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Volkmar Wirth

Abstract

This paper investigates stationary axisymmetric balanced flow of a stably stratified dry non-Boussinesq atmosphere on the f plane. The circulation is forced in the troposphere through thermal relaxation toward a specified equilibrium temperature and is damped through Rayleigh friction in the interior of the domain. Surface friction is sufficiently strong to ensure weak surface winds. As in the analogous zonally symmetric problem studied by Plumb and Hou there is threshold behavior in the frictionless limit with a thermal equilibrium solution for subcritical forcing and a highly nonlinear so-called angular momentum conserving (AMC) solution for supercritical forcing. The latter is characterized by a sharp outward edge of the vortex circulation and a nonvanishing secondary cross-vortex circulation. In the frictionless limit, the secondary circulation does not reach above the region of the thermal forcing. Noticeable differences of the current problem with respect to the zonally symmetric problem arise from the strong nonlinearity of the thermal wind equation and the nonzero thermal forcing right on the axis of symmetry. For the highly nonlinear AMC solution an approximate analytical theory is presented and verified by use of a numerical Eliassen balanced vortex model. This model is also used to investigate the nonlinear dependence of the secondary circulation on the Rayleigh friction coefficient and the penetration of the secondary circulation above the tropopause. An analytic Green’s function solution for the linearized problem gives insight into nonlinear asymptotic dependences. Thinking in terms of an Eliassen balanced vortex model offers a new view on the secondary circulation in the AMC regime.

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Volkmar Wirth

Abstract

Idealized axisymmetric anomalies of potential vorticity (PV) on a midlatitude f plane and their related response in terms of balanced wind and temperature are investigated with special focus on the static stability in the tropopause region. The PV anomalies are specified such that they can be interpreted as the result of conservative advection in the tropopause region across the gradients of a prescribed background atmosphere with piecewise constant buoyancy frequency squared N 2. Related cyclones and anticyclones are treated identically except for the sign of the tropopause potential temperature anomaly. Composite profiles of N 2 are computed, for which the thermal tropopause is used as a common reference level and where the number of cyclones in the composite equals the number of anticyclones. One obtains a pronounced peak of N 2 just above the tropopause and slightly enhanced values below the tropopause in comparison with the background profile. Within the framework of PV inversion various mechanisms are identified. Important contributions to the peak in N 2 are due to the pronounced cyclone–anticyclone asymmetry in the vertical structure of the tangential wind, and to the poleward advection of high values of PV from the subtropical lower stratosphere. Qualitatively, the key features of the composite profiles are in good agreement with observations above southern Germany that have recently been compiled.

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Volkmar Wirth

Abstract

The differences between upper-tropospheric cyclones and anticyclones are investigated regarding the height of the thermal and the dynamical tropopause. The problem is addressed in an idealized framework by analyzing axisymmetric balanced flows, which are characterized by a radial scale ΔR and a tropopause potential temperature anomaly Δθ, where cyclones and anticyclones differ only by the sign of Δθ. The height of the thermal tropopause significantly differs from the height of the dynamical tropopause unless the anomaly is shallow. There is a pronounced asymmetry in that the differences are much larger and more likely to occur in the case of cyclones. Two factors contribute to this asymmetry. First, for a given amplitude |Δθ|, cyclones and anticyclones have different aspect ratios in geometric space; second, for a high-latitude winter scenario the critical lapse rate of the WMO thermal tropopause is asymmetric with respect to typical tropospheric and stratospheric lapse rates. Simulated station statistics regarding the height of the two tropopauses share essential qualitative features with similar statistics from observations. The asymmetry in the model sensitively depends on the lower-stratospheric lapse rate. Multiple tropopauses may greatly enhance the asymmetry.

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Matthias Voigt
and
Volkmar Wirth

Abstract

Banner clouds are clouds in the lee of steep mountains or sharp ridges. Their formation has previously been hypothesized as due to three different mechanisms: (i) vertical uplift in a lee vortex (which has a horizontal axis), (ii) adiabatic expansion along quasi-horizontal trajectories (the so-called Bernoulli effect), and (iii) a mixing cloud (i.e., condensation through mixing of two unsaturated air masses).

