to Sea-Ice Nomenclature Overview page
1. Albedo as a function of ice thickness
2. Albedo of broken-up sea ice
3. Albedo
as a function of snow cover
The albedo of growing sea ice depends on its thickness. Experimental results and field measurements show a dramatic increase of the albedo of ice thicker than 5 cm, corresponding to the transition from dark to light nilas. This could be due to the drainage of brine, leaving air filled pore spaces behind, that scatter more efficiently. A brine tube of radius R can sustain a water column h through capillary forces:
rho g h = t/R
where rho = 1030-1050 kg/m3 is the density of brine, g
= 9.81 m/s2 is the acceleration due to gravity, and t =
0.034 J/m2 is the surface energy of a ice-water interface
(Ketcham and Hobbs, 1969). For brine tubes of the radius of 1 mm this
yields a head of 3.5 mm, and a total sea ice thickness of the order
of 5 cm. The following table provides a typical albedo for each
thickness class (Allison et al., 1993; Weller, 1972).
|
|
|
|
|
|
|
|
|
|
|
|
2. Albedo of broken-up sea ice
Under rough conditions the sea ice cover breaks and the scattering increases dramatically. The breaking up of the cover into smaller pieces depends on the strength of the ice (s0), its thickness (h), the wind speed (u), the fetch (f), and the drag coefficient (CD). A simple force balance (ignoring drag from the water) yields:
sxx h = CD rhoair u2 f
where sxx is the linear stress per unit width. If this stress exceeds the large scale strength s0 the ice will fail (i.e. break and raft) and the albedo will increase. Albedos as high as 0.7 can be expected (Allison et al., 1993). The failure criterion is:
(u2 f)/h < s0 /
(CD rhoair
)
low albedo (table in section 1)
>
high albedo (approx. 0.7)
Possible values for s0 = 10 - 100 kPa (Pritchard,
1976)
CD = 1.3 10-3 (Eicken, 1998)
3. Albedo as a function of snow cover
A snow cover of about 10 cm or possibly much less (Warren and
Wiscombe, 1980) completely dominates the albedo. The following table
gives a rough overview of snow albedos (Perovich, 1996):
|
|
|
|
|
|
|
|
To find the albedo of a snow cover of less than 10 cm, a
logarithmic interpolation between the bare ice albedo and the snow
albedo should be used. If the scattering and absorption properties of
the snow cover are uniform throughout it, the logarithmic
interpolation is justified.
Snow thus strongly affects the appearance of sea ice and therefore
the applicability of the sea ice nomenclature.
References
Allison, I. R. E. Brandt, and S. G. Warren (1993) East Antarctic sea ice: albedo, thickness distribution and snow cover. J. Geophys. Res., 98, 12417-12429.
Eicken, H. (1998) Sea ice geophysics. Lecture notes. 120 pp.
Ketcham, W. M. and P. V. Hobbs (1969). An experimental determination of the surface energies of ice. Philosophical Magazine, 19:1161-1173.
Perovich, D. K. (1996) The optical properties of sea ice. CRREL Monogr., 96-1, 25 pp.
Pritchard, R. S. (1976) Estimate of the strength of Arctic pack ice. AIDJEX Bull., 34, 94-113.
Wiscombe, W. J. and S. G. Warren (1980) A Model for the spectral
albedo of snow. I: Pure snow. J. Atm. Sc.,
37(12), 2712-2733.
Weller, G. (1972) Radiation flux investigation. AIDJEX Bull., 14, 28-30.