Quantifying the likelihood of persistent extreme weather events in a changing climate

Quantifying the likelihood of persistent extreme weather events in a changing climate

Research Question and Fit

This Exeter Mathematics and Statistics project asks how likely unusually long heatwaves, cold spells or wet seasons become as climate changes. Its distinctive challenge is estimating probabilities beyond a short observational record while demonstrating where extrapolation remains defensible. The advertised work combines large-deviation theory, uncertainty estimation, interpretable machine learning and atmospheric processes, with Frank Kwasniok and Jennifer Catto and named partners Met Office and JBA Risk Management. Mathematical or statistical depth matters more than arriving with extensive climate experience, which is advantageous rather than mandatory. Exact project

The 2027 UNRISK schedule gives 16 November 2026 as the application-system opening date and 13 January 2027 at 13:00 GMT as the deadline. International awards are competitive; full overseas fees are covered if an award is secured, but the 2027 maintenance amount is not yet confirmed. The useful immediate action is to prepare a research narrative and check Chinese qualification recognition, then consult the applicable application instructions before submitting. Opening warning, 2027 timeline

Research Problem and Doctoral Work

What makes persistence difficult

A damaging season can arise from repeated moderately unusual days rather than one record-breaking day. The project treats extended time or spatial averages of temperature, precipitation or vorticity as quantities whose unusually large values need probabilistic assessment. The analytical difficulty is that independent examples are few, the climate baseline moves, and events outside the record cannot be checked by simple counting. Atmospheric regimes also matter: the same local accumulation may have different physical drivers, durations and geographical footprints.

The advertised approach estimates a large-deviation rate function together with its uncertainty. That function describes how rare sustained deviations become as averaging scales change. Crucially, the advertisement conditions extrapolation on establishing convergence. A fitted curve alone is insufficient evidence for an unprecedented-duration event. Time-dependent representations and multivariate extensions are proposed directions, not completed solutions or compulsory use of a particular neural architecture.

A useful research sequence

An evidence-backed interpretation of the work is to start with clearly defined events, averaging windows and spatial domains, then distinguish finite-record uncertainty from changing-climate effects. Comparisons across models and observations should ask whether an apparent stable estimate reflects genuine convergence or choices of window, resolution and event definition. A credible result could identify where extrapolation fails as well as where it works; the project need not claim accurate probabilities at every duration.

The named data families—CMIP simulations, convection-permitting UKCP18, Central England Temperature and ERA5—offer different strengths and limitations. Model output can supply long samples but retains model error; observations anchor reality but may have changing measurement coverage; reanalysis is a model-informed reconstruction rather than an independent observation at every location. These distinctions are analytical implications of the proposed comparisons. No project-specific storage allocation, computing entitlement, version choice or partner dataset agreement has been verified.

Interpretable clustering could link persistent local extremes to circulation regimes. Its scientific value would come from stable, physically intelligible groupings and demonstrable predictive relevance, not merely attractive clusters. Nonstationary learning needs temporal validation: a method that explains a historical period may lose meaning as circulation relationships change. Compound-event extensions similarly require separating dependence uncertainty from uncertainty in each individual hazard.

The retrospective National Severe Weather Warning Service component creates a valuable bridge to decisions. Warning colours combine impact and likelihood, so a meteorological return probability should not be treated as a warning colour. Met Office guidance notes an October 2026 change to the impact matrix; historical comparisons need to respect the definitions used when warnings were issued. Official warning framework

Met Office interest centres on UK heatwaves and extreme precipitation; JBA's stated interest is cumulative precipitation and flood-risk applications. These are confirmed project collaborations. They do not establish guaranteed access to proprietary losses, an operational deployment, employment after graduation or an additional CASE payment: the project's CASE field is blank. A strong doctoral contribution would make the uncertainty relevant to a partner decision explicit while retaining a publishable scientific question.

School, Programme and Field Context

The host and expected degree-awarding institution are the University of Exeter, United Kingdom, with the project placed in Mathematics and Statistics. UNRISK is a multi-university training network; central Leeds administration and partner involvement do not imply a Leeds, UCL or joint degree. Exeter's institutional UK address corroborates the country. The precise registration title, campus and award conditions for this individual studentship should appear in the eventual host offer. Mathematics research degrees, University contact address

The department's Weather and Climate Science group connects climate modelling, probabilistic projections and uncertainty with strong Met Office links. Statistics and Data Science supplies complementary work on complex-model uncertainty and emulation. This overlap is more directly relevant than a general university reputation claim: the project needs mathematical estimation and a defensible understanding of atmospheric variability. A January 2026 supervisor booklet independently places Catto and Kwasniok within these relevant themes. None of these departmental resources establishes that every listed researcher will supervise this student. Weather and climate, Statistics and data science, Supervisor booklet, relevant sections

Exeter reports QS 2027 overall rank 136 and THE 2027 overall rank joint 157. Its Mathematics programme page also reports UK top-20 mathematics placements in the Times and Complete University Guide 2027. The cited Leiden 2024 top-10 result concerns the percentage of highly cited papers in the combined Mathematics and Computer Science category, rather than a mathematics teaching ranking. These measures provide institutional context, not a rating of this supervisory relationship. Official ranking summary

