6.3 Snow and Ice Albedo

The albedo depends upon spectral band, snow thickness, ice thickness and surface temperature. Snow and ice spectral albedos (visible $=vs$, wavelengths $< 0.7\mu m$ and near-infrared $=ni$, wavelengths $> 0.7\mu m$) are distinguished, as both snow and ice spectral reflectivities are significantly higher in the $vs$ band than in the $ni$ band. This two-band separation represents the basic spectral dependence. The near-infrared spectral structure, with generally decreasing reflectivity with increasing wavelength [56] is ignored. The zenith angle dependence of snow and ice is ignored [63,56], and hence there is no distinction between downwelling direct and diffuse shortwave radiation. The approximations made for the albedo are further described by Briegleb et al. [28].

Here we ignore the dependence of snow albedo on age, but retain the melting/non-melting distinction and thickness dependence. Dry snow spectral albedos are:

$$\null \vcenter{\openup\jot \mathsurround=0pt \ialign{\strut\hf... ...dry) = & {0.96} \cr \alpha_{nidf}^s(dry) = & {0.68} \cr\crcr}} .$$ (6.7)

To represent melting snow albedos, the surface temperature is used. Springtime warming produces a rapid transition from sub-zero to melting temperatures, while late fall values transition more slowly to sub-zero conditions. This is approximated by a temperature dependence out to $-1^\circ$C. If $T_{s} \ge -1^\circ$C, then

$$\null \vcenter{\openup\jot \mathsurround=0pt \ialign{\strut\hf... ...(melt) = & {\alpha_{nidf}^s(dry) - 0.15 \Delta T_s} \cr\crcr}} .$$ (6.8)

For bare non-melting sea ice thicker than 0.5 m, as is the case for all sea ice prescribed in CAM 3.0, the albedos are

$$\null \vcenter{\openup\jot \mathsurround=0pt \ialign{\strut\hf... ...}(dry) = & {0.73} \cr \alpha_{nidf}(dry) = & {0.33} \cr\crcr}} .$$ (6.9)

For bare melting sea ice, melt ponds can significantly lower the area averaged albedo. This effect is crudely approximated by the following temperature dependence:

$$\null \vcenter{\openup\jot \mathsurround=0pt \ialign{\strut\hf... ...}(melt) = & {\alpha_{nidf}(dry) - 0.075 \Delta T_s } \cr\crcr}}$$ (6.10)

for $T_{s} \ge -1^\circ$C.

The horizontal fraction of surface covered with snow is assumed to be

$$f_s = \frac{h_s}{h_s + 0.02}.$$ (6.11)

Finally, combining ice and snow albedos by averaging over the horizontal coverage results in

$$\null \vcenter{\openup\jot \mathsurround=0pt \ialign{\strut\hf... ... {\alpha_{nidf}(1 - f_{s}) + f_{s} \alpha_{nidf}^s} \cr\crcr}} .$$ (6.12)

The same equations applies for direct albedos.