# Physics of Global Warming

by Xnn
Tags: global, physics, warming
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Emeritus
PF Gold
P: 11,155
Several points of dissatisfaction already, at this juncture:

1. What is the emissivity of the Earth? Why doesn't it figure in the first equation? Or is it assumed to be equal to 1?

2. It is distracting to use \epsilon for albedo, when that is the symbol typically used for emissivity.

3. Where does the factor of 1/4 come from? Your derivation makes no mention of it, and only someone that had done the derivation independently or seen it done elsewhere will understand its origin. Presumably, it comes from actually doing the flux calculation (using Gauss' Law or taking dot products and integrating - either way will give a factor of 4 between the effective radiating surface area and the effective absorbing surface are, barring albedo).

4. Clearly, the temperature extracted here is some kind of average. What kind of average it is is obscured by the extent of hand-waving involved in the calculation. For instance, since half the planet receives virtually zero insolation at any point of time, so you are integrating over a period of some multiple of a one day to arrive at this number. Then, the insolation varies by latitude, even for the day half of the planet. But it looks like the integration over latitudes (not explicitly done) precedes the radiation calculation (which implicitly assumes that temperatures equilibrate across latitudes instantaneously, doesn't it?), rather than the other way round.

Personally, I find the above derivation to be too hand-wavy and irrigorous to be helpful. I have to read between lines and fill in too many missing steps, if I want to understand anything from this.
 P: 555 1. Emissivity averages about 0.62 for the earth and can be used to calculate surface temperature. It basically takes into account the greenhouse gas effect. As CO2 levels rise, emissivity will lower and surface temperature go up. 2. Sorry; I have edited it to an "a" in order to avoid confusion. 3. 1/4 is just a geometry measure that comes from the ratio of the area of a globes disk to it's surface area: pi r^2 to 4 pi r^2. pi r^2 cancels out leaving just the number 4. The earth receives radiation from the sun in proportion to the cross sectional area of its disk. However, it radiates energy over the larger area of it's surface. Dividing by 4 takes into account the geometry of a sphere. 4. No hand waving; just simplification. A completely accurate earth climate model requires lots of programming and a super computer to run. What is presented is just the simple overall physics for global warming. The temperature is what would be expected using the Stefan-Boltzmann law for Earth. 33°C (the delta between 287 to 254K) is the amount of warming on the surface from the greenhouse gases.
 P: 38 Physics of Global Warming Excellent opening post! "The earth is absorbing about 1.5 watt/meter^2 more energy than it is emitting." One quibble. Where does the 1.5W/m^2 figure come from. Hansen is famous for claiming 0.85W/m^2
 P: 555 Thanks WeatherRusty! The 1.5 watt/meter^2 comes from 2 places. First, satellite mission called the Earth Radiation Budget Experiment and the Earth’s Radiant Energy System (CERES) as well as sensors on NASA’s Terra and Aqua satellites have directly measured the imbalance. They have found it to be about 1.4 watts/meter^2. Of course it varies over time. Second, the IPCC in the Technical Summary on page 32 Figure TS.5 has calculated it and reported a value of 1.6 watts/meter^2 with a range of anywhere from 0.6 to 2.4 watts/meter^2. So, theory and measurements are in good agreement.
P: 813
I'm not convinced at this part:

 ERad = TSI*(1- є)/4 TSI is 1365.5 Watts/meter^2 Є, albedo which is 0.3 for Earth

Why is Є the albeto. What I'd say Є is, is is the fraction of the outgoing radiation that gets back radiated. You could call it an albedo but it is the albedo looking back out to space for IR radiation at 5KM altitude.

