Climate Oscillations and Linear Gaussian Nonequilibrium Steady-States

Climate oscillations such as the El Niño–Southern Oscillation (ENSO) and the Madden–Julien Oscillation (MJO) dominate aspects of climate variability, yet they are often challenging to accurately capture in climate models. Due to their disparate underlying physical processes, any potential commonality between different climate oscillations is obscured. Common underlying dynamics is suggested by the success of relatively low-dimensional linear inverse modeling (LIM). LIMs represent climate oscillations as linear Gaussian nonequilibrium steady states (LG-NESS) defined by stochastic differential equations. Here we develop the theory of LG-NESS’s and compare with observations and models of climate oscillations.

ENSO and the MJO are often described by two-dimensional indices such as the leading SST EOFs for ENSO, or the Realtime Multivariate MJO index. The LIM algorithm parameterizes the dynamics in the index coordinate system as a two-dimensional LG-NESS specified by seven parameters. We decompose the parameter space into four parameters that define the coordinate system of the index, and three parameters that define its intrinsic dynamics. This allows us to transform all 2d LG-NESS’s to a common three-dimensional dynamical parameter space. Coordinate-invariant quantities depend only on the three dynamical parameters, while coordinate-dependent quantities can be transformed back to the original index coordinate system and depend on all seven parameters.

We parameterize ENSO and the MJO in this three-dimensional dynamical parameter space and find that, despite their distinct physical mechanisms and timescales, they lie within a narrow region of parameter space, indicating a similarity in the underlying phase-space dynamics. We compare observed and modeled dynamics with those of their parameterized LG-NESS, evaluating predictability, thermodynamic properties, and event statistics. We find this minimal three-parameter model reproduces many features of climate oscillations, revealing a deep dynamical similarity  among climate oscillations.