# MATH5231 Prediction and Inverse Modelling

MATH5231 is available to Honours, Graduate Diploma and Masters programs in Mathematics, Statistics, Data Science, and Physical Oceanography.

Units of Credit: 6

Pre-requisite:   12 units of credit in Level 2 Maths courses including (MATH2501 or MATH2601) and (MATH2801 or MATH2901), or (both MATH2019/8 and MATH2089), or (both MATH2069 and MATH2099) or equivalent. Some computing experience (R, Fortran, Maple, Matlab, and/or Python) is strongly recommended.

Cycle of offering: T3 2021

This course is a graduate level overview of the mathematical foundations of inverse modelling and prediction and their application to real-world systems, primarily the ocean and atmosphere. The scientific emphasis is on the formal testing of models, formulated as rigorous hypotheses about the errors in all the information: dynamics, initial conditions, boundary conditions and data. Applications in meteorology, oceanography, and climate are presented in detail.

More information: Refer to the Course Outline for information about coufrse objectibves, assessment, course materials and the syllabus.

The Online Handbook entry contains informaiton about the course. (The timetable is only up-to-date if the course is being offered this year).

If you are currently enolled in MATH5231, you can long into UNSW Moodle for this course.

Course Overview:

This course aims to provide a graduate-level overview of the mathematical foundations of inverse modelling and prediction and their application to real-world systems, primarily the ocean and the atmosphere. The course introduces the fundamental mathematical underpinnings of forward and inverse modelling in the ocean and the atmosphere.  The process of assimilating data into models using the calculus of variations is discussed, and the concept of over-determined and ill-posed problems is introduced.

A step-by-step development of maximally-efficient inversion algorithms, using ideal models, is complemented by computer codes and comprehensive details for realistic models. Variational tools and statistical concepts are concisely introduced, and applications to contemporary research models, numerical weather prediction, climate forecasting, and observing systems, are examined in detail.