Understanding the hot shallow layer above the earth surface

[Ardit]

In Wikipedia page of Diurnal Temperature variation, there is a statement as following: "As solar energy strikes the earth’s surface each morning, a shallow (1–3 cm) layer of air directly above the ground is heated by conduction. Heat exchange between this shallow layer of warm air and the cooler air above is very inefficient. On a warm summer’s day, for example, air temperatures may vary by 30°F from just above the ground to waist height."

First of all, do you believe it? And if you do, how comes that there is such a discrete temperature separation (a difference of up to 30°F) of these two layers (the 3 cm one and the one above it)?

[Spyman]

Air is a very good insulator, it doesn't seem improbable with a temperature difference of around 1.1° Celsius (30°F) separated by a waist height.

[Ophiolite]

Spyman - how have you managed to convert a 30°F temperature difference to a mere 1.1° Celsius?

 

The answer appears to be that you have decided, for some bizarre and foolish reason, to subtract 30 from 32, the latter being the freezing point of water under standard conditions. For the record, a 30°F difference equates to a 16.6..° C difference.

 

Ardit, I see no particular reason to doubt the wikipedia data, though I should like to view the original research the comment is based upon. (Unfortunately wikipedi seems to be down at present.) You have already given us the explanation of why this is the case: "Heat exchange between this shallow layer of warm air and the cooler air above is very inefficient."

[Spyman]

Spyman - how have you managed to convert a 30°F temperature difference to a mere 1.1° Celsius?

 

The answer appears to be that you have decided, for some bizarre and foolish reason, to subtract 30 from 32, the latter being the freezing point of water under standard conditions. For the record, a 30°F difference equates to a 16.6..° C difference.

Yes, ~16.7°C represents a 30°F temperature difference and -1.1°C represents an actual temperature of 30°F.

 

 

I may have misinterpreted the text in the Wikipedia article, but I still think it is phrased a little vague and that the author could have meant to make a statement that the waist temperature can be 1.1°C colder than the ground layer instead of a temperature difference between them of 16.7°C.

 

I think that a difference of 16.7°C should cause the hotter air to raise and destroy any insulation borders, even if the sunlight would be strong enough to maintain that difference between the ground and waist level the temperature at the waist would raise fast, making the other statements of shallow layers and inefficient heat exchange somewhat incorrect or at least ruining the reasoning in the text.

 

However, in my house where air is trapped and not entirely able to flow freely, it is normal with an difference of around 2-4°C between the floor and the ceiling, so a difference of 1.1°C between the feet and the waist when the ground is heated by sunlight therefore seems probable even outdoors.

 

 

I admit that I am not an expert, neither on the English language nor on air temperatures and heat exchange, so I could very well be wrong on both the interpretation of the text and the possibility of shallow heat layers with temperature differences of 16.7°C caused by sunlight.

 

But I certainly do not agree that my above reasoning is "bizarre and foolish", which makes me wonder why you express yourself with such rude manners?

[CaptainPanic]

We are talking about a temperature difference, so the different zero degree reference points of the scales of F and C are irrelevant. You just divide by 9/5 to arrive at 16.7°C or Kelvin .

 

Btw, I believe this is just a case of the boundary layer theory of heat transfer phenomena.

If you have a cup of hot coffee (or a glass of cold beer), there is a layer of air immediately around that cup which has the temperature of the cup, not the air. And then there is a gradient which approaches the air temperature as you get further away from that cup.

 

Such a boundary layer is typically very thin, but on the ground, which is not very smooth, this layer can be thicker - either because there are some stones or some grass to prevent mixing of the air. According to the wikipedia article, this layer is 1-3 cm thick. I call b***shit, and say that the variation in that layer thickness is a lot more. On smooth surfaces, like stone or a road surface, this will be less. And on very rough surfaces, like a grassfield, it may be more. (Also, it can be debated where we start measuring).

 

What really matters is how strong the natural convection is, which is caused by temperature differences. This natural convection will effectively limit the thickness of that boundary layer.

 

The reason that the heat transfer between this boundary layer and the rest of the air is so poor is because it is mostly stagnant. It doesn't move. Higher above the ground, air moves more, and therefore mixes better, which massively increases the heat transfer.

 

It is also no surprise to me that this temperature difference of 16.6°C is mentioned. I think that in certain cases it can be even more, when you have a nice dark smooth surface. There are cases reported of people frying some eggs on a hot surface which was heated only by the sun. That requires at least 100°C. Since desert air temperatures rarely exceed 50°C, that implies a temperature difference of 50°C (three times more than in the wikipedia article)!

