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Manuela Lehner
,
Richard Rotunno
, and
C. David Whiteman

Abstract

Idealized two-dimensional model simulations are performed to study the frequent nocturnal occurrence of downslope-windstorm-type flows in Arizona’s Meteor Crater. The model topography is a simplified representation of the Meteor Crater and its surroundings, with an approximately 1° mesoscale slope upstream and downstream of the crater basin. A strong surface-based inversion and a katabatic flow develop above the mesoscale slope as a result of radiational cooling. The temperature and flow profiles are evaluated against observations over low-angle slopes from two field campaigns, showing that the model’s turbulence parameterization has a strong impact on the near-surface conditions. The interaction of the katabatic flow with the basin topography leads to the formation of waves and hydraulic jumps over the basin. The simplified two-dimensional simulations show good qualitative agreement with observations of downslope-windstorm-type flows from the Meteor Crater. The sensitivity of the flow solution over the basin to basin depth, basin width, and background wind speed is investigated. The resulting flow regimes include a sweeping of the basin atmosphere, a wake over the upstream crater sidewall, waves over the basin with one or two wave crests, and a hydraulic jump. The regimes are discussed in the context of stratified flow over mountains.

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David J. Muraki
,
Richard Rotunno
, and
Hugh Morrison

Abstract

A holepunch cloud is a curious phenomenon where a disturbance in a thin cloud layer initiates an expanding circular hole of clear air. Usually triggered by the passage of aircraft, observations of these holes in clouds date back to the earliest days of aviation, but only recently has a holepunch cloud been simulated within a full-physics numerical model. These computations confirm that ice crystal growth through the Wegener–Bergeron–Findeisen process creates a small cloud-free region whose subsequent outward spread defines the holepunch. The mechanics behind this continued expansion, however, has yet to be definitively identified. In this article, the motion of the cloud edge is explained as a propagating gravity wave front. To support this idea, a hierarchy of three idealizations is analyzed: a full-physics numerical model, a fluid mechanical model with simplified moisture effects, and a conservation law analysis for front motion. The essence of the holepunch cloud is established to be a moist air layer that is unsaturated (clear) and weakly stratified within the hole but saturated (cloudy) and moist neutral outside of it. The cloud edge thus represents a barrier to the outward propagation of gravity waves within the clear air—the result of this collision is a wave front whose velocity determines the growth rate of the hole.

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Ke Peng
,
Richard Rotunno
, and
George H. Bryan

Abstract

Axisymmetric and three-dimensional simulations are used to evaluate the theory of tropical cyclone (TC) intensification proposed by K. A. Emanuel, which is based on gradient wind balance and moist-neutral ascent along angular momentum (M) surfaces. According to the numerical model results, the intensification of the TC can be divided into two periods, phase I and phase II. During phase I, the TC intensifies while the M and saturation entropy (s*) surfaces evolve from nearly orthogonal to almost congruent. During phase II, the M and s* surfaces in the eyewall and outflow are congruent as the TC intensifies, which is consistent with Emanuel’s study. Therefore, the condition of moist slantwise neutrality in Emanuel’s study is sufficiently satisfied throughout the intensification in phase II. It is also found that the sensitivity of the intensification rates to the surface exchange coefficient for entropy C k matches Emanuel’s theoretical result, which is that the intensification rate is proportional to C k . However, the intensification rate varies in proportion to the surface exchange coefficient for momentum C d , while the Emanuel model growth rate is insensitive to C d . Furthermore, although the tendency diagnosed by Emanuel is qualitatively similar to the numerical model result during phase II, it is not quantitatively similar. The present analysis finds the inclusion of non–gradient wind effects in the theoretical framework of Emanuel’s study produces an intensification rate that is quantitatively similar to the numerical model results. The neglect of non–gradient wind effects in Emanuel’s study may be the reason for the different dependence of its intensification rate on C d compared to that of the numerical model. Other aspects of Emanuel’s study in the context of recent research on TC intensification are discussed.

