# Research about nontraditional Coriolis terms

Zonal temporal dispersion relations of the equatorially confined wave solutions with (black) and without (red) the nontraditional Coriolis terms (NCTs). Except the last frame of the animation, sound of piano is played at a sound frequency proportional to the effective buoyancy frequency used to plot every frame. (From Ong and Roundy 2020)

NCTs represent components of Coriolis force that turn eastward motion upward and upward motion westward, and vice versa.

# Motivation

Most of the current global atmospheric models use the hydrostatic approximation to predict atmospheric motion, omitting NCTs and the vertical acceleration term. To justify the hydrostatic approximation, according to a scale analysis, the buoyancy term is much larger than the vertical NCT for midlatitude atmospheric flow, and the vertical NCT is much larger than the vertical acceleration term for atmospheric flow whose width is larger than depth. However, on the pathway toward relaxing the hydrostatic approximation, many models restore the vertical acceleration term but not NCTs. Moreover, for tropical large-scale flow, the buoyancy term may be small enough to consider NCTs. Is there any consequence of these inconsistencies?

# Summary

In linear models, NCTs affect the flow response to heat sources by ~10%, and the hypsometric relation by ~5%, and the equatorial wave phase speed by ~0.25 m/s. Unlike many numerical errors in the models, these effects don’t start small and grow large with time integration. Instead, omitting these effects biases the initial pressure-height relation and biases the zonal wind and wave propagation every time step. These biases may grow even larger if nonlinear processes are considered, which is left for future studies. These results encourage restoring NCTs into the models for more-accurate simulations for tropical large-scale flow. This restoration is not going to resolve all the problems, and the importance of improving the representation of physical processes is not downgraded. However, the restoration of NCTs should be among the top priorities of model development, because all other parts of the development depend on the choice of governing equations.

# Broader Impact

My Ph.D. dissertation suggests that NCTs are considerable in tropical large-scale atmospheric dynamics, but NCTs are omitted in most of the current global models. The ongoing work may further improve our understanding of effects of NCTs and may also lead the weather and climate modeling community to include NCTs into their models to improve prediction, which improves our lives.

# Honors and Awards

Three of my honors and awards are directly related to this project.

Climate and Global Change Postdoctoral Fellowship, NOAA (2020-2022) (My name is not on the list of awardees because I declined the award)

Government Scholarship to Study Abroad, Ministry of Education, Taiwan (2019-2020)

Student Presenter Award - Poster 1st Place, Annual Meeting, AMS (2019)

# Video

Recorded PhD Dissertation Defense:

# Project Status

My ongoing main project (2018-)