With regards to the greenhouse effect I think the altitude of interest would be between 9km and 17km because bellow that convective forces control the temperate gradient.
http://www-das.uwyo.edu/~geerts/cwx/...p01/tropo.html

The problem is that radiation emitted back into space is not emitted at a single point, It is radiated from various altitudes at various frequencies. Also if you want to talk about the radiation emitted from the atmosphere remember that the atmosphere is not a black body because it is not optically dense. It consequently has an emissivity less then one and therefore you have to multiply the right hand of Stephan Boltzmann equation by the emissivity.
 P: 43 I have a comment and a question on the solar constant TSI: The magnetic field and the solar wind of the sun are changing in a 11yrs cicle and also on a monthly and even daily basis. This magnetic field must be coupled in a certain way to the sun's temperature, since the magnetic fields arise from plasma movements which should be driven be temperature and pressure gradients. Therefore the Planck's function of the sun can actually not be constant due to the changing temperature. And the integral over the Planck's function, the so called "Solar Constant" can't be a constant. Is there something wrong with my conclusion or is the name "constant" just missleading? Anyway, if the solar constant is used as a constant in climate models, I'm not surprised that they are wrong.
P: 4,512
 Quote by Xnn However, the Earth is not at equilibrium and is actually receiving slightly more energy that it is emitting.
Prove it.
 P: 555 John Creighto; Correct; radiation is emitted at various locations and frequencies. Emissivity is basically a measure of this and is effectively the greenhouse effect. What has been presented is ignoring the greenhouse effect in order to calculate the differance between reality and what surface temperature would be without it. Tanja; 1365.5 Watts/meter^2 is a typical value for Total Solar Irradiance. It does indeed change over time by about 1 watt/meter^2. Application of the Stefan-Boltzmann equation shows that this amounts to about 0.05 C. Phrak; First; a satellite mission called the Earth Radiation Budget Experiment and the Earth’s Radiant Energy System (CERES) as well as sensors on NASA’s Terra and Aqua satellites have directly measured the imbalance. They have found it to be about 1.4 watts/meter^2. Of course it varies somewhat over time. Second; Temperature measurements of the atmosphere and oceans as well as melting sea ice, and the Greenland and Antarctic ice caps have shown that all major parts of the earth are warming. Third, the IPCC in the Technical Summary on page 32 Figure TS.5 has calculated the inbalance and reported a value of 1.6 watts/meter^2 with a range of anywhere from 0.6 to 2.4 watts/meter^2.
 P: 38 The Solar constant or Total Solar Irradiance (TSI) is not a constant at all. Over the 11 years sunspot cycle it is measured by satellite to vary by 0.1% or 1.3W/m^2. This is enough to cause a 0.1C (+-0.05C) change in temperature at Earth's surface. Since the mid 1700's proxies indicate the Solar irradiance to have increased by 0.1% to 0.2% overall. It has not increased since satellite readings have been taken, beginning in 1979 I believe. When the Sun is more magnetically active the proportion of ultraviolet radiation reaching Earth is strongly enhanced, but most of this is absorbed in the upper atmosphere and thus not available to warm the surface directly. http://www.physorg.com/news129483836.html http://en.wikipedia.org/wiki/Solar_variation
 P: 555 By the Stefan-Boltzmann equation, 1.3 watts/meter^2 is 0.06C. No +-
P: 813
 Quote by Xnn John Creighto; Correct; radiation is emitted at various locations and frequencies. Emissivity is basically a measure of this and is effectively the greenhouse effect. What has been presented is ignoring the greenhouse effect in order to calculate the differance between reality and what surface temperature would be without it.
The emissivity is not the measure of the greenhouse effect. It is a measure of optical density. Low optical density implies and emissivity near zero. Large optical density implies an emissivity near one. The greenhouse effect is a result of the optical density being different for IR radiation then visible radiation. For an object to be a black body it must have an emissivity near one.
 P: 38 The Moon is at the same average distance from the Sun as Earth and so receives the same 1366W/m^2. It has an albedo of .12 as opposed to Earth's .30............but harbors no meaningful atmosphere. Mean surface temperature (day) 107°C Mean surface temperature (night) -153°C Lunar Mean surface temperature: -23C Earth's radiative equilibrium temperature: -18C (15C-33C greenhouse effect) Why might Earth without an atmosphere be 5C warmer than the Moon without an atmosphere even though the Moon is the darker (albedo) object? The oceans? The oceans are the great reservoir of accumulated heat which maintain a higher than equilibrium temperature near Earth's surface. Where does the additional accumulated heat come from? The greenhouse effect! The warmed atmosphere baths the oceans in thermal radiation warmer than an atmosphere containing no greenhouse gases. Night time temperatures drop very little over the liquid oceans because of the large heat carrying capacity of the water, maintaining a higher average diurnal temperature than over a solid surface.
 P: 555 John; Emissivity is the measure of an object's ability to emit radiation energy compared to a black body at the same temperature. In the case of a atmosphere, it is largely a function of the concentration of gases that can absorb and emit energy in the infrared. These gases are commonly called greenhouse gases...
P: 1,409
 Quote by Tanja I have a comment and a question on the solar constant TSI: The magnetic field and the solar wind of the sun are changing in a 11yrs cicle and also on a monthly and even daily basis. This magnetic field must be coupled in a certain way to the sun's temperature, since the magnetic fields arise from plasma movements which should be driven be temperature and pressure gradients. Therefore the Planck's function of the sun can actually not be constant due to the changing temperature. And the integral over the Planck's function, the so called "Solar Constant" can't be a constant. Is there something wrong with my conclusion or is the name "constant" just missleading? Anyway, if the solar constant is used as a constant in climate models, I'm not surprised that they are wrong.
The solar constant is not constant. In fact in all the universe the only constant is flux.

