MSc Weather and Climate Science

MTHM021: Advanced Mathematics Project

In this module, you will gain experience of independent work by conducting in-depth research into an open-ended problem agreed with your Project Supervisor. A Good Research Practice portfolio (20%) recognises your professionalism and research performance, and your participation in the wider research, academic, or professional environment associated with your project. Partway through the project, you will present your work to date to a group of academics and fellow students in order to obtain feedback on your progress and to help guide the remainder of your study. This forms 10% of the assessment. At the end of the project, you will write a coherent and comprehensible account of your work in the form of a dissertation that forms 70% of the assessment. Computational work using appropriate software may form part of the Advanced Mathematics Project.

This module provides the opportunity for you to produce a well-researched project in mathematics, either complementing or extending material in the taught part of the programme. By taking this module, you will develop research skills, including literature review, problem formulation, analysis, and communication of mathematical results.

You will receive guidance on the responsible use of AI-assisted tools to support aspects of your research, report writing and presentation preparation, in line with University policy.

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MTHM036: Research in Mathematical Sciences

This is a unique module that runs in several research themes and provides you with a taste for and experience in research in mathematical sciences. The themes are broadly aligned with Fourth Year options and would cover subjects from pure maths, applied maths and statistics, although the number and range of topics may change from year to year. Each theme consists of lectures, student-led discussion, reading, and practical sessions, getting deeper experience in research approaches and skills. Students will learn to write a short essay, make an oral presentation and write a longer scientific report.

Set in at least three distinct research themes, this module will introduce you to scientific thinking and abstraction and give you knowledge/experience in core research skills: reading (and understanding), writing and presenting for the mathematical sciences.

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MTHM051: Fundamentals of Weather and Climate Science

This module is designed to give you an overview of the key physical processes determining the behaviour of the Earth's atmosphere. An informative subtitle might be climate physics for the mathematically literate. Topics covered will include radiative energy transfer, the structure, motion and thermodynamics of the atmosphere, the surface energy balance, and the main components of the general circulation (Hadley cells, Walker cells, jet streams etc.). The emphasis, where possible, will be on simple analytical models for commonly observed phenomena and on the development of physical intuition.

By the end of this module, you will have an understanding of the basic physics of the Earth’s weather and climate, and will comprehend the structure and principal circulations of the atmosphere and the ocean. A good knowledge of these fundamental processes is key for careers involving meteorology, environmental science and modelling, and gives the foundation for the MSc programme in Weather and Climate Science.

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MTH3030: Mathematics of Climate Change

This module will provide a background in the mathematics underlying human-induced climate change. It will provide you with a good general understanding of the climate system, against which to assess the likely role of anthropogenic forcing factors. You will learn to apply a range of mathematical methods, including differential equations, calculus and the use of small parameters to approximate and simplify climate system problems. Topics of study will include observations of climate change, the greenhouse effect, regimes of atmospheric absorption, climate feedbacks, climate tipping points and geoengineering.

Climate change is a high-profile subject that is often covered in the media. However, debate about climate change is often presented in a polarized way, divided along political or ideological lines. In contrast, there is now an urgent need to develop a new generation of thinkers capable of objectively analyzing the evidence for climate change and its causes, and the options for dealing with it (including mitigation, adaptation and geoengineering). Mathematically-minded people are especially sort after by organizations such as the Met Office-Hadley Centre in Exeter. This module aims to develop the skills required to meet these needs, by providing a strong-background in the science surrounding the climate change issue to mathematically-minded undergraduates.

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MTHM019: Fluid Dynamics of Atmospheres and Oceans

This module lays the foundations for an understanding of large scale weather patterns and ocean circulation. It will introduce you to the kinds of dynamics that can occur in stratified and rotating fluids, and introduce key concepts, such as conservation and balance, that are used to understand and analyse such flows.

You will learn to explain, manipulate and analyse mathematical descriptions of different kinds of wave and vortical motion that can occur in stratified and rotating fluids. Furthermore, you will be able to explain the relevance of the mathematical descriptions to large scale motion of the atmosphere and oceans. You will study the application of a range of mathematical methods, including partial differential equations, vector calculus, fluid dynamics, and the use of small parameters to approximate and simplify problems. The material should develop your ability to relate physical problems to their mathematical formulation.

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MTHM502: Introduction to Data Science and Statistical Modelling

In this module you will be equipped with the tools required to collate, import and manipulate data together with methods for basic inference including probability, sampling variability, confidence intervals. You will be introduced to different types and sources of data and the tools for performing initial data analysis including producing simple graphical summaries of data and more sophisticated methods for visualising structures in data. You will learn the essential mathematical techniques that are required for the implementation and interpretation of statistical and machine learning methods.

