Dissertation

Predicting Compound Heat Stress Risk in Europe: A Copula-Based Framework with ML-Driven Dependence Estimation

Compound heat stress happens when high temperature and high humidity arrive together. Most climate risk assessments treat these variables as independent, which recent work shows significantly underestimates the probability of compound events. This dissertation develops a framework to model, diagnose, and correct the dependence structure using copulas and machine learning.

Research questions

1. How does the dependence structure between temperature and dew point temperature vary across European regions and seasons, and how well does an independence assumption perform for estimating compound heat stress risk?
2. Can atmospheric circulation patterns (particularly Z500) predict within-season variations in temperature and dew point dependence using machine learning?
3. How do trends in marginal warming versus dependence evolution separately contribute to changes in compound heat stress risk?

Why it matters

The main gap is laid out in Brett et al. (2025), Review article: The growth in compound weather and climate event research in the decade since SREX. The field has grown rapidly in characterising compound events, but very little work has moved toward predicting them. Most existing studies assume independence between temperature and dew point when estimating joint risk, which systematically underestimates compound heat stress probability.

Dew point serves as a direct proxy for atmospheric moisture and is a key driver of heat stress alongside air temperature. Copulas offer a natural framework for modelling the dependence between these variables, and linking them to large-scale atmospheric circulation (Z500 patterns) gives the work an operational angle for sub-seasonal forecasting.

For reinsurance and climate adaptation, the question is not just ‘will it be hot?’ but ‘will it be hot and humid at the same time?’ Getting that joint probability right is the difference between adequate and inadequate risk pricing.

Why I chose it

What drew me here was the intersection of statistics, climate science, and practical risk. The independence assumption is wrong in a way that has been repeatedly documented, yet most operational risk work still uses it. There is an opportunity to build something that bridges the academic compound-events literature and the operational forecasting world, and the methods involved (copulas, gradient boosting on circulation features) are concrete enough that the work can be used, not just cited.

Approach

The framework is built on three layers.

1. A multiplicative decomposition of compound hazard bias: M_total = M_marginal × M_dependence. This separates errors that come from getting individual variables wrong (marginal bias) from errors that come from getting their co-occurrence wrong (dependence bias).
2. Copula-based modelling of the dependence structure, fitted to ERA5 reanalysis as ground truth and evaluated against CMIP6 projections.
3. ML-driven dependence estimation using XGBoost to predict Kendall’s tau from large-scale circulation features (Z500, MSLP, jet-stream indices), enabling dependence prediction under future climate scenarios.

For a detailed visual introduction to copulas and why they matter for compound risk, see the interactive guide on the Writing page.

Data

ERA5 reanalysis (1981 to 2020) as the ground-truth dependence climatology. CMIP6 projections for historical and future scenarios. Destination Earth (DestinE) climate digital-twin output where available.