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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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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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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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Mark A. Askelson
,
Jean-Pierre Aubagnac
, and
Jerry M. Straka

Abstract

Spatial objective analysis is routinely performed in several applications that utilize radar data. Because of their relative simplicity and computational efficiency, one-pass distance-dependent weighted-average (DDWA) schemes that utilize either the Cressman or the Barnes filter are often used in these applications. The DDWA schemes that have traditionally been used do not, however, directly account for two fundamental characteristics of radar data. These are 1) the spacing of radar data depends on direction and 2) radar data density systematically decreases with increasing range.

A DDWA scheme based on an adaptation of the Barnes filter is proposed. This scheme, termed the adaptive Barnes (A-B) scheme, explicitly takes into account radar data properties 1 and 2 above. Both theoretical and experimental investigations indicate that two attributes of the A-B scheme, direction-splitting and automatic adaptation to data density, may facilitate the preservation of the maximum amount of meaningful information possible within the confines of one-pass DDWA schemes.

It is shown that in the idealized situation of infinite, continuous data and for an analysis in rectangular-Cartesian coordinates, a direction-splitting scheme does not induce phase shifts if the weight function is even in each direction. Moreover, for radar data that are infinite, collected at regular radial, azimuthal, and elevational increments, and collocated with analysis points, the direction-splitting design of the A-B filter removes gradients in the analysis weights. This is a beneficial attribute when considering the treatment of gradient information of rectangular Cartesian data by an analysis system because then postanalysis gradients equal the analysis of gradients. The direction-splitting design of the A-B filter is unable, however, to circumvent the impact of the varying physical distances between adjacent measurements that are inherent to the spherical coordinate system of ground-based weather radars. Because of this, even with the direction-splitting design of the A-B filter postanalysis gradients do not equal the analysis of gradients.

Ringing in the response function of a one-dimensional Barnes filter is illustrated. The negative impact of data windows on the main lobe of the response function is found to decrease rapidly as the window is widened relative to the weight function. Unless an analysis point is near a data boundary, in which case both ringing and phase shifting will adversely affect the analysis, window effects are unlikely to be significant in applications of the A-B filter to radar data.

The A-B filter has potential drawbacks, the most significant of which is misinterpretations owing to the use of the A-B filter without comprehension of its direction- and range-dependent response function. Despite its drawbacks, the A-B filter has the potential to improve analyses owing to the aforementioned attributes and thus to aid research efforts in areas such as multiple-Doppler wind analyses, pseudo-dual-Doppler analyses, and retrieval studies.

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Matthew S. Gilmore
,
Jerry M. Straka
, and
Erik N. Rasmussen

Abstract

Weisman and Klemp suggested that their liquid-only, deep convective storm experiments should be repeated with a liquid-ice microphysics scheme to determine if the solutions are qualitatively the same. Using a three-dimensional, nonhydrostatic cloud model, such results are compared between three microphysics schemes: the “Kessler” liquid-only scheme (used by Weisman and Klemp), a Lin–Farley–Orville-like scheme with liquid and ice parameterization (Li), and the same Lin–Farley–Orville-like microphysics scheme but with only liquid processes turned on (Lr). Convection is simulated using a single thermodynamic profile and a variety of shear profiles. The shear profiles are represented by five idealized half-circle wind hodographs with arc lengths (U s ) of 20, 25, 30, 40, and 50 m s−1. The precipitation, cold pool characteristics, and storm evolution produced by the different schemes are compared.

The Kessler scheme produces similar accumulated precipitation over 2 h compared to Lr for all shear regimes. Although Kessler's rain evaporation rate is 1.5–1.8 times faster in the lower troposphere, rain production is also faster via accretion and autoconversion of cloud water. In addition, nearly ∼40% more accumulated precipitation occurs in Li compared to Lr. This can be attributed primarily to increased precipitation production rates and enhanced low-level precipitation fluxes in Li for all shear regimes. Differences in the amount of precipitation reaching ground and the low-level cooling rates also cause differences in storm cold pools.

For the U s = 25 shear regime, microphysics cases with colder low-level outflow are shown to be associated with temporarily weaker (Li) or shorter-lived (Kessler) supercells as compared to cases with warmer outflow (Lr). This is consistent with a previous study showing that the cold pool has a greater relative impact on the storm updraft compared to dynamic forcing for weaker shear.

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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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Daniel E. Johnson
,
Pao K. Wang
, and
Jerry M. Straka

Abstract

The Wisconsin Dynamical-Microphysical Model is used in two simulations of the 2 August 1981 supercell that passed through the Cooperative Convective Precipitation Experiment in southeastern Montana. The first simulation uses liquid water-only microphysics and is denoted as the liquid water model (LWM). The second includes both liquid water and ice microphysics and is designated as the hail category model (HCM). Results from the two simulations show that the inclusion of ice significantly alters the dynamics, kinematics, thermodynamics, and distributions of water in the storm, especially at the lower levels. Supercell features such as a rotating intense updraft, bounded weak-echo region, large forward overhanging anvil, and hooklike structure in the low-level rainwater field are present in both simulations. These features are generally more pronounced, however, and have a longer lifetime in the HCM.

Hail embryo and graupel particles make up more than 85% of the total hail mass during the steady-state phase in the HCM. Many of these particles are advected into the anvil regions away from the updraft and sublimate slowly. As a result, distributions of graupel and hail in the HCM cover a more extensive but less concentrated region than do the distributions of rainwater in the LWM. Heavier more localized precipitation in the LWM results in a stronger low-level downdraft and a faster-moving gust front than in the HCM. The LWM gust front propagates ahead of the low-level updraft, cutting off the warm, moist, low-level easterly flow into the storm that leads to complete dissipation of the cloud by the end of the 150-min simulation period. Conversely, less concentrated precipitation failing to the surface in the HCM results in a weaker downdraft and a slower-moving gust front. The gust front propagates with the low-level updraft, thus allowing the storm to remain in a quasi-steady state for the final 80 min of the simulation. Overall, there is slightly more total surface precipitation in the HCM due to the larger areal coverage of precipitation and slower movement of the storm.

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Donald R. MacGorman
,
Jerry M. Straka
, and
Conrad L. Ziegler

Abstract

A new lightning parameterization has been developed to enable cloud models to simulate the location and structure of individual lightning flashes more realistically. To do this, three aspects of previous parameterizations have been modified: 1) To account for subgrid-scale variations, the initiation point is chosen randomly from among grid points at which the electric field magnitude is above a threshold value, instead of being assigned always to the grid point having the maximum electric field magnitude. 2) The threshold value for initiation can either be constant, as in previous parameterizations, or can vary with height to allow different flash initiation hypotheses to be tested. 3) Instead of stopping at larger ambient electric field magnitudes, extensive flash development can continue in regions having a weak ambient electric field but a substantial charge density. This behavior is based on lightning observations and conceptual models of lightning physics. However, like previous parameterizations for cloud models, the new parameterization attempts to mimic only the gross structure of flashes, not the detailed development of lightning channels, the physics of which is only poorly understood. Though the choice of parameter values affects the dimensions of a flash, the qualitative features of simulated flash structure are similar to those of observed lightning as long as the parameter values are consistent with the larger electric field magnitudes measured in storms and with simulated charge densities produced over reasonably large regions. Initial simulations show that, by permitting development of flashes in regions of substantial charge density and weak ambient electric field, the new parameterization produces flash structure much like that of observed flashes, as would be expected from the inferred correlation between observed horizontal lightning structure and thunderstorm charge.

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