Is the winter mean NAO white noise? Models and observations.

The NAO is a dominant mode of variability in the Northern Hemisphere with strong impacts on temperature, precipitation, and storminess. The predictive skill of the NAO on annual to decadal scales is therefore an important topic, which is often studied using, e.g., (initialized) climate models. The temporal structure is closely related to the predictability, and on inter-annual time scales the observed NAO is frequently described to have power at 2-7 years and sometimes with a distinct peak around 7 or 8 years.  However, the observational record is brief, and such estimations have high uncertainty.

Here, we present a thorough study to answer the questions: is the winter mean NAO different from white noise and is the observed NAO different from the NAO in historical experiments with contemporary climate models (CMIP6)? To this end we use a range of statistical tools in both the temporal and spectral domain: Power-spectra, wavelet-spectra, autoregressive models, and various well-known time-series statistics.

Overall, we find little evidence to reject that the NAO is white noise. For observations, the peak in the power-spectrum at 8 years is, taken individually, significant in the period after 1950 but not before. However, considering the complete spectrum, significant peaks will often occur at some frequency, even for white noise.  The large CMIP6 multi-model ensemble is statistically very similar to an ensemble of similar size of white noise, e.g., the ensemble averages of the power spectrum and the wavelet spectra are completely flat.  Furthermore, for both observations and the model ensemble the tests based on autoregressive modelling and time-series statistics do not reject the null-hypothesis of white noise.