Ice ablation

Ice ablation removes glacier or ice-sheet material by melting, sublimation, or mechanical loss. A negative net ice accumulation rate removes ice only where ice is present; an initially bare region cannot acquire negative thickness.

Salt lowers the freezing temperature of water. Consequently ice can ablate in saline water below the pure-water melting temperature if the ocean is warmer than its own liquidus. Solute diffusion towards the interface sustains the freezing-point depression. In the diffusive glacier-ablation interface law, small compositional Péclet number makes interfacial salinity close to ocean salinity and gives $P\simeq [T_{\infty }-T_m+\Gamma (C_{\infty }-C_s)]/[LD/(c_p\kappa )+\Gamma (C_{\infty }-C_s)]$ near the no-ablation threshold. This is diffusion-assisted dissolution rather than a supply of heat above the pure-water melting point; latent heat must still be supplied to complete the phase change.

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.