Near-term climate predictions may be decomposed into unpredictable (chaotic) noise and a constrained and therefore potentially predictable component.  Forecasts consisting of tens of ensemble members are run to allow the assessment of uncertainties and skill in seasonal-to-decadal predictions.  The mean of all the ensemble members is generally more highly correlated with observations than are individual ensemble members because the unpredictable component of the model forecasts is reduced by averaging. However, in a perfect model, each ensemble member should represent a potential realization of the true evolution of the climate system and therefore should correlate as highly with the ensemble mean as do the observations.

In almost all current seasonal-forecast systems, although the variability across different ensemble members is realistic, the predictable signal in these members across large regions of both the northern and southern hemispheres is weaker than expected for monthly and longer time scale forecasts and can get lost in the “noise” of the variability between members.  In other words, the ensemble mean correlates more highly with the observations than with the individual ensemble members.  This is the apparently paradoxical result, dubbed the ‘signal-to-noise paradox’, that the models predict the real world better than they can predict themselves.  Averaging across many more ensemble members than would be required for a perfect model is therefore necessary to reduce the noise and recover the skillful prediction, requiring significant computational resource.  Thus, there is currently a large effort within the seasonal and decadal forecasting communities to understand why predictable signals are too weak in climate models.

One theory for these weak predictable signals is that models do not sufficiently capture the impact of small-scale atmospheric waves (or eddies) on the large-scale features such as the jet stream, known as eddy feedback.  Whilst this is a difficult model deficiency to resolve, this study aims to demonstrate that there is indeed a link between eddy feedback deficiency in seasonal-forecasting systems and the weak signal-to-noise ratios found in their predictions.

To demonstrate this link, we consider the eddy feedback in the mid-troposphere in the mid-to-high latitudes of the northern hemisphere.  The correlation across different seasonal-forecast systems of this eddy feedback parameter with the above-described measures of how well the seasonal-forecast system can predict the real world (the model skill) and how well it can predict its own ensemble members, is statistically significant, demonstrating a link.  Furthermore, skill improves with increased and therefore more realistic values of eddy feedback (Figure 1a and 1b).  The ratio of these two measures is denoted the ratio of predictable components (RPC) and should equal 1 but is found in almost all current seasonal-forecast systems to be greater than 1.  For seasonal-forecast systems with greater, more realistic, values of eddy feedback, the value of RPC is closer to 1 (Figure 1c) meaning a reduced signal-to-noise error.

Figure 1:  There is a statistically significant correlation between the measure of eddy feedback in a seasonal-forecast system (the Eddy feedback parameter) and (a) the ability of the system to predict itself, (b) the ability of the system to predict the real world, and (c) the ratio of predictable components (RPC) which should equal 1.  The value of eddy feedback in atmospheric reanalysis is shown by vertical black lines (panels a and b) and a black circle (panel c).

Whilst Figure 1 considers the model skill and signal-to-noise ratio (RPC) for the Arctic Oscillation it is also possible to consider the regional links between eddy feedback and signal-to-noise ratio.  At each longitude/latitude we can compute the average model skill across all forecasting systems (Figure 1b) and estimate what skill a model may have if the eddy feedback were correctly represented (hollow black box in Figure 1b).  The difference between these values is the potential gain in skill that may come from removing eddy feedback deficiency.  It is found that skill could potentially double in many regions of the north Atlantic (Figure 2a and 2b).  This is consistent with the idea that improved eddy feedback in seasonal-forecast systems is linked to larger predictable signals in those systems.

Figure 2: (a) Average model skill (c.f. Figure 1b), and (b) potential gain in model skill from resolving eddy feedback deficiency (i.e., skill level suggested by hollow black box in Figure 1b).

In conclusion, our study demonstrates that eddy feedback deficiency is linked with weak predictable signals in current seasonal forecast systems, and that systems with more realistic eddy feedback show greater skill and a reduced signal-to-noise error.  This motivates further work in aiming to reducing eddy feedback deficiency in seasonal-forecast systems, by better understanding the physical mechanisms underlying eddy feedback and trying to conceive how to implement imposed eddy feedback or a parametrization of missing eddy feedback in forecast systems.