A more predictable Madden-Julian Oscillation index derived from Koopman spectral analysis
Abstract
The Madden-Julian oscillation (MJO) is a major source of subseasonal-to-seasonal (S2S) predictability. The MJO is commonly defined and tracked with indices such as the Real-time Multivariate MJO (RMM) index. Although the RMM provides a useful description of the MJO, its evolution can be noisy and difficult to predict. We define an MJO index using a data-driven approximation of the Koopman operator. The Koopman index captures similar tropical circulation and convection patterns to the RMM but evolves more smoothly and predictably. Skillful prediction extends to 46 days for the Koopman index compared to 11 days for the RMM under the same prediction framework. While this new approach does not recover the RMM as well as operational S2S models, which provide skillful forecasts up to 35 days, the Koopman index could complement existing MJO diagnostics in evaluating and developing extended-range forecast systems.
Related
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- Stochastic thermodynamics and predictability of Ornstein-Uhlenbeck processes: an application to the Madden-Julian Oscillation
- Changes to the Madden-Julian Oscillation with Surface Temperature Warming in Aquaplanet Simulations
- The Saharan Oscillation Index (1950-2024): Statistical Characterization, Persistence, and Spectral Variability
BibTeX
@misc{valva2026more,
title = {{A more predictable Madden-Julian Oscillation index derived from Koopman spectral analysis}},
author = {Claire Valva and Edwin P. Gerber},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.19435},
eprint = {2609.19435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19435},
}
RIS
TY - UNPB
TI - A more predictable Madden-Julian Oscillation index derived from Koopman spectral analysis
AU - Claire Valva
AU - Edwin P. Gerber
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.19435
UR - https://arxiv.org/abs/2609.19435
AB - The Madden-Julian oscillation (MJO) is a major source of subseasonal-to-seasonal (S2S) predictability. The MJO is commonly defined and tracked with indices such as the Real-time Multivariate MJO (RMM) index. Although the RMM provides a useful description of the MJO, its evolution can be noisy and difficult to predict. We define an MJO index using a data-driven approximation of the Koopman operator. The Koopman index captures similar tropical circulation and convection patterns to the RMM but evolves more smoothly and predictably. Skillful prediction extends to 46 days for the Koopman index compared to 11 days for the RMM under the same prediction framework. While this new approach does not recover the RMM as well as operational S2S models, which provide skillful forecasts up to 35 days, the Koopman index could complement existing MJO diagnostics in evaluating and developing extended-range forecast systems.
ER -