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Lei Wang
and
Paul J. Kushner

Abstract

Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the zonally asymmetric atmospheric general circulation. However, the dynamics of stationary wave nonlinearity, which is often calculated explicitly in stationary wave models, is not well understood. Stationary wave nonlinearity is examined here in the simplified setting of the response to localized topographic forcing in quasigeostrophic barotropic dynamics in the presence and absence of transient eddies. It is shown that stationary wave nonlinearity accounts for most of the difference between the linear and full nonlinear response, particularly if the adjustment of the zonal-mean flow to the stationary waves is taken into account. The separate impact of transient eddy forcing is also quantified. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A nonlinear stationary wave model, similar to those used in baroclinic stationary wave model studies, is also tested and is shown to capture the basic features of the full nonlinear stationary wave solution.

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Paul J. Kushner
and
Lorenzo M. Polvani

Abstract

An exceptionally strong stratospheric sudden warming (SSW) that spontaneously occurs in a very simple stratosphere–troposphere AGCM is discussed. The model is a dry, hydrostatic, primitive equation model without planetary stationary waves. Transient baroclinic wave–wave interaction in the troposphere thus provides the only source of upward-propagating wave activity into the stratosphere. The model’s SSW is grossly similar to the Southern Hemisphere major SSW of 2002: it occurs after weaker warmings “precondition” the polar vortex for breaking, it involves a split of the polar vortex, and it has a downward-propagating signature. These similarities suggest that the Southern Hemisphere SSW of 2002 might itself have been caused by transient baroclinic wave–wave interaction. The simple model used for this study also provides some insight into how often such extreme events might occur. The frequency distribution of SSWs in the model has exponential, as opposed to Gaussian, tails. This suggests that very large amplitude SSWs, though rare, might occur with higher frequency than might be naively expected.

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Paul J. Kushner
and
Isaac M. Held

Abstract

The use of eddy flux of thickness between density surfaces has become a familiar starting point in oceanographic studies of adiabatic eddy effects on the mean density distribution. In this study, a dynamical analogy with the density thickness flux approach is explored to reexamine the theory of nonzonal wave–mean flow interaction in two-dimensional horizontal flows. By analogy with the density thickness flux, the flux of thickness between potential vorticity (PV) surfaces is used as a starting point for a residual circulation formulation for nonzonal mean flows. Mean equations for barotropic PV dynamics are derived in which a modified mean velocity with an eddy-induced component advects a modified mean PV that also has an eddy-induced component. For small-amplitude eddies, the results are analogous to recent results of McDougall and McIntosh derived for stratified flow.

The dynamical implications of this approach are then examined. The modified mean PV equation provides a decomposition of the eddy forcing of the mean flow into contributions from wave transience, wave dissipation, and wave-induced mass redistribution between PV contours. If the mean flow is along the mean PV contours, the contribution from wave-induced mass redistribution is “workless” in Plumb’s sense that it is equivalent to an eddy-induced stress that is perpendicular to the mean flow. This contribution is also associated with the convergence along the mean streamlines of a modified PV flux that is equal to the difference between the PV flux and the rotational PV flux term identified by Illari and Marshall. The cross-stream component of the modified PV flux is related to wave transience and dissipation.

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Paul J. Kushner
and
Gabriel Lee

Abstract

A sector EOF analysis applied to the extratropical tropospheric circulation extracts robust circulation patterns that represent the regional signature of the annular modes. These regional patterns are eastward-propagating, long baroclinic wave structures with the dipolar meridional structure in the streamflow of the annular modes. The regional dipole patterns are also connected to the annular modes through their temporal correlation and their eddy flux signatures. These results serve to relate the hemispheric and the regional perspectives on the annular modes.

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Paul J. Kushner
and
Lorenzo M. Polvani

Abstract

The seasonal time dependence of the tropospheric circulation response to polar stratospheric cooling in a simple atmospheric general circulation model is investigated. When the model is run without a seasonal cycle, polar stratospheric cooling induces a positive annular-mode response in the troposphere that takes a remarkably long time—several hundred days—to fully equilibrate. One is thus led to ask whether the tropospheric response would survive in the presence of a seasonal cycle. When a seasonal cycle is introduced into the model stratosphere, the tropospheric response appears with a distinct time lag with respect to the stratospheric cooling, but, in the long-term mean, the pattern of the wind response is very similar to the one that results from stratospheric forcing in the absence of a seasonal cycle.

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Dmitry I. Vyushin
and
Paul J. Kushner

Abstract

The question of which statistical model best describes internal climate variability on interannual and longer time scales is essential to the ability to predict such variables and detect periodicities and trends in them. For over 30 yr the dominant model for background climate variability has been the autoregressive model of the first order (AR1). However, recent research has shown that some aspects of climate variability are best described by a “long memory” or “power-law” model. Such a model fits a temporal spectrum to a single power-law function, which thereby accumulates more power at lower frequencies than an AR1 fit. In this study, several power-law model estimators are applied to global temperature data from reanalysis products. The methods employed (the detrended fluctuation analysis, Geweke–Porter-Hudak estimator, Gaussian semiparametric estimator, and multitapered versions of the last two) agree well for pure power-law stochastic processes. However, for the observed temperature record, the power-law fits are sensitive to the choice of frequency range and the intrinsic filtering properties of the methods. The observational results converge once frequency ranges are made consistent and the lowest frequencies are included, and once several climate signals have been filtered. Two robust results emerge from the analysis: first, that the tropical circulation features relatively large power-law exponents that connect to the zonal-mean extratropical circulation; and second, that the subtropical lower stratosphere exhibits power-law behavior that is volcanically forced.

