Lectures about
19 to 24
To understand water in the atmosphere and the role it plays in clouds, weather,
climate, storms, etc., we need to
clarify a few things about pressure.
Pressure is force per unit area - i.e
total force/total area it acts on
For the atmosphere this force is the total Weight of the air above each
square metre of the surface
Weight is somewhat different from Mass - Mass is measured in kilograms
but Weight should really be measured in Newtons -
this difference arises because Weight is the Force that gravity exerts on an
object - if we have no gravity we would have no weight but we would still have our mass - in space we have no gravity so
we are weightless even if we still have the same mass - on Earth we have
gravity so we have both Weight and Mass
The Weight of an object (in Newtons) is given
by the Mass of the object (in kilograms) multiplied by 9.8 (this is known as 'g'-
the 'acceleration due to gravity')
The pressure at Earth's surface is really the total Weight of all the
air that lies above each square metre of the surface.
The total Mass of air over one square metre
of Earth's surface is about 10,200 kg (!)
Therefore the Weight of that air is about 100,000 Newtons
- i.e 10,200 x 9.8 rounded up
Therefore the Pressure = Weight/Area = 100,000 Newtons
m-2
Instead of saying 'Newtons per square metre' for pressure we call one Newton m-2 one 'Pascal'
Therefore the pressure at Earth's surface is normally about 100,000 Pascals. Since the normal pressure at the surface can
also be expressed as 1000 mbar, this means that 100,000
Pascals is the same as 1000 mbar or 1 mbar = 100 Pascals = 1 hectoPascal
Pressure can also be explained as the force exerted by moving gas
molecules hitting the sides of an imaginary container - this leads to The Gas
Law:
P (in Pascals) = r (kg m-3) x R (
Joules kg-1 K-1) x T (K)
where r
is the
density of the gas in kg m-3 and R is the 'Gas Constant'
The Gas 'Constant', R, is different for each gas but 'a constant' for
that gas
For pure dry air (20% O2 and 80% N2) the Gas
Constant is R = 287 Joules kg-1 K-1
Water can exist in three different 'phases' - solid (ice), liquid
(liquid water - 'water') and gas (water vapour)
ICE > liquid WATER latent heat of fusion
is absorbed =3.5x105 Joules kg-1
liquid WATER >WATER VAPOUR latent heat of vaporization
is absorbed = 2.2x106 Joules kg-1
liquid WATER >ICE latent heat of
fusion is released = 3.5x105 Joules kg-1
WATER VAPOUR > liquid WATER latent heat of vaporization is released
=2.2x106 Joules kg-1
ICE>WATER VAPOUR latent heat of sublimation
is absorbed = 2.8x106 Joules kg-1
WATER VAPOUR>ICE latent heat of sublimation is released =
2.8x106 Joules kg-1
Heat is also absorbed (required) to increase the temperature of any
substance without it changing phase
This is the Specific Heat of the substance
The Specific Heat, represented by the symbol C, is the
energy that must be supplied to raise the temperature of one kilogram of
the material by one degree C
For liquid water C = 4180 Joules kg-1 K-1
Humidity – Water Vapour in
Air
Water can evaporate at temperatures below the boiling point of 100 ° C
This leads to the concept of water's Saturation Vapour
Pressure - the SVP
If liquid water starts with a vacuum - i.e., no gas above it - water
molecules will leave the liquid to form a gas above. Some of these water vapour molecules will be recaptured by the liquid until an EQUILIBRIUM is established. At this equilibrium the number of molecules
escaping from the liquid will be exactly the same as the number being
re-captured and the water molecules (existing as a gas i.e. water vapour) will have some equilibrium pressure - this pressure
will depend on the temperature of the liquid water and it is known as the Saturation
Vapour Pressure (SVP) over water at that
particular temperature.
The SVP over liquid water varies with temperature - getting
larger at higher temperatures
At 0 ° C the SVP over water is 6 mb; at 30 ° C
it is 40 mb; at 40 ° C it is 70 mb
and at 100 ° C it
is 1000 mb.
If we have air with a water vapour pressure greater than the SVP for its
temperature the water vapour will condense to reduce its vapour pressure to its SVP
If we have air over water with a water vapour
pressure less than the SVP for its
temperature the liquid water will evaporate
to increase its water vapour pressure until it
reaches its SVP
Since the SVP changes greatly with temperature the amount of water vapour present in air is also highly variable
The amount of water vapour present in any
sample of air is described by the 'humidity' of that air
The humidity of air may be expressed in several ways:
Absolute Humidity = gms of water vapour per cubic metre of air, i.e. gm
(water) / m3 (air)
Specific Humidity = gms of water per kilogram
of air, i.e
gm (water)/ kg (air)
Relative Humidity = [pressure of water vapour
(mb)/ SVP of water at that temperature (mb)] x 100 %
The Relative Humidity can also be expressed in terms of the Water Vapour Capacity of air at that temperature - expressed in
terms of gms of water vapour per kilogram of air
i.e. when fully saturated at 40 ° C one kilogram of air can hold 47 gm of water vapour
when
fully saturated at 20 ° C one kilogram of air can hold 14 gm
of water vapour
when
fully saturated at 10 ° C one kilogram of air can hold 7 gm of water vapour
when
fully saturated at 0 ° C one kilogram of
air can hold 3.5 gm
of water vapour
Therefore air at 20 ° C containing only 7 gm
of water vapour per kilogram has a Relative Humidity
of 50% since at 100% RH it could contain 14 gm
Therefore if we start off with air that is unsaturated, i.e. RH less than 100% and cool it then
as its temperature drops it will eventually become saturated at some point (i.e. when its RH=100%) and the water vapour will start to condense since its RH cannot exceed
100%. The temperature at which it would start to condense if cooled is known as its Dew Point
Temperature.
