I asked Gemini (Flash 2.5) about the signal-to-noise paradox regarding the North Atlantic Oscillation, which is one of the emerging new ideas (or concepts) in climate research. Here is the reply.

Yes, I am familiar with the signal-to-noise paradox, especially as it relates to the North Atlantic Oscillation (NAO). It’s a significant and intriguing challenge in climate modeling and prediction.

Here’s a breakdown of what it means in the context of the NAO:

The North Atlantic Oscillation (NAO)

First, a quick recap of the NAO: The NAO is the most prominent mode of atmospheric variability in the Northern Hemisphere, particularly during winter. It’s characterized by a seesaw in atmospheric pressure between the Icelandic Low and the Azores High.

• Positive NAO phase: Stronger than average pressure difference, leading to stronger westerly winds across the North Atlantic, bringing milder, wetter winters to Northern Europe and colder, drier conditions to Southern Europe and the eastern US.
• Negative NAO phase: Weaker pressure difference, resulting in weaker westerlies, often leading to colder, snowier winters in Northern Europe and milder, wetter conditions in Southern Europe.

The NAO has broad and distinct climatic impacts, making its prediction crucial for various sectors.

The Signal-to-Noise Paradox

The paradox arises in climate models when trying to predict the NAO (and other climate phenomena) on seasonal to decadal timescales. It can be summarized as:

Climate models often show higher correlation skill between their ensemble mean forecasts and observations of the NAO than they do between individual ensemble members and their own ensemble mean.

In simpler terms:

• “Signal”: The predictable component of the climate system. In an ensemble forecast, this is represented by the ensemble mean, which averages out the chaotic “noise” from individual runs.
• “Noise”: The unpredictable, chaotic variability inherent in the climate system (and in the models).

The paradox implies that:

1. Models are “better at predicting the real world than they are at predicting themselves.” This is because the ensemble mean of a model can skillfully predict the observed NAO, even though the individual runs within that same model’s ensemble might show a very weak predictable signal (i.e., a low signal-to-noise ratio).
2. The predictability of the real world might be underestimated by current models. If the models struggle to represent the true predictable signal, it suggests that the actual climate system might be more predictable than what the models are capturing.

Why is it a paradox and why is it important?

• Paradoxical: Intuitively, you’d expect a good model to predict its own behavior (its individual ensemble members) very well if it’s accurately capturing the “signal.” The fact that the ensemble mean often correlates better with observations than with its own members suggests a fundamental mismatch in how the model represents predictability.
• Important implications:
  • Underestimated predictability: It implies that our current climate models might be underestimating the inherent predictability of the NAO and other climate phenomena.
  • Model deficiencies: It points to potential deficiencies in the models, such as:
    • Lack of persistence: Models might underestimate the persistence of certain climate states or teleconnections.
    • Weak external forcings: The strength of the predictable response to external forcings (like sea surface temperatures in other basins, or stratospheric influences) might be underestimated.
    • Overestimated internal variability/noise: Models might generate too much internal, unpredictable variability, masking the true signal.
    • Issues with physical processes: The representation of key physical processes, such as air-sea coupling, stratospheric-tropospheric coupling, or ocean mesoscale eddies, might be inaccurate.
  • Ensemble design: It has implications for how large ensemble forecasts need to be to extract a robust predictable signal.

Current research and hypotheses:

Scientists are actively researching the causes of this paradox. Some leading hypotheses include:

• Underestimation of predictable dynamics: Models may not fully capture all the physical processes that contribute to the predictable “signal” in the real world. For the NAO, this could involve:
  • Stratospheric influence: The coupling between the stratosphere and troposphere, which can influence the NAO, might be weaker or incorrectly represented in models.
  • Oceanic forcing: The influence of sea surface temperatures in other regions (e.g., tropical Pacific through ENSO) on the NAO might be underestimated.
  • Extratropical air-sea coupling: The interaction between the ocean and atmosphere in the North Atlantic itself.
• Overestimation of noise: Models might generate too much unpredictable, internal variability compared to the real climate system.
• Model resolution: The resolution of climate models, particularly in the ocean, can play a role in how well they capture processes that contribute to predictability.
• Non-stationarity and sampling uncertainty: The paradox can also be influenced by the period over which models are evaluated, as climate predictability itself can vary on multi-decadal timescales.

Addressing the signal-to-noise paradox is crucial for improving the skill and confidence in seasonal-to-decadal climate predictions, which are vital for societal planning and adaptation to climate change.

Figure from climate.gov: On average, the surface pressure near Iceland is relatively low (L), while the pressure near the Azores Island is relatively high (H). During a negative phase (left), this pressure difference weakens. During a positive phase (right), the difference becomes even stronger than usual. The variation in pressure patterns influences the strength and location of the jet stream and the path of storms across the North Atlantic. Schematic adapted from AIRMAP by Ned Gardiner and David Herring, NOAA.

Scaife, A.A., Smith, D. A signal-to-noise paradox in climate science. npj Clim Atmos Sci 1, 28 (2018). https://doi.org/10.1038/s41612-018-0038-4

Weisheimer, A., and Coauthors, 2024: The Signal-to-Noise Paradox in Climate Forecasts: Revisiting Our Understanding and Identifying Future Priorities. Bull. Amer. Meteor. Soc., 105, E651–E659, https://doi.org/10.1175/BAMS-D-24-0019.1.