Atmospheric Moisture

1. Atmospheric Moisture • Vapor pressure (e, Pa) The partial pressure exerted by the molecules of vapor in the air. • Saturation vapor pressure (es, 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 0oC. Rv= 461 JK-1kg-1, gas constant of water vapor • Mixing ratio ( kg/kg or g/kg)

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

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. Evaporative cooling 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, 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.

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 = 15 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 heat to sensible heat and return to 1000 mb It is approximately conserved during the moist process.

10. How to find from a skew-T log-P diagram? 303 K T Td

11. 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)

12. 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

13. 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),

14. => Thickness is proportional to 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

15. 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 1000-500 hPa thickness

16. 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

17. Atmospheric Pressure – Altitude calculations • We had • Substituting and integrating to find p2 at Z2 gives: =>

18. 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. P3?, Z3, T3 Step 2: Calculate G and then P3 P2?, Z2, T2 Step1: Calculate G and then P2 Z1, T1, P1

19. 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:

20. Atmospheric Pressure – Altitude calculations From an Oakland sounding Potential temperature

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

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

23. 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 Tslp using surface height, zs,and Ts. Then calculate pslpusing ps,Ts, and Tslp .