Love number computation within the Ice-sheet and Sea-level System Model (ISSM v4.24)

Abstract. The Love number solver presented here is a new capability within the Ice-sheet and Sea-level System Model (ISSM) for computing the solid-Earth response to tidal forcing and surface mass loading. This new capability allows solving zero-frequency free oscillation equations of motion decomposed into the well-known y_i system and enables high wave number computations with spherical harmonic truncation degree of ~10,000 and above. It facilitates capturing the high-resolution response of the solid Earth to a step-function forcing in terms of gravity potential changes, vertical and horizontal bedrock displacement, and polar motion. The model incorporates compressible isotropic elasticity and three forms of linear viscoelasticity for mantle rheology: the Maxwell, Burgers, and Extended Burgers Materials (EBM). We detail our approach to the paralellization and numerical optimization of the solver, and report the accuracy of our results with respect to community benchmark solutions. Our main motivation is to facilitate simulations of a coupled system of surface mass transport (e.g., changes in polar ice sheets and sea level) and solid Earth models at kilometer-scale lateral resolutions with numerical efficiency that supports the exploration of large model ensembles and uncertainty quantification.