Aquatic optics symbols and definitions

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Term

Symbol

Definition

Reference1

Alternative symbol2

Dimension

units

Aliases

Mathematical expression

Absorptance

A( )

The ratio of the radiant flux lost from a beam due to absorption

K
 J

 

-

-

 

Absorption coefficient

a( )

The fraction of radiant energy absorbed from an incident light beam as it traverses an infinitesimal distance

B

 

L-1

m-1

Beam absorption coefficient

Attenuance

C( )

The ratio of radiant flux lost (due to scatterance and absorptance) from a beam within an infinitesimal attenuating layer, to the radiant flux within the beam impinging upon that infinitesimal distance

B
K
 J

 

-

-

Optical Attenuation

= A + B

Attenuation length

The path length in an attenuating medium required to reduce the energy of a light beam by a factor of 1/e (i.e., to 0.367879 of its value)

B

 

L

m

Optical distance

Average cosine of scattering

( )

The average cosine of the singly scattered light field

K

 

-

-

Mean cosine

Azimuth angle

The angle between the vertical plane incorporating the light beam and some other reference vertical plane such as the sun

K

 

-

-

   

Backscattering coefficient

bb( )

The integral of the volume scattering function b(q) over the hemisphere trailing the incident flux [defined by the angular ranges (p/2  q  p) and (0  f  2p)]

B,K

 

L-1

m-1

 

=Bb

Backscattering probability

B( )

The ratio of the scattering in the backward hemisphere to the total scattering occurring in all directions

B

 

-

-

Normalized backward scattering coefficient

Beam attenuation coefficient

c( )

The fraction of the incident flux which is absorbed and scattered, divided by the thickness of the layer r traversed

K
B

 

L-1

m-1

1)Total attenuation coefficient

2)Attenuation coefficient

= a + b

Diffuse absorption coefficient (downwelling)

ad( )

The proportion of the downwelling incident radiant flux absorbed from the diffuse light stream by an infinitesimally thin horizontal plane parallel layer at that depth, divided by the thickness of that layer

K

 

L-1

m-1

 

Diffuse absorption coefficient (upwelling)

au( )

The proportion of the upwelling incident radiant flux absorbed from the diffuse light stream by an infinitesimally thin horizontal plane parallel layer at that depth, divided by the thickness of that layer

K

 

L-1

m-1

 

Diffuse attenuation coefficient (downwelling)

cd( )

The proportion of the downwelling incident radiant flux scattered and absorbed from the diffuse light  stream by an infinitesimally thin horizontal plane parallel layer at that depth, divided by the thickness of that layer

K

cdd

L-1

m-1

 

ad + bd

Diffuse attenuation coefficient (upwelling)

cu( )

The proportion of the upwelling incident radiant flux scattered and absorbed from the diffuse light  stream by an infinitesimally thin horizontal plane parallel layer at that depth, divided by the thickness of that layer

K

cdu

L-1

m-1

 

au + bu

Diffuse scattering coefficient

(downwelling)

bd( )

The proportion of the downwelling incident radiant flux scattered from the diffuse light  stream by an infinitesimally thin horizontal plane parallel layer at that depth, divided by the thickness of that layer

K

bdd

L-1

m-1

 

Diffuse scattering coefficient

(upwelling)

bu( )

The proportion of the upwelling incident radiant flux scattered from the diffuse light  stream by an infinitesimally thin horizontal plane parallel layer at that depth, divided by the thickness of that layer

K

bdu

L-1

m-1

 

Distribution function for downwelling light

Dd( )

The reciprocal of the average cosine of downwelling light

MK

 

-

-

Distribution factor

Distribution function for upwelling light

Du( )

The reciprocal of the average cosine of upwelling light

MK

 

-

-

Distribution factor

Downwelling scalar irradiance

E0d( )

The integrated radiance distribution over the hemisphere above the horizontal plane containing a selected point in an attenuating medium

B

 

MT-3

Wm-2

 

Forward scattering probability

F( )

The ratio of the scattering into the forward hemisphere to the total scattering into all directions

B

 

-

-

 

Forward scattering coefficient

bf ( )

The integral of the volume scattering function b(q) over the hemisphere ahead of the incident flux [defined by the angular ranges (0  q  p/2) and (0  f  2p)]

B

 

L-1

m-1

 


= F b

Geometric depth

z

Geometric depth measured from the air/sea interface to a defined horizontal plane within the water column.

