Formulation and solution of the inverse problem for Jupiter's atmospheric vortices

[Chapter 1] Jupiter's Great Red Spot (GRS) has been observed in sufficient detail that we can use it to determine properties of the Jovian atmosphere that cannot otherwise be found. These properties include: the potential vorticity of the GRS and its neighboring zonal jet streams, the shear imposed on the GRS by the jet streams, and the vertical entropy gradient (i.e., Rossby deformation radius). We show that the cloud cover of the GRS, which is often used to define the GRS's area and aspect ratio, differs significantly from the region of the GRS's potential vorticity anomaly.;[Chapter 2] The stratification of Jupiter's weather layer, as well as various parameters that describe the potential vorticity distribution of Jupiter's jetstreams and vortices, cannot be measured directly. On the other hand, the horizontal velocity fields of the vortices and jetstreams can be measured, and the PDEs that govern the flow---the Quasi-Geostrophic equations or the more complex Shallow-Water equations---show that the horizontal velocity field is a sensitive function of the unknown parameters. This suggests that the unknown parameters can be estimated by solving an inverse problem. Specifically, parameter values can be sought such that a velocity field described by the governing equations matches the measured velocity field to within the observational uncertainties. Previous attempts to solve this inverse problem used expensive initial-value simulations of the governing equations, and were therefore restricted to manual explorations of parameter space. Here a new numerical method is presented for computing steady-state velocity fields of the Quasi-Geostrophic and Shallow-Water equations that resemble flows on Jupiter. This numerical method, which is several orders of magnitude more efficient than an equivalent initial-value solver, is combined with a genetic algorithm to efficiently and robustly search a relatively large portion of parameter space for "best-fit" values of the unknown parameters.;[Chapter 3] Using a fast steady-solver coupled with a genetic algorithm, we have solved inverse problems for Jupiter's Great Red Spot (GRS), Oval BA and their ambient jet streams. We found "best-fit" values of the properties of the ambient atmosphere, such as its vertical stratification (parametrized by the Rossby deformation radius), as well as of the size, shape and strengths of the potential vorticity (PV) anomalies that define the GRS and Oval BA. We also found "best-fit" values of the locations and PV gradients of the jet streams. Uncertainties of the "best-fit" parameters are determined with Monte Carlo methods. Our main conclusions are that the areas of the clouds of the GRS and Oval are much larger than the areas of their PV anomalies.