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Johannes M. L. Dahl

Abstract

This study addresses the robustness of the baroclinic mechanism that facilitates the onset of surface rotation in supercells by using two idealized simulations with different microphysics parameterizations and by considering previous results. In particular, the importance of ambient crosswise vorticity relative to baroclinically generated vorticity in the development of near-ground cyclonic vorticity is analyzed. The storms were simulated using the CM1 model in a kinematic base state characterized by a straight-line hodograph. A trajectory analysis spanning about 30 min was performed for a large number of parcels that contribute to near-surface vertical-vorticity maxima. The vorticity along these trajectories was decomposed into barotropic and nonbarotropic parts, where the barotropic vorticity represents the effects of the preexisting, substantially crosswise horizontal storm-relative vorticity. The nonbarotropic part represents the vorticity produced baroclinically within the storm. It was found that the imported barotropic vorticity attains a downward component near the surface, while the baroclinic vorticity points upward and dominates. This dominance of the baroclinic vorticity is independent of whether a single-moment or double-moment microphysics parameterization is used. A scaling argument is offered as explanation, predicting that the baroclinic vertical vorticity becomes increasingly dominant as downdraft strength increases.

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Jannick Fischer
and
Johannes M. L. Dahl

Abstract

Although much is known about the environmental conditions necessary for supercell tornadogenesis, the near-ground vorticity dynamics during the tornadogenesis process itself are still somewhat poorly understood. For instance, seemingly contradicting mechanisms responsible for large near-ground vertical vorticity can be found in the literature. Broadly, these mechanisms can be sorted into two classes, one being based on upward tilting of mainly baroclinically produced horizontal vorticity in descending air (here called the downdraft mechanism), while in the other the horizontal vorticity vector is abruptly tilted upward practically at the surface by a strong updraft gradient (referred to as the in-and-up mechanism). In this study, full-physics supercell simulations and highly idealized simulations show that both mechanisms play important roles during tornadogenesis. Pretornadic vertical vorticity maxima are generated via the downdraft mechanism, while the dynamics of a fully developed vortex are dominated by the in-and-up mechanism. Consequently, a transition between the two mechanisms occurs during tornadogenesis. This transition is a result of axisymmetrization of the pretornadic vortex patch and intensification via vertical stretching. These processes facilitate the development of the corner flow, which enables production of vertical vorticity by upward tilting of horizontal vorticity practically at the surface, i.e., the in-and-up mechanism. The transition of mechanisms found here suggests that early stages of tornado formation rely on the downdraft mechanism, which is often limited to a small vertical component of baroclinically generated vorticity. Subsequently, a larger supply of horizontal vorticity (produced baroclinically or via surface drag, or even imported from the environment) may be utilized, which marks a considerable change in the vortex dynamics.

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Johannes M. L. Dahl
and
Jannick Fischer

Abstract

The authors explore the dynamical origins of rotation of a mature tornado-like vortex (TLV) using an idealized numerical simulation of a supercell thunderstorm. Using 30-min forward parcel trajectories that terminate at the base of the TLV, the vorticity dynamics are analyzed for n = 7 parcels. Aside from the integration of the individual terms of the traditional vorticity equation, an alternative formulation of the vorticity equation and its integral, here referred to as vorticity source decomposition, is employed. This formulation is derived on the basis of Truesdell’s “basic vorticity formula,” which is obtained by first formulating the vorticity in material (Lagrangian) coordinates, and then obtaining the components relative to the fixed spatial (Eulerian) basis by applying the vector transformation rule. The analysis highlights surface drag as the most reliable vorticity source for the rotation at the base of the vortex for the analyzed parcels. Moreover, the vorticity source decomposition exposes the importance of small amounts of vorticity produced baroclinically, which may become significant after sufficient stretching occurs. Further, it is shown that ambient vorticity, upon being rearranged as the trajectories pass through the storm, may for some parcels directly contribute to the rotation of the TLV. Finally, the role of diffusion is addressed using analytical solutions of the steady Burgers–Rott vortex, suggesting that diffusion cannot aid in maintaining the vortex core.

