Geostrophic vortex dynamics

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1988By generalizing the method of contour dynamics to the quasigeostrophic two layer model, we have proposed and solved a number of fundamental problems in the dynamics of rotating and stratified vorticity fields. A variety of rotating and translating potential vorticity equilibria (V-states) in one and two layers have been obtained, shedding new light on potential vorticity dynamics in the geostrophic context. In particular,the equivalent barotropic model is shown to be a singular limit of the two-layer model for scales large compared to the radius of deformation. The question of coalescence of two vortices in the same layer (merger) and· in different layers (alignment) is studied in detail. Critical initial separation distances for coalescence are numerically established as functions of the radius of deformation and the relative thickness of the layers at rest. The connection between coalescence and the existence of stable rotating doubly-connected V-states is shown to be an illuminating generalization of the Euler results. The question of filamentation of two-dimensional vorticity interfaces is addressed from a new geometrical perspective. The analysis of the topology of the streamfunction in a frame of reference rotating with the instantaneous angular velocity of the vorticity distribution (the corotating frame) is shown to yield new powerful insights on the nonlinear evolution of the vorticity field. In particular, the presence of hyperbolic (critical) points of the corotating streamfunction that come in contact with the vorticity interface is found to be directly responsible for the generation of filaments. The importance ofthe position of the critical points of the comoving streamfunction is found to generalize to the two-layer quasigeostrophic context. They are shown to play the crucial role in determining the limits, in parameter space, on the existence of a number of two-layer rotating and translating potential vorticity equilibria

Double Tropopause Formation in Idealized Baroclinic Life Cycles: The Key Role of an Initial Tropopause Inversion Layer

Recent studies have shown that double tropopauses exist in all seasons, and at all longitudes, in the midlatitudes. As of yet, the key mechanism responsible for their formation is not known. In this study, we explore the connection between double tropopauses and midlatitude baroclinic eddies. This is investigated in the context of idealized life cycle experiments. The key finding of this study is that large areas of double tropopauses form spontaneously at the nonlinear stage of the life cycle evolution, provided an extratropical tropopause inversion layer is present in the balanced initial temperature profile. We also show that the areas covered with double tropopauses grow as the strength of the initial tropopause inversion layer is increased. Without such a layer, as in canonical examples of baroclinic life cycles much studied in the literature, no double tropopause formation occurs. In agreement with observations, double tropopauses in our life cycle experiments form predominantly in areas of cyclonic flow at upper levels. However, the air masses that end up between the two tropopauses are found to originate from high latitudes. This appears to differ from a recently published case study, where the air between double tropopauses was shown to originate partly from low latitudes. Such a discrepancy suggests that more than one pathway may exist to advect air masses between the two tropopauses

Lifetime Dependent Flux into the Lowermost Stratosphere for Idealized Trace Gases of Surface Origin

The flux of idealized trace gases across the thermal tropopause is quantified as a function of their chemical lifetime using the Model of Atmospheric Transport and Chemistry (MATCH) driven by National Centers for Environmental Prediction (NCEP) reanalyses. The flux is computed in the limit of instant stratospheric chemical loss, and tropospheric chemistry is idealized as decay with a constant lifetime, τc. Emissions are idealized as time independent, with either a generic anthropogenic pattern or a uniform ocean source. We find that the globally averaged flux into the stratosphere normalized by surface emissions is ∼1% for τc= 8 days and ∼30% for τc ∼ 140 days, slowly approaching the long-lived limit of balance between stratospheric sinks and surface sources. The qualitative τc dependence of the globally averaged flux is captured by a simple one-dimensional model. The flux patterns computed with MATCH for the NCEP reanalyses are insensitive to τc and reveal preferred pathways into the stratosphere: The divergent circulation feeding isentropic cross-tropopause transport, storm tracks in the winter hemisphere, and isentropic transport to high latitudes

