On the Relationship Between Reliability Diagrams and the “Signal‐To‐Noise Paradox”

Strommen, Kristian; Macrae, Molly; Christensen, Hilary

doi:10.1029/2023gl103710

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…This is known as the signal‐to‐noise ‘paradox’ and corresponds to the model containing apparently little predictability when used to predict its own members and yet providing a skilful prediction of the real world. 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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A hypothesis on ergodicity and the signal‐to‐noise paradox

Brener

2024

Atmospheric Science Letters

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This letter raises the possibility that ergodicity concerns might have some bearing on the signal‐to‐noise paradox. This is explored by applying the ergodic theorem to the theory behind ensemble weather forecasting and the ensemble mean. Using the ensemble mean as our best forecast of observations amounts to interpreting it as the most likely phase‐space trajectory, which relies on the ergodic theorem. This can fail for ensemble forecasting systems if members are not perfectly exchangeable with each other, the averaging window is too short and/or there are too few members. We argue these failures can occur in cases such as the winter North Atlantic Oscillation (NAO) forecasts due to intransitivity or regime behaviour for regions such as the North Atlantic and Arctic. This behaviour, where different ensemble members may become stuck in different relatively persistent flow states (intransitivity) or multi‐modality (regime behaviour), can in certain situations break the ergodic theorem. The problem of non‐ergodic systems and models in the case of weather forecasting is discussed, as are potential mitigation methods and metrics for ergodicity in ensemble systems.

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On the Relationship Between Reliability Diagrams and the “Signal‐To‐Noise Paradox”

Abstract: It is now well established that weather forecasting models are able to generate skillful seasonal forecasts of the winter North Atlantic Oscillation (NAO) (

Cited by 2 publications

References 27 publications

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

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

A hypothesis on ergodicity and the signal‐to‐noise paradox

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