Meteo - Factors that influence QNH

[milchmachtmunter]

Hi all

This is my very first thread in here. Thank you for giving me the opportunity to post my question.

I am having a hard time understanding how the QNH is calculated.

Knowing that the temperature profile is rarely 0.65°/100m; 2°/1000ft, it makes sense to me that the values of QNH can vary with the elevation of the airport. See also http://www.pprune.org/tech-log/526510-high-qnh-high-altitude-airports.html

However - if I try to calculate the theoretical expected QNH of a station/airport considering the influence of temperature, I do not get useful results (see below).
So my question basically is: How is QNH calculated?

It seems to me that there are other influences of QNH, which I am not aware of:



1. Index error - the calibration of the index.

2. Temperature error - temperature at the barometer affects the mercury ie heat it up and it expands.

3. Latitude error - Remember that gravity is also acting on the mercury and of course gravity force varies with latitude

DFC

Is this the answer to how the QNH is calculated? If this is the case then how I am supposed to consider these points?

Calculation of QNH considering Temperature Difference:

Station 1:
T1 = 12.4°C ; QNH1 = 1014.1hPa; e1 = 577amsl

Station 2:
T2 = -5.3°C; QNH2 = to find; e2 = 3580amsl

17.7°K / (273.25°K+12.4°K) * 1014.1hPa = 62.8hPa; This would result in a QNH of 1014.1hPa + 62.8hPa = 1076.9hPa at station 2.

Obviously there is something wrong with this calculation :bored:

I am looking forward reading your answers.

[Alex Whittingham]

QNH is calculated by measuring the pressure at the station (ie QFE) and then increasing it to an equivalent sea level pressure assuming ISA conditions.

QNH is not the actual pressure at sea level (which is called QFF) unless the actual conditions are exactly ISA. If the atmosphere is colder than standard then the level that equates to QNH will be above mean sea level and QFF will be greater than QNH, if it is warmer than standard the opposites are true.

I think it is the question that is wrong. At station 1 we could deduce the QFE by working back from QNH and elevation using ISA conditions, but QFE at station 2 is not given and station 2 appears to bear no geographical relation to station 1.

[gfunc]

I think you are potentially overthinking this and muddling temperature lapse rates, density altitude and altimetry.

For simplicity (i.e. ATPL exams) it is normally assumed that 1 hPa is equivalent to a certain number of feet (typically 30ft), so that for a station at 300ft elevation with surface pressure (QFE) of 1000hPa, the QNH would be 1010 hPa (i.e. 1000 hPa + 300ft/30ft).

In ATPL exam world you'll only probably find temperature corrections in connection with density altitude (density altitude = pressure altitude + (ISA deviation x 120ft)).

In the real world, meteorologists reduce station pressure to MSL using the hyposometric equation (https://en.wikipedia.org/wiki/Hypsometric_equation) and pilots find the QNH by sitting at the threshold and winding the pressure until the altimeter reads threshold elevation.

[milchmachtmunter]

Hi :)

Thank you very much for your answers.

gfunc you are right, this will probably not be subject of the ATPL. However I doubt that I can find peace without understanding this ;)

It seems I did not express my question properly. I am familiar with DA, PA and the usage of QNH, QFF and QFE.

Although with the hyposometic equation I did not get along ;)

Alex I see your point, I should probably rephrase my question.

The initial question was: Why is QNH depending on the elevation of the station (when the stations are very close-by)
Apparently a difference in temperature explains part of this discrepancy of QNH.

But I cannot reconstruct this discrepancy of QNH accurately. How would this be made?

In the example station 1 and station 2 are close-by.

Thanks in advance :)

[Alex Whittingham]

The QNH calculated from the QFE using ISA (hypsometric equation) depends on the elevation of the station because the height of the air mass between station elevation and sea level (h) is an input into the equation. The temperature of the air mass is not an input, because the equation as applied assumes ISA.

Two close-by stations at different elevations should give very close values of QNH because the surface pressures in air masses do not change radically over short distances, unless it is a very intense low. Under normal slack to medium pressure gradient conditions the starting pressures (QFE) at your two stations will be different because of their different elevations but the value h will also correspondingly differ in each calculation leading to a very similar end result for calculated QNH. Thus the answer to your rephrased question "Why is QNH depending on the elevation of the station (when the stations are very close-by)" is "It isn't, you are starting from a false premise".

Although its not really relevant, the two stations in your example do not seem to be close. I say this because in the case of station 1 the temperature is around ISA -1.5, in the case of station 2 it is closer to ISA -13.5. That is either quite an unusual lapse rate or they are in different air masses.

However, because the QNH calculation ignores temperature deviation (and therefore any environmental lapse rates) assuming they are very close the paragraph above applies and the reasoning with the data given would simply be:

QNH at station 1 = 1014.1hPa
station 1 is very close to station 2
therefore QNH at station 2 is very close to 1014.1hPa

Temperature has nothing to do with it.

To find the actual and accurate QNH at station 2 you would need the measured QFE, which you do not have, and apply the hypsometric equation (or 30ft/mb as a rough approximation), and then you would eventually that find the actual QNH would be very close to that of station 1.

