Reposted from Dr. Roy Spencer’s blog
June 4th, 2019 by Roy W. Spencer, Ph. D.
Willis Eschenbach and I have been defending ourselves on Facebook against Joe Postma’s claims we have “flat Earth” beliefs about the radiative energy budget of the Earth. The guy is obviously passionate, as our discussion ended with expletive-laced insults hurled my way (I suspect Willis decided the discussion wasn’t worth the effort, and withdrew before the fireworks began).
Joe advertises himself as an astrophysicist who works at the University of Calgary. I don’t know his level of education, but his claims have considerable influence on others, which is why I am addressing them here. He has numerous writings and Youtube videos on the subject of Earth’s energy budget and greenhouse effect, and the supposed errors the climate research community has made. I get emails and comments on my blog from others who invoke his claims, and so he is difficult to ignore.
Here I want to address just one of his claims (repeated by others, and the basis of his accusation I am a flat-Earther), recently described here, regarding the value of solar flux at the top of the atmosphere that is found in many simplified diagrams of the Earth’s energy budget. I will use the same two graphics used in that article, one from Harvard and one from Penn State:
Joe’s claim (as far as I can tell) is that that the solar flux value (often quoted to be around 342 W/m2) is unrealistic because it is for a flat Earth. But as an astrophysicist, he should recognize the division by 4 (“Fs(1-A)/4” and “S/4”) in the upper-left portion of both figures, which takes the solar constant at the distance of the Earth from the sun (about 1,370 W/m2) and spreads it over the spherical shape of the Earth. Thus, the 342 W/m2 value represents a spherical (not flat) Earth.
Just because someone then draws a diagram using a flat surface representing the Earth doesn’t mean the calculation is for a “flat Earth”.
Next in that article, Joe’s (mistaken) value for the solar constant is then used to compute the resulting Earth-Sun distance implied by us silly climate scientists who believe the solar constant is 342.5 W/m2 (rather than the true value of 1,370 W/m2). He gets twice the true, known value of the Earth-Sun distance, simply because he used a solar flux that was off by a factor of 4.
Now, I find it hard to believe an actual astrophysicist could make such an elementary error. I can ignore Joe’s profane personal insults, but he ends up influencing many people, and then I have to deal with their questions individually. Sometimes it’s better if I can just point them to a blog post, which is why I wrote this.
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A real energy balance is conducted in kJ/h not W/m^2.
Since 1 W/m2 = 3.6 KJ/hr/m2, you can do a “real” energy balance in either one, and easily convert one to the other.
You can also do a balance in either watts or in KJ/hr.
Your claim is as foolish as saying that a real energy balance is only conducted in metric units and not imperial units … sorry, Nick, but you can use either unit. In climate science, such balances are generally done in W/m2, but please, feel free to use KJ/hr/m2 or KJ/hr if you want to stand out …
w.
OK, let’s do that. Jupiter receives many more kJ/h from the sun than does Earth. So, will Jupiter’s atmosphere be warmer than Earth’s atmosphere?
Does anyone know a reasonable value for the inherent radiative heat loss (in W/m^2 for the surface of the sphere) due to the fact that the earth is exothermic (i.e it generates and radiates heat from its interior)?
I know it’s small, but I’m curious.
If anyone else is curious, I get around 0.09 W/m^2.
Why not do your own homework and Google it?
Never mind! /E. Littella
https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget
I got about halfway through this thread and gave up on it. I don’t profess to understand all the ramifications of the discussion, but to look at an average, call it unrealistic, and dismiss it, is not very persuasive to me. I’m reminded of the saying attributed to statistician George Box: “all models are wrong, some are useful.” For sure, an average is going to be “unrealistic.” That does not matter. Is it a useful approximation? That should be the issue.
Exactly.
Joe is correct this is a first order thermal system. Input To the system is a variable half wave rectified Sine wave. Steady state Inputs/average values cannot be used to analyze the system maximum temerture is proportional to the Peak value of the input.
Average temperate is controlled by the system time constant
This is a follow-up to the previous video where I respond to Roy Spencer’s accusation that I am incorrectly and needlessly “ranting” about the fraud of flat Earth theory. I have some better graphics and a little bit more detail to discuss.
Joseph
I’m not a great fan of using averages to characterize variable systems. I think that using calculus to account for the changes that occur with the curvature of the Earth is a more rigorous approach than using some average.
