Implementation of higher-order advection schemes in a numerical ice-sheet model for ice-core studies

Computation of temperature and age fields by numerical ice-sheet models is an important issue for ice-core related studies.  Generally the evolution of temperature and/or age in an ice-sheet model is formulated using an advection equation.  There are many variation of the formulation, which differ in numerical aspects such as stability, accuracy, numerical diffusivity, conservation and/or computational costs.  Saito et al (2020, GMD) implement Rational Constrained Interpolation Profile (RCIP) scheme on vertical 1-d age computation of ice sheet, and demonstrate its efficiency, in particular, to preserve surface mass balance properties recorded at the deposit in terms of annual layer thickness.  Successively, we have been extending the development using RCIP or similar higher-order advection schemes on 3-d age or temperature computation.  In this study, we demonstrate 1-d temperature computation by various numerical schemes including classical upwind schemes and compare the accuracy of those schemes.