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John M. Peters

Abstract

This research develops simple diagnostic expressions for vertical acceleration dw/dt and vertical velocity w within updrafts that account for effective buoyancy and the dynamic pressure gradient force. Effective buoyancy is the statically forced component of the vertical gradient in the nonhydrostatic pressure field. The diagnostic expressions derived herein show that the effective buoyancy of an updraft is dependent on the magnitude of the temperature perturbation within an updraft relative to the air along the updraft’s immediate periphery (rather than relative to an arbitrary base state as in ), the updraft’s height-to-width aspect ratio, and the updraft’s slant relative to the vertical.

The diagnostic expressions are significantly improved over parcel theory (where pressure forces are ignored) in their portrayal of the vertical profile of w through updrafts from a cloud model simulation and accurately diagnosed the maximum vertical velocity w max within updrafts. The largest improvements to the diagnostic expressions over parcel theory resulted from their dependence on rather than . Whereas the actual w max within simulated updrafts was located approximately two-thirds to three-fourths of the distance between the updraft base and the updraft top, w max within profiles diagnosed by expressions was portrayed at the updraft top when the dynamic pressure force was ignored. A rudimentary theoretical representation of the dynamic pressure force in the diagnostic expressions improved their portrayal of the simulated w profile. These results augment the conceptual understanding of convective updrafts and provide avenues for improving the representation of vertical mass flux in cumulus parameterizations.

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John M. Peters and Sergey Kravtsov

Abstract

This study details properties of non-Gaussian regimes and state-dependent ensemble spreads of trajectories in a reduced phase space of an idealized three-level quasigeostrophic (QG3) dynamical model. Methodologically, experiments using two empirical stochastic models of the QG3 time series disentangle the causes of state-dependent persistence properties and nonuniform self-forecast skill of the QG3 model. One reduced model is a standard linear inverse model (LIM) forced by state-independent, additive noise. This model has a linear deterministic operator resulting in a phase-space velocity field with uniform divergence. The other, more general nonlinear stochastic model (NSM) includes a nonlinear propagator and is driven by state-dependent, multiplicative noise. This NSM is found to capture well the full QG3 model trajectory behavior in the reduced phase space, including the non-Gaussian features of the QG3 probability density function and phase-space distribution of the trajectory spreading rates.

Two versions of the NSM—one with a LIM-based drift tensor and QG3-derived multiplicative noise and another with the QG3-derived drift tensor and additive noise—allow the authors to determine relative contributions of the mean drift and multiplicative noise to non-Gaussian regimes and predictability in the QG3 model. In particular, while the regimes arise predominantly because of the nonlinear component of the mean phase-space tendencies, relative predictability of the regimes depends on both the phase-space structure of multiplicative noise and the degree of local convergence of mean phase-space tendencies.

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Hugh Morrison and John M. Peters

Abstract

An approximate analytic expression is derived for the ratio λ of the ascent rate of moist deep convective thermals and the maximum vertical velocity within them; λ is characterized as a function of two nondimensional buoyancy-dependent parameters y and h and is used to express the thermal ascent rate as a function of the buoyancy field. The parameter y characterizes the vertical distribution of buoyancy within the thermal, and h is the ratio of the vertically integrated buoyancy from the surface to the thermal top and the vertical integral of buoyancy within the thermal. Theoretical λ values are calculated using values of y and h obtained from idealized numerical simulations of ascending moist updrafts and compared to λ computed directly from the simulations. The theoretical values of 0.4–0.8 are in reasonable agreement with the simulated λ (correlation coefficient of 0.86). These values are notably larger than the from Hill’s (nonbuoyant) analytic spherical vortex, which has been used previously as a framework for understanding the dynamics of moist convective thermals. The relatively large values of λ are a result of net positive buoyancy within the upper part of thermals that opposes the downward-directed dynamic pressure gradient force below the thermal top. These results suggest that nonzero buoyancy within moist convective thermals, relative to their environment, fundamentally alters the relationship between the maximum vertical velocity and the thermal-top ascent rate compared to nonbuoyant vortices. Implications for convection parameterizations and interpretation of the forces contributing to thermal drag are discussed.

