Moisture Relationships

Troposphere

Tropopause barrier!

Moisture Relationships• Atmospheric Moisture is necessary for Precipitation.

That moisture is moved to the atmosphere by Evaporation and Transpiration

Humidity• The presence of moisture (water vapor, an

invisible gas) in the atmosphere is measured by the humidity of the air.

• Humidity and condensation are closely related as condensation inevitably occurs when the air is saturated with moisture (100% humidity).

“Latent Heat of Condensation”Gas to liquid droplet, heat is released to the atmosphere, air molecules move faster, move apart, less dense, rise

585 calories/gram

Some useful units• One Gram is the mass of liquid water in a little cube, one

centimeter on a side.

• A centimeter is less than half an inch. It is 1/100 of a meter.

• A meter is 39.37 inches, so a centimeter is about 0.394 inches

• A mole of anything is 6.023 x 1023

• 1023 means 10x10x10x10x10x … x10 twenty three times

Relative Humidity and Dew Point• Absolute humidity measures the amount of water vapor in

air. Grams H2O/m3 of air. This water is a gas, water vapor.

• Relative humidity measures the amount of water vapor in air relative to the maximum amount of water vapor the air could hold at that temperature.

• Relative humidity increases with increasing water vapor or decreasing temperature. Cold air can’t “carry” as much water vapor as warm air.

• The dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapor to condense into liquid water.

Absolute Humidity• Absolute humidity measures the amount (mass) of

water in a volume of air. Units are gramsH2O/meters3

• Problem: volume changes as parcel rises

So we will need some measures of humidity that do not depend on volume.

Same # grams in a larger volume, so abs. humidity decreases

25oC 72oF12oC

53.6oF

Various Temperature Scales

298.15K285.15K

oC = 5/9(F- 32) K=oC + 273.15

Gas Laws

• 1600’s to 1800’s

• Combined as ideal gas law:• n= # moles, and R is the universal gas constant• R = 8.314472 N·m·K−1·mol−1

Pressure times Volume is a constant

Increase Temp, Volume increases

Increase Temp, Pressure increases

Increase moles of gas, Volume increases

Md ~ 0.21*32+0.78*28 ~ 28.9

Avogadro’s lawEqual volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties. This number (Avogadro's number) is 6.022 X 1023 . These occupy 22.41 L for all gases at temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of 100 kPa.

Dry air (21% O2, 78% N2, 1% other )

Water vapor (H2O)

Dry air Moist air

Mv = 2*1 + 16 = 18

Moist air is lighter than dry air because number of Moist air is lighter than dry air because number of molecules is the same for equal volumes, and water is molecules is the same for equal volumes, and water is lighter than Olighter than O22 or N or N22

Moist Air vs. Dry Air 1• Air with water vapor in it (Moist Air) is lighter than

dry air Here’s Why:

• When water vapor H2O is added to air, other gases are pushed aside.

(Avogadro’s Law, # mol/vol = const)

• Recall that dry air is mostly Nitrogen N2 and Oxygen O2 molecules.

Moist Air vs. Dry Air 2 OR “why moist air rises”

• Water H2O “weighs” 18 grams per mole.

• Nitrogen N2 “weighs” 28 grams per mole

• Oxygen O2 “weighs” 32 grams per mole

• The number of molecules in air in some volume at constant T and P is constant.

• Since light water molecules displace much heavier molecules, air with water vapor in it is “lighter”, less dense, more buoyant. Moist air rises, forms storms.

Dalton’s Law of Partial Pressures

John Dalton studied the effect of gases in a mixture. He observed that the Total Pressure of a gas mixture was the sum of the Partial Pressure of each gas.

P total = P1 + P2 + P3 + .......Pn

The Partial Pressure is defined as the pressure of a single gas in the mixture as if that gas alone occupied the container

Partial Pressure of water vapor e or ew

• Partial Pressure is the pressure that would be exerted on a surface by a gas in a mixture if the other gases were absent. e = esat(Td)

• The Partial Pressure of water vapor ew is given by a form of the Ideal Gas Law

ew = RT

0.622

• where 0.622 is the ratio of the molecular weights of water (18) to an average molecular weight for air (28.9).

• 1 mb [mbar, millibar] = 100 Pascals

ew = water vapor pressure in mbarsw = vapor density or absolute hum.R = Dry Air Gas ConstantR= 2.87 x 103 mbar cm3/g . KT = absolute temperature Kelvin

Mixing Ratio, • Air pressure, P, is the total

pressure that air makes on a surface

• Ideal gas law relates pressure to density and absolute temperature T.

• Vapor pressure, e, is the pressure that water vapor exerts on a surface. Rv is the gas constant for water vapor

• Mixing Ratio is the ratio of vapor mass to dry air mass v/dry

• 0.622 is ratio of mol. wt. of water vapor to avg mol. wt. of dry air (=18/28.9)

TRe vv

TRP

Notice this mixing ratio doesn’t depend on volume (the v’s in density cancel) , and so will stay constant as a parcel ascends

=

Curve Fits

• Complex situations, such as mixtures of gases, often defeat modeling because the assumptions of physical equations aren’t true.

• In this case we do many experiments, plot the data, and fit a curve to the data.

Saturation vapor pressure, esatSaturation vapor pressure occurs when air is holding all the water vaporthat it can at a given air temperature, then RH = 100% and T=Tdew point

Then T dry bulb = T wet bulb

pws = water vapor saturation pressure (Pa)e = the constant 2.718.......T = dry bulb temperature of the moist air (K)

http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html

http://hurri.kean.edu/~yoh/calculations/satvap/satvap.html

Relative Humidity• The relative humidity of an air-water mixture is defined as

the ratio of the partial pressure of water vapor in the mixture, called ew or e, to the saturated vapor pressure of water at a prescribed temperature, called e*w or esat. I prefer e and esat, respectively.

• Relative humidity is normally expressed as a percentage and is calculated by using the following equation:

• This equation is useful for calculating e from esat and RH

Saturated Air Properties Appendix Cvaries slightly

http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html

e sat

Dry Air Properties at std. atm. sea-level

Water Vapor Density Curve Fit

• The density of water vapor can be expressed as:

ρv = 0.0022 pv / T where• pv = e =partial pressure water vapor (Pa, N/m2)

• ρv = density water vapor (kg/m3)

• T = absolute dry bulb temperature (K)

http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html

Specific Humidity, qv

• Specific humidity measures the mass of water vapor per unit mass of moist air

• It is dimensionless• Like mixing ratio, it doesn’t

change with volume.

• We still need the moist air density.

Density of Moist Air, m

• m = P/RT (1 - 0.378 e /

• We need this to calculate the specific

humidity.• Derivation in the handout follows this.