OC3522Summer 2001 OC Remote Sensing of the Atmosphere and Ocean - Summer 2001 Review of EMR & Radiative Processes Electromagnetic Radiation - remote sensing requires understanding of the nature of EMR emitted or backscattered from a surface or along a path.

Nature of Light Light is envisioned as consisting of numerous localized packets of electromagnetic (EM) energy called photon, which move through empty space with speed c = x 10**8 m/s. The energy of a photon is equal to h times its frequency (quantum of light), where h is the Planck's constant (= **-34 J s) But a photon is not a particle in the sense of classical mechanics: It has wave-like properties (wavelength and frequency). A photon is a localized wave-packet of time-varying, oscillating, self-sustaining electric (E) and magnetic (B) fields. The frequency of the oscillation of the EM fields is the photon's frequency. The state of polarization is related to the direction of the plane of vibration of the photon's E field. Wave-Particle duality of light: A photon is not either a particle or a wave, but both aspects are necessary for a proper understanding of light.

EM radiation can transport energy. E = hc/  Where E = energy of a photon in Joules h = Plank’s constant = 6.626e-34 Js c = speed of light Therefore - EM radiation travels at the speed of light and the frequency of the charge oscillation determines the wavelength.

Range of atmospheric/oceanic Remote Sensing

Definitions Energy spectrum can described in terms of: frequency Hz wavelength m wavenumber  m -1 radiant energy Q J Energy / unit of time radiant flux  Watts or Js -1 Flux crossing an area radiant flux densityM,EWm -2 leaving an area exitance  Wm -2 incident on an area irradiance  Wm -2

Defining a direction in space The direction of a line through any point on the Earth's surface is defined by 2 angles: the zenith angle , between the zenith (point on the celestial sphere located on the observer's ascending vertical) and the direction observed, the azimuth angle  between the North (on the local meridian) and the projection of the line on the Earth's surface. The height (altitude or elevation) is sometimes used instead of  : h = (  / 2) - ,  varies along the vertical plane from 0 to  /2 (0° to 90°),  varies along the horizontal plane from 0 to 2  (0° to 360°).

Light is a function of direction - and we use the concept of a solid angle; where 4  R 2 defines the total area of sphere and there are 4  steradians covering a sphere.

A solid angle d  delimits a cone in space: d  = dS / r 2 (in steradians, Sr) where dS is the area cut by the cone over a sphere of radius r the center of which is at the apex of the cone. The solid angle corresponding to all the space around a point equals 4  Sr. The solid angle of a revolving cone for which the plane half-angle at the apex is a equals:  = 2  (1 - cos  ) Sr. For an observer on Earth, the half-space formed by the celestial arch (in other words an hemisphere) therefore corresponds to 2  Sr  = 90°).

a) Point source Intensity: intensity is the power emitted by a point source A per solid angle unit. I A = d  /d  (in W.Sr-1) If the intensity is the same in all directions, the source is called isotropic. Whenever a source does not have the same power in all directions it is said to be anisotropic. 

b) Extended source Radiance: radiance (L) is the power emitted (d  ) per unit of the solid angle (d  ) and per unit of the projected surface (ds cos  ) of an extended widespread source in a given direction (  ). L = d  / (d . ds. cos  ) (in W.Sr -1. m -2 ) then total radiant flux  = ∫∫ L  d . cos   If radiance is not dependent on  and , i.e. if is the same in all directions, the source is said to be Lambertian Radiant flux/solid angle - outgoing (incoming) irradiance (brightness)  /BWm -2 Sr -1

All satellite remote sensing systems involve the measurement of EMR, which has been emitted, reflected or scattered by the atmosphere or the surface. These EMR measurements allow the determination of actual physical values of the atmosphere and the surface. Targets such as land and sea at the surface and water droplets and ice crystals in the atmosphere, reflect, absorb, emit and transmit radiant energy over a wide range of wavelengths. The emitted energy is described by a set of idealized blackbody (emits maximum Radiation at each wave radiation laws. The Plank function that describes blackbody radiation (perfect) is given by: Radiance emitted by a blackbody =  B (T) = [c 1 / exp(c 2 /( T)) - 1] -5  -4 T  (Rayleigh-Jean’s approx.) (for bodies around 300°K) Where c 1 = x W m 2 sr -1 = 2*Plank’s constant *C 2 ; C = speed of light c 2 = x m K = Plank’s constant * C /Blotzmann’s constant

Sun - temperature = 6000 K, peak at 0.5 mm, center of the visible Earth - temperature = 300 K, peak near 10 to 12 mm; IR For any temperature T; B (T) has a signal maximum; max is proportional to 1/T [Wein’s displacement law] [differentiate Plank’s function with respect to  set = to 0 and solve for 

Wein’s displacement law says: The spectral distribution of blackbody radiation depends on temperature. An object with very high surface temperature (i.e., the Sun), will emit very high energy radiation at shorter wavelengths, while a cooler object (i. e., the Earth) will emit a lower energy at longer wavelengths. max = T -1

Integrating Plank’s Function of all wavelengths Gives the Stefan-Boltzmann Law: M =          =  T 4 Wm -2 Where s == Stefan-Boltzmann constant = 5.67e-8 Wm -2 K -4

BUT… in reality - we have graybodies - not blackbodies (no perfect emitters) Emittance of a body is defined as emittance  no units   = emitted radiatance at /B (T); for a blackbody;  = 1 absorptance  no units  = absorbed radiation at /incident radiation at reflectance  no units  = reflected radiation at /incident radiation at transmittance  no units  = transmitted radiation at /incident radiation at  = 1

MaterialEmissivity Coal Spoil0.99 Grass0.97 Water, Distilled0.99 Water, Natural~0.95 Mirror0.02

Kirchhoff’s Law “Good emitters are good absorbers”   Good reflector is a poor emitter

SUMMARY Terms solid angle radiant energy radiant flux radiant flux density irradiance exitance emittance transmittance absorbtance Blackbody Graybody Basic Concepts Plank’s function Wein’s Displacement Law Stefan-Boltzmann Law Kirchhoff’s Law