Characterizing a Planet's Temperature

[cmc0605]

A number of recent discussions on this forum have centered around the factors that govern the global temperature of a body, as well as its ability to respond to radiative perturbations (like an increase in sunlight or CO2). I figured I'd start a thread to work up a starting point on the physics behind global temperature, and see how any discussion evolves from there.

a. We can start with the simplest model of a body in equilibrium with the incoming sunlight that it absorbs. We'll ignore any greenhouse effect or internal heating. We'll suppose it acts like a blackbody in the infrared, which is a reasonable approximation for solid surfaces. It receives energy at a rate Q (which for Earth is taken to be the "solar constant" of ~1365 Watts per square meter). It reflects a fraction of that energy back to space (α, or the albedo). Earth's current albedo is ~30%. But we are interested only in the amount of energy it absorbs, which is Q(1-α). That's the incoming energy side of the balance. For the outgoing side of the equation, then by the Stefan-Boltzmann law, it emits energy at a rate σT^4 (again, in Watts per square meter, where T is the surface temperature and σ is a constant).

b. We can thus write a balance between these terms as Q(1-α)=c σT^4.

Here, c is a geometrical redistribution term. It seems to me to be the source of confusion in previous threads. It comes about because the entire Earth is not bathed in sunlight at any given time, but the whole planet does emit thermal radiation to space. In particular, half the Earth is illuminated at any given time, but even here some areas (such as the equator at noon) receive more energy than other areas (such as New York at twilight). It is certainly possible to define the equilibrium radiative temperature at a point and at any specific time by taking into account the zenith angle, but suppose we're interested in a long-term average. We can also take advantage of the fact that the Earth is very good at mixing heat around. Temperatures do not vary substantially between day and night, or across latitude, at least not on the Kelvin (absolute temperature) scale...typical variations are less than 10%. The Earth is also rotating, and so many areas will probably not reach their maximum radiative equilibrium temperature unless the thermal inertia is very low. So to a first approximation we can do something a bit tricky, and distribute that 1365 W/m2 of energy over the entire planet.

How do we do that? Obviously, we can't let every square meter take in 1365 Watts. This would be valid for the equator at noon, but not valid if we want to redistribute that flux over the entire surface. You might think you could halve this value since half the planet is in sunlight, but again, even that half is not uniform in the amount of sunlight it gets. You could do a relatively complex integral to figure it out, but it's easier to think about. Think if you hold a ball in front of a projector screen, between the projector and the board that the projection is displayed against. On the display, you will only see the cross-section of the ball, or a circle. The ratio of the surface area of the sphere to the area of a circle is the correct redistribution term. Thus, if you choose c = 4 then you are obeying this simplistic approximation. That is, 1365 (1-0.3)/4 = 240 W/m2 is the solar flux redistributed and "averaged" over the entire planetary sphere. You obviously lose information about the day-night cycle, and about differences between the equator and noon. But you clump that together into a global average which turns out to be useful for the approximation we're using. Some of the nuances of defining an average temperature on a rotating planet with thermal inertia is in Smith (2008), but the average will not exceed the so-called "effective temperature" that is obtained by solving for T in the above equation.

c. The approximation is not useful for bodies such as Mercury or the moon that have day-night temperature gradients on the order of hundreds of degrees Kelvin. In situations where there is very little thermal inertia (no ocean or atmosphere) every point essentially reaches radiative equilibrium quickly and you need to treat each point locally, or take some sort of hemispheric average. The night side of the moon becomes extremely cold, and the day side becomes much hotter than anywhere on Earth.

d. In the Earth approximation, we can use the equation to write

1365(1-0.3)/4 = σT^4; after solving for T, you yield a value of the effective temperature, ~255 K. On Venus it's even lower, since the very high albedo (~75%) overcompensates for the fact that it is closer to the sun than Earth. In equilibrium, the Earth is absorbing an average of 240 W/m2 and emitting 240 W/m2. The resulting temperature that is consistent with satisfying this balance is ~255 K.

e. On gas planets/moons, this balance does not hold because there is significant internal heating from gravitational energy or tidal sources. That is, the outgoing energy on planets such as Jupiter or Saturn (Uranus is an exception) exceeds the amount of energy they absorb from the sun, and in fact the internal "luminosity" of these bodies can exceed the energy they get from the sun. This energy is the result of energy stored during the gravitational accretion phase of formation, or the contraction of the gas envelope over geologic time. Tidal heating, produced by the deformation of a planet/moon can heat the body. As a planet moves from perihelion (its closest approach to the star), to aphelion (the furthest point), and then back again, the difference in gravitational force causes an oscillating strain on the body that causes it to undergo periodic deformation which results in friction-induced heating. This is important on Io, and is being studied more in connection with exoplanets in highly eccentric orbits. None of these terms, however, are important on the rocky planets in the interior of our solar system. Even radioactive decay does not propagate onto the surface energy budget very much because of the crust, so internal heating on Earth is many orders of magnitude smaller than the energy it receives from the sun.

