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Richard Rotunno
and
Joseph B. Klemp

Abstract

In the present investigation we propose a simple theory to explain how a veering environmental wind shear vector can cause an initially symmetric updraft to grow preferentially to the right of the shear vector and acquire cyclonic rotation. The explanation offered is based on linear theory which predicts that interaction of the mean shear with the updraft produces favorable vertical pressure gradients along its right flank. To asses the validity of linear theory for large-amplitude updrafts, the three-dimensional, shallow, anelastic equations are numerically integrated using a simple parameterization for latent heating within a cloud and the linear and nonlinear forcing terms are separately analyzed. These results suggest that although the nonlinear effects strongly promote splitting of the updraft, the linear forcing remains the dominant factor in preferentially enhancing updraft growth on the right flank. We believe this differential forcing is a major contributor to the observed predominance of cyclonically rotating, right moving storms.

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Chanh Kieu
,
Richard Rotunno
, and
Quan Wang

Abstract

This study examines the role of frictional feedback in the atmospheric boundary layer during tropical cyclone (TC) development. Using a reduced model of TC dynamics, it is shown that a feedback between frictional convergence and convective heating in the absence of slantwise moist neutrality is capable of producing a stable maximum-intensity limit, even without surface fluxes. However, the efficiency of this frictional-convergence feedback depends crucially on how effectively boundary layer moisture convergence is converted into convective heating, which decreases rapidly as the TC inner core approaches a state of moist neutrality. This decreasing efficiency during TC intensification explains why the effect of the frictional-convergence feedback is generally small compared to that of the wind-induced surface heat exchange (WISHE) feedback under the strict conditions of slantwise moist neutrality. Examination of the reduced TC model with a constant-heating source reveals that TC intensification is not peculiar to any specific feedback mechanism but, rather, is a direct consequence of the inward advection of absolute angular momentum, regardless of feedback mechanism.

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Dandan Tao
,
Richard Rotunno
, and
Michael Bell

Abstract

This study revisits the axisymmetric tropical cyclone (TC) theory from D. K. Lilly’s unpublished manuscript (Lilly model) and compares it to axisymmetric TC simulations from a nonhydrostatic cloud model. Analytic solutions of the Lilly model are presented through simplifying assumptions. Sensitivity experiments varying the sea surface, boundary layer and tropopause temperatures, and the absolute angular momentum (M) at some outer radius in the Lilly model show that these variations influence the radial structure of the tangential wind profile V(r) at the boundary layer top. However, these parameter variations have little effect on the inner-core normalized tangential wind, V(r/r m )/V m , where V m is the maximum tangential wind at radius r m . The outflow temperature T as a function of M (or saturation entropy s*) is found to be the only input that changes the normalized tangential wind radial structure in the Lilly model. In contrast with the original assumption of the Lilly model that T (s*) is determined by the environment, it is argued here that T (s*) is determined by the TC interior flow under the environmental constraint of the tropopause height. The present study shows that the inner-core tangential wind radial structure from the Lilly model generally agrees well with nonhydrostatic cloud model simulations except in the eyewall region where the Lilly model tends to underestimate the tangential winds due to its balanced-dynamics assumptions. The wind structure in temperature–radius coordinates from the Lilly model can largely reproduce the numerical simulation results. Though the Lilly model is based on a number of simplifying assumptions, this paper shows its utility in understanding steady-state TC intensity and structure.

