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Science 123
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Spring 2020
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Atmospheric Moisture
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Atmospheric Vapor
Water's ability to exist, simultaneously in time and space, in all thre phases (ice, liquid and vapor) imparts great importance to its existence in the grant scheme of atmospheric phenomena. The change in phase allows great transport of latent heat. Of course, the precipitation of water in liquid or frozen form constitutes much of what we call "weather" on a daily basis. The extreme importance of water in the atmospheric system requires a careful look and how we measure vapor content in an atmopheric parcels and charaterize the "moistness" of the atmosphere.
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Total Pressure and partial pressure (video)
$P_T = \sum_{i = 1}^{n} P_i$ The total pressure $P_T$ of a parcel is the sum of the partial pressures $P_i$ exerted by its $n$ constituents.
$P_T = P_{N_2} + P_{O_2} + P_{Ar} + ... + P_{H_2O}$
The vapor partial pressure $P_{H_2O}$ will be denoted by $e$.
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Saturation vapor pressure (video)
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$e_s$ = saturation vapor pressure, occurs when the evaporation rate is equal to the condensation rate
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depends heavily on temperature
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not so much on pressure
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The Clausius-Clapeyron equation (video)
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$\displaystyle{e_s = e_0\cdot \mbox{exp}\left( \left[\frac{L}{R_v}\left(\frac{1}{T_0} - \frac{1}{T} \right)\right]\right) = e_0\cdot \mbox{exp} \left( \left[\frac{L}{R_v}\left(\frac{T - T_0}{T_0 \cdot T} \right)\right]\right)}$
gives the saturation vapor pressure, $e_s$, as a function of temperature $T$.
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$L$ = heat of vaporization (over a water surface) = 2.50 $\times 10^6$ J $\cdot$ kg$^{-1}$ or heat of sublimation (over an ice surface) =2.83 $\times 10^6$ J $\cdot$ kg$^{-1}$
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$R_v$ = 461 J $\cdot$ K$^{-1}$ kg$^{-1}$ is the gas constant for water vapor
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$T_0$ = 273
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$e_0$ = 6.11 mb, the saturation vapor pressure for $T$ = 273 K. ($e_s(T_0) = e_s(273) = e_0 = 6.11$ mb)
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Saturation vapor pressure - over water versus over ice (video)
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$e_s^w$ = saturation vapor pressure for water. A plot of the Clausius-Clapeyron curve for water.
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$e_s^i$ = saturation vapor pressure for ice. A plot of the Clausius-Clapeyron curves for water and ice.
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A plot of saturation vapor pressure of water and saturation vapor pressure over ice difference ($e_s^w$ - $e_s^i$).
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Dew point temperature $T_d$ (video)
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The dew point temperature is the temperature at which the parcel's vapor pressure $e$ would be the saturation vapor pressure $e_s$. The parcel's temperature $T$ is always greater than or equal to the parcels dew point temperature $T_d$ ($T_d \le T$).
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For condesation to occur in the parcel (a cloud to form), the temperature of the parcel will have to be as low (or near as low) as it's dew point temperature $T_d$.
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Saturation Vapor Pressure and Satuation Mixing Ratio (video)
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Moisture Measures: The following formulas are calculated for a given parcel of air
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Mixing ratio
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$MR = \frac{\mbox{mass of water vapor}}{\mbox{mass of dry air}} = \displaystyle{\frac{\epsilon \cdot e}{P - e}}$
where $\displaystyle{\epsilon = \frac{R_d}{R_v} = \frac{287}{461} = 0.622}$, $R_d$ = 287 J $\cdot$ K$^{-1}$ $\cdot$ kg$^{-1}$ is the gas constant for dry air, and $P$ is the total pressure on the parcel
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Specific humidity - (not covered)
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$SH = \frac{\mbox{mass of water vapor}}{\mbox{mass of air}}$
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Absolute humidity - (not covered)
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$AH = \frac{\mbox{mass of water vapor}}{\mbox{volume}}$
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Relative humidity
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$RH = \displaystyle{\frac{e}{e_s}} \times 100 = \frac{MR}{MR_s} \times 100 $
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Dew point and relative humidity
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$RH = \displaystyle{\frac{e(T_d)}{e_s(T)}} \times 100 $
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Measurement Facts
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Mixing ratio is not dependent on the parcel's temperature. It does depend on its vapor pressure $e$ and the pressure $P$.
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Dew point is not a function of parcel temprature. It depends on the parcel's vapor pressure only.
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Relative humidity: Even though it is commmonly used as a moisture measure, it dependes on both the parcel's temperature and its vapor pressure. For example, if the parcel's vapor pressure remains constant, it's relative humidity will increase during the day as the parcel warms, and decrease at night as the parcel cools.
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Exercise Videos