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John M. Peters, Walter Hannah, and Hugh Morrison

Abstract

Although it is well established that vertical wind shear helps to organize and maintain convective systems, there is a longstanding colloquial notion that it inhibits the development of deep convection. To investigate this idea, the vertical momentum budgets of sheared and unsheared moist thermals were compared in idealized cloud model simulations. Consistent with the idea of vertical wind shear inhibiting convective development, convection generally deepened at a slower rate in sheared simulations than in unsheared simulations, and the termination heights of thermals in sheared runs were correspondingly lower. These differences in deepening rates resulted from weaker vertical acceleration of thermals in the sheared compared to the unsheared runs. Downward-oriented dynamic pressure acceleration was enhanced by vertical wind shear, which was the primary reason for relatively weak upward acceleration of sheared thermals. This result contrasts with previous ideas that entrainment or buoyant perturbation pressure accelerations are the primary factors inhibiting the growth of sheared convection. A composite thermal analysis indicates that enhancement of dynamic pressure acceleration in the sheared runs is caused by asymmetric aerodynamic lift forces associated with shear-driven cross flow perpendicular to the direction of the thermals’ ascent. These results provide a plausible explanation for why convection is slower to deepen in sheared environments and why slanted convection tends to be weaker than upright convection in squall lines.

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John M. Peters and Russ S. Schumacher

Abstract

This research investigates the dynamics of a simulated training line/adjoining stratiform (TL/AS) mesoscale convective system (MCS), with composite atmospheric fields used as initial and lateral boundary conditions for the simulation.

An initial forward-propagating MCS developed within a region of elevated convective instability and low-level lifting associated with warm-air advection along the terminus of the low-level jet. The environmental conditions external to the MCS continued to provide lift, moisture, and instability to the western side of the forward-propagating MCS, and these conditions were initially responsible for backbuilding on the system’s western side. Most parcels that encountered the southwestern outflow boundary were lifted insufficiently far to reach their levels of free convection (LFCs), and their LFC heights were increased by latent heating above them. These parcels continued northeastward beyond the surface outflow boundary (OFB), were gradually lifted, and initiated convection 80–100 km beyond encountering the OFB. Eventually the surface cold pool became sufficiently deep so that gradual ascent of parcels with moisture and instability over the OFB began initiating new convection close to the OFB—this drove backbuilding during the later portion of the MCS lifetime. These results disentangle the relative contributions of large-scale environmental factors and storm-scale processes on the quasi-stationary behavior of the MCS and show that both contributed to upstream backbulding at different times during the MCS life cycle.

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John M. Peters and Russ S. Schumacher

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This study details the development and use of an idealized modeling framework to simulate a quasi-stationary heavy-rain-producing mesoscale convective system (MCS). A 36-h composite progression of atmospheric fields computed from 26 observed warm-season heavy-rain-producing training line/adjoining stratiform (TL/AS) MCSs was used as initial and lateral boundary conditions for a numerical simulation of this MCS archetype.

A realistic TL/AS MCS initiated and evolved within a simulated mesoscale environment that featured a low-level jet terminus, maximized low-level warm-air advection, and an elevated maximum in convective available potential energy. The first stage of MCS evolution featured an eastward-moving trailing-stratiform-type MCS that generated a surface cold pool. The initial system was followed by rearward off-boundary development, where a new line of convective cells simultaneously redeveloped north of the surface cold pool boundary. Backbuilding persisted on the western end of the new line, with individual convective cells training over a fixed geographic region. The final stage was characterized by a deepening and southward surge of the cold pool, accompanied by the weakening and slow southward movement of the training line. The low-level vertical wind shear profile favored kinematic lifting along the southeastern cold pool flank over the southwestern flank, potentially explaining why convection propagated with (did not propagate with) the former (latter) outflow boundaries.

The morphological features of the simulated MCS are common among observed cases and may, therefore, be generalizable. These results suggest that they are emergent from fundamental features of the large-scale environment, such as persistent regional low-level lifting, and with the vertical environmental wind profile characteristic to TL/AS systems.

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John M. Peters, Sergey Kravtsov, and Nicholas T. Schwartz

Abstract

Atmospheric regimes are midlatitude flow patterns that persist for periods of time exceeding a few days. Here, the authors analyzed the output of an idealized atmospheric model (QG3) to examine the relationship between regimes and predictability.

The regimes were defined as the regions of the QG3 phase subspace characterized by excess persistence probability relative to a benchmark linear empirical model (EMR) for geographically two-dimensional and then zonally averaged flow patterns. The regimes identified correspond to the opposite phases of the Arctic Oscillation (AO+ and AO) and to a more regional pattern reflecting the positive phase of the North Atlantic Oscillation (NAO+).

