Stochastic modeling of decadal variability in ocean gyres

Abstract

Decadal large-scale low-frequency variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper presents a novel fully data driven approach that addresses this challenge. Proposed is non-Markovian low-order methodology with stochastic closure and use of mode decomposition by multichannel Singular Spectrum Analysis. The multilayer stochastic linear model is obtained from the coarse-grained eddy-resolving ocean model solution, and with high accuracy it reproduces the main statistical properties of the decadal variability. The proposed methodology does not depend on the governing fluid dynamics equations and geometry of the problem, and it can be extended to other ocean models and ultimately to the real data. BackgroundMidlatitude atmosphere and ocean possess not only significant interannual variability but also several large-scale variability modes on decadal and interdecadal timescales: North Atlantic Oscillation, Atlantic Multidecadal Oscillation, and Pacific Decadal Oscillation. Oceanic evidence of these modes is found in the sea surface temperature [Hansen and Bezdek, 1996], hydrography [Qiu and Joyce, 1992], and altimetry [Qiu and Chen, 2005], and it is mostly expressed in structural changes of the eastward jet extensions and the adjacent recirculation zones of the main western boundary currents, such as the Gulf Stream and Kuroshio. Physical origins of these large-scale low-frequency variability (LFV) modes remain unclear, and it is not even known to what extent these origins are intrinsic atmospheric, intrinsic oceanic, or coupled oceanic-atmospheric. One of the reasons, why coupled ocean-atmosphere comprehensive general circulation models (GCMs) cannot distinguish between these scenarios, is inability of their oceanic model components to simulate mesoscale eddies and their impact on the large-scale currents accurately and for a long time. On the other hand, seasonally forced, eddy-resolving ocean-only GCMs exhibit significant intrinsic LFV variability of mesoscale activity [Penduff et al., 2011], intergyre heat transport [Hall et al., 2004], sea level height [Cabanes et al., 2006], western boundary currents [Taguchi et al., 2007], and meridional overturning circulation [Biastoch et al., 2008]. This suggests that not only significant part of the LFV is intrinsic to the ocean but also oceanic mesoscale eddies could play significant role in driving it.Present theoretical understanding of the intrinsic LFV of the ocean starts from the null hypothesis that the ocean integrates high-frequency atmospheric forcing and responds in terms of the red variability spectrum [Hasselman, 1976]. However, over the last 20 years it became evident that in the presence of stochastic, seasonal, or constant atmospheric forcing, the most significant intrinsic LFV of the ocean is not red but operates on interannual-to-interdecadal time scales. One idea is that this variability can be understood in terms of early bifurcations...

Eddy Trains and Striations in Quasigeostrophic Simulations and the Ocean

“…If the drifting eddy trains correspond to a significant spatially coherent mode of variability, they should be detectable by EOF analysis. EOF-based methods are proven to be effective in studying low-frequency variability of the ocean circulation (e.g., Kondrashov and Berloff 2015). We next calculate the EOFs of the monthly mean barotropic streamfunction within box 1 from the 20-yr model run.…”

On low-frequency variability of the midlatitude ocean gyres

“…Some of the LFV is either imposed by the atmosphere or is due to the ocean-atmosphere coupling, but this study focuses on the intrinsic, ocean-only LFV. Since the existence of the LFV was established observationally (Deser & Blackmon 1993;Kushnir 1994), many modelling studies attempted to determine its patterns and mechanisms (McCalpin & Haidvogel 1996;Berloff & McWilliams 1999;Meacham 2000;Chang et al 2001;Nauw & Dijkstra 2001;Schmeits & Dijkstra 2002;Berloff et al 2007a,b;Kravtsov et al 2010;Simonnet 2010;Feliks et al 2011;Pierini et al 2014;Kondrashov & Berloff 2015). It is known now that collective action of oceanic mesoscale eddies is one of the main drivers of the midlatitude LFV (Kwon et al 2010), which is generated in models only when significant part of mesoscale eddies is dynamically resolved.…”

“…Berloff et al (2007a) argue that this LFV is a fundamentally turbulent phenomenon driven by a dynamical competition between the eddy rectification process and the potential vorticity (PV) anomalies induced by changes of the intergyre PV transport. This LFV pattern and mechanism have been named the "turbulent oscillator", and its stochastic statistical models were recently developed by Kondrashov & Berloff (2015). Analysis of similar LFV from a comprehensive ocean model is presently underway (Sérazin et al 2015).…”

Dynamically Consistent Parameterization of Mesoscale Eddies—Part II: Eddy Fluxes and Diffusivity from Transient Impulses

“…Extension from linear to fully nonlinear transient impulses is another anticipated future development. Accounting for the large-scale low-frequency variability of the eastward jet and upgrading the transient-impulse forcing towards much more realistic multiscale patterns (e.g., by data-driven statistical models; see also [36]) will provide further advances to the whole approach. The transient-impulses approach can be also advanced as a powerful analytical tool for estimating eddy fluxes and diffusivities for both passive and active tracers.…”

“…Determining random forcing, deriving its parameters and relating them to the large-scale flow remains to be done. So far, construction of random forcing is achieved by fitting patterns from the eddy-resolving simulations (e.g., [35,36]). …”