MATH5295 is a Honours and Postgraduate Coursework Mathematics course. The Topic for T2 2020 is **Inverse Modelling and Prediction in the Atmosphere and Ocean.** See the course overview below.

**Units of credit:** 6

**Prerequisites: ** Nil

**Cycle of offering:** Term 2 2020.

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

**More information:** Please see the Course Outline (PDF).

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, our knowledge 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 modelling, 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 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.

A background in oceanic and atmospheric science is not a pre-requisite for this course, just a curiosity about how inverse methods and forecasting are used in real-world systems.