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Richard Rotunno
,
Chris Snyder
, and
Falko Judt

Abstract

Atmospheric predictability is measured by the average difference (or “error”) within an ensemble of forecasts starting from slightly different initial conditions. The spatial scale of the error field is a fundamental quantity; for meteorological applications, the error field typically varies with latitude and longitude and so requires a two-dimensional (2D) spectral analysis. Statistical predictability theory is based on the theory of homogeneous, isotropic turbulence, in which spectra are circularly symmetric in 2D wavenumber space. One takes advantage of this circular symmetry to reduce 2D spectra to one-dimensional (1D) spectra by integrating around a circle in wavenumber polar coordinates. In recent studies it has become common to reduce 2D error spectra to 1D by computing spectra in the zonal direction and then averaging the results over latitude. It is shown here that such 1D error spectra are generically fairly constant across the low wavenumbers as the amplitude of an error spectrum grows with time and therefore the error spectrum is said grow “up-amplitude.” In contrast computing 1D error spectra in a manner consistent with statistical predictability theory gives spectra that are peaked at intermediate wavenumbers. In certain cases, this peak wavenumber is decreasing with time as the error at that wavenumber increases and therefore the error spectrum is said to grow “upscale.” We show through theory, simple examples, and global predictability experiments that comparisons of model error spectra with the predictions of statistical predictability theory are only justified when using a theory-consistent method to transform a 2D error field to a 1D spectrum.

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Agata Moscatello
,
Mario Marcello Miglietta
, and
Richard Rotunno

Abstract

The presence of a subsynoptic-scale vortex over the Mediterranean Sea in southeastern Italy on 26 September 2006 has been recently documented by the authors. The transit of the cyclone over land allowed an accurate diagnosis of the structure of the vortex, based on radar and surface station data, showing that the cyclone had features similar to those observed in tropical cyclones. To investigate the cyclone in greater depth, numerical simulations have been performed using the Weather Research and Forecasting (WRF) model, set up with two domains, in a two-way-nested configuration. Model simulations are able to properly capture the timing and intensity of the small-scale cyclone. Moreover, the present simulated cyclone agrees with the observational analysis of this case, identifying in this small-scale depression the typical characteristics of a Mediterranean tropical-like cyclone. An analysis of the mechanisms responsible for the genesis, development, and maintenance of the cyclone has also been performed. Sensitivity experiments show that cyclogenesis on the lee side of the Atlas Mountains is responsible for the generation of the cyclone. Surface sensible and latent heat fluxes become important during the subsequent phase of development in which the lee-vortex shallow depression evolved as it moved toward the south of Sicily. During this phase, the latent heating, associated with convective motions triggered by a cold front entering the central Mediterranean area, was important for the intensification and contraction of the horizontal scale of the vortex. The small-scale cyclone subsequently deepened as it moved over the Ionian Sea and then maintained its intensity during its later transit over the Adriatic Sea; in this later stage, latent heat release continued to play a major role in amplifying and maintaining the vortex, while the importance of the surface fluxes diminished.

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Mario Marcello Miglietta
,
Jordi Mazon
, and
Richard Rotunno

Abstract

On 28 November 2012, a multivortex EF3 tornado occurred in southeastern Italy causing one fatality and estimated damage of 60 million euros. At approximately 1050 LT (0950 UTC), this tornado, which initially formed in association with a supercell thunderstorm over the Ionian Sea, moved inland. The environment where the tornadic supercell developed was characterized by large vertical wind shear in the lowest 1 km of the atmosphere and moderate conditional instability. Mesoscale-model numerical simulations show that it is possible to produce a simulated supercell thunderstorm with a track, change in intensity, and evolution similar to the actual one that spawned the tornado in Taranto, southern Italy. The genesis of the simulated supercell is due to a combination of mesoscale meteorological features: warm low-level air advected toward the Ionian Sea, combined with midlevel cooling due to an approaching trough, increased the potential instability; the intense vertical shear favored the possibility of supercell development; and boundary layer rolls over the Ionian Sea moved in phase with the cells produced by the orography of Calabria to supply ascent, moisture, and heat to the convection. An unusual feature of the present case is the central role of the orography, which was verified in a sensitivity experiment where it was reduced by 80%.

