The signal-to-noise paradox in a conceptual framework based on the 1963 Lorenz model

Seasonal prediction systems based on comprehensive Earth System Models are capable of skillfully predicting the winter North Atlantic Oscillation. However, the predictive skill reported for these systems is accompanied by a potential inconsistency: The quality of the predictions measured over a set of retrospective forecasts and quantified by the correlation coefficient between prediction and observation exceeds expectations based exclusively on model properties. This discrepancy is commonly referred to as the signal-to-noise paradox (SNP)

Current investigations of the SNP are predominantly looking at seasonal predictions systems based on comprehensive Earth System Models, focusing the uncertainties in the model formulation. In the present contribution, we investigate the SNP in a simple conceptual framework of an ensemble prediction system based on the simple three dimensional Lorenz 1963 Model (L63). This framework enables us to separate the influence of uncertainties in the model initialization and uncertainties in the model formulation on the occurrence of the SNP.

We show that in the absence of uncertainties in the model formulation the SNP is not apparent in L63, if the uncertainty assumed for the initialization of the ensemble is equal to the observational uncertainty. However, if we assume that the uncertainty in the initialization systematically overestimates the observational uncertainty, the SNP is also apparent in L63 - even if there are no uncertainties in the model formulation itself.

While these results obtained in the conceptual framework cannot directly translated to the SNP in comprehensive Earth System Models, we suggest to include in further investigations of the SNP in Earth System Models also a comparison of the magnitude of the initial ensemble spread and the observational uncertainty.