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Kelvin K. Droegemeier
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Jidong Gao
and
Kelvin K. Droegemeier

Abstract

Velocity folding, or aliasing, is one of most significant impediments to the use of radial winds from Doppler weather radar. In this note, a variational algorithm is developed in which dealiasing is performed using wind gradient information. The key to the proposed method is that, by operating on gradients of velocity rather than on the velocity itself, aliasing ambiguities are readily identified and eliminated. The viability of the method is demonstrated by applying it to Weather Surveillance Radar-1988 Doppler (WSR-88D) observations from a winter-weather event and a tornadic supercell storm.

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Steven Lazarus
,
Alan Shapiro
, and
Kelvin Droegemeier

Abstract

The authors present herein an analysis of a single-Doppler velocity retrieval (SDVR) technique whereby the unobserved wind components are determined from single-Doppler radar data. The analysis is designed to provide information about the behavior and/or sensitivity of the SDVR scheme as a function of various internal and external parameters as well as about observational errors and weights.

Results presented for retrieval of both the mean and local flow indicate that the SDVR breaks down if the reflectivity gradient vanishes or if a reflectivity isoline is locally perpendicular to the radar beam. In the absence of reflectivity or radial velocity errors, the mean flow solution is independent of the integration area, the radar location, the signal wavenumber, and the weights. Given perfect radial wind information, error in the reflectivity field degrades the solution. Contrary to the error-free solution, the solution with error depends on the integration area.

Error statistics indicate that radial wind information alone is not sufficient to retrieve the local wind. Reduced error norms reveal that an optimal (i.e., reduced error norms) integration area exists that is dependent upon the length of time between radar volume scans, suggesting that the velocity field is not stationary (as was assumed) over these scans.

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Ernanide Lima Nascimento
and
Kelvin K. Droegemeier

Abstract

An identical twin methodology is applied to a three-dimensional cloud model to study the dynamics of adjustment in deep convective storms. The principal goal is to diagnose how mass and velocity fields mutually adjust in order to better understand the relative information content (value) of observations, the physical interdependency among variables, and to help in the design of dynamically consistent analyses to ensure smooth startup of numerical prediction models.

Using a control simulation (“truth” or “nature” run) of an idealized long-lived bow echo convective system, a series of adjustment experiments is created by resetting, in various combinations, the horizontal and vertical velocity components of the control run to their undisturbed base state values during the mature stage of storm system evolution. The integrations then are continued for comparison against the control. This strategy represents a methodology for studying transient response to an impulsive perturbation in a manner conceptually similar to that used in geostrophic and hydrostatic adjustment.

The results indicate that resetting both horizontal velocity components alters the character of the convection and slows considerably the overall storm system evolution. In sharp contrast, when only the vertical velocity component is reset, the model quickly restores both updrafts and downdrafts to nearly their correct (control run) values, producing subsequent storm evolution virtually identical to that of the control run. Other combinations yield results in between these two extremes, with the cross-line velocity component proving to be most important in restoration toward the control run. This behavior is explained by acoustic adjustment of the pressure and velocity fields in direct response to changes in velocity divergence forced by the withdrawal of wind information.

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Kelvin K. Droegemeier
and
Robert B. Wilhelmson

Abstract

In this second paper in a series on outflow interactions, we use the three-dimensional model described in Part I to examine the effects of vertical wind shear variations on cloud development along intersecting thunderstorm outflow boundaries. Three wind shear profiles are used in this study: shear only above cloud base, shear only below cloud base, and shear both above and below cloud base. As in Part I, the shear is unidirectional and is oriented perpendicular to the line containing the two initial outflow-producing clouds (which are spaced 16 km apart). Using the environmental thermodynamic structure from the control simulation in Part I, we vary the shear magnitude in each profile and examine the properties of cloud development in the region where the two outflows collide (the outflow collision line or CL).

The model results show that the intensity and the time interval between successive cell updraft maxima of the first two clouds along the CL (both of which are triggered by the outflow collision) are controlled by the strength of the vertical wind shear. In strong shears, the upshear member of this pair of clouds has a head start in development and becomes the stronger cell of the two. The timing difference between these two clouds is a few minutes. In weaker shears, the two clouds grow at nearly the same rate, and therefore have similar intensities and a smaller timing difference. The presence of wind shear in the boundary layer is found to enhance the updrafts of these two cells in all cases.

The strength of the third and subsequent clouds which form along the CL is related to the speed at which the gust front moves away from the developing cells. The larger this separation speed, the more quickly the gust front-induced convergence is removed from the clouds, and thus the weaker they are. The third and subsequent cells along the CL are found to be more intense when shear is present in the cloud-bearing layer. The factors governing the timing difference of the third and successive cells to form along the outflow's leading edge are not clear at this time.

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Gary S. Dietachmayer
and
Kelvin K. Droegemeier

Abstract

The continuous dynamic grid adaption (CDGA) technique developed in astrophysics and aeronautics is applied, to our knowledge, for the first time to meteorological modeling. The aim of CDGA is to improve the accuracy of numerical solutions of partial differential equations (typically those governing fluid flow) by the use of nonuniform grids that have higher local resolution in regions where the numerical error is presumed to be large. Conceptually, CDGA has some relationship to the well-known technique of grid stretching, but its power lies in its ability to determine an appropriate spatial distribution of grid points automatically and to update this distribution in response to changes in the evolving numerical solution. Application of the technique is facilitated by transforming the governing equations from physical space in which the grid is nonuniform, nonorthogonal and for which the individual grid points are in continuous motion to computational space, which by definition has both a regular and stationary distribution of grid points. The distribution of grid points is found by the solution of “grid-generator” equations, which in turn can be derived as a weighted combination of several variational problems, each of which attempts to enforce a particular desirable property of the grid. These properties include the smoothness and orthogonality of the gridpoint distribution and its response to the user-defined “weight function,” which is a quantitative measure of where the local resolution is to be increased.

The method is applied to several problems of meteorological relevance. The first, Burgers’ equa`tion in one dimension, is used primarily to illustrate the method in a simple context, but also illuminates several features of CDGA, one of which is its ability to improve the accuracy of a numerical solution purely by inducing motion of the grid points. A kinematic frontogenesis problem is used to extend the method to two dimensions, and with the aid of a readily available exact solution, shows the very considerable gains in accuracy that may be achieved over fixed-grid methods. A surprising observation is that the formal order of accuracy of the adaptive results is, for certain parameters, actually greater than for the fixed-grid results. The ability of the technique to allocate multiple zones of high resolution is demonstrated by experiments in which several (four) “cones” are advected by a field of solid-body rotation. The final application is to the evolution of a slab-symmetric thermal in a neutral environment. Again, considerable improvements in accuracy over fixed-grid calculations are achieved, and it is shown that the problem of spurious numerical oscillations associated with rapid variation in an advected field, a problem that has received a great deal of attention in recent times, is greatly alleviated by the CDGA formulation.

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Seon Ki Park
and
Kelvin K. Droegemeier

Abstract

An automatic differentiation tool (ADIFOR) is applied to a warm-rain, time-dependent 1D cloud model to study the influence of input parameter variability, including that associated with the initial state as well as physical and computational parameters, on the dynamical evolution of a deep convective storm.

Storm dynamics are found to be controlled principally by changes in model initial states below 2 km; once perturbed, each grid variable in the model plays its own unique role in determining the dynamical evolution of the storm. Among all model-dependent variables, the low-level temperature field has the greatest impact on precipitation, followed by the water vapor field. Mass field perturbations inserted at upper levels induce prominent oscillations in the wind field, whereas a comparable wind perturbation has a negligible effect on the thermodynamic field. However, the wind field does influence the precipitation in a more complex way than does the thermodynamic field, principally via changes in time evolution.

The simulated storm responds to variations in three physical parameters (the autoconversion/accretion rate, cloud radius, and lateral eddy exchange coefficient) largely as expected, with the relative importance of each, quantified via a relative sensitivity analysis, being a strong function of the particular stage in the storm’s life cycle.

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Edwin J. Adlerman
and
Kelvin K. Droegemeier

Abstract

Building upon the authors’ previous work that examined the dynamics of numerically simulated cyclic mesocyclogenesis and its dependence upon model physical and computational parameters, this study likewise uses idealized numerical simulations to investigate associated dependencies upon ambient vertical wind shear. Specifically, the authors examine variations in hodograph shape, shear magnitude, and shear distribution, leading to storms with behavior ranging from steady state to varying degrees of aperiodic occluding cyclic mesocyclogenesis. However, the authors also demonstrate that a different mode of nonoccluding cyclic mesocyclogenesis may occur in certain environments.

Straight hodographs (unidirectional shear) produce only nonoccluding cyclic mesocyclogenesis. Introducing some curvature by adding a quarter circle of turning at low levels results in steady, nonoccluding, and occluding modes. When a higher degree of curvature is introduced—for example, turning through half and three-quarter circles—the tendency for nonoccluding behavior is diminished. None of the full-circle hodographs exhibited cycling during 4 h of simulation. Overall, within a given storm, the preferred mode of cycling is related principally to hodograph shape and magnitude of the ambient vertical shear.

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Michele M. Robertson
and
Kelvin K. Droegemeier

This paper describes results from a survey designed to establish the current level of radar and computer technology of the television weather industry, and to assess the awareness and attitudes of television weather forecasters toward the Next Generation Weather Radar (NEXRAD) program and its potential impact on the field of broadcast meteorology. The survey was distributed to one affiliate station in each of the 213 national television markets, and a 46% response rate was achieved over a 4-week period. The survey results indicate substantial awareness of and interest in NEXRAD, along with a willingness to learn more about its capabilities and potential for use in the private sector. Survey participants suggested that potential private NEXRAD users work directly with the National Weather Service (NWS) and its affiliates so as to fully utilize the capabilities of the new radar system.

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Kelvin K. Droegemeier
and
Robert B. Wilhelmson

Abstract

The Klemp–Wilhelmson three-dimensional numerical cloud model is used to investigate cloud development along intersecting thunderstorm outflow boundaries. The model initial environment is characterized by a temperature and moisture profile typically found in strong convective situations, and the initial wind field is prescribed by a constant unidirectional shear 2.9 m s−1 km−1 from 0.8 to 8.9 km, with a constant wind everywhere else. The wind shear vector is perpendicular to the line containing the two initial outflow-producing clouds (which are spaced 16 km apart and are triggered by thermal impulses centered at the top of the boundary layer).

The dynamics of the outflow collision are documented using time-dependent, kinematic air parcel trajectories and thermodynamic data. We find that ambient air in the outflow collision region is literally “squeezed” out of the way as the two outflows collide. Some of this air is lifted to saturation, triggering two convective clouds. The upshear member of the pair has a head start in development, and since the two clouds are growing close together and competing for the same air, the upshear cloud is the strongest. In addition to, the downshear cell is suppressed because it grows into the region occupied by the upshear cell's downdraft and rain region.

By looking at the various terms in the inviscid form of the vertical momentum equation, we find that low-level air approaching the gust front along the outflow collision line is forced to rise up and over the cold air pool due to a deflection by the pressure gradient force. A third cloud is triggered along the outflow collision line as a result of this frontal uplifting, which is in contrast to the first two cells which are triggered primarily by the forced uplifting from the outflow collision.

Air parcel trajectories indicate that even though the first two cells along the outflow collision line are triggered by a different mechanism than subsequent cells, the air comprising each updraft core is virtually undiluted, and comes from the same general region (z = 0 ∼ 0.3 km). On their way to the cloud updrafts, some low-level air parcels approaching the outflow cross the cold air interface. This is a manifestation of the well-known fact that the gust front is a region of turbulent mixing. Once above the outflow, these air parcels may pass through several updrafts and downdrafts as they traverse the cloud region.

The modeled clouds are found to be sensitive to the low-level (0–1 km) moisture. When the moisture in this layer is increased, the collision line clouds become stronger and the rapidity of new cell development increases markedly. Decreasing the low-level moisture has the opposite effect, to the point that only weak shallow clouds form along the outflow collision line. Furthermore, a decrease in the low-level moisture is accompanied by a decrease in the outflow temperature deficit. This in turn decreases the outflow speed, a result that is consistent with classical inviscid density current theory.

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