Fig. 4: Out-of-sample validation of the adaptative emergent constraint method.

The percentage differences in bias (a), variance (b) and root mean squared error (c) between the constrained and unconstrained changes in annual maximum daily precipitation during 2071–2100 relative to 1985–2014 under the SSP5-8.5 forcing scenario, as revealed by a model-based cross-validation (see Methods). Boxplots display the multi-model mean percentage differences across grid cells. In each boxplot, the horizontal line and the box represent the median and 16–84% range of the percentage differences, respectively, and the ‘whiskers’ extend to the 5–95% range. At each grid cell, a paired t-test is used to determine whether the multi-model percentage differences are significantly different from zero at a 5% level, as marked in the maps. Grid cells where the temperature constraint is not applicable in 80% or more of the considered climate models or scaling diagnostic is significantly biased are left blank. The validation is based on extreme precipitation changes estimated using data aggregation, and thus the bias and uncertainty changes are only due to the application of temperature constraint. See Fig. S8 for the results under other lower emissions scenarios.