The sampling method for optimal precursors of El Niño-Southern Oscillation events

Abstract

The El Niño-Southern Oscillation (ENSO) is a significant climate phenomenon that appears periodically in the tropical Pacific. The intermediate coupled ocean-atmosphere Zebiak-Cane (ZC) model is the first and classical one designed to numerically forecast the ENSO events. Traditionally, the conditional nonlinear optimal perturbation (CNOP) approach has been used to capture optimal precursors in practice. In this paper, based on state-of-the-art statistical machine learning techniquesGenerally, the statistical machine learning techniques refer to the marriage of traditional optimization methods and statistical methods, or, say, stochastic optimization methods, where the iterative behavior is governed by the distribution instead of the point due to the attention of noise. Here, the sampling algorithm used in this paper is to numerically implement the stochastic gradient descent method, which takes the sample average to obtain the inaccurate gradient., we investigate the sampling algorithm proposed in to obtain optimal precursors via the CNOP approach in the ZC model. For the ZC model, or more generally, the numerical models with a large number O(104-105) of degrees of freedom, the numerical performance, regardless of the statically spatial patterns and the dynamical nonlinear time evolution behaviors as well as the corresponding quantities and indices, shows the high efficiency of the sampling method compared to the traditional adjoint method. The sampling algorithm does not only reduce the gradient (first-order information) to the objective function value (zeroth-order information) but also avoids the use of the adjoint model, which is hard to develop in the coupled ocean-atmosphere models and the parameterization models. In addition, based on the key characteristic that the samples are independently and identically distributed, we can implement the sampling algorithm by parallel computation to shorten the computation time. Meanwhile, we also show in the numerical experiments that the important features of optimal precursors can still be captured even when the number of samples is reduced sharply.