However, since average TSI flux over time is ~0, a constant value for TSI is used in simpler models.

The models are not right or wrong, they are tools for understanding complex chaotic systems.
 P: 38 The atmosphere emits because it has a temperature. The solar photosphere emits because it has a temperature. Both are composed of gases radiating thermal radiation produced during the collisions between the atoms and molecules in bulk matter. The Sun (mostly hydrogen & helium) predominantly in the visible because it is at 5,780K, the Earth's atmosphere in the infrared because it is at 255K. You can think of it as frictional heat, some of the kinetic energy of the gas atoms and molecules is radiated away when the atomic and molecular structure is disturbed during collisions with others. This means that oxygen and nitrogen are radiating IR, though by a different mechanism than the greenhouse gases do at specific wavelengths.
P: 555
 Quote by WeatherRusty The Moon is at the same average distance from the Sun as Earth and so receives the same 1366W/m^2. It has an albedo of .12 as opposed to Earth's .30............but harbors no meaningful atmosphere. Mean surface temperature (day) 107°C Mean surface temperature (night) -153°C Lunar Mean surface temperature: -23C
The moon rotates very slowly which also contributes to the extreme differances between day and night. To calculate its temperature using the Stefan-Boltzmann equation, I'd be tempted to not use the 1/4 geometry factor and just figure the max temperature. In doing so, I come up with a value of 108°C, which is reasonably close to the mean day temperature quoted. So, I suspect that those temperatures are closer to the max and mins as opposed to an average or mean value.

Unfortunately, there aren't a lot of good references to check and since the day/night temps are so extreme, it may not be an easy task to measure the average temp of the moons surface.
P: 4,512
 Quote by Xnn Phrak; First; a satellite mission called the Earth Radiation Budget Experiment and the Earth’s Radiant Energy System (CERES) as well as sensors on NASA’s Terra and Aqua satellites have directly measured the imbalance. They have found it to be about 1.4 watts/meter^2. Of course it varies somewhat over time. Second; Temperature measurements of the atmosphere and oceans as well as melting sea ice, and the Greenland and Antarctic ice caps have shown that all major parts of the earth are warming. Third, the IPCC in the Technical Summary on page 32 Figure TS.5 has calculated the inbalance and reported a value of 1.6 watts/meter^2 with a range of anywhere from 0.6 to 2.4 watts/meter^2.
These data sources are science when practitioners are in a position to be objective. As the last is governed by a political body, it fails to meet this screening.

Provide critical sources for any of your remaining claims. Not the original reports, but the criticisms--pro or con if you can.

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