Sea-ice thickness distribution ($g(\mathbf{x},h,t)$)

A sea-ice thickness distribution assigns fractional horizontal area to ice thickness intervals: $g(h)dh$ is the fraction between $h$ and $h+dh$. Include open water as a mass at $h=0$ when normalizing over the entire ocean area. The first moment is ice volume per ocean area. With growth rate $f$ and velocity $v$, its conservative evolution is ${\partial }_{t}g+\nabla \cdot (vg)+{\partial }_h(fg)=\psi$, with mechanical redistribution of sea ice represented by $\psi$.

// Target: geophysics.bigb

Mechanical redistribution of sea ice changes thickness-class area through ridging, rafting and lead formation. In the conservative thickness-distribution equation, local volume conservation gives $\int h\psi (h)dh=0$; area normalization including open water gives $\int \psi (h)dh=\nabla \cdot v$ when thermodynamic boundary fluxes are accounted for consistently.

// Target: geophysics.bigb