Chaotic Lagrangian Trajectories around an Elliptical Vortex Patch Embedded in a Constant and Uniform Background Shear Flow

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 5 0, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed

Contrasting short and long term projections of the hydrological cycle in the Southern extratropics

Analysis of model output from phase 5 of the Coupled Model Intercomparison Project (CMIP5) reveals that, in the zonal mean, the near-term projections of summertime changes of precipitation in the Southern Hemisphere (SH) subtropics are very widely scattered among the models. As a consequence, over the next 50 years, the CMIP5 multimodel mean projects no statistically significant trends in the SH subtropics in summer. This appears to be at odds with the widely reported, and robust, poleward expansion of the subtropical dry zones by the end of the twenty-first century. This discrepancy between the shorter- and longer-term projections in SH summer, as shown here, rests in the recovery of the ozone hole in the coming decades, as a consequence of the Montreal Protocol. This is explicitly demonstrated by analyzing model experiments with the Whole Atmosphere Community Climate Model, version 4 (WACCM4), a high-top model with interactive stratospheric chemistry, and coupled to land, ocean, and sea ice components. Contrasting WACCM4 integrations of the representative concentration pathway 4.5 with and without trends in surface concentrations of ozone-depleting substances allows for demonstrating that stratospheric ozone recovery will largely offset the induced “wet gets wetter and dry gets drier” projections and the accompanying poleward expansion of the subtropical dry zone in the SH. The lack of near-term statistically significant zonal-mean changes in the SH hydrological cycle during summer is of obvious practical importance for many parts of the world, and it might also have implications for the Southern Ocean and the Antarctic continent

Contrasting short and long term projections of the hydrological cycle in the Southern extratropics

Analysis of model output from phase 5 of the Coupled Model Intercomparison Project (CMIP5) reveals that, in the zonal mean, the near-term projections of summertime changes of precipitation in the Southern Hemisphere (SH) subtropics are very widely scattered among the models. As a consequence, over the next 50 years, the CMIP5 multimodel mean projects no statistically significant trends in the SH subtropics in summer. This appears to be at odds with the widely reported, and robust, poleward expansion of the subtropical dry zones by the end of the twenty-first century. This discrepancy between the shorter- and longer-term projections in SH summer, as shown here, rests in the recovery of the ozone hole in the coming decades, as a consequence of the Montreal Protocol. This is explicitly demonstrated by analyzing model experiments with the Whole Atmosphere Community Climate Model, version 4 (WACCM4), a high-top model with interactive stratospheric chemistry, and coupled to land, ocean, and sea ice components. Contrasting WACCM4 integrations of the representative concentration pathway 4.5 with and without trends in surface concentrations of ozone-depleting substances allows for demonstrating that stratospheric ozone recovery will largely offset the induced “wet gets wetter and dry gets drier” projections and the accompanying poleward expansion of the subtropical dry zone in the SH. The lack of near-term statistically significant zonal-mean changes in the SH hydrological cycle during summer is of obvious practical importance for many parts of the world, and it might also have implications for the Southern Ocean and the Antarctic continent

Anthropogenic impact on Antarctic surface mass balance, currently masked by natural variability, to emerge by mid-century

Global and regional climate models robustly simulate increases in Antarctic surface mass balance (SMB) during the twentieth and twenty-first centuries in response to anthropogenic global warming. Despite these robust model projections, however, observations indicate that there has been no significant change in Antarctic SMB in recent decades. We show that this apparent discrepancy between models and observations can be explained by the fact that the anthropogenic climate change signal during the second half of the twentieth century is small compared to the noise associated with natural climate variability. Using an ensemble of 35 global coupled climate models to separate signal and noise, we find that the forced SMB increase due to global warming in recent decades is unlikely to be detectable as a result of large natural SMB variability. However, our analysis reveals that the anthropogenic impact on Antarctic SMB is very likely to emerge from natural variability by the middle of the current century, thus mitigating future increases in global sea level