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Raphaël Rousseau-Rizzi
,
Richard Rotunno
, and
George Bryan

Abstract

Theories for the maximum intensity of tropical cyclones (TCs) assume steady state. However, many TCs in simulations that run for tens of days tend to decay considerably from an early steady state in the core (CS), before stabilizing at a final equilibrium steady state (ES). This decay raises the question of whether CS or ES should be used as a comparison to the maximum intensity theories. To understand the differences between CS and ES, we investigate why TCs decay and attempt to simulate a TC with steady intensity over a 100-day period. Using the axisymmetric Cloud Model 1, we find that the CS TC decay is due to a large-scale drying of the subsidence region. Such a drying is very pronounced in axisymmetric models because shallow-to-midlevel convection is not represented accurately enough to moisten air in the subsidence region. Simulations with an added moisture relaxation term in the subsidence region and dry cyclones without any moisture both remain in a steady state for over 100 days, without decaying appreciably after the spinup period. These simulations indicate that the decay in TC simulations is due to the irreversible removal of precipitation combined with the lack of a moistening mechanism in the subsidence region. Once either of these conditions is removed, the decay disappears and the CS and ES intensities become essentially equivalent.

Open access
Chris Snyder
,
William C. Skamarock
, and
Richard Rotunno

Abstract

In the course of adapting a nonhydrostatic cloud model [or primitive-equation model (PE)] for simulations of large-scale baroclinic waves, we have encountered systematic discrepancies between the PE solutions and those of the semigeostrophic (SG) equations. Direct comparisons using identical, uniform potential vorticity jets show that 1) the linear modes of the PE have distinctively different structure than the SG modes; 2) at finite amplitude, the PE pressure field develops lows that are deeper, and highs that are weaker, than in the SG solution; and 3) the nonlinear PE wave produces a characteristic “cyclonic wrapping” of the temperature contours on both horizontal boundaries and has an associated “bent-back” frontal structure at the surface, while in the SG solutions (for this particular basic state jet) there is an equal tendency to pull temperature contours anticyclonically around highs and cyclonically around lows. An analysis of the vorticity and potential vorticity equations for small Rossby number reveals that the SG model errs in its treatment of terms involving the ageostrophic vorticity. Simulations based on an equation set that includes the leading-order dynamical contributions of the ageostrophic vorticity agree more closely with the PE simulations.

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Richard Rotunno
,
William C. Skamarock
, and
Chris Snyder

Abstract

A comparative analysis of simulations of baroclinic waves with and without surface drag is presented, with particular reference to surface features. As in recent studies, the present simulations show that, compared to simulations with no drag, those with surface drag are less inclined to develop a secluded warm sector, and that drag weakens the warm front while the cold front remains strong. The authors demonstrate that analogous effects occur when Ekman pumping is used in nonlinear quasigeostrophic numerical simulations of unstable baroclinic waves in a channel. However, since the quasigeostrophic model produces symmetric highs and lows in the unstable baroclinic wave, the cold and warm fronts are therefore also symmetric and hence equally affected by the Ekman pumping. The different effect that friction has on the warm front with respect to the cold front in the primitive-equation simulations is fundamentally related to the tendency for the lows to be strong and narrow and the highs weak and broad, and for the warm front to form just north of, and extend eastward from, the low, while the cold front extends between the high and the low. The authors’ thesis is that the Ekman pumping associated with the low, at the location where the warm front would form in the absence of surface friction, acts to resist the formation of the warm front, while the cold front, positioned between the high and the low where Ekman pumping associated with the baroclinic wave is weak, is therefore relatively unaffected.

Given the weakness of Ekman pumping associated with the baroclinic wave in the vicinity of the incipient cold front, the present simulations indicate that cold frontogenesis occurs in the drag case in much the same way as in the no-drag case. Present analysis shows that the horizontal advection creating the cold front is a combination of geostrophic and ageostrophic effects. A portion of the ageostrophic frontogenesis is a response to geostrophic frontogenesis, as in the case without surface drag; however with surface drag, a significant portion of the cross-front ageostrophic flow is due to the Ekman layer associated with the front itself.

