NFYK14019U Numerical methods in atmospheric and oceanic models

Volume 2014/2015
Education
M.Sc. physics

Can also be taken as elective on the last year of bachelor, if the teacher judges the student sufficiently qualified. A personal contact to the teacher from the student is required in this case.
Content

The course consists of a mixture between lectures, theoretical exercises and practical exercises in the form of designing, coding and executing smaller computer programs to solve simple problems in GFD modeling. If possible there will also be an excursion to a company/institution where GFD modeling is used in practice, e.g. DMI.

 

The course is essential if one wants to work with atmosphere and/or ocean models later in the study, or if one is interested in jobs, where such models are developed and maintained. Since fundamental and basic numerical methods are introduced in the course it will also be relevant for other students with a more general interest in computational fluid dynamical.

 

The course is initiated with a general overview of the set up and the design used in atmospheric and oceanic fluid dynamical models, and in climate models based on such components. This includes the division into a dynamical core and parameterized processes, and the coupling/interaction between the various components in climate models / Earth system models. Once the scene is set, we can start on the main subject, namely the numerical methods applied to solve the dynamical equations. There will be emphasis on the accuracy and efficiency of the solution of continuity equations for mass and on introduction of numerical schemes ensuring inherent (formal) conservation of invariant quantities such as mass and energy.

 

The course is finalized with a short overview of applications from the real world. This includes a general overview of methods for initializing models (the starting point for the first time step), and a brief introduction to the practical problems faced when running geophysical models on modern super-computers.

Learning Outcome

Skills

At the end of the course the student

  • can apply mathematical language to describe the main pros et cons of various numerical methods used for time stepping and spatial discretisation. These regard issues such as computational stability, accuracy, efficiency, conservation of invariants (e.g. mass), and monotonicity,
  • can set up simple programs to solve transport problems and general problems involving wave propagation.

 

Knowledge

The student will obtain an overview of the fundamental numerical methods used in modern models for use in ocean, weather and air-quality forecasts, and for dynamical (coupled) atmosphere-ocean climate simulations.

 

Competences

In particular the student will be familiar with and/or can apply/work with the following subjects/methods:

  • accuracy,
  • consistency,
  • stability,
  • convergence,
  • finite difference methods,
  • spectral methods,
  • semi-Lagrangian methods,
  • local mass conservation,
  • Eulerian and semi-Lagrangian finite volume methods,
  • domain of influence, and domain of dependence,
  • numerical dispersion and – dissipation,
  • monotonic and positive definite filters,
  • explicit versus semi-implicit schemes,
  • Arakawa A-, E and C-grids,
  • semi-implicit methods.

Numerical Methods for Fluid Dynamics. By Dale R. Durran. 2nd Edition., 2010, XV, 516 p. 110 illus.ISBN: 978-1-4419-6411-3
http:/​/​www.springer.com/​mathematics/​numerical+and+computational+mathematics/​book/​978-1-4419-6411-3?changeHeader
Furthermore, additional material to replace parts of book will be available on the home page of the course.

The course requires that MatIntro, Linear Algebra and Mat-F - or equivalent - have been taken. Since a number of exercises include programming of simple models elementary knowledge about MatLab, IDL or Fortran is needed. Furthermore, it will be an advantage if the student has his/her own Laptop with one of the above mentioned programming languages installed.
Lectures, theoretical exercises, practical exercises, excursions to e.g. DMI and Aarhus University.
  • Category
  • Hours
  • Exam
  • 50
  • Excursions
  • 3
  • Lectures
  • 32
  • Practical exercises
  • 23
  • Preparation
  • 86
  • Theory exercises
  • 12
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Three individually written reports (5-10 pages each including figures) based on theory and results from computer exercises. The three report subjects are formulated by the teacher and released one week before the due date. The evaluation follows the 7-level scale with internal grading. The two first exercises count 25% each, and the third 50%.
Marking scale
7-point grading scale
Censorship form
No external censorship
several internal examiners
Re-exam
One larger report (15-20 pages) based on theory and results from computer simulations. The subject is released to the students two weeks before the due date.
Criteria for exam assesment

Grade 12 is given for the outstanding performance demonstrating complete fulfilment of the above goals, with no or few, unimportant shortcomings.