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:
-------

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.

"Icebound" wrote in message ...
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.

lot of interesting stuff snipped

1. I find the 2C/1000' "rule" actually gets the bases right most of
the time when the temperature is much over 45 degrees where I fly in
New England.

2. Most GA flying happens within 6000' of the ground. I only go over
that on an IFR flight plan or when heading over the water. So things
that happen within that boundary layer are of maximum interest.

3. I've tried to learn weather interpretation beyond simple
METAR-reading. Since you seem to know something about this, what would
you say are the points about lapse rate that we as GA pilots might
want to actually look for in terms of flight planning?

-cwk.

"C Kingsbury" wrote in message
om...

1. I find the 2C/1000' "rule" actually gets the bases right most of
the time when the temperature is much over 45 degrees where I fly in
New England.

The cloud base calculation for convective cloud relies on the difference
between the dry adiabatic lapse rate (the rate at which the temperature of
lifted air falls with height) and the rate at which dewpoint falls with
height. The former is about 3 degC/1000ft at the lower levels, the latter
is about 0.5 degC/1000ft. Thus the difference is 2.5 degC/1000 ft or,
flipped around, the air can rise about 400 ft per 1 degC of spread before it
condenses.

That has little to do with the ISA average lapse rate of 2 degC/1000 ft, but
the value is similar, hence your observation is correct.

Julian Scarfe

"C Kingsbury" wrote in message
om...
"Icebound" wrote in message
...

3. I've tried to learn weather interpretation beyond simple
METAR-reading. Since you seem to know something about this, what would
you say are the points about lapse rate that we as GA pilots might
want to actually look for in terms of flight planning?



Before I answer that....

In this post, let me show you a tool that might help explain adiabatic lapse
rates a little more. In the next one, I will try to deal with some
specifics.

---

Note this diagram:

http://satellite.usask.ca/mcidas/fram32.gif (I hope they don't change it
before you get there :-)

(This is one of those inventions for meteorology that has a similar sublime
genius as does the E6-B computer for aviation)

Forget all the yellow stuff for the time being... that is specific
information for the particular station, in this case Corpus Christi. Ignore
all that, and draw your attention to the lines and number in the background.

This diagram is known as a tephigram, and it depicts all of the adiabatic
"laws" that we have been talking about. Print a copy off... (better still
would be to find a big original somewhere)... and you don't have to be
guessing as to how a lifted parcel is going to behave.



1. Height in metres goes up the left side.

This has already been converted from the original observed pressure (reduced
pressure upwards equals increasing height, of course). Unfortunately, the
tick marks are not any particular "scale". These are just the levels where
the temperature or dewpoint trend made a significant deviation from its
previous trend, in this particular sounding. The good news is that they
chose the pressure scale very carefully, so that when converted to height,
the height scale turns out to be very nearly linear, and you can
interpolate.


2. The temperature lines are slanted to the right, in grey.

The highest values are at the bottom right, and the coldest at the top left.
Note the value number along the right side and the top. (The lines are
slanted because it keeps real-world plots more vertically on the page.)

3. The green lines represent the behaviour of the dewpoint.

If I start a parcel at some level, and lift it, the dewpoint value will
decrease parallel to the green lines. For example, if a parcel of air, with
a dewpoint of 20 deg C, is somehow lifted to the 3000 metre level, the
dewpoint will decrease to about 15, (providing no condensation takes
place). If the parcel started with a dewpoint of 0 it will decrease to
about -5. ... just about the 0.5 per thousand feet that has been discussed.

The values on the green lines tells you the amount of water, in grams per
kilogram (g/kg) of dry air, for that particular dewpoint and pressure. A
dewpoint of 20 at 1500 metres represents about 17 or 18 g/kg. If that
starts to condense, its a lot of water. But a dewpoint of 0 at 1500 metres
represents only about one-quarter as much water, about 4.5 g/kg, and
at -30, just over one-quarter of a g/kg.

4. The slightly-curved grey lines slanted *backward* represent the rate of
cooling of unsaturated air...

....should it be lifted. This is the *dry adiabatic lapse rate*.

You find the height (pressure) and *temperature* of an air-parcel. Then
*if* it were somehow lifted, its temperature would drop at a rate parallel
to those grey lines.

For example, a parcel at 30 deg at 0 ASL, lifted to 3000 metres, would drop
from 30 to about -5, providing that it was dry enough so that it never
became saturated and no condensation took place.

5. The purple lines represent rate of cooling of a saturated air parcel...

....one where condensation would have to occur as the parcel rises. This is
the *wet adiabatic lapse rate*.

Note that these lines curve, because the rate of cooling changes (for a
saturated parcel) depending on the temperature...much slower at high
temperatures, and very quickly (almost as quickly as the dry rate) in the
cold minus-30 temperatures.


Now a typical scenario:

Using our diagram with an air-parcel whose Temperature is 30, dewpoint 20,
at 0 ASL.

*If* such a parcel were to be lifted, it would cool from 30 to about 18
around 11-1200 metres. In that same 1200 metres, the dewpoint would reduce
from 20 also to 18 ...at the same point.. Now the parcel would be saturated
and any further lifting would cool parallel to the purple lines...say it
lifted to 3000 metres, it would cool only about another 9 degrees to about
plus-9 deg C. But now note the green lines. Our parcel would have started
out with about 15 g/kg of moisture (20 deg dewpoint at 0 ASL), but now would
have only about 10 g/kg. The other 5 would have condensed into cloud.


