The Signal-to-Noise Paradox for Interannual Surface Atmospheric Temperature Predictions

The “signal-to-noise paradox” implies that climate models are better at predicting observations than themselves. Here, it is shown that this apparent paradox is expected when the relative level of predicted signal is weaker in models than in observations. In the presence of model error, the paradox only occurs in the range of small signal-to-noise ratio of the model, occurring for even smaller model signal-to-noise ratio with increasing model error. This paradox is always a signature of the prediction unreliability. Applying this concept to noninitialized simulations of Surface Atmospheric Temperature (SAT) of the CMIP5 database, under the assumption that prediction skill is associated with persistence, shows that global mean SAT is marginally less persistent in models than in observations. However, at a local scale, the analysis suggests that ∼70% of the globe exhibits the signal-to-noise paradox for local SAT interannual forecasts and that the Signal-to-Noise Paradox occurs especially over the oceans.