Electromagnetic Radiation

• Basic Radiometric Quantities
• Measures defining electromagnetic wave characteristics
• Wavelength - distance from peak to peak or trough to trough
• Units of length:
• Wave number - inverse of wavelength
• Units of length^-1:
• Frequency - number of peaks per unit time
• Units of time^-1:
• Monochromatic intensity or radiance:
• Energy in single wavelength passing through unit area perpendicular to direction of travel per unit time
• Commonly referred to as "pencil" of radiation
• Units are watts per square meter per steradian (solid angle) per unit wavelength
• Steradian defined as ratio of area of spherical surface divided by square of radius of sphere
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• Where is zenith angle and is azimuth angle
• Monochromatic flux density or irradiance:
• Integrate radiance over all solid angles
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• Amount of energy passing through plane surface from whole hemisphere above plane
• Units are watts per square meter per unit wavelength
• Exercise 4.1
• Calculate solid angle subtended by sky when viewed from earth's surface
• Integrate in spherical coordinates over zenith angle and azimuth angle
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• Intensity or radiance: I
• Integrate monochromatic radiance over range of wavelengths
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• Units are watts per square meter per steradian
• Total flux density or irradiance: F
• Integrate monochromatic flux density of range of wavelengths (often all wavelengths)
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• Units are watts per square meter
• Probably most commonly used measure for radiation flux in atmosphere
• Flux density of solar radiation reaching outside of atmosphere at mean earth/sun distance:
• Solar constant, F_s = 1,368 Wm^-2
• Exercise 4.2
• Given that solar constant is flux density of solar radiation at top of atmosphere
• Calculate solar intensity assuming solar radiation is isotropic
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• Solid angle subtended by sun in sky very small
• Ignore variations in cosine term in integration (parallel beam approximation)
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• Since zenith angle is 0
• Fraction of of sky occupied by sun:
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• So intensity is:
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• Blackbody Radiation
• Theoretical object that absorbs all radiation that hits it
• Well approximated by large cavity with small opening
• Intensity of blackbody emission defined by Planck function:
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• Stefan-Boltzmann law gives total energy emitted by integrating Planck function over all wavelengths:
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• Wien's Displacement law gives wavelength of maximum emission by differentiating Planck function:
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• Solar emission spectrum
• Peaks at about 0.475 microns
• Surface temperature from Wien's law is:
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• Equivalent blackbody temperature from solar constant:
• Earth-sun distance, d = 1.50 X 10¹¹ m
• Solar radius, R_s = 7.00 X 10⁸ m
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• Difference in two temperatures indicates sun does not emit as perfect blackbody
• Earth's emission spectrum
• Radiative equilibrium blackbody temperature
• Earth's planetary albedo approximately 0.30
• Solar flux illuminates one-fourth of earth's surface at any time
• Earth radiates from whole surface area
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• Surface temperature is about 289 K, difference reflects greenhouse effect
• Total flux density from earth's surface = 395 W m^-2
• Wavelength of maximum emission = 10 microns
• Radiative equilibrium temperatures for other planets

• Non Blackbody Materials
• All substances differ from blackbody model, some by large amounts
• Define emissivity as ratio between actual emission and amount predicted by Planck's law:
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• Also define absorptivity, reflectivity and transmissivity as fractions of incident radiance absorbed, reflected, or transmitted
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• Kirchhoff's Law
• States that emissivity equals absorptivity
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• Substances only emit in wavelengths they absorb
• Necessary condition for substances in thermal equilibrium
• Atmospheric gases and aerosols absorb and emit selectively

• Greenhouse Effect
• Atmospheric gases absorb terrestrial longwave radiation but not solar shortwave
• Simplified model of layered atmosphere transparent to shortwave, opaque to longwave
• Single layer atmosphere:
• Atmospheric temperature equals equivalent radiative equilibrium temperature
• Incoming solar radiation (F units) balanced by F units emitted to space by atmosphere
• Atmosphere also emits F units downward to surface
• Surface receives F units of solar radiation and F units of longwave from atmosphere
• Surface emits 2F units of longwave to atmosphere
• Results in surface temperature of 303 K
• Add a second atmospheric layer
• Top atmospheric layer emits F units to space and F units down to bottom layer
• Bottom atmospheric layer emits 2F units upward and 2F downward
• Surface receives F units of solar radiation and 2F units of longwave
• Surface temperature would be 334 K
• Radiative balance produces atmospheric lapse rate higher than dry adiabatic rate
• Convection transports energy upward to reduce lapse rate
• Some due to direct sensible heating - upward motion of warmed air, downward of cold air
• Larger proportion due to latent heating - evaporation from surface, uplift, condensation aloft