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Monday, Oct. 2:
Clear-sky radiation; solar attenuation,Thermal
nomenclature
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Sun Earth
Y-axis: Spectral radiance, aka monochromatic intensity units: watts/(m^2*ster*wavelength)
Blackbody curves provide the envelope to Sun, earth emission
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Sun Earth
visible
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1 Angstrom=10-10 m.
Photoionization @ wavelengths < 0.1 micron (1000 angstroms)Photodissociation @ wavelengths < 0.24 microns: O2 -> 2OOzone dissociation @wavelengths < 0.31 micron
Depth of penetraion into earth’s atmosphere of solar UV
Visible spectrum 0.39 to 0.76 micron
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Thermal Radiation: • scattering negligible• absorption,emission is what mattersMath gets complicated: thousands of absorption lines, eachvarying individually with pressure, temperature
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natural
Natural
Doppler broadening: Half-width goes as T1/2
Lorentz (Pressure)broadening: Half-width goes asP/T(0.5-1.0)
(Freq shift)/half-width
abso
rptio
n
< 20 km, pressure broadening> 50 km Doppler broadening
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Continuing efforts to improve databaseon line absorption strengths andHalfwidths: H20 continuum,Microwave lines, are examples
16 micron 7 micron
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Radiation transmits through an atmospheric layerAccording to:
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I = intensity= air densityr = absorbing gas amountk =mass extinction coeff.
rk = volume extinction coeff.Inverse length unit
Extinction=scattering+absorption
Path length ds
+J dsemission
Thermal
~ 0
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T = e-sec
Beer’s Law used to assess solar constant in pre-satellitedays, now used to calibrate instrumentation & determineaerosol&cloud optical depth from ground
Langley plot
Ln (Iinf/I) =sec
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dI = -I kabs sec dz
Transmission through a layer, ignoring scattering and emission:
After integration:
T = e-sec
T = transmissivity; = optical depth, or thickness
Beer’s Law or Lambert’s Law
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Consequence: mostradiation is absorbed/emittedat an optical depth of 1.
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Limb Effects
darkening
brightening
affects ALL terrestrialremote sensing
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Limb Sounding as a Remote Sensing Technique:• first get the temperature from Planck function radiance• then use radiance in an absorbing/emitting wavelengthto get atmospheric concentration at that height
HIRDLS
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To calculate the broadband infrared emission,One simplification is to group lines together,Use spectral-band-average values for absorption -“band” models.
A more elegant solution is to group lines bytheir absorption lines strengths, and integrateover that.
Only works in infrared
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attenuation emission
Full radiative transfer equation for infrared/microwave(I.e. ignores scattering):
Plane-parallel approximation: the earth is flat.-> the temperature, atmospheric density is a function ofheight (or pressure) alone. Curvature of earth ignored,atmosphere assumed to be horizontally homogeneous.
Flux density
with “flux transmissivity”
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Radiative heating rate profiles:
Manabe & Strickler, 1965
-or-
Cooling to space approximation:Ignore all intervening layers
Rodgers & Walshaw, 1966, QJRMS
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Remote temperature sensing• CO2 particularly suited (well-mixed & emissive)
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(what part of the Earth is this from ?)
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Weighting function
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If scattering is also included:
3 radiatively-important scatterer parameters:
• optical depth (how much stuffIs there ?)
• single-scattering albedo ksca/(kscat + kabs) (how much got
Scattered rather than absorbed ?)
• asymmetry parameter g, or phase function P(cos :(describe how it scatters)
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Wednesday:
• results from top of atmosphere radiationBalance
• questions up to 4.40
• some other aerosol, greenhouse gas,results
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Whether/how solar radiation scatters when it impactsgases,aerosols,clouds,the ocean surface depends on
1. ratio of scatterer size to wavelength:
Size parameter x = 2*pi*scatterer radius/wavelength
X large
X small
Sunlight on a flat oceanSunlight on raindrops
IR scattering off of air, aerosolMicrowave scattering off of clouds
Microwave(cm)
Scattering neglected