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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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Johannes M. L. Dahl

Abstract

In many supercell simulations, near-ground vortex formation results from the collapse of an elongated region of enhanced vertical vorticity. In this study, this “roll-up” mechanism is analyzed by investigating the behavior of several 2D elliptic vortex patches. The problem is treated as a nonlinear initial value problem, which is better suited to describe the roll-up mechanism than the more commonly employed normal-mode analysis. Using the Bryan Cloud Model 1, it is demonstrated that the condition for vortex formation is an initial finite-amplitude nonuniformity within the vortex patch. Vortex formation results from differential self-advection due to the flow induced by the patch itself. Background straining motion may either aid or suppress vortex-patch axisymmetrization depending on the initial orientation of the patch relative to the deformation axis. It is also found that in some cases numerical dispersion may lead to nonuniformities that serve as seed for axisymmetrization, thus resulting in unphysical vortex development.

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Johannes M. L. Dahl
and
Christian Boyer
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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

About 140 years ago, Lord Kelvin derived the equations describing waves that travel along the axis of concentrated vortices such as tornadoes. Although Kelvin’s vortex waves, also known as centrifugal waves, feature prominently in the engineering and fluid dynamics literature, they have not attracted as much attention in the field of atmospheric science. To remedy this circumstance, Kelvin’s elegant derivation is retraced, and slightly generalized, to obtain solutions for a hierarchy of vortex flows that model basic features of tornado-like vortices. This treatment seeks to draw attention to the important work that Lord Kelvin did in this field, and reveal the remarkably rich structure and dynamics of these waves. Kelvin’s solutions help explain the vortex breakdown phenomenon routinely observed in modeled tornadoes, and it is shown that his work is compatible with the widely used criticality condition put forth by Benjamin in 1962. Moreover, it is demonstrated that Kelvin’s treatment, with the slight generalization, includes unstable wave solutions that have been invoked to explain some aspects of the formation of multiple-vortex tornadoes. The analysis of the unstable solutions also forms the basis for determining whether, for example, an axisymmetric or a spiral vortex breakdown occurs. Kelvin’s work thus helps explain some of the visible features of tornado-like vortices.

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Matthew D. Parker
and
Johannes M. L. Dahl

Abstract

This study uses an idealized heat sink to examine the possible roles of the wind profile in modulating the production of surface vertical vorticity by a downdraft. The basic vorticity evolution in these idealized simulations is consistent with previous work: the process is primarily baroclinic and produces near-ground vertical vorticity within the outflow. Sensitivity experiments affirm that the only fundamental requirement for downdrafts to produce surface vertical vorticity is the existence of ambient downdraft-relative flow. Vertical vorticity production increases monotonically as the low-level downdraft-relative flow increases from zero up through intermediate values (in these experiments, 10–15 m s−1), followed by a monotonic decrease for greater values. This sensitivity has to do with the degree of cooling acquired by parcels as they pass through the idealized heat sink as well as the degree to which horizontal vorticity vectors subsequently attain an orientation that is normal to isosurfaces of vertical velocity. Although the addition of vertical wind shear is not directly helpful to surface vertical vorticity production in these simulations, increased realism of outflow structure is attained in hodographs with ambient streamwise vorticity. Furthermore, the necessary condition of flow through a region of downdraft forcing would in nature probably require the existence of ambient vertical shear. Therefore, shear in the lower troposphere has a possibly important indirect role in modulating the initial production of near-ground rotation.

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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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Christian H. Boyer
and
Johannes M. L. Dahl

Abstract

Despite their structural differences, supercells and quasi-linear convective systems (QLCS) are both capable of producing severe weather, including tornadoes. Previous research has highlighted multiple potential mechanisms by which horizontal vorticity may be reoriented into the vertical at low levels, but it is not clear in which situation what mechanism dominates. In this study, we use the CM1 model to simulate three different storm modes, each of which developed relatively large near-surface vertical vorticity. Using forward-integrated parcel trajectories, we analyze vorticity budgets and demonstrate that there seems to be a common mechanism for maintaining the near-surface vortices across storm structures. The parcels do not acquire vertical vorticity until they reach the base of the vortices. The vertical vorticity results from vigorous upward tilting of horizontal vorticity and simultaneous vertical stretching. While the parcels analyzed in our simulations do have a history of descent, they do not acquire appreciable vertical vorticity during their descent. Rather, during the analysis period relatively large horizontal vorticity develops as a result of horizontal stretching, and therefore this vorticity can be effectively tilted into the vertical.

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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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