TAO/TRITON TAKE TWO

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,

w.

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Bloke down the pub

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

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

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.

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?
Thanks

RockyRoad

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

Willis,
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.

Jessie

Willis,
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

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?:
http://www.pmel.noaa.gov/tao/proj_over/taohis.html
I’d also like to know about the geographical clustering/distribution of the quartiles you have identified.
Thank you.

HaroldW

Willis,
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

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. ”
http://wattsupwiththat.com/2011/07/25/prey-and-predator-model-of-clouds/

John S.

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.

timetochooseagain

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.

pochas

Willis,
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

Nice Willis, Thanks for your clear-headed work.

Steve Richards

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?

Mark

Wills,
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.

dlb

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

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?

Ellen

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.

beng

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.

JPeden

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?

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

Louis Hooffstetter

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?

Warren

@ 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.

Willis Eschenbach

Bloke down the pub says:
August 25, 2011 at 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?

This is a result of the type of analysis. For each buoy, what I did was choose entire days (1AM before the dawn to the next 1AM) based on whether the temperature at dawn was higher or lower than average. I then averaged the days. As a result, the end temperature of the day is not the same as the start of the day, nor is there any reason it should be.
Others have commented that the increase (on the cold days) is greater than the decrease (on the warm days), and that this would lead to an overall trend. In fact, the balance is restored by the fact that there are more warmer-than-average days than colder-than-average days, so the net result is general equilibrium.
w.

MindBuilder

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.

Willis Eschenbach

MindBuilder says:
August 25, 2011 at 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.

I’m not sure what you are calling “regression to the mean”, or how you distinguish it from a homeostatic process.
w.

timetochooseagain

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.

HR

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

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.

HR

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.

MindBuilder

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

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

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?

gnomish

this is win, willis. 🙂 wb.

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.
/p

Rosco

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

Sean

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?

Willis Eschenbach

HR says:
August 25, 2011 at 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.

The mainstream position is that there is no “equilibrium”. Instead, their position is that everything is linearly ruled by forcing.
But the solar forcing is increasing and decreasing throughout the day, and despite that the temperature response varies depending on both the temperature and the time of day. The net effect is that the system does not passively “return to equilibrium”, it actively restores the “preferred” temperatures.
In addition, if (as I show) the response is based on temperature, then there is no climate sensitivity as it is currently understood.
w.

Don Keiller

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

Willis Eschenbach

Sean says:
August 25, 2011 at 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?

Interesting, Sean. Hadn’t thought about that, but there might be something to be seen there. The TAO/TRITON buoys return a host of hourly information on things like wind, relative humidity, sea temperatures at various depths, and the like. I’ve barely scratched the surface of the data.

Willis Eschenbach

paulhan says:
August 25, 2011 at 1:42 pm

… 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).

First, thanks, paul. I’m glad someone out there sees the beauty of the way nature does it. I agree with you that there are a variety of homeostatic mechanisms, at a variety of temporal and spatial scales, that work in unison to modulate and control the temperature of the planet. Discovering what those mechanisms are and how they interact and intersect should be the job (and the joy) of the climate scientist, not looking for fancied linear relationships.
w.

Willis Eschenbach

Gary Swift says:
August 25, 2011 at 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?

The quartiles, as the name suggests, are broken up the way that you suggest—equal amounts above and below the median.
Gary Swift says:
August 25, 2011 at 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?

And good questions all. I have no answers. It’s early days yet, and there’s a monumental pile of unexplored TAO/TRITON data out there. I report things as and when I find them. To answer even a simple question (what is the difference when dawn is warmer versus when it is cooler than average) takes hours. New code has to be written and debugged, and I don’t speak R as fluently as I might wish. Then plot the results. Then slice it in quartiles. Plot each result with a different title. It’s a slow process.
So, I just send back periodic reports from the scientific battlefront as time and the tides allow.
All the best,
w.

Kevin Kilty

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

sorry, Mindbuilder in the previous post, not Mindbender!

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
/p

AusieDan

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.

Willis Eschenbach

AusieDan says:
August 25, 2011 at 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.

AusieDan, thanks for the thoughts. If it were a “random selection of chaotic data”, the tendencies would not vary by quartile. But they do vary by quartile (Figure 3), and in the expected direction—the warmer the average temperature at the buoy, the more separation and difference there is between the warm dawn and cool dawn days.
w.

Willis Eschenbach

Kevin Kilty says:
August 25, 2011 at 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, thanks for the thoughts. If this is just a regression to a mean, then how do you explain the difference between the shape of the temperature rises on the warm dawn and cool dawn days? (See lower right panel, Fig. 3)
Obviously, on the two types of days there are very different factors shaping the evolution of the daily temperature. When it is warm, cumulus reverses the temperature rise of the morning, and then thunderstorms knock down the expected afternoon peak temperatures to the point where the peak temperature actually occurs before noon.
And on cold days, there is little interference from clouds or thunderstorms, so the temperature rises throughout the day, with the afternoon much warmer than the morning.
Which is why my hypothesized mechanism is a better explanation than some relaxation towards a mean …
w.
PS–I got to thinking about this claim:

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.

Curiously, there’s no reason that should be true.
Consider a hypothetical temperature record where every day has a 50/50 chance of being either warmer or cooler than the previous day. This kind of a path is sometimes called a “drunkard’s walk”, meaning there’s equal change the drunk temperature will stagger warmer or cooler.
So we might end up with a daily record like 10°, 10.2°, 10°, 9.7°, 8.5°, 9.2°, and so on. These might have a mean of say 9.8° or something. Now here’s the question.
Is it true that if a day is hotter than the mean, it is more probable that the following day will be cooler?
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.
So the existence of a mean does not imply a tendency of a “reversion to the mean”. The days don’t know what the average temperature is.
w.

W.;
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.
😉