Guest Post by Willis Eschenbach
The Intergovernmental Panel on Climate Change, the bureaucratic agency which appropriated the role of arbiter of things climatic, has advanced a theory for the lack of warming since the turn of the century, viz:
The observed reduction in warming trend over the period 1998–2012 as compared to the period 1951–2012, is due in roughly equal measure to a cooling contribution from internal variability and a reduced trend in radiative forcing (medium confidence). The reduced trend in radiative forcing is primarily due to volcanic eruptions and the downward phase of the current solar cycle. However, there is low confidence in quantifying the role of changes in radiative forcing in causing this reduced warming trend.
So I thought I’d look at the CERES dataset, and see what it has to say. I started with the surface temperature question. CERES contains a calculated surface dataset that covers twelve years. But in the process, I got surprised by the results of a calculation that for some reason I’d never done before. You know how the IPCC says that if the CO2 doubles, the earth will warm up by 3°C? Here was the question that somehow I’d never asked myself … how many watts/m2 will the surface downwelling radiation (longwave + shortwave) have to increase by, if the surface temperature rises by 3°C?
Now, you’d think that you could just use the Stefan-Boltzmann equation to figure out how many more upwelling watts would be represented by a global surface temperature rise of 3°C. Even that number was a surprise to me … 16.8 watts per square metre.
Figure 1. Blue line shows the anomaly in total downwelling surface radiation, longwave plus shortwave, in the CERES dataset, March 2000 to September 2012. Red line shows the trend in the downwelling radiation, which is 0.01 W/m2 per decade. Gray area shows the 95% confidence interval of the trend. Black line shows the expected effect of the increase in CO2 over the period, calculated at 21 W/m2 per doubling. CO2 data are from NOAA. Trend of the expected CO2 change in total downwelling surface radiation is 1.6 W/m2 per decade. CO2 data from NOAA.
But as they say on TV, wait, there’s more. The problem is, the surface loses energy in three ways—as radiation, as sensible heat, and as the latent heat of evapotranspiration. The energy loss from the surface by radiation (per CERES) is ~ 400 watts per square metre (W/m2), and the loss by sensible and latent heat is ~ 100 W/m2, or a quarter of the radiation loss.
Now, the sensible and latent heat loss is a parasitic loss, which means a loss in a heat engine that costs efficiency. And as any engineer can testify, parasitic losses are proportional to temperature, and as the operating temperatures rise, parasitic losses rise faster and faster. In addition, the 100 W/m2 is the global average, but these losses are disproportionately centered at the hot end of the system. At that end, they are rising as some power factor of the increasing temperature.
But let’s be real generous, and ignore all that. For the purpose of this analysis, we’ll swallow the whopper that a 3° temperature rise wouldn’t drive evaporation through the roof, and we’ll assume that the parasitic sensible and latent heat losses from the surface stay at a quarter of the radiation losses.
This means, of course, that instead of the increase of 16.8 W/m2 in downwelling radiation that we calculated above, we need 25% more downwelling radiation to account for the parasitic losses from the surface. (As I said, the true percentage of parasitic losses would be more than that, likely much more, but we’ll use a quarter for purposes of conservative estimation.)
And what that means is that if the IPCC claim of three degrees of global warming per doubling of CO2 is true, when the top-of-atmosphere radiation goes up by a doubling of CO2, an additional TOA 3.7 watts per metre squared, the surface downwelling radiation needs to go up by no less than 21 W/m2 per doubling. And although I was surprised by the size of the number, to me was very good news, because it meant that if it were there, it should be large enough to be quite visible in the CERES data. So I took a look … and Figure 1 above shows what I found.
The red line shows the trend over the ~ 13 years of the record … which is 0.01 W/m2 per decade, statistically no different from zero.
