WAVETRISK-1.0: An adaptive wavelet hydrostatic dynamical core

This paper presents the new adaptive dynamical core <code>wavetrisk</code>. The fundamental features of the wavelet-based adaptivity were developed for the shallow water equation on the <span classCombining double low line"inline-formula">β</span> plane and extended to the icosahedral grid on the sphere in previous work by the authors. The three-dimensional dynamical core solves the compressible hydrostatic multilayer rotating shallow water equations on a multiscale dynamically adapted grid. The equations are discretized using a Lagrangian vertical coordinate version of the <code>dynamico</code> model. The horizontal computational grid is adapted at each time step to ensure a user-specified relative error in either the tendencies or the solution. The Lagrangian vertical grid is remapped using an arbitrary Lagrangian-Eulerian (ALE) algorithm onto the initial hybrid <span classCombining double low line"inline-formula">σ</span>-pressure-based coordinates as necessary. The resulting grid is adapted horizontally but uniform over all vertical layers. Thus, the three-dimensional grid is a set of columns of varying sizes. The code is parallelized by domain decomposition using <code>mpi</code>, and the variables are stored in a hybrid data structure of dyadic quad trees and patches. A low-storage explicit fourth-order Runge-Kutta scheme is used for time integration. Validation results are presented for three standard dynamical core test cases: mountain-induced Rossby wave train, baroclinic instability of a jet stream and the Held and Suarez simplified general circulation model. The results confirm good strong parallel scaling and demonstrate that <code>wavetrisk</code> can achieve grid compression ratios of several hundred times compared with an equivalent static grid model.