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Historical model biases in monthly high temperature anomalies indicate under-estimation of future temperature extremes

Lei Duan, Lyssa M. Freese, Govindasamy Bala, and Ken Caldeira · Communications Earth & Environment 6, 604 · 2025

Key finding. CMIP6 climate models understate how far a month's hottest day rises above that month's average temperature, so their projected monthly heat extremes for the end of this century are too low — by up to about 3 K in the worst-affected regions and months, and by more than 5 K for the rarest events.

Four panels. Panels A, B, and C are time series from 1980 to 2100 showing the trend, as a ratio relative to the 1980-2023 period, in the monthly maximum temperature TXx, the monthly mean temperature TMm, and the anomaly of TXx above the monthly mean. Each has a median line with shaded 25th-75th and 5th-95th percentile bands. TXx and TMm both rise steadily to about 1.01, while the anomaly stays flat at 1.00 with widening spread. Panel D shows violin plots of trends from linear regression in kelvin per kelvin for the three quantities, with TXx and TMm centred near 1.25 and the anomaly centred near zero.
Monthly maximum temperature and monthly mean temperature are projected to rise together at roughly the same rate, while the anomaly of the maximum above the mean shows essentially no global trend — the spread across models and regions, however, is wide, which is where the regional increases and decreases in anomalies are hidden. Figure 1 from Duan et al. (2025), Communications Earth & Environment 6, 604. Reproduced under CC BY-NC-ND 4.0. Used unmodified, as the licence requires.

What question did this research address?

The damage done by a heat extreme depends both on the mean climate state and on how far weather departs from that mean. Climate model evaluation has concentrated on the mean state; how well models reproduce high-temperature anomalies has been far less explored.

This paper asked how skilfully the models participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6) reproduce monthly high-temperature anomalies relative to monthly means, and what their historical errors imply for projected extremes.

What did we find?

The quantity examined is the monthly high-temperature anomaly — how far the hottest day of a month rises above that same month's mean temperature. Models are compared against ERA5 reanalysis as a ratio, so the bias is expressed as a percentage of an anomaly that is itself several degrees; the degree-valued consequences appear below.

Globally, the models underestimated 22-year-average monthly high-temperature anomalies by 2-3%, and underestimated 22-year maximum anomalies by 11-12%. The error is substantially larger for the extremes than for the average.

The biases are persistent. Both positive and negative biases remain largely unchanged, regionally and seasonally, across the two historical periods examined — 1980 to 2001 and 2002 to 2023 — which is what justifies projecting them forward.

The models project that as the planet warms, high-temperature anomalies will grow in subtropical regions and shrink in high latitudes, so the anomaly component of an extreme is not simply a fixed offset added to a rising mean.

In degrees rather than percentages, for the typical (22-year-average) anomaly in the warmest month of 2079 to 2100 under SSP2-4.5, correcting the bias shifts projections from more than 1 K cooler in low-latitude regions such as West Asia and South America to about 2 K warmer in the Russian Arctic; across all regions and months the largest warming corrections exceed 3 K.

For the rarest events — the single most extreme month in 22 years — the correction is warming almost everywhere, reaching about 3 K in North Europe and the Russian Arctic and about 2 K in North America and New Zealand in their warmest month, and exceeding 5 K in five regions when all months are considered.

Why does it matter?

Impacts from heat are driven by the extremes, not the averages, and a bias that is modest in the mean becomes large in the tail. An 11-12% underestimate of maximum anomalies translates into whole degrees of additional projected extreme heat — about 2 to 3 K in the worst-affected regions, and more than 5 K in a few.

Because the biases are stable across decades and identifiable by region and season, they can be corrected for rather than merely acknowledged — which makes this a usable adjustment to projections rather than only a caution about them.

Citation

Lei Duan, Lyssa M. Freese, Govindasamy Bala, and Ken Caldeira (2025). Historical model biases in monthly high temperature anomalies indicate under-estimation of future temperature extremes. Communications Earth & Environment 6, 604.