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Jannick Fischer
and
Johannes M. L. Dahl

Abstract

It has long been observed that interactions of a supercell with other storms or storm-scale boundaries sometimes seem to directly instigate tornadogenesis. First, the authors explore the frequency of such constructive interactions. Radar data from WSR-88D are used to categorize 136 tornadic supercells into isolated supercells and supercells that interacted with external factors within 20 min before tornadogenesis. Most cases (80%) showed some form of external influence prior to tornadogenesis. Common patterns of interactions, the typical supercell quadrant that is affected, and changes in azimuthal shear are also identified. To further study these interactions, two sets of idealized Cloud Model 1 (CM1) simulations are performed. The first set demonstrates that the speed of the near-ground horizontal flow relative to the updraft can control whether a vortex patch develops into a tornado. A weaker updraft-relative flow is favorable because the developing vortex stays in the updraft region longer and becomes less tilted. Building on these results, it is shown that external outflow can lead to tornado formation by a deceleration of the updraft-relative flow. The deceleration is caused by the pressure gradient force associated with the external outflow, which is already noticeable several kilometers ahead of the outflow boundary. This offers one possible mechanism by which external outflow can act as a catalyst for supercell tornadogenesis.

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Johannes M. L. Dahl

Abstract

The question of how rotation arises in sheared updrafts is analyzed using the shear and curvature vorticity framework. Local rotation exists where the shear and curvature vorticity have a similar magnitude and the same sign, such that parcels are in near-solid-body rotation. It is shown that the tilting terms of the vertical vorticity equation cannot explain the development of local rotation in the canonical cases where the horizontal vorticity is either purely streamwise or purely crosswise. Rather, vertical shear vorticity develops if crosswise vorticity is tilted, and vertical curvature vorticity develops if streamwise vorticity is tilted. To analyze how local rotation develops, two simulations of updrafts in an environment with crosswise and mostly streamwise vorticity, respectively, are discussed. A trajectory analysis is performed and shear and curvature vorticity budgets are analyzed. It is found that much of the horizontal vorticity near the updraft becomes streamwise, which results from pressure gradient accelerations in the vicinity of the updraft. Consequently, in the analyzed scenarios, the tilting mechanism results primarily in vertical curvature vorticity. Local rotation is achieved via an interchange process that facilitates a partial conversion of vertical curvature vorticity to vertical shear vorticity. Updraft rotation in supercells thus does not result from tilting of horizontal vorticity alone, but partial conversion of curvature to shear vorticity is also required.

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Johannes M. L. Dahl
and
Jannick Fischer

Abstract

The authors investigate the origin of prefrontal, warm-season convergence lines over western Europe using the Weather Research and Forecasting Model. These lines form east of the cold front in the warm sector of an extratropical cyclone, and they are frequently the focus for convective development. It is shown that these lines are related to a low-level thermal ridge that accompanies the base of an elevated mixed layer (EML) plume generated over the Iberian Peninsula and northern Africa. Using Q-vector diagnostics, including the components that describe scalar and rotational quasigeostrophic frontogenesis, it is shown that the convergence line is associated with the rearrangement of the isentropes especially at the western periphery of the EML plume. The ascending branch of the resulting ageostrophic circulation coincides with the surface velocity convergence. The modeling results are supported by a 3-yr composite analysis of cold fronts with and without preceding convergence lines using NCEP–NCAR Reanalysis-1 data.

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Andrew Vande Guchte
and
Johannes M. L. Dahl

Abstract

Parcel trajectory analysis has become commonplace in the study of simulated severe convection, particularly that which deals with the development and maintenance of near-ground vertical vorticity. However, there are a number of unsolved problems with analyzing simulated trajectories that exist near the ground. One of these unsolved problems is how to deal with parcels that pass beneath the lowest scalar model level. Using the CM1 model, which uses a Lorenz grid, the sensitivity of parcel characteristics such as location or potential temperature to the choice of common extrapolation methods is documented. Using potential temperature as an example, it is explained why unphysical tendencies of scalar variables along trajectories may arise once parcels descend beneath the lowest scalar model level. Given the poorly constrained flow (and scalar) fields beneath the lowest scalar model level, errors such as those documented here appear unavoidable when using free-slip boundary conditions.