f. Consider the case where we add an infrared-absorbing atmosphere (i.e., a greenhouse effect) to the current, simplistic planet in equilibrium with the sun. In keeping the temperature constant, the absorption of outgoing energy will result in less energy escaping to space. That is, it will now absorb more energy from star than is being emitted back to space, and the planet must warm. The Earth is an open energetic system, so this does not violate thermodynamics even though the greenhouse effect is not "creating energy"; rather, the reduction in outgoing energy flow shifts the equilibrium planetary temperature somewhere between its "effective temperature" and the temperature of the star's photosphere. This is shown below. The horizontal line is just the amount of energy the planet absorbs, which we'll treat as a constant and independent of the planet's temperature. In contrast, the outgoing longwave radiation (OLR) depends strongly on temperature, via σT^4. Adding greenhouse gases will, for any given temperature, reduce the OLR (blue curve). Alternatively, you need to go to higher temperatures to reach equilibrium with the incoming sunlight.

g. On Earth, the greenhouse effect results primarily from water vapor (~50% of the infrared absorption), clouds (~25%), and CO2 (~20%). Other gases make up the rest, and clouds actually raise the albedo to over-compensate for their greenhouse effect. That is, clouds cause a net cooling. If one could remove the entire greenhouse effect, and keep the absorbed sunlight the same, you'd reduce the equilibrium temperature of the planet to ~255 K. In reality, you'd also cool the surface enough to trigger a snowball and increase the albedo, resulting in an effective T much lower than 255 K. The dynamics of this state are interesting, and one I like to study in connection with snowball Earth or exoplanets at the outer edge of the habitable zone (but I'm not doing my graduate work on this right now, perhaps in the future). For a planet around a G-type star like our sun, the result is extreme seasonality between the summer and winter, because of the low thermal inertia of the ice surface. The ice-albedo feedback would prevent deglaciation even if pools of open water might temporarily form at the equator, but this is sensitive to the albedo too.

[PhillipS]

Thank you for your clear and concise writeup - I hope others learn as much from it as I did. But I have one (possibly dumb) question. In paragraph G you wrote "... clouds actually raise the albedo to over-compensate for their greenhouse effect". My question is - are clouds raising the Earth's albedo higher than the approximately 0.7 value used in the initial equations, or does that value include clouds? The idea of clouds increasing and providing a negative feedback to compensate for the GHE sounds like Lindzen's "Iris Effect" hypothesis - which I thought had been soundly refuted. Can you please help me understand what I'm missing?

[WeatherRusty]

A number of recent discussions on this forum have centered around the factors that govern the global temperature of a body, as well as its ability to respond to radiative perturbations (like an increase in sunlight or CO2). I figured I'd start a thread to work up a starting point on the physics behind global temperature, and see how any discussion evolves from there.

a. We can start with the simplest model of a body in equilibrium with the incoming sunlight that it absorbs. We'll ignore any greenhouse effect or internal heating. We'll suppose it acts like a blackbody in the infrared, which is a reasonable approximation for solid surfaces. It receives energy at a rate Q (which for Earth is taken to be the "solar constant" of ~1365 Watts per square meter). It reflects a fraction of that energy back to space (α, or the albedo). Earth's current albedo is ~30%. But we are interested only in the amount of energy it absorbs, which is Q(1-α). That's the incoming energy side of the balance. For the outgoing side of the equation, then by the Stefan-Boltzmann law, it emits energy at a rate σT^4 (again, in Watts per square meter, where T is the surface temperature and σ is a constant).

b. We can thus write a balance between these terms as Q(1-α)=c σT^4.

Here, c is a geometrical redistribution term. It seems to me to be the source of confusion in previous threads. It comes about because the entire Earth is not bathed in sunlight at any given time, but the whole planet does emit thermal radiation to space. In particular, half the Earth is illuminated at any given time, but even here some areas (such as the equator at noon) receive more energy than other areas (such as New York at twilight). It is certainly possible to define the equilibrium radiative temperature at a point and at any specific time by taking into account the zenith angle, but suppose we're interested in a long-term average. We can also take advantage of the fact that the Earth is very good at mixing heat around. Temperatures do not vary substantially between day and night, or across latitude, at least not on the Kelvin (absolute temperature) scale...typical variations are less than 10%. The Earth is also rotating, and so many areas will probably not reach their maximum radiative equilibrium temperature unless the thermal inertia is very low. So to a first approximation we can do something a bit tricky, and distribute that 1365 W/m2 of energy over the entire planet.

