Atmospheric Lapse Rate (calculating the altitude of cloud formation)

[Borborygmus]

This is probably more of a p-chem question but I figure you guys are smart enough to answer this.

FREEZING LEVEL CALCULATION:

Per FAA "A standard temperature lapse rate is when the temperature decreases at the rate of approximately 3.5 °F or 2 °C per thousand feet up to 36,000 feet"

Easy enough to use this to calculate freezing level.​

CLOUD BASE CALCULATION:

"As moist, unstable air rises, clouds often form at the altitude where temperature and dew point reach the same value. When lifted, unsaturated air cools at a rate of 5.4 °F per 1,000 feet and the dew point temperature decreases at a rate of 1 °F per 1,000 feet. This results in a convergence of temperature and dew point at a rate of 4.4 °F. Apply the convergence rate to the reported temperature and dew point to determine the height of the cloud base."

Also pretty easy.​

But wait does air cool at 3.5F or 5.4F per 1,000ft??

I think the issue here is whether we're talking about dry lapse rate or saturated lapse rate. Or an average. Per wikipedia, looks like 5.4F is dry, wet is 2.7F.

So my question is, wouldn't it be better to calculate freezing level by using 5.4F until you get to cloud base (which is saturation level) and then switch to 2.7F?

 

[jbriggs444]

As I understand the nomenclature, the "standard temperature lapse rate" refers to a typical rate of change of temperature with altitude. We are not talking here about how temperature changes as a parcel of air rises, but the temperature profile of the actual atmosphere.

The "dry adiabatic lapse rate" or "unsaturated lapse rate" refers to the rate of change of temperature of a parcel of air that is lifted and cools from adiabatic expansion.

If the actual temperature profile in the atmosphere were to have a gradient in excess of 5.4 degrees Fahrenheit per 1000 feet then that would constitute an inversion. Low altitude dry air could rise, expand and cool and still end up warmer than the high altitude air that it displaces. Obviously, such an inversion would be unstable. An actual dry gradient of 3.5 degrees Fahrenheit per 1000 feet is less than 5.4 and, so, is stable.

 

[Borborygmus]

I understand an inversion to be warm air on top of cold air. So the temperature gradient would have to be negative i.e. <0.

A skew-T chart shows the temperature over air pressrue as measured by a weather balloon. I'm not very good at reading these, but found this example
http://www.atmos.millersville.edu/~lead/SkewT_HowTo.html

In the sample graph, the actual lapse rate (red line) seems to mirror the trend of the adiabatic lapse rate (background lines) up until 200 mb at which point we see a temperature inversion. 200 mb is the end of the stratosphere and beginning of the troposphere which always has a temperature inversion.