Topic 3B: Moist Thermodynamics 10/13/09 MET 60 topic 03B

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 10/13/09 MET 60 topic 03B

mv = mass of water vapor in the air md = mass of dry air 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! 10/13/09 MET 60 topic 03B

e = wp/(w + ) Tv  T(1 + 0.61w) 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) 10/13/09 MET 60 topic 03B

dry air water Moisture parameters Saturation vapor pressure (es) Imagine a closed box with dry air above pure water at temperature T dry air water 10/13/09 MET 60 topic 03B

Vapor begins to collect, with vapor pressure e … evaporation Later… Vapor begins to collect, with vapor pressure e … evaporation moist air H2O molecules water 10/13/09 MET 60 topic 03B

Some vapor molecules return to the liquid … condensation Later still… Some vapor molecules return to the liquid … condensation moist air H2O molecules water 10/13/09 MET 60 topic 03B

Still later! Eventually … condensation = evaporation … saturation, with saturation vapor pressure es saturated air H2O molecules water 10/13/09 MET 60 topic 03B

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). 10/13/09 MET 60 topic 03B

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!! 10/13/09 MET 60 topic 03B

Saturation mixing ratio (ws) Using the gas law for both vapor and dry air, we get: 10/13/09 MET 60 topic 03B

Shown as green dashed lines on skew T-lnp diagrams Note… Shown as green dashed lines on skew T-lnp diagrams 10/13/09 MET 60 topic 03B

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) 10/13/09 MET 60 topic 03B

Dew point temperature (Td) The temperature to which air must be cooled (at constant pressure) so that saturation occurs At T = Td , w = ws and RH = 100%. 10/13/09 MET 60 topic 03B

T Td Td values are reported on weather maps (T – Td) = dew point depression = measure of how moist the air is T Td 10/13/09 MET 60 topic 03B

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 10/13/09 MET 60 topic 03B

Water evaporates from moist cloth cooling until Em is reached Wet bulb temperature 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 10/13/09 MET 60 topic 03B

Water occupies three phases: solid, liquid, vapor Latent heat Water occupies three phases: solid, liquid, vapor solid  liquid  vapor less energetic more energetic (molecules) 10/13/09 MET 60 topic 03B

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liquid water (lower energy)  vapor (higher energy) 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 10/13/09 MET 60 topic 03B

Solid (lower energy)  liquid (higher energy) 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 10/13/09 MET 60 topic 03B

Air rises & cools (@ adiabatic lapse rate) 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) … 10/13/09 MET 60 topic 03B

See http://wxpaos09.colorado.edu/windstorms/chinook.html 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 10/13/09 MET 60 topic 03B

Consider a parcel of unsaturated air forced to rise. 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… 10/13/09 MET 60 topic 03B

Environment cools less since  < d Suppose  < d This leads to… Parcel cools at d Environment cools less since  < d Thus, Tparcel < Tenv z Parcel rises to z2 Parcel at z1 Tparcel = Tenv 10/13/09 MET 60 topic 03B

T(parcel) < T(environment) when  < d (A) 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!!! 10/13/09 MET 60 topic 03B

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 10/13/09 MET 60 topic 03B

No vertical cloud development 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 10/13/09 MET 60 topic 03B

Unstable atmospheres… Characterized by: vertical cloud development Note: Vertical overturning motions destroy the instability by mixing! 10/13/09 MET 60 topic 03B

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! 10/13/09 MET 60 topic 03B

s = 6.5 C/km < env = 8 C/km < d = 10 C/km e.g., suppose s = 6.5 C/km < env = 8 C/km < d = 10 C/km This is called Conditional instability 10/13/09 MET 60 topic 03B