The black line, on the other hand, is the change in downwelling radiation expected from the change in CO2 from 2000 to 2012, calculated at 21 W/m2 per doubling of CO2. As you might imagine because of its steady increase, there is little difference between the CO2 data and the CO2 trendline, so I’ve left it off. For the same reason, there is virtually no error in the trend in downwelling radiation expected from CO2. The result is an expected increase in downwelling surface radiation of no less than 1.6 ± 0.007 W/m2 per decade. Over the period of the CERES data, it totals almost 2 W/m2, which in terms of the precision of the individual CERES datasets should certainly be visible.
So … does Figure 1 falsify the CO2 hypothesis? Not yet, we’ve got a ways to go, but it is an interesting finding. First, we need to look at the two explanations postulated by the good folks at the IPCC that I quoted at the head of the post—volcanoes and solar variations. And the amount that we are looking to explain is a missing increase of 1.6 W/m2 per decade.
Their first explanation was solar. Since the downwelling surface radiation has not increased as expected, perhaps there’s been a decrease in the incoming TOA solar radiation. This would offset a warming from CO2. Here’s that data:
Figure 2. Trend in TOA Solar Radiation, 2000-2012. Red line shows trend, a decrease of – 0.15 W/m2 per decade.
So the IPCC is right about the solar. And from having to explain 1.6 W/m2, we’ve explained 0.15 W/m2 of it which leaves 1.45 W/m2 of missing warming.
Next, volcanoes. The IPCC says that the effect of volcanoes over the period was to cut down the amount of sunshine hitting the surface, reducing the total downwelling radiation.
The reduced trend in radiative forcing is primarily due to volcanic eruptions …
Here are the anomalies in that regard:
Figure 3. Action of volcanoes in reducing surface solar radiation. This measures the anomaly in downwelling solar at the surface minus the anomaly in downwelling solar at the TOA. The trend in the transmission is a warming of +0.34 W/m2 per decade.
Bad news for the IPCC hypothesis. Rather than volcanoes counteracting the expected warming and decreasing the atmospheric transmission of sunshine over the period of record, we had a trend of increasing amounts of sunlight making it to the surface. The trend of this increase was 0.34 W/m2 per decade. Kinda blows holes in their theory about volcanoes, but all we can do is follow the data …
And as a result, instead of having to explain a missing warming of 1.6 – 0.15 = 1.45 W/m2 per decade, we now have to add the 0.34 W/m2 to the missing warming, and that gets us up to 1.8 W/m2 in missing warming. So rather than explaining things, overall the IPCC explanation just makes things worse …
Anyhow, that’s how it goes to date. If the IPCC theory about 3°C surface warming from a doubling of CO2 is true, we need to either a) come up with something else in the CERES data to explain the missing CO2 warming of 1.6 W/m2 per decade, b) back off on the IPCC climate sensitivity by a factor of about ten … or my perennial favorite, toss out the idea of “climate sensitivity” entirely and recognize that at equilibrium, temperature isn’t a simple function of TOA forcings because the climate system has emergent phenomena which respond and react to counteract the TOA changes.
The big problem that I see for the hypothesis that GHGs rule the temperature is that over the period of the CERES data, we should have seen a shift of almost two watts in the downwelling total radiation … but I find no such thing in the dataset. So I throw this question out to the climate science community at large.
Where in the CERES data is the missing warming? There is no trend (0.01 W/m2 per decade) in the surface downwelling radiation. The IPCC says that over the period, CO2 should have increased the downwelling surface radiation by ~ 2 W/m2. SO … if the IPCC hypothesis is correct, what is countering the expected increase of ~ 2 W/m2 in the downwelling surface radiation due to the increase in CO2 over the 2000-2012 time period?
Solar explains perhaps 10% of it, but the volcanoes push it the other way … so why can’t I find the two watts per square metre of expected CO2 warming in the CERES dataset?
w.
NOTES
USUAL REQUEST: If you disagree with something that I or someone else said, please QUOTE THE EXACT WORDS YOU DISAGREE WITH. Then, and only then, let us know what you disagree with. I can defend my own words. I cannot defend your interpretation of my words.
