Summary of the Article:

Radiation Penetration in Lake Models

1. Surface Absorption Fraction: 
   - If there are no resolved snow layers, the surface absorption fraction β is set based on the near-infrared fraction simulated by the atmospheric model.
   - This fraction is accounted for in the surface energy budget, and no additional radiation is absorbed in the top 0.6 m of unfrozen lakes.

2. Radiation Absorption in Frozen Lakes:
   - For frozen lakes (Tg ≤ Tf), the remaining (1-β)Sg fraction of surface-absorbed radiation that is not accounted for in the surface energy budget is absorbed in the top lake body layer.
   - This is a simplification, as lake ice is partially transparent.

3. Radiation Absorption in Unfrozen Lakes:
   - For unfrozen lakes, the solar radiation remaining at depth z > za in the lake body is given by the equation φ = (1-βSg) exp(-η(z-za)).
   - The flux absorbed by each lake body layer i, φi, is calculated using a separate equation.
   - The remaining flux exiting the bottom of the deepest layer is absorbed in the top soil layer.

4. Light Extinction Coefficient:
   - The light extinction coefficient η (m^-1) is a function of depth d (m), given by the equation η = 1.1925d^-0.424, if not provided as external data.