 

p.s. Spyman, don't think that anyone tried to be rude. Ophiolite, even though it was probably unintentional, your comment was interpreted as rude. Apologies will instantaneously fix everything.

[Spyman]

Very good explanation CaptainPanic +1.

[Ophiolite]

But I certainly do not agree that my above reasoning is "bizarre and foolish", which makes me wonder why you express yourself with such rude manners?

It was not my intention to be rude. For that I apologise. However, my opinion remains that thinking the temperatures were absolutes rather than relatives was bizarre and foolish. Bizarre because it runs counter to your normal well constructed posts and foolish because it gives you a completely wrong answer.

[alpha2cen]

In Wikipedia page of Diurnal Temperature variation, there is a statement as following: "As solar energy strikes the earth's surface each morning, a shallow (1–3 cm) layer of air directly above the ground is heated by conduction. Heat exchange between this shallow layer of warm air and the cooler air above is very inefficient. On a warm summer's day, for example, air temperatures may vary by 30°F from just above the ground to waist height."

First of all, do you believe it? And if you do, how comes that there is such a discrete temperature separation (a difference of up to 30°F) of these two layers (the 3 cm one and the one above it)?

 

[latex]buoyancy-potential=\Delta \rho Vg[/latex]

 

Assuming the temperature on the surface =26.6oC

 

[latex]\Delta \rho =\rho _{273+10}-\rho _{273+26.6}[/latex]

 

[latex]PV=\frac{W}{M}RT[/latex]

 

[latex]R=\frac{PM}{T\rho }[/latex]

 

[latex]\frac{P_{a}}{T_{a}\rho_{a} }=\frac{P_{b}}{T_{b}\rho_{b} }[/latex]

 

1; at surface, 2; at 3cm above

 

[latex]\rho _{1}=\frac{P_{1}T_{s}\rho _{s}}{P_{s}T_{1}}=\frac{(273K)(29\times 10^{-3}kg/22.4\times 10^{-3}m^{3})}{(273+10)K}[/latex]

 

[latex]\rho _{2}=\frac{P_{2}T_{s}\rho _{s}}{P_{s}T_{2}}=\frac{(273K)(29\times 10^{-3}kg/22.4\times 10^{-3}m^{3})}{(273+26.6)K}[/latex]

 

[latex]\Delta \rho =0.069kg/m^{3}[/latex]

 

[latex]F_{buoyancy}=\Delta \rho V g=(0.069kg/m^{3} )(1m^{2}\times 3\times 10^{-2}m)(9.8m/s^{2})(\frac{N}{kgm/s^{2}})[/latex]

 

[latex]=0.0203N[/latex]per surface m²

Edited November 23, 2012 by alpha2cen

[CaptainPanic]

alpha2cen, the assumption that the entire layer of 3 cm thickness has a 16.6°C temperature difference is completely wrong.

 

In addition, as shown in the link regarding Natural convection, the air will rise in specific spots, which causes hot air to flow along the surface to that spot where it rises. This can cause much larger forces...

 

I am afraid that the number you give is completely meaningless.

[Spyman]

It was not my intention to be rude. For that I apologise. However, my opinion remains that thinking the temperatures were absolutes rather than relatives was bizarre and foolish. Bizarre because it runs counter to your normal well constructed posts and foolish because it gives you a completely wrong answer.

Apology accepted and thanks for the nice compliment.

[overtone]

In addition, as shown in the link regarding Natural convection, the air will rise in specific spots, which causes hot air to flow along the surface to that spot where it rises.

Any lack of such compensating horizontal flow - resisted by some means, even simple viscosity within the air volume itself - will reduce this rise.

 

In thin layers (for various reasons) this horizontal flow can be (and often is) reduced to near zero. The air volume attempting to rise is then working against the pressure difference of a near vacuum "under" it. It is held in place as if glued there.

 

I have no trouble believing a 16C temp difference between the ground layer and free air at waist height. Most of that difference could even be in the first few centimeters.

 

People who study heat adaptation in insects noticed, years ago, that one common adaptation is simply long legs and greater height - a difference of less than a centimeter in a tiger beetle or desert ant on sand is significant, several degrees C.

[dirtyamerica]

There is a temperature gradient. It's the why weather stations' thermometers are placed at a standardized height of 4 or 5 feet off the ground.

[alpha2cen]

In this case uplifting is hard.

Upper blue air is cold and high density.

Density gradient exists, but stable layer, in the middle, blocks it's movement to the downward.

Edited December 4, 2012 by alpha2cen