Chaotic Lagrangian Trajectories around an Elliptical Vortex Patch Embedded in a Constant and Uniform Background Shear Flow

The Lagrangian flow around a Kida vortex [J. Phys. Soc. Jpn. 5 0, 3517 (1981)], an elliptical two‐dimensional vortex patch embedded in a uniform and constant background shear, is described by a nonintegrable two‐degree‐of‐freedom Hamiltonian. For small values of shear, there exist large chaotic zones surrounding the vortex, often much larger than the vortex itself and extremely close to its boundary. Motion within the vortex is integrable. Implications for two‐dimensional turbulence are discussed

The Three-Dimensional Structure of Breaking Rossby Waves in the Polar Wintertime Stratosphere

The three-dimensional nature of breaking Rossby waves in the polar wintertime stratosphere is studied using an idealized global primitive equation model. The model is initialized with a well-formed polar vortex, characterized by a latitudinal band of steep potential vorticity (PV) gradients. Planetary-scale Rossby waves are generated by varying the topography of the bottom boundary, corresponding to undulations of the tropopause. Such topographically forced Rossby waves then propagate up the edge of the vortex, and their amplification with height leads to irreversible wave breaking. These numerical experiments highlight several nonlinear aspects of stratospheric dynamics that are beyond the reach of both isentropic two-dimensional models and fully realistic GCM simulations. They also show that the polar vortex is contorted by the breaking Rossby waves in a surprisingly wide range of shapes. With zonal wavenumber-1 forcing, wave breaking usually initiates as a deep helical tongue of PV that is extruded from the polar vortex. This tongue is often observed to roll up into deep isolated columns, which, in turn, may be stretched and tilted by horizontal and vertical shears. The wave amplitude directly controls the depth of the wave breaking region and the amount of vortex erosion. At large forcing amplitudes, the wave breaking in the middle/lower portions of the vortex destroys the PV gradients essential for vertical propagation, thus shielding the top of the vortex from further wave breaking. The initial vertical structure of the polar vortex is shown to play an important role in determining the characteristics of the wave breaking. Perhaps surprisingly, initially steeper PV gradients allow for stronger vertical wave propagation and thus lead to stronger erosion. Vertical wind shear has the notable effect of tilting and stretching PV structures, and thus dramatically accelerating the downscale stirring. An initial decrease in vortex area with increasing height (i.e., a conical shape) leads to focusing of wave activity, which amplifies the wave breaking. This effect provides a geometric interpretation of the “preconditioning” that often precedes a stratospheric sudden warming event. The implications for stratospheric dynamics of these and other three-dimensional vortex properties are discussed

Comment on “Tropospheric Temperature Response to Stratospheric Ozone Recovery in the 21st Century” by Hu et al. (2011)

Stratospheric ozone recovery is expected to figure prominently in twenty-first century climate change. In a recent paper, Hu et al. (2011) argue that one impact of ozone recovery will be to enhance the warming of the surface-troposphere system produced by increases in well-mixed greenhouse gases. Furthermore, this enhanced warming would be strongest in the Northern Hemisphere, which is surprising since previous studies have consistently shown the effects of stratospheric ozone changes to be most pronounced in the Southern Hemisphere. Hu et al. (2011) base their claims largely on differences in the simulated temperature change between two groups of CMIP3 (Coupled Model Intercomparison Project 3) climate models, one group which included stratospheric ozone recovery in its twenty-first century simulations and a second group which did not. Both groups of models were forced with the same increases in well-mixed greenhouse gases according to the A1B emissions scenario. In the current work, we compare the surface temperature responses of the same two groups of models in a different experiment in which atmospheric CO2 was increased by 1% per year until doubling. We find remarkably similar differences in the simulated surface temperature change between the two sets of models as Hu et al. (2011) found for the A1B experiment, suggesting that the enhanced warming which they attribute to stratospheric ozone recovery is actually a reflection of different responses of the two model groups to greenhouse gas forcing