However, it appears to me that your second diagram should be showing a gross input of 675 W/m^2. That is 1370/2 because the surface area of a hemisphere is 2 pi r^2. Therefore, the average input spread over the entire hemisphere, per unit area, is half as great as would be received per unit area of a flat disk of the same diameter, albeit the total amount of energy received is approximately the same (ignoring secondary effects such as scattering and forward reflection.)
In the case of Mercury, which is tidally locked to the sun and only one side is presented, it is clear that is what is happening. So, we are confronted, perhaps, with a definitional problem. The radiant energy received by the sun-facing side of Mercury, per unit area, is one-half the energy that would be received per unit area of a flat disk facing the sun. However, the total energy received is equivalent to that received by a flat disk at the same distance. That is the simple case. Now, in the case of Earth, because it is rotating, the entire surface gets illuminated, but with a 50% ‘duty cycle.’ Taking into account time, We should again divide by 2 to get the average amount of radiant energy, per unit area, per rotation. That is mathematically equivalent to dividing TOA insolation by 4 to get the average per unit area of the full sphere.
As I stated in my opening paragraph, I’m not a fan of trying to do everything with averages. I would like to see a more rigorous, calculus-based approach to dealing with the rotation of an astronomical body so that it could be refined subsequently with the addition of land masses and water, and the angular influences on specular reflections, and dealing with the clouds. As I stated above, I think that the ‘cartoons’ Roy provided are a good first-order approximation to convey the processes for those who are mathematically challenged. However, I think that simplifying the processes to a ‘flat-land’ approach as you suggest, is bound to introduce errors and limit the flexibility of dealing with the real Earth.
Clyde Spencer June 5, 2019 at 9:11 pm
Joseph
I’m not a great fan of using averages to characterize variable systems. I think that using calculus to account for the changes that occur with the curvature of the Earth is a more rigorous approach than using some average.
However, it appears to me that your second diagram should be showing a gross input of 675 W/m^2. That is 1370/2 because the surface area of a hemisphere is 2 pi r^2. Therefore, the average input spread over the entire hemisphere, per unit area, is half as great as would be received per unit area of a flat disk of the same diameter, albeit the total amount of energy received is approximately the same (ignoring secondary effects such as scattering and forward reflection.)
The TSI is the flux perpendicular to the Earth therefore the Earth intercepts the flux passing through a plan of area 𝛑r^2. You’d get the same value if you use and perform the double integral over latitude and longitude.
Phil
I think you missed two points. 1) I was remarking about how surface reflectivity, atmospheric absorption, and atmospheric scattering changes with the angle of incidence; 2) I was commenting about energy per unit area of the surface.
This is a follow-up to the previous video where I respond to Roy Spencer’s accusation that I am incorrectly and needlessly “ranting” about the fraud of flat Earth theory. I have some better graphics and a little bit more detail to discuss.
[Delete the duplicate entry? .mod]
What Joe appears to fail to understand is that the division by four occurs in a correct application of the first law of thermodynamics: that is the sum of energy flux in over time is balanced by the sum of energy flux out. Average energy flux in is 1370*𝛑r^2, average energy flux out occurs over 4𝛑r^2 therefore the energy balance yields energy flux out per unit area= (1370*𝛑r^2)/4𝛑r^2, i.e. 1370/4.
It is nothing to do with a flat earth.
Of course if you present a diagram of a unit area on the earth and its energy budget, let’s say over one square meter it will necessarily appear flat. In a model of the earth the equations would have to include the effect of curvature (and they do), the methods of calculus involve consideration of a small area which can be approximated as flat, curvature effects are accounted for by the cos terms.
The earth receives solar insolation over pi r ^2, in 2d.
It radiates heat away over 4 pi r ^2, in 3d.
So the earth’s radiative balance is a question akin to Poincare’s Conjecture – how to reconcile 2d with 3d.
And probably about as complicated.
Postma is as likely to be right as Nikolov and Zeller, or Miskolczi, or anyone else.
Yes, Phil S. — input over 2 pi r^2 — output over 4 pi r^2.
Thus, making 4 pi r^2 input the inversion of reality that Postma claims.
This is what has been taught at major universities.
No one can deny that the Earth is not flat.
