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 Prediction and Predictability in the Atmosphere an  posted by  boym   on 2/9/2008  Add Courseware to favorites Add To Favorites  
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Abstract/Syllabus:

12.990 Prediction and Predictability in the Atmosphere and Oceans

Spring 2003

Structure of the stable manifold for a two-dimensional, chaotic map.
Structure of the stable manifold for a two-dimensional, chaotic map. Black dots are points on the model attractor and red line is the local structure of the stable manifold - all points on the stable manifold collapse to the same point as they are integrated forward in time. The colors are a representation of the distance between a point in the space and a specified model trajectory. Note that the stable manifold lies in the minimum of this cost function space. (Courtesy of Prof. Jim Hansen.)

Course Highlights

This course includes assignments and MATLAB® scripts.

Course Description

Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.

Technical Requirements

MATLAB® software is required to run the .m files found on this course site.

Syllabus

 
 
Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.

Each of the five major topics covered (chaos, probabilistic forecasting, data assimilation, adaptive observations, and impact of model error) could be a complete class on its own, so the course will necessarily be treated as an overview.


Expectations

It is presumed that students have a basic understanding of linear algebra, and a working knowledge of a visualization software package (such as MATLAB®), and a programming language (MATLAB® or Fortran, preferably).


Course Components

The course has four main components: 1) lectures, 2) readings, 3) problem sets, and 4) project.

  1. Lectures: The lectures are intended to introduce key concepts and to set them into the context of geophysical problems when appropriate.

  2. Reading: Relevant journal articles will be provided during class. There will be occasional reading assignments where groups of students will be expected to present the content of the reading to the class. There is no textbook, but there are several books relevant to the course material:

    Ott, E., T. Sauer, and J. Yorke. Coping with Chaos. 1994.

    Wilks, D. Statistical Methods in the Atmospheric Sciences. 1995.

    Daley, R. Atmospheric Data Analysis. 1991.

    Wunsch, C. The Ocean Circulation Inverse Problem. 1996.

    Kalnay, E. Atmospheric Modeling, Data Assimilation, and Predictability. 2003.

  3. Problem Sets: Problem sets will be assigned roughly every other week, and will contribute to half the final grade. It is anticipated that all problem sets will have a strong computing component. Homework assignments will be made during lectures and will be listed on the course web site. In general, late homework will not be accepted, although exceptions for extreme situations will be considered on a case-by-case basis.

  4. Project: Each student will be expected to complete a prediction/predictability related project that will have both a written and an oral component. The project will make up half the final grade. Suggested projects will be distributed at the beginning of the course, but students should feel free to contact the instructor directly to help define a project relevant to their area of research. The instructor must agree with all projects.


Exams and Grading

There will be no exams. Grading will be apportioned 50% Problem Sets, 50% Project.

Calendar

 
 
SES # TOPICS KEY DATES
1 Introduction/Prediction Needs

Course Description and Expectations

Motivation

Presentation of Possible Project Topics		  
2-4 Attractors and Dimensions

Definitions (Ses #2)

Attractor Dimensions (Ses #3)

Embedding (Ses #4)		 Problem Set 1 out (Ses #3)
5-10 Sensitive Dependence to Initial Conditions

Lyapunov Exponents (Ses #5-6)

Singular Vectors and Norms (Ses #7-9)

Validity of Linearity Assumption (Ses #10)		 Problem Set 1 due (Ses #5)

Problem Set 2 out (Ses #6)

Problem Set 1 returned (Ses #7)

Problem Set 2 due (Ses #8)

Problem Set 2 returned (Ses #10)

Problem Set 3 out (Ses #10)
11-18 Probabilistic Forecasting

Probability Primer (Ses #12)

Stochastic-Dynamic Prediction (Ses #11-12)

Monte-Carlo (Ensemble) Approximation (Ses #12)

Ensemble Forecasting Climate Change (Ses #13, 15, 17)

Ensemble Construction (Perfect, Unconstrained, Constrained) (Ses #16)

Ensemble Assessment (Ses #18)		 Problem Set 3 due (Ses #12)

Problem Set 3 returned (Ses #13)
19-22 Data Assimilation

Definition and Kalman Filter Derivations (Ses #19-20)

3dVar and 4dVar Derivations (Ses #20)

Adjoint Models (Ses #21)

Nonlinear Data Assimilation (Ses #21)

Ensemble-Based Data Assimilation (Ses #22)		 Problem Set 4 out (Ses #19)

Problem Set 4 due (Ses #22)



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