Isochrones and isotherms beneath migrating ice divides

Abstract

We use simple numerical and analytical models of ice flow and heat flow to characterize the shape of isochrones and isotherms beneath moving ice divides. Both nonlinear ice flow and reduced accumulation (wind scouring) at a divide can cause reduced downward flow in a region about one ice thickness wide under a divide. Greater downward velocities on the flanks cause isochrones and isotherms to become arched at depth. The magnitudes and shapes of these arches depend on the history of divide position. Arch amplitudes decrease by approximately e-1 for each increase in migration rate of 3-5 times the accumulation rate, the artches become asymmetric, with steeper leading edges and more gentle trailing edges, and the arch apex lags behind the divide. Isochrone and isotherm shapes can be used to infer past divide motions. In advection-dominated ice sheets, isochrone shapes record a longer history of divide position than do isotherm shapes. The opposite is true for diffusion-dominated ice sheets, in which a spatial array of ice-temperature measurements might extend the recorded history of divide position.