Statistical Inversion of Surface Ocean Kinematics from Sea Surface Temperature Observations

Abstract

The sea surface temperature (SST) record provides a unique view of the surface ocean at high spatiotemporal resolution and holds useful information on the kinematics underlying the SST variability. To access this information, we develop a new local matrix inversion method that allows us to quantify the evolution of a given SST perturbation with a response function and to estimate velocity, diffusivity, and decay fields associated with it. The matrix inversion makes use of the stochastic climate model paradigm—we assume that SST variations are governed by a linear transport operator and a forcing that has a relatively short autocorrelation time scale compared to that of SST. We show that under these assumptions, the transport operator can be inverted from the covariance matrices of the underlying SST data. The accuracy of the results depends on the length of the time series, and in general the inverted properties depend on the spatial and time resolution of the SST data. Future studies could use the methodology to explore the interannual variability of SST anomalies; to estimate the scale dependency of ocean mixing; and to estimate anomaly propagation, both at the surface and in the interior. The methodology can be easily used with any gridded observations or model output with adequate time and spatial resolution, and it is not restricted to SST. The inversion code is written in Python and distributed as a MicroInverse package through GitHub and the Python Package Index.

Diagnosing the Scale- and Space-Dependent Horizontal Eddy Diffusivity at the Global Surface Ocean

“…To this end we provide a global, spatially varying, empirical estimate of the magnitude of the diffusion tensor and its dependence on the spatial scale at the ocean surface. We base our estimates on satellite observations, a tracer simulation, and a recently developed statistical inversion methodology (MicroInverse; Nummelin et al 2018; see also Jeffress and Haine 2014a,b). While this paper and its supplement introduces the MicroInverse method, we encourage the readers who are interested in understanding the method in detail to read Nummelin et al (2018).…”

“…Observational and model-based evidence suggest that k varies in space both at the ocean surface (Shuckburgh et al 2009;Marshall et al 2006;Abernathey and Marshall 2013;Zhurbas et al 2014;Klocker and Abernathey 2014;Busecke et al 2017;Nummelin et al 2018) and at depth (Smith and Marshall 2009;Abernathey et al 2010;Vollmer and Eden 2013;Cole et al 2015;Roach et al 2018;Bachman et al 2020;Groeskamp et al 2020;Stanley et al 2020). Surface diffusivity also varies in time with the atmospheric forcing (Shuckburgh et al 2009;Busecke and Abernathey 2019).…”

“…The paper is structured as follows: in section 2a we present the MicroInverse method we use to estimate k [see also the online supplemental material and Nummelin et al (2018)] and in section 2b we review theory that links diffusivity to the kinetic energy spectra. Appendix A provides a link between the magnitude of the diffusivity tensor (focus of this paper) and suppressed across stream diffusivity (discussed in the literature).…”

A Bayesian Approach to Regional Decadal Predictability: Sparse Parameter Estimation in High-Dimensional Linear Inverse Models of High-Latitude Sea Surface Temperature Variability

“…Statistical estimation of stochastic models has a long history starting with ML and least squares estimates as a simplification; see Le Breton (1977) and DelSole and Yang (2010). In application to climate statistics, reviews can be found in DelSole and Hou (1999) and DelSole and Chang (2003) and comparisons in Mason and Mimmack (2002) and Nummelin et al (2018). From Penland (1989), the use of FDT approximations for the LIM to derive closed-form parameter estimation formulas makes this approach the method of choice in geoscience applications (Penland 1989;Penland and Sardeshmukh 1995;Nummelin et al 2018;Barnston et al 1999;Colman and Davey 2003), particularly over various autoregressive models (DelSole and Chang 2003;Penland et al 1993).…”

“…In application to climate statistics, reviews can be found in DelSole and Hou (1999) and DelSole and Chang (2003) and comparisons in Mason and Mimmack (2002) and Nummelin et al (2018). From Penland (1989), the use of FDT approximations for the LIM to derive closed-form parameter estimation formulas makes this approach the method of choice in geoscience applications (Penland 1989;Penland and Sardeshmukh 1995;Nummelin et al 2018;Barnston et al 1999;Colman and Davey 2003), particularly over various autoregressive models (DelSole and Chang 2003;Penland et al 1993). Barnston et al (2012) compares LIMs and other physically and statistically based models in the International Research Institute for Climate and Society (IRI) ENSO prediction plume.…”