The increasing likelihood of temperatures above 30 to 40 °C in the United Kingdom

Intensification of hot extremes has continued unabated in recent decades, posing a threat to human health and bringing socio-economic impacts. Europe is projected to experience more frequent and intense heatwaves, and while the UK has not historically borne the brunt of continental heat, its summer temperatures are rising. Attribution research shows hot extremes are becoming more frequent and intense due to anthropogenic climate change. The UK summer of 2018 was a joint record and estimated to have become 30 times more likely due to human influence; in 2019, the UK mean warmest daily temperature reached a new peak and the national record (38.7 °C in Cambridge) was set. These consecutive extremes highlight UK vulnerability, with impacts including spikes in mortality and economic effects. The study aims to quantify how the likelihood of exceeding high daily maximum temperature thresholds (30, 35, 40 °C) has changed since 1900 and how it may change through the 21st century under different emissions scenarios, and to attribute these changes to human influence.

The study situates itself within a body of work documenting increasing hot extremes globally and in Europe, their health and socio-economic impacts, and attribution of extremes to anthropogenic climate change. Prior work indicates no pause in the rise of hot temperature extremes, increased likelihood of extremely hot European summers since 2003, and specific attribution of recent UK heat (e.g., 2018 summer) to human influence. It also references scenario development (RCPs), the challenges of attribution at local scales due to model resolution and observational coverage, and previous use of downscaling and event attribution frameworks. This literature underpins the need for high-resolution observational datasets and robust attribution methodologies to assess changing risks of temperature extremes in the UK.

• Observational dataset: Used HadUK-Grid daily maximum temperature data at 1 × 1 km resolution (1960–present). Computed, for each grid cell, tx01 (warmest daily maximum temperature per year). Assessed trends (Mann–Kendall significance at 10% level) and mapped 1960–2019 trends.
• Transfer functions (downscaling from UK mean to local): For each 1 km grid cell, fitted a linear regression relating local tx01 to UK-mean tx01 using 60 annual pairs (1960–2019): tx01(local) = a0 + a1 × tx01(UK). To capture uncertainty in the response, derived confidence bounds for each percentile and represented these as 100 alternative “transfer functions” per grid box. Sampling uncertainty was quantified via Monte Carlo bootstrap resampling of the 60-year observational pairs to generate alternative fits; each bootstrapped fit also had 100 percentile-based variants, producing ensembles of transfer functions.
• Model ensemble: Used 16 CMIP5 coupled models with simulations including (i) all forcings (anthropogenic + natural) historically and into the future under RCP4.5 and RCP8.5, and (ii) natural forcings only (counterfactual). One realization per model per experiment; all regridded to 60 km to align with observations for UK-mean tx01 calculation. Applied a simple bias correction so that model all-forcings mean tx01 matches observations over 1961–1990; same correction applied consistently to all experiments of each model.
• Model evaluation: Compared simulated UK-mean tx01 (1960–2019) to HadUK-Grid-derived UK-mean tx01 using (a) trend comparison with ±2 SD ranges, (b) power spectra of detrended series, (c) distribution comparison via aggregated model distribution vs observations with Kolmogorov–Smirnov test (P = 0.620 > 0.1), and (d) Q–Q plots. Found models fit-for-purpose.
• Stationarity tests for transfer functions: Using models, derived transfer functions under three training regimes: strong forcing (all forcings 2020–2100), variability-only (natural-only), and mixed response (all forcings 1960–2019). Compared across multiple grid boxes; differences generally within ~1 °C and much smaller than sampling/response uncertainty encapsulated by the 100-function sets. Also assessed internal variability changes by removing forced response (multi-model mean) and computing 5-year rolling-window standard deviations; found no major long-term change in variability (1900–2100).
• Probability estimation (local exceedance): For each year and experiment, produced samples of local tx01 at each grid box by applying 100 transfer functions to the 16-model UK-mean tx01, yielding 1,600 samples per grid box per year. For all-forcings, probabilities were computed in overlapping 20-year rolling windows (1900–1919, …, 2081–2100), increasing effective sample size to 32,000. Defined present-day as 2011–2030; late-century as 2081–2100. For the natural climate, aggregated 1900–2005 natural-only years (stationary assumption), producing 169,600-sample distributions per grid box. Exceedance probabilities for thresholds 30, 35, and 40 °C were computed by counting exceedances; uncertainty quantified by repeating with bootstrapped transfer function sets (reporting 5–95% ranges).
• Probability of exceedance anywhere in the UK: For each 20-year window, each model year combined with each transfer function produced a high-resolution annual map; out of 32,000 such maps, counted how many had at least one grid cell exceeding each threshold. This yielded the annual probability (and return time = inverse probability) of exceeding thresholds anywhere in the UK, with uncertainty from bootstrapping. Natural-only probabilities were similarly aggregated to provide 5–95% ranges.
• Scenarios: Future projections under RCP4.5 and RCP8.5 were used; present-day probabilities used RCP4.5 extensions for continuity with historical all-forcings runs.