At his blog, Joe is digging himself deeper now showing his abysmal ignorance of these topics. He states:
“Think of cooking a turkey if it helps. Or invert the example: can you use 4-times the energy (with its equivalent transform to temperature via the Stefan-Boltzmann Law) but applied in ¼ of the time to get the same end result?”
All real ovens, whether gas or electric, use cyclic on/off application of power. Let’s say the oven requires 500 watts to maintain the cooking temperature of the turkey. The oven will turn on full power for some period of time, then fully off for another period. If this oven has a full power rating of 2000 watts, it will turn fully on for time X, then fully off for time 3X. So it is applying 4 times the power for 1/4 of the time, repeatedly!
The temperature in the oven will not be as constant as if it applied a steady 500 watts, but in reality it will be so close (typically varying 1 or 2 degrees) that applying the “average power” approximation gets you very close.
The man does not even understand how his oven works!
This supposed astrophysicist DOES NOT UNDERSTAND HOW HIS OVEN WORKS!!!
Ed B,
I don’t think you understand that your description is not an equivalent comparison, and it amounts to a diversion and an opportunity to berate somebody attempting to explain a basic flaw.
Now explain to me how a blower works.
RK:
JP objects vociferously to the use of average power input for rough calculations and conceptual illustrations, when the power input is really time varying. He calls this the “flat earth fallacy”. In the earth’s case, the average (over time and area) power input is 1/4 of the peak.
It was JP himself who brought up the turkey-in-the-oven analogy, arguing that it would be crazy to think that you could roast a turkey this way, with time-varying power inputs.
But, in fact, all ovens do indeed work this way, with time varying power input. The thermal power source for an oven is either full-on or full-off. If the time-averaged power requirements are less than the full-on power, the oven goes through on/off power-input cycles.
This is DIRECTLY analogous to the day/night cycle for a location on the earth, and it is common to use the average power value as a first approximation. JP cannot realize this, no matter how many times it is pointed out to him (and it has been explained to him multiple times).
Because of the time-varying input power, the temperature is not constant, and will vary somewhat each cycle. But that does not mean that the average is not a decent first-cut approximation.
Ed B, I carefully considered your reply:
Varying the oven’s power input relies on oven insulation to maintain a steady temperature. We are talking about the air molecules in the oven being contained and restrained from convecting to cool. How is this, in any way, correctly related to air in Earth’s atmsophere being heated by sunlight?
While the oven is full on, the turkey is cooking at full power. When the oven is full off, the oven insulation still maintains temperature for the off time, still cooking the turkey at the maintained temperature. The Earth does NOT have this insulation, and the sun is NOT blinking on and off to maintain a steady temperature. Are you really saying that the Earth’s atmosphere is like an oven, and the sun is like a blinking-on-and-off oven? On the other hand, I would agree that there are lots of turkeys living on Earth, trying to cook up greenhouse mythology.
No, it is not directly analogous. Plainly.
In the oven you so well describe, the temperature IS constant, with the aid of insulation designed to accomodate the power blinking on and off accordingly. How is this like the sun-Earth-atmosphere relationship again? I think you are going to great pains to deform the analogy incorrectly, slightly contradicting yourself in the process.
RK:
I see you have never taken an actual thermodynamics or heat transfer course, and you, like JP, don’t actually understand how your oven works, so you don’t realize the direct analogs.
In both cases, we have a very hot object (the sun, the heating element) transferring power to to a relatively warm object (the earth, the oven interior including the turkey) that exists in a colder ambient (deep space, the kitchen).
Both sources transfer power in a cyclic manner to the object. In the earth’s case, it is because a given location on earth rotates away from the sun each night. In the oven’s case, it is because the thermostat turns power to the element on and off.
In the earth’s case, the cycle is 24 hours long. In the oven’s case, the cycle is typically a few minutes long.
Both objects (earth and oven) have a certain thermal capacitance responding to the cyclic application of power. Both objects have a certain thermal resistance to losing thermal energy to ambient (space, kitchen).
You are just plain WRONG when you state that the temperature of the oven “IS constant” through the cycle because of the insulation. The insulation is NOT perfect (the thermal resistance is NOT infinite), so the temperature drops whenever power is not being applied.
