The North Atlantic Oscillation and the Signal to Noise Paradox

By: Daniel Hodson

 The North Atlantic Oscillation (NAO) is a key driver of European weather. It is an Atlantic pressure dipole (Figure 1a) and varies over time, with some interesting long-term trends (Figure 1b).

The NAO directly affects EU climate and weather – rainfall, temperature and winds follow swings in the NAO. These lead to significant impacts on society (Palin et al. 2016 Bell et al. 2017), and, with the surge in European wind and solar power generation, we are more exposed to NAO variability than ever (Ely et al. (2013), Clark et al. (2017)).
Is the NAO predictable, or just random? Analysis of the observed NAO are equivocal (Stephenson et al. 2000). Since the NAO has such a significant impact on society, predicting it would be of great value.

Figure 1: The North Atlantic Oscillation a) Spatial pattern (1st EOF of observed DJF MSLP) b) spatial variation over time, and smoothed with 10 year running mean (red).

Well, now we can (partly). In 2014, the Met Office’s seasonal forecasting system (GloSea) successfully predicted the winter NAO, months in advance (Scaife et al. 2014 ) Such models use ocean and atmosphere observations to produce an ensemble of forecasts for the coming winter.  Scaife et al  2014 showed that GloSea ensemble mean NAO forecast is correlated with the observed NAO (~0.6 ) This now presents some useful skill.
However, the amplitude of the ensemble mean NAO is smaller than observed – by a factor of 3.

This conundrum, predicting the variability, but not the amplitude is the Signal to Noise Paradox  (Scaife and Smith 2018).

We decided to examine this paradox using an optimal detection technique (Sutton and Hodson 2003, Venzke et al 1999). This allows us to extract the leading forced or predictable modes from an ensemble of forecasts. These modes are essentially Empirical Orthogonal Functions EOFS, but use extra steps to correct the statistical biases.

The output of this analysis is a set of spatial patterns that show how the model atmosphere responds to the common forcings. This allows to find the forcings for each mode; and compare the strength of these modes to observations.

The December-January leading mode (Figure 2) is an NAO-like dipole pattern, whilst the second mode is a canonical El Niño Southern Oscillation (ENSO) pattern – the atmospheric response to El Niño.
Figure 2 G&H shows how these modes correlate with the underlying Sea Surface Temperatures (SSTs). The ENSO mode (F) is correlated with tropical Pacific SSTs – a classic El Nino SST pattern. However, the NAO-like mode (E) shows no large coherent regions of strong correlations over the oceans (G).

Figure 2: First (E) and second (F) predictable modes in the GloSea early winter (DJ) hindcasts. G) SST correlations with first mode (E). H) as G, but for F.

This confirms that the ENSO pattern is driven by the SST variations (and hence initial ocean conditions), but the NAO-like pattern appears not to be. What is driving this predictable mode? The only other remaining factor are the atmospheric initial conditions. The troposphere is too noisy for initial conditions to persist until Dec-Jan, but perhaps the initial conditions of the stratosphere could. Studies have shown that signals can propagate slowly downwards from the stratosphere, into the troposphere (Baldwin and Dunkerton 2000). Could these be the source of predictability of the NAO in this model? Previous attempts largely ignored accurately initialising the stratosphere from observations, but the GloSea model does. A recent study (O’Reilly et al 2018) with a different model suggests that the stratosphere may indeed be key.

We have extracted the predictable variations from the forecasts, but we can also assess the magnitude of these variations compared to observations. Figure 3 shows this comparison for the NAO-like predictable mode in December-January. It is clear that the response in the model is much weaker; further analysis shows that this NAO-like predictable mode is indeed ~3 times weaker than in observations (Consistent with Eade et al 2014).Applying the same techniques, we can show that the ENSO mode is also weaker than observed, but by a noticeably smaller factor (~1.8).

Figure 3: Comparison of the magnitude of the NAO-like predictable mode in A) observations and B) GloSsea hindcast ensemble.

This suggests that the weaker response of the predictable modes in this forecast model is the not the same for all modes – some modes appear to be driven more weakly than others. This may be because, ultimately, different atmospheric processes are involved in driving these modes. Some of these processes may be weaker in the models than they are in the real world. If we can improve our understanding of these processes, we may be able to improve our seasonal NAO forecasts even more.

A few years ago, forecasting winter European climate months ahead seemed implausible. But now we know that useful NAO forecasts were there all along, buried in the noise. Further research may lead to routine, skilful forecasts of the NAO, months, or even seasons ahead.


Baldwin, M. P. and T.J. Dunkerton, 2001: Stratospheric harbingers of anomalous weather regimes. Sci., 294, 581–584,

Bell, V. A., H. N. Davies, A. L. Kay, A. Brookshaw, and A. A. Scaife, 2017: A national-scale seasonal hydrological forecast system: development and evaluation over Britain. Hydrol. and Earth Syst Sci., 21, 4681–4691,

Clark, R. T., P. E. Bett, H. E. Thornton, and A. A. Scaife: 2017, Skilful seasonal predictions for the European energy industry. Environ. Res. Lett., 12, 024002,

Eade, R., D. Smith, A. Scaife, E. Wallace, N. Dunstone, L. Hermanson, and N. Robinson: 2014, Do seasonal-to-decadal climate predictions underestimate the predictability of the real world? Geophys. Res. Lett., 41, 5620-5628,

Ely, C. R., D. J. Brayshaw, J. Methven, J. Cox, and O. Pearce, 2013: Implications of the North Atlantic Oscillation for a UK-Norway renewable power system. Energy Policy, 62, 1420–1427,

O’Reilly, C. H., A. Weisheimer, T. Woollings, L. Gray, and D. MacLeod, 2018: The importance of stratospheric initial conditions for winter North Atlantic Oscillation predictability and implications for the signal-to-noise paradox. Quart. J. Roy. Meteor. Soc., 145, 131-146,

Palin, E. J., A. A. Scaife, E. Wallace, E. C. D. Pope, A. Arribas, and A. Brookshaw, 2016: Skillful seasonal forecasts of winter disruption to the U.K. transport system. J. Appl. Meteor. Climatol., 55, 325–344.

Scaife, A. A., A. Arribas, E. Blockley, A. Brookshaw, R. T. Clark, N. Dunstone, R. Eade, D. Fereday, C. K. Folland, M. Gordon, L. Hermanson, J. R. Knight, D. J. Lea, C. MacLach- lan, A. Maidens, M. Martin, A. K. Peterson, D. Smith, M. Vellinga, E. Wallace, J. Waters, and A. Williams, 2014a: Skillful long-range prediction of European and North American winters. Geophys. Res. Lett., 41, 2514–2519.

Scaife, A. A. and D. Smith, 2018: A signal-to-noise paradox in climate science. npj Climate Atmos. Sci., 1,

Stephenson, D. B., V. Pavan, and R. Bojariu, 2000: Is the North Atlantic Oscillation a random walk? Int. J. Climatol., 20, 1-18.<1::AID-JOC456>3.0.CO;2-P

Sutton, R. T. and D. L. R. Hodson, 2003: Influence of the Ocean on North Atlantic Climate Variability 1871-1999. J. Climate, 16, 3296–3313.;2

Venzke, S., M. R. Allen, R. T. Sutton, and D. P. Rowell, 1999: The atmospheric response over the North Atlantic to decadal changes in sea surface temperature. J. Climate, 12, 2562–2584.;2

This entry was posted in Climate, Predictability, Stratosphere. Bookmark the permalink.