The contour-advective semi-Lagrangian hybrid algorithm approach to weather forecasting and freely propagating inertia-gravity waves in the shallow-water system

Abstract

This thesis is aimed at extending the spherical barotropic contour-advective semi-Lagrangian (CASL) Algorithm, written in 1996 by David Dritschel and Maarten Ambaum, to more complex test cases within the shallow-water context. This is an integral part for development of any numerical model and the accuracy obtained depends on many factors, including knowledge of the initial state of the atmosphere or ocean, the numerical methods applied, and the resolutions used. The work undertaken throughout this thesis is highly varied and produces important steps towards creating a versatile suite of programs to model all types of flow, quickly and accurately. This, as will be explained in later chapters, impacts both public safety and the world economy, since much depends on accurate medium range forecasting. There shall be an investigation of a series of tests which demonstrate certain aspects of a dynamical system and its progression into more unstable situations - including the generation and feedback of freely propagating inertia-gravity waves (hereafter “gravity waves"), which transmit throughout the system. The implications for increasing forecast accuracy will be discussed. Within this thesis two main CASL algorithms are outlined and tested, with the accuracy of the results compared with previous results. In addition, other dynamical fields (besides geopotential height and potential vorticity) are analysed in order to assess how well the models deal with gravity waves. We shall see that such waves are sensitive to the presence, or not, of sharp potential vorticity gradients, as well as to numerical parameter settings. In particular, large time-steps (convenient for semi-Lagrangian schemes) may not only seriously affect gravity waves, but may also have an adverse impact on the primary fields of height and velocity. These problems are exacerbated by a poor resolution of potential vorticity gradients, which we shall attempt to improve.