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MTHM506: Statistical Data Modelling

Statistical modelling lies at the heart of modern data analysis and is a vital part of the wider landscape of data science/machine learning/AI. There is currently an increasing pressure to regulate AI (used as a general umbrella term), so the future lies in interpretable and explainable AI approaches. As it happens, statistical modelling is both interpretable and explainable and has been used for the last 50 years or so. The point of this module is to introduce statistical modelling as such an approach and illustrate how it can be used to conduct both advanced and flexible data analyses with outputs that can be directly used for decision making. The module starts from simple linear regression familiar from most foundation courses in statistics and places this is the very broad framework of statistical data modelling. Generalized Additive Models (non-linear, hierarchical regression) will be introduced as a unifying modelling framework, that includes estimation, validation, selection and uncertainty quantification as part of the framework. The module will provide you with a toolbox and the ability to analyse any real world data set, including binary data, count data, contingency tables, data with temporal and spatial structure as well as data that are missing or partially missing. We will use the statistical software R (Rstudio) as the main platform to fit this wide range of models, and will use it in practical sessions so that, as well as a sound theoretical basis, you will develop an understanding of how to apply techniques discussed in the module in practical data analysis. The module will introduce a plethora of real data sets spanning a wide range of applications such as public health, weather, climate, ecology, biology, epidemiology, natural hazards and many others.

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MTHM023: Modelling the Weather and Climate

This module introduces you to modelling the weather and climate by providing you with an overview of modern weather and climate computational models. Using hands-on computational case studies, you will explore key aspects of mathematical and computational modelling within a simpler model framework. You will look at climate physics in more detail, and study the predictability of the atmosphere.

Prerequisite module: MTH3001 Theory of Weather and Climate

This module will give an introduction to both complex and simple models of weather and climate. Simple models are useful for improving our understanding of the climate system; however, to make detailed predictions requires large and complicated numerical models. In order to have a thorough understanding of the outputs from these models, it is important to have a grounding in the techniques employed.

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MTHM052: Mid-latitude Weather Systems

In this module you will develop a mathematical and physical understanding of the dynamics of synoptic scale weather systems in the mid latitudes, including extratropical cyclones and fronts. You will explore conceptual models for the development of these weather systems and compare these with analytical models and observations. You will develop quantitative skills in the analysis of these weather systems, which are relevant to understanding what we see outside, and to making sense of surface and upper-level synoptic charts and weather forecasts. Through quasi-geostrophic theory, concepts of potential vorticity (PV) thinking will be used to understand where we might expect to see vertical motion and rainfall within these systems, and what impact moisture has on the development of systems. You will explore and discuss recent research in the field of midlatitude weather systems, enabling you to develop your critical thinking skills. The module will include a mix of instruction methods, including traditional lectures, videos, discussion classes, giving you varied opportunities to develop learning and organisational skills. You will, with other students, explore some of the research literature related to the mid latitude weather systems and discuss how the theory informs this research.

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MTHM017: Advanced Topics in Statistics

This module offers an insight to cutting-edge statistical learning techniques that are at the forefront of current research and application. You will have opportunity to explore a range of important and current topics in statistics and data science, for example Bayesian computation, causality, agentic coding, statistics in the media and simulation. The choice of topics in any year may change to ensure that the content of the module reflects the rapid change in this exciting area. The aims are to expose the student to some recent developments in statistics and data science; to give the student exposure to cutting edge topics and current research trends.

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MTHM033: Statistical Modelling in Space and Time

In this course, we explore Gaussian processes (GPs), a powerful class of non-linear regression models widely used in Artificial Intelligence (AI), Machine Learning (ML), and modern statistics. We will look at the theoretical basis for the GPs and show how they can be used in statistics to model spatially correlated data (for example temperature across a domain such as the North Atlantic). In AI/ML, GPs serve as an alternative to Neural Networks for modelling complex patterns in data (a setting often referred to as GP regression). Finally, the course highlights the use of GPs for functional approximation and Uncertainty Quantification (UQ). Examples include approximating solutions to Partial Differential Equations or emulating the behaviour of computationally expensive numerical simulators. An important advantage of GPs is that they naturally produce estimates of uncertainty, which can be used as a measure of prediction reliability. This year, time series will not be covered.