Define Dew Point Temperature, Td (°C) and Wet Bulb
Temperature, Twb (°C)
The Td (°C) is the temperature the air would have to be cooled
to in order to make it's
water vapour condense
We could measure Td by cooling air and watching when it
condenses
From the temperature of the air T and Td we can work out its
Specific Humidity 'w' and its Relative Humidity R.H.
Air at T=20°C with a Td of 10°C has a R.H. of 50%. This comes from the tables identified in
Assignment 2.
Air at 10°C has w =7 gm/kg when saturated - air at 25°C would have w =
14 gm/kg when saturated, therefore R.H.= 7/14 x 100% = 50%
For two samples of air at same temperature the one with the lower Td
has lower R.H.
For condensing, i.e. saturated air, its Td is same as its T
The Wet Bulb temperature is the temperature to which the air would cool
if we let water evaporate into it without supplying any heat.
Twb lies between Td
and actual temperature T, i.e., Td <
Twb < T
Twb is measured using a Psychrometer - double thermometer with one bulb - the wet
bulb - covered with wet cloth.
The difference between the actual T (the dry bulb temperature) and Twb, ie T-Twb, is called the Depression of the Wet Bulb.
From the measured T-Twb and T, the
tables of Assignment 2 can be used to determine the R.H. and the Dew Point
temperature of the air. From these the
specific humidity can also be determined.
For example, if Twb=14°C and T dry
= 20°C, then depression of wet bulb is 6 °C and the tables of Assignment 2 give
R.H. =51% and Td = 10 °C.
For very humid air Twb will only be
slightly below T.
The Basis of
Cloud Formation
Clouds will, or will not, form depending on the humidity of the air and
the temperature structure of the local atmosphere.
T usually decreases with height in troposphere. The decrease in T
with height is called the Environmental Lapse Rate, Ge (gamma e).
GE is the decrease in T for an increase of 1 km in
height
If T decreasing by 12 °C per kilometer
then GE = 12 °C/km
If T happens to be decreasing by only 5 °C per kilometer then GE = 5 °C/km
The Environmental Lapse Rate, GE, usually changes
from place to place and also with height over any one location.
Another lapse rate is the Dry Adiabatic Lapse Rate (DALR) or GD.
This describes how the temperature of a parcel of uncondensing
air would decrease if we raised it up through the atmosphere. If we let air
expand and do not supply heat to it, it will cool ADIABATICALLY. If we
compress air, and do not remove heat from it, it will heat up. Uncondensing air will cool upon lifting at the DALR if we
lift it up.
GD= g/Cp and has a fixed value of 10 °C/km
If we raise saturated air up it will also want to cool at the DALR but
the latent heat released from the condensing water vapour
will provide some extra heat so it will cool less quickly than if it were not
condensing and saturated.
Saturated, i.e. condensing, air will cool at the Wet Adiabatic
Lapse Rate (WALR) given by the symbol GW. The value
of GW depends on the specific humidity of the condensing
air. For warm condensing air GW is about
5°C/km. For cold condensing air GW is about 9°C/km.
i.e. GW = 5 - 9 °C/km
If we have air at 32 °C at the surface with a Tdew
of 2 °C and we lift it up to 1 km it will cool at DARL to 22 °C and its T will
still be greater than its Tdew so it will
not condense.
If we lift it to 2 km it will cool another 10 °C to 12 °C and still not
condense.
But if we lift it to 3 km it will cool to 2 °C. Here it will be
just at its Tdew and so start to condense
and form a cloud
The height at which it first condenses is called the CONDENSATION LEVEL
If we keep lifting it up it will now cool at the WALR so at 4 km up it
will have cooled to -3°C if GW = 5
°C/km.
But how can we lift air to make it form a cloud?
Air can lift itself because of Archimedes Principle - if something is
less dense than its surroundings it will experience an upward BUOYANCY FORCE
acting against gravity.
If air is warmer than its surroundings it will be less dense than its
surroundings and so will want to rise on its own (just like a hot air balloon)
- this air is unstable.
Reading:
TL&T 13th edition, Ch. 17., Waters Changes of State , p. 490-492
'Water's Changes of State, 11th p466-468; 10th
p434-436(9th p406-407)
'Understanding Air Pressure', 11th p502
;10th p470 (9th 442)
TL&T 13th edition, Ch. 17., Humidity: Water Vapor in the Air.
p. 492-495
TL&T 13th edition, Ch. 17.,
Measuring Humidity. p. 496-498
TL&T 13th edition, Ch. 17., The Basis of Cloud Formation p.
498-500