Martin Juckes

Quasigeostrophic Dynamics of the Tropopause

Abstract The dynamical properties of potential temperature anomalies on the tropopause are analyzed for quasigeo-strophic flow on an f plane. The potential vorticity is taken to he piecewise constant, with a single discontinuity at the tropopause. The tropopause potential temperature, on scales too small to feel the lower boundary, is found to be proportional to the tropopause geopotential height. The constant of proportionality is the geometric mean of the stratospheric and tropospheric lapse rates. Results from a general circulation model are found to be in agreement with this prediction. The streamfunction associated with a combination of anomalies on the lower boundary and tropopause is also derived. The solution, determined completely by the potential temperature distributions, in general has a nonzero velocity at the lower boundary. Applying the theory to the time-mean zonal-mean jets, which must have a near-zero velocity at the ground, imposes a constraint on parameters defining the jet. The dynami...

The Static Stability of the Midlatitude Troposphere: The Relevance of Moisture

It is generally accepted that the action of baroclinic waves in midlatitude is responsible for raising the static stability of the troposphere above moist neutrality. Previous efforts to quantify this process have concentrated on the stability criteria for normal-mode baroclinic instability. The suggestion presented here is based on the observation that moist convection also plays a significant role in the latter stages of baroclinic disturbances. It is suggested that the minimum stability in midlatitudes is moist neutral, and further that the mean tropopause potential temperature can be estimated as the minimum, that is, moist neutral, plus half the variance. The variance is created by quasi-adiabatic meridional advection of the meridional gradient, so that the final prediction is that the change in saturated equivalent potential temperature between the surface and tropopause should be proportional to the meridional temperature change across the storm tracks. This is found to be in reasonable agreement with the Northern Hemisphere annual cycle in a 16-year climatology. The annual cycle in the Southern Hemisphere, on the other hand, does not fall into the same pattern.

A Shallow Water Model of the Winter Stratosphere

Abstract The shallow water equations are used to investigate the interaction of planetary wave-breaking with a “diabatic” forcing. The numerical integrations demonstrate the formation of a sharp gradient in potential vorticity at the edge of the polar vortex, despite “diabatic relaxation” towards a smooth gradient. Successive cycles of Rossby wave-breaking accentuate the distinction between the vortex and the surf-zone. Persistent easterly acceleration in the tropics eventually produces a flow regime of little relevance to the atmosphere. For the period when the flow has some qualitative resemblance to the middle stratosphere diffusion coefficients are calculated from the meridional fluxes of potential vorticity and of passive tracers. It is found that the unique dynamical nature of potential vorticity among tracers is not reflected in its diffusion coefficient.

Instability of Surface and Upper-Tropospheric Shear Lines

Abstract An analytic linear stability analysis is carried out for a shear line associated with a surface temperature anomaly in uniform potential vorticity, quasigeostrophic flow. Previous studies of this type of flow, albeit with more realistic basic states, have relied on numerical solution. The instability can be interpreted as the result of the interaction of counterpropagating edge waves on the two opposing potential temperature gradients that bound the shear line. The analytic normal mode analysis can easily be extended to investigate nonmodal disturbances. The disturbances defined by maximizing the growth of selected norms over the norms over the normal mode e-folding time generally show similar growth rates to the normal modes. There is weaker scale selectivity and a shift to longer wave-lengths. The enstrophy norm provides an exception to this behavior. This norm is sensitive to small-scale structures and can grow much faster than the large-scale disturbance. Nonlinear integrations show the insta...

Signatures of Induced Vertical Air Motion Accompanying Quasi-Horizontal Roll-Up of Stratospheric Intrusions

The quasi-horizontal roll-up of unstable stratospheric intrusions into isolated vortices is known to result in specific structures on satellite water vapor images that are characterized by intermingling dark and light filaments. The current paper investigates how these features are generated and how they relate to partly similar features found on concurrent maps of the tropopause height or potential vorticity (PV). The roll-up of a stratospheric intrusion is simulated numerically with an idealized quasigeostrophic model, which focuses on the dynamics induced by anomalies in the height of the tropopause. The upper-tropospheric adiabatic vertical wind is calculated explicitly and is used to simulate water vapor images in the model. These images show qualitatively the same characteristic features as observed. They are generated through a combination of horizontal advection of initial moisture anomalies and the creation of additional moisture anomalies resulting from the upper-tropospheric vertical air motion. The latter is, in turn, induced by the quasi-horizontal motion of the tropopause anomaly. It is suggested that a substantial portion of the spiral-like structures on the water vapor images is likely to reflect the vertical wind induced by the evolution of the intrusion itself. When the tropopause is defined through a fairly low value of PV, it may acquire similar spiraling structures, as it is being advected almost like a passive tracer. On the other hand, for the dynamically active core part of the intrusion, which is located at higher values of PV, one may expect an evolution leading to more compact vortex cores and less structure overall.

