{c}
{title2=$L_\infty=HU/F,\quad\tau=H/F$}

The simplest Pease polynya model balances offshore ice export at speed $U$ against production of new ice at thickness rate $F$ within an open strip of width $L$. Newly formed ice is collected into an edge of prescribed thickness $H$, with negligible residence time. Per unit coastline length, conservation gives $H(U-\dot L)=FL$. For constant positive parameters,
$$
\dot L=U-\frac FH L,\qquad L(t)=\frac{HU}{F}+\left(L(0)-\frac{HU}{F}\right)e^{-Ft/H}.
$$
Thus the equilibrium width is $HU/F$ and the relaxation time is $H/F$. If warming reduces $F$ while $U,H$ stay fixed, both increase. With $F\leq0$ the positive-freezing equilibrium ceases to apply. Finite <frazil ice> residence, variable atmospheric forcing and alongshore transport require extensions of the model.


 Pease polynya model (source code)