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Topic 3B: Moist Thermodynamics

Topic 3B: Moist Thermodynamics. Thermodynamics of moist air Definitions of amount of water vapor in the air Latent heat Lapse rates for moist & saturated air Stability of rising (sinking) air The 2 nd Law of Thermodynamics. Moisture parameters Mixing Ratio ( w ) Defined as:

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Topic 3B: Moist Thermodynamics

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  1. Topic 3B: Moist Thermodynamics MET 60 topic 03B

  2. Thermodynamics of moist air • Definitions of amount of water vapor in the air • Latent heat • Lapse rates for moist & saturated air • Stability of rising (sinking) air • The 2nd Law of Thermodynamics MET 60 topic 03B

  3. Moisture parameters • Mixing Ratio (w) Defined as: mv = mass of water vapor in the air md = mass of dry air w is a dimensionless number and is small • So we express the value as “grams per kilogram” e.g., 20 g/kg • BUT in calculations, MUST use “kg per kg” value! MET 60 topic 03B

  4. Moisture parameters • Specific humidity (q) Defined as: q is also dimensionless and small Examples… 3.6 → p = total pressure 3.7 → e = wp/(w + ) TvT(1 + 0.61w) MET 60 topic 03B

  5. Moisture parameters • Saturation vapor pressure (es) Imagine a closed box with dry air above pure water at temperature T dry air water MET 60 topic 03B

  6. Later… Vapor begins to collect, with vapor pressure e … evaporation moist air H2O molecules water MET 60 topic 03B

  7. Some vapor molecules return to the liquid … condensation • Later still… moist air H2O molecules water MET 60 topic 03B

  8. Eventually … condensation = evaporation … saturation, with saturation vapor pressure es • Still later! saturated air H2O molecules water MET 60 topic 03B

  9. Saturation vapor pressure, es, depends strongly on temperature, So See Fig. 3.9 (red line). The dependence of es on T is given by the Clausius-Clapeyron equation (Eq. 3.92; not covered). MET 60 topic 03B

  10. Incidentally, for T < 0C (below freezing), es > esi SVP over plane surface of pure water SVP over plane surface of pure ice Fig. 3.9 (blue line) – Has consequences for growth of ice particles in moist air See cloud physics chapter!! MET 60 topic 03B

  11. Saturation mixing ratio (ws) Using the gas law for both vapor and dry air, we get: MET 60 topic 03B

  12. Note… Shown as green dashed lines on skew T-lnp diagrams MET 60 topic 03B

  13. Relative humidity (RH) Depends strongly on temperature – not moisture content! RH min @ time of T-max (3-4 pm) RH max @ time of T-min (sunrise) MET 60 topic 03B

  14. Dew point temperature (Td) The temperature to which air must be cooled (at constant pressure) so that saturation occurs At T = Td , w = wsand RH = 100%. MET 60 topic 03B

  15. Td values are reported on weather maps (T – Td) = dew point depression = measure of how moist the air is T Td MET 60 topic 03B

  16. Lifting condensation level (LCL) The altitude to which unsaturated air must be lifted in order to become saturated. • As moist air rises (adiabatically), temperature falls (at d while unsaturated) • Thus ws decreases since ws = ws (p,T) • Meanwhile w stays the same (no water added or lost) • Thus RH increases to 100% LCL marks cloud base level! Example: http://icleveland.blogspot.com/2007/09/fair-weather-cumulus-clouds.html MET 60 topic 03B

  17. Water evaporates from moist cloth • cooling until Em is reached Very dry air…process takes a long time and wet-bulb temp. Tw<< T Moist air…process takes short time and wet-bulb temp Tw T • Wet bulb temperature MET 60 topic 03B

  18. Latent heat Water occupies three phases: solid, liquid, vapor solid  liquid  vapor less energetic more energetic (molecules) MET 60 topic 03B

  19. MET 60 topic 03B

  20. Evaporation liquid water (lower energy)  vapor (higher energy) Must supply energy to the water to get evaporation Latent heat of vaporization (Lv) is the heat energy we must supply to a unit mass of substance to convert it from liquid to vapor @ fixed temperature Water: at 1 atmosphere pressure and 100C, Lv = 2.25x106 J/kg MET 60 topic 03B

  21. Melting Solid (lower energy)  liquid (higher energy) Must supply energy to the ice Latent heat of melting (Lm) is the heat energy we must supply to a unit mass of substance to convert it from liquid to vapor @ fixed temperature Water: at 1 atmosphere pressure and 0C, Lm = 3.34x105 J/kg MET 60 topic 03B

  22. Ascent & descent - Ex. 3.10 Consider unsaturated air forced to rise (e.g., over the Sierras or Rockies). • Air rises & cools (@ adiabatic lapse rate) • Upon saturation, latent heat is released as vapor condenses  clouds • Further cooling is at the saturated adiabatic lapse rate • Assume some condensed water falls out in precip (non-adiabatic process) • … MET 60 topic 03B

  23. Upon descent, remaining vapor evaporates & air warms @ saturated lapse rate • Once all clouds have evaporated, further warming is at dry adiabatic lapse rate • Since some water substance has been lost, this happens at a higher altitude on the downwind side • Hence – air arrives @ foot of mountains (downwind) warmer than on upwind side • See http://wxpaos09.colorado.edu/windstorms/chinook.html MET 60 topic 03B

  24. Air parcel stability Consider a parcel of unsaturated air forced to rise. As it rises, it cools @ adiabatic lapse rate. At some higher elevation (z), we ask: How does T(parcel) compare to T(environment)? Answer depends on environmental lapse rate () as follows… MET 60 topic 03B

  25. Parcel cools at d • Environment cools less since  < d • Thus, Tparcel < Tenv Suppose  < d This leads to… z Parcel rises to z2 Parcel at z1 Tparcel = Tenv MET 60 topic 03B

  26. Thus, T(parcel) < T(environment) when  < d (A) …and thus the parcel sinks back down Conversely… T(parcel) > T(environment) when  > d (B) …and the parcel continues to rise!!! MET 60 topic 03B

  27. Case (A) is the stable case… • if we push air up, it sinks back down Case (B) is the unstable case… • if we push air up, it then continues to rise • Exciting!!! Can get deep convection! See Fig. 3.17 to better understand stability and instability MET 60 topic 03B

  28. Stable atmospheres… Characterized by: • No vertical cloud development • Gravity waves seen in cloud imagery (Fig. 3.14) An inversion is where lapse rate  < 0 In this case,  < d and the atmosphere is very stable. Example: Bay Area in summer MET 60 topic 03B

  29. Unstable atmospheres… Characterized by: • vertical cloud development Note: Vertical overturning motions destroy the instability by mixing! MET 60 topic 03B

  30. Conditional instability… This is where moisture comes in!!! • Moist unsaturated air rises • Cools at d • Suppose  < d … stable so far! • BUT…if we reach saturation, parcel continues to cool at s • Suppose s <  … situation becomes unstable! MET 60 topic 03B

  31. e.g., suppose s = 6.5 C/km < env = 8 C/km < d = 10 C/km This is called Conditional instability MET 60 topic 03B

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