Adiabatic warming is the process whereby parcels of air warm at a rate of
about 5.4 degrees F for each 1,000 feet they descend. As an air parcel
descends, the atmospheric pressure exerted upon the parcel increases,
causing the parcel to warm. In like manner, as a parcel rises, it cools at
a constant rate of 5.4 degrees F per 1000 feet.

Unless utterly parched, water vapor exists within a parcel of air and
exerts a pressure upon the surface of the parcel, conveniently termed
"vapor pressure". In fact, this vapor pressure is used to derive the
dewpoint temperature of the parcel of air. The greater the quantity of
water vapor within the parcel, the greater the pressure exerted and
visa-versa. Put another way, greater water vapor content translates to a
higher dewpoint. .

As a parcel of air ascends through the atmosphere, the pressure exerted upon
the parcel decreases and in turn the water vapor pressure within the parcel
decreases. It follows that the dewpoint of the parcel will decrease as
well. The rate of decrease of dewpoint is approximately 1 degree F for each
1000 feet the parcel ascends.

Lets say I observe Cumulus clouds If the surface temperature is 72F and
the surface dewpoint is 52F, estimate the height in feet of the bases of
these Cumulus clouds.

Can you derive a formula the will compute the height of Cumulus cloud bases
in feet given the surface temp and dewpoint?

Jot - Ashland, MA


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Jot Ross wrote in :

Adiabatic warming is the process whereby parcels of air warm at a rate
of about 5.4 degrees F for each 1,000 feet they descend. As an air
parcel descends, the atmospheric pressure exerted upon the parcel
increases, causing the parcel to warm. In like manner, as a parcel
rises, it cools at a constant rate of 5.4 degrees F per 1000 feet.

Unless utterly parched, water vapor exists within a parcel of air and
exerts a pressure upon the surface of the parcel, conveniently termed
"vapor pressure". In fact, this vapor pressure is used to derive the
dewpoint temperature of the parcel of air. The greater the quantity
of water vapor within the parcel, the greater the pressure exerted and
visa-versa. Put another way, greater water vapor content translates
to a higher dewpoint. .

As a parcel of air ascends through the atmosphere, the pressure
exerted upon the parcel decreases and in turn the water vapor
pressure within the parcel decreases. It follows that the dewpoint
of the parcel will decrease as well. The rate of decrease of dewpoint
is approximately 1 degree F for each 1000 feet the parcel ascends.

Lets say I observe Cumulus clouds If the surface temperature is 72F
and the surface dewpoint is 52F, estimate the height in feet of the
bases of these Cumulus clouds.

Can you derive a formula the will compute the height of Cumulus cloud
bases in feet given the surface temp and dewpoint?

Jot - Ashland, MA



Perhaps I can when I'm not right about to go to bed. But I do have time to
point out that I think the 5.4 dT for each 1000 feet assumes somewhat dry
(if not parched) air. At higher humidity for the parcel the lapse rate is
less.


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in article , EdM at
wrote on 6/20/04 1:55 AM:

Jot Ross wrote in :

Adiabatic warming is the process whereby parcels of air warm at a rate
of about 5.4 degrees F for each 1,000 feet they descend. As an air
parcel descends, the atmospheric pressure exerted upon the parcel
increases, causing the parcel to warm. In like manner, as a parcel
rises, it cools at a constant rate of 5.4 degrees F per 1000 feet.

Unless utterly parched, water vapor exists within a parcel of air and
exerts a pressure upon the surface of the parcel, conveniently termed
"vapor pressure". In fact, this vapor pressure is used to derive the
dewpoint temperature of the parcel of air. The greater the quantity
of water vapor within the parcel, the greater the pressure exerted and
visa-versa. Put another way, greater water vapor content translates
to a higher dewpoint. .

As a parcel of air ascends through the atmosphere, the pressure
exerted upon the parcel decreases and in turn the water vapor
pressure within the parcel decreases. It follows that the dewpoint
of the parcel will decrease as well. The rate of decrease of dewpoint
is approximately 1 degree F for each 1000 feet the parcel ascends.

Lets say I observe Cumulus clouds If the surface temperature is 72F
and the surface dewpoint is 52F, estimate the height in feet of the
bases of these Cumulus clouds.

Can you derive a formula the will compute the height of Cumulus cloud
bases in feet given the surface temp and dewpoint?

Jot - Ashland, MA



Perhaps I can when I'm not right about to go to bed. But I do have time to
point out that I think the 5.4 dT for each 1000 feet assumes somewhat dry
(if not parched) air. At higher humidity for the parcel the lapse rate is
less.

Until the parcel of air becomes satured (when temp = dewpoint) water vapor
has nil effect on the dry adiabatic lapse rate of about 5.4 degrees F/1000
feet. In other words. energy is hidden (latent) until condensation occurs
which will happen a height of base of Cumulus couds (Hint!). At that point,
as iar parcels continues to rise, water vapor releases its energy expressed
as heat and late rate is slowed (to perhaps 3 degrees/1000 feet). The lapse
rate is then termed moist adiabatic.

Awaiting your awnswer to the quiz...

Jot


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On 6/19/04 10:14 AM, in article , "Jot Ross"
wrote:

Adiabatic warming is the process whereby parcels of air warm at a rate of
about 5.4 degrees F for each 1,000 feet they descend. As an air parcel
descends, the atmospheric pressure exerted upon the parcel increases,
causing the parcel to warm. In like manner, as a parcel rises, it cools at
a constant rate of 5.4 degrees F per 1000 feet.

