Radiation Trapping in Sea

Comparisons of radiative transfer models used to compute irradiances and radiances in atmosphere-ocean systems have shown that they yield similar results for identical input, and have clearly demonstrated the influence of the atmosphere/ snow-sea ice/ocean interface on the transport of energy across it (Mobley et al., 1993; Gjerstad et al., 2003). Nevertheless, little attention has been paid to the enhanced downward irradiance (EDI) across the atmosphere-sea ice interface due to trapping of light caused by multiple scattering in the sea ice. The EDI is defined as:

where Fd(0~ ,A) is the downward irradiance just below the interface, and Fd(0+ ,2) is the downward irradiance just above the interface. By definition, if the irradiance difference across the interface is positive (AFd (A) > 0 ), there is an EDI effect across the interface; otherwise, there is no EDI effect.

The irradiance incident on the atmosphere-sea ice interface consists of two components:

where Fsol(0+ ,A) is the direct solar beam irradiance and Fdiff(0+ ,A) is the downward irradiance due to diffuse skylight. Similarly, the downward irradiance just below the interface consists of three components:

Fd(0- ,1) = Fttans(0- ,A) + Fpref(0- ,A) + Ff0~ ,A). (9.22)

Here Ftrans(0",A) = Fsoltr(0+ ,A) + Fdifftr(0+ ,A) is the sum of two downward irradiance components from the atmosphere that are transmitted through the interface, Fpref (0~, A) is the downward irradiance due to the upward radiation in the sea ice with directions inside the refraction cone that is partially reflected downwards by the interface, and Ftef (0~, A) is the downward irradiance due to the upward radiation in the sea ice with directions outside the refraction cone that is totally reflected downwards by the interface.

Using a radiative transfer model similar to the CASIO-DISORT model described above, Jiang et al. (2005) simulated the EDI effect. Table 9.1 shows all components of the computed downward irradiance just above and just below the atmosphere-sea ice interface for a solar elevation of 30° and for a wavelength of 550 nm under clear sky conditions. The incident downward solar irradiance is 4.21 ein m-2 s-1 nm-1 (0.92 W m nm ). We note that Ftef(0 ,A) is the main source of the EDI effect. Thus, the EDI effect is primarily due to radiation that is totally reflected by the interface. The dominance of scattering in the ice compared to absorption is the cause of the EDI effect. The biogeophysical significance of the EDI is that the mean intensity just below the interface will be enhanced, and so will the energy available for photolysis and melting of the sea ice.

The third column in Table 9.1 demonstrates that without a jump in the index of refraction, there is no EDI effect (AFd (A) = 0 ), and the fourth column demonstrates that in the absence of scattering in the sea ice (bice — 0), there is no EDI effect. In fact, AFd (A) < 0 when bice = 0, which is a consequence of energy conservation, because a fraction of the irradiance incident on the ice is (Fresnel) reflected, and no light can be backscattered from the sea ice when bice = 0 .

Table 9.1 Comparison of downward irradiance components (in units of ein m 2 s 1 nm 1) at 550 nm just above and just below the atmosphere-sea ice interface*

Component

m,el = 1.31

mrel = 1

bice = 0

^sol(0+ ,550)

2.47

2.47

2.47

Fiff (0+ ,550)

1 .20

1.29

1.02

Fd(0+,550)

3.67

3.76

3.49

Fsol,tr(0-,550)

2.34

2.47

2.34

Ff0-,550)

1.32

0

0

Fdlff>tI(0- ,550)

1.08

1.29

0.92

Fpref(0-,550)

0.11

0

0

Fd(0" ,550)

4.85

3.76

3.26

AFd(550)

1.18

0

-0.23

* The second column shows the EDI effect, the third column shows results obtained with no jump in the index of refraction, and the fourth column shows results when the scattering in the sea ice is ignored (see text above)

* The second column shows the EDI effect, the third column shows results obtained with no jump in the index of refraction, and the fourth column shows results when the scattering in the sea ice is ignored (see text above)

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