Guest Post by Ira Glickstein
Solar “light” radiation in = Earth “heat” radiation to Space out! That’s old news to those of us who understand all energy is fungible (may be converted to different forms of energy) and energy/mass is conserved (cannot be created nor destroyed).
My Visualizing series [Physical Analogy, Atmospheric Windows, Emission Spectra, and Molecules/Photons] has garnered almost 2000 comments, mostly positive. I’ve learned a lot from WUWT readers who know more than I do. However, some commenters seem to have been taken in by scientific-sounding objections to the basic science behind the Atmospheric “Greenhouse Effect”. Their objections seemed to add more heat than light to the discussion. This posting is designed to get back to basics and perhaps transform our heated arguments into more enlightened understanding :^)
As I’ve mentioned before, during my long career as a system engineer I’ve worked with many talented mathematical analysts who always provided precise results, mostly correct, but some precisely wrong, usually due to mistaken assumptions. I got into the habit of doing a “back of the envelope” calculation of my own as a “sanity check” on their results. If their results matched within reasonable limits, I accepted them. If not, I investigated further. In those days my analysis was really done using a slide rule and scrap paper, but I now use spreadsheets.
The graphic above is based on an excellent spreadsheet from http://serc.carleton.edu/files/introgeo/models/mathematical/examples/XLPlanck.xls. It uses Planck’s Law to calculate the black body radiation spectrum from the Sun, as observed at the top of the Earth’s Atmosphere. It also may be used to calculate the radiation spectrum from the Earth System (Atmosphere and Surface, see below for explanation) at any assumed temperature. (I will refer to this spreadsheet as “Carleton” in this posting.)
I modified the Carleton spreadsheet to compute the mean Solar radiation per square meter absorbed by the Earth System, which turns out to be 240 Watts/m^2. I then used the spreadsheet to determine the effective mean temperature of the Earth System that would emit an equal amount of energy to Space, and that turned out to be 255 Kelvins (-18ºC which is 1ºF).
Since the mean temperature at the surface of the Earth is 288 Kelvins (+15ºC which is 59ºF), that leaves 33 Kelvins (33ºC which is 58ºF) to be accounted for. Guess how we acount for it?
The yellow curve (above left) shows that Solar radiation is in a tall, narrow “shortwave” range, from about 0.1μm (microns, or millionths of a meter) to about 4μm, which we call ultra-violet, visual, and near-infrared. The vertical axis is Intensity of the radiation, measured in Watts/m^2/μm, and the horizontal axis is Wavelength, measured in μm. If you divide the area under the yellow curve into vertical strips, and add up the total area, you get 240 Watts/m^2.
Since we humans sense the visual portion of this radiation as “light”, that is the name we give it, and that has led to the false assumption that it contains no “heat” (or “thermal”) energy.
The violet curve (above right) shows that, assuming a mean temperature of 255 K, Earth System radiation to Space is in a squat, wide “longwave” range, from about 5μm to beyond 40μm, which we call mid- and far-infrared. If you divide the area under the violet curve into vertical strips, and add up the total area, you get the same 240 Watts/m^2 as is under the yellow curve.
DETAILED EXPLANATION
The graph on the left shows the actual observed Solar radiation spectrum (in red) as measured at the top of the Atmosphere. It is superimposed on a black body model (in blue) showing very good correlation. Thus, while the Sun is not exactly a black body, it is OK to assume it is for this type of “sanity check” exercise.
If you calculate the area under the curve you get about 1366 Watts/m^2. That means that a square meter of perfect black body material, held perpendicular to the Sun, would absorb 1366 Watts.
However, the Earth is not a perfect black body, neither is it a flat surface perpendicular to the Sun! So, to plot the yellow curve at the top of this posting, I had to adjust that value accordingly. There are two adjustments:
- The Earth may be approximated as a sphere, with the Sun shining on only half of it at any given time. The adjustment factor for this correction is 0.25.
- The albedo (reflectiveness) of the Earth system, primarily clouds and light-colored areas on the Surface such as ice, causes some of the Solar radiation to be reflected back out to Space without contributing any energy to the Earth System. The adjustment factor for this correction is 0.7.
After applying these adjustments, the net Solar energy absorbed by the Earth System is 240 Watts/m^2.
