)
Thermodynamic variables
Vapor pressure (e)
The atmospheric pressure due to water vapor.
Saturation vapor pressure ()
The saturation vapor pressure is a function
of temperature and it can be computed using the Clausius-Clapeyron
equation. There are other empirical formulas, such as the Tetan's
formula or the WMO formula based on curve fitting the laboratory
data.
Mixing ratio
where 
is the mass
of water vapor and 
is the mass of dry
air.
Divide by the volume V,
where 
is the density
of the water vapor and 
is the density
of the dry air.
Saturation mixing ratio
Specific humidity
Saturation specific humidity
In weather analysis, the difference between
the mixing ratio and the specific humidity is often ignored and
they are often used interchangeably.
Relative humidity
First law of thermodynamics (two forms)
where 
Dry adiabatic process dq = 0
Divide by the equation of state
we get
or 
Integrate this equation over any two pressure
levels of 
and 
with
temperatures of 
and 
or 
where 
This equation relates the change of temperature
due to the change of pressure under the dry adiabatic process.
Example:
Suppose at Lake Tahoe the pressure is 850
mb and the temperature is 5°C, and at Davis the pressure
1000 mb and the temperature is 10°C. If an air parcel is
brought from Lake Tahoe to Davis dry adiabatically, what will
be its temperature? (Answer: 18°C)
Potential temperature (
)
If an air parcel has a temperature of T
and pressure of p. The potential temperature of this air parcel
is the temperature after it is brought dry adiabatically to 1000
mb.
Substitute 
, 
,
, and
we get,
Be sure to use mb as the unit for 
when use this equation.
In the above example, the potential temperature
of Lake Tahoe is 18°C or 291K. The potential temperature
of Davis is 10°C or 283K. Davis is warmer than Lake Tahoe
but the air at Lake Tahoe is comparatively warmer if the air at
the two places is brought to the same reference level. This reference
level can be any level but we have chosen 1000 mb as the reference
level.
The value of 
does
not change for an air parcel under a dry adiabatic process. In
the above example, 
=291K for the air parcel
at Lake Tahoe. It is still 291K after it is brought dry adiabatically
to Davis or anywhere along the way to Davis.
Moist (or saturated) adiabatic process
In this process, the parcel is saturated.
There is no heat exchange between an air parcel and its environment
but condensation will provide latent heating to the air parcel.
The amount of condensation equals the decrease in the saturation
mixing ratio (
), and the amount latent
heat released by condensation can be written as:
where L is the latent heat of condensation,
which is 2500 x 
at 0°C.
Equivalent potential temperature (
)
is approximately
conserved during the moist adiabatric process.
Construction of the skew T - log p chart
There are 5 sets of lines in a skew T chart.
1. "y" coordinate is -log p
p - log p T (
=293K)
T (
) T(
=293K)
100 -2.00 -121.3
200 -2.30 -88.1
300 -2.48
400 -2.60 -47.5 0.3
500 -2.70
600 -2.78 -19.8 6.1
700 -2.85
800 -2.90 1.9 10.3
900 -2.95
1000 -3.00 20 13.7
2. "x" coordinate is T but it
is skewed 45° from the lower left to the upper right direction.
3. Dry adiabatic lines (
=
const)
For a given 
, the
temperature of the dry adiabatic line at every pressure level
can be computed by using:
Example:
For 
=293K, we can
compute T for every p, as shown in the third column of the about
table, and plot the dry adiabatic (or constant 
)
line on the skew T chart. The lines are labeled in °C.
4. Saturation mixing ratio lines (
=
const)
For a given 
, we
can compute the temperature of the saturation mixing ratio at
every pressure level and plot the constant saturation mixing ratio
line on the skew T chart. This computation can be simplified
is we assume
and relate 
to T
through the Clausius-Clapeyron equation. A more accurate method
using the empirical formulas is necessary to plot the constant
saturation mixing ratio lines on a skew T chart.
5. Moist (of saturation) adiabatic line
(
= const)
For a given 
, the
temperature of the saturated adiabatic line at every pressure
level can be computed using
However, this equation is only an approximation
and a more accurate computation using iterative method is needed
to plot an accurate moist (or saturated) adiabatic line on the
skew T chart. Furthermore, constant 
line and constant 
are identical on the
skew T chart and the lines are labeled with the constant 
in °C.
Plotting of the skew T chart.
Temperature
Mixing ratio (or dew point temperature)
Wind speed and direction
Determine the properties of an air parcel
using the skew T chart
Mixing ratio
Saturation mixing ratio
Vapor pressure
Saturation vapor pressure
Relative humidity
Potential temperature
Dew point temperature
Wet-bulb temperature
Web-bulb potential temperature
Equivalent temperature
Equivalent potential temperature
Virtual temperature
Lifting of an air parcel
Required data: Temperature and mixing ratio
(or dew point temperature) of the air parcel to be lifted.
Lifting condensation level
Level of free convection
Equilibrium level
If there is no mixing between the air parcel and the environment, these levels will not depend on the temperature and dew point sounding.