MAR572
- Fall 2013

Geophysical Simulations

Wed/Fri 3:00-4:20 pm

Endeavour 158

**Instructors**

Prof. Marat Khairoutdinov

**Office hours**

Endeavour 121; by email appt

**Email**

marat.khairoutdinov@stonybrook.edu

**Textbooks**

The course does not strictly follow any textbook. In fact, the field of computational fluid dynamics and related techniques is too broad to be covered in a single textbook. Therefore, it is important to take class notes. However, here is a short list of recommended books:

Fletcher, C. A. J., 1991: Computational Techniques for Fluid Dynamics, Vol. 1. 2nd ed. Springer-Verlag, 401 pp.

Durran, D. R., 1999: Numerical methods for wave equations in geophysical fluid dynamics. Springer, 465 pp.

Daley, R. 1991: Atmospheric data analysis. Cambridge University Press, 455pp

**Grading**

50% for exams (2) and 1 midterm project, 50% for homework assignments. Final grading will be based on the average of the three section scores.

**Special Note**

Hands-on experience is the best way to learn numerical methods. Homework will involve writing simple programs and plotting the results. You will need to have access to computers with programming and graphing software. Knowledge of high-level compiled (e.g., Fortran (preferred), C) or scripting (e.g., IDL, Matlab) computer languages is required for this course. It is, however, up to you which programming language or graphing application to use.

**Outline **

Fundamentals of Finite-Difference Schemes

Definitions of consistence, convergence, and stability; First and second order derivatives; Construction of higher order approximations; Numerical solution of nonlinear equations.

Methods for Initial-Value Problems of Linear Partial Differential Equations

Linear computational stability analysis; Classification and canonical forms; Basic numerical schemes for advection and diffusion equations; Upstream and downstream biased schemes; Time-integration schemes; Time-splitting and directional splitting schemes; Implicit and explicit schemes; Numerical diffusion and dispersion; Extension to multiple dimensions; Grid systems.

Methods for Nonlinear Initial-Value Problems

Fourier representation of discrete fields; Nonlinear interaction and instability; Methods to eliminate nonlinear instability; Construction of conservation schemes; Monotonic and positive definite schemes; Barotropic vorticity model; the Arakawa Jacobian; Basic concepts of spectral methods; Semi-Lagrangian and finite-volume methods

Methods to Solve Elliptic Equations

Fourier method; Relaxation methods; Multi-grid methods; Tri-diagonal matrix solver

Data Analysis

Classical objective analysis; Statistical estimation; Maximum likelihood estimation;

Least variance estimation; Kalman filtering; Statistical spatial interpolation; Variational analysis method; Adjoint models; Multivariant analysis

**Homework **

Presentations

Coding Efficiency

Americans with Disabilities Act

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information, go to the following web site. http://www.ehs.sunysb.edu/fire/disabilities/asp

Academic Integrity Statement

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Any suspected instance of academic dishonesty will be reported to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/

Adopted by the Undergraduate Council September 12, 2006

Geophysical Simulations

Wed/Fri 3:00-4:20 pm

Endeavour 158

Despite confusing title, this class is
not about how to simulate atmosphere or ocean flows using models.
Rather, it is an introduction to numerical methods of solving
differential and general nonlinear equations, which are common to many
geophysical problems, as well as to advanced data analysis methods.

Endeavour 121; by email appt

marat.khairoutdinov@stonybrook.edu

The course does not strictly follow any textbook. In fact, the field of computational fluid dynamics and related techniques is too broad to be covered in a single textbook. Therefore, it is important to take class notes. However, here is a short list of recommended books:

Fletcher, C. A. J., 1991: Computational Techniques for Fluid Dynamics, Vol. 1. 2nd ed. Springer-Verlag, 401 pp.

Durran, D. R., 1999: Numerical methods for wave equations in geophysical fluid dynamics. Springer, 465 pp.

Daley, R. 1991: Atmospheric data analysis. Cambridge University Press, 455pp

50% for exams (2) and 1 midterm project, 50% for homework assignments. Final grading will be based on the average of the three section scores.

Hands-on experience is the best way to learn numerical methods. Homework will involve writing simple programs and plotting the results. You will need to have access to computers with programming and graphing software. Knowledge of high-level compiled (e.g., Fortran (preferred), C) or scripting (e.g., IDL, Matlab) computer languages is required for this course. It is, however, up to you which programming language or graphing application to use.

Fundamentals of Finite-Difference Schemes

Definitions of consistence, convergence, and stability; First and second order derivatives; Construction of higher order approximations; Numerical solution of nonlinear equations.

Methods for Initial-Value Problems of Linear Partial Differential Equations

Linear computational stability analysis; Classification and canonical forms; Basic numerical schemes for advection and diffusion equations; Upstream and downstream biased schemes; Time-integration schemes; Time-splitting and directional splitting schemes; Implicit and explicit schemes; Numerical diffusion and dispersion; Extension to multiple dimensions; Grid systems.

Methods for Nonlinear Initial-Value Problems

Fourier representation of discrete fields; Nonlinear interaction and instability; Methods to eliminate nonlinear instability; Construction of conservation schemes; Monotonic and positive definite schemes; Barotropic vorticity model; the Arakawa Jacobian; Basic concepts of spectral methods; Semi-Lagrangian and finite-volume methods

Methods to Solve Elliptic Equations

Fourier method; Relaxation methods; Multi-grid methods; Tri-diagonal matrix solver

Data Analysis

Classical objective analysis; Statistical estimation; Maximum likelihood estimation;

Least variance estimation; Kalman filtering; Statistical spatial interpolation; Variational analysis method; Adjoint models; Multivariant analysis

Presentations

Coding Efficiency

Americans with Disabilities Act

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information, go to the following web site. http://www.ehs.sunysb.edu/fire/disabilities/asp

Academic Integrity Statement

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Any suspected instance of academic dishonesty will be reported to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/

Adopted by the Undergraduate Council September 12, 2006