A Linear Response Function Approach to the Midlatitude Jet Variability

The turbulent nature of the large-scale extratropical circulation complicates the studies aimed at understanding dynamical mechanisms, inferring causal relationships, interpreting the spatio-temporal characteristics, and quantifying eddy feedbacks. Linear Response Functions (LRFs), calculated for the observational data or General Circulation Models (GCMs), can significantly help such studies. Specifically, the LRFs can be used to 1) Identify the dominant modes of variability of the large-scale circulation in the observational or GCM data and investigate the dynamical interpretation of these modes; 2) Nudge the GCMs’ climatology to specified patterns using accurately calculated time-invariant forcings. Nudging the mean flow using the LRF is superior to commonly used methods based on relaxation, which results in time-varying forcings that can directly change the eddy field and low-frequency variability. It should be noted that while application (1) is limited to linear phenomena, application (2) is useful for studying linear as well as nonlinear phenomena.

In this presentation, we describe how LRFs can be calculated using the Green’s function method of Hassanzadeh and Kuang [2016, JAS] (only for GCMs) and using data-driven methods based on the Fluctuation-Dissipation Theorem (FDT) and Koopman operator theory (for GCMs and observational data). With problems related to the midlatitude jet variability on the intraseasonal to interannual timescales in mind, we compare the accuracy and discuss the advantages and disadvantages of these methods when applied to the GCMs or observational data. In particular, we address the challenges of applying the data-driven methods to short GCM or observational data.

To highlight the application (2) of LRFs, we also briefly present the key findings of several studies that have used an idealized GCM’s accurate LRF, calculated using Green’s functions, to study some problems about midlatitude jet variability. These problems include investigating causality in the relationship between blocking activity and the phase of Arctic Oscillation [Hassanzadeh and Kuang, 2015 GRL], identifying and quantifying the positive eddy-jet feedback in the annular mode dynamics [Ma et al., 2017 JAS], and particularly, understanding the mechanism of this feedback [Hassanzadeh and Kuang, in prep.].