A statistical perspective on the signal‐to‐noise paradox

Bröcker, Jochen; Charlton‐Perez, Andrew; Weisheimer, Antje

doi:10.1002/qj.4440

Cited by 4 publications

(3 citation statements)

References 41 publications

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“…Consequently, forecasts in these regions are underconfident (Eade et al, 2014; Strommen et al, 2023). Although the ‘paradox’ may be explained as a consequence of imperfect models (Bröcker et al, 2023; Scaife & Smith, 2018; Siegert et al, 2016)—and hence not a ‘paradox’ in some sense of the word—in what follows we use the phrase as shorthand for the too weak predictable fraction in models compared with the real world.…”

Section: Introductionmentioning

confidence: 99%

Signal‐to‐noise errors in free‐running atmospheric simulations and their dependence on model resolution

Cottrell,

Screen,

Scaife

2024

Atmospheric Science Letters

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Ensemble forecasts have been shown to better predict observed Atlantic climate variability than that of their own ensemble members. This phenomenon—termed the signal‐to‐noise paradox—is found to be widespread across models, timescales, and climate variables, and has wide implications. The signal‐to‐noise paradox can be interpreted as forecasts underestimating the amplitude of predictable signals on seasonal‐to‐decadal timescales. The cause of this remains unknown. Here, we examine sea level pressure variability from a very large multi‐model ensemble of uninitialized atmosphere‐only simulations, focusing on boreal winter. To assess signal‐to‐noise errors, the ratio of predictable components (RPC) is examined globally, as well as for regional climate indices: the North Atlantic Oscillation, Arctic Oscillation, Southern Annular Mode, and an Arctic index. Our analyses reveal significant correlations between the multi‐model ensemble‐mean and observations over large portions of the globe, particularly the tropics, North Atlantic, and North Pacific. However, RPC values greater than one are apparent over many extratropical regions and in all four climate indices. Higher‐resolution models produce greater observation‐model correlations and greater RPC values than lower‐resolution models in all four climate indices. We find that signal‐to‐noise errors emerge more clearly at higher resolution, but the amplitudes of predictable signals do not increase with resolution, at least across the range of resolutions considered here. Our results suggest that free‐running atmospheric models underestimate predictable signals in the absence of sea surface temperature biases, implying that signal‐to‐noise errors originate in the atmosphere or in ocean–atmosphere coupling.

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Section: Introductionmentioning

confidence: 99%

Signal‐to‐noise errors in free‐running atmospheric simulations and their dependence on model resolution

Cottrell,

Screen,

Scaife

2024

Atmospheric Science Letters

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“…Statistically however, an anomalous SNR indicates that EPS members are not statistically interchangeable with the verification, and an apparent “paradox” arises only if such an interchangeability is assumed. An anomalous SNR is a consequence of the relative magnitudes of the variance of the observations, the ensemble mean, and the error of the ensemble mean, and should be expected in such circumstances (Bröcker et al., 2023). A Bayesian framework, applied to minimal models, allows the calculation of posterior probabilities for hypotheses, including those related to SNRs (Siegert et al., 2016).…”

Section: Introductionmentioning

confidence: 99%

Diversity of Stratospheric Error Growth Across Subseasonal Prediction Systems

Lee,

Charlton‐Perez

2024

Geophysical Research Letters

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The stratosphere has previously been shown to be a significant source of subseasonal tropospheric predictability. The ability of ensemble prediction systems to appropriately exploit this depends on their ability to reproduce the statistical properties of the real atmosphere. In this study, we investigate predictability properties of the coupled stratosphere‐troposphere system in the sub‐seasonal to seasonal prediction project hindcasts by fitting a simple, minimal model. We diagnose the signal and noise components of each system in the stratosphere and troposphere and their coupling. We find that while the correlation skill scores are similar in most systems, the signal to noise properties can be substantially different. In the stratosphere, some systems are significantly overconfident, with a quantifiable impact on the tropospheric confidence. We link the method and details of the design of a prediction system to these predictive properties.

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“…A forecast is said to exhibit a “signal‐to‐noise paradox” when RPC > 1, which corresponds to a situation where the ensemble mean is a better predictor of the real world than of individual ensemble members (see Section 2.4). However, interpreting this situation and understanding how RPC relates to other skill metrics has proved challenging (Bröcker et al., 2023). Indeed, the choice of the word “paradox” suggests that this phenomenon is often viewed as strange and unintuitive by the weather forecasting community.…”

Section: Introductionmentioning

confidence: 99%