Summary:

Energy Conservation in the Lake Model

The article describes the process of checking energy conservation in the lake model. The total enthalpy of the lake system (H_tot) is calculated using the following equation:

H_tot = Σ[c_v,i(T_i - T_f) + M_liq,i H_fus] - W_sno,bulk H_fus

Where c_v,i is the volumetric heat capacity, T_i is the temperature, T_f is the freezing temperature, M_liq,i is the water mass, H_fus is the latent heat of fusion, and W_sno,bulk is the mass of snow-ice not present in resolved snow layers.

This expression is evaluated at the beginning and end of the timestep, and the change is compared with the net surface energy flux to yield the error flux (E_soi):

E_soi = (ΔH_tot / Δt) - G - Σ φ_i

If |E_soi| < 0.1 W/m^2, it is subtracted from the sensible heat flux and added to the ground heat flux (G). Otherwise, the model is aborted.

The article emphasizes the importance of ensuring energy conservation in the lake model to maintain accurate simulations.