Wednesday, April 25, 2007

Heat in the troposphere: Putting it all together

The thermodynamics of the lower atmosphere, including all the phenomena of weather, is shaped decisively by the Earth. Its gravity, in balance with air pressure, determines the way temperature, pressure, and density drop with altitude, all the way to outer space. The lower atmosphere is primarily heated from below, by visible and ultraviolet (UV) radiation absorbed from the Sun and re-released in various forms we'll discuss presently. That's one way to define what's meant by "lower atmosphere." Another, more descriptive way is captured by the name "troposphere," from the Greek tropein, "to turn over." It runs from the Earth's surface to the tropopause, at about 11 km altitude.

The lower atmosphere is where convection, evaporation, and condensation happen. They're important enough to significantly augment and alter the heat flow. And how heat flow is distributed is how temperature is determined. Heat flows from higher temperature to lower. But in a system not in thermodynamic equilibrium (without a single temperature and pressure), higher and lower temperatures are better thought of as being caused by pre-existing heat flows, rather than vice versa.

To understand the temperature distribution of the troposphere, keep in mind two principles:
  • It's best to understand the temperature of distinct entities first (in this case, the Earth's surface, the lower atmosphere, and the clouds); then secondarily, understand the vertical temperature profile as a continuum (that will come in the next posting).
  • If the atmosphere is a steady state (and it's never far from that), energy conservation can be applied to any entity you can draw a boundary around. For the climate, that means a balance of power flows for such entities: power in = power out.
There are three ways to apply power balance. For the surface by itself:
  • solar radiant power in (what isn't reflected or absorbed by the clouds) + heat emitted down by clouds + heat needed for evaporation = Earth heat radiated upward + Earth heat convected upward + net latent heat released by evaporation-condensation
For the lower atmosphere + surface as a whole:
  • solar radiant power in (what isn't reflected by the cloudtops) + latent heat in = heat radiated out from the surface under clear skies + heat radiated out from the cloudtops
For the clouds, treated as a single cloud deck:
  • solar radiant power absorbed (what isn't reflected and what isn't transmitted through) + Earth heat radiated upward + Earth heat convected upward = heat radiated up from the clouds + heat radiated down from the clouds

Now imagine a series of increasingly realistic Earth atmospheres, starting with an airless, waterless Earth. Although the Kelvin and Celsius scales have different zeros, their temperature increments are the same. The values here should be taken as representative of the temperate zone during spring or fall. In the actual atmosphere, the values vary quite a lot by latitude, season, time of day, and whether you're over land or water.

Airless, waterless Earth: T(surface) = 279 oK = 6 oC = 43 oF. The surface temperature is determined solely by the absorption and re-emission of solar radiation by the surface. The cases of dry air and wet air, with free water vapor only: same surface temperature.

Now let's get more realistic with the water. Allow it to condense as required by the law of water vapor saturation (but don't make clouds yet). Evaporation and condensation also inject an additional and continuing flow of heat into the air equivalent to about 22% of the total incoming solar radiation.

Wet air with heat injected by evaporation-condensation cycle: T(surface) = 304 oK = 31 oC = 89 oF.

Notice how hot the climate would be, not to mention humid. There are no clouds yet to block out the Sun, cool things off, and lower the evaporation rate. So let's add clouds, but not real ones. Instead, just add ultrathin clouds that reflect, but do nothing else - no absorption or re-emission of radiation and no internal convection. We'll add the cloud cover that our real Earth has.*

Wet air, evaporation, condensation, and clouds that only reflect: T(surface) = 269 oK = -4 oC = 25 oF. The clouds themselves have temperature T(clouds) = 226 oK = -47 oC = -53 oF. Brrr! Now it's pretty cold at the surface. Why isn't the Earth this cold? It's not because of convection. If we add that, the cloud temperature changes, but not the surface temperature.

Add clear air convection: T(surface) = 269 oK as before. But now T(clouds) = 247 oK = -26 oC = -15 oF.

Finally, add the last missing element: realistic clouds, with real thickness, internal convection, and above all, capable of absorbing and re-emitting radiation in their own right. Real clouds are as important radiators as the surface itself.

Add real clouds: T(surface) = 288 oK = 15 oC = 59 oF. Up in the sky, T(cloud bottoms) = 275 oK = 2 oC = 36 oF and T(cloud tops) = 250 oK = -23 oC = -9 oF. This is climate as we know it.

Here's another purely thought-experiment way of slicing up the climate. Imagine we had started with clouds that only reflect and only solar radiation as energy input flow, with no evaporation. This is obviously not realistic, but it forms as important, often-quoted, and sometimes misleading baseline to gauge the overall effect of the "damp and shiny-on-the-outside cloudy blanket-steambath." In that case, we would have: T(surface) = 250 oK = -23 oC = -9 oF, as well as T(clouds) = 210 oK = -63 oC = -81 oF. Again - brrr!

But now add evaporation and recover: T(surface) = 269 oK = -4 oC = 25 oF and T(clouds) = 226 oK = -47 oC = -53 oF. Finally, add real clouds again and recover the real climate: T(surface) = 288 oK = 15 oC = 59 oF, with T(cloud bottoms) = 275 oK = 2 oC = 36 oF and T(cloud tops) = 250 oK = -23 oC = -9 oF.

The actual surface temperature is 288 oK. The temperature enhancement due to water in the lower atmosphere is often quoted as this +38 oK. Of that total, +20 oK is due to evaporation, and +18 oK is due to having real clouds (as opposed to the fake, ultrathin but shiny clouds).

Why do climatologists and meteorologists think of the lower atmosphere in this way? It isolates temperature enhancements due to everything except the incoming solar radiation. By drawing up the heat flow "budget" in this way, we can see the enhancement of temperature by the rerouting and augmentation of heat flows in the lower atmosphere.

One striking result emerges from this approach: the actual cloudtop temperature is what the surface temperature would have been in this imaginary scenario. And the imaginary cloud temperature is close to the actual temperature at the tropopause, something to be explored in an upcoming posting. It's almost as if the imaginary climate constructed here is one in which "the sky has fallen to the ground." The polar regions during polar winter are as close to this scenario as can actually be achieved on our planet: almost no clouds, and virtually no convection.

But there's also a price for looking at climate this way: it's physically unreal. There are no clouds with zero thickness that reflect but don't absorb or radiate. And there are no clouds without evaporation of surface liquid water to support them. If we're thinking about how the climate might change with modification, addition, or subtraction of its components (air, water, radiation) or heat transport mechanisms (radiation, evaporation, convection), we have to take into account all the consequences of any hypothetical change. Failure to do this leads to faulty reasoning and wrong conclusions. This imaginary 250-oK climate is a mathematical fiction designed to isolate the effect of certain modifications of heat flow. No real climate could look like this.**

Of course, it's hard to trace out the consequences of real or imagined changes to basic climate inputs. For the purely radiative part, it isn't impossible. For the evaporative part, it's harder; and for convection, essentially impossible, at least to the accuracy needed for weather forecasting. This has serious consequences for attempts at long-term prediction - or for claims to have already made such predictions.
* Mean cloudiness is 0.54.

** Of the hypothetical alternative climates listed here, only one has any chance of being close to realizable: the no-cloud, evaporation-only climate with T(surface) = 304 oK = 31 oC = 89 oF. And a strange world it would be: mostly ice-free, hot, humid, but with few clouds - it would rain frequently in mini-showers, so clouds wouldn't persist. But wait - the Earth's climate not so long ago was sort of like that. We'll have reason to return to this point later.



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