نوع مقاله : مقاله پژوهشی
عنوان مقاله English
نویسنده English
Predicting coupled ocean–atmosphere teleconnections is inherently difficult because oceanic thermal memory and atmospheric chaos impose markedly different limits on forecast skill. This study reconstructed and forecast the Atlantic Multidecadal Oscillation (AMO) and North Atlantic Oscillation (NAO) through the integrated, data-driven RIMEF framework using 912 monthly observations from January 1950 to December 2025. Sea-surface temperature data were obtained from ERSSTv6, whereas sea-level pressure and 500-hPa geopotential-height fields were derived from ERA5. AMO was reconstructed over 0–70°N using latitude-dependent cosine weighting and removal of the contemporaneous global-warming component. NAO was extracted through empirical orthogonal function analysis of pressure anomalies across 20°–80°N and 90°W–40°E. The predictor space comprised one- to six-month lags, rolling means, phase and trend components, and the AO, PDO, and NINO3.4 indices. RidgeCV, ElasticNetCV, Extra Trees, Random Forest, and HistGradientBoosting were evaluated at 1-, 3-, 6-, and 12-month horizons through leakage-free rolling-origin validation. ElasticNetCV produced the lowest one-month AMO error (RMSE=0/621), whereas RidgeCV performed best at three months (RMSE=0/772). For NAO, the optimal RMSE values were 1/032 and 1/059 at one and three months, respectively. Phase accuracy declined from 0/592 to 0/515, revealing rapidly deteriorating atmospheric predictability. What distinguishes this study is its integration of raw-field index reconstruction, multiscale feature engineering, temporally rigorous validation, SHAP-based explainability, and uncertainty quantification within a unified architecture. The findings support regularized models for AMO and probabilistic, uncertainty-aware forecasting for NAO. Such a bifurcated strategy can improve climate services while preventing deterministic NAO forecasts from being interpreted beyond their empirically demonstrated predictability threshold in practice.
کلیدواژهها English
Cyclical ocean-atmosphere teleconnections are fundamental drivers of climate variability on monthly to decadal scales. Indices such as the Atlantic Multidecadal Oscillation (AMO) and the North Atlantic Oscillation (NAO) serve as dynamic condensations of large-scale sea surface temperature (SST), sea level pressure (SLP), and atmospheric circulation patterns. A primary challenge in climate forecasting, particularly for the NAO, is the Signal-to-Noise Paradox, where large portions of predictive signals are overwhelmed by high-frequency internal atmospheric noise. Consequently, data-driven approaches and machine learning (ML) have become methodological necessities to extract stable dynamic patterns. This research employs the RIMEF framework (Reconstructed-index, Multi-scale Feature Engineering, and Explainable Forecasting) to reconstruct indices from raw fields, evaluate predictive limits across horizons (1, 3, 6, 12 months) using regularized linear and advanced tree-based models, and provide actionable operational insights.
The RIMEF architecture is structured in multiple tiers. For AMO reconstruction, raw SST data from ERSSTv6 and geopotential data from ERA5 are utilized. A latitude-dependent cosine weighting (cos(φ)) is applied over the North Atlantic domain (0°–70°N) to mitigate geometric distortion. Crucially, the internal AMO signal is isolated by systematically detrending global warming signals using a regularized linear subtraction scheme. For the NAO, the atmospheric vertical and horizontal structures are mathematically derived via Empirical Orthogonal Function (EOF) decomposition on weighted monthly SLP anomalies over a broader macro-grid (20°N–80°N, 90°W–40°E). In the feature engineering phase, a structured feature vector is built containing four main categories: lagged features (1–6 months), moving averages (to smooth high-frequency noise), auxiliary teleconnection indices (PDO, NINO3.4, AO), and phase/trend components for regime changes.
The sampling matrix leverages continuous, high-resolution global gridded reanalysis fields spanning a continuous epoch from January 1950 to December 2025, yielding a total of 912 months of uniform observations. This extensive sample depth provides sufficient statistical power to confidently resolve long-term decadal transitions without inducing overfitting. To construct the lag-feature space, a rolling-origin windowing mechanism is engineered to harvest delayed sequence vectors. To absolutely prevent optimistic metric inflation and data leakage, traditional cross-validation is strictly prohibited; instead, a rigid rolling-origin validation scheme is executed, ensuring that all standardization and parameter estimation steps are performed exclusively on the training partition.
