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.

中文翻译：

---

用于模拟Rossby和重力波动力学的高精度全局预测模型

介绍了一种研究瞬时惯性-重力和罗斯比波动力学的模型（TIGAR）。模型中提出的水平分量使用霍夫谐波求解了球面上的非线性旋转浅水方程。使用霍夫谐波作为基础函数的光谱建模以物理可识别结构的形式描述了大气动力学：线性原始方程式的Rossby和惯性重力本征解。这为在高分辨率模拟中纠缠重力波动力学提供了一个有吸引力的框架。通过使用高阶积分因子和指数时差方法可以实现精确的计算，从而大大提高了计算效率和稳定性。与经典时步方案的比较表明，精度提高了几个数量级，而没有任何额外的计算成本。特别是，通过提高重力波的计算精度和效率而不是通过阻尼来实现稳定性。在新框架中，可以轻松实现使用Rossby和重力波的简化模型，这些模型旨在研究数据同化或波相互作用的动力学方面。