A hypothesis on ergodicity and the signal‐to‐noise paradox
Abstract 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 obser...
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Online Access: | http://dx.doi.org/10.1002/asl.1265 https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/asl.1265 |
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crwiley:10.1002/asl.1265 2024-09-15T18:22:10+00:00 A hypothesis on ergodicity and the signal‐to‐noise paradox Brener, Daniel J. Science and Technology Facilities Council 2024 http://dx.doi.org/10.1002/asl.1265 https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/asl.1265 en eng Wiley http://creativecommons.org/licenses/by/4.0/ Atmospheric Science Letters ISSN 1530-261X 1530-261X journal-article 2024 crwiley https://doi.org/10.1002/asl.1265 2024-08-13T04:12:03Z Abstract 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. Article in Journal/Newspaper North Atlantic North Atlantic oscillation Wiley Online Library Atmospheric Science Letters |
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Abstract 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. |
author2 |
Science and Technology Facilities Council |
format |
Article in Journal/Newspaper |
author |
Brener, Daniel J. |
spellingShingle |
Brener, Daniel J. A hypothesis on ergodicity and the signal‐to‐noise paradox |
author_facet |
Brener, Daniel J. |
author_sort |
Brener, Daniel J. |
title |
A hypothesis on ergodicity and the signal‐to‐noise paradox |
title_short |
A hypothesis on ergodicity and the signal‐to‐noise paradox |
title_full |
A hypothesis on ergodicity and the signal‐to‐noise paradox |
title_fullStr |
A hypothesis on ergodicity and the signal‐to‐noise paradox |
title_full_unstemmed |
A hypothesis on ergodicity and the signal‐to‐noise paradox |
title_sort |
hypothesis on ergodicity and the signal‐to‐noise paradox |
publisher |
Wiley |
publishDate |
2024 |
url |
http://dx.doi.org/10.1002/asl.1265 https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/asl.1265 |
genre |
North Atlantic North Atlantic oscillation |
genre_facet |
North Atlantic North Atlantic oscillation |
op_source |
Atmospheric Science Letters ISSN 1530-261X 1530-261X |
op_rights |
http://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.1002/asl.1265 |
container_title |
Atmospheric Science Letters |
_version_ |
1810461604326670336 |