The error in the rebuttal was the failure to recognise the difference between
the effective equilibrium temperature and the model - reported ECS.
Your definition specifically confuses the question of the efficacy of a forcing agent with the question of why there is a difference displayed in GCMs between
their effective equilibrium temperature and their reported equilibrium temperature.
Not exact matches
They conclude, based on study of CMIP5 model output, that
equilibrium climate sensitivity (ECS) is not a fixed quantity — as
temperatures increase, the response is nonlinear, with a smaller
effective ECS in the first decades of the experiments, increasing over time.
This includes those relative to the planet (mass, radius, orbital period, and
equilibrium temperature) and those relative to the star (mass, radius,
effective temperature, and metallicity).
Plugging S = 1367.6 and A = 0.306 into the equation above, we find that F is about 237 watts per square meter for the Earth, corresponding to an «
equilibrium temperature» (or «emission
temperature,» or «
effective temperature») of 254 ° K. Most formulations use a slightly different S and A and get 255 ° K.
The standard assumption has been that, while heat is transferred rapidly into a relatively thin, well - mixed surface layer of the ocean (averaging about 70 m in depth), the transfer into the deeper waters is so slow that the atmospheric
temperature reaches
effective equilibrium with the mixed layer in a decade or so.
The vapor pressure in
equilibrium with supercooled droplets (liquid H2O) is higher than that in
equilibrium with solid H2O at the same
temperature, so liquid droplets will evaporate to feed deposition on an
effective ice nucleus.
Depending on meridional heat transport, when freezing
temperatures reach deep enough towards low - latitudes, the ice - albedo feedback can become so
effective that climate sensitivity becomes infinite and even negative (implying unstable
equilibrium for any «ice - line» (latitude marking the edge of ice) between the equator and some other latitude).
The skin layer planet is optically very thin, so it doesn't affect the OLR significantly, but (absent direct solar heating) the little bit of the radiant flux (approximatly equal to the OLR) from below that it absorbs must be (at
equilibrium) balanced by emission, which will be both downward and upward, so the flux emitted in either direction is only half of what was absorbed from below; via Kirchhoff's Law, the
temperature must be smaller than the brightness
temperature of the OLR (for a grey gas, Tskin ^ 4 ~ = (Te ^ 4) / 2, where Te is the
effective radiating
temperature for the planet, equal to the brightness
temperature of the OLR — *** HOWEVER, see below ***).
In the absence of solar heating, there is an
equilibrium «skin
temperature» that would be approached in the uppermost atmosphere (above the
effective emitting altitude) which is only dependent on the outgoing longwave (LW) radiation to space in the case where optical properties in the LW part of the spectrum are invariant over wavelength (this skin
temperature will be colder than the
temperature at the
effective emitting altitude).
The
effective temperature is how hot the Earth looks from space, as a result of being in
equilibrium with incoming heat from the Sun: heat in equals heat out, and one can deduce the
effective temperature of the Earth from that balance.
On average, there won't be a change in the
equilibrium radiating
temperature of the Earth, but there will be a change in the
effective radiating altitude consequent on the change in the atmosphere's
effective thermal conductance.
I would also invite you to think about how perfect LTE could possibly be observed if it did exist; any device you use to measure the thermal radiation or the distribution of velocities or the population of excited states must itself be at a different
effective temperature from the gas in question, and must absorb energy from it, disturbing the very
equilibrium you are trying to observe.
The Earth's atmosphere, satisfying the energy minimum principle, is configured to the most
effective cooling of the planet with an
equilibrium global average vertical
temperature and moisture profile.
They conclude, based on study of CMIP5 model output, that
equilibrium climate sensitivity (ECS) is not a fixed quantity — as
temperatures increase, the response is nonlinear, with a smaller
effective ECS in the first decades of the experiments, increasing over time.
I have, incidentally, found using a multilayer diffusive ocean model that there is a near complete identity in the path of the model surface
temperature response to a step forcing, for the better part of a century, over a wide range of
equilibrium climate sensitivities if
effective ocean diffusivity is varied to compensate.
• The cloudy sky moves to that
equilibrium effective optical density whereby the net absorbed solar heat can be reradiated out into space with the minimum greenhouse effect, minimum surface
temperature or maximum entropy production.»