Atmospheric Moisture Vapor pressure (e, Pa) The partial pressure exerted by the molecules of vapor in the air. Saturation vapor pressure (e s, Pa ) The vapor pressure when in equilibrium with a plane surface of pure water. Only function of T. L=2.5E6 J/kg, latent heat of vaporization at 0 o C. Rv= 461 JK -1 kg -1, gas constant of water vapor Mixing ratio ( kg/kg or g/kg)

Atmospheric Moisture > Saturation mixing ratio (skew-T log-P diagram) function of P & T

Atmospheric Moisture Dew point (same unit as temperature) (T d ) The temperature at which saturation would occur if moist air was cooled isobarically (at constant pressure). xx TdTd T

Atmospheric Moisture Wet Bulb Temperature (T w ) The lowest temperature that can be reached by evaporating water into the air. xx TdTd T TwTw Evaporative cooling

Atmospheric Moisture Dew point (same unit as temperature) (T d ) The temperature at which saturation would occur if moist air was cooled isobarically (at constant pressure) Wet Bulb Temperature (T w ) The lowest temperature that can be reached by evaporating water into the air. Virtual temperature (T v ) Rather than use a gas constant for moist air, which is a function of moisture, 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.

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.

Atmospheric Moisture

If T = 300 K, p = 1000 mb, and e = 15 mb, what is the value of T v ? Moist air is less dense than dry air; therefore, T v is always greater than T. However, even for very warm, moist air T v exceeds T by only a few degrees.

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

How to find from a skew-T log-P diagram? TdTd T 303 K

Atmospheric Moisture Equivalent potential temperature Convert all latent heat to sensible heat and return to 1000 mb It is approximately conserved during the moist process. Relative humidity (RH)

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, so is vertical velocity. As a result, the pressure distribution in the vertical is hydrostatic, i.e., at any height, Pressure = weight of air mass above/area or ~ 1 cm/s

Atmospheric Pressure – Altitude calculations Replace density with the idea gas law for dry air Rearranging, approximating T to T v, and integrating from z 1 to z 2 If the column is isothermal (T =constant),

Atmospheric Pressure – Altitude calculations If the column is isothermal (T =constant), z 2 -z 1 is called the thickness of the layer between p 2 and p 1. Setting p 1 equal the surface pressure p s, and solving for p 2 gives, -- Hypsometric equation => Thickness is proportional to

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 (e-folding). If is 280 K, what is H?~ 8-9 km hPa thickness

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

Atmospheric Pressure – Altitude calculations We had Substituting and integrating to find p 2 at Z 2 gives: =>

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. Z 1, T 1, P 1 P 2 ?, Z 2, T 2 Step1: Calculate  and then P 2 Step 2: Calculate  and then P 3 P 3 ?, Z 3, T 3

Atmospheric Pressure – Altitude calculations In most meteorological work, p is used as the vertical coordinate (like, 500-mb surface) rather than geometric altitude. If pressures are known and z of a pressure surface needs to be computed, the corollary equation for a layer with a known lapse rate is:

Atmospheric Pressure – Altitude calculations Potential temperature From an Oakland sounding

Atmospheric Pressure – Altitude calculations How to calculate the lapse rate at each layer?

Atmospheric Pressure – Altitude calculations Potential temperature From an Oakland sounding θ decreases with height, absolutely unstable.

How to Calculate Sea Level Pressure Why we need sea level pressure? How to calculate it? Estimate the lapse rate (can use the first few layer data from radiosonde) Calculate T slp using surface height, z s, and T s. Then calculate p slp using p s, T s, and T slp.