You do understand that when you turn off your oven for good, it cools down to the kitchen’s ambient temperature, don’t you? That also means that its temperature does drop WHENEVER the power is not applied, including the OFF part of the cycle.
I design control systems with cyclic power application for a living, so I am keenly aware of the nature of the dynamic response to this type of power application. In a typical oven, the temperature drops about 5 degrees during the OFF cycle before the thermostat turns the power full-on again. This band is called the hysteresis of the system. Your house’s thermostat has about a 1 degree hysteresis.
Similarly, a location on the earth, as it rotates away from the sun, will start to cool down because it has no more solar power input but it is still transferring energy to space. Because there is thermal resistance to this transfer, the cooling is gradual, and the bigger the active thermal capacitance, the less the temperature drop due to the energy loss to space. This continues until dawn, when the next diurnal cycle begins, and the temperature starts to rise again. In many places, the diurnal temperature variation is about 10 degrees.
So yes,the two systems are directly analogous, and if you or Joe actually understood basic thermodynamics or heat transfer, you could grasp this.
P.S. I am not EdB. That is someone else.
Ed Bo
I realize that your analogy is not what you think it is.
The oven heating element transfers power, intermittently, in real-time doses, and these real-time doses have real-time effects. The simple, radiative greenhouse heuristic, on the other hand, starts with the diluted sunlight as the power input, and attributes to this diluted power the effects of the full sun in locations where its power does not exist in any full doses ever. With this diluted input power, as illustrated, there is never a place anywhere that the full power applies in real time to have real (i.e., cooking) power.
The power is full on, however, in those moments, and this is NOT what the radiative greenhouse heuristic shows — it shows a one-fourth-diluted sun power impinging on the entire planet all at once, instantaneously. There is no accounting there for cycling, as you put it. The math does NOT mean cycling, the way you put it.
Still you speak of cylces of full on and full off power, in the real-time moments during which they occurs. Again, this is NOT what the radiative greenhouse heuristic shows — it shows a given power, one-fourth of the sun power, impinging on the ENTIRE planet, all the time, each second, each day. There is no accounting for the fact that the power in those cycles is fully on — it clearly is one fourth fully on ALL THE TIME, EVERYWHERE.
Yes, but this thermal capacitance is reacting to the full power in the moments that it occurs. There are NOT any moments of full power in the radiative greenhouse heuristic. That heuristic shows the planetary output resulting from the full-time impingement of a quarter-power sun in those moments of cycling — NO full-power sun. EVER ! So, it’s NOT your oven, ED — its somebody else’s oven trying to cook that turkey at one fourth power that is one-fourth power ALL THE TIME. The on time is one-fourth power, and the off-time is one-fourth power. That’s what the diagram shows. That’s what the math there means.
When an oven says 350 F., most people trust that this is roughly correct, or else the turkey would not cook properly. Now, technically, you might be right that the temperature drops somewhat from this exact figure, but this is an insignificant technicality that really does not bear on the main flaw of your analogy. The fact is that the turkey cooks because of cycling of full-power-on moments with full-power-off moments.
You know perfectly well that I understand the oven’s cooling to kitchen ambient temperature. Asking me is an obvious swipe at my intelligence, which is, alas, an obvious swipe at your own for thinking that I cannot detect this. (^_^)
During cook time, the oven temperature does not drop appreciably anywhere near ambient temperature — it remains at a level that enables the turkey to keep cooking properly, just in time for the next power surge that prevents it from cooling too much to continue cooking properly.
So, my understanding is correct, it seems.
Now you seem to by trying to dazzle me with your expertise on a detail, which again is rather trivial in comparison to the main point we are talking about. Citation of your expertise on these fairly irrelevant details and your use of the associated technical lingo does not deter me from my conclusion.
Again, yes, but the power that it DID have was the full power of the sun in that moment when it did have power, NOT one-fourth power.
Yes, but again this would be a reaction to the full power applied at the beginning of the cycle. You continue to speak as though you are talking about full power applied in the moments of the cycle you speak of. You are NOT talking about full power, however, if you are using the radiative greenhouse heuristic as your illustration. That’s NOT what this diagram represents at all.
What I understand is that you are using a false analogy that assumes something that is not so.
P.S. I am not EdB. That is someone else.