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Richard Rotunno
,
William C. Skamarock
, and
Chris Snyder

Abstract

Using a primitive equation (PE) model, we revisit two canonical flows that were previously studied using a semigeostrophic equation (SG) model. In a previous paper, the authors showed that the PE and the SG models can have significantly different versions of the large-scale dynamics—here they report on the implications of this difference for frontogenesis. The program for the study of frontogenesis developed by B. J. Hoskins and collaborators is followed to show how, in the PE version of the canonical cases, the surface warm front develops before the cold front, and why the upper-level front is a long, nearly continuous feature going from ridge to trough. The frontogenesis experienced by an air parcel is computed following the parcel to illustrate better the mechanisms involved. As the present calculations are carried out longer than most previous ones, the relation of the upper frontogenesis to the formation of the upper-level “cutoff” cyclone is also examined. Trajectory and three-dimensional graphical analyses show, with respect to the latter, the extreme distortions of the isentropic surfaces and mixing-induced variations in the potential vorticity field.

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Chris Snyder
,
William C. Skamarock
, and
Richard Rotunno

Abstract

A nonhydrostatic numerical model is used to simulate two-dimensional frontogenesis forced by either horizontal deformation or shear. Both inviscid frontogenesis prior to frontal collapse and frontogenesis with horizontal diffusion following collapse are considered. The numerical solutions generally agree well with semigeostrophic (SG) theory, though differences can be substantial for intense fronts. Certain deviations from SG that have been previously discussed in the literature area, upon closer examination, associated with spurious gravity waves produced by inadequate resolution or by the initialization of the numerical model. Even when spurious waves are eliminated, however, significant deviations from SG still exist: gravity waves are emitted by the frontogenesis when the cross-front scale becomes sufficiently small, and higher-order corrections to SG may also be present. In the postcollapse solutions (where they are most prominent), the emitted waves are stationary with respect to the front and lead to a band of increased low-level ascent just ahead of the surface front. It is suggested here that, when small, the deviations from SG arise as the linear forced response to the cross-front accelerations neglected by SG.

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Monika Feldmann
,
Richard Rotunno
,
Urs Germann
, and
Alexis Berne

Abstract

This study investigates the effects of lakes in mountainous terrain on the evolution of supercell thunderstorms. With a newly developed radar-based, mesocyclone-detection algorithm, a recent study has characterized the occurrence and evolution of supercell thunderstorms in the Swiss Alpine region. That study highlights the influence of orography on both storm intensity and occurrence frequency. To disentangle the different influential factors, an idealized modeling framework is established here using the mesoscale model CM1. The modeling scenarios are based on a high-CAPE environment with unidirectional shear, where a warm bubble serves to initiate the convection. Mimicking the environment of the southern Prealps in central Europe, scenarios with a high mountain ridge, valleys, and lakes are explored. The effect on the supercells of the slopes, high-altitude terrain, and moisture sources emphasizes the highly localized nature of terrain effects, leading to a heterogeneous intensity life cycle with transitory enhancement and weakening of the supercell. The dynamic and thermodynamic impact of mountain valleys with lakes increases the range of atmospheric conditions that supports supercellular development through horizontal vorticity production, increased storm relative helicity, and higher moisture content. This influence results in a systematic location dependence of the frequency, intensity, and lifetime of supercells, as also found in observations.

Open access
Heather Dawn Reeves
,
Yuh-Lang Lin
, and
Richard Rotunno

Abstract

The aim of this research is to investigate the causes for an isolated maximum in precipitation that is typically found along the northern half of the Sierra Nevada mountains of California, in the vicinity of Plumas National Forest (PNF), during moderate to heavy precipitation events. Particular attention was paid to the role various mesoscale (i.e., <200 km) terrain features may have played in localizing the precipitation at PNF. Numerical simulations and sensitivity experiments for two cases of heavy precipitation at PNF reveal that the extent to which terrain acts to focus precipitation is case sensitive. In the first case, the upstream flow was characterized by a strong horizontal gradient in wind speed and moisture. This gradient led to differential deflection of airstreams incident to the range and, consequently, localized convergence and enhanced rain rates at PNF. This localized enhancement occurred regardless of whether any terrain variations were present in the simulations or not. The second case was characterized by more a horizontally uniform upstream flow and showed a much stronger sensitivity to terrain variations, in particular, short- and long-wavelength undulations along the leading (west) edge of the Sierra Nevada range. When these undulations were removed, no localized maxima in precipitation occurred.

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