Summary:

### Heat Capacities

The article discusses the calculation of vertically-integrated heat capacity for each lake layer in the model. The heat capacity is determined by the mass-weighted average of the heat capacities for the water and ice fractions within the layer:

- The heat capacity for each lake layer, c_v,i (J m^-2), is calculated using equation 2.12.47, which takes into account the thickness of the layer (Δz_i), the density of liquid water (ρ_liq), the specific heat capacity of liquid water (c_liq), the specific heat capacity of ice (c_ice), and the ice fraction (I_i) in the layer.

- The total heat capacity (c_v,i) for each soil, snow, and bedrock layer (J m^-2) is determined in a similar way as for vegetated land units, as the sum of the heat capacities for the water, ice, and mineral constituents.

The key points are the formulas used to calculate the heat capacity for lake layers and other soil/snow/bedrock layers, taking into account the composition of each layer.