# A new dynamical core of the Global Environmental Multiscale (GEM) model with a height-based terrain-following vertical coordinate

## TL;DR

This paper introduces a height-based dynamical core for the GEM atmospheric model, aiming to improve stability over steep terrain and offering an efficient direct solver alternative to iterative methods.

## Contribution

It presents a novel height-based vertical coordinate dynamical core with a simplified direct solver, enhancing stability and computational efficiency for high-resolution atmospheric modeling.

## Key findings

- Direct solver performs equivalently to iterative solver across resolutions
- Height-based core yields results comparable to existing pressure-based core
- Improved stability over steep terrain with the new vertical coordinate

## Abstract

A new dynamical core of Environment and Climate Change Canada's Global Environmental Multiscale (GEM) atmospheric model is presented. Unlike the existing log-hydrostatic-pressure-type terrain-following vertical coordinate, the proposed core adopts a height-based approach. The move to a height-based vertical coordinate is motivated by its potential for improving model stability over steep terrain, which is expected to become more prevalent with the increasing demand for very high resolution forecasting systems. A dynamical core with height-based vertical coordinate generally requires an iterative solution approach. In addition to a three-dimensional iterative solver, a simplified approach has been devised allowing the use of a direct solver for the new dynamical core that separates a three-dimensional elliptic boundary value problem into a set of two-dimensional independent Helmholtz problems. The new dynamical core is evaluated using numerical experiments that include two-dimensional nonhydrostatic theoretical cases as well as 25-km resolution global forecasts. For a wide range of horizontal grid resolutions---from a few meters to up to 25 km---the results from the direct solution approach is found to be equivalent to the iterative approach for the new dynamical core. Furthermore, results from the numerical experiments confirm that the new height-based dynamical core leads to results that are equivalent to the existing pressure-based core.