Semi-Lagrangian Advection Methods and Their Applications in Geoscience provides a much-needed resource on semi-Lagrangian theory, methods, and applications. Covering a variety of applications, the book brings together developments of the semi-Lagrangian in one place and offers a comparison of semi-Lagrangian methods with Eulerian-based approaches. It also includes a chapter dedicated to difficulties of dealing with the adjoint of semi-Lagrangian methods and illustrates the behavior of different schemes for different applications. This allows for a better understanding of which schemes are most efficient, stable, consistent, and likely to introduce the minimum model error into a given problem.
Beneficial for students learning about numerical approximations to advection, researchers applying these techniques to geoscientific modeling, and practitioners looking for the best approach for modeling, Semi-Lagrangian Advection Methods and Their Applications in Geoscience fills a crucial gap in numerical modeling and data assimilation in geoscience.
- Provides a single resource for understanding semi-Lagrangian methods and what is involved in its application
- Includes exercises and codes to supplement learning and create opportunities for practice
- Includes coverage of adjoints, examining the advantages and disadvantages of different approaches in multiple coordinate systems and different discretizations
- Includes links to numerical datasets and animations to further enhance understanding
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1. Introduction 2. Eulerian modeling of advection problems 3. Stability, consistency, and convergence of Eulerian advection based numerical methods 4. History of semi-Lagrangian methods 5. Semi-Lagrangian methods for linear advection problems 6. Interpolation methods 7. Stability and consistency analysis of semi-Lagrangian methods for the linear problem 8. Advection with nonconstant velocities 9. Nonzero forcings 10. Semi-Lagrangian methods for two-dimensional problems 11. Semi-Lagrangian methods for three-dimentional problems 12. Semi-Lagrangian methods on a sphere 13. Shape-preserving and mass-conserving semi-Lagrangian approaches 14. Tangent linear modeling and adjoints of semi-Lagrangian methods 15. Applications of semi-Lagrangian methods in the geosciences
Steven J. Fletcher is a Research Scientist III at the Cooperative Institute for Research in the Atmosphere (CIRA) at Colorado State University, where he is the lead scientist on the development of non-Gaussian based data assimilation theory for variational, PSAS, and hybrid systems. He has worked extensively with the Naval Research Laboratory in Monterey in development of their data assimilation system, as well as working with the National Atmospheric and Oceanic Administration (NOAA)'s Environmental Prediction Centers (EMC) data assimilation system. Dr. Fletcher is extensively involved with the American Geophysical Union (AGU)'s Fall meeting planning committee, having served on the committee since 2013 as the representative of the Nonlinear Geophysics section. He has also been the lead organizer and science program committee member for the Joint Center for Satellite Data Assimilation Summer Colloquium on Satellite Data Assimilation since 2016. Dr. Fletcher is the author of Data Assimilation for the Geosciences: From Theory to Application (Elsevier, 2017). In 2017 Dr. Fletcher became a fellow of the Royal Meteorological Society.