• Observed trends: The UK-wide warmest day (UK-mean tx01) reached a new peak in 2019. Local tx01 trends (1960–2019) show widespread warming, strongest in southeast England, locally approaching ~1 °C per decade; trends are significant over most regions (Mann–Kendall), with weaker or non-significant warming in parts of Scotland and isolated cooling patches.
• Model fidelity: The distribution of model-simulated UK-mean tx01 (1960–2019) is statistically indistinguishable from observations (KS P = 0.620). Observed variability and trends lie within the multi-model ranges; Q–Q plots show realistic representation of the distribution despite limited sampling of upper tails.
• London exemplar: In a London grid box, the CDF of tx01 shifts to higher temperatures from natural to present to late-century climates. Exceeding 30 °C is common even in the natural climate; exceeding 35 °C is now 2–3 times more likely than in the natural world and is projected to occur at least twice per decade by late century. Exceeding 40 °C locally remains rare today but the return time drops from thousands of years (natural) to hundreds, and to tens by 2100 (especially under higher emissions). Urbanization and anthropogenic heat release could further increase local risks.
• Spatial patterns of local risk (maps):
  • 30 °C: Present-day risks are elevated vs natural; by late century, most of northern UK is likely to experience ≥30 °C at least once per decade.
  • 35 °C: Present-day exceedances are most likely in southeast England. By late century, exceedance becomes common in the southeast under RCP4.5 and widespread over most of England under RCP8.5.
  • 40 °C: Still very rare locally today, even in the southeast. By late century, ≥40 °C is expected at least once per century in the London area under RCP4.5, and several times per century across much of southeast England under RCP8.5.
• UK-wide exceedance (anywhere in the UK in a given year):
  • ≥35 °C: Present-day return time is ~5 years; by 2100, almost every year under both scenarios (faster under RCP8.5).
  • ≥40 °C: Natural climate return time is 100–1000s of years; present-day is 100–300 years. By 2100, return time drops to ~15 years under RCP4.5 and ~3.5 years under RCP8.5.
• Overall: Human influence has markedly increased the likelihood of UK hot-day extremes, with the strongest present and future risks in southeast England; continued emissions sharply increase the frequency of both 35 °C and 40 °C events.

The findings directly address the research question by demonstrating that anthropogenic climate change has already increased, and will continue to increase, the probability of exceeding high temperature thresholds in the UK. The risk-based attribution shows substantial shifts in the distributions of local and UK-wide warmest-day temperatures from the natural to present-day climate, with implications for record-setting events. Spatial analyses identify southeast England as the hotspot for severe extremes, while northern regions also see substantial increases for lower thresholds (≥30 °C). The UK-wide perspective reveals that even if local probabilities remain low for 40 °C at a given site, the chance of at least one location exceeding 40 °C in a given summer rises rapidly with warming, implying heightened national risk management needs. Model evaluation supports confidence in the results, and sensitivity tests suggest the observationally derived transfer functions are robust to non-stationarity and variability interplay within assessed uncertainties. These results are highly relevant to public health planning, infrastructure resilience, and adaptation strategies, especially under higher-emission trajectories.

The study provides a high-resolution, observation-anchored attribution of changing risks for UK warmest-day temperature extremes. It shows that: (i) temperatures above 35 °C are increasingly common in southeast England; (ii) many northern areas are likely to exceed 30 °C at least once per decade by 2100; and (iii) the UK-wide return time for ≥40 °C has already shortened to 100–300 years and could drop to ~15 years (RCP4.5) or ~3.5 years (RCP8.5) by 2100. The approach leverages simple transfer functions linking local to UK-mean extremes and multi-model ensembles with and without human influence to quantify changing probabilities. Future research could refine urban heat risk by incorporating dynamic urbanization and anthropogenic heat fluxes, extend to compound heat–humidity metrics, explore other return periods and thresholds, and assess outcomes under mitigation-consistent pathways aligned with the Paris Agreement to better inform adaptation and risk management.

Key limitations include: (1) Transfer functions are derived from a 60-year observational period, introducing sampling uncertainty; addressed via bootstrapping but still a constraint, especially for upper-tail behavior. (2) Potential non-stationarity in the relationship between local and UK-mean extremes; sensitivity tests suggest small impacts relative to other uncertainties, but changes in circulation or land-surface conditions could affect future relationships. (3) Model ensemble limitations: only 16 CMIP5 models and one realization each; although evaluated as fit-for-purpose, structural and sampling uncertainties remain. (4) Bias correction aligns means but not necessarily higher moments; extreme tails may still carry model biases. (5) Urbanization and anthropogenic heat release changes are not explicitly modeled; future local extremes in urban areas may be under-estimated. (6) Scenario dependence: projections are sensitive to emissions pathways; lower-emissions pathways would yield lower probabilities than shown for RCP4.5/8.5.