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Louis J. Wicker

Abstract

Split-explicit integration methods used for the compressible Navier–Stokes equations are now used in a wide variety of numerical models ranging from high-resolution local models to convection-permitting climate simulations. Models are now including more sophisticated and complicated physical processes, such as multimoment microphysics parameterizations, electrification, and dry/aqueous chemistry. A wider range of simulation problems combined with the increasing physics complexity may place a tighter constraint on the model’s time step compared to the fluid flow’s Courant number (e.g., the choice of the integration time step based solely on advective Courant number considerations may generate unacceptable errors associated with the parameterization schemes). The third-order multistage Runge–Kutta scheme has been very successful as the split-explicit integration method; however, its efficiency arises partially in its ability to use a time step that is 20%–40% larger than more traditional integration schemes. In applications in which the time step is constrained by other considerations, alternative integration schemes may be more efficient. Here a two-step third-order Adams–Bashforth–Moulton integrator is stably split in a similar manner as the split Runge–Kutta scheme. For applications in which the large time step is not constrained by the advective Courant number it requires less computational effort. Stability is demonstrated through eigenvalue analysis of the linear coupled one-dimensional velocity–pressure equations, and full two-dimensional nonlinear solutions from a standard test problem are shown to demonstrate solution accuracy and efficiency.

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Corey K. Potvin and Louis J. Wicker

Abstract

Under the envisioned warn-on-forecast (WoF) paradigm, ensemble model guidance will play an increasingly critical role in the tornado warning process. While computational constraints will likely preclude explicit tornado prediction in initial WoF systems, real-time forecasts of low-level mesocyclone-scale rotation appear achievable within the next decade. Given that low-level mesocyclones are significantly more likely than higher-based mesocyclones to be tornadic, intensity and trajectory forecasts of low-level supercell rotation could provide valuable guidance to tornado warning and nowcasting operations. The efficacy of such forecasts is explored using three simulated supercells having weak, moderate, or strong low-level rotation. The results suggest early WoF systems may provide useful probabilistic 30–60-min forecasts of low-level supercell rotation, even in cases of large radar–storm distances and/or narrow cross-beam angles. Given the idealized nature of the experiments, however, they are best viewed as providing an upper-limit estimate of the accuracy of early WoF systems.

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David C. Dowell and Louis J. Wicker

Abstract

An “additive noise” method for initializing ensemble forecasts of convective storms and maintaining ensemble spread during data assimilation is developed and tested for a simplified numerical cloud model (no radiation, terrain, or surface fluxes) and radar observations of the 8 May 2003 Oklahoma City supercell. Every 5 min during a 90-min data-assimilation window, local perturbations in the wind, temperature, and water-vapor fields are added to each ensemble member where the reflectivity observations indicate precipitation. These perturbations are random but have been smoothed so that they have correlation length scales of a few kilometers. An ensemble Kalman filter technique is used to assimilate Doppler velocity observations into the cloud model. The supercell and other nearby cells that develop in the model are qualitatively similar to those that were observed. Relative to previous storm-scale ensemble methods, the additive-noise technique reduces the number of spurious cells and their negative consequences during the data assimilation. The additive-noise method is designed to maintain ensemble spread within convective storms during long periods of data assimilation, and it adapts to changing storm configurations. It would be straightforward to use this method in a mesoscale model with explicit convection and inhomogeneous storm environments.

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Robert B. Wilhelmson and Louis J. Wicker

Abstract

No Abstract available.

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Corey K. Potvin and Louis J. Wicker

Abstract

Kinematical analyses of mobile radar observations are critical to advancing the understanding of supercell thunderstorms. Maximizing the accuracy of these and subsequent dynamical analyses, and appropriately characterizing the uncertainty in ensuing conclusions about storm structure and processes, requires thorough knowledge of the typical errors obtained using different retrieval techniques. This study adopts an observing system simulation experiment (OSSE) framework to explore the errors obtained from ensemble Kalman filter (EnKF) assimilation versus dual-Doppler analysis (DDA) of storm-scale mobile radar data. The radar characteristics and EnKF model errors are varied to explore a range of plausible scenarios.

When dual-radar data are assimilated, the EnKF produces substantially better wind retrievals at higher altitudes, where DDAs are more sensitive to unaccounted flow evolution, and in data-sparse regions such as the storm inflow sector. Near the ground, however, the EnKF analyses are comparable to the DDAs when the radar cross-beam angles (CBAs) are poor, and slightly worse than the DDAs when the CBAs are optimal. In the single-radar case, the wind analyses benefit substantially from using finer grid spacing than in the dual-radar case for the objective analysis of radar observations. The analyses generally degrade when only single-radar data are assimilated, particularly when microphysical parameterization or low-level environmental wind errors are introduced. In some instances, this leads to large errors in low-level vorticity stretching and Lagrangian circulation calculations. Nevertheless, the results show that while multiradar observations of supercells are always preferable, judicious use of single-radar EnKF assimilation can yield useful analyses.

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Louis J. Wicker and William C. Skamarock

Abstract

Two time-splitting methods for integrating the elastic equations are presented. The methods are based on a third-order Runge–Kutta time scheme and the Crowley advection schemes. The schemes are combined with a forward–backward scheme for integrating high-frequency acoustic and gravity modes to create stable split-explicit schemes for integrating the compressible Navier–Stokes equations. The time-split methods facilitate the use of both centered and upwind-biased discretizations for the advection terms, allow for larger time steps, and produce more accurate solutions than existing approaches. The time-split Crowley scheme illustrates a methodology for combining any pure forward-in-time advection schemes with an explicit time-splitting method. Based on both linear and nonlinear tests, the third-order Runge–Kutta-based time-splitting scheme appears to offer the best combination of efficiency and simplicity for integrating compressible nonhydrostatic atmospheric models.

