CGD's Dr. Grant Branstator

Abstract

In order to identify and quantify indications of linear and nonlinear planetary wave behavior and their impact on the distribution of atmospheric states, characteristics of a very long integration of an atmospheric general circulation model (GC) in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500hPa geopotential heights.

First it is established that nonlinear tendencies similar to those reported in an earlier study of the phase space behavior in this GCM have the potential to lead to non-Gaussian features in the probability density function (PDF) of planetary waves. Then using objective measures it is demonstrated that the distribution of model states has distinctive non-Gaussianity features. These features are characterized in various subspaces of dimension as high as four. A key feature is the presence of three radial ridges of enhanced probability emanating from the mode, which is shifted away from the climatological mean. There is no evidence of multiple maxima in the full PDF, but the radial ridges lead to three distinct modes in the distribution of patterns.

It is demonstrated that these key aspects of non-Gaussianity are captured by a two-Gaussian mixture model fitted in four dimensions. The two circulation states signifying the means of the component Gaussians are very similar to those associated with the two dynamical regimes identified in Branstator and Berner (2005) through analysis of model trajectories. It is concluded that the behavior of planetary waves can be conceptualized as being approximately piecewise linear in each dynamical regime, leading to a two-Gaussian mixture with three preferred patterns.

Figure caption: Two-dimensional histograms of 30 day mean 500 hPa states from an atmospheric general circulation model projected onto various leading EOFs. Values in the corners are measures of nonGaussianity including two-dimensional skewness (S) and kurtosis (K).

Support: NOAA.

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Gritsun, A. and G. Branstator, 2007: Climate Response Using a Three-Dimensional Operator Based on the Fluctuation-Dissipation Theorem. J. Atmos. Sci., 64, 2558-2575.

Abstract

The fluctuation-dissipation theorem (FDT) states that for systems with certain properties it is possible to generate a linear operator that gives the response of the system to weak external forcing simply by using covariances and lag-covariances of fluctuations of the undisturbed system. This paper points out that the theorem can be shown to hold for systems with properties very close to the properties of the earth's atmosphere.

As a test of the theorem's applicability to the atmosphere, a three-dimensional operator for steady responses to external forcing is constructed for data from an atmospheric general circulation model (AGCM). The response of this operator is then compared to the response of the AGCM for various heating functions. In most cases the FDT-based operator gives three-dimensional responses that are very similar in structure and amplitude to the corresponding GCM responses. The operator is also able to give accurate estimates for the inverse problem in which one derives the forcing that will produce a given response in the GCM. In the few cases where the operator is not accurate, it appears that the fact that the operator was constructed in a reduced space is at least partly responsible.

As an example of the potential utility of a response operator with the accuracy found here, the FDT-based operator is applied to a problem that is difficult solve with a AGCM. It is used to generate an influence function that shows how well heating at each point on the globe excites the the AGCM's Northern Annular Mode (NAM). Most of the regions highlighted by this influence function, including the Arctic and tropical Indian Ocean, are verified by AGCM solutions as being effective locations for stimulating the NAM.

Figure caption: Average temperature response at four levels in the troposphere and stratosphere to a midtropospheric heat source on the equator as given by an atmospheric general circulation model and by an operator based on the fluctuation-dissipation theorem.

Support: NOAA, DOE.

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Franzke, C., A. Majda, and G. Branstator, 2007: The origin of nonlinear signatures of planetary wave dynamics: Mean phase space tendencies and their information. Accepted for publication in J. Atmos. Sci.

Abstract

Mean phase space tendencies are investigated to systematically identify the origin of nonlinear signatures and the dynamical significance of small deviations from Gaussianity of planetary low-frequency waves. A general framework for the information content of mean phase space tendencies in complex geophysical systems is derived. In the special case of purely Gaussian statistics, this theory predicts that the interactions amongst the planetary waves themselves are the source of the nonlinear signatures in phase space, whereas the unresolved waves contribute only an amplitude independent forcing, and cannot contribute to any nonlinear signature.