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MTHM503: Applications of Data Science and Statistics

This module will enable you to learn new Data Science and Statistical methods, and to use the techniques learnt in other modules, by working on analyses of real data examples. There will be a strong emphasis throughout on understanding the practical application of statistical and machine learning methods including clustering, data reduction, methods for handling missing data, study design and introductory methods for time series data. Theory and ideas will be developed to allow the implementation of methods in examples drawn from industry, medicine, finance, public health and environmental challenges, including climate change and air pollution.

Pre-requisites: None

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BIOM568: Blue Planet

This module provides you with an opportunity to engage with ocean issues and investigate practical and policy opportunities for change. You will consider the importance of the ocean including the different goods and services that it provides to humans and the planet. You will also evaluate and create solutions for the identified challenges and learn about the processes needed to support a sustainable ocean.

This module, suitable for both science and non-science graduates, introduces fundamental principles of marine research. It provides a solid platform upon which to explore key issues in marine science, including impacts such as climate change, deep sea mining, ocean pollution and aquaculture. Taught sessions from leading marine biologists and policy experts will provide introductions to a range of topics, whilst subsequent interactive discussion sessions and debates will deepen your understanding and develop critical awareness and creative solutions-focussed thinking.

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GEOM141: Global Challenges

This module will give you an introduction to real-world sustainability challenges and potential solutions, training in problem-solving research and how it can be applied to effect meaningful change. This includes an introduction to earth system science and humans' impacts. You will receive training sessions that will develop core skills such as communication, project management, researching the literature, critical thinking, and presenting.

This module will provide you with an understanding of the global context of sustainability and how this can be downscaled to specific challenges, with an emphasis on how to connect sustainability and systems theory to real-world challenges. You will receive guidance and training on critically assessing a proposed sustainability solution. This will give you first-hand experience of working in wicked problem spaces and the challenges and opportunities they provide. A formative assessment will allow you to develop a short factual 'explainer' film that will effectively communicate a particular global challenge to an online general audience.

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MTHM018: Dynamical Systems and Chaos

Dynamical systems are mathematical models of real systems (for example, climate, brain, electronic circuits and lasers) that evolve in time according to definite (deterministic) rules expressed as nonlinear differential equations or iterated maps. Given the set of rules, the purpose of this module is to explain the resulting behaviour. The main questions that dynamical systems theory addresses are: What are the possible long-term behaviours of such systems? How do these depend on initial conditions? How do these depend on system parameters (bifurcations)? In particular, we highlight how seemingly random behaviour (chaos) is possible even in such deterministic systems.

Pre-requisite Module: MTH2003 Differential Equations or equivalent

The aim of this module is to expose you to qualitative and quantitative methods for dynamical systems, including nonlinear ordinary differential equations, maps, bifurcations and chaos. The phenomena you will study occur in many physical systems of interest.

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MTHM031: Magnetic Fields and Fluid Flows

This module deals with the motion of electrically conducting fluids in the presence of magnetic fields, a subject known as magnetohydrodynamics (MHD). MHD flows play a crucial role in the dynamics of a variety of astrophysical systems (including stars, planets, accretion discs and galaxies). MHD flows are also studied in the laboratory with a view towards engineering applications (e.g. electromagnetic stirring and fusion plasmas). In this module, you will see how the mutual interaction of the fluid flow and the electromagnetic field reveals a variety of new and interesting phenomena. You will learn how to formulate a real physical problem in terms of a system of partial differential equations. We will solve these using a variety of techniques of applied mathematics.

The aim of this module is to give you an introduction to the subject of electrically conducting fluid dynamics. This module can be seen as an extension of the third year module MTH3007 on viscous fluids. You will learn how the equations of fluid dynamics are modified when electromagnetic effects are taken in account. The mathematical theory will be illustrated with examples from astrophysics, geophysics and laboratory plasma physics.

Pre-requisite module: MTH3007 Fluid Dynamics, or equivalent. Good knowledge of vector calculus and standard applied mathematical methods is assumed.

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MTHM045: Space Weather and Plasmas

Major new discoveries and knowledge gained from space missions and ground-based observations, theory, and modeling are providing a wealth of engaging and inspiring topics for mathematicians and physicists to explore the physics of our space environment. This module includes interactive experiments (in-class demonstrations and online tools for independent study) while dealing with the mathematics of heliospheric physics, covering the solar wind, Sun-Earth relations and space weather. Heliospheric physics is a major application of the field of magnetohydrodynamics (MHD) but can go beyond MHD and captures fundamentals of plasma physics.