DATA AND CODE: I’ve put the data and code used to produce the graphs and calculations online. There are three code files: CERES Setup.R, CERES Functions.R, and the code for this post, CO2 and CERES.R. In addition, there are two datafiles, one for the CERES TOA files, and the other for the CERES surface files, entitled CERES 13 year (230 Mbytes), and CERES 13 year surface (112 Mbytes). I think that the data is turnkey, just pull up the CO
All of them need to be in the same folder, because the CO2 and CERES.R file calls the setup file, which loads the data files and the function file. If you’ve downloaded the CERES 13 year file, it is unchanged, no need to reload. Open the CERES Setup.R file to see the names of all of the datafiles loaded, and open the CERES Functions.R file for functions and constants.
And as Steven Mosher recommended to me, use RStudio as your portal into R, much the best I’ve found.
CERES Data: The top-of atmosphere CERES data is measured by the satellites. On the other hand, the CERES surface data is calculated from the TOA CERES data, plus data from the MODIS and GOES satellites. The calculated surface data is energy balanced, meaning that the surface flows sum up to the TOA flows.
I’ve run my own version of ground truthing on the CERES surface data by comparing it to the surface temperature data I was using previously. Differences were small overall, and both sets shows the same small details and fluctuations.
Is this how I’d like to do the analysis? Not at all. I’d rather that everything were measured … but this is the best we have, and the various climate scientists involved have used all of the available observational data from a variety of satellites to determine the various values, and have ground truthed the surface data in a variety of ways. So until we have better data, the CERES datasets are the closest we have to actual measurements … and as near as I can tell they show no sign of the claimed 2 W/m2 increase in downwelling radiation that we are assured is going on over the period of record.
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Dr. Strangelove says:
January 16, 2014 at 7:04 pm
Thanks, Doc. You are right … but only some of the time. Actually, at times hot air can move very fast (see a hot air balloon that’s been sucked up into a thunderstorm).
In addition, the heat moving from the surface up to where it enters the thunderstorm is mostly in the form of latent heat … and that is not subject to radiation.
Next, while the rising column of air is inside the thunderstorm tower, it is isolated completely and not free to radiate.
As a result of all of these, heat is able to move by means of hot air from the surface to the top of the troposphere and lose almost no energy to radiation.
Best regards,
w.
”
Gino says:
January 14, 2014 at 7:42 pm
Willis says:
“Now, emissivity is on the order of 1.0 for the surface of the planet.”
I’m not sure why this is valid given the emissivities of common materials:
http://www.omega.com/literature/transactions/volume1/emissivityb.html
Water : .67
Soil (surface): .38
Granite: .45
snow: .89
Sand: .76
”
http://www.infrared-thermography.com/material-1.htm
shows water at 0.98. omega is a catalog sales company. At surface temperatures, one finds practically everything having an emissivity of very close to 1.
“As a result of all of these, heat is able to move by means of hot air from the surface to the top of the troposphere and lose almost no energy to radiation.”
Willis, air above absolute zero temperature is radiating energy all the time even as it cools. My point was if you heat air, you will detect a change in radiation flux following S-B law. In response to the claim that you can heat air and detect no change in radiation flux because heat is directly converted to potential energy.
“Before a parcel of air rises, its temperature must be higher than surrounding air. ”
Not quite right.
The additional energy received by an individual air parcel via conduction both reduces the surface temperature below it and reduces the density of the air parcel. Reduction in density is also a cooling effect. Any ‘extra heat’ disappears into the reduction of density and subsequent uplift.
Furthermore, since the amount of incoming energy is fixed any extra warming in one location is offset by a correspondingly reduced warming in another location which is why it is the unevenness of surface heating which is critical.
No net gain or loss of total energy, just uneven distribution of energy is sufficient to cause the density differentials that lead to convection. GHGs not needed.
It is the reduction in density that allows the parcel to rise and not an increase in temperature.
Willis said:
“Whaaaaa? Climate is what is called a “radiative-convective” system. I just discussed and linked to my Excel model of said radiation AND convection.
