Tuesday, November 10, 2009

Cold Temperature Correction

While nominally the aircraft altimeter measures altitude, what it really measures is air pressure, so the needle shows the pressure difference between the altimeter setting source and the aircraft. An altimeter setting source is just a station (usually an aerodrome) that gives out altimeter settings. When you call a station for their "altimeter setting" they tell you a number that instructs you how to set the altimeter to display station elevation at that station. If the air pressure where you are is the same as at the station, your altimeter will read station elevation. For every one inch of mercury ("inches of mercury" is a measure of atmospheric pressure) difference between the pressure at the altimeter setting source and at the airplane, the altimeter displays an altitude gain of one thousand feet.

If the air is at standard temperature, then a column of air a thousand feet deep exerts just enough pressure to equal one inch of mercury. But if the air is colder than standard, it's denser, so a column of a thousand feet of air actually weighs more. Or, equivalently, the column of air sufficient to produce a one inch of mercury change in pressure is less than a thousand feet thick. So an airplane with an altimeter that claims it has climbed a thousand feet over the aerodrome is actually less than a thousand feet over the aerodrome.

I've written about the above before, but yesterday I was in the position of simultaneously knowing the laser-measured, linear height above sea level of the cloud base (5536') and the altitude displayed on a correctly set altimeter at that altitude (5700'). Was the altimeter wrong? No, the altimeter was correctly displaying what the altimeter is legally required to display. This cold weather discrepancy is one that pilots are trained to be aware of, and to compensate for.

There are formulae for those who like that sort of thing, and also a table for those who would rather not have to work everything out from first principles. Neither way is convenient to do in situ, so you work out the corrections ahead of time and scrawl them on a photocopy of the the approach plate. I'm guessing that if you have modern avionics you can tell it the location and temperature of the altimeter setting source and it will work out and display all your new minima for you, right on the EFIS.

Imagine that for safety I was supposed to be at 5536' asl, perhaps because there was a hill on approach. In cold weather, I would want to know how high to fly by my altimeter in order to know that I was really that high. The elevation of the altimeter setting source is 2255' and it was -10 on the ground. So I go to the table in Figure 9.1. (You're welcome to use the formula instead. Let me know how that works out for you.) Minus ten is the second row. You can see that's really not all that cold by chart standards. It is, after all, only October. The height above the elevation of the altimeter setting source is 5536-2255=3281'. I think of that as 3000 + 200 + 81. The correction at -10 are:

3000': 290'
200': 20'
81': .4 x 20 = 8'
total: 318'

The example uses the 2000' correction to work out the per-foot correction, but if you look carefully at the -10 row, you'll see it's a 10% correction all the way to 2000, and that's close enough for me.

Three hundred eighteen feet is about double the correction I actually observed, and admittedly not what I was expecting when I started to blog this. Reflecting back I recall that there was a temperature inversion that day, so when we cruising at 8500' it was only zero outside. The table is very conservative, rounding up at every opportunity and assumes a decrease in temperature with altitude. So while it's not a very good example, it is real life. I was thinking of reworking the numbers to make it work out to match the table, but I'm too honest.

Cloud bases on a METAR are given as height above the aerodrome. That value may be measured with a laser ceilometer, reported with reference to the height of a nearby mountain, calculated based on the temperature-dewpoint spread, or transcribed from a PIREP. The METAR never indicates which of these methods has been used, but to properly estimate ones chances of seeing the field at minimums, the ceiling should be compared to the uncorrected minima for the first two case and to the cold-corrected minima for the second. That is, a pilot breaking through a ceiling measured at 5500' asl with a ceilometer could be indicating over 5800' at the relatively mild temperature of -10. With very cold temperatures and high minima, there would be a considerable discrepancy between accurately reported and pilot-observed ceilings. I wonder if Nav Canada has a policy about this, if the FSS applies a correction to PIREPs, or if the METAR/ATIS ceilings fluctuate between pilot reports and observations relative to mountain heights.


Chris said...

I really struggled with this topic in Navigation, maybe because training in Australia I have so little very cold weather experience? Maybe just because I am thick. The only thing I remember is that in cold weather the altimeter will over-read.

Aviatrix said...

A lot of people have trouble with cold weather altimetry. I believe the key is really understanding how the altimeter works. Don't even think of the altimeter displaying an altitude. Think of it as reacting to pressure changes. The pressure changes when you go up or down and when flying through a high or low pressure area. The amount the pressure changes with altitude is greater when it's cold and less when it's hot.

amulbunny's random thoughts said...