For all of these phase-space regime regions, the leading modes of the QG3 state vector decay to climatology at a slower rate than predicted by the EMR, which contributes to the maintenance of non-Gaussian regime anomalies. Predictable regimes are connected to “regime precursor” regions of the phase space, from which trajectories flow into regime regions following mean phase-space velocities. Packets of trajectories originating from these regions are characterized by anomalously low spreading rates due to a combination of low local stochastic diffusivity and convergence of the nonlinear component of mean phase-space velocities along the trajectory pathways. While unpredictable regimes do have precursor regions, trajectories emanating from these regions are characterized by relatively high spreading rates.

The predictable regimes AO+ and AO are insensitive to the metric used to identify the regimes; however, the unpredictable regime NAO+ in the 2D space is not directly associated with its zonal-metric counterpart.

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John M. Peters, Christopher J. Nowotarski, and Gretchen L. Mullendore

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This research investigates a hypothesis posed by previous authors, which argues that the helical nature of the flow in supercell updrafts makes them more resistant to entrainment than nonsupercellular updrafts because of the suppressed turbulence in purely helical flows. It was further supposed that this entrainment resistance contributes to the steadiness and longevity of supercell updrafts. A series of idealized large-eddy simulations were run to address this idea, wherein the deep-layer shear and hodograph shape were varied, resulting in supercells in the strongly sheared runs, nonsupercells in the weakly sheared runs, and variations in the percentage of streamwise vorticity in updrafts among runs. Fourier energy spectrum analyses show well-developed inertial subranges in all simulations, which suggests that the percentages of streamwise and crosswise vorticity have little effect on turbulence in convective environments. Additional analyses find little evidence of updraft-scale centrifugally stable flow within updrafts, which has also been hypothesized to limit horizontal mass flux across supercell updrafts. Results suggest that supercells do have smaller fractional entrainment rates than nonsupercells, but these differences are consistent with theoretical dependencies of entrainment on updraft width, and with supercells being wider than nonsupercells. Thus, while supercells do experience reduced fractional entrainment rates and entrainment-driven dilution, this advantage is primarily attributable to increased supercell updraft width relative to ordinary convection, and has little to do with updraft helicity and rotation.

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John M. Peters, Christopher J. Nowotarski, and Hugh Morrison

Abstract

Observed supercell updrafts consistently produce the fastest mid- to upper-tropospheric vertical velocities among all modes of convection. Two hypotheses for this feature are investigated. In the dynamic hypothesis, upward, largely rotationally driven pressure gradient accelerations enhance supercell updrafts relative to other forms of convection. In the thermodynamic hypothesis, supercell updrafts have more low-level inflow than ordinary updrafts because of the large vertical wind shear in supercell environments. This large inflow makes supercell updrafts wider than that of ordinary convection and less susceptible to the deleterious effects of entrainment-driven updraft core dilution on buoyancy. These hypotheses are tested using a large suite of idealized supercell simulations, wherein vertical shear, CAPE, and moisture are systematically varied. Consistent with the thermodynamic hypothesis, storms with the largest storm-relative flow have larger inflow, are wider, have larger buoyancy, and have faster updrafts. Analyses of the vertical momentum forcing along trajectories shows that maximum vertical velocities are often enhanced by dynamic pressure accelerations, but this enhancement is accompanied by larger downward buoyant pressure accelerations than in ordinary convection. Integrated buoyancy along parcel paths is therefore a strong constraint on maximum updraft speeds. Thus, through a combination of processes consistent with the dynamic and thermodynamic hypotheses, supercell updrafts are able to realize a larger percentage of CAPE than ordinary updrafts.

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Jake P. Mulholland, John M. Peters, and Hugh Morrison

Abstract

The influence of vertical wind shear on updraft entrainment in squall lines is not well understood. To address this knowledge gap, a suite of high-resolution idealized numerical model simulations of squall lines were run in various vertical wind shear (hereafter “shear”) environments to study the effects of shear on entrainment in deep convective updrafts. Low-level horizontal mass flux into the leading edge of the cold pool was strongest in the simulations with the strongest low-level shear. These simulations consequently displayed wider updrafts, less entrainment-driven dilution, and larger buoyancy than the simulations with comparatively weak low-level shear. An analysis of vertical accelerations along trajectories that passed through updrafts showed larger net accelerations from buoyancy in the simulations with stronger low-level shear, which demonstrates how less entrainment-driven dilution equated to stronger updrafts. The effects of upper-level shear on entrainment and updraft vertical velocities were generally less pronounced than the effects of low-level shear. We argue that in addition to the outflow boundary-shear interactions and their effect on updraft tilt established by previous authors, decreased entrainment-driven dilution is yet another beneficial effect of strong low-level shear on squall line updraft intensity.

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