Announcement of a new course

Term: Spring 1997

Title: METO 658O "Estimation Theory and Foundations of Data Assimilation"

Credits: 3

Time and days: Monday and Wednesday, 5:15-6:45 pm

Location: CSS 2114 (old classroom)

Prerequisites: Consent of instructor.

The course is a joint effort between Ricardo Todling and Peter Lyster of GSFC who are affiliated with JCESS, and Jim Carton and Ferd Baer of UMCP/Dept. Of Meteorology. Details follow.

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Details of 658O with a draft syllabus.

The goal of this class is to give a solid introduction to atmospheric data assimilation. As such, we will start by studying concepts in statistics and estimation theory which consist the mathematical basis of data assimilation. The first half of the lectures will be devoted to the basic mathematical framework, while the second half will be devoted to the problems of atmospheric data assimilation.

In the first half we will discuss concepts of probability theory such as probability densities, Bayes Theorem, random variables, stochastic processes, and random fields. We will also discuss the basics of stochastic dynamical systems for continuous and discrete time processes. Concepts in estimation theory such as minimum variance, maximum likelihood and maximum a posteriori estimation will be discussed with emphasis on their similarities and differences. The linear Kalman filter will be presented as the approach for linear estimation problems; its properties and computational requirements will be discussed. The first half of these lectures will end with a brief introduction to nonlinear estimation where we will derive the extended Kalman filter and discuss its range of applicability and weaknesses.

In the second half of the course, we will present the basics of atmospheric dynamics, thus requiring no prior knowledge of the subject. The basic equations governing atmospheric flows will be introduced; some important balance relations will be discussed; the linear shallow water equations will be used to illustrate the approach of numerical weather prediction where a simple finite difference scheme will be applied. The problem of initialization will be studied in the linear context. After these basic concepts we will discuss conventional data assimilation techniques such as dynamic relaxation and optimal interpolation. A fair amount of time will be devoted to advanced data assimilation techniques: balanced error covariance generation; non-separable error covariance models; and error covariance tuning are among the techniques to be discussed. The behavior of advanced techniques like the Kalman filter will addressed in a simple context. Assimilation for nonlinear systems will be briefly studied for simple chaotic dynamics. Variational four-dimensional data assimilation will also be a topic of study.

PRE-REQUISITES:

This course is mostly directed to beginning graduate students, although senior undergraduate students with good mathematical background will also be capable of following the lectures. The students are expected to have had at least an introduction to the following subjects: basic calculus, ordinary differential equations, introduction to partial differential equations. The students are also expected to be familiar with some programming language; at least one of: FORTRAN, C, Matlab, IDL, or equivalent.

PLANNED LECTURES: (not scaled to UMCP lecture times)

1. Probability Theory

2. Stochastic Processes and Stochastic Fields

3. Introduction to Stochastic Differential Equations

4. Introduction to Estimation Theory

5. Introduction to Estimation Theory (cont.)

6. The Linear Kalman Filter

7. The Kalman Filter Properties

8. Basic Concepts in Nonlinear Filtering

9. Basic Concepts in Atmospheric Dynamics

10. Conventional Data Assimilation Methods

11. Conventional Data Assimilation Methods (cont.)

12. Advanced Data Assimilation Methods

13. Advanced Data Assimilation Methods (cont.)

STUDENT'S EVALUATION:

Students will be evaluated on the basis of take home problems. These problems will be both analytical and computational, requiring the student to solve them on the computer.