## 2.12.3. Surface Albedo[¶](#surface-albedo "Permalink to this headline")
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For direct radiation, the albedo _a_ for lakes with ground temperature \\({T}\_{g}\\) (K) above freezing is given by ([Pivovarov, 1972](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#pivovarov1972))

(2.12.1)[¶](#equation-12-1 "Permalink to this equation")\\\[a=\\frac{0.5}{\\cos z+0.15}\\\]

where _z_ is the zenith angle. For diffuse radiation, the expression in eq. is integrated over the full sky to yield _a_ = 0.10.

For frozen lakes without resolved snow layers, the albedo at cold temperatures _a_0 is 0.60 for visible and 0.40 for near infrared radiation. As the temperature at the ice surface, \\({T}\_{g}\\), approaches freezing \[ \\({T}\_{f}\\) (K) ([Table 2.2.7](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Ecosystem/CLM50_Tech_Note_Ecosystem.html#table-physical-constants))\], the albedo is relaxed towards 0.10 based on [Mironov et al. (2010)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#mironovetal2010):

(2.12.2)[¶](#equation-12-2 "Permalink to this equation")\\\[a=a\_{0} \\left(1-x\\right)+0.10x,x=\\exp \\left(-95\\frac{T\_{f} -T\_{g} }{T\_{f} } \\right)\\\]

where _a_ is restricted to be no less than that given in [(2.12.1)](#equation-12-1).

For frozen lakes with resolved snow layers, the reflectance of the ice surface is fixed at _a_0, and the snow reflectance is calculated as over non-vegetated surfaces (Chapter [2.3](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Surface_Albedos/CLM50_Tech_Note_Surface_Albedos.html#rst-surface-albedos)). These two reflectances are combined to obtain the snow-fraction-weighted albedo as in over non-vegetated surfaces (Chapter [2.3](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Surface_Albedos/CLM50_Tech_Note_Surface_Albedos.html#rst-surface-albedos)).

