entertaining to the rest of us. Are you masochist enough?

August 25, 2011 9:24 am

@ Time to choose again
one needs to center the records on something like sunrise or sunset for each day, because the time of each varies through the year.
Sunrise in Honiara, Solomon Islands, varies between 5.50am and 6.10 am, Sunset is between 17.50 and 18.10, at 9* south of the Equator. It is remarkably stable, there is only one high tide each day a well.

August 25, 2011 9:57 am

This looks to me like just regression to the mean. If a day is unusually hot then it is more likely that it will cool down to a more common normal temp day, and if a day is unusually cool then it is more likely that it will warm up to a more normal temp day. Hot days are more likely to cool, and cool days are more likely to warm. I see no need for any thermostatic principle to explain it other than just settling to the average after disturbances.
It could even be partly a simple result of the progress of the seasons. If you start out at 1AM on the average hottest day of the year, then on average, 1AM on the next day is going to be cooler. This will continue until the average coolest day of the year, where the next day will on average be warmer.
This would be more obvious if the graph were plotted so that instead of how they’ve been adjusted to coincide at the beginning of the day, they were instead adjusted to coincide at the end of the day.

August 25, 2011 10:17 am

I appreciate the comments pointing out that near the equator there is virtually no variation in time of sunrise and sunset. With the resolution of data Willis is working with, then, my suggestion is not really necessary. I would however like to know what the picture looks like for the other tropical oceans besides the Pacific. Likely they will be similar, but it would still be interesting.

August 25, 2011 10:19 am

Any or all of this may be wrong so feel free to correct it.
The mainstream view is that temperature is controlled by radiative forcing which can be approximated to a linear relationship. But that doesn’t mean that temperature slavishly follows RF just that it averages out over a long time.There are other processes that can lead to temperature moving away from this linear relationship on different time scales (such as ENSO). So you have temperature ‘trying’ to be in equilibrium with radiative forcing but never quite getting there. Either being pushed higher (or lower) by multiple mechanisms.
In this scenario any higher than average temperature induced by non-radiative mechanisms would more likely be followed by lower temps as the system “tries to return to equilibrium’. And the reverse if the temperature is lower. This is what you have found on a daily basis. So I don’t necessarily see that your result distinguishes between your mechanism and the mainstream position.

Charlie A
August 25, 2011 10:24 am

Some have commented above about the need to adjust for sunrise/sunset times. There are a couple of other corrections that are of the same magnitude or greater.
The array in the eastern pacific is spaced at 15 degrees of longitude, so using the zone time for each works well. For the western half of the array the longitudes are not on the same grid and local mean noon will have +/-30 minute offsets from the mean noon at longitude of the center of the time zone. So one easy correction to get things to correspond better would be to use a fixed correction for the difference between the center longitude of the time zone and the longitude of the buoy.
The other correction is the Equation of Time; the difference between actual sun longitude and the longitude of the mean sun. +14 minutes to -16 minutes over a year period. It can be expressed neatly as the sum of two sine functions. One has a period of one year, the other a period of 1/2 year.
This is a very interesting, intriguing, though-provoking series of posts.

August 25, 2011 10:28 am

I guess the wider question is whether Willis mechanism can induce long term trends. Whether he has identified a processes that maintains temperature around a sort of equilibrium or optimal temperature on a daily basis. But that equilibrium or optimal temperature is constantly being changed by the change in radiative forcing.

August 25, 2011 10:51 am

By regression to the mean I just mean that days that are warmer than normal tend to cool towards normal and days that are colder than normal tend to warm towards normal.
A homeostatic process implies something in the system that resists external forcings other than mere thermal inertia or settling to the average resulting from the long term balance of incoming and outgoing radiation. This tropical thunderstorm/cloud cooling effect is sort of homeostatic, but the graph you’ve presented today which shows that warm days cool and cool days warm, is kind of a separate issue. It doesn’t establish the homeostatic nature of the thunderstorms.
I doubt that the thunderstorms are really homeostatic anyway. It looks to me more like they are reacting to differences in temperature rather than stabilizing towards any particular temperature. Perhaps a difference between the temperature of the water and the air, or a difference between the air temp at low and high altitudes. In one of the previous analysis it was shown that this thunderstorm cooling happens at a wide range of buoys that have considerably different average temperatures. So I suspect that if the entire globe warmed up one degree, for example from a steady long term increase in solar output, these thunderstorms may resist the change at first, but after a while the new average temperature around a buoy would settle in, and then these thunderstorms would resist changes away from the new average, even if the change was back toward the old average.

