Dew Point and Temperature vs altitude

In a recent post we discussed a very simple (clearly over simplified) method of coming up with a way to estimate cloud ceilings in special circumstances. A point of the discussion was that the dew point lapse rate, as used in this model, was less than the environmental air temp lapse rate. We came up with something like -1º /1000 ft for the dew point drop with altitude, compared to an average value of the environmental air temp lapse rate, which we took to equal the Standard Atmosphere value of -3.6º/1000 ft.

So now we have to face the truth to see if this model can be justified at all by looking at real soundings and then real cloud height measurements. Soundings are the measured values of T, DP, and pressure (among other parameters) as a function of altitude. Soundings are nicely presented at the University of Wyoming. As you surf around the world looking at these, the  first thing you notice is the the temperature and dew point changes with altitude are all over the place. First reaction would be there is no way at all to predict this behavior.

But we are looking at very special cases, namely we must  have low clouds there in the first place, which means the air temp must drop to the dew point at some altitude less than 7,000 feet (2134 m). In other words, we were not predicting clouds at a certain altitude based on T and DP, but instead saying that if we do have low clouds, then we might estimate the ceiling or cloud base from the T and TP on the surface.

So step one in the data search is to find those cases were we do see the T and DP coming together at some height less than 2000 m. Below is a pic explaining the diagrams (details here), followed by some pictures taken at random. After that we analyze then in the light of our past discussions.

The dew point is always on the left. Background lines are theoretical values of the dry rate (green, 9.8C ~ 5F) and the moist rate (blue, 6C~3F). Notice that the dry rate slope is about 10º shallower, and this 10º corresponds to a lapse rate difference of about 2º F. Notice, too, there are no low clouds in this case; it is even an inversion. For a while the temp is increasing with altitude.

Here are some examples taken at random.  Again, only criteria was that T and DP met below 2000m. In each of the pictures, we marked the temp with a green line, the DP with a red one, then we duplicated a segment of the green line and moved it to the base of the DP so you can see the difference in slope more clearly.

We see first that indeed in these cases the DP lapse rate is lower than the temperature. To get a better feeling we can analyze the slopes of the lines we marked in the figures (1 top, 8 bottom), and from these compute the lapse rates.

Sample	slope		lapse rate °C/km		lapse rate °F/1000ft		Delta
	DP	T	DP	T	DP	T	T-DP
1	349	333	-3.8	-9.9	-2.1	-5.4	-3.3
2	350	341	-3.4	-6.7	-1.9	-3.7	-1.8
3	351	341	-3.1	-6.7	-1.7	-3.7	-2.0
4	346	339	-4.8	-7.4	-2.6	-4.1	-1.4
5	347	337	-4.5	-8.2	-2.5	-4.5	-2.1
6	352	336	-2.7	-8.6	-1.5	-4.7	-3.2
7	344	338	-5.6	-7.8	-3.0	-4.3	-1.2
8	349	340	-3.8	-7.0	-2.1	-3.9	-1.8
Averages=			-3.9	-7.8	-2.2	-4.3	-2.1

This brief analysis seems to imply that a 2º DP lapse rate is better than the 1º we came up with, but the closing rate used to estimate cloud ceilings is reasonably close. This shows an average of 2.1 and we had 2.6.  But we have to admit this is all very crude analysis. It can only show there is some ballpark value and that the standard values we see in pilot's license training materials and other books (usually 2.5) might not be unreasonable.

There is still another way we can look into the usefulness of this approach and that is to check actual metar reports from airports. They report T, DP, and cloud height, which is presumably measured with some form of a ceilometer–a laser device for measuring cloud height.  We have started this list, but we are already detecting the limits of this analysis, namely they ceilometer data are not being reported to a very high precision.  In fact, it is lower than some standards say it should be.

station	T (ºC)	DP (ºC)	Cloud height (m)	k (ºF/1000 ft)
KCHS	18.3	15	300	1.8
MIAMI	26.7	23.3	600	1.9
YBRK	19.6	18.5	600	0.6
KMFL	30.6	23.9	600	3.7
8557	14	7.8	600	3.4
FZAB	31	20.4	600	5.8
KLAX	21.7	15.6	600	3.3
KLGA	12.8	4.4	1000	4.6
DULUTH	4.4	-5	1500	5.2
KDLH	7.2	-2.2	1500	5.2
			Average =	3.5

We need to get a lot more of this data before any conclusions. We have limited the cloud height to below 2000 m, but what we find in the data is the next step up is 2500 m, and the other 6 stations found with cloud heights all reported 2500m, which can't be right. Reminds me of the old days when all ship reports had wind only from the cardinal and intercardial directions!

So far we did a crude analysis and predicted k = 2.6, but this came from an estimated DP lapse rate of 1ºF/1000 ft, which was then subtracted from an estimated average T lapse rage of 3.6. This is not consistent with the soundings which showed averages of 2.2 and 4.3 for an average k = 2.1 ±1

The 10 metar data so far gives k= 3.5 ±2.  We do not have a lot of data, but the data included all that matched our criteria: in soundings, we took all we found that had T and DP meeting before 2000m and the metar data we have taken all we found that gave measured cloud heights below 2000m. So the statistics are low, but should form some realistic sample. (PS it could be I am misinterpreting the metar data. i will check that.)

Therefore I must conclude that  I cannot see that there is not a simple way to predict useful cloud heights based on surface values of T and DP.  So we have to change our textbook from saying this is a formula for estimating cloud height, to something like this is the formula some books say can be used to estimate cloud height, but it must have large uncertainties.

This is the end of this discussion for now.  I have to wait to see if someone who knows about these matters might shed some light on this topic... i am a bit in the dark here.