How do we do that? Obviously, we can't let every square meter take in 1365 Watts. This would be valid for the equator at noon, but not valid if we want to redistribute that flux over the entire surface. You might think you could halve this value since half the planet is in sunlight, but again, even that half is not uniform in the amount of sunlight it gets. You could do a relatively complex integral to figure it out, but it's easier to think about. Think if you hold a ball in front of a projector screen, between the projector and the board that the projection is displayed against. On the display, you will only see the cross-section of the ball, or a circle. The ratio of the surface area of the sphere to the area of a circle is the correct redistribution term. Thus, if you choose c = 4 then you are obeying this simplistic approximation. That is, 1365 (1-0.3)/4 = 240 W/m2 is the solar flux redistributed and "averaged" over the entire planetary sphere. You obviously lose information about the day-night cycle, and about differences between the equator and noon. But you clump that together into a global average which turns out to be useful for the approximation we're using. Some of the nuances of defining an average temperature on a rotating planet with thermal inertia is in Smith (2008), but the average will not exceed the so-called "effective temperature" that is obtained by solving for T in the above equation.

c. The approximation is not useful for bodies such as Mercury or the moon that have day-night temperature gradients on the order of hundreds of degrees Kelvin. In situations where there is very little thermal inertia (no ocean or atmosphere) every point essentially reaches radiative equilibrium quickly and you need to treat each point locally, or take some sort of hemispheric average. The night side of the moon becomes extremely cold, and the day side becomes much hotter than anywhere on Earth.

d. In the Earth approximation, we can use the equation to write

1365(1-0.3)/4 = σT^4; after solving for T, you yield a value of the effective temperature, ~255 K. On Venus it's even lower, since the very high albedo (~75%) overcompensates for the fact that it is closer to the sun than Earth. In equilibrium, the Earth is absorbing an average of 240 W/m2 and emitting 240 W/m2. The resulting temperature that is consistent with satisfying this balance is ~255 K.

e. On gas planets/moons, this balance does not hold because there is significant internal heating from gravitational energy or tidal sources. That is, the outgoing energy on planets such as Jupiter or Saturn (Uranus is an exception) exceeds the amount of energy they absorb from the sun, and in fact the internal "luminosity" of these bodies can exceed the energy they get from the sun. This energy is the result of energy stored during the gravitational accretion phase of formation, or the contraction of the gas envelope over geologic time. Tidal heating, produced by the deformation of a planet/moon can heat the body. As a planet moves from perihelion (its closest approach to the star), to aphelion (the furthest point), and then back again, the difference in gravitational force causes an oscillating strain on the body that causes it to undergo periodic deformation which results in friction-induced heating. This is important on Io, and is being studied more in connection with exoplanets in highly eccentric orbits. None of these terms, however, are important on the rocky planets in the interior of our solar system. Even radioactive decay does not propagate onto the surface energy budget very much because of the crust, so internal heating on Earth is many orders of magnitude smaller than the energy it receives from the sun.

f. Consider the case where we add an infrared-absorbing atmosphere (i.e., a greenhouse effect) to the current, simplistic planet in equilibrium with the sun. In keeping the temperature constant, the absorption of outgoing energy will result in less energy escaping to space. That is, it will now absorb more energy from star than is being emitted back to space, and the planet must warm. The Earth is an open energetic system, so this does not violate thermodynamics even though the greenhouse effect is not "creating energy"; rather, the reduction in outgoing energy flow shifts the equilibrium planetary temperature somewhere between its "effective temperature" and the temperature of the star's photosphere. This is shown below. The horizontal line is just the amount of energy the planet absorbs, which we'll treat as a constant and independent of the planet's temperature. In contrast, the outgoing longwave radiation (OLR) depends strongly on temperature, via σT^4. Adding greenhouse gases will, for any given temperature, reduce the OLR (blue curve). Alternatively, you need to go to higher temperatures to reach equilibrium with the incoming sunlight.

g. On Earth, the greenhouse effect results primarily from water vapor (~50% of the infrared absorption), clouds (~25%), and CO2 (~20%). Other gases make up the rest, and clouds actually raise the albedo to over-compensate for their greenhouse effect. That is, clouds cause a net cooling. If one could remove the entire greenhouse effect, and keep the absorbed sunlight the same, you'd reduce the equilibrium temperature of the planet to ~255 K. In reality, you'd also cool the surface enough to trigger a snowball and increase the albedo, resulting in an effective T much lower than 255 K. The dynamics of this state are interesting, and one I like to study in connection with snowball Earth or exoplanets at the outer edge of the habitable zone (but I'm not doing my graduate work on this right now, perhaps in the future). For a planet around a G-type star like our sun, the result is extreme seasonality between the summer and winter, because of the low thermal inertia of the ice surface. The ice-albedo feedback would prevent deglaciation even if pools of open water might temporarily form at the equator, but this is sensitive to the albedo too.

Nice summation explaining the physics which defines the effective temperature of a planet similar to Earth who's surface receives essentially all warming energy from it's parent star. Knowledge of just a few fundamental parameters is sufficient to determine the effective temperature, which would define the Earth's surface temperature at complete thermodynamic equilibrium with incoming solar radiation.

