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Summary of achievements

Investigations of large-scale atmospheric dynamics and predictability of the climate system have resulted in significant progress on three fronts. In one project undertaken in collaboration with H. Teng (CCR), the predictability of upper layer ocean temperatures on decadal timescales has been estimated through experimentation with CCSM3. By considering two large ensembles of greenhouse gas scenario integrations and a control integration they have quantified the rate at which information in the initial state is lost. In northern basins, on average there is a predictable signal for about a decade at which point the signal from greenhouse gases becomes more important. Furthermore predictability from the initial state is highly dependent on the structure of this state and on the region. These dependencies occur because predictability preferentially residing in special intrinsic modes of the system. In a second project a generalization of the fluctuation-dissipation theorem has been investigated. This generalization results in response operators that estimate how the atmosphere will react to any specified, time dependent heat source of sufficiently weak amplitude. Tests in which operators are designed to match the response of a general circulation model have been very successful. This will make it possible to address questions concerning sensitivity, control and attribution that cannot be considered with GCMs. Applications to tropical phenomena including the Madden-Julian Oscillation and moist mixed Rossby-gravity waves are planned. The third project concerns a prominent oscillation in northern midlatitudes which holds promise as a vehicle for breaking the one to two week predictability limit that governs predictions of most atmospheric phenomena. Through collaboration with Andrey Gritsun (RAS) it has been found that this 25 day oscillation has signatures that are similar to those of unstable periodic orbits (UPOs) of chaotic systems. Moreover, using advanced numerical techniques, UPOs of the barotropic vorticity equation have been calculated, and it has been found that there is a family of UPOs whose structure and period matches the observed 25d phenomenon. These UPOs are among the least unstable for this model and suggest that it may be an especially predictable mode of atmospheric variability.

Publications

Branstator, G. and F. Selten. 2009: "Modes of Variability" and Climate Change. Journal of Climate, 22, 2639-2658, doi:10.1175/2008JCLI2517.1.

Figure 1: High resolution figure

Abstract: A 62-member ensemble of coupled general circulation model (GCM) simulations of the years 1940-2080, including the effects of projected greenhouse gas increases, is examined. The focus is on the interplay between the trend in the Northern Hemisphere December-February (DJF) mean state and the intrinsic modes of variability of the model atmosphere as given by the upper-tropospheric meridional wind. The structure of the leading modes and the trend are similar. Two commonly proposed explanations for this similarity are considered.

Several results suggest that this similarity in most respects is consistent with an explanation involving patterns that result from the model dynamics being well approximated by a linear system. Specifically, the leading intrinsic modes are similar to the leading modes of a stochastic model linearized about the mean state of the GCM atmosphere, trends in GCM tropical precipitation appear to excite the leading linear pattern, and the probability density functions (PDFs) of prominent circulation patterns are quasi-Gaussian.

Figure caption: Steady response of the primitive equations linearized about the time-average DJF state for experimental years 1950-79 when forced by an elliptical heat source at 10°N, 150°E. The plotted field is meridional wind at σ = .336. (Contour interval is 0.3 m s^-1).

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Gritsun A., G. Branstator, and A. Majda, 2008: Climate response of linear and quadratic functionals using the fluctuation dissipation theorem. J. Atmos. Sci., 65, 2824-2841, doi:10.1175/2007JAS2496.1.

Figure 2: High resolution figure

Abstract: A generalization of the fluctuation–dissipation theorem (FDT) that allows generation of linear response operators that estimate the response of functionals of system state variables is tested for a system defined by an atmospheric general circulation model (AGCM). A sketch of the proof of this generalization is provided, followed by comparison of response estimates based on the theory and actual responses of the AGCM for various idealized anomalous equatorial heat sources. Tested response quantities include precipitation, variances of bandpass and low-pass streamfunction, and momentum and heat fluxes. The solutions from the FDT operators are very similar to the AGCM solutions in terms of structure while overestimating response amplitudes by about 20%. As an example of an application of such response operators, the FDT operator that estimates the response of bandpass upper-tropospheric streamfunction variance is used to find the most efficient means of disturbing the Atlantic storm tracks by tropical heating. The results of the study suggest that the generalized FDT is an attractive method for systematically studying response attributes of the climate system that are of interest to climate scientists and society.

Figure caption: Anomalies of bandpass streamfunction variance at s = 0.336 forced by a circular heat source centered at 10°N, 120°W with central value of 2.5°C day^-1 as given by solutions to (a) a FDT operator and (b) CCM0 and forced by a heat source centered at 10°S, 90°E as given by solutions to (c) a FDT operator and (d) CCM0. Contours are 6.0 × 10¹¹ m^-4 s^-2 for all panels.