Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 77 / 3 / b

The extra ocean heat flux supplies energy per unit areaIn a fixed heat-removal estimate, this offsets the latent heat of fusion that would otherwise form thickness $\Delta H=\Delta Q/({\rho }_i{L}_f)$. Using a standard ice mass density ${\rho }_i\simeq 917\mathrm{kg}{\mathrm{m}}^{-3}$, an additional material assumption,For any other assumed ice density, retain $\Delta H=1.4256\times 10^8/(336000{\rho }_i)$ metres. This is the latent-heat equivalent of the added energy, not an exact coupled growth calculation. Thinner ice conducts heat more readily, so the atmospheric heat-removal budget can respond; a full sea ice thermodynamics model, such as the single-category sea-ice thermodynamic model, includes that compensation.