UNRISK combines research from the outset with cohort training, residential events and at least two academic supervisors. The advertised funding runs for 45 months including an expected three-month placement; it is not 45 months of research plus an extra paid placement. Exeter describes advanced mathematics/statistics training opportunities, including MAGIC and APTS. The balance between this training, CDT activities and the thesis, and any extension or writing-up charges beyond funding, remains an offer-stage question. UNRISK training

Supervisors and Recent Original Research

Dr Frank Kwasniok works on mathematical and statistical methods for weather and climate, dynamical systems and data-driven modelling. His current profile connects him to Exeter Climate Systems and environmental-intelligence research. Professor Jennifer Catto combines observations and models to explain high-impact weather and climate resilience. Their complementary directions support the proposed combination of probabilistic method development and physical interpretation. Current profiles establish research directions, not availability, meeting frequency or allocation of thesis responsibilities. Kwasniok, Catto

Project materials list F.Kwasniok@exeter.ac.uk and J.Catto@exeter.ac.uk for research enquiries; UNRISK application enquiries go to ENV-PGR@leeds.ac.uk. The Leeds administrative address does not change the Exeter host.

Three recent originals by the named supervisors provide relevant team context; none is represented as having solved this exact project. The discussion covers selected substantive sections and does not claim complete coverage of supplements, code or raw data.

Probabilistic validation: Wessel, Ferro and Kwasniok (2024)

Lead-time-continuous ensemble postprocessing. Splines pool information across forecast lead times within distributional postprocessing. Lorenz96 and MOGREPS-G evaluations show comparable skill with efficient fitting and advantages when training samples are small. Crucially, the authors note the absence of large temperature extremes in the evaluated data. This supports disciplined probabilistic validation, not validated unprecedented-event extrapolation. CRediT assigns Kwasniok conceptualization, funding, methodology, administration, supervision and review; Wessel leads analysis, software and original drafting. Data, methods, selected results, discussion and contributions were read; code and all supplements were not audited. Original article, DOI 10.1002/qj.4701

Compound-event context: Sauter and colleagues (2023)

Compounding heatwave–extreme-rainfall events. Rain-gauge data, reanalysis and weather types examine rainfall following heatwave endings in Europe and Australia. Fronts, moisture and instability help explain the observed combinations. Station sampling and observational association constrain interpretation: the study does not establish general causal direction or nonstationary return periods. Catto's declared roles are conceptualization, data curation and review/editing; Sauter leads formal analysis, visualization and drafting. Selected methods, results, discussion and contributions were read, not all supporting data. It offers physical and compound-event context for the proposed multivariate work. Original institutional PDF, DOI 10.1029/2023JD038761

Dynamical reduction: Kwasniok (2022)

Optimal mode decomposition of atmospheric flow. The method jointly optimizes a reduced subspace and linear operator against prediction error instead of selecting variance-dominant modes first. Pedagogical systems and an intermediate atmospheric model show benefits for dynamical identification and prediction. These are controlled model tests; they do not validate operational ERA5 extreme probabilities. Non-Markov behaviour and nonlinear representation remain limitations. Kwasniok is sole and corresponding author, but no separate task-level contribution declaration was found. Selected methods and results/conclusions were read, including the optimization objective; the full appendix and implementation were not verified. Published original PDF, DOI 10.1175/JAS-D-21-0193.1

Together these studies demonstrate adjacent capability in probabilistic forecasts, physically informed compound events and dynamical reduction. The new thesis still has to establish rate-function convergence, estimate extrapolation uncertainty and handle climate change. A linked climate paper is not used as methods-level evidence, and a review is not substituted for an original study.

Funding, Application and Twelve-Month Living Costs

UNRISK's funding page covers tuition, a standard UKRI maintenance stipend, £6,000 individual research/training support and £5,000 cohort training allocation per student. The last two are research resources rather than disposable living income. International awards are limited and competitive, with full international fees covered if awarded. Visa, health surcharge and relocation costs are outside this coverage. Funding is a studentship; no employee salary or pension entitlement has been established. Funding terms, FAQs expressly valid for 2027

The UKRI table gives £21,805 for 2026/27, not a confirmed 2027/28 stipend. Exeter lists £27,600 annual international Mathematics research tuition for 2027/28; this illustrates the importance of the award's full-fee promise, rather than a fee bill to add to an awarded full-fee studentship. Confirm the scholarship letter covers the individual fee classification and funded period. UKRI current table

Exeter's April 2026 budget gives a published total of £316–421 per week. Multiplying by 52 gives an illustrative £16,432–21,892 for twelve months. This is a dated planning range, not a 2027 rent quote or a guaranteed stipend surplus. Private rents exclude bills, while some hall rents include them; do not add utility costs twice. Deposits, moving, visa/IHS charges, dependants and exceptional expenditure need separate provision. Official living-cost table

The cited Student visa financial rule gives £1,171 per month for up to nine months outside London, or £10,539, alongside relevant course-fee evidence. That administrative threshold is different from a realistic twelve-month Exeter budget. Chinese nationals fall within differential evidence arrangements, but evidence can still be requested and financial requirements still apply; scholarship documentation and individual circumstances matter. Government financial requirements

Applicant Requirements and Preparation

The exact advert asks for strong mathematics, statistics, physics, meteorology or related preparation and an interest in weather/climate applications. It explicitly makes previous climate experience advantageous, not mandatory. Computational proficiency, dependence modelling, reproducible statistical work and clear physical interpretation are sensible preparation suggestions, not additional published mandatory prerequisites.

