Understanding the Signal-to-Noise Paradox in Seasonal-to-Decadal Climate Predictions

Increasing evidence has been documented in recent years for the existence of the signal-to-noise paradox, where in the ensemble-based climate prediction, model ensemble mean forecast generally shows higher correlations with observations than with any individual ensemble member. This seems to lead to a paradox referred to as the signal-to-noise paradox that the model makes better predictions for reality than predicting itself. The signal-to-noise paradox highlights a potentially serious problem with climate model predictions as previous seasonal-to-decadal model predictions may be underestimated due to the existence of the paradox. Here we introduce a simple Markov model to represent the ensemble forecasts and aim to explain why the paradox exists. Alternative to the ratio of predictable component, the ratio of squared correlation is used to determine if the model is better at predicting the observations than itself. We argue that the signal-to-noise problem exists primarily because model ensemble members contain more unpredictable noise than the reality, while the observed variability is more persistent than model ensemble members. Based on observations and 40 coupled models from the fifth phase of the Coupled Model Intercomparison project, analysis of surface temperature, precipitation, sea level pressure, and the North Atlantic Oscillation index suggests widespread existence of the signal-to-noise paradox in seasonal-to-decadal predictions.