The fundamental properties describing the radiation field are defined in precise physical terms, but their symbolic notations in the literature are far from universal. To minimize confusion and to adhere to the increasingly popular conventions emerging from the field of hydrologic optics, the symbols and definitions used here (Table 1) will conform to those of Kirk (1994) and Mobley (1994). The reader is encouraged to consult these excellent texts for a significantly deeper understanding of the fundamental concepts of hydrologic optics introduced here. Although values for the terms and functions defined below are spectrally dependent, the parenthetical notation (A) has been omitted from the equations for simplicity. Direction within the light field is generally expressed in terms of the zenith, nadir, and

A. WD. Larkum et al. (eds.), Seagrasses: Biology, Ecology and Conservation, pp. 295-301. © 2006 Springer. Printed in the Netherlands.

azimuth angles (9, 9n, and 0, respectively) as illustrated in Fig. 2.

The radiant flux represents the time rate of flow of radiant energy, and is denoted by the symbol O. Radiant flux can also be expressed in molar units, where 1 mol = 6.02 x 1023 photons (Avogadro's number). According to Kirk (1994), terms such as 'fluence rate' or 'photon fluence rate' should be avoided when describing properties of the radiation field. The field radiance (L) is the radiant flux projected onto a surface dA oriented at right angles to the incident beam (Fig. 2) and has units of W (or quanta s-1) m-2 steradian-1. The surface radiance is the radiant flux in a given direction per unit solid angle projected onto a horizontal surface (dS) oriented at some angle (9, 0) to the beam. It is denoted by the symbol L (9, 0) and also has units of W (or quanta s-1) m-2 steradian-1. The surface radiance is related to the field radiance according to the Cosine Law because the horizontal surface area (d£) is defined by cA.

Irradiance is the total radiant flux incident upon a surface of defined area. It is denoted by E, and has units of W (or quanta s-1 ) m-2. The scalar irradiance

Abbreviations: See Table 1 for a list of symbols, definitions, and units used in this chapter.

(Eo) integrates the radiance distribution equally over all directions of a sphere:

Scalar irradiance can be partitioned into downward and upward scalar irradiances, but it will be more useful to consider downward and upward plane irradiances in the discussion of seagrass-light interactions found in Chapter 13. The downward and upward plane irradiances (Ed and Eu) illuminate the upper and lower faces of a surface, respectively. Like scalar irradiances, they are obtained by integrating the radiance over all solid angles (m) of the upper and lower hemispheres, separately. Unlike scalar irradiances, however, plane irradiances are affected by the Cosine Law, which simply states that the irradi-ance incident on a plane surface is proportional to the angle between the photon direction and the surface normal (Fig. 2). Hence:

Symbol |
Definition |
Dimensions | ||

Fundamental quantities | ||||

<P |
Azimuth angle |
deg or rad | ||

e |
Polar angle |
deg or rad | ||

On |
Zenith polar angle |
deg or rad | ||

en |
Nadir polar angle |
deg or rad | ||

f1 |
Cosine of polar angle |
Dimensionless | ||

Z |
Depth |
m | ||

Radiometric quantities | ||||

L |
Radiance |
W (or quanta s- |
) m- |
-2 -1 2 sr 1 nm |

L u |
Upwelling radiance |
W (or quanta s- |
)m- |
2 -1 2 sr 1 nm |

L w |
Water-leaving radiance |
W (or quanta s- |
) m- |
2 -1 2 sr 1 nm |

E |
Irradiance |
W (or quanta s- |
)m- |
2 -1 2 nm 1 |

Eo |
Scalar irradiance |
W (or quanta s- |
) m- |
2 -1 2 nm 1 |

Ed |
Downwelling plane irradiance |
W (or quanta s- |
)m- |
2 -1 2 nm 1 |

Eu |
Upwelling plane irradiance |
W (or quanta s- |
) m- |
2 -1 2 nm 1 |

Inherent optical properties | ||||

A |
Beam absorptance |
Dimensionless | ||

B |
Beam scatterance |
Dimensionless | ||

T |
Beam transmittance |
Dimensionless | ||

D |
Optical density |
Dimensionless | ||

a |
Beam absorption coefficient |
m-1 | ||

b |
Beam scattering coefficient |
m-1 | ||

c |
Beam attenuation coefficient |
m-1 | ||

P |
Volume scattering function |
m-1 sr-1 | ||

Apparent optical properties | ||||

R |
Irradiance reflectance |
Dimensionless | ||

Rrs |
Remote sensing reflectance |
sr-1 | ||

Kd |
Coefficient of downwelling attenuation |
m-1 | ||

Ku |
Coefficient of upwelling attenuation |
m-1 | ||

Md |
Average cosine of downwelling irradiance |
Dimensionless | ||

An |
Average cosine of upwelling irradiance |
Dimensionless |

Similarly, the upward plane irradiance is obtained by integrating the radiance over all solid angles of the lower hemisphere, with respect to the Cosine Law:

Application of the Cosine Law means that Eo is always greater than the sum (Ed + Eu).

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