The Atlantic ocean's decadal variability in mid-Holocene simulations using Shannon's entropy

Abstract

Quantifying climate variability in a way that is comparable across models, experiments, and observations remains challenging, particularly at decadal time scales where nonlinear dynamics dominate. Traditional variance-based metrics are sensitive to anomaly amplitude, mean-state biases, and units of measurement, limiting their robustness for inter-model analyses. Here, we introduce an informationtheoretic framework that characterizes climate variability as trajectories in a discrete phase space and quantifies system organization using Shannon’s entropy. Using four coupled models (EC-Earth, GISS, iCESM, and CCSM-Toronto), we apply our methodology to compare the models' tropical and South Atlantic decadal variability, analyzing their sea surface temperature (SST) and precipitation under PreIndustrial and mid-Holocene boundary conditions, including Green Sahara experiments, and compare the results with observational datasets. Mid-Holocene forcings lead to modeldependent entropy changes, indicating a reorganization of Atlantic decadal variability rather than a uniform response across models. Green Sahara boundary conditions reduced SST entropy in EC-Earth and GISS models, implying a more organized Atlantic system, while precipitation responses are more heterogeneous. Entropy values derived from principalcomponent-based phase spaces have shown a more consistent framework to compare numerical models varaibility with observational estimates than using the traditional regional SST boxes index-based phase space. These findings highlight the diverse representations of climate variability across models. As such, this framework enables robust comparisons of low-frequency climate variability across models, paleoclimate simulations, and observations, complementing traditional variance-based diagnostics.