I've tried to stay off posting about 'climate science' because I lost my audience months ago, but I still keep digging in my own time. I stumbled across another meteorological concept recently and added another paragraph to my summary on why the Earth is 33K warmer at sea level than its effective temperature (the temperature we would expect from incoming solar radiation and 'albedo' alone). The starting point is to realize that the average temperature of the atmosphere = the effective temperature.
The Holy Trinity of basic atmospheric physics are (is?) three formulae or concepts. These are all text book physics and they are mutually supporting and internally consistent (as well as matching up well with observations). The starting point is to realize that the average temperature of the atmosphere = the effective temperature. There is nothing special about sea level! It just happens to be about 5 km below the mid-point of the atmosphere where actual temperature = effective temperature.
1. The lapse rate (this is the easiest to calculate, it's just acceleration due to gravity ÷ specific heat capacity). To get it to match the real world observed moist lapse rate and to take latent heat of evaporation/condensation into account, you have to bump up specific heat capacity from just over 1,000 J/K/kg to about 1,425 J/K/kg.
2. The Barometric Formula (aka 'Barry'), which predicts local atmospheric pressure at a given altitude, based on pressure and temperature at sea level (and various constants, heinously complicated to calculate). This overstates pressure at higher altitudes, but such is physics.
3. Potential temperature, a term which meteorologist use to describe the sum total of the actual temperature plus the 'latent heat of convection' (i.e. the potential energy) of air at a given altitude (fairly easy to calculate). You can use the same inputs as for the lapse rate and Barry, and then use the pressure at altitude from Barry to predict the potential temperature of air at the given altitude.
To tie them in, you can predict local actual temperature using 1, sea level temperature - (altitude x lapse rate) or combine 2. and 3 and deduct the potential energy at that altitude from the potential temperature. Both answers match up and are a good prediction of actual temperature.
There, that's all you need to know, that's where the extra 33K or 33C come from. Has nothing to do with 'Greenhouse Gases' or 'radiative forcing' or all these other made-up, non-scientific terms.
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