The Earth is not in thermal equilibrium however, it has fluid oceans of water and air which create vertical and horizontal temperature gradients where the effective temperature is radiated from some height above the surface. The 255K 'surface' height varies but on average resides at an average altitude of 16,000'. All levels below that height must on average be be warmer due to increasing atmospheric pressure.

[donsutherland1]

Wonderful and very readable discussion, cmc0605. Many thanks for taking the time to write and post it.

[WeatherRusty]

Thank you for your clear and concise writeup - I hope others learn as much from it as I did. But I have one (possibly dumb) question. In paragraph G you wrote "... clouds actually raise the albedo to over-compensate for their greenhouse effect". My question is - are clouds raising the Earth's albedo higher than the approximately 0.7 value used in the initial equations, or does that value include clouds? The idea of clouds increasing and providing a negative feedback to compensate for the GHE sounds like Lindzen's "Iris Effect" hypothesis - which I thought had been soundly refuted. Can you please help me understand what I'm missing?

I think if given the heads up, the OP would more correctly read "clouds actually raise the albedo to partially compensate for their greenhouse effect".

Cloudiness is a feedback to temperature. Therefore clouds can not totally negate the factors which causes their formation, the net effect of additional water vapor entering the atmosphere is a strengthening of the greenhouse effect, partially (how much is the question) negated both from water vapor (last sentence) and the clouds themselves acting to both enhance the greenhouse effect and scatter incoming sunlight back to space. Interestingly, another negative feedback produced by additional water vapor is the lapse rate feedback which warms the troposphere with increasing height, while the greenhouse effect seeks to cool the upper air.

[cmc0605]

Thank you for your clear and concise writeup - I hope others learn as much from it as I did. But I have one (possibly dumb) question. In paragraph G you wrote "... clouds actually raise the albedo to over-compensate for their greenhouse effect". My question is - are clouds raising the Earth's albedo higher than the approximately 0.7 value used in the initial equations, or does that value include clouds? The idea of clouds increasing and providing a negative feedback to compensate for the GHE sounds like Lindzen's "Iris Effect" hypothesis - which I thought had been soundly refuted. Can you please help me understand what I'm missing?

Well for one thing, I was talking about the current equilibrium climate that we're in, not how it might change. In the present climate the albedo (cooling) effect of clouds outweighs the greenhouse (warming) effect of clouds by the equivalent of about five doublings of CO2. But that says absolutely nothing about cloud feedbacks, which refers to the change in cloudiness as we go into a new climate. It's perfectly possible that clouds cool the present climate while still providing a positive feedback to small perturbations in our climate. Don't confuse the sign of a function with its derivative!

By the way, the albedo is ~30%, so you'd have a smaller number than 0.7 if albedo went up...

As far as Lindzen's IRIS hypothesis- actually this hypothesis concerns itself with the feedback on the longwave part of the spectrum and says little about the albedo. The idea is that high clouds reduce their fraction at higher SST's; higher clouds are predominately a longwave effect and thus reducing their coverage would let more outgoing radiation to space, cooling the planet). I fully agree that major parts of the IRIS idea have been blown apart, but our current understanding of cloud feedback is limited and is still compatible with a small negative feedback from clouds. But our limited understanding is also compatible with positive feedback which is why you get a range of ~2-5 C for a doubling of CO2 in most estimates. Unfortunately, there's no unified and robust theory for cloud feedbacks that applies at all heights, latitudes, and for both the longwave and shortwave spectral bands.

[physicsguy21]

I contend that the 255K value is wrong, weighting insolation *first* to determine heat attained by a receptive body is a big no-no given Holder's inequality.

A few months ago, NASA's Diviner mission pinned the Moon's temperature to lie between 192K-197K. I was waiting for this, after running the numbers I get a greybody temperature for the Earth being nowhere near 255K, but instead lies closer to 188K, at most. Weighting the insolation flux first is unacceptable and I'd defend this to the end of time if I could.

This is basically a copy of my earlier response to another member. Recalling this clear demonstration, envision a flat blackbody at Earth's distance from the Sun with area of 1m2 with little mass but placed full so insolation = 1362Wm2, one side lit, the other dark. Correct, application is a flat sunlit half, Full S-B is 1362Wm2 = 5.6704 x 10^-8 x T^4, 394K = T. Nighttime side is set to the 2K deep space value. (394K+2K)/2 = 198K (Reality). If flux is averaged first before being used to calculate temp, You get S_o/2 = 681Wm2. T^4 = 120 x 10^8 = 331K. That value is clearly wrong.

If the temperature of the atmosphere is determined radiatively by emissive photon firing frequency from the surface (it clearly isn't), you CANNOT expect any global 'layer' of the atmosphere to be *colder* than the greybody temperature by the conservation of energy. The temperature at the top of the stratosphere averages -65C at warmest, the face of the incorrectly calculated greybody -18C. See the problem?