The predictions of the general framework are studied for a simple stochastic climate model which represents key features of low-frequency planetary waves. This toy model has a strong nonlinear signature in the form of a double swirl in the mean phase space tendencies of its low-frequency variables, much like recently identified signatures of nonlinear planetary wave dynamics in prototype and comprehensive atmospheric General Circulation Models (GCM). As predicted by the general framework, the double swirl results from nonlinear interactions of the low-frequency variables.

Mean phase space tendencies in a reduced space of a prototype atmospheric GCM are also investigated. Analysis of the dynamics producing nonlinear signatures in these mean tendencies shows a complex interplay between waves resolved in the subspace and unresolved waves. The interactions amongst the resolved planetary waves themselves do not produce the nonlinear signature. It is the interaction with the unresolved waves which is responsible for the nonlinear dynamics. Interpreting this within the general framework suggests that this impact of the unresolved waves is due to their small deviations from Gaussianity and has significant contributions from both additive and multiplicative triad interactions between resolved and unresolved modes.

Figure caption: Mean tendencies in four planes of a phase space defined by the leading energy norm EOFs of a three level quasi-geostrophic model. Speeds are represented by shading in units of std dev. This paper's goal is to isolate those properties that lead to departures from circular tendencies, like those in panels a) and d).

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Meehl, G., J. Arblaster, G. Branstator, and H. van Loon, 2007: A coupled air-sea response mechanism to solar forcing in the Pacific region. Accepted for publication in J. Climate.

Abstract

The 11 year solar cycle (Decadal Solar Oscillation, or DSO) at its peaks strengthens the climatological precipitation maxima in the tropical Pacific during northern winter. Results from two global coupled climate model ensemble simulations of 20th century climate that include anthropogenic (greenhouse gases, ozone, and sulfate aerosols) and natural (volcanoes and solar) forcings agree with observations in the Pacific region, though the amplitude of the response in the models is about half the magnitude of the observations. These models have poorly resolved stratospheres and no 11 year ozone variations, so the mechanism depends almost entirely on the increased solar forcing at peaks in the DSO acting on the ocean surface in clear sky areas of the equatorial and subtropical Pacific. Due mainly to geometrical considerations and cloud feedbacks, this solar forcing can be nearly an order of magnitude greater in those regions than the globally averaged solar forcing. The mechanism involves the increased solar forcing at the surface being manifested by increased latent heat flux and evaporation. The resulting moisture is carried to the convergence zones by the SE-trades thereby strengthening the Intertropical Convergence Zone (ITCZ) and South Pacific Convergence Zone (SPCZ). Once these precipitation regimes begin to intensify, an amplifying set of coupled feedbacks similar to that in cold events (or La Nina events) occurs. There is a strengthening of the SE-trades and greater upwelling of colder water that extends the equatorial cold tongue farther west and reduces precipitation across the equatorial Pacific, while increasing precipitation even more in the ITCZ and SPCZ. Experiments with the atmosphere component from one of the coupled models are performed in which heating anomalies similar to those observed during DSO peaks are specified in the tropical Pacific. The result is an anomalous Rossby wave response in the atmosphere and consequent positive sea level pressure anomalies in the North Pacific extending to western North America. These patterns match features that occur during DSO peak years in observations and the coupled models. This "fast" response of the Pacific climate system with a cold event-like pattern to peaks of the DSO could give way to a warm event-like pattern and a more general warming of the tropics with a lag of a couple of years as noted in previous studies.

Figure caption: Sea level pressure anomalous response of CAM3 to idealized heating in the three tropical regions given in the figure legends. These regions correspond to three regions of anomalous precipitation during solar max years and demonstrate how each precipitation feature affects midlatitude conditions. (Contour interval is 0.5 hPa.)

Support: National Science Foundation and NASA