A revised interpretation of signal-to-noise ratio paradox and its application to constrain regional climate projections

The signal-to-noise ratio paradox is interpreted as the climate model’s ability to predict observations better than the model itself. This view is counterintuitive, given that climate models are simplified numerical representations of complex earth system dynamics. A revised interpretation is provided here: the signal-to-noise ratio paradox represents excessive noise in climate predictions and projections. Noise is potentially reducible, providing a scientific basis for improving the signal in regional climate projections. The signal-to-noise ratio paradox was assessed in long-term climate projections using Single-model and Multi-model Large Ensemble climate data. A null hypothesis was constructed by performing bootstrap resampling of climate model ensembles to test its ability to predict the 20th-century temperature and precipitation trends locally and compare it with the observations. The rejection of the null hypothesis indicates the existence of a paradox. The multi-model large ensemble does not reject the null hypothesis in most places globally. The rejection rate in the single-model large ensemble is related to the model's fidelity to simulate internal climate variability rather than its ensemble size. For regions where the null hypothesis is rejected in the multi-model large ensemble, for example, India, the paradox is caused by a smaller signal strength in the climate model's ensemble. The signal strength was improved by 100% through ensemble selection and based on past performance, which reduced uncertainty in India's 30-year temperature projections by 25%. Consistent with previous studies, precipitation projections are noisier, leading to a paradox metric value 2-3 times higher than that of the temperature projections. The application of ensemble selection methodology significantly decreased uncertainty in precipitation projections for the United Kingdom, Western Australia, and Northeastern America by 47%, 36%, and 20%, respectively. Overall, this study makes a unique contribution by reducing uncertainty at the temporal scale, specifically in estimating trends using the signal-to-noise ratio paradox metric.