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Matthew S. Gilmore and Louis J. Wicker

Abstract

This work studies the relationship between midtropospheric dryness and supercell thunderstorm morphology and evolution using a three-dimensional, nonhydrostatic cloud model. Environments that differ only in midtropospheric dryness are found to produce supercells having different low-level outflow and rotational characteristics. Thunderstorms forming in environments with moderate vertical wind shear, large instability, and very dry midtropospheric air produce strong low-level outflow. When this low-level outflow propagates faster than the midlevel mesocyclone, the storm updraft and low-level mesocyclone weaken. However, in environments with larger vertical wind shear or with higher-altitude dry midtropospheric air, the low-level outflow is not as detrimental to the supercell. This provides a possible explanation for why some environments that appear favorable for the development of strong low-level mesocyclones in supercells fail to do so.

Downdraft convective available potential energy (DCAPE) is also investigated as one possible index for estimating potential downdraft strength. Trajectory analysis shows that the strongest downdrafts are subsaturated and diluted due to mixing between the downdraft and the surrounding environment. These significant violations of parcel theory make DCAPE a worse estimate for supercell downdraft intensity than convective available potential energy is for the updraft. A more sophisticated parameter is needed in order to determine downdraft intensity and low-level outflow strength within supercells.

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Louis J. Wicker and Robert B. Wilhelmson

Abstract

A three-dimensional numerical simulation using a two-way interactive nested grid is to study tornado-genesis within a supercell. During a 40-minute period, two tornadoes grow and decay within the storm's mesocyclone. The tornadoes have life spans of approximately 10 minutes. Maximum ground-relative surface wind speeds exceed 60 m s−1 during both tornadoes, and horizontal pressure gradients reach 18 hPa km−1 during the second tornado. Comparison of the simulated storm evolution with Doppler and field observations of supercells and tornadoes shows many similar features.

Vertical vorticity in the mesocyclone and the tornado vortex at low levels is initially created by the tilting of the environmental vorticity and baroclinically generated vorticity along the forward gland gust front of the storm. Tornadogenesis is initiated when mesocyclone rotation increase above cloud base. The increased rotation generates lower pressure in the mesocyclone, increasing the upward pressure gradient forces. The upward pressure gradient forces accelerate the vertical motions near cloud base, creating 20–30 m s−1 updrafts at this level. As the updraft intensifies at cloud base, the convergence in the subcloud layer also increases rapidly. The vertical vorticity is the stretched in the convergent flow, creating the tornado vortex. Tornado decay begins when the vertical pressure gradient forces decrease or even reverse at cloud base, weakening the updraft above tornado. As the updraft weakens, the low-level flow advects the occlusion downdraft completely around the tornado, surrounding the vortex with downdraft and low-level divergence. Cut off from its source of positive vertical vorticity, the tornado then dissipates, leaving a broad low-level circulation behind.

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Louis J. Wicker and William C. Skamarock

Abstract

A forward-in-time splitting method for integrating the elastic equations is presented. A second-order Runge–Kutta time integrator (RK2) for the large-time-step integration is combined with the forward–backward scheme in a manner similar to the Klemp and Wilhelmson method. The new scheme produces fully second-order-accurate integrations for advection and gravity wave propagation. The RK2 scheme uses upwind discretizations for the advection terms and is easily combined with standard vertically semi-implicit techniques so as to improve computational efficiency when the grid aspect ratio becomes large. A stability analysis of the RK2 split-explicit scheme shows that it is stable for a wide range of advective and acoustic wave Courant numbers.

The RK2 time-split scheme is used in a full-physics nonhydrostatic compressible cloud model. The implicit damping properties associated with the RK2’s third-order horizontal differencing allows for a significant reduction in the value of horizontal filtering applied to the momentum and pressure fields, while qualitatively the solutions appear to be better resolved than solutions from a leapfrog model.

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Louis J. Wicker and William C. Skamarock

Abstract

An adaptive implicit–explicit vertical transport method is implemented in the Advanced Research version of the Weather Research and Forecasting Model (WRF-ARW), and improved integration efficiency is demonstrated for configurations employing convective-allowing horizontal and vertical resolutions. During the warm season over the continental United States, stable forecasts at convective-allowing resolutions are more challenging because localized regions of extreme thermodynamic instability generate large vertical velocities within thunderstorms that cause the integrations to become unstable because of violations of the Courant–Friedrichs–Lewy (CFL) condition for the explicit advection scheme used in WRF-ARW. The implicit–explicit vertical transport scheme removes the CFL instability but maintains accuracy for typical vertical velocities. Tests using this scheme show that the new scheme permits a time step that is 20%–25% percent larger, and it reduces the wall clock time by 10%–13% percent relative to a configuration similar to a current operational convection-allowing model while also producing more realistic updraft intensities within the most intense storms. Other approaches to maintain stability are either less efficient (e.g., reducing the time step) or significantly impact the solution accuracy (e.g., increasing the damping and/or reducing the latent heating, which severely limits the updraft magnitudes during the forecasts).

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