The graph on the right shows the black body model for an Earth System at a mean temperature of 255 K, a temperature that results in the same 240 Watts/m^2 being emitted out to Space.
Of course, the Earth System is not a perfect black body, as shown by the graph in the upper panel of the illustration below, which plots actual observations from 20 km looking down. (Adapted from Grant Petty, A First Course in Atmospheric Radiation, Figure 8.2, http://www.sundogpublishing.com/AtmosRad/Excerpts/index.html.)
The actual measured radiation is the dark squiggly curve. Note that it jigs and jags up and down between the topmost dashed curve, which is the black body spectrum for a temperature of 270 K and a lower dashed curve which is the black body spectrum for 230 K. This data was taken over the Arctic, most likely during the daytime. The Petty book also has a graph looking down from over the Tropical Pacific which ranges from 300 K down to 210 K. Observations will vary by tens of degrees from day to night, summer to winter, and Tropical to Polar.
However, it is clear that my result, based on matching 240 Watts/m^2, is within a reasonable range of the true mean temperature of the Earth System as viewed from Space.
NOTE ABOUT THE ABOVE ILLUSTRATION
WUWT readers will notice some apparent inconsistencies in the graphs above. The top and bottom panels, from Petty, peak at 15μm to 20μm, while the purple, blue, and black curves in the middle panel, and the Earth System curves from the Carleton spreadsheet I used (see above) peak in the 9μm to 11μm range. Also, the Petty black body curves peak at a “Radiance” around 100 mW/m^2/sr cm^-1 while the black body curves from Carleton peak at an “Intensity” of around 14 W/m^2/μm. Furthermore, if you look closely at the Petty curves, the labels on the black body curves are mirror image! What is going on?
Well, I know some of the reasons, but not all. (I hope commenters who are more fluent in this than I am will confirm my explanations and provide more information about the differences between “Radiance” and “Intensity”.) I have Googled and Wikied the Internet and am still somewhat confused. Here is what I know:
- The horizontal axis in Petty’s plots are what he calls “Wavenumber”, increasing from left to right, which is the number of waves that fit into a cm (centimeter, one hundredth of a meter).
- This is proportional to the frequency of the radiation, and the frequency is the inverse of the wavelength. Thus, his plots are the mirror image of plots based on wavelength increasing from left to right.
- The spreadsheet I used, and my previous experience with visual, and near-, mid-, and far-IR as used in military systems, always uses wavelength increasing from left to right.
- So, when I constructed the above illustration, I reversed Petty’s curves, which explains why the labels on the black body curves are mirror image.
- Fortunately, Petty also included a wavelength legend, which I faithfully reproduced, in non-mirror image, at the top of each plot.
But, that still does not explain why the Petty black body curves peak at a longer wavelength than the Carleton spreadsheet and other graphics on the Internet. I tried to reproduce Petty’s blackbody curves by multiplying the Carleton values by the wavelength (μm) and that did not move the peak to the right enough. So, I multiplied by the wavelength again (μm^2) and, voila, the peaks agreed! (I hope some WUWT reader will explain why the Petty graphs have this perverse effect. advTHANKSance!)
ANSWERING THE OBJECTIONS TO BASIC ATMOSPHERIC “GREENHOUSE EFFECT” SCIENCE
First of all, let me be clear where I am coming from. I’m a Lukewarmer-Skeptic who accepts that H2O, CO2 and other so-called “greenhouse gases” in the Atmosphere do cause the mean temperature of the Earth Surface and Atmosphere to be higher than they would be if everything was the same (Solar radiation, Earth System Albedo, …) but the Atmosphere was pure nitrogen. The main scientific question for me, is how much does the increase in human-caused CO2 and human-caused albedo reduction increase the mean temperature above what it would be with natural cycles and processes? My answer is “not much”, because perhaps 0.1ºC to 0.2ºC of the supposed 0.8ºC increase since 1880 is due to human activities. The rest is due to natural cycles and processes over which we humans have no control. The main public policy question for me, is how much should we (society) do about it? Again, my answer is “not much”, because the effect is small and a limited increase in temperatures and CO2 may turn out to have a net benefit.
