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Friday, May 29, 2015

Energy contributions to the Earth's surface temperature

Here are nearly all energy sources that contribute to the Earth's Global Means Surface Temperature (GMST):


Heating Source
W/m^2
0K
Solar
240
255.06
Cosmic Background Radiation
3.13E-6
2.73
Starlight
6.91E-6
3.32
Cosmic Rays
3.2E-6
2.74
Meteorites
2.27E-8
0.80 
Combined off planet sources
240
255.06
Geothermal
0.09
35.49
Tidal
0.01
18.74
Geothermal &Tidal
0.1
36.17
Total Energy Sources
240.1
255.09
CO2
30.21
151.93
Greenhouse Feedbacks
128.79
218.31
Total Greenhouse
159
230.12
Total
399.1
289.65
Observed Surface Energy
398
Observed Surface Temperature
287.15

The most important factor not shown is albedo, which is included within the solar value for convenience.  I have also ignored industrial waste heat, and the effects of emissivity (which increases the effective temperature) and uneven surface temperatures (which decrease it).  Also not shown is seismic energy.  The reason it is missing is that the vast majority of seismic energy is dissipate as heat deep within the Earth's surface, where it contributes to geothermal energy.  Including it as a seperate item would have merely been double counting.  Likewise, volcanic energy is included with geothermal energy, and so not shown as a separate item.

The most important thing to notice is that the smaller items on the list are almost completely irrelevant.  Based on caculations above, for example, we can determine that if the Earth floated far from any sun in galactic space, it would still maintain a surface temperature of around 36-37 oK.  That represents the combined energy effects of geothermal heat (35.5 oK by itself), the cosmic background radiation, starlight, and cosmic rays.  Assuming it orbited a dark star, providing the the further effects of tides and meteors, that would raise the temperature to 37-38 oK.  But adding all these factors to the effect of sunlight would only raise the GMST by 0.03 oK, significantly less than the observational error of the Earths absolute GMST.  Their contribution becomes even less when the greenhouse effect is also included.

The reason for the low contribution of factors that by themselves would contribute more to temperature is the relationship between radiation and temperature captured by the Stefan-Boltzmann Law.  Specifically, j* = εσT^4, where j* is the energy radiated, ε is the emissivity, σ is the Stefan-Boltzmann constant, and T is the surface temperature.  Because of the conservation of energy, once equilibrium is reached the temperature matches that of a near black body radiating the same amount of energy it receives.  This equation means, however, that the temperature increase for a given power input is proportional to the fourth root of the  total power.

The second most important thing to notice is that, despite their inclusion on the table, the greenhouse effect does not represent an additional source of energy.  That is because for every joule returned to the Earth's surface by the greenhouse effect, an additional joule leaves the Earth's surface by means of radiation, increase convection or increased evaporation or transpiration.  The greenhouse effect only makes the existing energy sources more efficient at heating the surface by recycling the energy.  In that way, greenhouse gases act like blankets (an analogy which is exactly correct with reference to the thermodynamics, although completely inaccurate with regard to mechanism).  The values shown for the greenhouse effect on the table, therefore, are best understood as the amount of additional energy from other sources that the Earth's surface would need to maintain the same GMST without a greenhouse effect.

Finally, every now and again, somebody will pop up and insist that geothermal energy or some other equally obscure source of heating is the primary driver of GMST.  Such theories fail absolutely once the relative energy inputs are calculated (something they never do).  The theories are complete drivel on the same level as those of Flat Earth Society.

Update 11 Feb, 2016:  I can now add the energy contribution from the solar wind, which amounts to 0.00035 W/m^2, and hence is the second largest of the off planet heating sources.  It does not, however, rise above the error of the heating from direct sunlight.  Source:  Tenfjord and Ostgaard (2013)

Sources:
Solar and Total GHE -  IPCC AR5 Fig 2-11
CO2 proportion of GHE - Schmidt et al (2010)
Cosmic Background Radiation - Calculated from temperature
Starlight and Cosmic Rays - Bowen et al (1933)
Meteorites - Lovel, Geophysics II, p. 452
Geothermal and Tidal - Skeptical Science
Observed Surface Energy - IPCC AR5 Fig 2-11
Observed absolute GMST - IPCC AR5 Fig 9-08

2 comments:

  1. Ha, about 38 K there would be no tides!! :)

    (Was that a subtle way to correct all those °K to K? No idea where that convention came from, but it is what it is.)

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  2. Victor, tides are more prominent in liquid medium, but still exist in solid matter. The M2 vertical component of the Earth tide is given as 384.83. That tidal motion will also result in friction, transferring some of the Earth's energy of rotation into a transient energy flux. So with no oceans, or more correctly, with solid blocks of ice in place of oceans, the tidal energy component may be reduced, but no eliminated.

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