Summary of the Article:

Surface Properties of Lakes

1. Shortwave Radiation Absorption:
   - The fraction of shortwave radiation absorbed at the surface (β) depends on the lake state.
   - If snow layers are present, β is set equal to the absorption fraction predicted by the snow-optics submodel.
   - Otherwise, β is set equal to the near-infrared fraction of the shortwave radiation reaching the surface.

2. Surface Roughness:
   - For unfrozen lakes (T_g > T_f):
     - The momentum roughness length (z_0m) is calculated using the Subin et al. (2012a) equation, which considers the kinematic viscosity of air and the friction velocity.
     - The scalar roughness lengths (z_0q and z_0h) are calculated based on the momentum roughness length and the near-surface atmospheric roughness Reynolds number.
   - For frozen lakes (T_g ≤ T_f) without snow layers:
     - z_0m is set to a constant value of 2.3 × 10^-3 m (Meier et al. 2022).
   - For frozen lakes with snow layers:
     - z_0m is calculated based on the accumulated snow melt (M_a) using the equations provided (Meier et al. 2022).
   - For frozen lakes, the initial scalar roughness lengths are derived assuming θ_* = 0, and then updated within the stability iteration.

The article provides the detailed equations and parameters used to calculate the surface properties of lakes, including the shortwave radiation absorption and the surface roughness characteristics for different lake states.