Edited to add: In the light of my post below this can be seen to be incorrect reasoning. In the second paragraph my error is to assume that the height differences will cancel out the differences in QFE and produce similar values for QNH, which will differ by a fixed amount from QFF. This is not so, because the difference between calculated QNH and QFF increases with h and with temperature deviation.

[milchmachtmunter]

Alex,
Thank you again for your response and thoughts, I really appreciate it.

It came to my mind that it's probably the easiest if I show you the measurements I am talking about. For this purpose I just made a screenshot of the measurements including the measurements of station 1 (Interlaken) and station 2 (Jungfraujoch). They both show QFE and QNH. The air-line distance between them is very roughly 20km / 12 miles. Do you consider this as close too?

Pressure:
http://up.picr.de/29982067ea.jpg

Temperature:
http://up.picr.de/29982091pv.jpg

The difference in QNH varies, but higher altitude stations generally show a higher QNH, regardless of the prevailing weather situation.

Jungfraujoch: 3580m / 11'745ft amsl
Interlaken: 577m / 1'893ft amsl


And yes you are right of course with the calculation of QNH from QFE:

Interlaken
948.5hPa + 1893ft / 27.3ft/hPa = 948.5hPa + 69.3hPa = 1017.8hPa = close enough to 1016.3 (which is the actual QNH)

I think for Jungfraujoch the linear approximation is too inaccurate..

Sidenote:
Adelboden: 1327m / 4'354ft amsl
Thun: 570m / 1'870ft amsl


Can you explain the difference in QNH in the pictures above?

[gfunc]

If you look at the SLP (QNH) gradient on the map (22hPa in ~20km) this is completely unphysical: it's getting on for 10 times larger that you'll find in a hurricane. If you plug those numbers into the geostrophic wind equation:

(1/f * (change in pressure [Pa])/(change in distance [m]))
where f = (2*pi*86400)*sin(lat)

You'll get an answer telling you the wind is supersonic. I've not been to Interlaken, but I would suggest it's not normally that brisk.

I would wager that in this example the mountain pressure measurement is in error either because the calculation is not done correctly, the sensor is situated at an altitude different from that used in the calculation, or the sensor is outside of it's design operating range.

[Alex Whittingham]

Thanks! I would agree the stations are close, now to find the answer ...

First of all a quick check through an online hypsometric calculator (http://www.hochwarth.com/misc/AviationCalculator.html). This gives a QNH of 1038 hPa which confirms the calculation on your app.

Second, a check of the synoptic charts shows a slack pressure gradient over the Alps at 1800 on the 3rd of August with QFFs around 1013 hPa.

Next a check of temperature deviations, Interlaken is about ISA +17, Jungfraujoch about ISA+15.

So we have a situation where the calculated QNH in an atmosphere warmer than ISA gives a level below sea level, as expected. What isn't quite expected is that the difference is so large, in this case 25hPa = roughly 750ft, in the case of Interlaken only 90ft.

What I also had not anticipated was that the QNH pressure would be so variable, but on thinking about it it does make sense. My reasoning would be:

1. QFF is calculated taking account of the actual atmospheric conditions (ISA+15), QNH is not, therefore the pressures will differ.

2. The calculated values will differ by an amount that can be worked out from the height considered (h) and the temperature deviation.

3. Because the calculations for Interlaken and Jungfraujoch have different values for h, the difference between QFF and QNH for Interlaken will not be the same as that for Jungfraujoch.

I'll try a rough calculation based on the temperature error formula of 4% of height difference for every 10 degrees of deviation.

For Interlaken the difference should be 1893 x 1.7 x 4% = 129 ft
For Jungfraujoch the difference should be 11745 x 1.5 x 4% = 704 ft

That's close.

So the answer to your question seems to be that the calculation for QNH makes no reference to the temperature of the air mass and therefore there will be a difference between QNH and QFF (which does).

The difference depends on h and the temperature deviation. Assuming the temperature deviation is relatively constant, as is the QFF, where there are large height differences between measuring stations and a significant temperature variation the differing value of h will cause the calculated QNH to vary significantly even between geographically close stations.

[milchmachtmunter]

Very nice. This calculation shows the same correct result on several other measurements, including a few where T < T (ISA).

Thank you!

[victoriano]

Good morning.
Another case similar to the question made by milchmachtmunter; high difference of QNH.
SCFA 181300Z 18005KT 140V220 CAVOK 20/15 Q1011 NOSIG=
SCCF 181300Z 05008KT CAVOK 18/06 Q1025=
Distance between SCFA and SCCF is 102 NM.
SCFA elevation 456 ft.
SCCF elevation 7543 ft.

SCAR 181300Z 00000KT CAVOK 24/16 Q1010=
SLLP 181300Z 27006KT 9999 FEW004 SCT013 09/07 Q1041
Distance between SCAR and SLLP is 165 NM.
SCAR elevation 167 ft.
SLLP elevation 13323 ft.
Thanks!!