Gary Swift
August 25, 2011 12:31 pm

Willis said in comments:
“the balance is restored by the fact that there are more warmer-than-average days than colder-than-average days”
So that says that the magnitude of the colder than average days was greater than the magnitude of the warmer than average days, which is evident by the sharp point on the bottom of the morning temperatures on the cool days. If, in stead of dividing the days according to deviation from the mean, you divide them so that there are an even quantity of warm and cool days, does that change the results of the analysis? Do you still see the increasing trend when you break the data up into quartiles?

Gary Swift
August 25, 2011 12:35 pm

Another question:
How many days follow this pattern, and how many days stray from this pattern? What is the probability distribution of any given day fitting the pattern you suggest? Does that distribution say anything informative about the strength of the pattern you suggest? How statistically significant is it?

August 25, 2011 1:31 pm

this is win, willis. 🙂 wb.

August 25, 2011 1:42 pm

The more I hear about the governor/thermostat approach, the more I like it. It seems a lot more intuitive than the “cycle” approach in regard to what drives the weather and climate.
With the governor approach, the weather/climate makes its own cycle in the sense that it gets out of whack, and through its own in built mechanisms, it corrects itself, and because it does this over time, it looks like a cycle.
It also shows that the Earth is a very resilient (robust) planet, in that it can accommodate a wide range of extremes, and still have a mechanism to bring itself back to/through equilibrium.
It’s probably just me, but since Willis elucidated the idea, I’m seeing thermostats everywhere. It’s govern(ors/esses) all the way down to the bottom.
For instance, it seems that open water at the poles dissipates a lot more energy than it can possibly get at those latitudes, so counterintuitively, low sea ice extent ends up leading to a cooler Earth (ergo is a cooling mechanism).
Stephen Wildes’ “iris” effect would be another one that springs to mind.
I’ll thank the alarmists for one thing (and one thing only), and that is that in their disasturbating, they’ve made me open my eyes and realises what an amazing place this planet is.

August 25, 2011 1:42 pm

Imagine how different Earth would be if all the land mass in the northern hemisphere was centred on the equator.

August 25, 2011 1:43 pm

Your analysis is really about how cloud formation responds to the local temperature to moderate variations. Since everyone is talking about the CERN cloud experiment, have you looked at different periods of time such as near or just after a solar maximum (about 1999-2001) or near or just after solar minimum (such as 2007-2009). Do clouds form more easily and are they more persistent just after solar minimums?

Don Keiller
August 25, 2011 3:29 pm

To R Gates – where are you when we need the voice of sanity?

Kevin Kilty
August 25, 2011 5:29 pm

I agree with Mindbender on this. If a day begins hotter than a mean, then there is a smaller probability that it will end hotter still, than there is it will end cooler. There may be many reasons for this regression toward the mean, one of which could be the hypothesized thermostat.

Kevin Kilty
August 25, 2011 5:32 pm

sorry, Mindbuilder in the previous post, not Mindbender!

August 25, 2011 5:49 pm

Willis Eschenbach says:
August 25, 2011 at 4:59 pm
And thank You, Willis. You’re among the top five people that have really opened my eyes. I always look forward to your postings

August 25, 2011 7:35 pm

Hi Willis this is most interesting.
From your write up and from subsequent comments, I can see two possibilities:
(1) you have found a true homeostatic phenomenum.
(2) your results ae just due to random fluctiations.
I note your comments about the practical difficulties of doing such analysis.
However, I would like to see the data combined into sets of say ten days duration.
If there really is a daily homeostatic reaction at work, then it should persist – if it starts high then it will end low which creates a low start for the next day and so forth.
If not, then the trend will quickly evaporate.
I tend to suspect the latter – that what you have got is just a random selection of chaotic data.
If I’m wrong and you’re right, then you are on to something big which is not at all recognised in the IPCC style modelling.
So I feel that it would be worth the effort to extend your analysis as suggested.
I’d do it myself, but my skill at R is far less than yours (close to zero in fact Pr 0.000001 in reality).
Fascinating stuff anyway and thanks for sharing it with us.

August 25, 2011 10:15 pm

yes, “reversion to the mean” is just a matter of any current deviation from the true average/mean being swamped and reduced to insignificance by the piling up of future instances which will, by definition, average out to the mean. Since that’s what mean means.