In reality, the molecular temperature (analogous to density) and radiative temperature (analogous to velocity) must be separated in equation, these are two completely different types of physical temperature parameters with no connecting physics relating in-step to a lone source-parameter. This is why the boiling point of water varies with altitude. The atmosphere itself is what slows surface cooling at night via direct molecular contact for the most part, while also diminishing stellar radiation during the daytime. The net effect of attained thermal energy is somewhat of a 'middle ground' so to speak, but a significant net warming over the incorrectly calculated S-B constant. The effect is not 33C, but rather it is well over 100C. Our notorious 288K is what results instead of the expected 188K.

The next step is to realize that 'space' in the vicinity of the heliosphere is actually, in a sense, a sea of plasma rather than a vacuum. The charge field otherwise simply cannot exist in space or here within Earth's atmosphere without free electrons/electrons in general, and since 'charge' is totally absent in the calculation of the most vital physical parameters, we see plenty of "mask parameters" implemented to patch up reality gaps in the time-space continuum. Plasma, the free electron particle state, exists both inside and outside of atmosphere in vast numbers. These particles react strongly to gravitational, electric, and especially to magnetic

forces. This is why massless light photons cannot escape black holes, alongside the bending of the time-space continuum itself. Plasma cannot by mechanism directly avect *thermal* energy away from the planet, but through maximum load-separation, numerous *free* EMR pulses are easily 'avected' away from Earth through the plasma-driven charge field. This has recently been measured. This is also why the Sun and global mechanical energy mean so much to climate.

Perhaps it will soon be realized that the Sun is not powered by nuclear fusion deep within, but rather it is clearly an electric star. The current theory also contains physical impossibilities, as such we have incorrect explanations for the sunspot cycle, the solar wind, the darkness under the photosphere, thr Sun's age, and most importantly, it's effect on our climate.

[physicsguy21]

Insolation varies by over 100Wm2 on a seasonal scale, we're closest to the Sun in January so we can directly measure the changes in atmospheric profile after correcting for topography, but most importantly, whether or not there is any effect on the upper atmosphere from topographical effects.

The surface emits hottest during the northern hemispheric summer for clear reasons. The lower troposphere follows this seasonal emission pattern, but the upper atmosphere does not, in fact it shows an opposite sign. Most of that can be attributed to ozone but the radiative effect from the surface is non-existent well before then. This is because we're talking about two very different 'temperature' parameters.

14K feet, notice the peak during July: http://discover.itsc.uah.edu/amsutemps/execute.csh?amsutemps+002

56K feet: http://discover.itsc.uah.edu/amsutemps/execute.csh?amsutemps+006

135K feet: http://discover.itsc.uah.edu/amsutemps/execute.csh?amsutemps+011

That should make the effect pretty clear, in my humble opinion.

[WeatherRusty]

This is the correct application of Stefan-Boltzmann

physicsguy21 leaves out two important factors, the geometry of the Earth and the Earth's albedo. Also his application treats the Earth as a body far from thermal equilibrium like the Moon. The thermal gradient on Earth is small compared to the Moon, S-B applies to a body in near thermal equilibrium or uniform temperature, which the Earth is on the Kelvin temperature scale.

Also, he treats the dark side of the moon as being at 2K, which it obviously is not. The dark side of the moon does not fall to cosmic background temperature.

From Wikipedia:

Temperature of the Earth

Similarly we can calculate the effective temperature of the Earth T_E by equating the energy received from the Sun and the energy radiated by the Earth, under the black-body approximation. The amount of energy, E_S, emitted by the Sun is given by:

At Earth, this energy is passing through a sphere with a radius of a₀, the distance between the Earth and the Sun, and the energy passing through each square metre of the sphere is given by

The Earth has a radius of r_E, and therefore has a cross-section of . The amount of solar energy absorbed by the Earth is thus given by:

The amount of energy emitted must equal the amount of energy absorbed, and so:

T_E can then be found:

where T_S is the temperature of the Sun, r_S the radius of the Sun, and a₀ is the distance between the Earth and the Sun. This gives an effective temperature of 6°C on the surface of the Earth, assuming that it perfectly absorbs all emission falling on it and has no atmosphere.

The Earth has an albedo of 0.3, meaning that 30% of the solar radiation that hits the planet gets scattered back into space without absorption. The effect of albedo on temperature can be approximated by assuming that the energy absorbed is multiplied by 0.7, but that the planet still radiates as a black body (the latter by definition of effective temperature, which is what we are calculating). This approximation reduces the temperature by a factor of 0.7^1/4, giving 255 K (−18 °C).