Exactly what is it you think I “cannot reconcile” between the two ?”
The link with conduction.
Convection results from conduction and temporarily removes energy from the radiation budget by converting it to gravitational potential energy.
For your thermostat hypothesis to work you need some way of adjusting the radiation budget to counter any forcing elements.
Hello again, Willis
“Now, you are right that that is a significantly large difference. But for many things, it doesn’t make much difference.”
That is true, but if the issues are to be addressed properly, we need to understand which things it makes a difference for and which it doesn’t, before we rely on methods and approximations that we know a priori to be inexact. And then the question arises, if we have done the two calculations to show that the difference between using an exact and an inexact method is small, why not just stick with the exact method ? After all computer cycles are cheap, and it would save others from making erroneous deductions from our results when they don’t read the caveats in the small print.
…when it is a hot day on the highway, it’s a hot day on the grass and a hot day on the river.
Hmm…. When it is a hot day, the river is distinctly below air temperature. It has a lot of ‘thermal mass’ to move and mixing keeps bringing cooler water to the surface while evaporation recools the surface itself. The asphalt, however, does not mix and has poor thermal conductivity, so that in sunshine it can get a lot hotter than air temperature. The grass is somewhere between the two, moderated by transpiration, some evaporation and some conduction but not by mixing.
When it is a cold day, the river surface can be considerably warmer than air temperature, due to thermal mass and mixing, whereas the grass and asphalt are much closer to air temperature.
On average the anomaly on the asphalt is higher than the anomaly on the grass which is higher than the anomaly on the river. When we use a spatially average anomaly it will works fine with effects which are linear functions of temperature, but quartics, like S-B and quadratics like the ‘Robert Brown’ correction are another matter. Both will be understated.
OT, this discussion make me wonder if the Urban Heat Island effect has been understated by averaging before making S-B calculations, because urban areas will have larger diurnal and annual variation than nearby farmland / woodland / jungle.
***
Ken Gregory says:
January 15, 2014 at 3:56 pm
Willis has compared the downward radiation trend (0.14 W/m2/decade) to an estimated downward radiation trend that would give a 3 C temperature rise per double CO2, but that is not the appropriate comparison. The IPCC’s estimate of 3 C/ 2X CO2 is the equilibrium climate sensitivity, which means you double the CO2 then wait a thousand years for the oceans to reach temperature equilibrium.
***
IMO the IPCC & others are wrong on this. There’s no significant time-lag for CO2 warming — a yr or two would be a stretch. Unlike solar SW forcing, CO2 IR doesn’t penetrate surfaces to any extent, so warming (less cooling to be accurate) from that is essentially immediate — a combination of surface warming and added water vapor. Yeah, there’d be alittle mixing at the water surfaces, but almost nothing would be “stored”.
An important point is that that any surface warming from any cause will be uneven on a rough surfaced rotating sphere illuminated by a point source of energy.
As soon as any unevenness is introduced the densities at the surface vary and a convective circulation begins as the less dense parcels rise above the more dense parcels.
If GHGs produce more DWIR the effect on the surface will be uneven and density differentials in the horizontal plane just above the surface will become greater.
Such greater density differentials in the horizontal plane must accelerate the rate of overturning which would have the capability of negating the effect of GHGs by increasing atmospheric heights due to the increased upward force of the reduced local densities at the surface.
That way one can have the increased DWIR beloved of AGW proponents yet still have the thermal effect negated by the conductive / convective response.
Is it? Is the Sun’s surface really no hotter than the inside of our planet Earth?
Is this a serious question? I will pretend that it is:
http://en.wikipedia.org/wiki/Photosphere
although you should obviously read the entire article on the Sun if you have to ask the question. The temperature is determined by its spectrum:
http://en.wikipedia.org/wiki/File:EffectiveTemperature_300dpi_e.png
At the moment it is a crap shoot as to whether this temperature is a bit hotter or colder than the temperature at the Earth’s core:
http://en.wikipedia.org/wiki/Inner_core
Until recently, the Sun would have narrowly won over the best estimates, but new estimates have bumped the Earth’s core temperature up substantially. It might well be hotter than the surface of the sun.
