= Ocean-heat correction to seasonal ice growth
{title2=$F_O=\lambda_O(T_O-T_m)$}
For $T_A=T_m+\Delta T\cos(t/\tau)$ and $F_O=\lambda_O(T_O-T_m)$, put $r=F_O/(\lambda_A\Delta T)$. Open-water freezing requires $r<1$ and starts at $t_1=\tau\arccos(-r)$. Neglecting ocean heat during growth is a bulk approximation when $r(1+\lambda_Ah_m/k)\ll1$. It cannot hold pointwise at the onset or maximum, where the atmospheric removal and ocean input are comparable. The actual maximum satisfies $-\cos(t_2/\tau)=r[1+\lambda_Ah(t_2)/k]$; neglecting $F_O$ gives $t_2=3\pi\tau/2$.
Back to article page
