Chapter 3 Radiative transfer processes in the aquatic medium Remote Sensing of Ocean Color Instructor: Dr. Cheng-Chien LiuCheng-Chien Liu Department of Earth Science National Cheng-Kung University Last updated: 13 March 2003

3.1 Incident light  Incident sky irradiance Rigorous models of surface irradiance  HITRAN, FASCODE, LOWTRAN, …  the size and computational complexity of these models  impractical for many oceanographic applications Simple atmospheric radiative transfer models  (Justus and Paris, 1985) (Bird and Riordan, 1986) (Green and Chai, 1988)  Pros:  Simple  Both direct and diffuse irradiance are calculated globally  Cons:  Specific to continental aerosols

3.1 Incident light (cont.)  Incident sky irradiance (cont.) A simple spectral solar irradiance model for cloudless maritime atmospheres (Gregg and Carder 1990)

3.1 Incident light (cont.)  Cloud effect Kasten and Czeplak (1980)

3.1 Incident light (cont.)  Incident sky radiance Crude approximation  A heavily overcast day  cardioidal distribution  e.g. L( ,  ) = L 0 (1+2cos  ), 0    /2  A cloudless day  a collimated direct solar beam plus an isotropic diffuse sky radiance

3.1 Incident light (cont.)  Incident sky radiance (cont.) A cloud cover model of sky radiance Harrison and Coombes (1988).

3.1 Incident light (cont.)  Incident sky radiance (cont.) A cloud cover model of sky radiance (cont.)  The normalized sky radiance N( ,  ) can be given analytically by combining the normalized overcast sky radiance N o ( ,  ) and the normalized clear sky radiance N c ( ,  )  where  is the sky zenith angle,  is the sky azimuth angle relative to the Sun,  s is the solar zenith angle, and  is the scattering angle between sky and the Sun directions.

3.2 Transmission across the air-water interface  The level surface Refraction – Snell’s law  Air-incident case  Water-incident case

Fig Fig Schematic diagrams for trajectories of photons passing through a flat air- water surface. Redrawn from (Mobley 1994)

3.2 Transmission across the air-water interface (cont.) Reflection – Fresnel’s equation  Air-incident case  Water-incident case

Fig Fresnel reflectance function Fig 3.2.2

3.2 Transmission across the air-water interface (cont.)  Capillary waves The relation between the mean-square wave slope  2 over the sea surface and the surface wind speed V wind can be described by an equation proposed by Cox and Munk (1954)  2 = V wind

3.2 Transmission across the air-water interface (cont.)  Capillary waves (cont.) The probability function P(  ws ) of the occurrence of wave slope where  ws is the angle between the vertical and the normal to the sea surface at a given point

3.2 Transmission across the air-water interface (cont.)  Whitecaps effect The probability of reflectance can be further corrected by taking the white cap effect into consideration (Kirk 1994)

3.3 Radiative transfer process within the aquatic medium  Path length The path length of a photon before it hits another particle (Gordon 1994) where  j is a sequence of random numbers between 0 and 1 explanation

3.3 Radiative transfer process within the aquatic medium (cont.)  Absorption Bio-optical model of absorption (Prieur and Sathyendranath 1981)

3.3 Radiative transfer process within the aquatic medium (cont.)  Scattering Bio-optical model of scattering (Gordon et al. 1983, Morel 1991)

3.3 Radiative transfer process within the aquatic medium (cont.)  Probability of photon survival

3.3 Radiative transfer process within the aquatic medium (cont.)  Direction of scattering The average VSF derived from Petzold’s measurements (Mobley 1994) Henyey-Greenstein phase function (1941) Fournier-Forand phase function (1994)

3.4 Bottom boundary  Lambertian assumption  Bi-directional reflectance  Reflectance of various bottom types

Fig Reflectance of various bottom types Fig 3.4.1

3.5 Radiative transfer equation  Classic radiative transfer equation

Fig Illustration of radiative transfer equation