Unless utterly parched, water vapor exists within a parcel of air and
exerts a pressure upon the surface of the parcel, conveniently termed
"vapor pressure". In fact, this vapor pressure is used to derive the
dewpoint temperature of the parcel of air. The greater the quantity of
water vapor within the parcel, the greater the pressure exerted and
visa-versa. Put another way, greater water vapor content translates to a
higher dewpoint. .

As a parcel of air ascends through the atmosphere, the pressure exerted upon
the parcel decreases and in turn the water vapor pressure within the parcel
decreases. It follows that the dewpoint of the parcel will decrease as
well. The rate of decrease of dewpoint is approximately 1 degree F for each
1000 feet the parcel ascends.

Lets say I observe Cumulus clouds If the surface temperature is 72F and
the surface dewpoint is 52F, estimate the height in feet of the bases of
these Cumulus clouds.

Can you derive a formula the will compute the height of Cumulus cloud bases
in feet given the surface temp and dewpoint?

I'll give it a shot.

Let ST stand for surface temp; SD for surface dewpoint
temp at X thousand feet = ST - 5.4X
dewpoint at X thousand feet = SD - 1X

cloud bases form when temp=dewpoint or when
ST - 5X = SD - X

or when X = (ST-SD)/4 (in thousands of feet)

ST = 72; SD = 52 yields 5000 feet.

Is this right?
Are those factors only good for the troposphere?

- Steve Stein


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On 6/21/04 7:28 PM, in article ,
"Stephen Stein" wrote:

Let ST stand for surface temp; SD for surface dewpoint
temp at X thousand feet = ST - 5.4X
dewpoint at X thousand feet = SD - 1X

cloud bases form when temp=dewpoint or when
ST - 5X = SD - X

or when X = (ST-SD)/4 (in thousands of feet)

Ack! Make that:
ST - 5.4X = SD - X
X = (ST-SD)/4.4

ST = 72; SD = 52 yields 5000 feet.

4545 feet - make it 4500 to 2 significant digits.

- Steve Stein


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Jot Ross wrote in :

in article , EdM at
wrote on 6/20/04 1:55 AM:

Jot Ross wrote in
:

Adiabatic warming is the process whereby parcels of air warm at a
rate of about 5.4 degrees F for each 1,000 feet they descend. As an
air parcel descends, the atmospheric pressure exerted upon the
parcel increases, causing the parcel to warm. In like manner, as a
parcel rises, it cools at a constant rate of 5.4 degrees F per 1000
feet.

Unless utterly parched, water vapor exists within a parcel of air
and exerts a pressure upon the surface of the parcel, conveniently
termed "vapor pressure". In fact, this vapor pressure is used to
derive the dewpoint temperature of the parcel of air. The greater
the quantity of water vapor within the parcel, the greater the
pressure exerted and visa-versa. Put another way, greater water
vapor content translates to a higher dewpoint. .

As a parcel of air ascends through the atmosphere, the pressure
exerted upon the parcel decreases and in turn the water vapor
pressure within the parcel decreases. It follows that the dewpoint
of the parcel will decrease as well. The rate of decrease of
dewpoint is approximately 1 degree F for each 1000 feet the parcel
ascends.

Lets say I observe Cumulus clouds If the surface temperature is
72F and the surface dewpoint is 52F, estimate the height in feet of
the bases of these Cumulus clouds.

Can you derive a formula the will compute the height of Cumulus
cloud bases in feet given the surface temp and dewpoint?

Jot - Ashland, MA



Perhaps I can when I'm not right about to go to bed. But I do have
time to point out that I think the 5.4 dT for each 1000 feet assumes
somewhat dry (if not parched) air. At higher humidity for the parcel
the lapse rate is less.

Until the parcel of air becomes satured (when temp = dewpoint) water
vapor has nil effect on the dry adiabatic lapse rate of about 5.4
degrees F/1000 feet. In other words. energy is hidden (latent) until
condensation occurs which will happen a height of base of Cumulus
couds (Hint!). At that point, as iar parcels continues to rise, water
vapor releases its energy expressed as heat and late rate is slowed
(to perhaps 3 degrees/1000 feet). The lapse rate is then termed moist
adiabatic.

Awaiting your awnswer to the quiz...

Jot



I hadn't realized that it was a "step" function (dry vs moist lapse
rates). Thanks for the explanation. Once again it is too late, but
since I've shot my mouth off, I'll stay up a little later.

It seems like a simple algebra problem (which has me worried). But
assuming the constants you have provided...


t=surface temperature
td=surface dewpoint
h=height of the cloud base

The cloud begins to form at the height where t=td, or at the point where
the lowering temperature of the rising parcel "overtakes" the lowering
dewpoint of the parcel.

At this height (where I presume we will find the base of the cumulus),

t-(5.4h/1000) = td-(1.0h/1000)

Solving for h yields

h = (1000/4.4) * (t-td) = 227.27(t-td)

So, unless I've missed the trick part of the question (which is entirely
possible), in the example that you gave,

h = 227.27 (72 - 52) = ~4545 feet

This of course, assumes there are no inhibiting factors
(inversion/capping...and probably a few hundred others that I am not
familiar with).

Ed





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