= Diffusive glacier-ablation interface law
{title2=$A_TP=T_\infty-T_m+\Gamma(C_\infty-C_s)/(1+P)$}
In a constant-thickness laminar <boundary layer> at an ablating glacier, approximate fluxes by $\kappa(T_\infty-T_i)/\delta$ and $D(C_\infty-C_i)/\delta$. Neglect solid diffusion and sensible heating relative to <latent heat>. With ablation speed $U>0$, solute balance gives $U(C_i-C_s)=D(C_\infty-C_i)/\delta$, so $C_i=C_s+(C_\infty-C_s)/(1+P)$, $P=U\delta/D$. The <liquidus> $T_i=T_m-\Gamma(C_i-C_s)$ and <Stefan condition> $UL/c_p=\kappa(T_\infty-T_i)/\delta$ then give the displayed law, where $A_T=LD/(c_p\kappa)$. Its positive root exists when the ocean is above its own freezing point. In the small-$P$ regime, interface salinity approaches ocean salinity; in the large-$P$ regime it approaches the ice composition.
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