A Linear Stochastic Model of a GCM’s Midlatitude Storm Tracks

Abstract

A linear stochastic model is used to simulate the midlatitude storm tracks produced by an atmospheric GCM. A series of six perpetual insolation/SST GCM experiments are first performed for each month. These experiments capture the ''midwinter suppression'' of the Pacific storm track in a particularly clean way. The stochastic model is constructed by linearizing the GCM about its January climatology and finding damping and stirring parameters that best reproduce that model's eddy statistics. The model is tested by examining its ability to simulate other GCM integrations when the basic state is changed to the mean flow of those models, while keeping the stirring and damping unchanged. The stochastic model shows an impressive ability to simulate a variety of eddy statistics. It captures the midwinter suppression of the Pacific storm track qualitatively and is also capable of simulating storm track responses to El Niño. The model results are sensitive to the manner in which the model is stirred. Best results for eddy variances and fluxes are obtained by stirring the temperature and vorticity at low levels. However, a better simulation of the spatial structure of the dominant wave train as defined by covariance maps is obtained by stirring the temperature equation only, and at all levels.

Recovery of atmospheric flow statistics in a general circulation model without nonlinear eddy‐eddy interactions

“…Our results indicate that the eddy length scale is not directly determined by eddy-eddy interactions, and so it may be possible to make simple modifications to the simulation without eddy-eddy interactions to better match the full simulation. For example, the addition of stochastic noise and damping to the linearized equations of motion has been shown to capture some of the effects of eddy-eddy interactions in a GCM [Zhang and Held, 1999] and in quasigeostrophic models [Delsole and Farrell, 1996]. This also opens up the possibility of constructing a GCM in which climate statistics are obtained by solving a closed set of moment equations directly rather than by explicitly resolving eddies [Marston et al, 2007], although further approximations might be needed.…”

An applied mathematics perspective on stochastic modelling for climate

“…Such models can be determined empirically from data or by using the linearized equations of motion. These models can be forced either by a random forcing (Branstator 1990;Newman et al 1997;Whitaker & Sardeshmukh 1998;Zhang & Held 1999) or by an external forcing representing tropical heating (Branstator & Haupt 1998). To ensure stability of these linear models, damping is added according to various ad hoc principles.…”

Structural Stability of Turbulent Jets

“…Perturbation dynamics in turbulent shear flow is dominated by transient growth and the excitation and damping of this linear transient growth by processes including nonlinear wave-wave interactions can be represented by a combination of stochastic driving and eddy damping (Farrell and Ioannou 1993a,b, 1994DelSole 1996DelSole , 1999DelSole , 2001bDelSole andFarrell 1995, 1996). The turbulence theory that results produces an accurate description of the structure and spectra of midlatitude eddies as well as their more subtle velocity covariances and this allows momentum fluxes to be accurately determined Ioannou 1994, 1995;Whitaker and Sardeshmukh 1998;Zhang and Held 1999;DelSole 2001a). We will assume that the perturbation field and the associated momentum transports are adequately described by this turbulence model.…”