The Structure of Idealized Upper-Tropospheric Shear Lines

Abstract The structure of idealized two-dimensional shear lines has been calculated for specified tropopause potential temperature anomalies. A cold anomaly corresponds to an intrusion of stratospheric air into the troposphere. A balanced hydrostatic primitive equation structure is derived using an iterative technique. The resulting wind and vertical displacement of the tropopause are compared with a recent result extending quasigeostrophic theory to situations where the variation of potential vorticity along an isentrope or isobar is large, as is the case, for instance, when the isosurface intersects the tropopause. The formulation of the theory is clarified by analyzing the relation between quasigeostrophic potential vorticity and Ertel’s potential vorticity. The comparison between the low–Rossby number theoretical approximation and primitive equation structures confirms the theoretical prediction that the relative error is proportional to the Rossby number. The constant of proportionality is close to u...

The Resonant Interaction of a Tropical Cyclone and a Tropopause Front in a Barotropic Model - Part II: Frontal Waves

Abstract The influence of frontal waves on the interaction of a tropical cyclone and a tropopause front is investigated in an idealized framework. In a nondivergent barotropic model the front is represented by a vorticity step with a superimposed sinusoidal perturbation. This gives rise to a jet that meanders to the north and south and can be viewed as a sequence of upper-level troughs and ridges. The model evolution depends sensitively on the position of the cyclone relative to the troughs and ridges. Here a bifurcation point is identified that is located on the trough axis at a distance where the zonal speed of the background flow equals the phase speed of the wave. Arbitrarily small displacements from this position determine whether a cyclone is advected toward the front or repelled. Only a limited range of wavelengths can lead to track bifurcations. The largest effects are obtained for resonant frontal waves propagating with a phase speed matching the initial zonal translation speed of the cyclone. We...

The Resonant Interaction of a Tropical Cyclone and a Tropopause Front in a Barotropic Model. Part I: Zonally Oriented Front

Abstract The interaction of a tropical cyclone and a zonally aligned tropopause front is investigated in an idealized framework. A nondivergent barotropic model is used in which the front is represented by a vorticity step, giving a jetlike velocity profile. The excitation of frontal waves by a cyclone located south of the front and the impact of the wave flow on the cyclone motion is studied for different representations of the cyclone and the jet. The evolution from the initial wave excitation until after the cyclone has crossed the front is discussed. The interaction becomes stronger with increasing jet speed. For cyclone representations containing negative relative vorticity, anticyclones develop and can influence the excitation of frontal waves significantly. Resonant frontal waves propagating with a phase speed matching the zonal translation speed of the cyclone are decisive for the interaction. The frontal wave spectrum excited by a cyclone on the front is dominated by waves that are in resonance i...

Evaluation of MIPAS ozone fields assimilated using a new algorithm constrained by isentropic tracer advection

A new data assimilation algorithm, using the isen- tropic advection equation, is applied to MIPAS and SBUV measurements of stratospheric ozone. The system is solved separately on each isentropic level, with neither vertical ad- vection nor chemical reactions represented. The results are validated against HALOE, POAM III, SAGE II & III, OSIRIS and ozone sonde data. The new assimilation algo- rithm has the accuracy of the Kalman smoother but is, for the systems studied here with up to 200 000 variables per time step and 61 million control variables in total, many or- ders of magnitude less computationally expensive. The anal- ysis produced minimises a single penalty function evaluated over an analysis window of over one month. The cost of the analysis is found to increase nearly linearly with the num- ber of control variables. Compared with over 800 profiles from Electrochemical Concentration Cell sondes at 29 sites the analysis is found to be merely 0.1% high at 420 K, ris- ing to 0.4% at 650 K. Comparison against the other satel- lites imply that the bias remains small up to 1250 K (38 km) and then increases to around -10% at 1650 K (44 km). Be- tween 20 and 35 km the root-mean-square difference relative to HALOE, SAGE II & III, and POAM is in the 5 to 10% range, with larger discrepancies relative to other instruments. Outside this height range rms differences are generally larger, though agreement with HALOE remains good up to 50 km. The assimilation has closer agreement to independent obser- vations than found in direct near-neighbour comparisons be- tween profiles, demonstrating that the assimilation can add value to the observations.

An algorithm for retrieving atmospheric motion from satellite measurements of tracer behavior

An algorithm is developed for determining three-dimensional atmospheric motion from global measurements of tracer behavior. The latter constitute observations of the material field, which underlies essential dynamical budgets that govern the circulation. Because it treats the material behavior as an observable, the algorithm provides a more direct means of determining atmospheric motion from space than the traditional scheme, in which material behavior must be derived from remote measurements of temperature. Incorporating observations of an ensemble of tracers (e.g., from multiple instruments or multiple orbiting platforms) leads to a variational problem for the Lagrangian displacement field, the solution of which determines the global distribution of air motion. The algorithms direct relationship to material behavior circumvents well-known limitations of the traditional scheme for inferring atmospheric motion from space. Further, since it is based on kinematic constraints that follow directly from observables, the retrieved motion is not artificially biased towards approximate forms of the governing equations and uncertainties accompanying them, e.g., as are inherent in assimilations based on numerical models. For this reason, motion in the tropics is determined as reliably as elsewhere on the globe. Calculations under realistic conditions illustrate that the accuracy of the retrieved motion is limited chiefly by the number and quality of tracer observations. Those calculations also demonstrate that the accuracy can be improved dramatically by increasing the number of orbiting platforms from which tracer measurements are provided.