The scientific method has an experimental and a theoretical aspect. Basic theoretical science is expressed in the language of mathematics and relies on the methods of mathematics of logical reasoning (axiom-definition-theorem) and symbolic/digital computation. Experimental science concerns observations of real phenomena,

Mathematics is used to construct mathematical models of real (or imagined) phenomena, which then can be simulated by letting the model transform input data to output data by computation, with input data from observations (or invented).

Typically the mathematical model consists of differential equations expressing basic physical laws such as conservation of mass, momentum and energy. A basic example is Maxwell's equations describing all of electromagnetics in four differential equations. It all started with the Calculus of Leibniz and Newton initiating the scientific revolution in the late 17th century.

Understanding of real phenomena can be achieved by understanding the mathematical model,

which is open to inspection, while reality is not, as formulated by Edsger Dijkstra:

- Originally I viewed it as the function of the abstract machine to provide a truthful picture of the physical reality. Later, however, I learned to consider the abstract machine as the true one, because that is the only one we can think ; it isthe physical machine's purpose to supply a working model, a (hopefully) suciently accurate physical simulation of the true, abstract machine.

- should be made as simple as possible, but not simpler.

A too simple model would then represent non-science, rather than science.

Let us now consider a specific area of science: climate science. The mathematical model describing global weather with climate being global weather averaged over time, is the Navier-Stokes equations expressing conservation of mass, momentum and energy, describing the thermodynamics of atmosphere and oceans, combined with a model of the radiative warming by the Sun and radiative cooling into space. In short: Navier-Stokes with radiative forcing as a thermodynamics model, which is as simple as possible, but not simpler.

In climate science another model, Stefan-Boltzmann's Radiation Law, forms the basis of the CO2 climate alarmism advocated by IPCC by supplying a starting value for climate sensitivity of 1.2 C (upon doubling of CO2 in the atmosphere), which is boosted by feed-backs to an alarming 2-4.5 C.

However, this model is too simple, because thermodynamics is not included, only the simple algebraic Stefan-Boltzmann Radiation Law. This argument is developed in more detail in Climate Thermodynamics.

We conclude that the basic postulate of CO2 alarmism of a climate sensitivity of 1.2 C, is not verified using the scientific method, and thus has the role of an ad hoc assumption, which until properly verifed represents non-science. Without this basic postulate feed-backs have nothing to feed on and alarmism collapses.

Thanks for the update, I very much appreciate your efforts and contributions. However, I think there are still some unanswered questions:

SvaraRadera1. "The effective blackbody temperature of the Earth with atmosphere is −18C, which

can be allocated to a TOA at an altitude of 5 km at a lapse rate (temperature drop with

increasing altitude) of 6.5C/kmconnecting TOA to an Earth surface at 15C with a total

warming of 5×6.5 = 33C."

Do you have any justification for this boundary condition, other than it seems to conform with observation?

2. "We will argue that an initial lapse rate of g = 9.81C/km is instead determined

by thermodynamics (and not by radiation) as an equilibrium state without heat transfer"

How shall we interpret this? Do you put a hydrostatically stable lapse rate of 9,81/km as your initial condition? What would happen if you start with an isothermal lapse rate, would it approach the isentropic lapse rate over time?

There is no "boundary" of course. This is just a fictitious mathematical construct to have a simple mental model.

SvaraRaderaWhy would you start with an isothermal stat, in the discussion? Physics pushes towards an isothermal state rather than away from it.

Yes you are right that physics pushes towards an isothermal state normally. But as I see it you treat it as a heat transport problem with solar forcing.

SvaraRaderaFor example, suppose you have a house in the winter that is not heated and hence in thermal equilibrium with the surrounding. Then you put on the radiators, and the house reaches a stationary state characterized by a temperature gradient under radiator forcing.

My point is that your model should be able to seek up this stationary state even if it had an isothermal initial state.

Does it?

I agree: We are testing the model computationally and we'll see...

SvaraRaderaThe isothermal state is not stable, so even if there is a tendency towards

SvaraRaderathis state there is also a tendency away from it, and that is what generates interesting dynamics.