[physicsguy21]

WeatherRusty, that is largely irrelevant if not a total misconception of the issue. You apparently did not read my post because I was not referencing the moon in my calculations, I said 'a flat blackbody'. Albedo, surface heat retention, so on are all greybody-bound properties.

You're making the same basic mistake, this is why the Moon's temperature happens to lie between 192K-197K, over 50K colder than the assigned value. You're incorrectly accounting for Holder's inequality. You're weighting insolation first. Why are you defending physics that you know are incorrect?

The current assigned greybody temperature is disprovem by the fact that no global layer of the atmosphere can be *colder* than greybody temperature by the physics you and I both cite and discuss. If atmospheric temperature is determined radiatively and this supposed mythical 'emission height' is 16K, then the atmosphere should NOT cool an additional 50C over the following 100K feet up.

But it does, because molecular temperature is analogous to density, radiative temperature is analogous to velocity. This is why water's boiling temperature varies with altitude. Why are you still defending an imaginary 'emission height'?

[WeatherRusty]

WeatherRusty, that is largely irrelevant if not a total misconception of the issue. Albedo can only be taken into account after the blackbody temperature is determined.

You're making the same basic mistake, this is why the Moon's temperature happens to lie between 192K-197K. You're incorrectly accounting for Holder's inequality.

Furthermore the current assigned greybody temperature is DISPROVEN by the fact that no global layer of the atmosphere can be *colder* than greybody temperature by the physics you and I both cite and discuss. If atmospheric temperature is determined radiatively and this mythical emission height is 16K, then the atmosphere should not cool an additional 50C over the following 100K feet up.

Get real. The Earth is not a perfect black body, so we must adjust S-B to account for .3 albedo. The Earth is a sphere rather than a flat plain with one side at near absolute zero and the other 255K.

The tropopause is colder than the layer of emissivity at 16,000', therefore your ideas are disproven.

As viewed from space the spectral 'temperature' or Planck curve indicates 255K. Direct observation.

Holder's shmolder's. You're to quick to adopt some far flung, left field overturning of standard physics.

[physicsguy21]

Get real. The Earth is not a perfect black body, so we must adjust S-B to account for .3 albedo. The Earth is a sphere rather than a flat plain with one side a near absolute zero and the other 255K.

As viewed from space the spectral 'temperature' or Planck curve indicates 255K. Direct observation.

What on earth? You misinterpreted my flat-blackbody example that had nothing to do with the Moon, then took an incorrect S-B temperature, picked the point in the atmosphere that matches the incorrect S-B temperature, then *poof* you magically called it an 'emission height'?

The tropopause is than the layer of emissivity at 16,000', therefore your ideas are disproven.

Huh? This disproves your ideas, not mine. By your theory, how can any layer of the atmosphere average colder that the emission avg at 255K? Impossible. There is no effective emission height because the correct S-B temp is 188K.

If the 255K value is accurate, why does upper stratosphere average -65C, almost 50C colder than this imaginary 'emission height'? Why is the moon 192K-197K, over 50K colder than the assigned greybody temperature? I know why.

Why is it that when the Earth surface emits at it's hottest, during the Northern Hemispheric summer, the upper atmosphere shows a reverse sign while the lower atmosphere follows in sync? I know why.

[physicsguy21]

this is all y'all need to read to know not to further respond to BethesdaBoy. hopefully the mods will get around to rebanning him.

this started off as an excellent thread and hopefully it'll be cleaned up so the real discussion can continue.

What are you talking about? You're the 5th person to say this and I have no idea what it means but it is clearly wrong.

Maybe you can answer my question. If the S-B constant is somehow 255K, how can any portion of the global atmosphere reside at a colder temperature? Why is the Moon over 50K colder than the assigned greybody?

How does discussing the S-B temperature and planetary energy budgets contradict this thread? Do you feel this way because it contradicts your views? If so then perhaps you shouldn't clutter it with false accusations? Thankyou.

[LocoAko]

What are you talking about? You're the 5th person to say this and I have no idea what it means but it is clearly wrong.

Convincing...

BB also had trouble grasping the geometrical correction to this equation that must be done because of Earth's shape, a very simple concept. Coincidence?

[physicsguy21]

Convincing...

BB also had trouble grasping the geometrical correction to this equation that must be done because of Earth's shape, a very simple concept. Coincidence?

The blackbody formula for a planet does handle geometrical complexities, all formulae must take into account Holder's inequality, otherwise the final value will be wrong. What makes you think it doesn't handle geometrical bodies such as a sphere?

Surface heat retention and albedo are greybody parameters. There are no known blackbodies in the universe.

[LocoAko]

The blackbody formula for a planet does handle geometrical complexities, all formulae must take into account Holder's inequality, otherwise the final value will be wrong. What makes you think it doesn't handle geometrical bodies such as a sphere?

Surface heat retention and albedo are greybody parameters. There are no known blackbodies in the universe.

