= Single-category sea-ice thermodynamic model
{title2=$h(t)$}
A single-category model represents local ice by one thickness $h$ and one surface temperature $T_s$. With basal freezing temperature $T_m$, atmospheric temperature $T_A$, <thermal conductivity> $k$ and atmospheric <heat transfer coefficient> $\lambda_A$, quasistatic <thermal conduction> gives
$$
T_s=\frac{kT_m+\lambda_AhT_A}{k+\lambda_Ah}
$$
while $T_s<T_m$. If $F_O$ is upward ocean <heat flux>, the <Stefan condition> gives $\rho L\dot h=\lambda_A(T_m-T_A)/(1+\lambda_Ah/k)-F_O$. During surface melting, $T_s=T_m$ and $\rho L\dot h=-\lambda_A(T_A-T_m)-F_O$ when $T_A\ge T_m$. Thickness is constrained to be nonnegative, and the open-water energy balance applies after complete melt.
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