1. Topic 3B: Moist Thermodynamics
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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
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3. 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!
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4. 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( w)
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5. 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
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6. Vapor begins to collect, with vapor pressure e … evaporation
Later…
Vapor begins to collect, with vapor pressure e … evaporation
moist air
H2O molecules
water
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7. Some vapor molecules return to the liquid … condensation
Later still…
Some vapor molecules return to the liquid … condensation
moist air
H2O molecules
water
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8. Still later!
Eventually … condensation = evaporation … saturation, with saturation vapor pressure es
saturated air
H2O molecules
water
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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).
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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!!
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11. Saturation mixing ratio (ws)
Using the gas law for both vapor and dry air, we get:
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12. Shown as green dashed lines on skew T-lnp diagrams
Note…
Shown as green dashed lines on skew T-lnp diagrams
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13. Relative humidity (RH)
Depends strongly on temperature – not moisture content!
RH time of T-max (3-4 pm)
RH time of T-min (sunrise)
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14. 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%.
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15. T Td Td values are reported on weather maps
(T – Td) = dew point depression
= measure of how moist the air is T Td
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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:
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17. 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
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18. Water occupies three phases: solid, liquid, vapor
Latent heat
Water occupies three phases:
solid, liquid, vapor
solid  liquid  vapor
less energetic more energetic
(molecules)
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20. 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 fixed temperature
Water: at 1 atmosphere pressure and 100C,
Lv = 2.25x106 J/kg
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21. 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 fixed temperature
Water: at 1 atmosphere pressure and 0C,
Lm = 3.34x105 J/kg
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22. 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) …
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23. See http://wxpaos09.colorado.edu/windstorms/chinook.html
Upon descent, remaining vapor evaporates & air 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 foot of mountains (downwind) warmer than on upwind side
See
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24. 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 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…
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25. 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
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26. 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!!!
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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 to better understand stability and instability
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28. 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
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29. Unstable atmospheres… Characterized by: vertical cloud development
Note:
Vertical overturning motions destroy the instability by mixing!
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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!
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31. 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