Good day, Professor. I am on your side, but I wonder if the likes of Monckton, Lindzen and Spencer would agree with you that, under the IPCC radiation-forcing model (or at least their version of it), the effect of adding CO2 would be to increase the lapse rate, as opposed to the opposite effect in your thermodynamic model. In his article, "Greenhouse Warming? What Greenhouse Warming?", on www.scienceandpublicpolicy.org, Monckton describes the situation as: "When the Earth is in radiative balance with space, net incoming solar radiation (NISR) is balanced by outgoing longwave radiation (OLR) from the characteristic emission level T=1.... When greenhouse gases are added to the atmosphere, the characteristic emission level is raised in altitude. Since atmospheric temperature decreases with altitude at about 10 degrees C per mile, the new characteristic emission level is colder than the previous level.... The Earth is no longer in thermal balance with space.... To re-establish balance, the temperature at the new T=1 level must increase to about the temperature that had existed at the initial T=1 level." So he's saying the effect is to cause the same temperature difference between the surface of the Earth and the "characteristic emission level" to be spread over a greater vertical distance--thus, decreasing the lapse rate. This is the same effect you describe for your thermodynamic model. This doesn't spoil your model, but I take it he wouldn't agree with you that there is a clear predictive difference between his model (and Lindzen's, I take it)and yours.

SvaraRaderaThe idea with the "raising the emission level to colder levels" is strange because it let's the radiation "climb" on a lapse rate set by thermodynamics, which is assumed to be constant during change of radiation pattern. The idea of Lindzen &Co is that since the emission

SvaraRaderahas to stay constant to keep heat in-out balance, the whole temp profile will have to be "lifted" (without changing the lapse rate) thus causing warming on the ground. Thermodynamics can change the lapse rate, but I don't see that the radiation argument does that (since the lapse rate is assumed to not change).

Good day Harry.

SvaraRaderaAs I understand it, the version of the greenhouse effect that you quote says that increasing the amount of greenhouse gases puts the effective radiating level at a lower pressure and that the ground temperature is then recovered by following an adiabat down to the ground level pressure according to the formula

T(p) = \Theta (p/p_0)^(R/C_p)

which relates temperature and pressure. In passing it should be noted that the momentary lapse rate exhibits a very good correlation between temperature and pressure (as far as I know), where on the other hand there is no clear relationship between temperature and altitude.

However, this only serves as a very formal argument. The important thing to realize is that according to the theory the greenhouse gases are responsible for destabilizing the isothermal state (in quite a rough way too) and the adiabat only forms when the atmosphere has become unstable to convection.

In other words, finding cause and effect are crucial. I myself is convinced that water vapour for example has a stabilizing effect, whereas gravity has a destabilizing effect. The opposite holds in greenhouse theory. I guess Claes' simulations could maybe shed some light on this. But I agree that the question of boundary conditions and where the atmosphere "ends" and so on are important questions that do not have an answer at the moment. My intuition tells me that the altitude of TOA is temperature dependent for example.

I agree with you both (except about the "gravity has a destabilizing effect"--that's odd, since it provides for the lapse rate in any event, through your p/p0 term), and I'm glad you have made those points, especially about "finding cause and effect are crucial". I don't know how they would explain the physical process by which the lapse rate would decrease with added so-called greenhouse gases; I suspect they would say something along the lines of your "very formal argument". I only know that Monckton's description clearly indicates the lapse rate would decrease. My impression of it all so far, which you both seem to share, is that they hamper themselves (and any competent physicists watching) by starting from the almighty Blackbody Radiation power formula, generally wrongly applied, and leaving all that nasty thermodynamics as just so much number crunching they are generally content to let the weather-cum-climate models crank through. I like to keep it simple, as far as possible, so I would suggest they might be, deep down, afraid of the lapse rate, because it strikes at the heart of the greenhouse gas hypothesis, and demands the thermodynamics behind it be put first.

SvaraRaderaYes, I think you describe a reality.

SvaraRadera