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Johannes M. L. Dahl
,
Hartmut Höller
, and
Ulrich Schumann

Abstract

In this study a straightforward theoretical approach to determining the flash rate in thunderstorms is presented. A two-plate capacitor represents the basic dipole charge structure of a thunderstorm, which is charged by the generator current and discharged by lightning. If the geometry of the capacitor plates, the generator-current density, and the lightning charge are known, and if charging and discharging are in equilibrium, then the flash rate is uniquely determined.

To diagnose the flash rate of real-world thunderstorms using this framework, estimates of the required relationships between the predictor variables and observable cloud properties are provided. With these estimates, the flash rate can be parameterized.

In previous approaches, the lightning rate has been set linearly proportional to the electrification rate (such as the storm’s generator power or generator current), which implies a constant amount of neutralization by lightning discharges (such as lightning energy or lightning charge). This leads to inconsistencies between these approaches. Within the new framework proposed here, the discharge strength is allowed to vary with storm geometry, which remedies the physical inconsistencies of the previous approaches.

The new parameterization is compared with observations using polarimetric radar data and measurements from the lightning detection network, LINET. The flash rates of a broad spectrum of discrete thunderstorm cells are accurately diagnosed by the new approach, while the flash rates of mesoscale convective systems are overestimated.

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Johannes M. L. Dahl
,
Hartmut Höller
, and
Ulrich Schumann

Abstract

In Part I of this two-part paper a new method of predicting the total lightning flash rate in thunderstorms was introduced. In this paper, the implementation of this method into the convection-permitting Consortium for Small Scale Modeling (COSMO) model is presented.

The new approach is based on a simple theoretical model that consists of a dipole charge structure, which is maintained by a generator current and discharged by lightning and, to a small extent, by a leakage current. This approach yields a set of four predictor variables, which are not amenable to direct observations and consequently need to be parameterized (Part I).

Using an algorithm that identifies thunderstorm cells and their properties, this approach is applied to determine the flash frequency of every thunderstorm cell in the model domain. With this information, the number of flashes that are accumulated by each cell and during the interval between the activation of the lightning scheme can be calculated.

These flashes are then randomly distributed in time and beneath each cell. The output contains the longitude, the latitude, and the time of occurrence of each simulated discharge.

Simulations of real-world scenarios are presented, which are compared to measurements with the lightning detection network, LINET. These comparisons are done on the cloud scale as well as in a mesoscale region composing southern Germany (two cases each). The flash rates of individual cumulonimbus clouds at the extreme ends of the intensity spectrum are realistically simulated. The simulated overall lightning activity over southern Germany is dominated by spatiotemporal displacements of the modeled convective clouds, although the scheme generally reproduces realistic patterns such as coherent lightning swaths.

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Johannes M. L. Dahl
,
Matthew D. Parker
, and
Louis J. Wicker

Abstract

This study addresses the sensitivity of backward trajectories within simulated near-surface mesocyclones to the spatiotemporal resolution of the velocity field. These backward trajectories are compared to forward trajectories computed during run time within the numerical model. It is found that the population of backward trajectories becomes increasingly contaminated with “inflow trajectories” that owe their existence to spatiotemporal interpolation errors in time-varying and strongly curved, confluent flow. These erroneous inflow parcels may mistakenly be interpreted as a possible source of air for the near-surface vortex. It is hypothesized that, unlike forward trajectories, backward trajectories are especially susceptible to errors near the strongly confluent intensifying vortex. Although the results are based on model output, dual-Doppler analysis fields may be equally affected by such errors.

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