Monday, 13 September 2021

Why are clouds at that particular altitude?

If you round up two-thirds cloud cover to 100% cloud cover and assume they have an albedo of 0.3, then the real reason for the apparent 33 degree Greenhouse Effect is immediately obvious, as I explained a month ago.

The next question to be answered is, why do clouds form so that the average altitude of their upper surface (the surface which absorbs and is warmed by solar radiation) is at about 5 km* (with a resulting sea level temperature of 288K)? Why not 4 km or 10 km? I've struggled with this for the past month, and, much head scratching, calculating, sketching and Bingling later, what it boils down to is as follows:

* Clearly, cloud cover is not 100% at 5 km and clouds don't have an alebdo of 0.3. Cloud cover is about two-thirds; their upper surface is higher than 5 km (call it 7 km); and clouds have an albedo of 0.4. But if you do a weighted average altitude and albedo of 'what the sunshine hits first' it's 5 km and 0.3.

1. The dew point of the water vapour in any 'parcel' of air depends on three variables. For a start let's focus on i. air temperature and ii. air density/pressure. We'll get back to variable iii. Relative Humidity later, You can merge ii. and iii. into one variable called 'partial water vapour pressure', but it's easier to treat them separately:

For a given R.H., in warm air, water vapour is likely to stay as a gas; in cold air it is more likely to condense and fall as rain. There's a narrow range of temperatures where it remains as tiny droplets which remain suspended in the air: 2. For a given R.H., if air has low pressure/density, the water vapour is more likely to remain as vapour. If it's high pressure/density, it is more likely to condense and fall as rain: 3. We can put those two together into a table of all possible temperature/pressure combinations.

Some vapour in the air will condense into tiny droplets, small enough to stay suspended and form clouds. Only those clouds which happen to form at the altitude where that particular temperature-pressure combination is in the white band will remain as clouds. So they could be low and warm or cold and high: 4. But the upper surfaces of clouds tend towards the same temperature because they absorb solar radiation. With an albedo of 0.3, they will reach an average temperature of 255K (average of day and night). So they mainly form at the altitude where the pressure/density is such that they fall into the white 'just right' band. Any higher, they will evaporate again, any lower and they will condense and fall as rain: 5. OK, so some clouds have formed at the 'right' altitude and are stable for now. We know the temperature of their upper surface, and that that temperature plus altitude x lapse rate (also known) determines sea level temperature.

But wouldn't this be positive feedback? Higher clouds = warmer surface = overall warmer atmosphere = atmosphere expands verrtically = higher clouds? For example, the whole tropsphere over the Equator and Tropics is twice as high as over the Poles, with a correspondingly higher 'right' cloud altitude.

What sets the upper limit..? 6. The upper limit is set by the third main factor for determining dew point - Relative Humidity. It is chaotic and dynamic but self-correcting. If the clouds are too high, so is sea level temperature, which leads to more evaporation, higher R.H. and higher R.H. means lower clouds again, and vice versa: 7. Some clouds will form at the 'Goldilocks' altitude where the resulting sea level temperature generates enough R.H. to maintain the clouds at that particular altitude. This is arrived at by trial and error, and while the precise calculations are beyond human comprehension, clouds do it for us by simply following basic laws of physics until they 'get it right': 8. Finally, you end up with what you expect to see. Sea level temperature 288K; clear air up to a certain altitude (too warm for clouds to form); a layer of clouds 1 or 2 km thick (the 'Goldilocks altitude'); above that clear air again (the pressure/density is so low that clouds evaporate again). Clearly, this is weather, so these are not exact values. They are all constantly overshooting in both directions, but it all oscillates around some sort of equilibrium and averages out. 9. What other evidence to we have to support this, apart from it matching up to observations and being entirely consistent with basic physics and everything else in the overall theory?

a. All I can think of for now is that areas with higher R.H. tend to have lower clouds (as you would expect. If there's more water vapour it's more likely to condense at a lower altitude) and their sea level temperature tends to be a bit lower (lower cloud altitude means the difference in temperature between upper surface of clouds and sea level is lower, as there are fewer km to multiply by lapse rate) than in drier areas.

b. Higher R.H. and lower clouds also mean a much smaller day-night ('diurnal') temperature range - water vapour is good at holding on to thermal energy and the lower clouds are good at reflecting upwelling IR back down to sea level in the night time. This is also observed in real life.

c. Venus and Mars follow exactly the same pattern, even though their atmospheres are nearly 100% CO2 and other 'greenhouse gases'.


James Higham said...

Goodness me again. You never fail to surprise. Dewpoint eh?

Mark Wadsworth said...

JH, this is important!

Ralph Musgrave said...

Hi Mark, I'd be interested in seeing some calculations done on the amount of global cooling achieved by covering a square kilometer of the Earth's surface with some sort of reflective material. They're doing this in Los Angeles. See: