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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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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

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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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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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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Robert B. Wilhelmson and Louis J. Wicker

Abstract

No Abstract available.

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Matthew S. Gilmore and Louis J. Wicker

Abstract

Radar, cloud-to-ground (CG) lightning characteristics, and storm reports were documented for 20 long-lived supercell thunderstorms that occurred during a 6-h period in the west Texas Panhandle on 2–3 June 1995. These thunderstorms occurred in proximity to a preexisting mesoscale outflow boundary.

Storms that remained on the warm side of the mesoscale outflow boundary and storms that formed directly on the boundary tended to produce weaker low-level rotation, lower maximum heights for the 40-dBZ echo top, and had the largest negative CG flash rates. The largest negative flash rate was produced as each storm was gradually weakening. In contrast, out of 11 boundary-crossing storms, several important radar-based measurands increased unambiguously after storms crossed the boundary: 40-dBZ echo-top height in 5 cases, radar reflectivity above the environmental freezing level in 6 cases, and low-level mesocyclone strength in 9 cases. Trends of the first two measurands were ambiguous for 4 of 11 cases affected by a ±15 min estimated boundary-position uncertainty. Five out of 11 storms dramatically increased their positive flash rate within 60 min after crossing the outflow boundary. These large positive flash rates were associated with descending reflectivity cores that were larger in magnitude and areal extent compared to other storms in this study.

The local mesoscale environment and its horizontal variations of 0–3-km vertical wind profile, CAPE below the in-cloud freezing level, and boundary layer mixing ratio appeared to greatly influence storm structure and evolution. The observed environmental variations are hypothesized to support changes in charge structure that might lead to the observed changes in flash rate and polarity.

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Steven E. Peckham and Louis J. Wicker

Abstract

The effects of topography, wind shear, and zonal wind speed on dryline formation and evolution are investigated using a three-dimensional nonhydrostatic mesoscale model. Rather than conduct a case study a parameter study was performed to examine factors that control the depth and strength of the dryline circulation.

This study reveals that the potential for convective storm formation is greatest in those environments in which the cross-dryline flow is weak above the dryline location. This results in boundary layer flow nearly parallel to the north–south-oriented dryline boundary. Under these conditions, the subsiding westerly flow and elevated residual layer formation do not strengthen the capping inversion above the eastern convective boundary layer. In addition, moist air parcels from near the surface are able to reside within the dryline updraft resulting in higher midtropospheric relative humidity subsequently increasing the likelihood of convective storm initiation.

As downslope westerly flow strengthens above the dryline subsidence warming increases and the capping inversion east of the boundary lowers. In response to the subsidence pressure falls occur east of the dryline. Consequently, the east–west horizontal pressure gradient weakens reducing the convergence and frontogenetical circulation along the dryline. The depth of the vertical circulation decreases and air parcels resident within the dryline updraft are detrained at lower altitudes.

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Ryan A. Sobash and Louis J. Wicker

Abstract

Storm-scale ensemble Kalman filter (EnKF) studies routinely use methods to accelerate the spinup of convective structures when assimilating convective-scale radar observations. This typically involves adding coherent perturbations into analyses at regular intervals in regions where radar observations indicate convection is ongoing. Significant uncertainty remains as to the most effective use of these perturbations, including appropriate perturbation magnitudes, spatial scales, fields, and smoothing kernels, as well as flexible strategies that can be applied across a spectrum of convective events with negligible a priori tuning. Here, several idealized experiments were performed to elucidate the impact and sensitivity of adding coherent perturbations into storm-scale analyses of convection. Through the use of toy experiments, it is demonstrated that various factors exhibit substantial influence on the postsmoothed perturbation magnitudes, making tuning challenging. Several OSSEs were performed to document the impact of these perturbations on the analyses, particularly thermodynamic analyses within convection. The repeated addition of coherent perturbations produced temperature and moisture biases that are most pronounced in analyses of the surface cold pool and aloft near the tropopause, and eventually lead to biases in the dynamic fields. In an attempt to reduce these biases and make the noise procedure more adaptive, reflectivity innovations were used to restrict the addition of noise to areas where these innovations are large. This produced analyses with reduced thermodynamic biases and RMSE values comparable to the best-performing experiment where the noise magnitudes were manually adjusted. The impact of these findings on previous and future convective-scale EnKF analyses and forecasts are discussed.

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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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