Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics

A Very Large, Spontaneous Stratospheric Sudden Warming in a Simple AGCM: A Prototype for the Southern Hemisphere Warming of 2002?

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

Tropospheric Response to Stratospheric Perturbations in a Relatively Simple General Circulation Model

The sensitivity of the tropospheric extratropical circulation to thermal perturbations of the polar stratosphere is examined in a dry primitive equation general circulation model with zonally symmetric forcing and boundary conditions. For sufficiently strong cooling of the polar winter stratosphere, the winter-hemisphere tropospheric jet shifts polewards and strengthens markedly at the surface; this is accompanied by a drop in surface pressure at high latitudes in the same hemisphere. In addition, this extratropical tropospheric response is found to be very similar to the model's leading pattern of internal variability. These results are tested for robustness at several horizontal and vertical resolutions, and the same tropospheric response is observed at all but the lowest resolution tested. The behavior of this relatively simple model is broadly consistent with recent observational and modeling studies of trends in extratropical atmospheric variability

Stratosphere–Troposphere Coupling in a Relatively Simple AGCM: Impact of the Seasonal Cycle

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

Linear interference and the initiation of extratropical stratosphere-troposphere interactions

Vertical fluxes of wave activity from the troposphere to the stratosphere correlate negatively with the Northern Annular Mode (NAM) index in the stratosphere and subsequently in the troposphere. Recent studies have shown that stratospheric NAM variability is also negatively correlated with the amplitude of the wave pattern coherent with the large-scale climatological stationary wavefield; when the climatological stationary wavefield is amplified or attenuated, the stratospheric jet correspondingly weakens or strengthens. Here we quantify the importance of this linear interference effect in initiating stratosphere-troposphere interactions by performing a decomposition of the vertical wave activity flux using reanalysis data. The interannual variability in vertical wave activity flux in both the Northern and Southern Hemisphere extratropics is dominated by linear interference of quasi-stationary waves during the season of strongest stratosphere-troposphere coupling. Composite analysis of anomalous vertical wave activity flux events reveals the significant role of linear interference and shows that "linear" and "nonlinear" events are essentially independent. Linear interference is the dominant contribution to the vertical wave activity flux anomalies preceding displacement stratospheric sudden warmings (SSWs) while split SSWs are preceded by nonlinear wave activity flux anomalies. Wave activity variability controls the timing of stratospheric final warmings, and this variability is shown to be dominated by linear interference, particularly in the Southern Hemisphere. The persistence of the linear interference component of the vertical wave activity flux, corresponding to persistent constructive or destructive interference between the wave-1 component of climatological stationary wave and the wave anomaly, may help improve wintertime extratropical predictability

The Coupled Stratosphere–Troposphere Response to Impulsive Forcing from the Troposphere

A simple atmospheric general circulation model (GCM) is used to investigate the transient response of the stratosphere–troposphere system to externally imposed pulses of lower-tropospheric planetary wave activity. The atmospheric GCM is a dry, hydrostatic, global primitive-equations model, whose circulation includes an active polar vortex and a tropospheric jet maintained by baroclinic eddies. Planetary wave activity pulses are generated by a perturbation of the solid lower boundary that grow and decay over a period of 10 days. The planetary wave pulses propagate upward and break in the stratosphere. Subsequently, a zonal-mean circulation anomaly propagates downward, often into the troposphere, at lags of 30–100 days. The evolution of the response is found to be dependent on the state of the stratosphere–troposphere system at the time the pulse is generated. In particular, on the basis of a large ensemble of these simulations, it is found that the length of time the signal takes to propagate downward from the stratosphere is controlled by initial anomalies in the zonal-mean circulation and in the zonal-mean wave drag. Criteria based on these anomaly patterns can be used, therefore, to predict the long-term surface response of the stratosphere–troposphere system to a planetary wave pulse up to 90 days after the pulse is generated. In an independent test, it is verified that the initial states that most strongly satisfy these criteria respond in the expected way to the lower-tropospheric wave activity pulse

Limited Influence of Localized Tropical Sea-Surface Temperatures on Moisture Transport into the Arctic

Arctic moisture transport is dominated by planetary-scale waves in reanalysis. Planetary waves are influenced by localized Sea-Surface Temperature (SST) features such as the tropical warm pool. Here, an aquaplanet model is used to clarify the link between tropical SST anomalies and Arctic moisture transport. In a zonally uniform setup with no climatological east-west gradients, Arctic moisture transport is dominated by transient planetary waves, as in reanalysis. Warming tropical SSTs by heating the ocean strengthens Arctic moisture transport, mediated mostly by changes in water vapor rather than eddies. This strengthening occurs whether the tropical warming is zonally uniform or localized. Cooling tropical SSTs weakens Arctic moisture transport; however, unlike warming, the pattern matters, with localized cooling producing stronger transport changes owing to nonlinear feedbacks in the surface energy budget. Thus, the simulations show that localized tropical SST anomalies influence Arctic moisture transport differently than uniform anomalies, but only in cooling scenarios.publishedVersio

Climate‐related variations in mixing dynamics in an Alaskan arctic lake

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109805/1/lno2009546part22401.pd

Experimental and numerical study of fast gas heating and O atom production in a capillary nanosecond discharge

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140420/1/6.2014-1030.pd