Math..... my head is exploding. I am glad you know what you're writing about. Now if you want the finer point of currency transaction in pre Revoluntion France, I'm your gal.

Aviatrix said...

Amulbunny, sounds like a great guest post.

Anonymous said...

From High to Low watch out below --

that's about all I know, whether it be pressure changes or temperature changes... I know it's more scientific than that, but it makes my head hurt.

And by the way. If anyone has built temperature corrections into altimetry in the new avionics, Airbus must not have known about it because I'm still having to make manual corrections when required.

jk said...

I'm trying to grasp this well because I'm working on my initial flight instructor certification.

That said, the basics: the height of a column of air at various temperatures, compared to standard, with that applied to what the altimeter is telling me makes perfect sense;

The correction table you cited (as well as other references I've seen) base a correction on the height of an airplane above the elevation in which the setting is made;

This implies that an altimeter setting isn't merely sea-level barometric pressure; its corrected for altitude. If you think about it one way to easily to this would be to take a known accurate altimeter on the ground, turn the adjustment mechanism until field elevation were displayed, and then read off the altimeter setting;

Here's what doesn't make sense: the table must make some assumptions about lapse rate. It cannot know whether an inversion exists, or whether the air is very unstable (meaning a high ambient lapse rate).

Consider this site's formula for calculating true altitude (http://williams.best.vwh.net/avform.htm#Altimetry). This, I think, would correct the issue I brought up above.

I'm not convinced that's all there is to it, though: What other factors or meteorological phenomena might be at play which would have a (significant) impact on true altitude calculation

Mario in PY said...

I do have a logic problem with your statement that "a column of air one thousand feet high equals one inch of mercury". Given that the standard air pressure is given at 29.92 inches of Hg, that would imply that every jet airliner flying above FL300 is essentially flying in a vacum or "outer space". And those who follow space flights know that NASA considers the top of the atmosphere for Entry Interface to be at 400,000 feet.

Maybe the equation of 1" Hg = 1000' air holds only for the first 2000 or so feet of altitude. Because as you go higher the air becomes less dense.

Cirrocumulus said...

The "thickness" of the layer of atmosphere between the levels where it's at two different pressures varies even close to the ground: it's a useful measure of the temperature of an airmass.
So the rule's true only to a first approximation, and it gets less accurate with altitude because air's compressible and mercury isn't. Above the tropopause things are different.
Are you in Pyrenees-orientales? Try working it out in modern units, it's easier!

A Squared said...

@ Mario:

Yes, the "1 inch Hg = 1000 ft" is an approximation that only holds true at lower altitudes.

Anonymous said...

Mario, you are absolutely right. If "one inch Hg = 1000 feet" were linear then in a standard pressure atmosphere air would end at 29,920 feet ASL. It doesn't, of course, since air compressability is non-linear.

The "rule" is reasonably accurate closer to the ground, and also happens to involve nice round numbers, and so is a useful quick references.

N6349C said...

A question for all: I read about the use of correction tables in Canada, in a US IFR publication. In the USA, does anyone know if the approach plate TERPS take the likely coldest temperature into account, when identifying intermediate legs or MDA's on non-precision approaches? Or if I find myself flying outside sunny TX in the USA (perhaps skiing in Colorado), do I need to go to Nav Canada and find yet another set of correction tables?

Sarah said...


The AIM, 7-2-3 has exactly the same altitude correction table.

I don't think MDA/DH includes the cold-wx temperature correction. The local altimeter setting would be 'exact' on the ground. The error with a 200' Height above the airport at -10C is 20', and I can't fly that precisely anyway.

For enroute in mountainous areas, you may want to add 500' or even 1000' to MOCA altitudes if it's really really cold.

Thanks for the lesson, Aviatrix. :) Still haven't taken the instrument written, this week for sure.

Aviatrix said...

N6349C, the Jeppesen plate for Whitehorse shows the same altitudes as the Nav Canada one, suggesting that Jeps also leave it to the pilot to adjust for temperature.

The Canadian AIM, like Sarah, suggests adding 1000' to MOCAs in the winter. Her point about the 200' agl minima is a good one: the US has ILSes everywhere, and if you're on the glideslope, you don't need to correct for temperature, although your indicated altitude will be higher than you expected. It's when you're doing a night circling NDB at forty below that failing to apply temperature correction will smite you.