I'm completely confused by what you're saying. What does Holder's inequality have to do with this? When dealing with fluxes you can't treat a rounded, spherical surface as if it was a flat surface normal to the plane of incident radiation. Agree or disagree?

[physicsguy21]

I'm completely confused by what you're saying. What does Holder's inequality have to do with this? When dealing with fluxes you can't treat a rounded, spherical surface as if it was a flat surface normal to the plane of incident radiation. Agree or disagree?

Huh? Are you aware what Holder's inequality is? Why are you asking what it has to do with correctly determining an S-B temperature? Isn't it upfront?

http://erionhasanbelliu.com/multiple-shape-matching-holders-inequality/

[LocoAko]

Huh? Are you aware what Holder's inequality is? Why are you asking what it has to do with correctly determining an S-B temperature? Isn't it upfront?

http://erionhasanbel...ers-inequality/

I'd be curious for you to explain, in your own words, that derivation and how, specifically, it proves your theory of why we can treat the Earth this way.

[donsutherland1]

How does discussing the S-B temperature and planetary energy budgets contradict this thread? Do you feel this way because it contradicts your views? If so then perhaps you shouldn't clutter it with false accusations? Thankyou.

Reasonably, one would expect a discussion based on generally recognized principles of science. If one is offering a novel hypothesis, as you are about the earth's effective temperature, one should at least draw upon relevant literature that supports it. One needs to offer a compelling reason why one should depart from standard scientific principles. Simply claiming that standard and widely-used calculations are "wrong" without providing credible evidence is what some find problematic.

As for the point about the sun, that is nothing more than pseudoscience. Stars undergo nuclear fusion, though the specific nature of the fusion differs among groups of stars. Small stars such as the sun undergo proton-proton nuclear fusion. That there might be some electrical activity does not mean that fusion is not taking place.It's a product of the fusion, not proof of a lack of fusion.

[physicsguy21]

I'd be curious for you to explain, in your own words, that derivation and how, specifically, it proves your theory of why we can treat the Earth this way.

What is 'this way' supposed to mean? The celestial bodies in the solar system are spheres so they must be accounted for as such. My flat blackbody example was used to show why weighting insolation first leads to values much to high, and this is proven by the upper atmosphere residing over 50K cooler than the currently assigned greybody temperature. That is actually physically impossible. I explained this in mathematical detail above, the solar vector varies across the surface of the Earth which is the source for most of the error.

[physicsguy21]

This was my earlier post.

I contend that the 255K value is wrong, weighting insolation *first* to determine heat attained by a receptive body is a big no-no given Holder's inequality.

A few months ago, NASA's Diviner mission pinned the Moon's temperature to lie between 192K-197K. I was waiting for this, after running the numbers I get a greybody temperature for the Earth being nowhere near 255K, but instead lies closer to 188K, at most. Weighting the insolation flux first is unacceptable and I'd defend this to the end of time if I could.

This is basically a copy of my earlier response to another member. Recalling this clear demonstration, envision a flat blackbody at Earth's distance from the Sun with area of 1m2 with little mass but placed full so insolation = 1362Wm2, one side lit, the other dark. Correct, application is a flat sunlit half, Full S-B is 1362Wm2 = 5.6704 x 10^-8 x T^4, 394K = T. Nighttime side is set to the 2K deep space value. (394K+2K)/2 = 198K (Reality). If flux is averaged first before being used to calculate temp, You get S_o/2 = 681Wm2. T^4 = 120 x 10^8 = 331K. That value is clearly wrong.

If the temperature of the atmosphere is determined radiatively by emissive photon firing frequency from the surface (it clearly isn't), you CANNOT expect any global 'layer' of the atmosphere to be *colder* than the greybody temperature by the conservation of energy. The temperature at the top of the stratosphere averages -65C at warmest, the face of the incorrectly calculated greybody -18C. See the problem?

In reality, the molecular temperature (analogous to density) and radiative temperature (analogous to velocity) must be separated in equation, these are two completely different types of physical temperature parameters with no connecting physics relating in-step to a lone source-parameter. This is why the boiling point of water varies with altitude. The atmosphere itself is what slows surface cooling at night via direct molecular contact for the most part, while also diminishing stellar radiation during the daytime. The net effect of attained thermal energy is somewhat of a 'middle ground' so to speak, but a significant net warming over the incorrectly calculated S-B constant. The effect is not 33C, but rather it is well over 100C. Our notorious 288K is what results instead of the expected 188K.

[physicsguy21]

Reasonably, one would expect a discussion based on generally recognized principles of science. If one is offering a novel hypothesis, as you are about the earth's effective temperature, one should at least draw upon relevant literature that supports it. One needs to offer a compelling reason why one should depart from standard scientific principles. Simply claiming that standard and widely-used calculations are "wrong" without providing credible evidence is what some find problematic.