The module also introduces students to research-area-specific computational and visualisation tools (e.g. heliophysics data platforms and modelling environments). Assessments are designated as AI-assisted under institutional guidelines, allowing the responsible and transparent use of generative AI tools where appropriate.

You will explore the rapidly evolving field of heliophysics, space weather and space plasma physics, developing a strong foundation in plasma physics by giving an extended view of the applications of MHD and the subject of electrically conducting fluid dynamics. The module examines the basic physics underlying the dynamics of the Sun, to provide a background in the description of physical processes in the solar system in terms of MHD and to show the results of recent observations.

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NSC3009: Aerosols, Clouds and Climate

Climate change is arguably one of the most urgent issues over the next two decades as humanity struggles to meet the 1.5C above pre-industrial target set by the Paris COP21. Concentrations of both greenhouse gases (GHG) and aerosols (particulate matter suspended in the atmosphere) have increased considerably since pre-industrial time. Whilst anthropogenic emissions of GHG warm the planet, aerosol emissions exert a significant, yet poorly quantified cooling that acts to offset a fraction of global warming from GHG.

Reducing current uncertainties associated with estimates of climate change sensitivity to GHG emissions is hampered by our understanding of the strength of the cooling effect aerosol particles have on the climate via their interactions with clouds and sunlight. Despite decades of research the Intergovernmental Panel on Climate Change Assessment Report continue to highlight our low understanding of aerosol-cloud-interactions (ACI) as the key uncertainty hampering our understanding of climate change.

This module is designed to explore the atmospheric physical processes determining the role of aerosols and their interaction with clouds on the climate to provide insight on the importance in reducing current uncertainties associated with aerosol - cloud - interactions (ACI) for adoption of more robust adaptation and mitigation strategies.

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ECMM461: High-Performance Computing

The demand for ever-increasing computational power drives the development and exploitation of high-performance computing that underpins leading edge research in computationally intensive engineering technologies fields. This module is designed to equip you with a solid foundation and useful skills in high-performance and distributed computing. In this module, you will learn about current high-performance computer architectures and how the computer architecture influences the performance of algorithms and programs. You will also develop skills in parallel algorithm design and parallel programming, and will gain experience of using a high-performance computing system.

This module aims to provide you with a thorough grounding in parallel programming and the architectures used in high-performance computing. After presenting the fundamental ideas and basic concepts of high-performance computing, the module outlines the architectures, components and parallel programming of high-performance computers. The module will introduce you to recent developments and future trends in architecture and algorithms in high-performance computing.

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GEOM145: Theory for Sustainable Transitions

This module will provide a deep understanding of key sustainability theory and its relevance for practice. The focus will be on theory that has importance for understanding global sustainability solutions, including some of the theories and concepts that have been most influential within contemporary policy and practice. Through the module you will develop abilities for critical engagement with sustainability policy and practice, as well as increasing your capacities to interpret the challenges and opportunities that exist for contemporary solutions. Though social science led, the module is interdisciplinary and with a focus on practical application and reflection will be suitable for students from diverse backgrounds.

The module will equip you with an understanding of key influential sustainability theory and provide a firm basis for critically engaging with sustainability debates in real world contexts. Leading academics actively engaged in research on environment and sustainability will lead interactive sessions designed to enhance your critical and analytic faculties and give insight into theory that has been important in shaping agendas relating to global sustainability. There will be opportunities for peer-to-peer as well as independent learning, and expectations for you to engage in debate, discussion, and activities during module sessions.

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MTHM054: Climate Change Science and Solutions

This module will expose you to some of the most vibrant frontiers in the science of anthropogenic climate change. It will provide an overview of the natural science underlying projections of future climate change, enabling you to distinguish between what is known with high-certainty from aspects that remain uncertain. These latter ‘Frontiers in Climate Change Science’ will be introduced by a number of international experts from the University and other renowned research institutions (such as the nearby Met Office-Hadey Centre). Though natural science led, the module is interdisciplinary with a focus on understanding the climate change problem as part of the wider sustainability agenda.

The module will equip you with an understanding of the science that underpins projections of anthropogenic climate change, and separate what is well known from what remains unknown. It will help you to understand the frontiers of climate change science, through guest lectures by international experts (from the university, the Met Office and other centres), and through student-led discussions. There will be opportunities for peer-to-peer as well as independent learning, and expectations for you to engage in debate and discussion during module sessions. As part of the module assessment, you will work in interdisciplinary groups to explain a proposed climate change solution through a group presentation.

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