A high‐accuracy global prognostic model for the simulation of Rossby and gravity wave dynamics

A model for studying Transient Inertia–Gravity And Rossby wave dynamics (TIGAR) is introduced. The presented horizontal component of the model solves the nonlinear rotating shallow‐water equations on the sphere using Hough harmonics. Spectral modelling using Hough harmonics as basis functions describes atmospheric dynamics in terms of physically identifiable structures: Rossby and inertia–gravity eigensolutions of linearized primitive equations. This offers an attractive framework for detangling gravity wave dynamics in high‐resolution simulations. Accurate computations are achieved through the use of higher order integrating factor and exponential time‐differencing methods, leading to a major increase in computational efficiency and stability. A comparison with classical time‐stepping schemes shows accuracy improvements of several orders of magnitude at no additional computational cost. In particular, stability gains are achieved through enhanced accuracy and efficiency in the computation of gravity waves, rather than through their damping. In the new framework, reduced models using Rossby and gravity waves aimed at studying dynamical aspects of data assimilation or wave interactions are easily implemented.

We present new global forecast model for Transient Inertia–Gravity And Rossby wave dynamics (TIGAR). By decomposing the flow into Rossby and gravity wave components and employing exponential time‐differencing schemes, TIGAR achieves remarkable gains in accuracy, efficiency, and stability. The figure compares forecast errors in Rossby and gravity waves computed by TIGAR with different time‐stepping algorithms in a barotropic instability test at T170 resolution.