CLIM Spring 2018: Data Assimilation in Dynamical Systems

Schedule
Tuesdays 4:30 pm-7:00pm at SAMSI, Research Triangle Park, NC, beginning Tuesday, January 16, 2018
No class March 13, 2018
Last class: Tuesday, April 24, 2018
Final Presentation: TBD

Date Class Speaker Presentation
Jan 16 Intro to DA and Basic Examples Amit Apte
Jan 23 Dynamical Systems: Stability, Chaos, Predictability Chris Jones
Jan 30 Computations of Dynamical Systems and Lab Amit Apte
Feb 6 Lyapunov Exponents and Lab Erik Van Vleck
Feb 13 Variational Methods Chris Jones
Feb 20 Filtering Theory Introduction Amit Apte
Feb 27 Discrete State Space Models Erik Van Vleck
Mar 6 Ensemble Kalman Filter Erik Van Vleck
Mar 13 **NO CLASS – Spring Break**
Mar 20 Particle Filtering Chris Jones
Mar 27 Computations and filtering (EnKF, PF) Erik Van Vleck
Apr 3 Lagrangian DA (LaDA) and Parameter Estimation (PE) Chris Jones
Apr 10 Computations in LaDA and PE Amit Apte
Apr 17 Project presentations

Instructors:

  1. Chris Jones, University of North Carolina at Chapel Hill
  2. Amit Apte, International Center for Theoretical Sciences (ICTS)
  3. Erik Van Vleck, University of Kansas

Course Outline: This course is being offered in conjunction with the SAMSI year-long research program on Mathematical and Statistical Methods for Climate and the Earth System. The course will cover statistical and computational methods for the analysis of data arising in climate research. Specific topics will include:

  • Dynamical systems: unstable manifolds and attractors, Lyapunov exponents, sensitivity to initial conditions and concept of predictability.
  • Data assimilation and filtering theory: Bayesian viewpoint
  • Nonlinear Filtering: Particle filtering and sampling methods
  • Advanced topics: parameter estimation, Lagrangian data assimilation

Prerequisites: The course is intended for graduate students in statistics, mathematics or other mathematically related disciplines. Students in fields such as atmospheric and oceanic sciences are welcome to attend provided they have exposure to mathematical courses at an appropriate level, such as a standard undergraduate calculus, a course in linear algebra and some course in probability or statistics

Assessment: Each student will be expected to conduct a small project developed in consultation with the instructors. Depending on the number of students in the course, students may be grouped into teams of two or three students. Each student or team will present their findings at the final class sessions, and should also prepare a short written report.

Grading: Final grades will be based on course projects and some assigned out-of-class work. There will be no exams.

Registration: (processed through the respective university)

  • UNC-CH: STOR 894.001 and MATH 892.001
  • Duke: STA 790.01 (MATH 790-71-01)
  • NCSU: MA 810.001

Questions: email climate@samsi.info