At this point we have said nothing about the actual, environmental
conditions, the *environmental lapse rate". The adiabatic lapse rates, as
shown by this diagram, are "what if" tools, used to see what *could* happen
if a parcel got lifted independently of its environment.

"C Kingsbury" wrote in message
om...
"Icebound" wrote in message
...
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.

lot of interesting stuff snipped

1. I find the 2C/1000' "rule" actually gets the bases right most of
the time when the temperature is much over 45 degrees where I fly in
New England.

This works for determining cloud bases because dewpoint increases with
altitude. It does not work for determining stability.

Mike
MU-2

2. Most GA flying happens within 6000' of the ground. I only go over
that on an IFR flight plan or when heading over the water. So things
that happen within that boundary layer are of maximum interest.

3. I've tried to learn weather interpretation beyond simple
METAR-reading. Since you seem to know something about this, what would
you say are the points about lapse rate that we as GA pilots might
want to actually look for in terms of flight planning?

-cwk.

"C Kingsbury" wrote in message
om...
"Icebound" wrote in message
...
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.

lot of interesting stuff snipped

....

3. I've tried to learn weather interpretation beyond simple
METAR-reading. Since you seem to know something about this, what would
you say are the points about lapse rate that we as GA pilots might
want to actually look for in terms of flight planning?


Now draw your attention to the yellow plot on the tephigram

http://satellite.usask.ca/mcidas/fram32.gif

This is the vertical sounding of temperature (solid line) together with
dewpoint (dashed line). The sounding starts at the surface, and goes up
until the balloon expanded too much and broke, somewhere near 35,000 metres.

[Aside: These soundings are done twice a day, nominally 0000Z and 1200Z
(typically takes something over an hour to complete). The goal is to have
stations every 250 km, but the actual density is somewhat variable,
especially in the Arctic. I estimate there are somewhere around 200 such
sites in North America...I couldn't find a definitive number quickly... most
in the USA, about 30 in Canada. The soundings for USA, Canada and the world
are accessible at

http://www-frd.fsl.noaa.gov/mab/soundings/

but it is not a very user-friendly site... and the list of stations do not
all have soundings, but they don't tell you which ones.... I keep looking
for a better public site within NOAA and/or Environment Canada to find them,
but have not yet been able to do so.... maybe somebody knows. ]




This particular sounding was Corpus Christi 1200Z morning of Nov 3rd. You
can see that the environmental lapse rate is all over the place:

Right near the surface we have an early morning inversion.
Then around 200 to 500 metres, a 3 degree drop from 10 to 7.
Then a rise back up to 12... another, thicker inversion.
Above 3000 metres a steep drop from 10 to zero.
....etc.

Certainly nothing near the 2-degree per 1000 feet that we are told is
"average".


In mid afternoon, the lower levels may have received sufficient sun heat to
raise the surface temperature to, say, 25. If we took just the surface and
the 3200 metre temperature, we would say, oh the lapse rate is 25 minus 0
equals 25 deg in 3200 metres equivalent to about 25 deg in 10.5 thousand
feet, about 2.4 deg per 1000, pretty close to 2, right? Even more than 2,
so somewhat unstable, right?

But it does not describe that very stable layer around 1500-2000 metres.
Nor does it describe the *very* unstable layer between about 2500 and 3200
metres.
Nor does it describe the extreme dryness of the layer immediately above 1000
metres, dewpoint down to minus 10.


****
For this reason, I am very loath to interpret *anything* about the lapse
rate from isolated temperature readings such as I might get from the surface
plus FD forecasts at 6000 and 9000 feet. Even with a "sounding" as I might
get from my OAT sensor... a) ...pretty much has to be a continuous plot, not
just a few points when I happened to look away from my other piloting
duties, and b) ...is a lot more interested if I had the dewpoint along with
the temperature.
****


If I could get a tephigram plots such as this for my area, even within a
couple of hundred kilometres, then we could use those dry and wet adiabatic
laws to play some "what if" games. And we can also use your real-time
temperature measurements to understand how the sounding is changing and what
that may imply:

In the morning, the small dewpoint spread suggests there may have been a
thin layer of fog or low cloud, capped by that inversion at about 200
metres. It was stable above that to at least 2000 metres, and then fairly
unstable (temperature drops rapidly from plus 10 to zero, for just a few
thousand metres to about 3300, etc...

If we showed up ready to go flying early that afternoon, and the surface
temperature/dewpoint was now 30/10....then...

....You could see right away that any parcels lifted from the surface would
reach saturation about 1800-2000 metres or so, but would be about 5 degrees
colder than the environment at that level. So it might be bumpy in the
lower 1500 metres, but would be get stable again between 1500 and 2000
metres, thus limiting any Cumulus formation. We could see that to get
significant instability the surface dewpoint would have to increase to
more than about 14 degrees, and the temperature to around 33. Is that what
they are forecasting for a high?

etc...

If we looked at a surface chart for that date, it would not surprise me if
Corpus Christi was in some kind of high pressure system. Those thick dry
layers (the big dewpoint spreads) are typical of a gently-subsiding airmass.

Did you get a pirep that the 3300 metre temperature has decreased? If so
(ie: the environment is cooling), this increases the chances of instability
because the environment will not be as much warmer as a lifted parcel... as
compared to this morning. Especially if the temperature/dewpoint *do*
increase to about 33/14.... If a saturated parcel can get past that warm
bulge at 3300 metres (parallel to the purple lines) it may top out at 8 or 9
thousand metres. Not huge thunderstorms, but pretty good Towering Cumulus.

And so on...