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Russell Blackport
and
Paul J. Kushner

Abstract

In this study, coupled ocean–atmosphere–land–sea ice Earth system model (ESM) simulations driven separately by sea ice albedo reduction and by projected greenhouse-dominated radiative forcing are combined to cleanly isolate the sea ice loss response of the atmospheric circulation. A pattern scaling approach is proposed in which the local multidecadal mean atmospheric response is assumed to be separately proportional to the total sea ice loss and to the total low-latitude ocean surface warming. The proposed approach estimates the response to Arctic sea ice loss with low-latitude ocean temperatures fixed and vice versa. The sea ice response includes a high northern latitude easterly zonal wind response, an equatorward shift of the eddy-driven jet, a weakening of the stratospheric polar vortex, an anticyclonic sea level pressure anomaly over coastal Eurasia, a cyclonic sea level pressure anomaly over the North Pacific, and increased wintertime precipitation over the west coast of North America. Many of these responses are opposed by the response to low-latitude surface warming with sea ice fixed. However, both sea ice loss and low-latitude surface warming act in concert to reduce subseasonal temperature variability throughout the middle and high latitudes. The responses are similar in two related versions of the National Center for Atmospheric Research Earth system models, apart from the stratospheric polar vortex response. Evidence is presented that internal variability can easily contaminate the estimates if not enough independent climate states are used to construct them.

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Oliver Watt-Meyer
and
Paul J. Kushner

Abstract

The distribution of temperatures in the wintertime polar stratosphere is significantly positively skewed, which has important implications for the characteristics of ozone chemistry and stratosphere–troposphere coupling. The typical argument for why the temperature distribution is skewed is that radiative balance sets a firm lower limit, while planetary wave driving can force much larger positive anomalies in temperature. However, the distribution of the upward Eliassen–Palm (EP) flux is also positively skewed, and this suggests that dynamics may play an important role in setting the skewness of the temperature distribution. This study explains the skewness of the upward EP flux distribution by appealing to the ideas of linear interference. In this framework, fluxes are decomposed into a linear term (LIN) that measures the coherence of the wave anomaly and the climatological wave and an additional nonlinear term (NONLIN) that depends only on the wave anomaly. It is shown that when filtered by wavenumber, there is a clear nonlinear dependence between LIN and NONLIN: the terms cancel when LIN is negative, but they reinforce each other when LIN is positive. This leads to the positive skewness of the upward wave activity flux. A toy model of wave interference is constructed, and it is shown that the westward vertical tilt of the climatological wave is the key ingredient to a positively skewed upward EP flux distribution. The causes of the skews of the LIN and NONLIN distributions themselves are shown to be related to relationships between wave phase and amplitude, and wave phase and vertical tilt, respectively.

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Stephanie Hay
and
Paul J. Kushner

Abstract

The response to Antarctic sea-ice loss within a coupled modelling framework is examined in comparison to the response to Arctic sea-ice loss and within the context of general greenhouse warming. Sea-ice loss responses are found to be linear (particularly in response to Antarctic or global sea-ice loss) with respect to the degree of imposed perturbation and additive when perturbations are applied in hemispheres separately and concurrently. Globally, and in the tropical Pacific in particular, Antarctic sea-ice loss plays a relatively larger role than Arctic sea-ice loss in both the atmosphere and the ocean, within the parameters of our experiments. The pattern of response to Antarctic sea-ice loss is also found to more closely resemble that of greenhouse warming, again particularly in the tropics. An extension to multi-parameter pattern scaling is developed to include a scaling factor for Antarctic change in addition to those for tropical warming and Arctic sea-ice loss. The decomposition is applied to the modelled response to Antarctic sea-ice loss to break it down into component partial responses that scale with Antarctic, tropical, and Arctic changes. This reveals the aspects of the response that are directly related to Antarctic change, such as an equatorward intensification of tropical precipitation in the Northern Hemisphere, and those that are modified via the induced changes in the tropics and Arctic, such as Northern Hemisphere temperature change. With this, we hope to gain a deeper understanding of the role of each of these changes for the development of physical mechanisms of the response.

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Oliver Watt-Meyer
and
Paul J. Kushner

Abstract

Northern Hemisphere stratospheric polar vortex strength variability is known to be largely driven by persistent anomalies in upward wave activity flux. It has also been shown that attenuation and amplification of the stationary wave is the primary way in which wave activity flux varies. This study determines the structure of the wave anomalies that interfere with the climatological wave and drive this variability. Using a recently developed spectral decomposition it is shown that fixed-node standing waves are the primary drivers of the “linear interference” phenomenon. This is particularly true for the low-frequency component of the upward wave activity flux. The linear part of the flux is shown to be more persistent than the total flux and has significant tropospheric standing wave precursors that lead changes in the strength of the stratospheric polar vortex. Evidence is presented that current-generation high-top climate models are able to credibly simulate this variability in wave activity fluxes and the connection to polar vortex strength. Finally, the precursors to displacement and split sudden stratospheric warmings are examined. Displacement events are found to be preceded by about 25 days of anomalously high upward wave activity flux forced by standing waves amplifying the climatology. Split events have more short-lived wave activity flux precursors, which are dominated by the nonlinear part of the flux.

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