MATH 6790: Numerical Modeling of Geophysical Flow
Spring 2006
Philosophy and Objectives
Atmospheric flow represents a forced dissipative nonlinear system which is extremely difficult to predict. As part of "Case studies in Computational Engineering" (MATH 6790), I will give a 5 week long sequence (Jan 10th - Feb 9th) on numerical modeling of environmental flow systems. The goal of this class is to understand the prospects and limitations in forecasting dynamical systems such as the atmosphere or the oceans, to demonstrate how the problem can be approached using numerical methods, and to give some hands-on experience in running a rather simple but illuminating atmospheric model. The format of the class will be primarily lectures.

Students from the Department of Meteorology are welcome to audit the 5 week long course sequence. The class will meet in 490 INSCC except for the first class (Jan 10th), which will take place in 208 JWB.

The class MATH 6790 fulfills one of the requirements for the Computational Engineering and Science (CES) Program here at the University. Enrollment in the program is necessary to obtain CES Certificate or MS credit. If you are interested in learning more about the CES program, please visit CES or contact Coralee Bernard (coralee@cs.utah.edu, 581-3455).

Course outline
We will begin with a discussion of the primitive equations that govern geophysical flow systems and we will learn how those equations can be simplified. Common numerical methods for the solution of those equations (and those of any other dynamical system) will be discussed, such as finite differences, and the more specialized spectral transform technique. Then, we will discuss the problem of forecasting the atmosphere using the simple Lorenz system. Using this system, we will study basic concepts of predictability and chaos in dynamical systems, and we will learn how these concepts can be applied to geophysical flow systems. Later in the course, we will explore those ideas using a realistic but still quite simple atmospheric model which integrates a spectral version of the fully non-linear divergent barotropic vorticity equation.

Class
TuTh 2-3:20 pm
208 JWB (January 10) (map)
490 INSCC (January 12 - February 9) (map)

Instructor
Thomas Reichler
office: 484 INSCC
phone: 585-0040
e-mail: thomas.reichler (at) utah.edu
office hours: after lecture + by appointment

Movie "The day after tomorrow" and Free Pizza
 Fr 01/13, 2-4:30 pm, 490 INSCC
See link for more info.

Prerequisites
Graduate standing and instructor's consent. The class is aimed primarily at first and second year graduate students in all areas of the earth and computer sciences. Working knowledge of algebra and calculus, and basic programming skills (Fortran/C, UNIX, Matlab or similar) will be assumed.

Lecture Notes
I will make available the power point presentation slides after the lecture under the link "Lecture Notes". However, you should be aware that these notes are not meant to be a self contained study material. You are expected to take your own notes during the lecture.

Homework
A total of four homeworks will be assigned every Thursday. Hoemworks are due the following Thursday at the end of class. Check the "Homework" page on the class web page to find your weekly assignment. Late homeworks will not be accepted unless you have a pretty good reason. You are encouraged to work in small groups on your homeworks, but make sure you understand what you write down. Each person in the class must turn in an individual written response to the questions. You are also required to hand in a print-out of your programming code.

Grading
Participation in class discussions and raising questions during lecture are strongly encouraged. Grades will be determined solely from the homeworks.

Required Text
This class requires no particular text book.

Books

  • Lorenz, E. (1993): The essence of chaos, University of Washington Press.
  • Sparrow, C. (1982): The Lorenz equations: Bifurcations, chaos, and strange attractors, Springer.
  • Burden, R., and J. Faires (1997): Numerical analysis, Brooks/Cole Publishing Company.
  • Kreyszig, E. (1993): Advanced engineering mathematics, Wiley and Sons.
  • Kalnay, E. (2004): Atmospheric modeling, data assimilation, and predictability, Cambridge University Press.
  • Trenberth, K.E., ed. (1992): Climate System Modeling, Cambridge University Press.
  • Peixoto, J., and A. Oort (1992): Physics of Climate, American Institute of Physics.
  • Wallace, J. M., and P. V. Hobbs (1977): Atmospheric Science, An Introductory Survey, Academic Press.
  • Washington, W., and C. Parkinson (2005): An introduction to three-dimensional climate modeling, University Science Books.

    Articles

  • Lorenz, E. (1963): Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141.
  • Lorenz, E. (1984): Irregularity: A fundamental property of the atmosphere, Tellus, 36A, 98-110.
  • Lorenz, E. (2005): Designing chaotic models, J. Atmos. Sci., 62, 1574-1587.
  • Sardeshmukh, P., and B. Hoskins (1988): The generation of global rotational flow by steady idealized tropical divergence, J. Atmos. Sci., 45(7), 1228-1251.
  • Palmer, T. (1993): Extended range atmospheric prediction and the Lorenz model, Bull. Amer. Met. Soc., 74(1), 49-65.
  • Palmer, T. (1998): Nonlinear dynamics and climate change: Rossby's legacy, Bull. Amer. Met. Soc., 79(7), 1411-1423.
  • Palmer, T. (1999): A nonlinear dynamical perspective on climate prediction, J. Clim., 12, 575-591.
  • Palmer, T. (2005): Quantum reality, complex numbers, and the meteorological butterfly effect, Bull. Amer. Met. Soc., 86(4), 519-530.
  • Evans, E., et al. (2004): Undergraduates find that regime changes in Lorenz's model are predictable, Bull. Amer. Met. Soc., 85(4), 521-524.

    Programming language tutorials
    Some of your homework will include simple programming and the analysis of specific code, which is usually written in Fortran, and which runs under the various flavours of Unix. IDL and Matlab are powerful data analysis tools, which combine a high level programming language with useful libraries and plotting routines. Help for those languages can be found at:

    Fortran
  • Fortran1
  • Fortran2 Unix
  • Unix1
  • Unix2
  • Unix3
    • Matlab
  • Matlab1
  • Matlab2
  • Matlab3
  • Tips
    • IDL
  • IDL1
  • IDL2
  • IDL3
    •

    ADA Accommodations
    The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangement for accommodations. All written information in this course can be made available in alternative format with prior notification to the Center for Disability Services.

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    Last updated: January 6, 2006.