Trenberth et al 2011jcli24 Figure 10
This popular balance graphic and assorted variations are based on a power flux, W/m^2. A W is not energy, but energy over time, i.e. 3.4 Btu/eng h or 3.6 kJ/SI h. The 342 W/m^2 ISR is determined by spreading the average 1,368 W/m^2 solar irradiance/constant over the spherical ToA surface area. (1,368/4 =342) There is no consideration of the elliptical orbit (perihelion = 1,416 W/m^2 to aphelion = 1,323 W/m^2) or day or night or seasons or tropospheric thickness or energy diffusion due to oblique incidence, etc. This popular balance models the earth as a ball suspended in a hot fluid with heat/energy/power entering evenly over the entire ToA spherical surface. This is not even close to how the real earth energy balance works. Everybody uses it. Everybody should know better.
A real heat balance based on Btu/h looks like this. Basically (Incoming Solar Radiation spread over the cross sectional area) = (U*A*dT et. al. leaving the lit side perpendicular to the spherical surface ToA) + (U*A*dT et. al. leaving the dark side perpendicular to spherical surface area ToA) The atmosphere is just a simple second year HVAC heat transfer, heat balance, thermo problem.
“Technically, there is no absolute dividing line between the Earth’s atmosphere and space, but for scientists studying the balance of incoming and outgoing energy on the Earth, it is conceptually useful to think of the altitude at about 100 kilometers above the Earth as the “top of the atmosphere.” The top of the atmosphere is the bottom line of Earth’s energy budget, the Grand Central Station of radiation. It is the place where solar energy (mostly visible light) enters the Earth system and where both reflected light and invisible, thermal radiation from the Sun-warmed Earth exit. The balance between incoming and outgoing energy at the top of the atmosphere determines the Earth’s average temperature. The ability of greenhouses gases to change the balance by reducing how much thermal energy exits is what global warming is all about.”
ToA is 100 km or 62 miles. It is 68 miles between Denver and Colorado Springs. That’s not just thin, that’s ludicrous thin.
The GHE/GHG loop as shown on Trenberth Figure 10 is made up of three main components: upwelling of 396 W/m^2 which has two parts: 63 W/m^2 and 333 W/m^2 and downwelling of 333 W/m^2.
The 396 W/m^2 is determined by inserting 16 C or 279K in the S-B BB equation. This result produces 55 W/m^2 of power flux more than ISR entering ToA, an obvious violation of conservation of energy created out of nothing. That should have been a warning.
ISR of 341 W/m^2 enter ToA, 102 W/m^2 are reflected by the albedo, leaving a net 239 W/m^2 entering ToA. 78 W/m^2 are absorbed by the atmosphere leaving 161 W/m^2 for the surface. To maintain the energy balance and steady temperature 160 W/m^2 rises from the surface (0.9 residual in ground) as 17 W/m^2 convection, 80 W/m^2 latent and 63 W/m^2 LWIR (S-B BB 183 K, -90 C or emissivity = .16) = 160 W/m^2. All of the graphic’s power fluxes are now present and accounted for. The remaining 333 W/m^2 are the spontaneous creation of an inappropriate application of the S-B BB equation violating conservation of energy.
But let’s press on.
The 333 W/m^2 upwelling/downwelling constitutes a 100% efficient perpetual energy loop violating thermodynamics. There is no net energy left at the surface to warm the earth and there is no net energy left in the troposphere to impact radiative balance at ToA.
The 333 W/m^2, 97% of ISR, upwells into the troposphere where it is allegedly absorbed/trapped/blocked by a miniscule 0.04% of the atmosphere. That’s a significant heat load for such a tiny share of atmospheric molecules and they should all be hotter than two dollar pistols.
Except they aren’t.
The troposphere is cold, -40 C at 30,000 ft, 9 km, < -60 C at ToA. Depending on how one models the troposphere, average or layered from surface to ToA, the S-B BB equation for the tropospheric temperatures ranges from 150 to 250 W/m^2, a considerable shortfall from 333.
(99% of the atmosphere is below 32 km where energy moves by convection/conduction/latent/radiation & where ideal S-B does not apply. Above 32 km the low molecular density does not allow for convection/conduction/latent and energy moves by S-B ideal radiation et. al.)
The GHGs reradiate in all directions not just back to the surface. Say a statistical 33% makes it back to the surface that means 50 to 80 W/m^2. A longer way away from 333.
Because the troposphere is not ideal the S-B equation must consider emissivity. Nasif Nahle suggests CO2 emissivity could be around 0.1 or 5 to 8 W/m^2 re-radiated back to the surface. Light years from 333.
All of the above really doesn’t even matter since there is no net connection or influence between the 333 W/m^2 thermodynamically impossible loop and the radiative balance at ToA. Just erase this loop from the graphic and nothing else about the balance changes.
BTW 7 of the 8 reanalyzed (i.e. water board the data till it gives up the right answer) data sets/models show more power flux leaving OLR than entering ASR ToA or atmospheric cooling. Trenberth was not happy. Obviously, those seven data sets/models have it completely wrong because there can’t possibly be any flaw in the GHE theory.
The GHE greenhouse analogy not only doesn’t apply to the atmosphere, it doesn’t even apply to warming a real greenhouse. (“How Global Warming was Discovered” Spencer Weart) It’s the physical barrier of walls, glass, plastic that traps convective heat, not some kind of handwavium glassy transparent radiative thermal diode.
The surface of the earth is warm for the same reason a heated house is warm in the winter: Q = U * A * dT, the energy flow/heat resisting blanket of the insulated walls. The composite thermal conductivity of that paper thin atmosphere, conduction, convection, latent, LWIR, resists the flow of energy, i.e. heat, from surface to ToA and that requires a temperature differential, 213 K ToA and 288 K surface = 75 C.
The flow through a fluid heat exchanger requires a pressure drop. A voltage differential is needed to push current through a resistor. Same for the atmospheric blanket. A blanket works by Q = U * A * dT, not S-B BB.
Open for rebuttal. If you can explain how this GHG/GHE upwelling/downwelling/”back” radiation actually works be certain to copy Jennifer Marohasy as she has posted a challenge for such an explanation.