age_flow_line-1.0: a fast and accurate numerical age model for a pseudo-steady flow tube of an ice sheet

Numerical age models are useful tools for investigating the age of the ice in an ice sheet. They can be used to date ice cores or to interpret isochronal horizons which are observed by radar instruments. Here, we present a new numerical age model for a flow line of an ice sheet. The assumption here is that the geometry of the flow line and the velocity shape functions are steady (i.e. constant in time). A time-varying factor can only be applied to the surface accumulation rates and basal melting rates. Our model uses an innovative logarithmic flux coordinate system (π , θ ), previously published, which is suitable for solving transport equations because it tracks ice trajectories. Using this coordinate system, solving the age equation is simple, fast and accurate, because the trajectories of ice particles pass exactly through the nodes of the grid. Our numerical scheme, called Eulerian-Lagrangian, therefore combines the advantages of Eulerian and Lagrangian schemes. We present an application of this model to the flow line going from Dome C to the Beyond EPICA Little Dome C drill site and show that horizontal flow is a non-negligible factor which should be considered when modelling the age-depth relationship of the Beyond EPICA ice core. The code we developed for age modelling along a flow tube is named age_flow_line-1.0 and is freely available under an open-source license.