On the Seasonal Cycle of the Statistical Properties of Sea Surface Temperature

Abstract

Sea Surface Temperature (SST) is a fundamental variable of the Earth climate system due to its role in regulating climate and weather (Deser et al., 2010) and its dynamical connection to ocean currents . Moreover, the availability of a long time series of global high resolution satellite measurements of SST (Merchant et al., 2019) makes it well suited for addressing a wide range of problems such as monitoring Climate Change (Gulev et al., 2021); retrieving ocean currents (Isern-Fontanet et al., 2017); or calibrating and validating ocean and climate models (Skákala et al., 2019). It is, therefore, of major importance to understand how ocean processes contribute to SST statistics to exploit such a wealth of data and get insight into the functioning of the ocean and climate.A prominent feature of SST is the presence of fronts, which are known to be sinks of energy (D'Asaro et al., 2011; and significantly contribute to the vertical transport of nutrients and, thus, to primary production (Mahadevan, 2016). The variability of the characteristics of fronts, such as the density of fronts or their intensity, are expected to be mirrored by the variability of some SST statistics. A popular approach is based on the spectral slope of SST because it can be connected to theories of turbulence. Nevertheless, they provide an incomplete framework, if only because different theories may predict the same slope (Callies & Ferrari, 2013) and the underlying turbulence regime may not change in spite of the seasonal changes in the properties of fronts.The structure functions of a turbulent variable, that is, the moments of the differences between two points, are also at the core of theories of turbulence (Pope, 2000) and extend the information provided by spectral slopes (Sukhatme et al., 2020;Yu et al., 2017). Moreover, the anomalous scaling of the power laws deduced from the structure functions, that is, its deviation from a straight line, can be related to the geometry of gradients making use of the multifractal framework . The relevance of this approach has already been demonstrated in the oceanic context (Isern-Fontanet et al., 2007), and it has been used to develop metrics for