6 Impacts of Saharan Dust on the Marine Environment in the Area . . .
123
where Q PAR (z) included the spectral effect and Q PAR (z, S = 1) excluded this effect.
The PAR was defined by the equation
Q PAR (z) =
1
hc
∗
700
400
λ ∗ E d (z, λ)dλ.
(6.3)
The quantity h was the Planck’s constant, c was the velocity of light in vacuum, λ was
the wavelength and z was the water depth. The quantity E d (z, λ) was the downward
irradiance below the water surface determined by
E d (z, λ) = E d (0
− , λ) exp [ −
z
0
K d (z, λ)dz]
(6.4)
The exponential described the change of downward irradiance in the water column by
the light attenuation expressed in terms of the diffuse attenuation coefficient K d (z, λ).
The downward irradiance just below the water surface was given by
E d (0
− , λ) = (1 − σ + σ ∗ r(λ)) ∗ E d (0
+ , λ)
(6.5)
The first term defined the modification of the downward irradiance by reflection processes at the interface between air and water ( σ - reflection coefficient for downward
irradiance from air to water, σ - reflection coefficient for upward irradiance from
water to air, r(λ)- total internal reflectance given by r(λ) = πL u (0
− , λ)/E d (0
+ , λ)
with the upward radiance just below the water surface L u (0
− , λ) and the above water
downward irradiance E d (0
+ , λ)). The second term was the downward irradiance just
above the water surface given by
E d (0
+ , λ) = E
gc
d,cs (0
+ , λ) ∗ M(0
+ , λ) ∗ N (0
+ , 490 nm) ∗ S(0
+ , λ, N )
(6.6)
The first term described the downward irradiance of clear skies using the model of
Gregg and Carder (1990) and the second one the correction of instrumental errors
or inaccurate modeling. The third term is a normalization factor and determined
the influence of dust on magnitude of incident radiation. The quantity S(0
+ , λ, N )
described the effect of dust on the spectral distribution of the incident radiation
(Bartlett et al. 1998; Ohde and Siegel 2012b).
6.2.2.2 Optical Model Input
The application of the optical model required the knowledge of the clear sky downward irradiance E
gc
d,cs , the correction term M, the normalization factor N, the spectral
effect S, the total internal reflectance r, the diffuse attenuation coefficient K d as well
as the reflection coefficients σ and σ . The detailed description was given in Ohde
and Siegel (2012b).
123
where Q PAR (z) included the spectral effect and Q PAR (z, S = 1) excluded this effect.
The PAR was defined by the equation
Q PAR (z) =
1
hc
∗
700
400
λ ∗ E d (z, λ)dλ.
(6.3)
The quantity h was the Planck’s constant, c was the velocity of light in vacuum, λ was
the wavelength and z was the water depth. The quantity E d (z, λ) was the downward
irradiance below the water surface determined by
E d (z, λ) = E d (0
− , λ) exp [ −
z
0
K d (z, λ)dz]
(6.4)
The exponential described the change of downward irradiance in the water column by
the light attenuation expressed in terms of the diffuse attenuation coefficient K d (z, λ).
The downward irradiance just below the water surface was given by
E d (0
− , λ) = (1 − σ + σ ∗ r(λ)) ∗ E d (0
+ , λ)
(6.5)
The first term defined the modification of the downward irradiance by reflection processes at the interface between air and water ( σ - reflection coefficient for downward
irradiance from air to water, σ - reflection coefficient for upward irradiance from
water to air, r(λ)- total internal reflectance given by r(λ) = πL u (0
− , λ)/E d (0
+ , λ)
with the upward radiance just below the water surface L u (0
− , λ) and the above water
downward irradiance E d (0
+ , λ)). The second term was the downward irradiance just
above the water surface given by
E d (0
+ , λ) = E
gc
d,cs (0
+ , λ) ∗ M(0
+ , λ) ∗ N (0
+ , 490 nm) ∗ S(0
+ , λ, N )
(6.6)
The first term described the downward irradiance of clear skies using the model of
Gregg and Carder (1990) and the second one the correction of instrumental errors
or inaccurate modeling. The third term is a normalization factor and determined
the influence of dust on magnitude of incident radiation. The quantity S(0
+ , λ, N )
described the effect of dust on the spectral distribution of the incident radiation
(Bartlett et al. 1998; Ohde and Siegel 2012b).
6.2.2.2 Optical Model Input
The application of the optical model required the knowledge of the clear sky downward irradiance E
gc
d,cs , the correction term M, the normalization factor N, the spectral
effect S, the total internal reflectance r, the diffuse attenuation coefficient K d as well
as the reflection coefficients σ and σ . The detailed description was given in Ohde
and Siegel (2012b).