### 2.12.5.5. Radiation Penetration[¶](#radiation-penetration "Permalink to this headline")

If there are no resolved snow layers, the surface absorption fraction \\(\\beta\\) is set according to the near-infrared fraction simulated by the atmospheric model. This is apportioned to the surface energy budget (section [2.12.4.1](#surface-properties-lake)), and thus no additional radiation is absorbed in the top \\(z\_{a}\\) (currently 0.6 m) of unfrozen lakes, for which the light extinction coefficient \\(\\eta\\) (m\-1) varies between lake columns (eq. ). For frozen lakes (\\(T\_{g} \\le T\_{f}\\) ), the remaining \\(\\left(1-\\beta \\right)\\vec{S}\_{g}\\) fraction of surface absorbed radiation that is not apportioned to the surface energy budget is absorbed in the top lake body layer. This is a simplification, as lake ice is partially transparent. If there are resolved snow layers, then the snow optics submodel (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)) is used to calculate the snow layer absorption (except for the absorption predicted for the top layer by the snow optics submodel, which is assigned to the surface energy budget), with the remainder penetrating snow layers absorbed in the top lake body ice layer.

For unfrozen lakes, the solar radiation remaining at depth \\(z>z\_{a}\\) in the lake body is given by

(2.12.44)[¶](#equation-12-39 "Permalink to this equation")\\\[\\phi =\\left(1-\\beta \\vec{S}\_{g} \\right)\\exp \\left\\{-\\eta \\left(z-z\_{a} \\right)\\right\\} .\\\]

For all lake body layers, the flux absorbed by the layer _i_, \\(\\phi \_{i}\\) , is

(2.12.45)[¶](#equation-12-40 "Permalink to this equation")\\\[\\phi \_{i} =\\left(1-\\beta \\vec{S}\_{g} \\right)\\left\[\\exp \\left\\{-\\eta \\left(z\_{i} -\\frac{\\Delta z\_{i} }{2} -z\_{a} \\right)\\right\\}-\\exp \\left\\{-\\eta \\left(z\_{i} +\\frac{\\Delta z\_{i} }{2} -z\_{a} \\right)\\right\\}\\right\] .\\\]

The argument of each exponent is constrained to be non-negative (so \\(\\phi \_{i}\\) = 0 for layers contained within \\({z}\_{a}\\)). The remaining flux exiting the bottom of layer \\(i=N\_{levlak}\\) is absorbed in the top soil layer.

The light extinction coefficient \\(\\eta\\) (m\-1), if not provided as external data, is a function of depth _d_ (m) ([Subin et al. (2012a)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#subinetal2012a)):

(2.12.46)[¶](#equation-12-41 "Permalink to this equation")\\\[\\eta =1.1925d^{-0.424} .\\\]

