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Atmospheric Water. Global energy balance Atmospheric circulation Atmospheric water vapor Reading: Sections 3.3 and 3.4 for next Tues. Atmospheric Water. Global energy balance Atmospheric circulation Atmospheric water vapor. Radiation. Basic laws Stefan-Boltzman Law

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atmospheric water
Atmospheric Water
  • Global energy balance
  • Atmospheric circulation
  • Atmospheric water vapor
  • Reading: Sections 3.3 and 3.4 for next Tues
atmospheric water1
Atmospheric Water
  • Global energy balance
  • Atmospheric circulation
  • Atmospheric water vapor
  • Basic laws
    • Stefan-Boltzman Law
      • R = emitted radiation (W/m2)
      • T = absolute temperature (K),
      • and s = 5.67x10-8W/m2-K4
      • with e = emissivity (0-1)
        • Water, Ice, Snow (0.95-0.99)
        • Sand (0.76)

Valid for a Black body or “pure radiator”

“Gray bodies emit a proportion of the radiation of a black body

net radiation r n
Net Radiation, Rn

Ri Incoming Radiation

  • Ro =aRi Reflected radiation
  • = albedo (0 – 1)


Rn Net Radiation

Average value of Rn over the earth and

over the year is 105 W/m2

net radiation r n1
Net Radiation, Rn

H – Sensible Heat

LE – Evaporation

G – Ground Heat Flux

Rn Net Radiation

Average value of Rn over the earth and

over the year is 105 W/m2

energy balance of earth
Energy Balance of Earth












Sensible heat flux 7

Latent heat flux 23


diurnal variation
Diurnal Variation

Diurnal variation

of fluxes,

July 2003

San Marcos


Downward shortwave

Upward Longwave

Downward longwave

Upward shortwave


Fluxes in W/m2



energy balance in the san marcos basin from the narr july 2003
Energy Balance in the San Marcos Basin from the NARR (July 2003)

Note the very large amount of longwave radiation exchanged between land and atmosphere

Average fluxes over the day








Net Shortwave = 310 – 72 = 238; Net Longwave = 415 – 495 = - 80


Increasing carbon dioxide in the atmosphere (from about 300 ppm in preindustrial times)

We are burning fossil carbon (oil, coal) at 100,000 times the rate it

was laid down in geologic time

atmospheric water2
Atmospheric Water
  • Global energy balance
  • Atmospheric circulation
  • Atmospheric water vapor
heating of earth surface
Heating of earth surface is uneven

Solar radiation strikes perpendicularly near the equator (270 W/m2)

Solar radiation strikes at an oblique angle near the poles (90 W/m2)

Emitted radiation is more uniform than incoming radiation

Heating of earth surface

Amount of energy transferred from equator to the poles is approximately 4 x 109 MW

hadley circulation
Hadley circulation

Atmosphere (and oceans) serve to transmit heat energy from the equator to the poles

Warm air rises, cool air descends creating two huge convective cells.

conservation of angular momentum coriolis force
Conservation of Angular Momentum (Coriolis Force)

No external forces on air, so mV1r1 = mV2r2


r1 < r2 so V1 > V2


Intertropical Convergence Zone







Earth rotation

Looking down from North Pole, earth is rotating


Near equator, air starts to “fall behind” the earth

atmospheric circulation
Atmospheric circulation

Circulation cells

Polar Cell

  • Hadley cell
  • Ferrel Cell
  • Polar cell

Ferrel Cell


  • Tropical Easterlies/Trades
  • Westerlies
  • Polar easterlies


  • Intertropical convergence zone (ITCZ)/Doldrums
  • Horse latitudes
  • Subpolar low
  • Polar high
effect of land mass distribution
Effect of land mass distribution

Uneven distribution of land and ocean, coupled with different thermal properties creates spatial variation in atmospheric circulation

A) Idealized winds generated by pressure gradient and Coriolis Force. B) Actual wind patterns owing to land mass distribution

shifting in intertropical convergence zone itcz
Shifting in Intertropical Convergence Zone (ITCZ)

Owing to the tilt of the Earth\'s axis in orbit, the ITCZ shifts north and south. 

Southward shift in January

Creates wet Summers (Monsoons) and dry winters, especially in India and SE Asia

Northward shift in July

itcz movement
ITCZ movement

atmospheric water3
Atmospheric Water
  • Global energy balance
  • Atmospheric circulation
  • Atmospheric water vapor
atmospheric water4
Atmospheric water
  • Atmospheric water exists
    • Mostly as gas or water vapor
    • Liquid in rainfall and water droplets in clouds
    • Solid in snowfall and in hail storms
  • Accounts for less than 1/100,000 part of total water, but plays a major role in the hydrologic cycle
water vapor
Water vapor

Suppose we have an elementary volume of atmosphere dV and

we want quantify how much water vapor it contains

Water vapor density


ma = mass of moist air

mv = mass of water vapor

Air density

Atmospheric gases:

Nitrogen – 78.1%

Oxygen – 20.9%

Other gases ~ 1%\'s_atmosphere.html

specific humidity q v
Specific Humidity, qv
  • Specific humidity measures the mass of water vapor per unit mass of moist air
  • It is dimensionless
vapor pressure e
Vapor pressure, e
  • Vapor pressure, e, is the pressure that water vapor exerts on a surface
  • Air pressure, p, is the total pressure that air makes on a surface
  • Ideal gas law relates pressure to absolute temperature T, Rv is the gas constant for water vapor
  • 0.622 is ratio of mol. wt. of water vapor to avg mol. wt. of dry air (=18/28.9)
dalton s law of partial pressures
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. In other words, Dalton maintained that since there was an enormous amount of space between the gas molecules within the mixture that the gas molecules did not have any influence on the motion of other gas molecules, therefore the pressure of a gas sample would be the same whether it was the only gas in the container or if it were among other gases.

avogadro s law
Avogadro’s law

Equal 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 6.023 X 1023 in 22.41 L for all gases.

Dry air ( z = x+y molecules)

Moist air (x dry and y water vapor)

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

Md ~ 0.22*32+0.78*28

~ 28.9

Water vapor (H2O)

Mv = 2*1 + 16 = 18

rd = (x+y) * Md/Volume

rm = (x* Md + y*Mv)/Volume

Moist air is lighter than dry air

rm < rd, thus moist air is less dense than dry air

saturation vapor pressure e s
Saturation vapor pressure, es

Saturation vapor pressure occurs when air is holding all the water vapor

that it can at a given air temperature

Vapor pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m2

1 kPa = 1000 Pa

relative humidity r h
Relative humidity, Rh



Relative humidity measures the percent

of the saturation water content of the air

that it currently holds (0 – 100%)

dewpoint temperature t d
Dewpoint Temperature, Td




Dewpoint temperature is the air temperature

at which the air would be saturated with its current

vapor content

water vapor in an air column
Water vapor in an air column
  • We have three equations describing column:
    • Hydrostatic air pressure, dp/dz = -rag
    • Lapse rate of temperature, dT/dz = - a
    • Ideal gas law, p = raRaT
  • Combine them and integrate over column to get pressure variation elevation



Element, dz


precipitable water
Precipitable Water
  • In an element dz, the mass of water vapor is dmp
  • Integrate over the whole atmospheric column to get precipitable water,mp
  • mp/A gives precipitable water per unit area in kg/m2



Element, dz

Area = A