So, my motivation for this Visualizing series is not to add to the Alarmist “the sky is falling” panic, but rather to help my fellow Skeptics avoid the natural temptation to fall into an “equal and opposite” falsehood, which some of those on my side, who I call “Disbelievers”, do when they fail to acknowledge the basic facts of the role of H2O and CO2 and other gases in helping to keep temperatures in a livable range.
Objection #1: Visual and near-visual radiation is merely “light” which lacks the “quality” or “oomph” to impart warmth to objects upon which it happens to fall.
Answer #1: A NASA webpage targeted at children is sometimes cited because they say the near-IR beam from a TV remote control is not warm to the touch. Of course, that is not because it is near-visual radiation, but rather because it is very low power. All energy is fungible, and can be changed from one form to another. Thus, the 240 Watts/m^2 of visible and near-visible Solar energy that reaches and is absorbed by the Earth System, has the effect of warming the Earth System exactly as much as an equal number of Watts/m^2 of “thermal” mid- and far-IR radiation.
Objection #2: The Atmosphere, which is cooler than the Earth Surface, cannot warm the Earth Surface.
Answer #2: The Second law of Thermodynamics is often cited as the source of this falsehood. The correct interpretation is that the Second Law refers to net warming, which can only pass from the warmer to the cooler object. The back-radiation from the Atmosphere to the Earth Surface has been measured (see lower panel in the above illustration). All matter above absolute zero emits radiation and, once emitted, that radiation does not know if it is travelling from a warmer to a cooler surface or vice-versa. Once it arrives it will either be reflected or absorbed, according to its wavelength and the characteristics of the material it happens to impact.
Objection #3: The Atmospheric “Greenhouse Effect” is fictional. A glass greenhouse works mainly by preventing or reducing convection and the Atmosphere does not work that way at all.
Answer #3: I always try to put “scare quotes” around the word “greenhouse” unless referring to the glass variety because the term is misleading. Yes, a glass greenhouse works by restricting convection, and the fact that glass passes shortwave radiation and not longwave makes only a minor contribution. Thus, I agree it is unfortunate that the established term for the Atmospheric warming effect is a bit of a misnomer. However, we are stuck with it. But, enough of semantics. Notice that the Earth System mean temperature I had to use to provide 240 Watts/m^2 of radiation to Space to balance the input absorbed from by the Earth System from the Sun was 255 K. However, the actual mean temperature at the Surface is closer to 288 K. How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Ira, the basic bookkeeping of the simplest greenhouse calculations assumes that the re-emission of infra-red radiation by the greenhouse gas molecules is spatially symmetrical. I am well aware that spontaneous emission is equally likely to be in any direction so that approximately 1/2 will head downward to the surface. However, there is another kind of emission – stimulated emission – and it is massively biased in the same direction of travel as the direction of travel of the stimulating photon. Thats what creates laser light, but stimulated emission can occur without lasing. IF there were any significant amount of stimulated emission happening in the atmosphere then the basic 1/2 back down calculation would likely be wrong because most of the IR through the atmosphere comes from the ground up and, if it is stimulating atmospheric emission, would enhance outgoing IR. Has anyone ever looked for evidence of stimulated emission of outgoing IR in the atmosphere?
Let’s add two more objections to this partial visualization of the Earth System.
1. Where are the storages? Oceans store and release huge amounts of energy. Elaborate your views of the energy/radiation balance.
2. Energy is not just radiation. Earth System is more complex than that. For example, absorbed radiation energy may result in increased cloudiness that has impact on who much radiation reaches the earth. Ignoring major part of the system does not help in believing your conclusions.
CO2 vs Earth’s Atmosphere Screen Saver!
1. Find out how many pixels there are on your computer screen. Using basic math calculate the proportional size in pixels of an image that represents 380 and 400 ppm.
For example if your screen had exactly 1million pixels the image would be exactly 380 or 400.
2. (Sticking with the above example) Go to Google images and search for images that are…380…400..or 20 pixels. Download and place in the centre of an empty screen.
3. Show the images to people who Believe and ask them if they still think that CO2 is anything other than a trace gas and ask them if the eensy teensy baby image; 20 pixels (the increase in CO2) looks sufficient to destabilize the other 999,980 parts of the atmosphere!
This posting is designed to get back to basics and perhaps transform our heated arguments into more enlightened understanding :^)
A little humour goes a long way… Nice, Ira!