Bear in mind that the core temperature of the Sun is much, much hotter. The sun seriously traps radiation — even though the power density of the Sun’s core is comparatively tiny, it takes tens of thousands of years for core photons to make it out of the Sun.
The Sun and stars in general are actually very, very interesting.
But the point is that the Earth is an open system. In order to make all of the tired old arguments about “cold heating hot” — which is not at all what happens — step one is to ignore the fact that Sun is not, actually, cold on its surface and it is the Sun’s surface that produces and delivers well over 99% of the energy that maintains the temperature distribution of the Earth as it is transiently absorbed, retained for a time, and eventually lost en route to 3 K background “space”. The atmosphere differentially passes this energy through the system — energy “in” via SW radiation emitted by a very hot source through a mostly transparent atmosphere; energy “out” via LWIR emitted by the much cooler Earth surface and atmosphere in a complex and variable spectral pattern generated by the three substantial absorber/emitters of LWIR in the atmosphere: H2O, CO2 and O3 (in that order of importance).
These are the greenhouse gases, and this is the greenhouse effect.
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rgb,
I recall reading somewhere [maybe here] that on average, any part of the sun puts out about the same amount of heat as a similar-sized compost pile. It is the enormous mass of the sun, versus its surface area, which makes it so bright.
Is that true? Or is that one of those factoids that just sound good on the internet?
And so on and so forth. Blah-blah. Dr. Brown, you’re completely circumventing the issue here. This is all about an object absorbing two smaller fluxes and as a result end up giving off a flux larger than any of them. Why not then just surround a warm object with a million cool objects and watch the warmer one literally melt from the immense ‘total’ flux it receives? Because that would be ridiculous. The solar and the atmospheric flux are coming from the same area of the sky. That’s the only reason you feel you could add them. But the problem is, the sun is the energy source of the surface and the surface in turn is the energy source of the atmosphere. Energy is transferred only from the sun to the earth’s surface. Between the surface and the atmosphere, the energy transfer is up. There is no point adding something that cannot heat the surface. Your downward radiative flux isn’t a heat flux, like the solar flux. The radiative (and convective) heat flux between surface and atmosphere goes … up. There is nothing to add.
and 
. It doesn’t say a word about ice cubes heating anything at all — the sun provides all of the heat — but the LW-absorptive atmosphere absorbs part of the heat radiated from the surface and re-radiates part of it back down at the surface. It is the condition for detailed balance and the requirement that net heat can only flow from warmer things to cooler ones that causes the surface to warm. It is really no different from any insulator. The power pumped in has to equal the power that comes out. Putting anything in between the continually heated reservoir and the cold reservoir it must continually lose heat to will cause that reservoir to get warmer. Slow conduction? It will get warmer. Slow radiation? It will get warmer. Slow convection? It will get warmer. Reduce latent heat transfer? It will get warmer. That’s because all of the different heat flow equations are driven by a monotonic temperature difference — to make the second law happy.
So what part of the Steel Greenhouse — which you stated that you agreed with, curiously — do you not get? Look, do yourself a favor. Buy a copy of Petty’s book A First Course in Atmospheric Radiation”. I did. And I actually already understand all of the physics that is in it on a standalone basis. It is often really useful to see how the physics all fits together.
Go Read section 6.4.3. That’s the “single layer nonreflecting atmosphere model”. One limit of its very, very simple parameters is the steel greenhouse — which you agree with. Study the equations for detailed balance until you understand them. Study equation 6.37 — the limit that becomes the steel greenhouse for
This really is very simple to understand if you don’t have an agenda and simply try to understand the science and mathematics itself. You’ve asserted that you aren’t a dragonslayer. Prove it. Actually pick up a textbook on this and read it before continuing to make absurd statements that are literally irrelevant to the actual primary processes that are going on in radiative energy transfer in the atmosphere.