In the present work, these hypotheses are tested and quantitatively evaluated against each other by means of large-eddy simulation. The model setup is chosen such as to represent idealized but prototypical conditions for banner cloud formation. In this setup the lee-vortex mechanism is clearly the dominant mechanism for banner cloud formation. An essential aspect is the pronounced windward–leeward asymmetry in the Lagrangian vertical uplift with a plume of large positive values in the immediate lee of the mountain; this allows the region in the lee to tap moister air from closer to the surface. By comparison, the horizontal pressure perturbation is more than two orders of magnitude smaller than the pressure drop along a trajectory in the rising branch of the lee vortex; the “Bernoulli mechanism” is, therefore, very unlikely to be a primary mechanism. Banner clouds are unlikely to be “mixing clouds” in the strict sense of their definition. However, turbulent mixing may lead to small but nonnegligible moistening of parcels along time-mean trajectories; although not of primary importance, the latter may be considered as a modifying factor to existing banner clouds.

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Christian Hauck
and
Volkmar Wirth

Abstract

In the past, linear quasigeostrophic theory has proven successful in modeling the vertical and meridional propagation of stationary planetary waves in the stratosphere. Since in such models the wave solution does not sensitively depend on the wave damping, the latter was usually implemented as relaxation with a simple damping coefficient. As far as the damping is concerned, this is likely to be unrealistic, since it does not account for the locally enhanced dissipation arising from stratospheric Rossby wave breaking. In the present study, a parameterization for Rossby wave breaking (Garcia) is applied to obtain an improved representation of wave damping throughout the stratosphere. Although solving for the wave turns into a nonlinear problem, the model remains linear in the sense that both the basic-state zonal wind and the wave at the tropopause level are specified and kept fixed. The divergence of the Eliassen–Palm flux and the steady-state residual circulation are computed in order to diagnose the impact of the waves on the mean flow. Both quantities depend sensitively and in a complex manner on the given basic-state zonal flow. The model is applied to different scenarios representing the different phases of an idealized quasi-biennial oscillation (QBO). The dependence of the wave forcing on the phase of the QBO is consistent with results from previous studies. The current model allows a clear attribution of differences in wave–mean-flow interaction to differences in the basic flow.

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Sebastian Schappert
and
Volkmar Wirth

Abstract

Banner clouds are clouds in the lee of steep mountains or sharp ridges. Previous work suggests that the main formation mechanism is vertical uplift in the lee of the mountain. On the other hand, little is known about the Lagrangian behavior of air parcels as they pass the mountain, which motivates the current investigation. Three different diagnostics are applied in the framework of large-eddy simulations of airflow past an isolated pyramid-shaped obstacle: Eulerian tracers indicating the initial positions of the parcels, streamlines along the time-averaged wind field, and online trajectories computed from the instantaneous wind field.

All three methods diagnose a plume of large vertical uplift in the immediate lee of the mountain. According to the time-mean Eulerian tracers, the cloudy parcels originated within a fairly small coherent area at the inflow boundary. In contrast, the time-mean streamlines indicate a bifurcation into two distinct classes of air parcels with very different characteristics. The parcels in the first class originate at intermediate altitudes, pass the obstacle close to its summit, and proceed directly into the cloud. By contrast, the parcels in the second class start at low altitude and take a fairly long time before they reach the cloud on a spiraling path. A humidity tracer quantifies mixing, revealing partial moistening for the first class of parcels and drying for the second class of parcels. For the online trajectories, the originating location of parcels is more scattered, but the results are still consistent with the basic features revealed by the other two diagnostics.

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Isabelle Prestel
and
Volkmar Wirth

Abstract

Banner clouds are clouds that are attached to the leeward slope of a steep mountain. Their formation is essentially due to strong Lagrangian uplift of air in the lee of the mountain. However, little is known about the flow regime in which banner clouds can be expected to occur. The present study addresses this question through numerical simulations of flow past idealized orography. Systematic sets of simulations are carried out exploring the parameter space spanned by two dimensionless numbers, which represent the aspect ratio of the mountain and the stratification of the flow. The simulations include both two-dimensional flow past two-dimensional orography and three-dimensional flow past three-dimensional orography.

Regarding flow separation from the surface, both the two- and the three-dimensional simulations show the characteristic regime behavior that has previously been found in laboratory experiments for two-dimensional orography. Flow separation is observed in two of the three regimes, namely in the “leeside separation regime,” which occurs preferably for steep mountains in weakly stratified flow, and in the “postwave separation regime,” which requires increased stratification. The physical mechanism for the former is boundary layer friction, while the latter may also occur for inviscid flow. However, flow separation is only a necessary, not sufficient condition for banner cloud formation. The vertical uplift and its leeward–windward asymmetry show that banner clouds cannot form in the two-dimensional simulations. In addition, even in the three-dimensional simulations they can only be expected in a small part of the parameter space corresponding to steep three-dimensional orography in weakly stratified flow.

