But the reason that the models are failing to reproduce what we see that they are based on an approximation of the radiative
transfer equation which does not apply to the boundary layer where the ice is melting.
Not exact matches
Think it seems like a fab idea but when items don't
transfer easily from country to country it completely takes the convenience out of the
equation which is what makes this app seem so appealing.
Radiative
transfer models use fundamental physical
equations and observations to translate this increased downward radiation into a radiative forcing,
which effectively tells us how much increased energy is reaching the Earth's surface.
In this case you have the diffusion
transfer equation,
which similarly has a differential of hot and cold terms describing the heat flow, as does the radiation
transfer equation, and we all understand that heat does not physically diffuse from cold to hot and that physical contact between a cold object and warm object does not make the warmer object warmer still.
Instead atmospheric physics uses the fundamental
equations (the radiative
transfer equations)
which determine absorption and emission of radiation by water vapor, CO2, methane, and other trace gases.
Although your math seems to work, it appears to me that your conclusion may not be correct, at least if Velasco et al. are; if I interpret their paper correctly, the kinetic - energy profile of their
Equation 8 is the maximum - entropy configuration, from
which I would conclude that a strictly isothermal microcanonical ensemble will spontaneously undergo (an incredibly small) heat
transfer to assume that (ever so slightly non-isothermal) configuration.
Absorb it at the top (
which will clearly happen, see radiative
transfer equations, this is hotter to colder).
This is described by the
equation for conductive heat
transfer,
which in (relatively) plain English says:
Steve I will ask you to show the radiative heat
transfer equation in
which you input an emission from another body, gas / solid or fluid and show where it lowers the rate of cooling.
So the conclusion (furthermore the
equation has a term for the emissivity of the object and no term for the emissivity of the surroundings or the absorptiveness of the object, both of
which would be required if the surroundings were
transferring energy to the object.)
In this
equation, q is the rate of heat
transfer,
which is the NET rate of energy
transfer.
There is a very simple
equation of radiative
transfer which is used to illustrate the subject at a basic level and it is called the semi-grey model (or the Schwarzschild grey model).
(24),
which yields a value very close to that of IPCC (2007), is such that progressively smaller forcing increments would deliver progressively larger temperature increases at all levels of the atmosphere, contrary to the laws of thermodynamics and to the Stefan - Boltzmann radiative -
transfer equation (Eqn.