A Nonhydrostatic Mass-Conserving Dynamical Core for Deep Atmospheres of Variable Composition

TL;DR

This paper introduces two formulations of a nonhydrostatic dynamical core for deep, variable composition atmospheres, demonstrating improved mass conservation and reduced numerical errors in high-altitude atmospheric modeling.

Contribution

It develops and tests a novel nonhydrostatic dynamical core with variable composition capabilities, enhancing accuracy and mass conservation for deep atmospheric simulations.

Findings

Both formulations accurately simulate deep-atmosphere dynamics.

The no-PR version conserves mass to machine precision.

Numerical results agree with established models and codes.

Abstract

This paper develops and tests a deep-atmosphere, nonhydrostatic dynamical core (DyCore) targeted towards ground-thermosphere atmospheric prediction using the spectral element method (SEM) with Implicit-Explicit (IMEX) and Horizontally Explicit Vertically Implicit (HEVI) time-integration. Two versions of the DyCore are presented and tested, each based on a different formulation of the specific internal energy and continuity equations, which, unlike standard potential temperature formulations, are valid for variable composition atmospheres. The first version, which uses a product-rule (PR) forms of the continuity and specific internal energy equation, contains an additional pressure dilation term and does not conserve mass. The second version, which does not use the product-rule (no-PR) in the continuity and specific internal energy, contains two terms to represent pressure dilation and conserves mass to machine precision regardless of time truncation error. The pressure gradient and gravitational forces in the momentum balance equation are reformulated to reduce numerical errors at high altitudes. These new equation sets were implemented in two SEM-based atmospheric models: the Nonhydrostatic Unified Model of the Atmosphere (NUMA) and the Navy Environmental Prediction sysTem Using a Nonhydrostatic Engine (NEPTUNE). Numerical results using both a deep-atmosphere and shallow-atmosphere baroclinic instability, a balanced zonal flow, and a high-altitude orographic gravity wave verify the fidelity of the dynamics at low and high altitudes and for constant and variable composition atmospheres. These results are compared to existing deep-atmosphere dynamical cores and a Fourier-ray code, indicating that the proposed discretized equation sets are viable DyCore candidates for next-generation ground-to-thermosphere atmospheric models.