Information Entropy Approaches to Climate Model Uncertainty Quantification

Abstract

Climate projections are conventionally summarized by ensemble mean and variance, but these moments can
obscure structural disagreement between models when projected distributions are multimodal or skewed. We
applied information-theoretic entropy measures, Shannon entropy of binned projection distributions and
Kullback-Leibler (relative) entropy between individual models and a multi-model reference distribution, to an
ensemble of 34 CMIP-class climate models projecting end-of-century (2081-2100) surface temperature and
precipitation change under a high-emissions scenario across 22 land regions. Shannon entropy of the cross-model
temperature-change distribution varied more than twofold across regions, from 1.42 bits over the Amazon basin to
3.05 bits over the Arctic, with the five highest-entropy regions all located at high latitudes or in regions with strong
land-atmosphere feedback processes, indicating that model disagreement is concentrated in physically specific
regions rather than distributed uniformly across the globe. Relative entropy between individual models and the
multi-model mean distribution ranged from 0.09 to 1.87 bits across the 34 models, and the eight models identified
as high-relative-entropy outliers (top quartile, mean KL divergence 1.31 bits) disagreed with the ensemble mean
particularly strongly in Arctic amplification magnitude, contributing disproportionately, 61% of total ensemble
variance in Arctic temperature projections despite representing only 24% of the ensemble membership. A
regression of regional Shannon entropy against six candidate physical predictors identified sea-ice feedback
strength and land-atmosphere coupling strength as the strongest joint predictors of projection entropy (adjusted R^2
= 0.68, p < 0.001, n = 22), outperforming a baseline model using only mean warming magnitude (adjusted R^2 =
0.31). Cross-validated removal of the eight high-entropy outlier models reduced overall ensemble Shannon entropy
by 34% on average across regions while shifting the ensemble-mean projection by less than 0.15°C, showing that a
substantial share of headline model spread can be attributed to a structurally distinct minority of models without
materially changing the central estimate. These results argue for reporting information-entropy diagnostics
alongside conventional ensemble statistics to better communicate where, physically, climate projection uncertainty
is concentrated and which models drive it.