   

L

m

   

Energy of a Photon

A function of the speed of light in a vacuum, Planck’s constant and its wavelength

BK

E

L2MT-2

J

 

 

Irradiance

E( )

The radiant flux per unit area at a point within a radiative field or at a point on an extended surface

B

 

M T-3

W m-2

 

Irradiance (downwelling)

Ed( )

The irradiance at a point due to the stream of downwelling light

B

 

M T-3

W m-2

 

Irradiance (upwelling)

Eu( )

The irradiance at a point due to the stream of upwelling light

B

 

M T-3

W m-2

 

Irradiance Attenuation Coefficient

K( )

The logarithmic depth derivative of the spectral irradiance E at depth z

B

 

L-1

m-1

Vertical attenuation coefficient

Irradiance Reflectance

R( )

The ratio of the upwelling irradiance at a point in an attenuating medium to the downwelling irradiance at that point within a water body

B
K

-

-

-

1) Volume reflectance

2) Subsurface irradiance reflectance

3) Reflectance

Mean Cosine for Downwelling Light

( )

The average value, in an infinitesimally small volume element at that point in the field, of the cosine of the zenith angle of all the downwelling photons in the volume element

K

 

-

-

Average cosine for downwelling light             

Mean Cosine for Total Light

( )

The average value, in an infinitesimally small volume element at that point in the field, of the cosine of the zenith angle of all the photons in the volume element.

K

 

-

-

1) Average cosine for total light              

2) Average cosine

3) Mean cosine

Mean Cosine for Upwelling Light

( )

The average value, in an infinitesimally small volume element at that point in the field, of the cosine of the nadir angle of all the upwelling photons in the volume element.

K

 

-

-

Average cosine for upwelling light

Net Downward Irradiance

The difference between the downward and upward irradiance at any point in the radiative field.

B

M T-3

Wm-2

 

Ed - Eu

Optical depth

The integration of the downwelling irradiance attenuation coefficient over depth z

BK

 

-

-

 

= Kd z

Optical length

The geometric length of a path multiplied with the total attenuation coefficient associated with the path

J

 

-

-

 

c( ) r

Planck’s constant

h

A constant that relates the energy of a photon to its wavelength or frequency.

   

L2MT-1

J s

 

6.626 x 10-34 J s

Radiance

L( )

The radiant flux per unit solid angle dW per unit area dA at any point in a radiative field

B

 

M T-3

Wm-2sr-1

 

Radiant Energy

Q

The quantity of energy in joules transferred by radiation.

B

 

L2M.T-2

J

 

Radiant Flux

F( )

The time rate of flow of radiant energy

BK

 

L2MT-3

W

 

Radiant Intensity

I( )

The radiant flux  per unit solid angle in a specified direction

B
K

 

L2MT-3

Wsr-1

 

Scalar Irradiance

E0( )

The measure of irradiance at a point in the radiative field in which the radiation from all directions are treated equally.

B

 

MT-3

Wm-2

 

Scatterance

B( )

Fraction of the radiant flux lost to scattering

K

 

-

-

 

Scattering albedo

The number of scattering interactions that occur within a fixed volume of an attenuating medium expressed as a fraction of the total number of optical interactions (both scattering and absorption) that occur within that fixed volume.

B

 

-

-

 

b / c

Scattering Coefficient

b( )

The fraction of radiant energy scattered from an incident light beam as it traverses an infinitesimal distance

B

 

L-1

m-1

 

Scattering Phase Function

The volume scattering function normalized to the scattering coefficient

K
B

 

-

sr-1

Normalized volume scattering function

Shape factors

ru,d( )

A measure of the contribution of the forward lobe of the volume scattering function to the upward or downward light stream during a scattering event

A

 

-

-

   

Solid Angle

W

The ratio of surface area of the sphere  subtended at the center of that sphere to the square of the radius of the sphere.

S

 

-

sr

   

Specific absorption coefficient

ai*( )

The absorption that may be attributed to a unit concentration of aquatic component i

B

 

L2 M

m2mg-1

Absorption Cross Section

 

Specific backscattering coefficient

bbi*( )

The backscattering that may be attributed to a unit concentration of aquatic component i

B

 

L2 M

m2mg-1

Backscattering cross section

 

Specific scattering coefficient

bi*( )

The scattering that may be attributed to a unit concentration of aquatic component i

B

 

L2 M

m2mg-1

Scattering cross section

 

Transmittance

T( )

The ratio of the radiant flux within a beam emerging from an infinitesimal attenuating layer to the incident radiance flux within the beam impinging upon that layer

B

 

-

-

 

Upwelling scalar irradiance

E0u( )

The integrated radiance distribution over the hemisphere below the horizontal plane containing a selected point in an attenuating medium

B

 

M T-3

W m-2

 

Velocity of light in vacuum

cl

The velocity of light in a vacuum

O

 

LT-1

cm s-1

 

2.9979 x 1010 cm.s-1

Volume scattering function

 

The scattered radiant intensity in a given direction per unit scattering volume normalized to the value of the incident irradiance.

B

 

L-1

m-1sr-1

 

Wavelength

The speed of light divided by its frequency

K

 

L

nm

 

Zenith Angle

The angle between a thin parallel beam and the upward vertical

K

 

-

-

   

1B = Bukata et al. , K = Kirk,  S = Slater, J = Jerlov, M= Mobley, A= Aas
2 Subscripts u and d  refer to upwelling and downwelling light stream, respectively.
 3 F0 = Incident flux
Last Modified on Friday, December 26, 2003 [an error occurred while processing this directive]