Probabilistic nonlinear lagged teleconnections of the sea surface temperature field

The monthly anomaly sea surface temperature field over the global ocean exhibit probabilistic dependencies between remote points and lagged times, which are explained eventually by some oceanic or atmospheric bridge of information transfer. Despite much of the bivariate SST dependencies appear to be linear, others are characterized by robust and statistically significant nonlinear correlations. In order to enhance that, we present a general method of extracting bivariate (X,Y) dependencies, seeking for pairs of polynomials P(X) and Q(Y) which are maximally correlated. The method relies on a Canonical correlation Analysis (CCA) between sets of standardized monomials of X and Y, up to a certain (low) degree (e.g. 4). Polynomial coefficients are obtained from the leading CCA eigenvector. Polynomials are calibrated and validated over independent periods, being afterwards subjected to marginal Gaussian anamorphoses. The bivariate non-Gaussianity in the space of marginally Gaussianized polynomials remains residual because of the correlation concentration and maximization. Consequently, the bivariate Gaussian pdf or in alternative, a copula pdf in the space of maximally correlated polynomials can accurately approximate the bivariate dependency. That probabilistic model is then used to determine conditional pdfs, cdfs and probabilities of extremes.

The method is applied to various (X,Y) pairs. In the first example, X is an optimized polynomial of the El-Niño 3.4 index while Y is that index lagged to the future. For lags between 6 and 18 months, the nonlinear El-Niño forecast clearly surpasses the linear one, contributing to lower the El-Niño seasonal predictability barrier. In the second example, we relate El-Niño (X) with the lagged Atlantic multidecadal oscillation index (Y). Nonlinear, robust correlations appear, both for positive and negative lags up to 5 years putting in evidence Pacific-Atlantic basin oceanic teleconnections.

The above probabilistic (polynomial based) model appears to be a good candidate tool for the statistical (seasonal up to decadal) forecast of regime probabilities (e.g. dry/wet) and extremes, given certain antecedent precursors.

This work was funded by the Portuguese Fundação para a Ciência e a Tecnologia (FCT) I.P./MCTES through national funds (PIDDAC) – UIDB/50019/2020- IDL and the project JPIOCEANS/0001/2019 (ROADMAP: ’The Role of ocean dynamics and Ocean–Atmosphere interactions in Driving cliMAte variations and future Projections of impact–relevant extreme events’). Acknowledgements are also due to the International Meteorological Institute (IMI) at Stockholm University.