The CDT's general minimum is a relevant 2:1 honours degree or equivalent; a relevant Master's is considered, and existing or currently registered PhD holders are excluded. Exeter's China page, however, says doctoral applicants generally need a completed three-year Chinese Master's, with graduation and degree certificates. The page's institution-specific grade mapping is not a universal PhD cut-off. A Chinese applicant should resolve this host-registration mapping before treating the CDT's generic bachelor-level minimum as sufficient. International openness creates a funding route in principle, not approval of an individual's credentials. Chinese qualification guidance

Exeter programme materials link Mathematics research at Streatham to English Profile A, while Penryn uses B2. Profile A requires IELTS 6.0 overall and 6.0 in every component, with the listed validity conditions; it accepts One Skill Retake. TOEFL requirements distinguish tests before and after 21 January 2026, so a score should be checked against its test date. Confirm the individual offer's campus and profile rather than applying a different Exeter project's requirement. English evidence is needed by registration, not necessarily the CDT application deadline. Profile A

For Chinese citizens, ATAS is a conditional administrative check. China is not on the nationality exemption list, but whether this particular course requires clearance depends on the university-confirmed CAH3 subject classification and visa conditions. There is no evidence here of a nationality ban, automatic clearance or a requirement inferred solely from the word “climate”. Official ATAS guidance

Preparation can be concrete: explain an earlier quantitative project in terms of assumptions, dependence, validation and failure cases; show how those lessons inform persistent extremes; and identify an initial question that can be investigated without assuming proprietary data. The published structured application narrative is a useful planning guide, but parts of the current instructions still refer to the 2026 round. Recheck the late-October update and correct 2027 codes after opening. The common process applies to Exeter as well as Leeds and UCL; successful Exeter applicants subsequently complete host registration, potentially with referees.

Career and Transferable Research Skills

The career value lies in transferable uncertainty assessment, statistical computation and translating atmospheric evidence into risk decisions. Named collaborators and those skills support relevance to research and climate-risk work; they do not establish a hiring promise or a verified graduate salary.

Next Actions and Questions to Verify

Before applying: verify the updated 2027 instructions after 16 November, the Chinese degree equivalence and English profile, and the initial event definition with the supervisory team. Prepare evidence of quantitative reasoning instead of claiming expertise in every advertised dataset. No submission should be attempted before the announced opening.

At interview: ask what constitutes convincing rate-function convergence, how nonstationarity will be separated from finite-sample error, which dataset is feasible first, and how physical regime interpretation will be validated. Clarify partner data permissions, placement expectations, supervision responsibilities and publication arrangements. These determine whether the attractive research agenda is manageable within the funded period.

Before accepting: obtain the precise Exeter degree/campus registration, 2027 stipend and fee coverage in writing; confirm expenses outside the award, ATAS/CAS requirements and conditions for extensions.

Evidence and Sources

The project materials list 16 November 2026 as the application opening date and 13 January 2027 at 13:00 GMT as the deadline; these dates do not establish current portal availability. The report distinguishes the cited original papers by authorship and relevance and summarizes selected substantive sections, without claiming complete supplementary-material, code or raw-data coverage. Policy dates and fees remain dated references. Individual admission, funding, data access and immigration conditions are unconfirmed.

Project, programme and training

• Exact 2027 Exeter persistent extremes project
• Exeter Mathematics MPhil/PhD current programme
• Exeter January 2026 doctoral supervisor booklet
• UNRISK current application opening warning
• UNRISK 2027 application timeline
• UNRISK funding and eligibility
• UNRISK FAQs expressly valid for 2027
• UNRISK training and registration

Supervisors and original publications

• Frank Kwasniok current Exeter profile
• Professor Jennifer Catto current Exeter profile
• Wessel, Ferro and Kwasniok (2024), lead-time-continuous ensemble postprocessing
• Sauter et al. (2023), compounding heatwave–rainfall events
• Kwasniok (2022), optimal mode decomposition of atmospheric flow

Institution, qualifications, costs and decision context

• Exeter Chinese qualification guidance
• Exeter English Profile A
• Exeter April 2026 living-budget table
• Met Office current impact-based weather warnings guide
• UKRI stipend 2026/27 and award guidance
• UK Student visa maintenance rules
• Exeter Statistics and Data Science
• Exeter Weather and Climate Science
• Exeter ranking context
• University of Exeter official UK postal address
• UK ATAS scope and university CAH3 confirmation