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Damn you, closing ! Grrrr.
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Closing left bracket slash b right bracket! Arrgh!
zyz says:
January 17, 2014 at 6:04 am
Thanks, zyz. I, along with virtually all serious researchers in the field, utilize and average radiation whenever possible. However, you are overestimating the problem. Let me illustrate with another example. Suppose we average the planet’s temperature. Then, everywhere on the planet warms by half a degree, much like the 20th century. How much does our average of the temperature warm up? Well … half a degree, 0.5°C.
Now, suppose we do it the other way. Start by averaging the radiation rather than the temperature. Then add the equivalent of half a degree in the form of radiation to each gridcell. Re-average the radiation and convert to temperature … and we find the difference is 0.498°C.
Now, that’s a difference of two thousandths of a degree, a meaninglessly small error … like I said, most of the time, your issue is a difference that doesn’t make any difference.
Finally, you are correct when you say it should be done the right way, by averaging radiation … but overwhelmingly, climate scientists already do that wherever it makes a difference. As I said, that’s why Trenberth’s global energy budget is in W/m2, not in degrees C …
w.
gbatduke says:
January 17, 2014 at 1:27 pm
Is it? Is the Sun’s surface really no hotter than the inside of our planet Earth?
Is this a serious question? I will pretend that it is:
…..although you should obviously read the entire article on the Sun if you have to ask the question. The temperature is determined by its spectrum: light.http://en.wikipedia.org/wiki/File:EffectiveTemperature_300dpi_e.png
The Sun and stars in general are actually very, very interesting.
Of course it is a serious question, I also find them very, very interesting. I find estimating the temperature by the photosphere to have problems..
The photosphere, although often referred to as the surface, is but a 300 mile wide band of visible light being bounced around by some calcium, if I recall, much like visible light is bounced around our atmosphere by the electrons of nitrogen and oxygen, it is not the surface of the Sun, but its first layer of atmosphere – the surface of the Sun is the convection zone below that being cooked by the heat streaming off from the millions of degrees core by the radiative zone. It seems to me absurd that this tiny band of visible light is somehow stopping the millions of degrees heat from the Sun to give itself a temperature of 6,000°C, and then, somehow, and no one knows how, the further millions of miles atmospheres of the Sun are again millions of degrees hot.
It does not compute. What it says, to me, is that the estimate by planckian colour coding is not accurate, because millions of degrees heat are still streaming away from the Sun through the insignificant scant three hundred mile wide ring of visible light .
At the moment it is a crap shoot as to whether this temperature is a bit hotter or colder than the temperature at the Earth’s core:..Until recently, the Sun would have narrowly won over the best estimates, but new estimates have bumped the Earth’s core temperature up substantially. It might well be hotter than the surface of the sun.
And that’s the other problem, what appears to me to a complete absence of any sense of scale..
The heat we feel from the Sun is thermal infrared, longwave infrared, – it takes around 8 minutes to travel some 93 millions miles to reach us – do you really think that the heat from something let’s call it fire, of 6,000°C could be felt by us 93million miles away?
But the point is that the Earth is an open system. In order to make all of the tired old arguments about “cold heating hot” — which is not at all what happens — step one is to ignore the fact that Sun is not, actually, cold on its surface and it is the Sun’s surface that produces and delivers well over 99% of the energy that maintains the temperature distribution of the Earth as it is transiently absorbed, retained for a time, and eventually lost en route to 3 K background “space”. The atmosphere differentially passes this energy through the system — energy “in” via SW radiation emitted by a very hot source through a mostly transparent atmosphere; energy “out” via LWIR emitted by the much cooler Earth surface and atmosphere in a complex and variable spectral pattern generated by the three substantial absorber/emitters of LWIR in the atmosphere: H2O, CO2 and O3 (in that order of importance).
