Pressure levels in warm & cold air
 

In Jeremy Pratts Navigation & Meteorology, on page met25 its states that

"In warm air, any given pressure level is higher than it is in cold air."

Given that the pressure is caused by the weight of the air above, and that cold air is denser and therefore heavier than warm air, surely any given pressure level will be lower in warm air?

Am I missing something here?

Yes. Warm air expands. Think of a column of air. There will be a certain height gain for each drop in pressure. In ISA that is 27/hPa. In other words, as you gain height in that column of air there will be a pressure reduction of 1hPA for each 27' of height gained. An altimeter isn't really measuring height (in feet). It's measuring pressure and then using that 27'/hPa relationship to show an equivalent number of feet.

If that column of air is warmed then it will expand. Now the number of feet gained for each 1 hPa reduction in pressure will be greater. An altimeter that read a certain height in the cooler air mass will now be physically higher when reading the same height in this warmer air mass. Remember, the altimeter is calibrated for a certain ratio of feet/hPa and is only accurate when the air mass it's in conforms to that assumed ratio. Warm the air mass and the actual ratio might be 30'/hPa - but the altimeter is still using 27'/hPa, so it will show a lower height than the true distance above the surface.

A good analogy is a long elastic, marked with feet along its length. At some level of stretch it will be accurate. Stretch it a bit and you will be further from the start for any given reading. Let it shrink a bit and you will be closer.

Very good explanation given by Tinstaafl. I'd never thought of the "long elastic" analogy. In my dim and distant youth as a military trainee pilot, we were given these aphorisms for use when thinking of altimeters and how accurate they might be.


"From warm to cold, don't be bold" to cater for the temperature effect described by Tinstaafl.


"From high to low, careful go" to warn of reduction in actual altitude when flying towards a region of lower pressure without adjusting your altimeter's subscale.

Thanks for the replies, would I be right in thinking that what is missing from

"In warm air, any given pressure level is higher than it is in cold air." is the word "indicated".

i.e. In warm air, the indicated altitude at any given pressure level is higher than it is in cold air?

No, you are talking about pressure levels, indicated altitude is the same at any one pressure level and so if you are at say the 900mb pressure level it will allways indicate the same indicated altitude (~3,400' with 1013 set)because what it is measuring IS the pressure so it is measuring the 900mb, what will change is your ACTUAL elevation.

OK let me try to explain why I am confused. Take 2 columns of air, lets say 100,000ft high.
One is warm and one is cold. At a point 5,000 foot from the surface, one column has 95,000 feet of cold, dense and heavy air above it and the other has 95,000 feet of warm, less dense and lighter air above it. At this 5000 foot point, the pressure will be higher in the cold air. The point at which the same amount of warm air would produce the same pressure must be lower right?? Where am I going wrong??

Firstly in your fixed column height example your ground level pressures wouldn't be the same ( h times rho times g etc, where g and h are fixed but rho varies with temperature), so your 5000 foot comparison isn't valid.

Even so stick with the basics of your model because it might help, keeping the top i.e . Zero pressure level of your cold column at 100,000 feet but allowing the top of the hot one to move. If we now actually magically ensure that ground level pressure is the same under the two columns and we know (by definition) that the cold column tops out at zero pressure at 100,000 feet, how high up relatively, will the top (zero pressure level) of the hot column be?

Finally I get it! In the book there is an illustration alongside the statement "In warm air, any given pressure level is higher than it is in cold air." it shows the pressure at each column base as 1000mb. Somewhat confusing.
Thanks for clearing this up

Yep, I'd agree that the initial statement in isolation needed a qualification somehow/somewhere about "base" pressure.

Glad it got sorted out.