fredag 18 juni 2010

The Atmosphere as Refrigerator 2

The previous posts lead us into the following basic scenarios of global climate with top of the atmosphere TOA temperature always - 18 C:
  • isothermal opaque atmosphere: surface temp: - 18 C
  • isothermal transparent atmosphere: surface temp: - 18 C
  • isentropic opaque atmosphere: surface temp: + 32 C
  • thermodynamic semitransparent real atmosphere: surface temp:  + 15 C.
We understand that an isothermal atmosphere at - 18 C is possible both in the case of a fully transparent atmosphere without greenhouse gases GHG  and fully opaque atmosphere filled by GHG. The real case at 15 C is somewhere between these extremes with a semi-transparent atmosphere with thermodynamics including latent heat/evaporation/condensation. 

Isothermal (lapse rate = 0) and isentropic (lapse rate = 10 K/km) thermodynamic equilibrium states are possible without heat transport from the Earth surface to TOA. Convective heat transport tends to reduce the lapse rate. A reduced lapse rate connects to decreased radiative heat transport.

A simple calculation based on observed incoming = outgoing radiation = 240 W/m2 and a temperature drop dT of say 30 K from the Earth surface to TOA, gives heat transport by radiation = 4 x 30 = 120 Watts (by dQ = 4 dT), which fits with observed heat transport of 120 W by convection-evaporation/condensation (reducing the lapse rate by observed 3 K/km). This corresponds to a semi-opaque atmosphere absorbing 60 W and letting through 180 W to the Earth surface, and transporting back 120 W by convection and 120 W by radiation to TOA for radiation of 240 W to outer space at - 18 C.

We observe that in this model, increase of convective heat transport may reduce the lapse rate further and thus decrease the surface temperature. A balancing decrease of radiative heat transport fits with a smaller dT and a decrease of surface temperature. Less radiative heat transport may thus fit with increasing GHG. As noted in previous posts, the net result could be global cooling by more GHG!

Thus, not even the sign of climate sensitivity is clear, warming or cooling, not to speak of its magnitude: Whether increasing GHG will increase or decrease surface temperature will depend on the effect on incoming surface radiation and the thermodynamical heat transport including evaporation/condensation. In particular, the common belief that  doubled CO2 will cause a basic global warming of 1 C, may lack scientific rationale.

Compare with Basic Thermodynamics of the Atmosphere derived from basic properties of turbulent solutions of the Navier-Stokes equations.

Also compare with Roy Spencer's dicussion of the role of PDO in global temperature variations based on the simplest possible thermodynamic model. Spencer shows that even such a simplest model can be made to fit with observations quite well, and then indicates much smaller climate sensitivity that the simple radiative model used by IPCC to predict a basic climate sensitivity of 1 C upon doubling of atmospheric CO2 (augmented  to 1.5 - 4.5 C by various feedbacks).

The conclusion is that any climate model must include thermodynamics, and the natural model is then the Navier-Stokes equations with gravitation and radiation. 

23 kommentarer:

  1. In the thread "Elementary Climate Mathematics: CO2 Cooling" you came up with 12, 18, 22 or 42 C as possible values for an Earth without greenhouse gases. Now you finally realize it would have a temperature of -18.

    You are also right about the temperature if the atmosphere is opaque. However, that requires that it is opaque *both* to IR and visible light. Since CO2 only absorbs IR we are not in a situation between your two extremes but in something quite different. More GHG:s have no effect in incoming radiation.

    SvaraRadera
  2. Yes they have, because incoming is more than 40% IR.

    SvaraRadera
  3. IR covers a large range of wavelengths and the overlap between incoming solar radiation and absorption by greenhouse gases is small, as I'm sure you know.

    Am I to understand this post mean you have concluded that your earlier model was wrong since your new claim of -18 C without greenhouse gases contradict that model?

    SvaraRadera
  4. An atmosphere entirely without greenhouse gases, including water vapor,
    is hypothetical and without interest in the context of global climate.

    SvaraRadera
  5. I think that an atmosphere without water vapour is interesting and relevant since it applies to many atmospheres in the solar system. Since you are (rightfully) questioning every physical theory from blackbody radiation to QED, why not begin to scrutinize some elementary data we are working with. How do we know that the earth surface temperature is 15 degrees C? So far I have not seen any convincing arguments to show that the atmosphere is not isothermal, which would be the default position from elementary thermodynamics.

