Understanding the Development and Application of Simplified Dynamical Models

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The goal of this research is to provide improved understanding of the dynamics of the tropical atmosphere through the development and application of filtered models. Filtered models are simplified dynamical models that describe low-frequency atmospheric motions but do not allow freely propagating inertia-gravity waves. This project builds on the Principal Investigator's (PI's) research expertise in tropical dynamics and advances his previous work. The project has two main parts, both of which involve the application of filtered models to the tropical atmosphere. Part I focuses on large-scale tropical dynamics and involves the theoretical development of the new and improved filtered models to be used. Part II utilizes theory based on an existing filtered model and focuses on hurricane dynamics. The longwave model is an existing filtered model designed for large-scale tropical applications and has been an important tool in tropical research. It accurately describes Kelvin waves and long Rossby waves, but has the deficiency that it badly distorts short Rossby waves. In part I of this project, the PI will improve the longwave model and thereby provide the tropical research community with an important new tool for understanding large-scale tropical motions. In addition, he will generalize this new filtered model, developed in the framework of equatorial beta-plane theory, to the sphere. This will provide, for the first time, a filtered dynamical model that accurately describes both the global PV dynamics of Rossby-Haurwitz waves and the non-PV dynamics of Kelvin waves. Among the many possible generalizations and applications of these new filtered models, the following will be studied in detail: (a) improved simulations of the MJO; (b) generation of accurate analytical solutions to Laplace's tidal equations; (c) derivation and solution of a "tropical omega-equation" to understand vertical motion fields associated with the Hadley and Walker circulations; (d) derivation and application of a ray tracing theory on the sphere for both inertia-gravity waves and Rossby-Haurwitz waves, with the goal of improved understanding of midlatitude-tropical interactions; (e) development of new spheroidal harmonic (as opposed to spherical harmonic) analysis tools for geophysical turbulence, with the goal of extending the concept of the Rhines' barrier from two-dimensional wavenumber space to three-dimensional wavenumber space.Part II of this project will utilize the Eliassen balanced vortex model, a filtered model designed for tropical cyclone applications, to help us better understand hurricane dynamics, especially the process of rapid intensification. Here the PI will use the geopotential tendency equation, derived from the original momentum, continuity, and thermodynamic equations, to isolate the conditions under which warm-core and warm-ring thermal structures can rapidly develop in a tropical cyclone and the conditions under which a steady state can be approached. Intellectual Merit. While climate simulation and numerical weather prediction usually rely on primitive equation models, understanding of the underlying atmospheric dynamics has come primarily from studies using simplified models. The research will create new filtered model tools for further understanding of atmospheric dynamics, especially in the tropical region. The knowledge gained from applying these models to the problems studied in this project will help answer a number of key questions concerning large-scale atmospheric dynamics and the rapid intensification of hurricanes. Broader Impacts. User-friendly software for the new filtered models will be developed during this project and will be made available to other researchers to facilitate additional studies of atmospheric dynamics. The graduate students involved in this work will receive training and experience which will help prepare them for careers in research. The increased knowledge of fundamental large-scale dynamics and fundamental hurricane dynamics gained from this project should someday contribute to an improved ability to predict both large-scale tropical weather patterns and the mesoscale patterns that lead to changes in hurricane intensity.