## tisdag 10 mars 2015

### Basic Model of Greenhouse Effect: Climate Sensitivity=0.2 C

Model of an Earth-atmosphere system absorbing energy from the Sun, which is partially transferred to the ground surface thermodynamically and emitted to outer space partially from the ground through an "atmopsheric window" and partially from the atmosphere. The effect of "closing the window" is at most 2 C as the maximal "total greenhouse effect" of all "greenhouse gasses", thus  with a "climate sensitivity" as a 10% change from doubled CO2 emission of at most 0.2 C, which is so small that it can never be observed. The model indicates that CO2 global warming alarm of 3 C is false alarm.

The standard basic model of the Earth's energy budget predicts a "total greenhouse effect" of 33 C as the difference between the presently observed global Earth surface temperature of + 15 C and a projected temperature of - 18 C of an Earth with fully transparent atmosphere without any "greenhouse gas", or an Earth without any atmosphere at all like the Moon, cf. PS2 below.

The projection of - 18 C results from a direct application Stefan-Boltzmann's law as the radiative equilibrium temperature of a black body (or grey body) at the same distance to the Sun as the Earth.

This model is extremely simplistic but yet is used as a starting point for projections of alarming global warming from small changes in the radiative properties of the atmosphere by human emission of CO2. A 10% change of  a "total greenhouse effect" of 33 C is presently sending an alarm of 3 C propagated to humanity by IPCC.

Following Einstein one should always seek a model which is as simple as possible, but not too simple. Viewing the above 1-stage model as too simple, we consider instead the following 3-stage model of an Earth-atmosphere system "without greenhouse gas effect":
1. Radiative absorption of 240 W/m2 out of incoming 340 W/m2 from the Sun with absorptivity 0.7 by Earth+atmosphere system.
2. Thermodynamic transfer of 240 W/m2 from Earth+atmosphere to Earth ground surface (without loss).
3. Radiative emission of 240 W/m2 from ground directly to outer space through "fully open atmospheric window" with emissivity 0.7 at 280 K = 7 C according to Stefan-Boltzmann $240 = 0.7\times\sigma\times 280^4$ with $\sigma = 5.67\times 10^{-8}Wm^{-2}K^{-4}$.
We compare with present observation of ground temperature of 15 C with emission of 40 W/m2 directly from the ground to outer space, with thus "1/6-open atmospheric window".

Extrapolation to fully closed window, then predicts a ground temperature of 15+ 8/5 C, say 17 C.

The total effect of closing the present atmospheric window of 40 W/m2 by massive emission of a greenhouse gas, thus could at most cause a warming of 2 C.

We have thus with a less simplistic model arrived at a "total greenhouse effect" of 2 C instead of the 33 C by the too simple model.

Incidently, this connects to the so-called "2-degree goal", but now with the 2 C as the maximally possible "total greenhouse effect", with thus 10% changes of size 0.2 C as an upper estimate of climate sensitivity as global warming by doubled CO2. Reducing 33 C to 2 C reduces global warming alarm to nothing.

The maximal change of global temperature under varying radiative properties of the atmosphere including clouds and "greenhouse gasses", could thus be estimated to be at most 2 C. This conforms to the observed temperature variation during the last 10.000 years after the last ice age, see below where the alarming dotted 3 C prediction reflects the too-simple-model.

Note that the crucial element in the not-too-simple model is the thermodynamic step 2 separating emission from absorption resulting in a double reduction with absorptivity=emissivity= 0.7, to be compared with one reduction with absorptivity=emissivity in the too-simple-model.

Notice further that the thermodynamics including lapse rate et cet is included in the observation of 15 C with 5/6 closed window.  The model thus isolates the crucial role of the "greenhouse effect" in the CO2 global warming scenario through a variable "atmospheric window".

PS1 The too-simple-model is used to predict the "total greenhouse effect" to be 33 C and is also used for the basic prediction of CO2 global warming of 1 C by Stefan-Boltzmann from an estimated "radiative forcing" of 4 W/m2 from doubled CO2 from an estimated 10% broadening of the "ditch" of the CO2 OLR-spectrum.  For a comparison with the not-too-simple model, see the next post.

PS2 The max and min temperatures of the Moon at the equator is 390 K and 120 K, respectively, which gives a mean of about 255 K = - 18 C.

#### 10 kommentarer:

1. Hi Claes - I see you now do accept that there is a Greenhouse Effect, that's wonderful!

Now what happens in your model when there is more than one "layer" of atmosphere?

2. Wonderful? If the added greenhouse effect is 0. 2 C it is the same as non existence.

The model has three layers: outer space, atmosphere and Earth surface. That is the beauty and usefulness of the model: It is as simple as possible, but not too simple.
There are endless ways of making the model less simple, but not necessarily more informative.

3. I don't actually follow the argument at all here, but it does seem to be ignoring that a large fraction of the outgoing flux is essentially emitted from within the atmosphere. If the window were to be closed completely, then it would all be emitted from within the atmosphere and the surface temperature would then be set by the effective emission height in the atmosphere and the lapse rate (set by convection). I think this is a point that Ray made in his correspondence with Claes and which Claes appears to not have properly considered.

4. No, look at the picture showing partial emission from the atmosphere.

5. Claes,
Ahh, but as I think Arthur is trying to point out, our real atmosphere is not simply a single layer. You're arguing - I assume - that if we close the window, that the layer in the atmosphere simply has to warm up a little so as to then emit the extra energy that was coming from the surface. What this ignores is that, in reality, closing that window will also influence the emission from within the atmosphere. Consider Venus, for example. Most of the emission to space comes from an altitude of around 50km. It's a dry atmosphere, which means the lapse rate will be the dry adiabatic rate (10K/km) and hence the surface temperature is 50 x 10 = 500K warmer than the non-greenhouse equilibrium temperature. Your argument would appear to be suggesting that Venus is impossible, which is clearly not true.

6. For Venus the model would say that added CO2 would make no difference since the window is closed. Thus the observed 450 C or whatever would remain after added CO2.

7. Claes, if so, then that would suggest that your model is wrong. If you add more CO2, then the emission to space would occur higher in the atmosphere and - as Ray tried to point out in his letters to you - if you then followed the adiabat down to the ground (10K/km for the dry adiabatic lapse rate) the surface temperature would go up.

8. The extrapolation in the model accounts for all effects. Yes, the model is simple but probably better than the too-simple-model used as starting point CO2 alarm of 33 C "greenhouse effect", which is misleading the world into meaningless CO2 emission control. Meaningless.

9. Yes, the model is simple but probably better than the too-simple-model used as starting point CO2 alarm of 33 C "greenhouse effect", which is misleading the world into meaningless CO2 emission control. Meaningless.

Seriously? Okay, I'll leave you to your model that accounts for all effects, but that still happens to be completely wrong.

10. All effects are included in an observation of 15 C at 5/6 closed window.