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Grant Branstator

Abstract

Monthly and seasonally averaged upper-tropospheric Northern Hemisphere winter fields are examined to determine whether the waveguiding effect of the time-averaged tropospheric jets on low-frequency disturbances that is predicted by theory does affect the behavior of these disturbances. It is found that, indeed, disturbances in the vicinity of the mean jets, particularly the jet that stretches across South Asia, are fundamentally different from those that reside in regions where the mean winds have weaker meridional gradients, like the mid-Pacific. Patterns of variability in the jets tend to be smaller scale and to consist of zonally oriented chains of anomalies while variability in the mid-Pacific is composed of patterns with distinct meridional orientation. Because they are meridionally trapped and zonally elongated, patterns associated with the jet stream waveguide connect activity at points that are much farther apart than do patterns in other regions of the globe.

Within the South Asian waveguide, variability tends to be composed of a zonal wave-5 feature with no favored longitudinal phase. One phase of this pattern is special in that it covaries with distant regions in midlatitudes producing a pattern of variability that circumscribes the hemisphere. This special pattern has a noticeable zonal mean component. Furthermore, it is prominent enough that for the upper troposphere it is embedded in the leading EOF of streamfunction and is essentially the same as the leading EOF of the υ wind component. Over the North Atlantic, its structure has a great deal in common with the structure of the North Atlantic Oscillation, so that its features can make significant contributions to plots of hemispheric circulation anomalies associated with that phenomenon.

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Eigil Kaas
and
Grant Branstator

Abstract

The degree to which Northern Hemisphere blocking activity is controlled by variations in zonal mean conditions is investigated.

A set of Northern Hemisphere winter season 500-hPa analyzed fields is examined for blocks using an objective index defined solely from the eddy fields. With this blocking index, it is shown that in most regions enhanced blocking activity is associated with relatively strong zonally averaged winds around 30°N and weak winds around 50°–60°N. Also, the preferred zonal positions of blocks are related to the state of the zonal mean flow. A similar analysis is carried out using data from a perpetual January GCM simulation and the same relationship between blocking activity and zonally averaged conditions is found to be valid to an even stronger degree for these data.

To investigate whether anomalous zonal mean flows are actually controlling the associated level of blocking activity, two experiments with the GCM are performed. In one experiment the zonal mean state of the GCM is forced toward a configuration that is statistically associated with enhanced blocking activity in the control simulation. In the other, the zonal mean is forced toward a state associated with suppressed blocking activity. Blocking frequency is enhanced in the first experiment and weakened in the second. Furthermore, the preferred locations for blocking in the experiments match the locations found to be associated with zonal mean anomalies in the control. This suggests the zonal mean state is influencing blocking activity.

Results from a steady barotropic linear model indicate that adjustments made by the planetary waves in reaction to anomalies in the zonal mean flow are partly responsible for the relationship between blocking and the zonal mean state.

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Grant Branstator
and
Isaac Held

Abstract

Eigenvectors and eigenvalues of the nondivergent barotropic vorticity equation linearized about zonally asymmetric wintertime mean flows are calculated to determine which barotropic modes might contribute to westward propagating disturbances observed in nature. Of particular interest are modes that correspond to a recurring pattern concentrated in the Western Hemisphere with a period of about 25 days reported by Branstator and Kushnir.

The most unstable modes of November–March means from individual years tend to be westward propagating and have a structure that is similar to the observed 25-day pattern.

By following the evolution of each Rossby–Haurwitz mode as the basic state is gradually changed from a state of rest to an observed mean state, it is demonstrated that all but about eight of the Rossby–Haurwitz modes will be modified beyond recognition by the action of the time mean flow. One of these, the second gravest antisymmetric zonal wavenumber-one mode (denoted {1, 3} and sometimes referred to as the 16-day wave), has a structure that bears some resemblance to the observed 25-day pattern, but it is typically neutral. The structural similarity between this mode and the 25-day pattern is not as pronounced as the similarity between the most unstable modes and the 25-day pattern. Furthermore, the mode for the observed basic state that {1, 3) evolves to depends on the path by which the resting state is transformed into the observed state, suggesting that {1, 3} cannot always be thought of as a distinct mode in the presence of a realistic background. The results indicate that even if {1, 3) can be considered to exist in wintertime mean flows, it is distinct from the most unstable modes on those flows.

By slowly changing the basic states that support the westward propagating unstable modes until they are equal to the climatological January state that earlier studies have shown produces quasi-stationary teleconnection-like modes, it is demonstrated that the unstable westward propagating and quasi-stationary modes are related to each other.

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Andrey Gritsun
and
Grant Branstator

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 AGCM. 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 to solve with an AGCM. It is used to generate an influence function that shows how well heating at each point on the globe excites the AGCM’s Northern Hemisphere 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.

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Grant Branstator
and
Judith Berner

Abstract

To identify and quantify indications of linear and nonlinear planetary wave behavior, characteristics of a very long integration of an atmospheric general circulation model in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa geopotential heights, and the primary investigated characteristic is the state dependence of mean phase space tendencies. Defining the linear component of planetary wave tendencies as that part which can be captured by a least squares fit linear operator driven by additive Gaussian white noise, the study finds that there are distinct linear and nonlinear signatures. These signatures are especially easy to see in plots of mean tendencies projected onto phase space planes. For some planes the mean tendencies are highly linear, while for others there are strong departures from linearity.

The results of the analysis are found to depend strongly on the lag time used to estimate tendencies with the linear component monotonically increasing with lag time. This is shown to result from the ergodicity of the system. Using the theory of Markov models it is possible to remove the lag-dependent component of the tendencies from the results. When this is done the projected mean dynamics in some planes is found to be almost exclusively nonlinear, while in others it is nearly linear.

