Semi-Lagrangian Advection Methods and Their Applications in Geosciences provides a much-needed resource on semi-Lagrangian theory and methods. Covering a variety of applications, the book brings together developments in a single source, offering a comparison of semi-Lagrangian and Eulerian based approaches. The book also includes a chapter dedicated to the difficulties of dealing with the adjoint of semi-Lagrangian methods and illustrates the behavior of different schemes for different applications. Users will gain 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 or advection, and for researchers and practitioners applying these techniques to geoscientific modeling, this book 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
- Presents exercises and codes to supplement learning and create opportunities for practice
- Covers 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
2. History of Semi-Lagrangian methods
3. Eulerian Modelling of Advection/Transport
4. Stability and Consistency of Eulerian Methods
5. Semi-Lagrangian for constant linear Advection/Transport
6. Interpolation Methods
7. Non-constant velocity methods
8. Non-zero/non-Linear Forcing
9. Semi-Implicit Semi-Lagrangian Methods
10. 2D modelling
11. 3D Modelling
12. Semi-Lagrangian methods on the sphere
13. Adjoints of Eulerian and Semi-Lagrangian methods
14. Applications in the geosciences.
Dr. Fletcher obtained his Bachelor's degree with honors in Mathematics and Statistics from the University of Reading in 1998. He obtained his Master's degree in Numerical Solutions to Differential Equations from the University of Reading in 1999. He obtained his Ph.D. in Mathematics/Data Assimilation in 2004, again from the University of Reading.
Since 2004, Dr. Fletcher has been a postdoctoral fellow, Research Scientist II, and is currently a Research Scientist III at the Cooperative Institute for Research in the Atmosphere (CIRA) at Colorado State University, where he has worked extensively on extending the Gaussian bases for variational and PSAS based data assimilation methods to allow for the minimization of lognormally distributed errors. He has also derived the theory to allow for Gaussian and lognormally distributed errors to be minimized simultaneously through deriving a mixed Gaussian-lognormal multivariate distribution. This mixed distribution has been applied for 3D and 4DVAR theory, for both full field and incremental formulations. Recently, Dr. Fletcher was able to derive a representer based formulation of 4DVAR for the mixed distribution, which is the basis of NAVDAS-AR, the US Navy's numerical weather prediction system. The mixed distribution has also been applied in a retrieval system at CIRA for the retrieval of temperature and mixing ratio values given microwave based brightness temperatures, and it was shown that the mixed approach would obtain better fits to the observations compared to a logarithmic transform and a Gaussian fits all approach.
Dr. Fletcher is an active member in the Nonlinear Geophysics focus group of the American Geophysical Union, where he fills the role of the focus group's representative on the program committee for the Annual Fall meeting, which is the largest meeting of geoscientists in the world.