Abstract
Abstract. Numerical simulations of ice sheets rely on the momentum balance to determine how ice velocities change as the geometry of the system evolves. Ice is generally assumed to follow a Stokes flow with a nonlinear viscosity. Several approximations have been proposed in order to lower the computational cost of a full-Stokes stress balance. A popular option is the Blatter–Pattyn or higher-order model (HO), which consists of a three-dimensional set of equations that solves the horizontal velocities only. However, it still remains computationally expensive for long transient simulations. Here we present a depth-integrated formulation of the HO model, which can be solved on a two-dimensional mesh in the horizontal plane. We employ a specific polynomial function to describe the vertical variation in the velocity, which allows us to integrate the vertical dimension using a semi-analytic integration. We assess the performance of this MOno-Layer Higher-Order (MOLHO) model to compute ice velocities and simulate grounding line dynamics on standard benchmarks (ISMIP-HOM and MISMIP3D). We compare MOLHO results to the ones obtained with the original three-dimensional HO model. We also compare the time performance of both models in time-dependent runs. Our results show that the ice velocities and grounding line positions obtained with MOLHO are in very good agreement with the ones from HO. In terms of computing time, MOLHO requires less than 10 % of the computational time of a typical HO model, for the same simulations. These results suggest that the MOno-Layer Higher-Order formulation provides improved computational time performance and a comparable accuracy compared to the HO formulation, which opens the door to higher-order paleo simulations.
Highlights
Projecting the future evolution of the ice sheets of Greenland and Antarctica and their potential contribution to sea level rise often relies on computer simulations carried out by numerical ice sheet models (e.g., Aschwanden et al, 2019; Goelzer et al, 2020; Seroussi et al, 2020; Edwards et al, 2021)
We present the formulation of a vertically integrated MOno-Layer Higher-Order (MOLHO) model and compare its performance with the three-dimensional Blatter– Pattyn model (HO) using two benchmarks: ISMIP-HOM and MISMIP3D
In the experiments with no basal sliding of the ISMIP-HOM setup, MOLHO produces surface velocities close to the ones obtained by the higher-order model (HO) model for wavelengths of bedrock elevation equal to or higher than 40 km
Summary
Projecting the future evolution of the ice sheets of Greenland and Antarctica and their potential contribution to sea level rise often relies on computer simulations carried out by numerical ice sheet models (e.g., Aschwanden et al, 2019; Goelzer et al, 2020; Seroussi et al, 2020; Edwards et al, 2021). These ice sheet models solve a set of flow equations based on the conservation of momentum to obtain the ice velocity field over the entire ice sheet. This model is computationally demanding, especially in time-dependent numerical simulations, which restricts its use to short-term projections or regional applications
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