These are the greenhouse gases, and this is the greenhouse effect.
But, you have given the Sun a cold surface, 6000°C is not very hot..
Traditional science disagrees with your “Shortwave In” scenario, please, seriously, read the NASA quote I have given. The Sun produces both heat and light and they are not the same thing. We feel the invisible heat from the Sun and that is Longwave wave infrared – we cannot feel shortwaves as heat.
This is important, we cannot physically feel shortwaves from the Sun. They are not the great heat you feel from the Sun.
I really do not understand this, I have given a direct quote from NASA which you are all, apparently, completely ignoring..
Trenberth et al’s energy budget is complete crock, just like the ‘temperature’ records and hockey stick…
And, my other example of an incandescent lightbulb which radiatiates out 5% visible and 95% longwave infrared heat – why is the Sun any different to that? The visible part of the Sun’s total spectrum is very tiny, most of the Sun’s radiant energy is invisible.
Of that energy reaching the Earth’s surface the division between Visible UV and Infrared is:
Wikipedia:
“…The total amount of energy received at ground level from the sun at the zenith is 1004 watts per square meter, which is composed of 527 watts of infrared radiation, 445 watts of visible light, and 32 watts of ultraviolet radiation.”
Since AGW claims only “shortwave in” and says of that its shortwave infrared is only an insignificant 1% – what has it, AGW/CERES/Trenberth done with the rest of the infrared from the Sun? It pretends it comes from ‘backradiation’ …
On the NASA revises Earth’s radiation budget thread, a different radiation budget from NASA has just been posted – it does not show ‘backradiation’ as does the NASA/Trenberth one…
dbstealey says: January 17, 2014 at 1:37 pm
I recall reading somewhere [maybe here] that on average, any part of the sun puts out about the same amount of heat as a similar-sized compost pile. It is the enormous mass of the sun, versus its surface area, which makes it so bright.
Is that true? Or is that one of those factoids that just sound good on the internet?
***************************
It’s just one of those factoids that sound good on the internet. The sun’s radiation is very close to that of a blackbody at 5778K. At the sun’s surface, the flux density can be calculated as:
q = sigma * T^4 = 5.67 x 10^-8 * (5778)^4 = 63.2 million W/m^2
This compares to the approximately 400 W/m^2 from the earth’s surface. (The sun’s surface temperature is about 20 times higher than the earth’s surface temperature, so its radiation flux density is about 20*20*20*20=160,000 times greater.)
But that is the density at the sun’s surface. Of course, it spreads out a lot by the time it gets to the earth’s orbital radius. The sun’s radius is about 700,000 km. The earth’s orbital radius is about 150,000,000 km. By the inverse square law, the density at the earth’s orbital radius is about:
q = 6.32 x 10^7 * (7 x 10^5)^2 / (1.5 x 10^8)^2 = 1376 W/m^2
Even with these very simple calculations, we are very close to the “solar constant” value commonly cited.
beng says:
January 17, 2014 at 8:20 am
I agree with beng on this question. The tail of the exponential decay may be long, but we’re not looking at a single long exponential decay. Instead, there seems to be both a short time constant on the order of a couple of years, and a longer time constant on the order of a number of decades.
And as with any exponential decay, you get the largest change in the first time period, second largest in the second time period, and so on … which is why you get most of the change in the first few years.
However, I disagree on the logic. Both long- and short-wave radiation affect only the instant—the sun doesn’t shine tomorrow, only right now. In addition, energy in many respects is fungible—whether you are adding 1 w/m2 of shortwave deeper in the ocean, or slowing the loss of energy at the surface by 1 W/m2 by adding longwave at the surface, the total energy content of the ocean is changed by the same amount.
As a result, the time constant is a factor of the thermal mass, and not of the method of heating.
w.
Willis said:
“As a result, the time constant is a factor of the thermal mass, and not of the method of heating.”
The time constant is what gives rise to the temperature rise by slowing transmission of solar energy through the system.
