the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Explaining the high skill of Reservoir Computing methods in El Niño prediction
Abstract. Accurate prediction of the extreme phases of the El Niño Southern Oscillation (ENSO) is important to mitigate the socioeconomic impacts of this phenomenon. It has long been thought that prediction skill was limited to a 6 months lead time. However, Machine Learning methods have shown to have skill at lead times up to 21 months. In this paper we aim to explain for one class of such methods, i.e. Reservoir Computers (RCs), the origin of this high skill. Using a Conditional Nonlinear Optimal Perturbation (CNOP) approach, we compare the initial error propagation in a deterministic Zebiak-Cane (ZC) ENSO model and that in an RC trained on synthetic observations derived from a stochastic ZC model. Optimal initial perturbations at long lead times in the RC involve both sea surface temperature and thermocline anomalies which leads to a decreased error propagation compared to the ZC model, where mainly thermocline anomalies dominate the optimal initial perturbations. This reduced error propagation allows the RC to provide a higher skill at long lead times than the deterministic ZC model.
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CC1: 'Comment on npg-2024-24', Paul Pukite, 23 Nov 2024
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Because of the importance of the thermocline in ENSO behavior, the impact of long-period tides in a reduced effective gravity environment has to be included in any predictive analysis. This is particularly appropriate for machine learning, where known tidal data can be straightforwardly included as with any other input. It's obvious from the paper that the concentration focuses on natural responses (see the reproduced Fig.A2(a ) below) which clearly shows the damping characteristic of the perhaps stochastically-selected (via noise) eigenvalue solution to a differential equation.
" This distinction hinges on whether ENSO variability occurs as a sustained oscillation or limit cycle (supercritical) or is a damped oscillation excited by stochastic forcing (subcritical)."
Yet, it's more than likely that ENSO is the result of a forced response to tidal forces, with the annual nonlinear interaction creating an erratic cycling about the approximate 4 year mean period estimated from an index such as NINO3. For the main long-period tidal factors of Mf and Mm, the annually sidebanded periods are calculated at 3.8 and 3.9 years. The complete nonlinear solution of the shallow-water Laplace's tidal equations used to model oceanic fluid dynamics is described in [1]. A similar training/validation/test procedure is used for finding an optimal predictive fit as that used in machine learning. The main point in this type of modeling is that predictive analysis can conceivably be made years in advance. The continually forcing of the mixed lunar and annual cycles will create the requisite temporal boundary/guiding conditions to maintain coherence over a long range, much like conventional tides do for sea-level height (SLH) analysis.
[1] Pukite, P., Coyne, D., & Challou, D. (2019). Mathematical Geoenergy: Discovery, Depletion, and Renewal (Vol. 241). John Wiley & Sons. https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch12. Also see the following site for recent information: https://geoenergymath.com/2024/11/10/lunar-torque-controls-all
Citation: https://doi.org/10.5194/npg-2024-24-CC1
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