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



 Where is zenith angle and is azimuth angle
 Monochromatic flux density or irradiance:
 Integrate radiance over all solid angles

 Amount of energy passing through plane surface from whole hemisphere above plane
 Units are watts per square meter per unit wavelength
 Exercise 4.1
 Intensity or radiance: I
 Integrate monochromatic radiance over range of wavelengths
 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)
 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
 Solid angle subtended by sun in sky very small
 Ignore variations in cosine term in integration (parallel beam approximation)
 Since zenith angle is 0
 Fraction of of sky occupied by sun:
 So intensity is:
 Blackbody Radiation
 Theoretical object that absorbs all radiation that hits it
 Solar emission spectrum
 Peaks at about 0.475 microns
 Surface temperature from Wien's law is:
 Equivalent blackbody temperature from solar constant:
 Earthsun distance, d = 1.50 X 10^{11} m
 Solar radius, R_{s} = 7.00 X 10^{8} m
 Difference in two temperatures indicates sun does not emit as perfect blackbody
 Earth's emission spectrum
 Radiative equilibrium blackbody temperature
 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:
 Also define absorptivity, reflectivity and transmissivity as fractions of incident radiance absorbed, reflected, or transmitted
 Kirchhoff's Law
 States that emissivity equals absorptivity
 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