The Linear Response Function of an Idealized Atmosphere. Part I: Construction Using Green’s Functions and Applications

Abstract

A linear response function (LRF) determines the mean-response of a nonlinear climate system to weak imposed forcings, and an eddy flux matrix (EFM) determines the eddy momentum and heat flux responses to mean-flow changes. Neither LRF nor EFM can be calculated from first principles due to the lack of a complete theory for turbulent eddies. Here the LRF and EFM for an idealized dry atmosphere are computed by applying numerous localized weak forcings, one at a time, to a GCM with Held-Suarez physics and calculating the mean-responses. The LRF and EFM for zonally-averaged responses are then constructed using these forcings and responses through matrix inversion. Tests demonstrate that LRF and EFM are fairly accurate. Spectral analysis of the LRF shows that the most excitable dynamical mode, the neutral vector, strongly resembles the model's Annular Mode. The framework described here can be employed to compute the LRF/EFM for zonally-asymmetric responses and more complex GCMs. The potential applications of the LRF/EFM constructed here are i) forcing a specified mean-flow for hypothesis-testing, ii) isolating/quantifying the eddyfeedbacks in complex eddy-mean flow interaction problems, and iii) evaluating/improving more generallyapplicable methods currently used to construct LRFs or diagnose eddy-feedbacks in comprehensive GCMs or observations. As an example for iii, in Part 2, the LRF is also computed using the fluctuation-dissipation theorem (FDT), and the previously-calculated LRF is exploited to investigate why FDT performs poorly in some cases. It is shown that dimension-reduction using leading EOFs, which is commonly used to construct LRFs from the FDT, can significantly degrade the accuracy due to the non-normality of the operator.

Size of the Atmospheric Blocking Events: Scaling Law and Response to Climate Change

“…Furthermore, the strength and latitude of the jet, and w and λ are interconnected (Barnes & Polvani, ; Barnes & Screen, ; Kidston & Vallis, ; Peings et al, , ; Ronalds et al, ). To quantitatively separate the effects of these parameters on each other, controlled experiments using linear response functions can be used (Hassanzadeh & Kuang, , , , ; Khodkar et al, ; Ma et al, ); this is left for future work.…”

Data-driven reduced modelling of turbulent Rayleigh–Bénard convection using DMD-enhanced fluctuation–dissipation theorem

“…Because of the latter, L cannot be derived directly from (3.1)-(3.3). Khodkar et al (2018) showed that L can be accurately calculated using the Green's function (GRF) method (Kuang 2010;Hassanzadeh & Kuang 2016a), which requires many forced DNS of Eqns. (3.1)-(3.3).…”

Technical note: Simultaneous fully dynamic characterization of multiple input–output relationships in climate models

“…Linear, time-invariant emulators, of which pattern scaling is a special case, show good fidelity to general circulation model simulations for a wide range of variables and forcings (e.g., Barnes and Barnes, 2015;Kravitz et al, 2016a;MacMartin and Kravitz, 2016;Santer et al, 1990). Other methods, such as Green's function approaches (Hassanzadeh and Kuang, 2016) or application of the fluctuation dissipation theorem (Leith, 1975;Gritsun and Branstator, 2007;Ring and Plumb, 2008;Cooper and Haynes, 2011;Fuchs et al, 2015), are other linear methods that have shown skill in recovering complex climate model behavior. Each of these methods has advantages and disadvantages; there is a great deal of promise in utilizing multiple complementary approaches to understand (linearized) input-output relationships in climate models.…”