Thursday, December 30, 2010

Surface Cooling, Part IV

In our previous post, we concluded that air above the desert cools down by 10°C in the first hour after sunset because cold air descends slowly from above as the day's convection cycle comes to a stop. This explanation is not one of the several you will find on the web if you search for "Why does the desert get so cold at night?" These other explanations talk about dry air allowing heat to radiate away into space. But our calculations in Day and Night showed that the rate at which the Earth and its atmosphere radiate heat is barely adequate to cool the air by half a degree in ten hours, let alone ten degrees in one hour.

One of our readers points us to another night-time cooling phenomenon called "night inversion". According to this description, the air immediately above a forest can be 10°C cooler at night than the air 100 m up. In our explanation of the desert cooling, the cold air above the desert was still warmer than the air higher up, but in this case, the air above the forest is actually colder than the air higher up. We will conclude our Surface Cooling series by offering an explanation for nigh inversion also.

The first 100 m of the atmosphere has heat capacity 100 kJ/K/m2. The forest is a good black body, so it will radiate of order 100 W/m2 directly into space through a clear night sky. A leaf, being roughly 1 mm thick, and consisting mostly of water, has heat capacity roughly 4 kJ/K/m2. When it radiates 100 W/m2 it will tend to cool by more than 1°C every minute. It is the heat capacity of the air around it that will stop the leaf from freezing.

The forest leaves will set up a convection cycle in which air is cooled by the upper leaves, which are the ones radiating into space, and warmed by the surface of the Earth below. The air immediately above the forest will be sucked into this cycle, and the air immediately above that also, so that the very cold air of the tree-tops mixes slowly with the air ten to a hundred meters up, creating a layer of air that is colder and more dense than the air above. The convection cycle transports roughly 100 W/m2. Suppose that the mixing we describe causes 30 W/m2 to be removed from the heat capacity of the first 100 m of air. In that case, the average temperature of the first 100 m will drop by 5°C in six hours.

So we see that radiation by leaves held ten or twenty meters above the ground can cause the first hundred meters of the atmosphere to cool by several degrees compared to the air above, and so create a static, cold layer of air above the forest. If there is any wind, of course, the leaves will no longer need their convection cycle to keep them warm: the wind will warm them, and blow away any cold air as well. The night must be still for such inversion to take place, and air is more often still in a bowl or valley.

Our Surface Cooling posts have introduced us to the heat capacity of the atmosphere, and shown us that traditional explanations for cooling and warming may be unreliable. But we have no proof that it is an exchange of warm air for cold air that causes the sudden drop in temperature at sunset in the desert. Nor do we have any proof that a cold convection cycle in a forest causes night inversion. Both explanations are merely hypotheses. Any help devising experiments to test either hypothesis would be much appreciated. Our ideas so far, which involve helium balloons and battery-powered thermometers, appear impractical, not to mention expensive.

1. Dear Kevan,
I think the answer could be found in the Hadley and Ferrel circulation cells that cause the sink of tropopause cold air toward the ground in the predominantly desert subtropical regions and in daily cycle of Atmospheric Boundary Layer.
In daytime the rising warm convective air flow contrasts the down welling flow of both two cells and blocks it at an altitude not too high that results by momentum equilibrium of two flows and varies according the radiation absorbed by sand. That’s, the surface acts as a heat-driven fan causing an upward flow.
In the afternoon the altitude of equilibrium drops and the ABL thickness becomes very thin. After sunset, when the ground becomes cooler than air by radiation, the heat-driven fan reverses its working and sucks downward the air. The ABL is so quite immediately squeezed away both by the down welling flow of Hadley - Ferrel circulation cells and by the surface and the cool down welling air of circulating cells soon arrives at ground.
I have the feeling it works well. Isn’t it?
Michele

2. Dear Michele,

I think I follow your argument, but I don't see how the the cold sand can suck air downwards because the fans you are talking about, if I understand them correctly, operate by warm air rising and cold air sinking. So air cooled by the sand will tend to stay where it is, not rise. Am I missing something?

Yours, Kevan

3. Dear Kevan,
I mean what occurs in the stairwell of a building.
In the winter the cooler external air enter at the bottom and puts away the internal warmer air that exits at the top.
In the summer the internal cooler air comes out in the open at the bottom sucking the external warmer air at the top and setting a down welling flow.
Both the flows are driven by heat.
Michele

4. Dear Michele, In the case of the stairwell, we have an inclined air passage made of a solid material that is warmer (in winter) or cooler (in summer). What is the air passage is there to create such a fan in the atmosphere? Yours, Kevan

5. Dear Kevan,
The fan is the surface. If it cools, also the closest layer of air cools becoming heavier and pushing the air sideways and so setting an horizontal radial flow. The mass continuity requires an analogous quantity of air enter from another way that can be only from above. The cool surface causes a local high pressure that produces a down welling air flow also in the free atmosphere. The working is that of a centrifugal fan impeller rotating around a vertical axis with gas inlet above and radial gas outlet.
Michele

6. I am getting stuck on your second sentence. When you say the heavier air pushes lighter air sideways. When air cools by 10% in absolute temperature, it becomes 10% heavier because it contracts by 10%. It occupies less space. I don't see how a flat surface can cause convection by cooling from below. It seems to me that the cooling must always take place at a higher point, so that the cold air can sink towards a warmer point.

7. Let’s assume one cube of air on the ground at temperature lower than surrounding and so heavier. This air cannot sink because it is on the ground but it spreads out horizontally over the surface because there’s an horizontal gradient in its concentration that produces the horizontal motion of cooler air towards the surrounding regions. Globally, according to continuity, there is an outgoing flow across the four lateral faces and one incoming flow across the top face. It’s another form of convection but always a convection that could be named “advection”.
This motion will continue while the cool surface will be able to create an horizontal gradient of temperature in the lowest layer of atmosphere.
Michele

8. Dear Michele,

I think I'm beginning to understand.

What you describe sounds similar to what I see when I put a beaker of liquid nitrogen on a table. Air cools over the liquid nitrogen, slides down the sides of the beaker, and spreads across the table. I can see the spreading, cold air because it is white with condensed water vapor.

If we had a cold region on a flat surface, I can now see how this cold region would cause a slow, lateral flow of air in all directions. Thus a few hundred trees clustered in the middle of a field might, by the cooling of their upper leaves at night, cause cold air to spread out across the field, the field being warmer by virtue of its clay soil.

Is this what you mean to say? Thank you for your continued patience.

Yours, Kevan

9. A trivial point: "advection" is the transport of something by a moving fluid. So the fog in my nitrogen-cooled air was traveling by advection, but the air itself is traveling by... I don't know, I guess you're right to have called it convection in the first place. Kevan

10. Kevan,
You have perfectly centered my thought.
Really, “advection” is the transfer of a property of the atmosphere, such as heat, cold, or humidity, by the horizontal movement of an air mass. That’s an horizontal convection due to an heat-activated gradient of pressure.
Is it less or more effective than buoyancy? I think the motion of cooled molecules will wholly traced putting your “beaker of liquid nitrogen” high over the table.
Michele