Ira, the Second Law of thermodynamics works at every level and you cannot transfer heat from a colder body to a warmer body. A black body cannot also reabsorb and re-emit lower intensity radiation that it has already emited. I’d say that it is also possible to arrive at the temperature difference between the black body radiating temperature and the average surface temperature without any recourse to radiant heating (adiabatic compression by gravity) and same for the surface temperature on the surface of venus. Greenhouse heating by back radiation is surely wrong because it says that if you put a frozen steak inside a vacuum flask with reflective interior that the steak would cook, that if you stand in front of a mirror you will heat up from the reflected rays or that you can save on your heating bills by filling the loft with CO2?
I agree that we can shoot down the dire predictions of the AGW whilst acknowledging that the basic greenhouse theory is correct but there are many now refuting that there is any greenhouse effect.
It should be pointed out that the 33K difference referred to is the effect of the heat-trapping gases in the atmosphere. In the case of each gas, the first small amount has the greatest effect, with diminishing effect as more is added, as according to Beer’s Law. For CO2, it’s effect is 90-95% spent and, thus, the hypothetical doubling of atmospheric CO2 would have little effect, possibly 0.10–0.01 K.
It should also be pointed out that, as CO2 partitions 50 to 1 into the oceans, we would have to emit 50 times more CO2 that required to simply double atmospheric CO2. There is not enough carbon available to do this. If we really tried, we might be able to do 20%.
So, where is the majority of atmospheric CO2 coming from? Outgassing from the oceans with warming, as according to Henry’s Law. And, of course, with cooling, the oceans will soak up CO2. There is a lag period before increases reverse to decreases, but with 30–50 years of cooling ahead, we will be able to see it happen.
Ira is just doing a gross energy balance, so it seems to me that JT’s and Cherry Pick’s objections all occur within the black box of the Earth-black-body emitter.
I don’t like that Ira treats albedo as a constant. That sounds like a fudge factor you would throw into a GCM.
“The adjustment factor for this correction is 0.7.”
What is that? 70%? I don’t think so but I wait to be illuminated after Ira reflects on this.
How much heat energy gets transferred to the Earth black box by the electromagnetic interactions between the Sun and the Earth?
240 Watts/m^2. What’s the error margin on that for the Sun (solar “constant” anyone?) and for the Earth? Seems you could hide a great deal of heat in there.
3. Show the images to people who Believe and ask them if they still think that CO2 is anything other than a trace gas and ask them if the eensy teensy baby image; 20 pixels (the increase in CO2) looks sufficient to destabilize the other 999,980 parts of the atmosphere!
Yes! and then replace “CO2” with Cyanide and “atmosphere” with your body. If they don’t believe you, just ingest 2mg of cyanide for each kilogram of your body weight (1:500,000) and show those iteyucktuals what for!
Ira; The surface air temperature is higher then theoretical because of the insulative mass of the air of the atmosphere. Just like the insulation in the wall of a cooler or a kiln.
Energy out equals energy in. The air is heated at the ground level and looses energy to space. So the air at ground level has more energy per unit then the theoretical black body temperature. The thicker and less dense the insulation the slower the energy flow out. The thinner more dense the insulation (atmosphere) the faster energy lose.
The solar radiation incoming is of wave lengths that are mostly transparent to the atmosphere and heat the oceans and land. Thermal energy as heat and that carried in water vapor is transported through the atmosphere towards space. The surface air temperature is just a single point of measurement in this energy flow. Solar radiation that energizes the atmospheric constituents change the density and thickness of the insulation and therefore the rate of energy flow to space. Ultraviolet and shorter wavelengths are more effective at energizing gas molecules to effect changes in the insulative value of the atmosphere. pg
The basis for the adjustments to the total absorption due to geometric and reflectivity are based on???
“The only rational explanation is the back-radiation from the Atmosphere to the Surface.”
aren’t you overlooking the obvious? ever fry an egg on the sidewalk from back radiation of the atmosphere?
One often meets the assertions that (a) the sea in polar and sub-polar regions is commonly several degrees warmer than the air above it; and (b) in these regions, incoming solar energy has heated the air which in turn heats the sea.
Please expand?
