“Convection can only begin once it becomes more energy efficient than radiating heat directly to space. Some refractive/absorbent atmosphere is needed to tip the energy balance.”

I recently wrote that statement on a blog discussion. The convective flow of heat to the top of the atmosphere needs energy because the convection cycle does work. That is because convection and the maintenance of the lapse rate is a heat engine. I have tried to analyse this statement quantitatively through two thought experiment – one for radiation and one for convection. Firstly lets look at radiation.

Case 1 as shown in Figure 1. In this scenario there is 100% Radiative transfer of heat to space through an absorbant atmosphere and no convection. Here we imaging an Earth like surface but with a vacuum gap immediately above it. Above this vacuum gap follows a 100% IR absorbant layer acting like a black body, and above that empty space. Convection from the surface is impossible so it can only cool by radiation. Energy balance ensures that the top layer reaches 255K and acts like a black body radiating equally upwards and downwards. It then follows that the ground surface temperature must be 303 C in order to radiate the 480 watts/m2 – a total extra energy cost of 240 watts/m2. The actual extra radiation on Earth today is 150 watts/m2.

Case 2 as shown in Figure 2. This scenario is of an Earth like surface which can only lose heat through convection. This thought experiments takes an exactly opposite situation to Case 1. Now the planet surface is assumed to have zero emissivity (it is covered with a completely reflective IR foil transparent to solar radiation) so no radiation can escape to space. The atmosphere is the same as that on Earth, and all energy is transported to the top of the atmosphere by convection where it then radiates away to space. The atmosphere follows the dry adiabatic lapse rate. To simplify the maths we are going to make some simple and (unphysical) assumptions. Air is warmed at the surface rises immediately (isothermally) to the TOA where it cools. It then descends immediately (isothermally) to the surface where it again warms to cycle again.

These assumptions allow us to make a minimum estimate of the work done by the convective heat engine based on the carnot cycle. To balance the incident solar energy maintaining a surface temperature of 288K and a TOA temperature of 255K needs 7.5g/sec m^2 to be convected expending a minimum of 40 watts/m2. In reality of course the air rises adiabatically cooling as it rises so this is just a ball park figure.

A planet with no atmosphere can only radiate IR from its surface to balance energy. Imagine it slowly gaining an atmosphere which absorbs IR. Little changes until the absorption length becomes about the same as the distance to the top of the atmosphere. Convection starts once a small amount of energy is absorbed by the atmosphere thereby setting up an initial lapse rate. This now allows heat to pass directly to the free radiation zone higher up, and it also enables radiative transfer of heat through the atmosphere to begin. Eventually the balance between radiative transfer of heat and convective transfer of heat will depend on the optical depth of the atmosphere. This also determines the height of the troposphere. On Venus for example convection dominates heat transfer from the surface and the tropopause is over 60 km above the surface.

Now consider a volcanic vent deep underneath the Atlantic Ocean. The lava oozing out of it is say at 1000C and radiating as a black body. All that radiation is absorbed within 100m by the surrounding water and cannot escape (to space) to cool the vent. Instead the surrounding water gets super-heated and then rises by convection to be replaced by colder water. All the heat is carried away by convection currents and essentially none of it by radiation. Eventually the excess heat reaches the surface and is exchanged with the atmosphere. Convection wins hands down in this case.

Exactly the same process happens in the atmosphere as it is heated from below by the surface. Even though some of the IR can escape directly to space most of the heat is instead transported away by convection and especially for the 70% of the surface covered by oceans by evaporation. It is convection that sets up and maintains the lapse rate. Latent heat release reduces the dry adiabatic lapse rate up to cloud tops. The lapse rate itself makes it thermodynamically possible for radiative transfer of heat. Without it there would be no greenhouse effect.

The subtle point though is that it is only because the IR refractive index of the atmosphere is less than 1, that convection can start and be maintained at all. I think everything is linked together through one “atmosphere effect” which includes convection, latent heat and radiative transfer. So to discuss the “greenhouse effect” in isolation from convection and evaporation is wrong and so is discussing thermodynamic effects without including radiation.

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