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Richard Rotunno
,
David J. Muraki
, and
Chris Snyder

Abstract

Quasigeostrophic theory is an approximation of the primitive equations in which the dynamics of geostrophically balanced motions are described by the advection of potential vorticity. Quasigeostrophic theory also represents a leading-order theory in the sense that it is derivable from the primitive equations in the asymptotic limit of zero Rossby number. Building upon quasigeostrophic theory, and the centrality of potential vorticity, the authors have recently developed a systematic asymptotic framework from which balanced, next-order corrections in Rossby number can be obtained. The approach is illustrated here through numerical solutions pertaining to unstable waves on baroclinic jets. The numerical solutions using the full primitive equations compare well with numerical solutions to our equations with accuracy one order beyond quasigeostrophic theory; in particular, the inherent asymmetry between cyclones and anticyclones is captured. Explanations of the latter and the associated asymmetry of the warm and cold fronts are given using simple extensions of quasigeostrophic– potential-vorticity thinking to next order.

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David J. Muraki
,
Chris Snyder
, and
Richard Rotunno

Abstract

Quasigeostrophic theory is an approximation of the primitive equations in which the dynamics of geostrophically balanced motions are described by the advection of potential vorticity. Quasigeostrophy also represents a leading-order theory in the sense that it is derivable from the full primitive equations in the asymptotic limit of zero Rossby number. Building upon quasigeostrophy, and the centrality of potential vorticity, a systematic asymptotic framework is developed from which balanced, next-order corrections in Rossby number are obtained. The simplicity of the approach is illustrated by explicit construction of the next-order corrections to a finite-amplitude Eady edge wave.

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Rebecca E. Morss
,
Chris Snyder
, and
Richard Rotunno

Abstract

Results from homogeneous, isotropic turbulence suggest that predictability behavior is linked to the slope of a flow’s kinetic energy spectrum. Such a link has potential implications for the predictability behavior of atmospheric models. This article investigates these topics in an intermediate context: a multilevel quasigeostrophic model with a jet and temperature perturbations at the upper surface (a surrogate tropopause). Spectra and perturbation growth behavior are examined at three model resolutions. The results augment previous studies of spectra and predictability in quasigeostrophic models, and they provide insight that can help interpret results from more complex models. At the highest resolution tested, the slope of the kinetic energy spectrum is approximately at the upper surface but −3 or steeper at all but the uppermost interior model levels. Consistent with this, the model’s predictability behavior exhibits key features expected for flow with a shallower than −3 slope. At the highest resolution, upper-surface perturbation spectra peak below the energy-containing scales, and the error growth rate decreases as small scales saturate. In addition, as model resolution is increased and smaller scales are resolved, the peak of the upper-surface perturbation spectra shifts to smaller scales and the error growth rate increases. The implications for potential predictive improvements are not as severe, however, as in the standard picture of flows exhibiting a finite predictability limit. At the highest resolution, the model also exhibits periods of much faster-than-average perturbation growth that are associated with faster growth at smaller scales, suggesting predictability behavior that varies with time.

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Y. Qiang Sun
,
Richard Rotunno
, and
Fuqing Zhang

Abstract

With high-resolution mesoscale model simulations, the authors have confirmed a recent study demonstrating that convective systems, triggered in a horizontally homogeneous environment, are able to generate a background mesoscale kinetic energy spectrum with a slope close to −5/3, which is the observed value for the kinetic energy spectrum at mesoscales. This shallow slope can be identified at almost all height levels from the lower troposphere to the lower stratosphere in the simulations, implying a strong connection between different vertical levels. The present study also computes the spectral kinetic energy budget for these simulations to further analyze the processes associated with the creation of the spectrum. The buoyancy production generated by moist convection, while mainly injecting energy in the upper troposphere at small scales, could also contribute at larger scales, possibly as a result of the organization of convective cells into mesoscale convective systems. This latter injected energy is then transported by energy fluxes (due to gravity waves and/or convection) both upward and downward. Nonlinear interactions, associated with the velocity advection term, finally help build the approximate −5/3 slope through upscale and/or downscale propagation at all levels.

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