Rhoda Ramirez
August 25, 2011 10:29 pm

Rosco: Didn’t we have our global snowball during the times when the land masses were concentrated around the equator?

wayne Job
August 26, 2011 12:53 am

This is excellent work Willis. The tropics are the heat source for heat pump Earth, the poles are the radiators dumping excess heat. The chaotic unplumbed system in between gives us weather.
The last few rampant sun cycles gave us a little extra heat so the poles after lag dumped more heat as shown by a reduction in ice.
Indeed you have found the control that tries to maintain a constant heat input into the heat pump.
This is scary stuff for the AGW mob as radiative forcings become irrelevant in the grand scheme of things. You are very naughty dropping this on them as they are trying to digest the cloud stuff.
You will probably also find that the temperature in the tropics does not vary much with solar changes, the rampant sun gives less cloud cover to the oceans outside the tropics, thus more heat.
It would seem that the CERN experiment shows another thermostat, yours is for constance and theirs for the variability following the sun cycles, it will be found that there are others, and CO2 is not one off them.
Thank you Willis

August 26, 2011 2:25 am

Willis forget these “reversions to the mean” arguments. They are irrelevant.
Dynamical, causal processes never “revert” to any mean for the simple reason that they “produce” the mean as they go.
A dynamical causal process never knows what the FUTURE mean will be so it can’t revert to it. It may know about the PAST mean but there is no reason to “revert” to past mean.
This kind of argument is just confusing a dynamical causal process with a random process with constant mean and variance (a stationary process).
Indeed if the weather was a stationary random process then the temperatures would just be independent random variables distributed along an invariant frequency curve and would behave like a die throw.
As the proportion of events above and below the mean must stay invariant (not necessarily equal) then one has necessarily more hot->cold and cold->hot sequences than hot->hot and cold->cold sequences.
But of course we all know that the weather is neither a die throw nor a random stationary process.
Averages and variances are not constant etc.
That’s why the behaviour of dynamical variables like temperature must have a cause and what you show is that your causal hypothesis – “clouds are the cause of the temperature evolution and act like a negative feedback” is supported by the data. The negative feedback “looks” like a “reverting” to the mean but has nothing to do with it.
Of course if you had cloudiness data on the same chart, the hint would transform in a proof.

Ian B
August 26, 2011 5:00 am

Very interesting and well presented results – also noce to hear that there is a lot more data available from this source to allow further investigation. I’d certainly say however that as a first test of your hypothesis, this looks to be confirming rather than countering it.
The quartiles data are particularly interesting – the coolest quartile suggests that below a certain temperature threshold the effect is insignificant, but that as the temperature rises the differing behaviour intensifies.
As has already been suggested, is there sufficient data on cloudiness to improve the analysis? There are a couple of questions that this data would help with:
1 – Are hotter nights related to increased cloud between sunset and sunrise (i.e. slower loss of heat overnight), or are these clear nights where the previous day has ended warmer?
2 – From the above, is there a marked change in the rate of cumulus formation in the mornings depending on the cloudiness of the previous night?

Beth Cooper
August 26, 2011 8:32 am

Those quartiles sure show cycles.

Septic Matthew
August 26, 2011 9:55 am

mindbuilder wrote: This looks to me like just regression to the mean.
Except that there is no regression toward the mean; instead there is what might be called “overshoot” or some such, producing persistent negative correlations from one day to the next.
Willis, this is nice. It would be good if you could access actual cloud data, and relate your results to the Lottka-Volterra (predator prey) modeling done earlier this year and cited above Note that the Lottka-Volterra models are “negative feedback” models and not “regime change” models (apropos an earlier interchange between us.) It is possible, or at least conjecturable, that increased concentrations of CO2 will produce increased magnitude of the day-to-day oscillation, without changing the time-averaged mean temperature. Can you see a change in magnitude of the oscillation with change in measured atmospheric CO2? The record is probably too short to to show much, but it might be worth looking at now, and following in subsequent decades.

Septic Matthew
August 26, 2011 10:04 am

Brian H wrote: yes, “reversion to the mean” is just a matter of any current deviation from the true average/mean being swamped and reduced to insignificance by the piling up of future instances which will, by definition, average out to the mean. Since that’s what mean means.
That is incorrect. When paired observations are positively correlated (Galton’s pioneering study collected heights of fathers and their sons), and you select a group that is extreme on one measure (tall fathers), the values of the other measure (sons’ heights), while still extreme (tall fathers have tall sons), are less extreme (the sons’ mean height is intermediate between the selected fathers’ mean and the population mean.)
If you select days that are way below average at morning, they are way above average at evening. That is not “regression to the mean”. Regression to the mean would produce evenings that are not as below average as the mornings.

Gary Swift
August 26, 2011 11:06 am

I don’t mean to heckel, but I have one more suggestion which will, onfortunately require more work, but maybe not too much.
Willis said in comments:
“Well … absolutely not. Remember that despite the fact that it has a mean, it is a drunkards walk. At every point, the odds of warming and cooling are equal, 50/50”
You can settle this issue by using a control data set. Try feeding data generated from a semi-random number generator into your functions. I believe there are plenty of R codes already written which simulate the drunkard’s walk of temperature. It shouldn’t be hard to produce some test data. If the random data doesn’t show the increasing trend in your quartile analysis, then that should settle it. Or, if the random data shows the same thing, then you’ll know it’s a statistical artefact.

