Iceberg melt heat budget ($Q=\int {\rho }_i[L_f+c_i(T_m-T_i)]dV$)

For an initially cold iceberg, melting to liquid at temperature $T_m$ requires both latent heat of fusion $L_f$ and sensible warming determined by the ice specific heat capacity $c_i$. Spatial mass density and temperature profiles determine their mass-weighted integrals. Additional warming of the meltwater requires a separate heat contribution.