Tuesday, May 15, 2007

Adjusting the thermostat

I've been working with heat flows and not temperatures mainly, because energy is conserved: I can add and subtract power flows and even create an "energy flow" or "heat budget." I can't do that with temperatures. Contrary to the nonsense of averaging temperatures over space, temperature is not a simple proxy for heat content or heat flow.

All of the discussion during the "climate weeks" on this blog has been based on a reconstructed heat budget for the Earth's atmosphere. Alternative climates have involved at most switching various heat sources and flows on and off.* Cause-and-effect (dynamical) explanations have not entered the picture, except in a limited way. For this and the next posting, this restriction will be relaxed somewhat. In this posting, causal mechanisms will be examined in a qualitative way, without numerical details. The underlying question is, what happens if different mechanisms are modified, either alone or in combination? It's impossible to give a general answer, but the questions can be broken down into more tractable pieces. In some cases, fairly exact answers are possible; in others, decent estimates; and finally, in yet others, only vague guesses - plausible hand-waving. Even this is progress, because it isolates the sources of uncertainty.

Generating and redistributing heat: Summary. There are only two sources of atmospheric heat: incoming solar radiation and the extra latent heat of water liberated by the evaporation-condensation cycle (which itself is catalyzed by the incoming solar radiation). Adding heat to the lower atmosphere requires either reducing cloud cover or accelerating the evaporation-condensation cycle. The other mechanisms mentioned over the months (adding clouds, steepening the lapse rate by enhancing convection or radiative transport) redistribute the heat flow, circulating it in the lower atmosphere or accelerating its departure. Consider each in turn.

Accelerating the evaporation-condensation cycle, while changing nothing else. Accelerating this cycle releases more latent heat from water and definitely raises atmospheric temperatures.

Adding clouds, while changing nothing else. Adding clouds - and making no changes in the hydrologic cycle and neglecting convection - definitely reduces atmospheric temperatures. The clouds at their tops reflect more solar radiation back into space than they absorb and re-emit below.

Accelerating radiative heat transport, while changing nothing else means raising the rad term and steepening the lapse rate. At first sight, it might seem that this should lower the temperatures, but it actually raises them. The reason has to do with where the temperature slope is anchored (the boundary condition). For radiation, the anchoring point is the top of the atmosphere. Only radiation gets out into space, and the total radiative power flow out has to equal what went in (what wasn't reflected from the cloudtops to start with) plus the injection of net heat from the water cycle. Follow a steeper temperature slope from the edge of space down, and you end up with a higher temperature at the surface, and an elevated temperature profile the whole way.

Enhancing convection, while changing nothing else, OTOH, accelerates the departure of heat from the lower atmosphere and lowers the temperatures. The difference between radiative and convective heat transport here stems from the fact that convection has to be anchored (have its boundary condition) at the surface, because the heating that drives it comes from below.

Turbulence is the wildcard. Convection is a form of heat transport. But it looks different from the point of view of fluid mechanics. There it's just a special case of fluid currents. If it's slow and not turbulent, convection can be understood theoretically in a complete way. But generally the flow is moderately to extremely fast - then convection overlaps with turbulence. Turbulence becomes more important if the fluid viscosity is smaller, and viscosity is much smaller in gases than in liquids. Convection in our atmosphere is moderately turbulent - not that fast in terms of speed (a tenth of a meter per second).** The approximate "mixing length" model used to represent convection (like a waterwheel, except it's air parcels that lift up and deposit heat before coming back down) is a decent approximation for convection in clouds. For the inefficient convection in clear air, the model shouldn't be taken as anything more than suggestive. There is no general theoretical solution for fluid turbulence; various approximation schemes, starting with the "mixing length" picture and moving on to more sophisticated cousins of same, are commonly used to fill this gap.

Conditions for convection. For convection to happen at all, the Schwarzschild criterion must be satisfied, meaning that it "pays," thermodynamically speaking, to move heat in an organized motion from higher to lower temperature; the entropy gained thereby is larger than the entropy lost in organizing the flow, and everything's copacetic with the Second Law. In a continuous atmosphere, the Schwarzschild criterion requires that the vertical temperature profile be steeper than a certain critical steepness: the temperature has to fall faster with altitude than it would if the atmosphere were perfectly adiabatic (no heat flow). When the slope (dT/dz) is more than that steep, an overheated air parcel feels an upward bouyancy force. The actual criterion is a little tougher: the slope has to be more negative than the adiabatic lapse rate by some amount related to the viscosity of air. Viscosity holds the overheated parcel down when it rubs past the surrounding air. The bouyancy force has to not only be positive, it has to reach a critical value above zero to overcome viscosity. These criteria are just the minimum to get convection going. Once it's going, it can be slow or wildly turbulent, largely depending on the viscosity and the size of the heat flow to be transported.

Efficiency of convection. There's no guarantee that, once it starts, convection has to be an efficient trasporter of heat. The efficiency is a direct result of whether or not the parcel loses much of its extra heat before it travels one mixing length and loses its identity. Convection in clear air is inefficient, because the overheated parcel radiates its excess heat quickly in the relatively transparent surroundings. (The surroundings have free water vapor and are partly opaque to infrared (IR) radiation - but only mildly.) Convection in clouds is a little faster and a whole lot more efficient: the parcel doesn't radiate much heat when surrounded by IR-opaque clouds.

Combined changes of evaporation and clouds. While it might sound perverse, accelerating this cycle has nothing to do with making more clouds, at least not directly. The whole cycle is meant here, evaporation followed by condensation - which can make a lot of rain, or just stay up there as clouds.

Combined changes of convection and clouds. Clear-air convection without clouds cools things off and lowers temperatures. With clouds, it does raise the temperature of the cloud bottoms. But within the clouds, it also reroutes heat up to the cloudtops, where it radiates away into space. On the whole, enhanced convection, with or without (realistic) clouds, lowers the temperatures.

Combined changes of evaporation and convection. Near the Earth's surface, where liquid water is evaporating, the water has to absorb the heat of vaporization from somewhere to change to a gas. While some of the heat comes from direct solar radiation - and that's enough to evaporate small puddles - the heat needed to evaporate large bodies of water comes from the air right above the surface, the inversion layer. Enhanced convection above the inversion layer undercuts the evaporative heat flow downward, slows evaporation, and lowers the heat flow from the hydrologic cycle.
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* In physics language, the analysis so far has been kinematic (descriptive), not dynamical (causal).

** It's important to again distinguish convection (here restricted to mean a type of heat transport) from general fluid flow. General updraft speeds in the atmosphere are about a meter per second, larger - sometimes much larger - in clouds, but the updraft speeds actually cover a large range of speeds. One small part (and not even a representative part) of that speed range convects heat.

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