 # MATH5295 Special Topics (Applied) Mathematics: Inverse Modeling and Prediction in the Ocean and Atmosphere

MATH5295 is a Honours and Postgraduate Coursework Mathematics course. See the course overview below.

Units of credit: 6

Prerequisites:  12 units of credit in Level 2 Maths courses including (MATH2011 or MATH2111) and (MATH2120 or MATH2130 or MATH2121 or MATH2221), or (both MATH2019 (DN) and MATH2089), or (both MATH2069 (DN) and MATH2099). Some computing experience (R, Fortran, Maple, Matlab, or Python) is strongly recommended.

Cycle of offering: Term 3 in Trimester; there is a different topic each year.

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: Please see the course handout (pdf).

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

If you are currently enrolled in MATH5295, you can log into UNSW Moodle for this course.

#### Course Overview

Real-world physical systems, like the ocean and atmosphere, are immensely complicated, and understanding and predicting the future behaviour of these systems is crucial for weather forecasting, marine operations, and climate science. However, ourknowledge of the real world sits upon two shaky pillars: imperfect observations on the one hand, and incomplete models (both mathematical and computational) on the other. The mathematical discipline for merging observations and models, plus their relative uncertainties, to form a best-guess estimate for the true state of a system is called inverse modeling, also known as data assimilation (in the applied mathematics literature) or filtering (in engineering).

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 modeling 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.