Revisiting lapse rates (From: How high is that cloud?)

I have been following the thread about "How high is that cloud", and quite a
few of the posters seems to have some misconceptions about lapse rate.

Some of you, especially, are comparing apples and oranges:

The *environmental lapse rate* is a measurement of the real atmosphere. The
*dry adiabatic* and *wet adiabatic* lapse rates are scientific laws. Be
sure that you understand the difference.

We use the laws to only estimate the temperature of an air parcel of known
temperature-dewpoint properties, should it get lifted a specified number of
feet in the *real* atmosphere.

That estimate of the bubble's temperature, only when compared to the
temperature of the actual environment at that level, will help us to
determine the stability.

The lurid details below:
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1. The real atmosphe

Its temperature changes with height; this is the *Environmental Lapse
Rate*; it can be such that the temperature is lower at higher altitudes
(normal, and commonly measured in degrees per thousand feet, or similar);
temperature can be higher with increases in altitude (inversion); it can
even not change with changes in altitude (isothermal). The rate of change
(in degrees per thousand feet) can change from one layer to another.

We know that Performance varies with atmospheres of different properties, so
ICAO came up with a hypothetical *Standard* atmosphere so that we can
compare. In this hypothetical atmosphere, the Temperature at Sea level is
15 deg C, and the temperature drops off at about 1.98 (let's call it 2) deg
C per 1000 feet. The 2 degrees C per 1000 can be considered an *average* of
a large number of real atmospheres, but is only occasionally representative
of any particular single atmosphere, and especially not over all layers of
it.


2. A hypothetical bubble of air: whose dew point is lower than its
temperature, and which does not mix with the surrounding air:

When such a bubble is *lifted*, the pressure on it decreases and it cools.
No heat is added nor released, hence *adiabatic*. Such a bubble will cool
at just about 3 degrees C per 1000 feet. This is more or less constant at
all pressures (hence at all levels), but remember: it will be 3 deg per
1000 *only as long as the dew point remains lower than the temperature*.
Once the temperature cools to the point of the dew point, the rules
change...see 3, below.

The rate of cooling is called the "dry adiabatic lapse rate".

Note that the *Environmental lapse rate* is a *difference in the
temperature* from one layer of the real atmosphere compared to another. The
"dry adiabatic lapse rate" does not measure anything in the real atmosphere
at all. It is a known *rate of cooling* should a parcel of air be lifted to
lower pressure (or rate of warming should it be lowered to higher pressure.

3. The same hypothetical bubble of air as in number 2.: but now with the
temperature equal to the dewpoint:
When such a bubble is lifted it tries to cool as per 2, above. But it
cannot cool much below the dew point, so the dewpoint has to decrease also.
The only way the dewpoint can decrease, is if some of the water vapour
leaves the air, and becomes real water (cloud droplets, fog droplets). Heat
is released in the process of condensing into water and that heat is used to
warm the bubble somewhat.... now it cannot cool at 3 degrees per 1000, but
somewhat less.

This is known as the "wet adiabatic lapse rate".

Once again, it does not measure the real atmosphere, it is a "rate of
cooling" should a bubble with Temperature-equal-to-dewpoint start to rise to
lower pressures.

How much cooling, depends on how much water condenses to release heat...
Since the most moisture condenses from air that is at very high dewpoints,
that is the sort of bubble that will cool the slowest, say about 1 deg C per
1000. In very cold arctic air with dewpoints of minus 30, there is hardly
any more moisture, so very little heat is added in condensation, and such a
bubble cools very nearly at 3 degrees per 1000, almost the same as a *dry*
bubble.



In the real atmosphere, *environmental* lapse rates of greater than 3
degrees per 1000 are rare, because they are *absolutely* unstable... any
small lift of a parcel would be automatically warmer than the surrounding
air. If conditions are ripe to try to achieve such a steep (3-degree per
1000) *environmental* lapse rate.... hot summer afternoons.... the
self-induced mixing will create a near-3-degree-per-1000 lapse rate.

What will happen is an immediate mixing... bringing cooler
upper air down, and convection of the warmer lower air upward.... The
*environmental* lapse rate will stabilize right around the 3-degree per 1000
rate in the surface layer.

How deep can this layer be? Depends on the strength (angle) of the sun, the
length of the day and few other things, such as the type of surface.... but
it will be rarely more than 6,000 feet in most areas. I am not too familiar
with deserts so it may be a bit more there, but I would still
estimate well short of 10,000 feet.

Above this surface layer, the *environmental* lapse rate typically is
considerably less than 3 degrees per thousand feet, perhaps more like
somewhere around the "standard" 2 deg per 1000.

Therefore, if we tried to lift a *bubble*, say from 8000 to 10000 feet (and
its dewpoint is lower
than temperature), it will cool at 3 degree per 1000, but after a 2000 foot
lift it will likely be considerable cooler than the environment and will
sink back (stable).

The most common scenario is a high-dewpoint bubble near the surface is
lifted convectively. If the boundary layer's lapse rate is near 3 deg C per
1000, the bubble will not be particularly unstable, because it will cool at
3 deg per 1000, and be very nearly the same temperature as the environment.
But if the bubble has a high dewpoint, and the temperature cools to the
point where water has to condense, *thereafter* it will cool at only about 1
degree per 1000. *NOW* it stands a good chance of being warmer than the
environment and hence unstable.