Paul B said...

when you do these calculations, do you ever cross check the figures against the height shown by the gps? If so, do the figures usually agree reasonably well?

Aviatrix said...

I don't even have altitude set as one of the fields to display on the GPS, and it a VFR GPS so it isn't in my scan on approach.

I'll check that out next time I'm in the appropriate situation, though.

It's not so much about "true" altitude--you'll never know that, given factors like temperature inversions, the curvature of the Earth, and local variations in g--as it is about flying a safe altitude while still making the field, (and getting the right answer on your IFR written).

Of course in the US all the questions are available ahead of time, so if there's any concept you don't get, you can just find all the question bank entries on that concept and learn the answers. I know someone who went to an exam cram school and that's how they taught it!

Brrr said...

re: approaches in 40 below...

I think it's runway 31 in YWG... if you fly the procedure ILS intercept altitude and find you are crossing the FAF and you're still under the glideslope, you should have added that temp correction to the procedure turn, gp intercept altitude... And given the fact that there is/was a significantly tall apartment building under that approach, it could become a very "interesting" oversight.

Of course this is only gathered from hearing others talk about it .... (whistling innocently) ...

Brrr again said...

Aha - found an online version. If this is accurate then I think that the procedure turn/intercept altitude has been bumped up significantly. It used to be much closer to the FAF/Tesom crossing alt 'back in the day.'

Maybe someone in that apartment building complained!?

Brrr yet again said...

oops ... edit Tesom for Forks
I'm going back to bed...

Aviatrix said...

Brr indeed. I've never flown an approach in 40 below just done the math. Thanks for underlining the fact that you have to get on the glideslope before it offers you any protection from the cold, cold ground (and apartment buildings).

It seems sensible to have a single PTA for summer or winter. I imagine that's what they do in Colorado, but I also imagine that in places like SLC with really high terrain very close to the airport ... ahhh got it. In the US you are on radar everywhere, and radar vectoring altitudes are already corrected for temperature. US pilots don't have as much emphasis on cold temperature correction because they are almost never maneuvering for an approach without having ATC watching out for you.

Sarah said...

Thanks, Brrr. First TC plate I've seen.
I wish TC released them on the net like the US does. But no:

© 2006 Her Majesty The Queen in Right of Canada, Department of Natural Resources All rights reserved Source of Canadian Civil Aeronautical Data: © 2006 NAV CANADA All rights reserved

Richard said...

Forgive me, Ma'am, but isn't this post simply distinguishing between QFE and QNH? (Or have the Q codes been abandoned to Radio Amateurs?)

Aviatrix said...

Canadians do not use Q-codes; the altimeter is always set to read height above sea level. It didn't even occur to me to bring strange foreign practices into an already complex post.

Matt said...

Richard, using QFE does not abrogate the need to apply a temperature correction. The only difference between using QNH and QFE is that QFE gives you zero at field elevation rather than MSL; one still would need to apply a correction factor to account for the higher density of cold air.

Incidentally, a quick rule of thumb is 4 feet per degree deviation from ISA per 1000 feet. So, at sea level, a temperature of 0 is ISA -15. If your target altitude is 2000 feet, the correction is (15*4*2) = 120. Standard ISA lapse rate is 2 degrees C per 1000 feet, which is sufficiently small that you can assume away variations in field elevation unless operating into a very high elevation airport.

This approach actually comes pretty close to the table values. In the example Aviatrix used, temp was -10 (ie ISA -25) and height above airport elevation was 3281. Using this approach, you get (25*4*3.28) or 328. It's a little higher than the table value of 318, but pretty close.

Aviatrix said...

Oh thank you Matt. I misread Richard's comment and thought he was asking why I hadn't distinguished between QNH and QFE.

No indeed! Merely subtracting the field elevation from the indicated altitude above seal level would give no protection whatsoever from cold temperature errors. In the wrong conditions your altimeter would still indicate hundreds of feet high.

Richard said...

Matt & Aviatrix: Much obliged - I've re-read, and think I now understand!

RobinMaiden said...

Here are some posts I made on the topic of Cold Weather Altimetry. I also made a video that explains the principle. Here's the link: http://www.robinmaiden.com/?s=cold+weather