What? My evidence is the Moon, it has been recently measured at 192K via NASA's Diviner mission just last month, and earlier measurements have pinned it down to a similar value. The IPCC assigns it 255K which is now proven wrong. I also mathematically proved the error in our calculations with a simple flat blackbody. To add on, I have shown it to be physically impossible for Earth to have a 255K greybody temperature because no atmospheric layer should be colder than the greybody temperature of the planet.

Did you read my post at all? I'm not the only scientist who feels this way.

As for the point about the sun, that is nothing more than pseudoscience. Stars undergo nuclear fusion, though the specific nature of the fusion differs among groups of stars. Small stars such as the sun undergo proton-proton nuclear fusion.

Based on what? Modeling and speculation, the same embarrassing thinking present in climate science. Galileo's observations were considered pseudoscience, and we don't know any more about the dynamics of our Sun now than they knew about the dynamics of our solar system then.

This is for another thread, but I can demonstrate the physical implausibility of the nuclear fusion nonsense or discuss it with you via personal message. The fusion concept is no more than hypothesis.

That there might be some electrical activity does not mean that fusion is not taking place.It's a product of the fusion, not proof of a lack of fusion.

Fusion cannot explain why the Solar wind accelerates to Millions of mph from the Sun, heating up to millions of degreesF. The solar wind completely stopped in May of 1999 if I remember the date correctly, impossible in fusion theory. To add on, the Sunspots on Earths surface represent holes torn into the photosphere by intense magnetic activity, revealing the interior of the sun to be dramatically darker.

[WeatherRusty]

What on earth? You misinterpreted my flat-blackbody example that had nothing to do with the Moon, then took an incorrect S-B temperature, picked the point in the atmosphere that matches the incorrect S-B temperature, then *poof* you magically called it an 'emission height'?

Huh? This disproves your ideas, not mine. By your theory, how can any layer of the atmosphere average colder that the emission avg at 255K? Impossible. There is no effective emission height because the correct S-B temp is 188K.

If the 255K value is accurate, why does upper stratosphere average -65C, almost 50C colder than this imaginary 'emission height'? Why is the moon 192K-197K, over 50K colder than the assigned greybody temperature? I know why.

Why is it that when the Earth surface emits at it's hottest, during the Northern Hemispheric summer, the upper atmosphere shows a reverse sign while the lower atmosphere follows in sync? I know why.

This is basically a copy of my earlier response to another member. Recalling this clear demonstration, envision a flat blackbody at Earth's distance from the Sun with area of 1m2 with little mass but placed full so insolation = 1362Wm2, one side lit, the other dark. Correct, application is a flat sunlit half, Full S-B is 1362Wm2 = 5.6704 x 10^-8 x T^4, 394K = T. Nighttime side is set to the 2K deep space value. (394K+2K)/2 = 198K (Reality). If flux is averaged first before being used to calculate temp, You get S_o/2 = 681Wm2. T^4 = 120 x 10^8 = 331K. That value is clearly wrong.

You're formula for the moon's temperature takes the sunlit half value, adds the cosmic background and divides it by 2. The dark side of the moon is not at 2C,,,,period....................

[physicsguy21]

You're formula for the moon's temperature takes the sunlit half value, adds the cosmic background and divides it by 2. The dark side of the moon is not at 2C,,,,period....................

The formula I used has nothing to do with the Moon, for the umpteenth time.

You even bolded the portion of my post where I said this. Please read my posts before replying, thanks.

[physicsguy21]

what are your degrees in? what journals have you published in?

I have an MS in atmospheric chemistry. I'll remain anonymous regarding the rest, except that I am just starting out and have not yet published any papers and I have not attempted to. I hope to get there in a year or two, though.

[physicsguy21]

LOL.

What? I answered your question. Why are you attacking my character? I didn't say anything rude towards you. Apparently it isn't possible to disagree with someone without being disrespectful.

[LocoAko]

I have an MS in atmospheric chemistry. I'll remain anonymous regarding the rest, except that I am just starting out and have not yet published any papers and I have not attempted to. I hope to get there in a year or two, though.

You havent tried to? Not while in grad school or thereafter? It would be one thing to try to publish and get rejected (which would speak for itself) but to not want to or try to seems very odd.

[physicsguy21]

You havent tried to? Not while in grad school or thereafter? It would be one thing to try to publish and get rejected (which would speak for itself) but to not want to or try to seems very odd.

I'm trying to find employment that fits my personal and financial desires, but I'm finding thst my potential there would be limited if I were to publish a paper aligning with science of lesser interest within the broader community, whether it be accurate or not. I do not want to make a name for myself until I am firmly employed so I elected to remain silent. This is a big problem actually, but off topic for this thread.

[cmc0605]

Well, this pseudoscience has been fun...

[LocoAko]

Well, this pseudoscience has been fun...

What, you don't want to talk to physicsguy about Holder's inequality and how it disproves the entire Earth's radiative balance model?