A&OS 180/229 - Numerical Modeling (Winter, 2005):

Instructor: Robert Fovell
Class meetings: Lecture - MWF 1-1:50 (MW in MS 7124A; F in MS 7121); Lab - F 2-3:20 in MS 7101

Office: 7162 Math Sciences
Phone: (310) 206-9956
E-mail: rfovell@ucla.edu
Class notes: Download PDF here   Warning: File size exceeds 10MB.
VMO reference: Download PDF here

Course description:

This course concerns the numerical simulation of atmospheric fluid flow from both a theoretical and applied setting. It provides the student the opportunity to construct a two-dimensional numerical model and apply it to interesting phenomena. The course is taught from the perspective of mesoscale atmospheric convection, but the tools acquired and lessons learned are generally applicable to a wide range of atmospheric and oceanic phenomena on a variety of temporal and spatial scales.

Text:

None. Download class notes at link above.

Grading:

Grading will be based on a modeling project, to be described in both a written report as well as an oral presentation (during the final exam period). Programming assignments leading up to the modeling project will be given through the quarter. Homeworks reinforcing the theory will be assigned.

Course outline:

• Weeks 1-2. Introduction.

  Theory: Numerical solution of simple ordinary differential equations; review of basic dynamics; Taylor series and other elementary tools.

  Application: Compute model base state, including mean profiles of potential temperature, vapor mixing ratio, pressure, density, relative humidity and geometric height, from a given thermodynamic sounding.

• Week 3. Assess convective instability of atmospheric sounding.

  Theory: Review of basic thermodynamics; isobaric saturation adjustment. Numerical solution of simple integrals (trapezoidal rule). Basic equations. ``Quasi-compressible'' framework.

  Application: Calculate convective instability of the sounding, implementing isobaric saturation adjustment.

• Weeks 4-5. Set up model base grid.

  Theory: Finite difference approximations to one- and two-dimensional hyperbolic partial differential equations. Consistency and stability; CFL criteria. Grid staggering.

  Application: Set up code to implement model on two-dimensional, staggered grid in a laterally periodic domain.

• Weeks 6-7. Model test problem: a buoyant thermal.

  Theory: Background on thermals: structure, evolution.

  Application: Introduce buoyant thermal into model; compare results with theory and among students. Provoke linear computational instability.

• Week 8. Add temporal and spatial smoothing to model.

  Theory: Nonlinear computational instability and aliasing.

  Application: Numerical diffusion.

• Weeks 9-10. Adapt model to specific projects.

  Theory: Other dynamical frameworks (anelastic, Boussinesq, fully compressible). Adjoint models.

  Application: Past student projects have included: simulation of a simple cloud, density currents, Rayleigh convection, sea-breeze and urban heat island circulations, atmospheric response to maintained heat sources, transport of passive tracers; assessment of sensitivity to artificial acoustic wave speed adjustment and to different numerical schemes.