I know your handle — it is Ed Bo — I knew it, when I typed “Ed B” — I abbreviate last names, in order to be less formal and less direct in addressing people sometimes, because it seems a bit less finger-pointery, and keeps a bit of anonymity in the exchange for viewers who are not familiar with the players in the discussion. Feel free to address me as “Robert K” or “RK”, if you want.
Interesting that Ed Bo says that JP doesn’t know how an Oven works and yet it is he that does not know how a Gas Cooker Oven works.
It is on full power until the thermostat temperature setting is reached, it does not “turn off”, it only turns down sufficiently to maintain that temperature.
It would normally only go back to Full On if the door is opened and substaintial heat is lost or a higher temperature is chosen.
RK:
I’m afraid you’re still missing the whole point, which is why I have begun to question your basic competence.
You obviously consider the average-power model to be a reasonable approximation for an oven with on-off control. And I’m glad you are no longer disputing me when I claim that the temperature falls during the off cycle. (When you earlier flat out argued against me and claimed “in the oven you so well describe, the temperature IS constant”, you were arguing that the temperature did not go down when the input power was off. I’m sorry, but you deserved the mockery that followed.)
Now, at least you acknowledge the existence of a temperature drop, saying “During cook time, the oven temperature does not drop appreciably anywhere near ambient temperature.” Similarly, during the night half of the earth’s diurnal cycle, the earth temperature does not drop appreciably anywhere near ambient temperature. In the case of the earth, “ambient temperature” is 3K (-270C).
By the way, on its website, the GE appliance division says that the typical variation for its ovens over a cycle is between +30F and -30F about the set point, for a total variation of 60F!
You still have not given any real argument why you consider the average-power model to be a decent approximation for the oven with cyclic power input, but not for a location on the earth that has cyclic power input. That diagram is only a simple conceptual illustration using the average-power model.
There is NOTHING about the science of the “greenhouse effect” that is in any way “based” on this simplified model, just as there is nothing about the science of an oven that is in anyway based on the simplified average-power model for the oven. Any serious calculations do split the earth into small sections at small time intervals, respecting the location varying and time varying inputs for each section and time step.
JP’s continued inability to realize that the diagrams he mocks are just simplified conceptual illustrations, rather than the analytical basis for the effect, just goes to underline his complete confusion in these matters.
I cannot comprehend how stupid some people can be. The oven switches on and off to maintain a fixed TEMPERATURE. You cook at a fixed temperature in an oven and the control system of the regulates this by modulating the power inpout to maintain the temperature which is monitored by a thrmocouple. Stick a live turkey in an oven and cook at 280f for 6 hours and the turkey will die and get cooked. Put the live turkey in an oven at a lower temperture for a much longer period and the turkey gets warmer but lives quite happily. The total energy input is exactly the same. Very hot temperature for a few hours, then nothing, versus a moderate temperature over a long time. The outcomes are very different!
As has been pointed out, the world and physical processes occur in real time…not some arbitrary average. I think it has also been shown in numerous places that chemical reactions have an activation energy. You have to supply a certain amount of energ to indce a reaction to occur. The example of the burning paper and the heater is a perfect example. To burn, paper must be raised to a certain temperature. If you do not raise the paper to that temperature it will never burn. So although (in the heater case) the the energy supplied over a period of 24hrs is the same for both examples, the physical reality of what can be done with that total enery is very different. In one case the paper burns, in the other it never can. This is what you normally learn at school at the age of 14.
Similarly, during the night half of the earth’s diurnal cycle, the earth temperature does not drop appreciably anywhere near ambient temperature. In the case of the earth, “ambient temperature” is 3K (-270C).
Yes, and in the case of the moon with a much longer diurnal cycle the temperature drops much closer to the baseline. For a very small diurnal cycle one can make a reasonable approximation by using averages, Earth is near to that case.
This is typical diversionary nonsense.
You simply cannot achieve the 180+°C required to cook anything in an oven by using “average” energy flux.
As a simple blackbody calculation a body 180°C emits ~2390 W/m2 therefore by the law of energy in = out requires similar input to reach 180°C. You can cook something in an hour for a total energy input of 2390 Watt hours.
But you cannot cook something by adding 10 hours worth of 239 W/m2 for the same energy input of 2390 Watt hours.
It doesn’t add up so why not simply admit it ?
