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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

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

Continuing efforts to improve databaseon line absorption strengths andHalfwidths: H20 continuum,Microwave lines, are examples

16 micron 7 micron

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

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.

Limb Effects

darkening

brightening

affects ALL terrestrialremote sensing

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

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

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”

Radiative heating rate profiles:

Manabe & Strickler, 1965

-or-

Cooling to space approximation:Ignore all intervening layers

Rodgers & Walshaw, 1966, QJRMS

Remote temperature sensing• CO2 particularly suited (well-mixed & emissive)

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(what part of the Earth is this from ?)

Weighting function

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

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