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Jerry M. Straka
and
John R. Anderson

Abstract

The minimal aliasing local spectral (LS) method is a numerical technique that embodies features of both finite-difference (FD) and spectral transform (ST) methods. Anderson first described this method in the context of the one-dimensional advection-diffusion equation. In the current paper, we describe the extension of the LS method to multidimensions. First, we review the one-dimensional version of the LS method from a more rigorous view. In addition, we describe interpolation, differentiation, and dealiasing fitters for the LS method based on Lagrange polynomials. Without the dealiasing filters, this version of the LS method collapses to a standard high-order Taylor series FD scheme. When filter lengths span the integration domain and the dealiasing stage is retained, the LS method becomes an ST method, as described by Anderson. Issues concerning the implementation of the LS method in multidimensions are also discussed. These issues include the form of the high-resolution grid, the implementation of the interpolation stage, and the implementation of the dealiasing stage. Then, we test the LS method with a two-dimensional nonlinear density current problem using idealized boundary conditions. Comparisons are made with a high-resolution reference solution from a reference model, as well as with solutions from a high-order FD model. Results from simulations of the test problem demonstrate that the LS method is more accurate than high-order FD schemes at coarse grid resolutions, and as accurate at finer grid resolutions. Furthermore, the results show that solutions from LS models are more robust than solutions from FD models. After this, we show that dealiasing the nonlinear advection tendencies plays an important role in the success of the LS method, especially for simulations with sharp boundaries that are marginally resolved. For adequately resolved flows, dealiasing does not necessarily improve solutions for the short-term integrations that are presented. However, aliasing errors still must be controlled to prevent a catastrophic buildup of energy at the smallest resolvable wavelengths. Finally, the LS method is tested using open lateral boundary conditions. As the LS method is a higher-order scheme, special treatment of the vertical and lateral boundaries is required. One possibility is to use lower-order versions of the LS method as boundaries are approached, and outflow conditions at the lateral boundaries. This simple treatment results in solutions that compare very favorably to the reference solution of the test problem.

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Erik N. Rasmussen
and
Jerry M. Straka

Abstract

It is hypothesized that the precipitation intensity beneath a supercell updraft is strongly influenced by the amount of hydrometeors that are reingested into the updraft after being transported away in the divergent upper-level flow of the anvil. This paper presents the results of a climatological analysis of soundings associated with three types of isolated supercells having distinctive precipitation distributions, the so-called classic, low-precipitation (LP), and high-precipitation (HP) storms. It is shown that storm-relative flow at 9–10 km above the ground is strongest in the environments of LP storms, and relatively weak in the environments of HP storms, with classic storms occurring in environments with intermediate magnitudes of upper storm-relative flow. It is plausible that comparatively strong flow in the anvil-bearing levels of LP storms transports hydrometeors far enough from the updraft that they are relatively unlikely to be reingested into the updraft, leading to greatly diminished precipitation formation in the updraft itself. Conversely, the weak upper flow near HP storms apparently allows a relatively large number of hydrometeors to return to the updraft, leading to the generation of relatively large amounts of precipitation in the updraft. It also is apparent that thermodynamic factors such as convective available potential energy, low-level mixing ratio, and mean relative humidity are of lesser importance in determining storm type from a climatological perspective, although important variations in humidity may not be well sampled in this study. This climatological analysis does not directly evaluate the stated hypothesis; however, the findings do indicate that further modeling and microphysical observations are warranted.

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Mark A. Askelson
and
Jerry M. Straka

Abstract

The response function is a commonly used measure of analysis scheme properties. Its use in the interpretation of analyses of real-valued data, however, is unnecessarily complicated by the structure of the standard form of the Fourier transform. Specifically, interpretation using this form of the Fourier transform requires knowledge of the relationship between Fourier transform values that are symmetric about the origin. Here, these relationships are used to simplify the application of the response function to the interpretation of analysis scheme properties.

In doing so, Fourier transforms are used because they can be applied to studying effects that both data sampling and weight functions have upon analyses. A complication arises, however, in the treatment of constant and sinusoidal input since they do not have Fourier transforms in the traditional sense. To handle these highly useful forms, distribution theory is used to generalize Fourier transform theory. This extension enables Fourier transform theory to handle both functions that have Fourier transforms in the traditional sense and functions that can be represented using Fourier series.

The key step in simplifying the use of the response function is the expression of the inverse Fourier transform in a magnitude and phase form, which involves folding the integration domain onto itself so that integration is performed over only half of the domain. Once this is accomplished, interpretation of the response function is in terms of amplitude and phase modulations, which indicate how amplitudes and phases of input waves are affected by an analysis scheme. This interpretation is quite elegant since its formulation in terms of properties of input waves results in a one-to-one input-to-output wave interpretation of analysis scheme effects.

