Estimating present temperature climate in a warming world: probabilistic verification of a model-based approach for years 2008–2025

Abstract When climate changes, statistics derived from past observations become unrepresentative of the true present climate. In 2008, Räisänen and Ruokolainen proposed a model-based method for alleviating this bias. Here, the fidelity of this method in predicting the probability distributions of monthly mean temperatures is evaluated, focusing on the 16 years 2008–2023 that post-date the original study. Compared with the traditional approach in which the distributions are estimated directly from observations, a major improvement is found in both the continuous ranked probability score (CRPS) and the logarithmic score (L). The rank histograms that describe the positions of the verifying observations within the predicted distributions also become far more balanced. In addition, the optimal length of the baseline period from which observations are used increases when the observed temperatures are adjusted for climate change. The verification statistics are further improved when augmenting the model-based climate change estimates with information from local observed temperature trends. Conversely, both CRPS and L are degraded when the t-distributions fitted to the climate-change-adjusted observations are replaced with more flexible Stochastically Generated Skewed distributions. However, a blend between the two distributions using the Akaike information criterion yields statistics nearly identical to those for the t-distribution.