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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

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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 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 and Russ S. Schumacher

Abstract

In this research, rotated principal component analysis was applied to the atmospheric fields associated with a large sample of heavy-rain-producing mesoscale convective systems (MCSs). Cluster analysis in the subspace defined by the leading two resulting principal components revealed two subtypes with distinct synoptic and mesoscale characteristics, which are referred to as warm-season-type and synoptic-type events, respectively. Subsequent composite analysis showed that both subtypes typically occurred on the cool side of a quasi-stationary, low-level frontal boundary, within a region of locally maximized low-level convergence and warm advection. Synoptic-type events, which tended to exhibit greater horizontal extent than warm-season-type events, typically occurred downstream of a progressive upper-level trough, along a low-level potential temperature gradient with the warmest air to the south and southeast. Warm-season-type events, on the other hand, occurred within the right-entrance region of a minimally to anticyclonically curved upper-level jet streak, along a low-level potential temperature gradient with the warmest low-level air to the southwest. Synoptic-scale forcing for ascent was stronger in synoptic-type events, while low-level moisture was greater in warm-season-type events. Warm-season-type events were frequently preceded by the passage of a trailing-stratiform- (TS) type MCS, whereas synoptic-type events often occurred prior to the passage of a TS-type system. Analysis of the composite vertical wind profiles at the event location suggests that quasi-stationary behavior in warm-season events predominantly resulted from upstream propagation that nearly canceled advection by the mean steering flow, whereas in the case of synoptic-type events training predominantly resulted from system motion that paralleled a front.

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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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Russ S. Schumacher and John M. Peters

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This study investigates the influences of low-level atmospheric water vapor on the precipitation produced by simulated warm-season midlatitude mesoscale convective systems (MCSs). In a series of semi-idealized numerical model experiments using initial conditions gleaned from composite environments from observed cases, small increases in moisture were applied to the model initial conditions over a layer either 600 m or 1 km deep. The precipitation produced by the MCS increased with larger moisture perturbations as expected, but the rainfall changes were disproportionate to the magnitude of the moisture perturbations. The experiment with the largest perturbation had a water vapor mixing ratio increase of approximately 2 g kg−1 over the lowest 1 km, corresponding to a 3.4% increase in vertically integrated water vapor, and the area-integrated MCS precipitation in this experiment increased by nearly 60% over the control. The locations of the heaviest rainfall also changed in response to differences in the strength and depth of the convectively generated cold pool. The MCSs in environments with larger initial moisture perturbations developed stronger cold pools, and the convection remained close to the outflow boundary, whereas the convective line was displaced farther behind the outflow boundary in the control and the simulations with smaller moisture perturbations. The high sensitivity of both the amount and location of MCS rainfall to small changes in low-level moisture demonstrates how small moisture errors in numerical weather prediction models may lead to large errors in their forecasts of MCS placement and behavior.

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John M. Peters and Paul J. Roebber

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This study examines the degree to which the downscale cascade of information from synoptic-scale motions constrains error growth in simulations of a particular type of heavy-rain-producing mesoscale convective system known as training lines. A total of 21 cases of training convection over a 7-yr period from 2000 to 2006 that produced extreme rainfall were dynamically downscaled from reanalysis data using a high-resolution convection-permitting configuration of the Weather Research and Forecasting Model. The NCEP/Department of Energy (DOE)-II and Interim ECMWF Re-Analysis (ERA-Interim), representing lower- and higher-resolution datasets, respectively, were used for this purpose. In most cases the model simulations were able to reproduce qualitative aspects of observed storm structure, including subjectively classified mesoscale convective system archetype and training characteristics, despite the absence of mesoscale features in the reanalysis datasets used to provide initial conditions and lateral boundary conditions to the simulations. Furthermore, models were capable of predicting that a heavy-precipitation event would occur in nearly every case. Increasing the horizontal resolution of the reanalysis dataset used for initial conditions and lateral boundary conditions did not result in measurable improvement in simulated precipitation placement skill relative to observations. A quantitative relationship between a measure of synoptic-scale uncertainty in the atmospheric state and error in the model forecast accumulated precipitation was established, with larger synoptic-scale uncertainty tending to be associated with larger model error. This result suggests that synoptic-scale uncertainty in numerical weather prediction model simulations partially controls error in the placement of heavy convective precipitation.

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John M. Peters, Walter Hannah, and Hugh Morrison

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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

In this research, a numerical simulation of an observed training line/adjoining stratiform (TL/AS)-type mesoscale convective system (MCS) was used to investigate processes leading to upwind propagation of convection and quasi-stationary behavior. The studied event produced damaging flash flooding near Dubuque, Iowa, on the morning of 28 July 2011.

The simulated convective system well emulated characteristics of the observed system and produced comparable rainfall totals. In the simulation, there were two cold pool–driven convective surges that exited the region where heavy rainfall was produced. Low-level unstable flow, which was initially convectively inhibited, overrode the surface cold pool subsequent to these convective surges, was gradually lifted to the point of saturation, and reignited deep convection. Mechanisms for upstream lifting included persistent large-scale warm air advection, displacement of parcels over the surface cold pool, and an upstream mesolow that formed between 0500 and 1000 UTC.

Convection tended to propagate with the movement of the southeast portion of the outflow boundary, but did not propagate with the southwest outflow boundary. This was explained by the vertical wind shear profile over the depth of the cold pool being favorable (unfavorable) for initiation of new convection along the southeast (southwest) cold pool flank.

A combination of a southward-oriented pressure gradient force in the cold pool and upward transport of opposing southerly flow away from the boundary layer moved the outflow boundary southward. Upward transport of southerly momentum by convection along the southward-moving outflow boundary, along with convectively induced southward pressure gradient forces cut off southerly inflow to the MCS, which temporarily disrupted backbuilding.

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