I still have issues with down welling or back radiation in the troposphere. It needlessly complicates the simple fact that clouds, air have a temperature that varies. Increased CO2 can change that temperature but doesn’t beam back little phaser blasts of photons. The layering of temperatures in the atmosphere just complicates the radiative cooling like walls of differing layers of insulation thickness. Without the cutesy back radiation into a warmer surface invention, it might be easier to explain the potential radiative impact of CO2 and with a better model of the atmospheric layers, understand why it is not living up to its potential. Other than that, nice post.
Show the images to people who Believe and ask them if they still think that CO2 is anything other than a trace gas
Remove that “trace” gas and all photosynthetic life of earth dies. And us with it.
Small concentrations can have powerful effects.
“I modified the Carleton spreadsheet to compute the mean Solar radiation per square meter absorbed by the Earth System, which turns out to be 240 Watts/m^2. I then used the spreadsheet to determine the effective mean temperature of the Earth System that would emit an equal amount of energy to Space, and that turned out to be 255 Kelvins (-18ºC which is 1ºF).”
When you say absorbed by earth system, this mostly means amount the surface warms up and the atmosphere itself is only absorbing a small percentage of the incoming solar flux?
And assuming this is the case wouldn’t different material absorb different amounts. Or has this been simplified to mostly account for how much the oceans absorb energy, and since ocean absorb the vast majority of energy that reaches the earth surface, anything else can be mostly be ignored?
Ira,
Thanks for your visualization.
I’d like to comment on your sentence and adress some of the comments here:
“The only rational explanation is the back-radiation from the Atmosphere to the Surface.”
To start, here is my view that I already posted on Climate etc awhile ago..
As I understand it: “backradiation” is the downwelling infrared radiation integrated over all directions that go into the surface.
I am an experimentalist. For me a physical cause is something that I can switch on and off, at least in a thought experiment, and get an intended effect.
If I switch off the sun in a thought experiment, I get cooling of the atmosphere and the surface. If I switch on the sun again, I get warming of the atmosphere and the surface.
If I switch off ”back radiation” in a thought experiment on the night side I get a higher cooling rate.
If I switch on “backradiation” on the night side I get a lower cooling rate.
If I switch on “backradiation” on the day side I get a higher heating rate. Combining my thought experiments I deduct that if I switch on “back radiation” on the day side I get a higher heating rate due to a lower cooling rate because of the “back radiation”
Moreover, I can deduct that with “back radiation” the earth system gets or stays warmer than a reference system without “back radiation”, because of a lower cooling rate.
One might also say “back radiation” leads to a warmer surface compared with a reference system.
However, I do consider sentences as incorrect with respect to physics that state only: “back radiation” is warming the surface.
Of course in any private conversation we state things like: my new coat is warming me nicely. But in a scientific discussion, we need to employ the correct wording, especially in lectures or papers.
For my opinion sentences like: “back radiation” is warming the surface
cause therefore a lot of misunderstanding in the blogosphere. The Gerlich and Tscheuschner discussion is based on it.
Thanks again for your article.
Best regards
Günter
Ira, the radiance formula involves either a “df” or “dλ” at the end. Converting from frequency to wavelength thus involves replacing df by -cdλ/λ², which explains why multiplying the frequency data by λ² puts the peak back in the right place.
This same issue arises in Wien’s Law. The “peak color” is different, depending on whether you use wavelength or frequency as a variable. Intensity, however, is integrated over all colors, and gives the same result for either variable.
/dr.bill
In re Objection #2:
Gas molecules follow ballistic trajectories between collisions…
… unless all the work on Gravity since Galileo is wrong, and doesn’t apply at the molecular level, of course.
Would it make any difference if we doubled the average insolation for half a day, then dropped it to zero for the other half (we’ll call that half night)? We’re radiating outward the entire time, day and night. Messes up the simplicity of the model, but since the temperature varies on a 24 hour clock, the outward radiation does, too.
“As I’ve mentioned before, during my long career as a system engineer I’ve worked with many talented mathematical analysts who always provided precise results, mostly correct, but some precisely wrong, usually due to mistaken assumptions. I got into the habit of doing a “back of the envelope” calculation of my own as a “sanity check” on their results. If their results matched within reasonable limits, I accepted them. If not, I investigated further. In those days my analysis was really done using a slide rule and scrap paper, but I now use spreadsheets.”
