Vapor pressure e

1
Atmospheric Moisture

• Vapor pressure (e)
• The partial pressure exerted by the molecules
  of vapor in the air.
• Saturation vapor pressure
• The vapor pressure when in equilibrium with a
  plane surface of pure water. Only function of T.
• Mixing ratio ( kg/kg or g/kg)

2
Atmospheric Moisture

• Saturation mixing ratio

3
Atmospheric Moisture

• Dew point (same unit as temperature) (Td)
• The temperature at which saturation would
  occur if moist air was cooled isobarically (at
  constant pressure).

x
x
Td
T
4
Atmospheric Moisture

• Wet Bulb Temperature (Tw)
• The lowest temperature that can be reached by
  evaporating water into the air.

x
x
T
Td
Tw
5
Atmospheric Moisture

• Dew point (same unit as temperature) (Td)
• The temperature at which saturation would
  occur if moist air was cooled isobarically (at
  constant pressure)
• Wet Bulb Temperature (Tw)
• The lowest temperature that can be reached by
  evaporating water into the air.
• Virtual temperature (Tv)
• Rather than use a gas constant for moist air,
  it is more convenient to retain the gas constant
  for dry air and define a new temperature (called
  virtual temperature) in the equation of the ideal
  gas law.

6
Atmospheric Moisture

• Virtual temperature (Tv) (continue)
• The virtual temperature is the temperature
  that dry air must have in order to have the same
  density as the moist air at the same pressure.

7
Atmospheric Moisture
8
Atmospheric Moisture

• If T 300 K, p 1000 mb, and e 9 mb, what is
  the value of Tv ?
• Moist air is less dense than dry air therefore,
  Tv is always greater than T.
• However, even for very warm, moist air Tv exceeds
  T by only a few degrees.

9
Atmospheric Moisture

• Equivalent potential temperature
• Convert all latent to sensible heat and
  return to 1000 mb
• It is approximately conserved during the
  moist process.

• Relative humidity (RH)

10
How to find from skew-T log-P diagram?
T
Td
11
Atmospheric Pressure Altitude calculations

• Pressure is an important thermodynamic variable
  in itself and gradients in pressure drive the
  wind!
• In most places, most of the time, the vertical
  accelerations in atmosphere are quite small.
• As a result, the pressure distribution in the
  vertical is hydrostatic, i.e., at any height,
• Pressure weight of air mass above/area
• or

Storm
12
Atmospheric Pressure Altitude calculations

• Replace density with the idea gas law for dry air
• Rearranging, approximating T to Tv, and
  integrating from z1 to z2
• If the column is isothermal (T constant),

13
Atmospheric Pressure Altitude calculations

• If the column is isothermal (T constant),
• z2-z1 is called the thickness of the layer
  between p2 and p1.
• Setting p1 equal the surface pressure ps, and
  solving for p2 gives,

-- Hypsometric equation
14
Atmospheric Pressure Altitude calculations

• Where H is the scale height or the height in an
  isothermal atmosphere where the pressure has
  fallen to 1/e of its surface value.

15
Atmospheric Pressure Altitude calculations

• In reality, T is not a constant with height but
  decreases with increasing altitude in the
  troposphere. Hence, we need to account for this
  temperature variation when integrating the
  hydrostatic equation.
• Assuming
• Then

16
Atmospheric Pressure Altitude calculations

• We had
• Substituting and integrating to find p2 at Z2
  gives

gt
17
Atmospheric Pressure Altitude calculations

• With these relations, p at any altitude or the
  altitude of any pressure level can be calculated.
  Typically the T lapse rates are assumed constant
  through discrete layers so the integration
  derived above is done piecewise through layers
  for which is approximately constant in each
  layer.
• In most meteorological work, p is used as the
  vertical coordinate rather than geometric
  altitude (like, 500-mb surface).
• If pressures are known and z of a presure surface
  needs to be computed, the corollary equation for
  a layer with a known lapse rate is

18
Atmospheric Pressure Altitude calculations
Potential temperature
19
Atmospheric Pressure Altitude calculations

• How to calculate lapse rate?

20
Atmospheric Pressure Altitude calculations

• Skew-T Log-P diagram

21
Atmospheric Pressure Altitude calculations
Poisson equation
1 and 2, which one change faster?
22
How to Calculate Sea Level Pressure

• Why we need sea level pressure?
• How to calculate it?
• Estimate the lapse rate
• Calculate Tslp using surface height, zs, and Ts
• Calculate pslp