Septic Matthew
August 26, 2011 1:44 pm

Willis wrote: in other words, a thermostatic mechanism.
If you have not already studied the Lottka-Volterra equations, among the many systems of equations whose solutions are oscillations, you might do so — in your “spare time” of course. Probably you already have studied the Lorentz equations, another well known example.

August 26, 2011 2:43 pm

You introduced a qualification that renders the issue tautological: “when paired observations are positively correlated”. I was speaking of the general case, in which a “spike” or run in a random sequence temporarily seems to introduce a trend or new mean. 6 “heads” in a row up front looks very significant; add 1000 more flips that show a fair and accurate representation of the mean and you get 506 heads vs 500 tails, not significant. So the apparent “pattern” or trend “regressed to the mean” by expansion of the denominator.

August 26, 2011 4:12 pm

The observed facts that the temperature recordings throughout the tropics are usually 10 degrees less for environments close to the ocean than those in the middle of a land mass of substantial size ought to convey that water controls the climate on the planet not carbon dioxide.
Enormous quantities of energy are absorbed by evaporating water molecules that otherwise would heat land surfaces. The ocean’s heat capacity is greater than the atmosphere and evaporation involves large input of energy with no temperature increase.
This so called positive feedback effect of water vapour is obviously wrong.
If it were right Singapore, almost on the equator with high humidity year round would be far hotter than Baghdad during summer with low humidity.
But observation show the opposite – Singapore almost never exceeds 32 C while Baghdad regularly exceeds 42 C.
I won’t call that a negative feedback because that term doesn’t sit well with me.
It simply shows how water controls the heat –
Near water – cooler during day, warmer at night
Away from water – hotter during day, cooler at night.
I would have thought water as the thermostat was so obvious scientists would have to be brain dead to ignore the observable results of at least decades of meterological data.

Septic Matthew
August 26, 2011 4:38 pm

Brian H. wrote: You introduced a qualification that renders the issue tautological: “when paired observations are positively correlated”. I was speaking of the general case, in which a “spike” or run in a random sequence temporarily seems to introduce a trend or new mean. 6 “heads” in a row up front looks very significant; add 1000 more flips that show a fair and accurate representation of the mean and you get 506 heads vs 500 tails, not significant. So the apparent “pattern” or trend “regressed to the mean” by expansion of the denominator.
So, first off you misused the phrase “regression to the mean” which technically applies as I described it.
Second, your example is based on independent events, but Willis E. has demonstrated that the day-night pairs are negatively correlated, not independent.

George E. Smith
August 26, 2011 5:47 pm

This may seem like a bit of a nit picky question but your posting does say: “”””” Figure 1. Locations of the TAO/TRITON buoys (pink squares). Each buoy is equipped with a sensor array C and other meteorological variables. “””””
Now the interesting wording there to me, was this part: “”””” measuring air and sea temperatures “””””
Note that both air Temperatures and sea surface Temperatures are measured.
BUT your report purportedly graphs ALL Buoy records; presumably including both sea surface and air Temperatures. So why would you add them all in together ?
And is it not just these Buoy records, that John Christy et al reported on in Jan 2001, that proved that sea surface Temperatures, and air Temperatures (Lower Troposphere) are not even correlated (why would they be ?)
Seemingly a minor point, but it proved that the previous 150 years of global Temperature data records, for about 73% of the earth surface are pure garbage, (sea surface temperatures) and since they aren’t correlated, the corresponding Lower Troposphere air Temperatures are forever unrecoverable.
Also because oceanic currents, like rivers, meander, you can return to the very same GPS co-ordinates, and be in totally different waters from where you were last year; so even the sea surface Temperatures, are not reliable. The air and the surface, are seldom in contact for long enough to equlibrate, so they should never be the same; or correlated. Air over the Sargasso Sea a week ago, will be over Martha’s Vineyard pretty soon, thanks to Irene.

August 27, 2011 3:41 am

Great stuff Willis. This sort of reasoning gets the cart properly behind the horse – so to speak. Could you do a ‘nightlight’ style analysis over the buoy locations using cloud cover imagery to verify that it is actually cloudier when it’s supposed to be?
It occurred to me that Anthony’s banner pic is very appropriate to this topic with that bright cumulonimbus tower casting its long shadow 🙂

Septic Matthew
August 27, 2011 9:32 pm

Willis: You can’t explain the results as being merely a “regression to the mean’ without answering the question of why the day-night pairs are negatively correlated.
Reread my comments in order. You agree with me, and I specifically deny that “regression to the mean” applies to your result.

August 29, 2011 2:07 am

I agree Matthew .
The “regression to the mean” argument can be falsified by just one sentence :
The process described by Willis is not a stationary random process.
Being non stationary , it has no constant mean which it could “regress to” etc etc .

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