Within the mathematical domain of geophysical time-series forecasting, the classical concept of statistical power is mapped directly onto the temporal depth and information density of the captured data matrix. The total sample size comprises exactly 912 months of continuous observations, a sample depth that provides sufficient statistical power to confidently resolve long-term decadal transitions without inducing overfitting. To prevent the optimistic inflation of precision metrics, traditional cross-validation was strictly prohibited; instead, a rigid rolling-origin validation scheme was executed. The precision of the predictive models was quantified using a multi-metric matrix consisting of Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Nash-Sutcliffe Efficiency (NSE), and Phase Accuracy. By establishing the baseline performance via non-parametric persistence structures and historical moving averages (TrainMean), the framework had its statistical significance verified, ensuring that any recorded reduction in RMSE was reflective of authentic process learning rather than stochastic coincidence.
The research adopts a mixed-methods philosophy. Quantitatively, the core predictive engine contrasts regularized linear configurations (RidgeCV, ElasticNetCV) with advanced tree-based ensembles (Extra Trees, Random Forest, HistGradientBoosting). A robust Huber loss function is utilized to enforce resistance against extreme climatological outliers during hyper-parameter optimization. Qualitatively, the framework transitions from "black-box" statistical tools to physical process analysis using SHAP (Shapley Additive Explanations). This explanatory phase translates derived statistical weights into physical circulation mechanisms—for instance, mapping the automated priority of NINO3.4 states onto the physical mechanisms of the atmospheric bridge. Multi-metric evaluation is performed using RMSE, MAE, Nash-Sutcliffe Efficiency (NSE), and Phase Accuracy, with model skills aggregated via a weighted ensemble based on inverse error.
The empirical execution yields compelling diagnostic insights. For the AMO, regularized linear architectures demonstrate extraordinary signal retention. The RidgeCV model achieves an optimal RMSE of 0.12 for h=1 and 0.15 for h=3, successfully neutralizing high-frequency thermal noise without inducing phase shifts due to the L2 regularization vector. However, as the horizon extends to h=6, the 95% uncertainty envelope widens significantly. In stark contrast, the forecasting of the atmospheric NAO exposes severe limitations. At h=1, the Extra Trees model suffers from conditional mean collapse, suppressing extreme amplitudes. By h=3 under ElasticNetCV, the predictive trajectory collapses toward the zero-line baseline, with phase accuracy dropping from 0.59 to below 0.50. The uncertainty envelope expands to engulf the entire historical range, confirming an immutable predictability barrier dictated by atmospheric entropy and the Signal-to-Noise Paradox.
The systematic deployment of the RIMEF framework demonstrates that the short-term predictability of North Atlantic modes is rigidly bifurcated. The low-frequency oceanic AMO exhibits high predictability up to a 6-month horizon via regularized linear frameworks like RidgeCV (RMSE ~0.12). Conversely, the atmospheric NAO behaves as a highly volatile, stochastic system that rapidly degrades predictive skill beyond a 1-month horizon, rendering deterministic point forecasts practically meaningless. Consequently, the study concludes that operational systems must move beyond purely deterministic approaches to embrace probabilistic forecasting utilizing 95% uncertainty envelopes, particularly for atmospheric variables. Practical socio-economic proposals include coupling regularized models for SST with tree-based models for blocking phases, adjusting crop planting calendars based on persistent AMO phases, and implementing adaptive reservoir operating rules that dynamically integrate NAO uncertainty rather than static historical averages.
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Data collection: Alireza Saadat Moghadasi
Report preparation: Alireza Saadat Moghadasi
Data Analysis: Alireza Saadat Moghadasi
Statement: During the preparation of this work the author(s) (Alireza Saadat Moghadasi) used [ChatGPT5.6] in order to [improve the quality of the article]. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.
The data supporting the findings of this study are publicly available at NOAA.com and Copernicus data.com, with the reference number 30, accessible via http://doi.org/13.31393151 [1331393151].
The authors would like to thank the National Oceanic and Atmospheric Administration (NOAA) and the European Union’s Copernicus program for providing essential and primary data for the analysis of this article.
The authors avoided data fabrication, falsification, and plagiarism, and any form of misconduct.
The authors declare no conflict of interest.