Rosco:
Like Joe and Robert, you have absolutely no idea how your oven works! Don’t you realize that your kitchen oven, whether gas or electric, applies power in a cyclic on/off manner? And that these ovens are perfectly capable of cooking things at 180C? This is a simple empirical everyday FACT!
Let’s say your well insulated oven (not able to radiate directly to the kitchen), when at 180C inside, loses thermal power to the kitchen ambient (~25C) at a rate of 500 watts. If the full-on power of the oven is 2000 watts, the thermostat will turn on the power for 1/4 of the cycle, and off for 3/4 of the cycle, producing an average power input of 500 watts.
During this cycle, the temperature inside the oven will rise several degrees (say, to 183C) while the power is on, and drop several degrees (say,to 178C) when the power is off. Typically this cycle is a few minutes long. And the turkey cooks just fine. And nobody thinks the extra cost and complexity of allowing the oven to apply partial power continuously is worth it!
Apparently you don’t understand how they work. A gas oven absolutely does NOT cycle itself on/off .. I used to be a chef, I have used many gas stoves and ovens. You are a blooming idiot !!!
No Squidly:
It is absolutely standard for thermostatically controlled gas ovens to cycle on and off. Every gas oven I have ever used does this. Websites are full of people’s questions as to why their ovens do this. They have answers such as “Your oven is constantly cycling on and off automatically to maintain a temperature range close to what you have set at the oven thermostat.”
Home furnace systems work this way as well, and so do hot water systems.
My point stands
GE says they do:
https://products.geappliances.com/appliance/gea-support-search-content?contentId=18068
It sounds like GE ovens are electric.
Gas Ovens never “Switch Off”, they only lower their flame to maintain the temperature.
I have cooked with gas forthe last 60 years and not one of them ever switched off and switched back to full on unless the door was opened.
AC:
Read the very first sentence on the web page Phil links to. It says:
“Gas and electric ovens will cycle on and off throughout the cycle to maintain the set temperature.”
Notice the first word! Are you claiming GE doesn’t know how its own ovens work?
Automatically controlled variable gas valves are expensive and finicky compared to simple on/off valves. Ditto for the electronics needed to control them. They are very difficult to justify in a cost-competitive market.
That is why every gas oven, gas home furnace, or gas water heater I have ever used employs on-off control.
Well, I have had 5 Gas Cookers in the UK and not one of them Turned itself off, it turned itself down just low enough to maintain the set temperature.
The only cooker I know of that turns itself off is one that does so on stupid safety grounds when you open the door.
So my 5 gas cookers do not work the same as yours or GEs and neither did Squidly’s when he was cheffing.
We spend enormous effort debating the how a trace gas in the atmosphere retards the passage of IR radiation to space thereby reducing the cooling of the planet, but we tend to ignore a much larger trapping of heat by the oceans.
Most of the incoming solar energy strikes the planet in the Tropics, about 40% of the earth’s surface area. This area is 36% land mass, 64% water. The greater portion of the radiation penetrates the oceans where it is effectively trapped as heat. Consider how this heat can dissipate. Water is opaque to IR, convection is suppressed because the water nearer the surface is already warmer, sideways conduction is possible. The main distribution is by currents but the heat in the oceans can remain there for very long periods. The oceans control our climate.
On any given day on earth some surface area at + 40°C and some at -40°C(rough min/max). 273+/-40 is approximately a +/- of 15%. 1.15^4 ~ 1.75, 0.85^4 ~ 0.5 that is a 3.5 to 1 non-linear variation in W/m^2 . 275/273 ~ 1.007. 1.007^4 ~ 1.03% change for 2°C warming. Whatever co2 warming there may be is totally lost in the errors of using linear averages on non-linear equations.
Climate change needs what physics needs: A Theory of Everything. What I have read here and elsewhere makes it abundantly clear that there are many schools on climate change theory and none actually agree. There are arguments all the time over what the theory does and does not say. That’s okay in theoretical physics—no one is attempting to create world government and shut down capitalism with string theory. It’s very, very bad in climate change. Until someone can explain global warming in a way everyone agrees upon, we don’t need action. Trying to fix an undefined entity is just plain foolish.
So, if this energy from the sun is now hitting a disk then the bright side of the disk ‘should’ equate to the average hot temperature of the Earth (average Tmax?), so the dark side of the disk should be cold (average Tmin?).
If not why so?