Atmospheric Transmission Beer's Law

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3/31/10Optical thickness and transmittance of clouds• Note that N and r are difficult to measure, but we can measure or estimatethe cloud water density ρ w (typically 0.1-1 g m -3 )• For a monodisperse cloud, the cloud water density is N times the mass ofwater in each droplet:ρ w= N 4 3 πr 3 ρ l• where ρ l is the density of pure water (~1000 kg m -3 )• This gives us a new expression for the volume extinction coefficient:€ β e= NQ eπr 2 = k eρ w= k eN 4 3 πr 3 ρ l€• And solving for k e gives:k e= 3Q e4ρ lrNote inversedependence on r!€Rain and fogr ≈ 1 mmk e = 1.5 m 2 kg -1ρ w = 0.1 g m -3Q e ≈ 2 at visible wavelengthsk e= 3Q e4ρ lrr ≈ 10 µmk e = 150 m 2 kg -1ρ w = 0.1 g m -3β e = 0.15 km -1β e= k eρ wβ e = 15 km -1€€28
3/31/10Indirect Effect in Nature (from MODIS)What are these?MODIS visible image; Atlantic coast of Europe; January 27, 2003Ship TracksShip Ship Exhaust CDNC = Cloud Droplet Number Concentration(# cloud condensation nuclei)⎡⎡ 9πL 2 Hτ* = Q e ⎢⎢ 2⎣⎣ 16ρ l⎤⎤N⎥⎥⎦⎦13L = liquid water path, H = geometric cloud thicknessi.e. Optical thickness proportional to N 1/3€29
Page 1 and 2: 3/31/10Atmospheric TransmissionBeer
Page 3 and 4: 3/31/10Extinction of radiation• A
Page 5 and 6: 3/31/10• β e = β a + β sExtinc
Page 8 and 9: 3/31/10Properties of Beer’s Law
Page 10 and 11: 3/31/10Optical depth problemThe opt
Page 12 and 13: 3/31/10More Beer’s LawNow taking
Page 14 and 15: 3/31/10Deviations from Beer’s Law
Page 16 and 17: ONREMOTE CONTROLTX IN RX IN PPS-CON
Page 18 and 19: 3/31/10Slant and vertical atmospher
Page 20 and 21: 3/31/10Atmospheric transmittanceUV-
Page 22 and 23: 3/31/10Extinction and scattering by
Page 24 and 25: 3/31/10Measuring solar intensity fr
Page 26 and 27: 3/31/10Mass pathτ (z) = k aw 1ρ 0
Page 30 and 31: 3/31/10The Aerosol Indirect Effect

Atmospheric Transmission Beer's Law

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