Climate Science Without Physical Basis

Global climate is governed by physical laws and physical laws are expressed mathematically.

A physical law without a mathematical expression is not a physical law. Global climate is 

a coupled ocean-atmosphere thermodynamical process powered by radiation from the Sun and 

rotation of the Earth, which is described by mathematical equations for

• convection-diffusion-conduction of  (in)compressible flow (Navier-Stokes equations) 
• phase-change: ice-water-vapour
• radiation

based on in particular the following physics of heat transfer with heat represented as atomic

vibrations: 

• conduction in a material medium by successive excitation of atomic vibrations
  
• convection by transfer of the material medium carrying the heat as atomic vibrations
• radiation without medium by electromagnetic waves.

The basic law for heat conduction is Fourier's Law: 

                                                  q = - c  gradT

where q is heat flow, gradT is temperature gradient and c a positive constant. Fourier's Law states that heat flows from hot to cold with a magnitude proportional to the difference or gradient hot-cold.

Convective heat transfer has a very simple mathematical expression as material motion.

The heat exchange between phases of ice-water-vapour can also be described mathematically.

The basic law of heat transfer by radiation from a hot body of temperature Thot to a colder body of temperature Tcold, is Stefan-Boltzmann's Radiation Law

                                     q = c (Thot^4 -Tcold^4)

where c is a positive constant. 

We understand that basic physics tells that conduction-radiation is not by itself capable of transferring heat from a cold body to a hotter body (2nd Law of Thermodynamics if you like). Only convection (or phase change) can do that.

We now apply our knowledge to the coupled system Earth-atmosphere with the Earth

absorbing heat radiated from a hot Sun, which is somehow transferred through the atmosphere consisting of the troposphere connecting to the Earth and the stratosphere on top, and then 

radiated out into space.

We start from the observation that the (mean) temperature drops from 15 C  at the Earth surface through the troposhere to about - 55 C at its top (the tropopause), and then in the 

stratosphere increases to 0 C at its top (the stratopause). 

The heat accumulated from the Sun is thus first transferred from hot (15 C) to cold (-55 C) 

and then from cold (-55 C) to hot (0 C).  

We conclude that convection is necessary; radiation alone cannot transfer heat through the 

atmosphere with the observed temperature profile.

The basic postulate of IPCC climate alarmism is the relation dQ = 4 dT connecting 

global warming dT to change of heat forcing dQ. This relation is a consequence of using

Stefan-Boltzmann's Radiation Law as a model for global climate, as shown in previous posts.  

But we just realized that a model including only radiation is incompatible with observation. It is necessary to include convection in the model. But then the derivation of the relation dQ = 4 dT is no longer valid, and no other derivation is available.

The net result is that the basic postulate of climate alarmism of dQ = 4 dT lacks physical/mathematical basis. It is derived from a mathematical model which is not compatible with observation, and thus it is not scientific. 

Let us take an analogous example. Suppose someone (a climate scientist e.g.) explains why a bird can fly as follows: We start from a model saying that on birds there is an upward force balancing the downward gravitational force, because there is a physical law that states that all bodies (thus also birds) are acted upon by an upward force which balances gravitation. 

Do you buy this argument? Probably not: Such a law would be contradicted by observing an apple fall. The conclusion is that the law is false in the case of an apple and also for a bird without a further explanation. It doesn't matter that it is valid in some other case, namely the case of zero gravitation, or a mass-less apple/bird.

We repeat: If we make the observation that the Radiation Law as a model of global climate, is (completelly) incompatible with observation, then we must (if we are scientists) draw the conclusion that the Radiation Law as a model for global climate is (completely) useless. Climate alarmism on this basis is not scientific.

Note that it is the Radition Law as model of global climate which is incorrect, not the 

Radition Law per se,  possibly being valid for something else (like the radiation from the Sun).

Or a combination of the Radiation Law with e.g. convection.

To claim that the Radiation Law as a model of global climate is correct, because it is correct when applied to the Sun (or when augmented by convection), is nothing but Penguin Logic, which is not the logic of science even if practiced by climate scientists.

And with Penguin Logic you can do wonders: For example, you can argue that an estimated 

d T = 0.7 C during the 20th century, from and increase of CO2 from 280 to 380 ppm, corresponds to dQ = 2.8 W/m2, and then make the prediction that further increase of CO2 will double dQ and thus dT to 1.5 C, the lower IPCC prediction. You can then feed your climate models with both dT and dQ and boost to at least 4.5 C. Penguin Logic at its best, used by IPCC.

For a simple mathematical model of global climate including conduction-convection-evaporation-condensation-radiation, see Temperature Sensitivity of a Basic Climate Model.

Also compare what the English factory worker Derek Alker comes up with in Do IR Budgets Make Sense?? Better than any Royal Academy...

But the Royal Academy is not alone: According to Huffington Post:

• Ninety seven percent of climatologists agreed that climate change is real and largely man-made in a poll released last year. At least 60 major scientific organizations across the globe also concur, while not one of any repute holds an opposing opinion. 
  

All major scientific organizations give their praise to a climate science without physical basis. 

How is this possible?

PS Maybe an alarmist would argue as follows: Let's skip the kink in the temperature profile

and just concentrate on an Earth at 15 C radiating infrared through a infrared transparent

atmosphere to a cold outer space. That is possible, but in this case the Earth surface temperature would have to drop to its black body temperature 0 C, in contradiction to observation.  The temperature profile of a non-transparent radiative atmosphere cannot have a kink.