# What is meant by 'Earth's surface temperature'?

• Graeme M
In summary,Satellite measurements of Earth's temperature have only been in place since the 1970s. The figure of -18 °C is what you get when you consider the amount of solar radiation hitting the Earth, and consider the Earth to be an imperfect black body (reflection of 30%). At equilibrium, you then get a temperature of 255 K. The fact that this is obviously not what is observed means that there is an additional source of heat, which happens to be the atmosphere trapping radiation that is sent back to the ground, making the temperature higher.
DrClaude said:
Compressing a gas heats it, but a gas under pressure (whatever that means, as a gas always has a pressure) does not produce heat.

DrClaude, is that the case in an atmosphere? A gas in a gravitational field is attracted by gravity. In the case of the Earth's atmosphere, this would increase the density of the gasses closer to the ground and hence the pressure wouldn't it. As gravity is the agent for that process, wouldn't the atmosphere be constantly in a state of compression? Even though the air may be free to move and for high and low pressure regions to form, on average the air is being compressed by the air higher in the atmosphere.

Graeme M said:
DrClaude, is that the case in an atmosphere? A gas in a gravitational field is attracted by gravity. In the case of the Earth's atmosphere, this would increase the density of the gasses closer to the ground and hence the pressure wouldn't it. As gravity is the agent for that process, wouldn't the atmosphere be constantly in a state of compression? Even though the air may be free to move and for high and low pressure regions to form, on average the air is being compressed by the air higher in the atmosphere.
That is entirely consistent with what DrClaude wrote. In a static atmosphere, the lower levels are at a higher pressure, but that in itself does not imply a higher temperature. Any difference in temperature will lead to conduction, if not convection. To maintain a difference in temperature requires a heat source and a heat sink.

I don't see how you can use the ideal gas law to obtain any information about what temperature the atmosphere/surface of the Earth should be. As haruspex mentioned, the atmosphere will adjust to the conditions imposed, and any calculation will only confirm that the law works. In other words, you have to be weary of circular arguments: using the current conditions in the atmosphere to show that the atmosphere should be hotter than the simple blackbody model simply shows that the Earth is hotter than the simple blackbody model. It doesn't say anything as to what is the source of that temperature difference.

Graeme M said:
As gravity is the agent for that process, wouldn't the atmosphere be constantly in a state of compression?
It is constantly under pressure, but not under additional compression. If you close a container with some amount of gas in it, and put it in space, you constantly have pressure in the gas. Do you expect it to heat up?

mfb said:
If you take tens of thousands of temperature values, your estimate for the average gets very precise.
Sorry, that is not true. If you were talking about "tens of thousands" measurements of the same thing, it would have been true. What we are talking about is temperature, it varies both in time and in space. An example: Taking hundreds of temperature measurements across Africa does not say very much about the temperature in Copenhagen. Another: Having access to temperatures all across the globe one day, does not say very much about the temperature in New York three months later.

mfb said:
It is constantly under pressure, but not under additional compression. If you close a container with some amount of gas in it, and put it in space, you constantly have pressure in the gas. Do you expect it to heat up?

No, but the pressure in the container in space is primarily due to its density and temperature, there is no gravity. On earth, gravity is doing work by trying to pull all of the atmosphere to the surface. The pressure at the surface is due to the density which is caused by gravity.

I'm not disagreeing, just idly wondering whether the effect of gravity is to impose a compressing force and hence add some heat to the atmosphere. Without having a clue, I am for example wondering whether that means a region that undergoes a change from low pressure to high pressure due to weather system movements also undergoes some compressive heating.

Graeme M said:
wondering whether the effect of gravity is to impose a compressing force and hence add some heat to the atmosphere.
Yes, it imposes a compressive force, but no, it adds no heat. This is because the force does no work. For the force to do work, the mean height (by mass) of the atmosphere would have to descend, increasing the compression. Were this to happen for some reason (e.g. increased Earth mass), there would be a warming, but it would not last. As the atmosphere settles at its new height, the excess heat would dissipate.

Graeme M said:
No, but the pressure in the container in space is primarily due to its density and temperature, there is no gravity. On earth, gravity is doing work by trying to pull all of the atmosphere to the surface. The pressure at the surface is due to the density which is caused by gravity.
Pressure does not have a tag "is related to gravity". A small volume of gas feels pressure because it constantly gets hit from particles outside.

Graeme M said:
I'm not disagreeing, just idly wondering whether the effect of gravity is to impose a compressing force and hence add some heat to the atmosphere.
No.
If you would start with a low-density cloud in space and let it fall onto earth, then yes, this cloud would heat up. But that is a one-time process that happened 5 billion years ago (and the rocky equivalent of it made the early Earth very hot).
Graeme M said:
whether that means a region that undergoes a change from low pressure to high pressure due to weather system movements also undergoes some compressive heating.
A tiny bit (if compression comes from wind for example), but in the same way you get cooling from the opposite direction.

Svein said:
Sorry, that is not true. If you were talking about "tens of thousands" measurements of the same thing, it would have been true. What we are talking about is temperature, it varies both in time and in space.