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Matthew S. Gilmore
and
Jerry M. Straka

Abstract

The simplified version of the Berry and Reinhardt parameterization used for initiating rain from cloud droplets is presented and is compared with 12 other versions of itself from the literature. Many of the versions that appear to be different from each other can be brought into agreement with the original parameterization by making the same assumptions: a mean diameter based upon mass or volume and distribution shape parameters chosen to give the same cloud mass relative variance as the original Berry and Reinhardt parameterization. However, there are differences in how authors have chosen to parameterize the cloud number concentration sink and rain number concentration source, and those choices, along with model limitations, have important impacts on rain development within the scheme. These differences among versions are shown to have important time-integrated feedbacks upon the developing initial rain distribution. Three of 12 implementations of the bulk scheme are shown to be able to reproduce the original Berry and Reinhardt bin-model solutions very well, and about 6 of 12 do poorly.

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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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Erik N. Rasmussen
and
Jerry M. Straka

Abstract

The life cycle of the 2 June 1995 Dimmitt, Texas, tornado cyclone, observed during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX), is described. The tornado cyclone here is defined as a significantly axisymmetric flow larger than the visible tornado and characterized by increasing angular momentum with increasing radius. Its life cycle included three phases with somewhat differing evolution of angular momentum, herein called intensifying, transition, and weakening. During the intensifying stage, the funnel and debris cloud gradually increased in size. The azimuthally averaged secondary circulation of the larger-scale tornado cyclone, as determined using high-resolution single-Doppler data obtained by a mobile radar, was primarily inward and upward, consistent with the presence of a wall cloud outside the tornado. The azimuthally averaged angular momentum increased monotonically away from the tornado, so inward advection allowed the angular momentum to increase slowly with time in part of the tornado cyclone. During the transition phase, downdrafts began to occur within the tornado cyclone. The transport of angular momentum by the secondary circulation nearly was offset by eddy flux convergence of angular momentum so that the azimuthally averaged angular momentum tendency was only weakly negative at most radii. The tornado was visually impressive during this stage, featuring a 400-m diameter debris cloud extending to cloud base, while the surrounding wall cloud shrank and eroded. During the weakening phase, the funnel and debris cloud gradually shrank, and the funnel went through a rope stage prior to disappearing. The weakening phase was characterized by extensive downdrafts at all radii outside the tornado, and large-scale near-ground outflow as observed by mobile mesonet systems in a portion of the tornado cyclone. The secondary circulation acted to transport smaller angular momentum downward from aloft, and outward along the ground. All terms of the angular momentum budget became negative throughout most of the low-level (0–800-m AGL) tornado cyclone during the weakening phase. Several hypotheses for this evolution are evaluated, including changes in water loading in the tornado cyclone, cooling of the near-ground air, and the distribution of tangential velocity with height with its concomitant influence on the nonhydrostatic vertical pressure gradient force.

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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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Valery Melnikov
and
Jerry M. Straka

Abstract

A novel method of retrieving the mean axis ratio (width/length) and standard deviation of orientation angles (σθ , which is called herein the intensity of fluttering) of ice cloud particles from polarimetric radar data is described. The method is based on measurements of differential reflectivity Z DR and the copolar correlation coefficient in cloud areas with Z DR > 4 dB. In three analyzed cases, the values of the retrieved axis ratio were in an interval from 0.15 to 0.4 and σθ found in an interval from 2° to 20°. The latter values indicate that the particles experienced light to moderate fluttering. Ambiguities in the retrievals because of uncertainties in the bulk ice density of the particles and possible presence of columnar crystals are considered. The retrieval method is applicable for centimeter-wavelength radars; the analyzed data were collected with the dual-polarization S-band Weather Surveillance Radar-1988 Doppler (WSR-88D).

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Amanda K. Kis
and
Jerry M. Straka

Abstract

Very few studies on nocturnal tornadoes have been performed, and operational forecasting of nocturnal tornadoes is often guided by the results of studies that are biased toward daytime tornadoes. However, it is likely that tornado environments vary significantly over the diurnal cycle. For example, the depth and nature of storm inflow may change as the daytime boundary layer transitions into a stable nighttime boundary layer, and a low-level jet (LLJ) may form above in the residual layer and free atmosphere. The study performed herein is used to investigate features unique to nocturnal boundary layers and the free atmosphere above that may affect nocturnal tornadoes.

A climatology of significant (F2–F5) nocturnal tornadoes in the contiguous United States between 2004 and 2006 shows that environments deemed by previous climatologies as unfavorable for late afternoon/early evening tornadogenesis are in fact conducive to significant nocturnal tornadogenesis. These nocturnal environments may be characterized by marginal convective instability with shallow stable boundary layers. Substantial low-level shear, storm relative helicity (SREH), and exceptionally strong nocturnal low-level jets stand out as the most common features of significant nocturnal tornadoes and have utility in distinguishing environments of weak nocturnal tornadoes from environments of significant nocturnal tornadoes. Analysis of the data gathered in the climatology shows that the suggestions of existing tornado climatologies are inadequate and even misguiding for forecasting nocturnal tornadoes. Several recommendations for operational forecasting of nocturnal tornadoes are made based on the results of this climatology.

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