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Jerry M. Straka
and
Edward R. Mansell

Abstract

A single-moment bulk microphysics scheme with multiple ice precipitation categories is described. It has 2 liquid hydrometeor categories (cloud droplets and rain) and 10 ice categories that are characterized by habit, size, and density—two ice crystal habits (column and plate), rimed cloud ice, snow (ice crystal aggregates), three categories of graupel with different densities and intercepts, frozen drops, small hail, and large hail. The concept of riming history is implemented for conversions among the graupel and frozen drops categories. The multiple precipitation ice categories allow a range of particle densities and fall velocities for simulating a variety of convective storms with minimal parameter tuning. The scheme is applied to two cases—an idealized continental multicell storm that demonstrates the ice precipitation process, and a small Florida maritime storm in which the warm rain process is important.

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Jerry M. Straka
and
Erik N. Rasmussen

Abstract

Prognostic equations are proposed for use in gridpoint models for the purpose of providing Lagrangian information without the need for computing Lagrangian trajectories. The information provided by the proposed methods might lead to improved representations of microphysical conversion processes. For example, the proposed methods could help improve the timing and location of the onset of precipitation in cloud models.

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Jerry M. Straka
and
John R. Anderson

Abstract

In the first part of this paper, the characteristics of microburst-producing storms are examined with a three-dimensional cloud model using soundings from the Cooperative Huntsville Meteorological Experiment (COHMEX). With a grid resolution of 500 m, it is shown that the general characteristics of observed vertical velocities, vertical draft sizes, water contents, radar reflectivities, and surface outflow strengths can be simulated. In addition, observed microburst precursors such as midlevel convergence and descending precipitation cores can also be simulated. Using a grid resolution of 250 m, the observed structure of a particularly well-documented storm on 20 July 1986 during COHMEX is simulated, including a hail shaft 1–2 km wide that descended to the ground.

In the second part of this paper, the influence of microphysical processes in the production of low-level downdrafts in simulated COHMEX storms is investigated. It is shown that low-level downdrafts are in some cases stronger and deeper in simulations made with the ice phase than in simulations made without the ice phase. These differences are due, in part, to the additional cooling associated with the melting of ice, and are consistent with findings of several other recent studies of low-level downdraft production in deep convective storms.

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Katharine M. Kanak
,
Jerry M. Straka
, and
David M. Schultz

Abstract

Mammatus are hanging lobes on the underside of clouds. Although many different mechanisms have been proposed for their formation, none have been rigorously tested. In this study, three-dimensional numerical simulations of mammatus on a portion of a cumulonimbus cirruslike anvil are performed to explore some of the dynamic and microphysical factors that affect mammatus formation and evolution. Initial conditions for the simulations are derived from observed thermodynamic soundings. Five observed soundings are chosen—four were associated with visually observed mammatus and one was not. Initial microphysical conditions in the simulations are consistent with in situ observations of cumulonimbus anvil and mammatus. Mammatus form in the four model simulations initialized with the soundings for which mammatus were observed, whereas mammatus do not form in the model simulation initialized with the no-mammatus sounding. Characteristics of the modeled mammatus compare favorably to previously published mammatus observations.

Three hypothesized formation mechanisms for mammatus are tested: cloud-base detrainment instability, fallout of hydrometeors from cloud base, and sublimation of ice hydrometeors below cloud base. For the parameters considered, cloud-base detrainment instability is a necessary, but not sufficient, condition for mammatus formation. Mammatus can form without fallout, but not without sublimation. All the observed soundings for which mammatus were observed feature a dry-adiabatic subcloud layer of varying depth with low relative humidity, which supports the importance of sublimation to mammatus formation.

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Mark A. Askelson
,
Patricia M. Pauley
, and
Jerry M. Straka

Abstract

Distance-dependent weighted averaging (DDWA) is a process that is fundamental to most of the objective analysis schemes that are used in meteorology. Despite its ubiquity, aspects of its effects are still poorly understood. This is especially true for the most typical situation of observations that are discrete, bounded, and irregularly distributed.

To facilitate understanding of the effects of DDWA schemes, a framework that enables the determination of response functions for arbitrary weight functions and data distributions is developed. An essential element of this approach is the equivalent analysis, which is a hypothetical analysis that is produced by using, throughout the analysis domain, the same weight function and data distribution that apply at the point where the response function is desired. This artifice enables the derivation of the response function by way of the convolution theorem. Although this approach requires a bit more effort than an alternative one, the reward is additional insight into the impacts of DDWA analyses.

An important insight gained through this approach is the exact nature of the DDWA response function. For DDWA schemes the response function is the complex conjugate of the normalized Fourier transform of the effective weight function. In facilitating this result, this approach affords a better understanding of which elements (weight functions, data distributions, normalization factors, etc.) affect response functions and how they interact to do so.

Tests of the response function for continuous, bounded data and discrete, irregularly distributed data verify the validity of the response functions obtained herein. They also reinforce previous findings regarding the dependence of response functions on analysis location and the impacts of data boundaries and irregular data spacing.

Interpretation of the response function in terms of amplitude and phase modulations is illustrated using examples. Inclusion of phase shift information is important in the evaluation of DDWA schemes when they are applied to situations that may produce significant phase shifts. These situations include those where data boundaries influence the analysis value and where data are irregularly distributed. By illustrating the attendant movement, or shift, of data, phase shift information also provides an elegant interpretation of extrapolation.