That doesn't mean mfb's statement about the statistics is not true. Statistics is just statistics; the error estimate for an average based on the number of samples is a particular formula, you calculate what it says and that's it.

If you want to argue about what that calculated average and its error estimate mean, in terms of predicting future temperatures, that's a separate question; but it's not a question about statistics, it's a question about models and predictions. It doesn't change the fact that applying particular statistical formulas to a set of measurements gives particular results, which is what mfb has been talking about.

Graeme M said:
The pressure at the surface is due to the density which is caused by gravity.

More precisely, gravity is one of the causal factors that contributes to the pressure at the Earth's surface. But it's not the only one. To see why, just look at the ideal gas law: there is not a single possible solution for pressure equal to 1 atmosphere, there is a continuous range of solutions corresponding to different combinations of density and temperature. The presence of gravity doesn't change that: gravity relates the gradient of pressure at the surface to the density, but that still leaves the boundary condition, the pressure at the surface, as a free parameter. To pick out the unique solution that describes the actual Earth's atmosphere, you need to look at more than just gravity.

PeterDonis said:
More precisely, gravity is one of the causal factors that contributes to the pressure at the Earth's surface. But it's not the only one. To see why, just look at the ideal gas law: there is not a single possible solution for pressure equal to 1 atmosphere, there is a continuous range of solutions corresponding to different combinations of density and temperature. The presence of gravity doesn't change that: gravity relates the gradient of pressure at the surface to the density, but that still leaves the boundary condition, the pressure at the surface, as a free parameter. To pick out the unique solution that describes the actual Earth's atmosphere, you need to look at more than just gravity.
Hmm... but it's not a fixed volume, so I'm not sure your appeal to the gas laws works.
The atmosphere is pretty thin beyond a few tens of km, so you can take g as constant. That means there is a known weight spread over a known area. The local pressure varies, because of convection, but the average is fairly steady. Of course, the moisture content can vary a bit, which does affect the total weight.

haruspex said:
it's not a fixed volume, so I'm not sure your appeal to the gas laws works.

The gas law can be written to relate density, pressure, and temperature in the neighborhood of any point you choose; you don't need a fixed volume.

haruspex said:
there is a known weight spread over a known area

If all you're talking about is the average pressure, then yes, I agree, this constrains it to pretty narrow limits. But as you note, local pressure can vary.

Also, density and temperature can vary even if the pressure is held constant, and your original statement that I responded to was that the pressure at the surface was caused by density. If you had said the pressure at the surface was caused by the total weight of the atmosphere, I wouldn't have objected to that--though I might have pointed out that this by itself doesn't constrain the density or temperature. After all, the point of this discussion is to identify the causal factors that affect surface temperature, not pressure. Holding the pressure fixed does not fix the surface temperature; it can still vary, because the density can vary.

PeterDonis said:
The gas law can be written to relate density, pressure, and temperature in the neighborhood of any point you choose; you don't need a fixed volume.
Sure, but I meant the way you appeared to be using the gas laws to draw an inference. However, your argument was a bit vague, so I may have inferred too much.
PeterDonis said:
your original statement that I responded to was that the pressure at the surface was caused by density.
Not my statement, and not one I would support. My post was triggered largely by this:
PeterDonis said:
To pick out the unique solution that describes the actual Earth's atmosphere, you need to look at more than just gravity.
My point is that atmospheric mass, Earth surface area, and gravity do combine to determine mean surface pressure. Temperature and density can vary much more.

haruspex said:
Not my statement

Oops, you're right, it was Graeme M's. Sorry for the mixup.

PeterDonis said:
That doesn't mean mfb's statement about the statistics is not true. Statistics is just statistics; the error estimate for an average based on the number of samples is a particular formula, you calculate what it says and that's it.
Well, as a famous author said: "There are lies, damn lies and statistics".

Svein said:
as a famous author said: "There are lies, damn lies and statistics".

That doesn't mean all statistics are lies. Nor does it mean that statistics is invalid.

PeterDonis said:
That doesn't mean all statistics are lies. Nor does it mean that statistics is invalid.
No, but it is a warning. Using statistics as a "sausage machine" (putting numbers into a formula and blindly accepting whatever comes out), is what gives statistics a bad name.

To be very concrete: Most statistics theorems are valid only under very specific circumstances. Those are spelled out in the proofs. Unfortunately, people have a tendency to skip verifying that.

I could refer horrible misuse of statistics tools - most often the linear regression, where some "researchers" run various sets of numbers through that "machine", get a correlation with an r2 of 0.1 and then announce a causal connection.

Svein said:
Using statistics as a "sausage machine" (putting numbers into a formula and blindly accepting whatever comes out), is what gives statistics a bad name.

I agree with this as a general statement, but I don't see an instance of it in this thread. Nobody has been claiming that knowing the past history of global average temperature let's you make accurate predictions about local temperatures at a particular place.

PeterDonis said:
Nobody has been claiming that knowing the past history of global average temperature let's you make accurate predictions about local temperatures at a particular place.
As long as that remains true, I am satisfied.

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