    SvaraRadera
  6. There are many possible (default) equilibrium states, from isothermal with surface temp - 18 C and 0 lapse rate, to isentropic with + 32 C and max lapse rate 10 K/km, in which the heat transport from surface to TOA is zero. Adding thermodynamic heat transport including evaporation/condensation gives something in between - 18 and 32 C, which turns out to be 15 C as the result of complex thermodynamics driven by insolation controled by clouds...It is natural that heat transport comes along with a temperature gradient = lapse rate.

    One way of thinking of the isothermal and isentropic states is that isothermal results from maximal and isentropic from minimal turbulent dissipation.

    SvaraRadera
  7. Claes, "to isentropic with + 32 C and max lapse rate 10 K/km, in which the heat transport from surface to TOA is zero"

    If you have a heat gradient you have heat transport. Through conduction and radiation, and at 10 K/km you just have onset of convection in a dry atmosphere.

    SvaraRadera
  8. Of course, this is just to state that there is a possible equilibrium state
    with lapse rate 10 K/km, without conduction, convection, radiation, insolation and heat transport.

    SvaraRadera
  9. Claes, no there isn't! To get a non-equilibrium situation like that you need energy input and energy transport, otherwise the system will become isothermal. I'm beginning to understand the frustration of the reviers in your so called "dAlembertgate".

    SvaraRadera
  10. No you don't understand: an isentropic equilibrium state is defined by
    (1) gas law (2) gravitational equilibrium and (3) 2nd Law in the form dE + pdV =0. See books on thermodynamics or better
    http://www.nada.kth.se/~cgjoh/atmothermo.pdf

    I seems that you don't understand d'Alembert's paradox either, nor our
    peer-reviewed published resolution.

    SvaraRadera
  11. Claes, take your "equilibrium" planet with a temperature gradient of 10 K/km in the atmosphere. Now build a high tower. The temperature at the top will be lower than at the bottom, and I can run a heat engine using that temperature difference. Extracting useful energy from an equilibrium state is a perpetuum mobile of the second kind. Does that seem reasonable to you?

    SvaraRadera
  12. No you cannot because the height is different: ekat you gain in height is lost in temp and vice versa.

    SvaraRadera
  13. Claes, if I use a liquid as working medium in my steam engine it will not lose any 10 K/km. Even if I use a gas other than air I will get a different temperature gradient and thus a temperature difference. (as long as the other gas has different Cp). Worst case I can always use an evacuated tube and get a net transfer of thermal radiation between the top and bottom of the tower.

    If there is a temperature gradient in equilibrium in a gravitational field it has to be the same regardless of the material, and the adiabatic lapse rate certainly isn't. I suspect there is a very tiny gradient from relativistic effects, to match the gravitational redshift of the thermal radiation.

    What do you mean by your "zero conduction"?

    SvaraRadera
  14. 2nd Law dE + PdV = 0: no dissipation no diffusion of heat.

    SvaraRadera
  15. Claes, I have no idea what you mean. Try to explain in words why my example is wrong instead.

    SvaraRadera
  16. Isentropic means that a parcel of air rises by cooling off by paying the
    gain in potential energy in terms of lost heat energy. This can give a temp gradient without any net input or gain of energy: simply transfer of heat energy to potential energy. And there is no flow of heat by the temp gradient because heat conductivity is assumed to be zero. Elementary thermodynamics.

    SvaraRadera
  17. Claes, you accused me of being unrealistic when asking about what Earth would be like with no greenhouse gases, and now you postulate a gas with no heat conductivity!??? Such a beast doesn't exist.

    If you postulate no conduction, no radiation, no external object such as my tower, then sure, *any* temperature profile that at no point has a larger gradient than 10 K/km (assuming your unphysical gas has the same Cp as air) will be stable. You can never actually have any convection in an equilibrium situation since this would cause turbulence.

    There still no particular reason why you should reach that maximum gradient. Any heat conductivity, no matter how small, will drive the gradient to zero.

    SvaraRadera
  18. As I have said, turbulent convection will reduce the max isentropic lapse rate. Observation shows a reduction of 3 K/km.

    SvaraRadera
  19. Claes, the reduction has nothing to do with turbulence, only that moist air cools slower when it rises and heat is released by condensation of water vapor.

    You still don't seem to understand why a statement like "We observe that in this model, increase of convective heat transport may reduce the lapse rate further" is nonsense. I think I have to give up.

    SvaraRadera
  20. Yes, evaporation/condensation also decreases the lapse rate.
    Why give up? Are you no longer convinced that CO2 causes dangerous global warming?

    SvaraRadera
  21. Claes, I give up because you are too stubborn to accept new information and correct your own misunderstandings.

    SvaraRadera