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Paul M. Markowski
,
Jerry M. Straka
, and
Erik N. Rasmussen

Abstract

Despite the long-surmised importance of the hook echo and rear-flank downdraft (RFD) in tornadogenesis, only a paucity of direct observations have been obtained at the surface within hook echoes and RFDs. In this paper, in situ surface observations within hook echoes and RFDs are analyzed. These “mobile mesonet” data have unprecedented horizontal spatial resolution and were obtained from the Verifications of the Origins of Rotation in Tornadoes Experiment (VORTEX) and additional field experiments conducted since the conclusion of VORTEX. The surface thermodynamic characteristics of hook echoes and RFDs associated with tornadic and nontornadic supercells are investigated to address whether certain types of hook echoes and RFDs are favorable (or unfavorable) for tornadogenesis.

Tornadogenesis is more likely and tornado intensity and longevity increase as the surface buoyancy, potential buoyancy (as measured by the convective available potential energy), and equivalent potential temperature in the RFD increase, and as the convective inhibition associated with RFD parcels at the surface decreases. It is hypothesized that evaporative cooling and entrainment of midlevel potentially cold air may play smaller roles in the development of RFDs associated with tornadic supercells compared to nontornadic supercells. Furthermore, baroclinity at the surface within the hook echo is not a necessary condition for tornadogenesis. It also will be shown that environments characterized by high boundary layer relative humidity (and low cloud base) may be more conducive to RFDs associated with relatively high buoyancy than environments characterized by low boundary layer relative humidity (and high cloud base).

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Paul M. Markowski
,
Erik N. Rasmussen
, and
Jerry M. Straka

Abstract

During the Verifications of the Origins of Rotation in Tornadoes Experiment, nearly 70% of the significant tornadoes occurred near low-level boundaries not associated with the forward or rear flank downdrafts of supercells. In general, these were preexisting boundaries readily identified using conventional data sources. Most of the tornadoes occurred on the cool side of these low-level boundaries and generally within 30 km of the boundaries. It is likely that the low-level boundaries augmented the “ambient” horizontal vorticity, which, upon further generation in the forward-flank region, became sufficient to be associated with tornadic low-level mesocyclones. Some implications for forecasting and further research are discussed.

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Paul M. Markowski
,
Jerry M. Straka
, and
Erik N. Rasmussen

Abstract

Idealized numerical simulations are conducted in which an axisymmetric, moist, rotating updraft free of rain is initiated, after which a downdraft is imposed by precipitation loading. The experiments are designed to emulate a supercell updraft that has rotation aloft initially, followed by the formation of a downdraft and descent of a rain curtain on the rear flank. In the idealized simulations, the rain curtain and downdraft are annular, rather than hook-shaped, as is typically observed. The downdraft transports angular momentum, which is initially a maximum aloft and zero at the surface, toward the ground. Once reaching the ground, the circulation-rich air is converged beneath the updraft and a tornado develops. The intensity and longevity of the tornado depend on the thermodynamic characteristics of the angular momentum-transporting downdraft, which are sensitive to the ambient low-level relative humidity and precipitation character of the rain curtain. For large low-level relative humidity and a rain curtain having a relatively small precipitation concentration, the imposed downdraft is warmer than when the low-level relative humidity is small and the precipitation concentration of the rain curtain is large. The simulated tornadoes are stronger and longer-lived when the imposed downdrafts are relatively warm compared to when the downdrafts are relatively cold, owing to a larger amount of convergence of circulation-rich downdraft air. The results may explain some recent observations of the tendency for supercells to be tornadic when their rear-flank downdrafts are associated with relatively small temperature deficits.

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Jerry M. Straka
,
Katharine M. Kanak
, and
Matthew S. Gilmore

Abstract

This paper presents a mathematical explanation for the nonconservation of total number concentration Nt of hydrometeors for the continuous collection growth process, for which Nt physically should be conserved for selected one- and two-moment bulk parameterization schemes. Where possible, physical explanations are proposed. The assumption of a constant no in scheme A is physically inconsistent with the continuous collection growth process, as is the assumption of a constant Dn for scheme B. Scheme E also is nonconservative, but it seems this result is not because of a physically inconsistent specification; rather the solution scheme’s equations simply do not satisfy Nt conservation and Nt does not come into the derivation. Even scheme F, which perfectly conserves Nt , does not preserve the distribution shape in comparison with a bin model.

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Youngsun Jung
,
Ming Xue
,
Guifu Zhang
, and
Jerry M. Straka

Abstract

A data assimilation system based on the ensemble square-root Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of assimilating additional polarimetric observations on convective storm analysis in the Observing System Simulation Experiment (OSSE) framework. The polarimetric variables considered include differential reflectivity Z DR, reflectivity difference Z dp, and specific differential phase K DP. To simulate the observational data more realistically, a new error model is introduced for characterizing the errors of the nonpolarimetric and polarimetric radar variables. The error model includes both correlated and uncorrelated error components for reflectivities at horizontal and vertical polarizations (ZH and ZV , respectively). It is shown that the storm analysis is improved when polarimetric variables are assimilated in addition to ZH or in addition to both ZH and radial velocity Vr . Positive impact is largest when Z DR, Z dp, and K DP are assimilated all together. Improvement is generally larger in vertical velocity, water vapor, and rainwater mixing ratios. The rainwater field benefits the most while the impacts on horizontal wind components and snow mixing ratio are smaller. Improvement is found at all model levels even though the polarimetric data, after the application of thresholds, are mostly limited to the lower levels. Among Z DR, Z dp, and K DP, Z DR is found to produce the largest positive impact on the analysis. It is suggested that Z DR provides more independent information than the other variables. The impact of polarimetric data is also expected to be larger when they are used to retrieve drop size distribution parameters. The polarimetric radar data thresholding prior to assimilation is found to be necessary to minimize the impact of noise. This study is believed to be the first to directly assimilate (simulated) polarimetric data into a numerical model.

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