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Christopher Polster
and
Volkmar Wirth

Abstract

Recently, Nakamura and Huang proposed a theory of blocking onset based on the budget of finite-amplitude local wave activity on the midlatitude waveguide. Blocks form in their idealized model due to a mechanism that also describes the emergence of traffic jams in traffic theory. The current work investigates the development of a winter European block in terms of finite-amplitude local wave activity to evaluate the possible relevance of the “traffic jam” mechanism for the flow transition. Two hundred members of a medium-range ensemble forecast of the blocking onset period are analyzed with correlation- and cluster-based sensitivity techniques. Diagnostic evidence points to a traffic jam onset on 17 December 2016. Block development is sensitive to upstream Rossby wave activity up to 1.5 days prior to its initiation and consistent with expectations from the idealized theory. Eastward transport of finite-amplitude local wave activity in the southern part of the block is suppressed by nonlinear flux modification from the large-amplitude blocking pattern, consistent with the expected obstruction in the traffic jam model. The relationship of finite-amplitude local wave activity and its zonal flux as mapped by the ensemble exhibits established characteristics of a traffic jam. This study suggests that the traffic jam mechanism may play an important role in some cases of blocking onset and more generally that applying finite-amplitude local wave activity diagnostics to ensemble data is a promising approach for the further examination of individual onset events in light of the Nakamura and Huang theory.

Significance Statement

Blocking is an occasional phenomenon in the mid- and high-latitude atmosphere characterized by the stalling of weather systems. Episodes of blocking are linked to extreme weather but their occurrence is not completely understood. A recent theory suggests that blocks may form in the jet stream like traffic jams on a highway. The onset mechanism contained in the theory could explain why forecasts of blocking are sometimes poor. In this work, we investigate the formation of a 2016 European winter block in the context of the traffic jam theory. Though questions remain regarding the implications for forecast uncertainty, our findings strongly support the notion of a traffic jam onset.

Open access
Volkmar Wirth
and
Christopher Polster

Abstract

The waveguidability of an upper-tropospheric zonal jet quantifies its propensity to duct Rossby waves in the zonal direction. This property has played a central role in previous attempts to explain large wave amplitudes and the subsequent occurrence of extreme weather. In these studies, waveguidability was diagnosed with the help of ray tracing arguments using the zonal average of the observed flow as the relevant background state. Here, it is argued that this method is problematic both conceptually and mathematically. The issue is investigated in the framework of the nondivergent barotropic model. This model allows the straightforward computation of an alternative “zonalized” background state, which is obtained through conservative symmetrization of potential vorticity contours and that is argued to be superior to the zonal average. Using an idealized prototypical flow configuration with large-amplitude eddies, it is shown that the two different choices for the background state yield very different results; in particular, the zonal-mean background state diagnoses a zonal waveguide, while the zonalized background state does not. This result suggests that the existence of a waveguide in the zonal-mean background state is a consequence of, rather than a precondition for, large wave amplitudes, and it would mean that the direction of causality is opposite to the usual argument. The analysis is applied to two heatwave episodes from summer 2003 and 2010, yielding essentially the same result. It is concluded that previous arguments about the role of waveguidability for extreme weather need to be carefully reevaluated to prevent misinterpretation in the future.

Open access
Gabriel Wolf
and
Volkmar Wirth

Abstract

Upper-tropospheric Rossby wave packets have received increased attention recently. In most previous studies wave packets have been detected by computing the envelope of the meridional wind field using either complex demodulation or a Hilbert transform. The latter requires fewer choices to be made and appears, therefore, preferable. However, the Hilbert transform is fraught with a significant problem, namely, a tendency that fragments a single wave packet into several parts. The problem arises because Rossby wave packets show substantial deviations from the almost-plane wave paradigm, a feature that is well represented by semigeostrophic dynamics. As a consequence, higher harmonics interfere with the reconstruction of the wave envelope leading to undesirable wiggles. A possible cure lies in additional smoothing (e.g., by means of a filter) or resorting to complex demodulation (which implies smoothing, too). Another possibility, which does not imply any smoothing, lies in applying the Hilbert transform in semigeostrophic coordinate space. It turns out beneficial to exclude planetary-scale wavenumbers from this transformation in order to avoid problems in cases when the wave packet travels on a low wavenumber quasi-stationary background flow.

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