Addressing climate variability and extreme events in the ocean with spectral time series analysis and neural network models

In the context of the Copernicus Climate Change Service project (C3S) we outline a set of time series analysis methods, showing their application to oceanic essential climate variables, mainly Sea Surface Temperature (SST), both globally and in regions of particular interest, such as the North Atlantic, tropical Pacific and Indian Oceans as well as the Mediterranean basin. The goal is to decompose observations into their main components, to be considered as average conditions, anomaly patterns, slow varying trend components, evaluating main periodicities and studying variability patterns. We introduce and show the comparison between linear and nonlinear methods for extraction of main features in SST data, where the nonlinear method is obtained with the application of a feed-forward neural network with the architecture of an autoencoder. The Singular Spectral Analysis method (SSA) is shown for extracting the main periodic oscillations in time series, showing both its ability of treating climate indices and usability for spatio-temporal gap-filling of data records, which is typically the case that occurs with when dealing with satellite data. We also highlight the importance of studying extreme events as defined by SST, that is those events which represent the tails of observations’ probability distribution, known as the Marine Heat Waves (MHWs). We outline their hierarchical characterisation and the detection procedure, presenting results on the global scale but also giving insight of a specific study-case in the Mediterranean basin. Indeed, the Mediterranean Sea has been experiencing a nearly constant positive trend over the last decades, accounting for a total increase of 1.5°C in the satellite era (from 1981 to present), and we analyse how this influences the MHWs detection. Hence we propose a second detection approach, based on first detrending the series, wanting to evaluate the variability itself once decoupled from a changing baseline climate and give comparison of results. Within the framework of neural networks, we investigate the equivalence of two paradigmatic models, the Hopfield model (HN) and the Boltzmann Machine (BM), firstly when dealing with random centred patterns and secondly also generalising duality to biased patterns. Since HN has a robust statistical mechanics background that enables a clear picture of retrieval capabilities, and BMs constitute the building block of deep neural architectures, this duality gives a route to follow in addressing explainable Artificial Intelligence (AI), which is nowadays an always more demanded feature for such methods, to allow further comprehension of results, as well as increased control and capability of improving these.