If the time constant is a factor of thermal mass does that not relegate any effect from radiative characteristics to insignificance ?
Stephen:
In systems analysis, the time constant is the product of the resistance to the “flow” and the capacitance of the thing into which (or out of which) the flow occurs. Electrical engineers speak all the time of the “RC time constant” of a circuit.
The same concept applies to thermal systems. The time constant will be increased by either and increase in the thermal resistance to power flow or the increased thermal capacitance of the system. (Note that in natural thermal systems like the earth, things are not mathematically linear and we can really only talk about these things in a qualitative sense, but these concepts are still important to understand what is going on.)
On another topic, in above comments, you seem to assert that if a radiatively active gas like H20 or CO2 is convecting, it won’t be radiating. Is that really your claim, or am I misunderstanding you?
” if a radiatively active gas like H20 or CO2 is convecting, it won’t be radiating. Is that really your claim,”
No it is not.
I’m saying that the mass of the atmosphere (including radiative gases) is absorbing kinetic energy by conduction, converting it to gravitational potential energy via convection then returning it to the surface or near surface as kinetic energy a while later thus forming a closed loop which warms the surface above S-B without destabilising the radiative exchange between surface and space.
The radiative characteristics of CO2 or H2O continue throughout but only affect the size or speed of the convective cycle which alters to negate their potential thermal effects on the surface.
Convection always changes so as to ensure that the correct amount of kinetic energy is returned to the effective radiating height thereby keeping the radiative exchange with space stable.
So, the radiative characteristics might increase the time constant for solar energy flow through the system but if it does then the conduction / convection exchange will change so as to decrease the time constant in an equal and opposite reaction.
The very concept of a thermostat hypothesis requires something along those lines.
Lieber Herr Frey, Futter für die nächste Woche.
Ich danke und verbleibe mit freundlichen Grüßen Ihr Michael Limburg Vizepräsident EIKE (Europäisches Institut für Klima und Energie) Tel: +49-(0)33201-31132 http://www.eike-klima-energie.eu/
Curt,
Thanks for that explanation.
The photosphere, although often referred to as the surface, is but a 300 mile wide band of visible light being bounced around by some calcium, if I recall, much like visible light is bounced around our atmosphere by the electrons of nitrogen and oxygen, it is not the surface of the Sun, but its first layer of atmosphere – the surface of the Sun is the convection zone below that being cooked by the heat streaming off from the millions of degrees core by the radiative zone. It seems to me absurd that this tiny band of visible light is somehow stopping the millions of degrees heat from the Sun to give itself a temperature of 6,000°C, and then, somehow, and no one knows how, the further millions of miles atmospheres of the Sun are again millions of degrees hot.
Dude, if you find the Sun interesting, you might start by learning how big it is. That way you won’t be tempted to make statements about “further millions of miles” of atmosphere that reveal your ignorance at the “kids in elementary school” level and hence unqualified to pretend that you are actually contributing to a discussion of the science. You also won’t be tempted to state that “no one knows how” the core of the sun is millions of degrees hotter than the outside. Actually, lots and lots of people know. What you mean to say is that you have no idea how it could be hotter, which is manifestly a true statement but again no more relevant than the statement that a four year old kid doesn’t know either.
The heat we feel from the Sun is thermal infrared, longwave infrared, – it takes around 8 minutes to travel some 93 millions miles to reach us – do you really think that the heat from something let’s call it fire, of 6,000°C could be felt by us 93 million miles away?
Well, let’s see. I walk outside into the sun. My skin warms from the sunlight falling on it. Gee, I guess that the answer is yes. Except that the heat we feel is not all, or primarily LWIR.
I think that you want to imply that this makes no sense. I assure you that if you take the time to learn the physics and mathematics needed to understand it, it makes complete sense and is in fact amazingly consistent. It makes no sense to you, but that is because you cannot do the mathematics, do not understand the physics, and are reduced to making statements that make you sound wise and knowledgeable but that in fact have the opposite effect.
Good luck with that.
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