During my long career as a nuclear engineer, I got into the habit of doing a “back of the envelope” calculation of my own as a “sanity check” on other’s results. If their results matched within reasonable limits, I accepted them. If not, I investigated further. I also encouraged new engineers to do the same.
What happened to your previous thread. It was getting interesting until no more comments could be posted
http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/
This above thread convinced me even more that backradiation does not further heat the planet. Luke warmers are as scientifically wrong as alarmists if they believe this
The average temperature might slightly increase due to more CO2. But the highest temperature is due entirely to the Sun. In no way can CO2 and backradiation further heat the surface. It can only slow the cooling rate and by so doing might raise the average temperatures
But a colder object can never further heat a warmer one. And saying this time and time again will not make it true. So this objection is correct IMHO.
“Objection #2: The Atmosphere, which is cooler than the Earth Surface, cannot warm the Earth Surface”.
I’d like to comment the “However, it is clear that my result, based on matching 240 Watts/m^2, is within a reasonable range of the true mean temperature of the Earth System as viewed from Space.”
Actually for an inhomogeneous body, and even more if it is not a perfect black body, there is nothing like “the true mean temperature”. You can define different averages, but not a single one; the important thing (never clearly stated by climate scientists, although they probably know it very well), is that the average surface temperature (the integral of TdS divded by the surface), is different from the effective temperature Teff which is such that Prad = S.sigma.Teff^4 , where sigma is the Stefan constant. And these temperatures would also be different from a “best fit Black Body temperature”.
The important thing is that you can easily make one of the temperature vary , holding another one constant ! for instance, the average temperature can vary without varying the effective temperature, that is with the same energy budget – and conversely. This can be demonstrated very simply by noticing that the local temperature can be written as +∆T where is the average surface temperature and ∆T a surface (not temporal) “anomaly”. But the only condition is that = 0. Any repartition with a vanishing surface average gives the same average temperature, but NOT the same effective temperature, since on average the won’t vanish.
This lets a lot of room for spontaneous variation even with no change of forcings. This is carefully hidden under the name of “unforced variability”. After all during El Niño/La Niña cycles, the average temperature changes by several tenths of °C (= several decades of observed trend ! ) without any significant change in the energy budget.
The gospel of climate science is that the unforced variability is restricted to 30 years, which would mean that its power spectrum is cut-off for longer variations. But it can be easily seen that this cannot be true. Natural variability is necessary to explain that long term, secular variations, at century and millenium scales. If it were restricted to 30 years, for instance, the paleoclimate data should show that the average temperature should follow very closely the forcing (Milankovitch) curve, which is obviously not the case. And there are obvious physical reason why the Earth climate could oscillate naturally on millenium scale – for instance that’s the characteristic timescale of thermo-haline circulation and it can be expected to give cycles at this frequency. This is much overlooked by climate scientists, in my sense.
(sorry for the italic tags, can you fix it Anthony. Sorry also for the possible bad english, that’s not my mother language 🙂 ).
Ira
Congratulations, you have provided a good, visual explanation of the basic energy inputs and outputs for the earth. The devil is, of course, as I am sure you would agree, in the detail.
When calculating surface temperatures, variations in the assumed constants in the equations need to be considered. To me the most obvious ‘variable’ constant is that assumed for the earth’s albedo. Spatial and temporal variations due, amongst other things, to the ability of H2O to exist as all three of its phases within the surface and atmospheric regions of the earth, coupled with the large amounts of energy emitted or absorbed at the transition temperatures result in variations in cloud and ice cover, affecting both incoming and outgoing radiation and provide major feedbacks.
When these are coupled with the vast energy storage capabilities of the oceans and more subtle long-term variations of energy input imposed on the earth and solar system from ‘external’ sources known and unknown, the prediction of the earth’s surface temperature variation over an extended period is not within our present capabilities.
In my view the attempts by the powers that be to convince us that the science is settled are the only significant source of ‘hot air’ in the debate!
“How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.”
Since the earth’s core is molten (very hot), there must also be convection of heat from the core to the surface. How much of the extra 33K heat can be attributed to earth’s own heat source? Is it none?… a little?…. or perhaps a significant amount of the 33K? Just wondering.