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Lecture 7 Water Vapor

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**Water Vapor amount in the air is variable.**

Concentration of water vapor can be quantified by: Vapor pressure Mixing ratio Specific humidity Absolute humidity Relative humidity Dew point depression Wet-bulb temperature

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**Warmer air can hold more water vapor at equilibrium than colder air.**

Air that holds this equilibrium amount is saturated. If air is cooled below the saturation temperature, some of the water vapor condenses into liquid, which releases latent heat and warms the air. Thus, temperature and water vapor interact in a way that cannot be neglected.

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**Saturation Vapor Pressure**

Air is a mixture of gases. All of the gases contribute to the total pressure. The pressure associated with any one gas in a mixture is called the partial pressure. Water vapor is a gas, and its partial pressure in air is called the vapor pressure. Symbol e is used for vapor pressure. Units are pressure units: kPa.

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**Saturation Air can hole any proportion of water vapor.**

For humidities greater than a threshold called the saturation humidity, water vapor tends to condense into liquid faster than it re-evaporates. This condensation process lowers the humidity toward the equilibrium (saturation) value. The process is so fast that humidities rarely exceed the equilibrium value.

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Saturation Thus, while air can hold any portion of water vapor, the threshold is rarely exceeded by more than 1% in the real atmosphere. Air that contains this threshold amount of water vapor is saturated. Air that holds less than that amount is unsaturated.

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Saturation The equilibrium (saturation) value of vapor pressure over a flat surface of pure water is given the symbol: es For unsaturated air, e < es Air can be slightly supersaturated (e > es). When there are no surfaces upon which water vapor can condense.

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**Saturation – Technical Definition**

Sealed Container Water Vapor Liquid Water

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**Water Vapor Fluxes Flux of water molecules from vapor to liquid**

Flux of water molecules from liquid to vapor

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Saturation Saturation exists when these two fluxes of water vapor are equal Flux of water molecules from vapor to liquid Flux of water molecules from liquid to vapor

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**Saturation Vapor Pressure**

Formula for es(T) called the Clausius-Clapeyron Equation Approximation: Where e0 = kPa, T = 273 K, Rv = 461 J K-1 Kg-1 is the gas constant for water vapor. Absolute temperature in Kelvins must be used for T.

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**Clausius-Clapeyron Equation**

This equation describes the relationship between temperature and saturation vapor pressure. Because clouds can consist of liquid droplets and ice crystals suspended in air, we must consider saturations with respect to water and ice.

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Teten’s Formula Is an empirical expression for saturation vapor pressure with respect to liquid water that includes the variation of latent heat with temperature. B = , T1 = K, T2 = K

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Exercise Calculate es(T) for T = 0C, 10C, 20C, 30C, 40C

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**Graph of Clausius-Clapeyron Equation**

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**System of Dry Air + Water Vapor**

Assume system is closed i.e., no exchange of mass with environment Dry air + water vapor

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**Saturation, Sub-Saturation, Super-Saturation**

Super-saturated air Saturated air Sub-saturated air

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**Super-Saturation and Condensation**

Suppose air becomes super-saturated “Excess” water vapor will condense

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**Supersaturation Supersaturation occurs when e > es**

Supersaturation is a temporary state Water vapor condenses until state of supersaturation is relieved

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**Humidity Variables Mixing Ratio**

the ratio of mass of water vapor to mass of dry air is called the mixing ratio, r or w. It is given by: (W&H 3.57) If neither condensation or evaporation take place, w of a parcel remains constant. Therefore, it is a conserved quantity. Units are g/g but is usually presented as g/kg, but when solving numerical problems, must be expressed as a dimensionless quantity: kg/kg or g/g.

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**Humidity Variables Mixing Ratio**

the ratio of mass of water vapor to mass of dry air is called the mixing ratio, r or w. It is given by: (Stull 5.3) Where ε = rd/rv = g vapor/g dry air is the ratio of gas constants for dry air to that for water vapor. r is proportional to the ratio of partial pressure of water vapor (e) to partial pressure of the remaining gases in the air (P-e).

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**Humidity Variables The saturated mixing ratio, rs,**

is where es is used in place of e. Units are g/g but is usually presented as g/kg: = grams of water vapor per kilogram of dry air.

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**Humidity Variables Specific Humidity**

The ratio of mass of water vapor to mass of total (moist+ dry) air, q, to a good approximation is given by: (Stull) (W&H)

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**Humidity Variables Absolute Humidity**

The concentration of water vapor in air is called the absolute humidity, and has units of grams of water vapor per cubic meter (g/ m3). Because absolute humidity is essentially a partial density, it can be found from the partial pressure using the ideal gas law for water vapor:

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**Humidity Variables Relative Humidity**

The ratio of actual amount of water vapor in the air compared to the equilibrium (saturation) amount at that temperature is called the relative humidity.

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**Cooling a Parcel -- Constant Pressure**

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Reminder Recall where nv = number of moles of water vapor and n = total number of moles i.e., e is proportional to p.

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**Cool the system at constant pressure**

Closed system nv and n remain constant e remains constant

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**Start with Sub-Saturated Air**

Cool air at constant pressure e

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**Cool at Constant Pressure**

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**Cool at Constant Pressure**

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**Cool at Constant Pressure**

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**Cool at Constant Pressure**

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**Cool at Constant Pressure**

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Saturation Achieved Continue to cool air e

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Super-Saturation! e

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Dew Dew forms when super-saturation occurs near a surface, e.g., a blade of grass

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DEW

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Dew Point (Td) Definition: The temperature at which saturation would first be achieved if the air were cooled at constant pressure

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**Temperature and Dew Point**

So, Td is the temperature that satisfies es(Td) = e. e Td T

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**Note If the Td < 0C and super-saturation occurs, frost forms**

Water vapor turns directly to ice Note: Frost is not frozen dew!

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Frost

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**Relative Humidity (RH)**

where w is the mixing ratio and ws is the saturation mixing ratio

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**Relative Humidity Approximation**

Simpler, as es is a function of T only.

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**Exercise Let T = 20.0C and e = 12.0 hPa**

Calculate RH using the approximate form First, calculate es(T)

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Increased Accuracy For greatest accuracy, use the exact form of RH and use tabulated values of ws Best source: Smithsonian Meteorological Tables (SMT)

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Supersaturation When condensation is occurring on a surface, a thin layer of air next to the surface is supersaturated i.e., RH > 100% Technically, Td > T where condensation is occurring However, Td – T is quite small and cannot be measured by standard instruments So, for practical purposes, Td T

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**(Adiabatic expansion due to falling pressure)**

Adiabatic Cooling (Adiabatic expansion due to falling pressure)

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**Closed system nv/n is constant**

But, p is decreasing Therefore, e is decreasing

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**RH of Expanding Parcel e is decreasing due to expansion**

But, parcel is cooling es is also decreasing It turns out that es decreases faster than e

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**e and es for a rising parcel**

z es decreases faster than e e decreases as parcel rises e es

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**e and es for a sinking parcel**

z es e

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**RH and Adiabatic Processes**

RH of a rising parcel increases condensation can occur if parcel can be lifted sufficiently RH of a sinking parcel decreases condensation will not occur if air is sinking

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**Lifting Condensation Level (LCL)**

Definition: Level at which saturation is first achieved if an air parcel is lifted adiabatically The LCL is usually an accurate indication of the height of the cloud base

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LCL z LCL e es

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