This book offers an overview of advanced techniques to study atmospheric dynamics by numerical experimentation. It is primarily intended for scientists and graduate students working on interdisciplinary research problems at the intersection of the atmospheric sciences, applied mathematics, statistics and physics. Scientists interested in adopting techniques from the atmospheric sciences to study other complex systems may also find most of the topics covered in the book interesting. The specific techniques covered in the book have either proven or potential value in solving practical problems of atmospheric dynamics.
The Atmospheric Governing Equations: Introduction; The Governing Equations; Alternate Vertical Coordinates; Filtered Model Equations; Atmospheric Waves; Global Energetics; Potential Vorticity; Numerical Models: Introduction; Toy Models; Simple Models; Realistic Models; Data Assimilation: The Generation of Initial Conditions: Introduction; General Formulation of the Analysis Problem; Nonlinear Case: Extended Kalman Filter; 3-Dimensional Algorithms; 4-Dimensional Algorithms; Ensemble-based Kalman Filtering; Account for the Effect of Model Errors in Data Assimilation; Local Diagnostics: Atmospheric Wave Packets; Local Energetics; PV-thinking; Ensemble based Diagnostics.