Abstract

The validity of the moist tangent linear model (TLM) derived from a time-dependent 1D Eulerian cloud model is investigated by comparing TLM solutions to differences between results from a nonlinear model identically perturbed. The TLM solutions are found to be highly sensitive to the amplitude of the applied perturbation, and thus the linear approximation is valid only for a specific range of perturbations. The TLM fails to describe the evolution of perturbations when the initial variation is given on a parameter in the vicinity of a nonlinear regime change, a result that has important implications for many cloud-scale processes. Uncertainty imposed on certain aspects of microphysical processes can have a significant influence on the behavior of the TLM solutions, and in some cases this behavior can be explained by the particular discretizations used to solve the equations. The frequency at which the nonlinear basic state is updated in the TLM can also have a profound effect on the TLM validity, though this sensitivity is in some cases modulated by the numerical scheme and model configuration used.

Abstract

In a previous paper, a three-dimensional numerical model was used to study the evolution of successive mesocyclones produced by a single supercell storm, that is, cyclic mesocyclogenesis. Not all supercells, simulated or observed, exhibit this behavior, and few previous papers in the literature mention it. As a first step toward identifying and understanding the conditions needed to produce cyclic redevelopments within supercell updrafts, this paper examines the effect on cyclic mesocyclogenesis of variations in model physical and computational parameters. Specified changes in grid spacing, numerical diffusion, microphysics options, and the coefficient of surface friction are found to alter, in some cases dramatically, the number and duration of simulated mesocyclone cycles.

For example, a decrease from 2.0 to 0.5 km in horizontal grid spacing transforms a nearly perfectly steady, noncycling supercell into one that exhibits three distinct mesocyclone cycles during the same time period. Decreasing the minimum vertical grid spacing at the ground tends to speed up the cycling process, while increasing it has the opposite effect. Ice microphysics is shown to cut short the initial cycling, while both simple surface friction and increased numerical diffusion tend to slow it down. Combining competing effects (i.e., ice microphysics with friction) tends to bring the simulation back to the evolution found in the control case. Explanations for these results are offered in the context of nonlinear feedbacks associated with the cycling process. In addition, the implications of these findings in our understanding of storm behavior as well as in the context of storm-scale numerical weather prediction are discussed.

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.

Abstract

In this study a nonhydrostatic 3D cloud model, along with an automatic differentiation tool, is used to investigate the sensitivity of a supercell storm to prescribed errors (perturbations) in the water vapor field. The evolution of individual storms is strongly influenced by these perturbations, though the specific impact depends upon their location in time and space. Generally, perturbations in the rain region above cloud base have the largest impact on storm dynamics, especially for subsequent storms, while perturbations in the ambient environment above cloud base influence mostly the main storm. Although perturbations in the subcloud layer have a relatively small impact on upper-level storm structure, they do impact the low-level structure, especially during the period immediately following insertion.

Sensitivities are also examined in the context of variational data assimilation and forecast error. For perturbations added inside the active storm, the cost function, which is prescribed to measure the discrepancy between forecast and observations for all variables over time and space, is found to be most sensitive to temperature, followed by pressure and water vapor. This implies that the quality of variational data assimilation can be affected by the inaccuracy of observing or retrieving those quantities. It is also noted that, at least for the case studied here, the pressure field has the largest influence on forecast error immediately after the errors are inserted, while the temperature field does so over a longer time period.

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.

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.

Abstract

In this first paper of a two-part series, a two-dimensional numerical model is developed and used to investigate the dynamics of thunderstorm outflows. By focusing only on the outflow and using essentially inviscid equations and high spatial resolution, we are able to explicitly represent important physical processes such as turbulent mixing. To simplify interpretation of the results, the model atmosphere used in all experiments is calm and dry adiabatic. This approach allows us to establish basic characteristics of modeled outflows in simple physical settings, and provides a foundation for future studies using more realistic environments.

All simulated outflows are initialized by prescribing a (controlled) horizontal flux of cold air into the model domain through a lateral boundary. In a series of sensitivity tests, we examine three parameters of the cold air source region: 1) the vertical temperature deficit profile, 2) the magnitude of the temperature deficit, and 3) the cold-air depth. By holding two of these quantities fixed while varying the third, we establish relationships among outflow speed, depth, and internal temperature deficit by comparing model results with laboratory density current experiments, inviscid fluid theory, and observations of thunderstorm outflows.

Our simulations indicate that the internal outflow head circulation is governed primarily by the outflow's vertical temperature distribution, and that this circulation plays a key role in determining the gust front propagation speed and outflow head depth. A pressure jump precedes the onset of cold air at the surface, and is shown to be dynamically induced by the collision of the outflow and environmental air masses at the gust front. In addition, the surface pressure distribution behind the outflow head is a consequence not only of hydrostatic effects, but also horizontal rotation aloft associated with a breaking head wave.

Turbulent mixing within the modeled outflows is associated with breaking Kelvin-Helmholtz billows which form at the shear interface atop the cold-air pool. These billows are qualitatively and quantitatively similar to turbulent eddies found in laboratory density currents, and are found to be sensitive to the magnitude of the computational smoothing as well as the grid resolution. Time-dependent air parcel trajectories are utilized to elucidate the kinematic structure of the simulated flow fields.

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.

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.