In the four-dimensional space the linear component of the dynamics is largely a reflection of a westward propagating Northern Hemisphere pattern concentrated over the Pacific and North America. The nonlinear signature can be approximated by two linear functions, each operating in a different region of phase space. One region is centered around a Pacific blocking pattern while the other is centered on a state with enhanced zonal symmetry. It is concluded that reduced models of the planetary waves should strive to include these state-dependent dynamics.

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Judith Berner
and
Grant Branstator

Abstract

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 (GCM) in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa 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 model’s distribution of states has distinctive non-Gaussian 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 circulation 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 at the centroids of the component Gaussians are very similar to those associated with two nonlinear features identified by Branstator and Berner in their analysis of the trajectories of the GCM. These two dynamical features are locally linear, so it is concluded that the behavior of planetary waves can be conceptualized as being approximately piecewise-linear, leading to a two-Gaussian mixture with three preferred patterns.

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Grant Branstator
and
Jorgen Frederiksen

Abstract

Various aspects of the seasonal cycle of interannual variability of the observed 300-hPa streamfunction are documented and related to dynamical influences of the seasonality of the mean circulation. The stochastically excited nondivergent barotropic vorticity equation linearized about upper-tropospheric climatological mean states from each month of the year is used to identify characteristics of interannual variability that the seasonal cycle of the mean state should modulate. The result is interannual variability with (a) extratropical centers of variance that are much stronger in winter than summer and that are confined to midlatitudes during the warm season, (b) an annual cycle of preferred scales in midlatitudes with largest scales occurring during winter and a semiannual cycle of scales in the subtropics, and (c) streamfunction tendencies from interannual fluxes that adjust to the seasonally varying climatological eddies in such a way as to damp them. Because these same properties are also shown to exist in nature, it is concluded that the linear framework is a useful means of understanding the seasonality of interannual disturbances and that seasonality of the mean state leaves a pronounced imprint on interannual variability.

Analysis of an ensemble of general circulation model integrations indicates the signatures of seasonality produced in the stochastically driven linear framework are more useful for understanding intrinsic interannual variability than variability caused by seasonally varying sea surface temperature anomalies. Furthermore, it is found that the intrinsic variability of the GCM has properties very much like those in nature, another indication that organization resulting from anomalous forcing structure is not required for production of many aspects of the observed seasonality of interannual variability.

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Ulrich Achatz
and
Grant Branstator

Abstract

This work discusses the formulation and testing of a simplified model of atmospheric dynamics. The model, which has only 200- and 700-mb streamfunctions as its prognostic fields, is designed to have a climate that approximates that of a comprehensive perpetual January general circulation model. Its governing equations are based on a Lorenz-type filtered two-layer model, but its linear terms are replaced by an empirically determined operator; the simplified model is semiempirical. Its basis consists of three-dimensional empirical orthogonal functions that are calculated using a total energy metric. The linear operator is intended to serve as a parameterization of fields, patterns, and dynamics not explicitly represented in the model. The operator is found through an optimization procedure that ensures that the semiempirical model optimally predicts streamfunction tendencies observed to occur in an extended control integration of the general circulation model.

It turns out that a model determined in this way simulates the GCM climatology quite well. The time mean state, time mean transient fluxes, and leading patterns of variability are all very similar to those in the GCM. Notable superiority over the behavior of a standard filtered two-layer model is also found. In order to understand this, calculations are undertaken to identify processes, not explicitly represented in a standard filtered two-layer model, that can be especially well parameterized linearly. Results point to a dynamical balance in the GCM such that deviations of its tendencies from the tendencies given by a standard filtered model are smaller and more nearly a linear function of streamfunction anomaly than are individual terms contributing to the deviations. An analysis of the possibility of reducing the number of basis functions in the semiempirical model shows that, whereas short-time prediction is best for the nontruncated model, in the simulation of climate mean state and transient fluxes the optimum is at rather small pattern numbers (between 30 and 70).

The leading eigenmodes of the empirically determined linear component of the simplified model are found to be nearly neutral.

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Haiyan Teng
and
Grant Branstator

Abstract

California droughts are often caused by high-amplitude and persistent ridges near and off the west coast of North America without apparent connections with ENSO. Here with a hierarchy of climate models, it is demonstrated that extreme ridges in this region are associated with a continuum of zonal wavenumber-5 circumglobal teleconnection patterns that originate from midlatitude atmospheric internal dynamics. Although tropical diabatic heating anomalies are not essential to the formation and maintenance of these wave patterns, certain persistent heating anomalies may double the probability of ridges with amplitudes in the 90th percentile occurring on interannual time scales. Those heating anomalies can be caused by either natural variability or possibly by climate change, and they do not necessarily depend on ENSO. The extreme ridges that occurred during the 2013/14 and 2014/15 winters could be examples of ridges produced by heating anomalies that are not associated with ENSO. This mechanism could provide a source of subseasonal-to-interannual predictability beyond the predictability provided by ENSO.

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Grant Branstator
and
Frank Selten

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.

There are, on the other hand, some subtle indications that an explanation for the similarity involving preferred states (which necessarily result from nonlinear influences) has some relevance. For example, though unimodal, PDFs of prominent patterns have departures from Gaussianity that are suggestive of a mixture of two Gaussian components. And there is some evidence of a shift in probability between the two components as the climate changes. Interestingly, contrary to the most prominent theory of the influence of nonlinearly produced preferred states on climate change, the centroids of the components also change as the climate changes. This modification of the system’s preferred states corresponds to a change in the structure of its dominant patterns. The change in pattern structure is reproduced by the linear stochastic model when its basic state is modified to correspond to the trend in the general circulation model’s mean atmospheric state. Thus, there is a two-way interaction between the trend and the modes of variability.

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