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Yu Du
and
Richard Rotunno

Abstract

A simple analytical model including both diurnal thermal forcing over sloping terrain (the “Holton” mechanism) and diurnally varying boundary layer friction (the “Blackadar” mechanism) is developed to account for the observed amplitude and phase of the low-level jet (LLJ) over the Great Plains and to understand better the role of each mechanism. The present model indicates that, for the pure Holton mechanism (time-independent friction coefficient), the maximum southerly wind speed occurs (depending on the assumed friction coefficient) between sunset and midnight local standard time, which is earlier than the observed after-midnight maximum. For the pure Blackadar mechanism (time-independent thermal forcing), the present model shows that generally occurs later (closer to sunrise) than observed and has a strong latitudinal dependence. For both mechanisms combined, the present model indicates that occurs near to the observed time, which lies between the time obtained in the pure Holton mechanism and the time obtained in the pure Blackadar mechanism; furthermore, is larger (and closer to that observed) than in each one considered individually. The amplitude and phase of the LLJ as a function of latitude can be obtained by the combined model by allowing for the observed latitude-dependent mean and diurnally varying thermal forcing.

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Juerg Schmidli
and
Richard Rotunno

Abstract

In a recent study, the authors investigated the mechanisms leading to the formation of diurnal along-valley winds in a valley formed by two isolated mountain ridges on a horizontal plain. The main focus was on the relation between the valley heat budget and the valley–plain pressure difference. The present work investigates the influence of the valley surroundings on the evolution of the valley winds. Three valley–plain configurations with identical valley volumes are studied: a periodic valley, an isolated valley on a plain (the former case), and an isolated valley entrenched in an elevated plateau. According to the valley volume argument (topographic amplification factor), these three cases should develop identical temperature perturbations and thus similar along-valley winds. However, substantial differences are found between the three cases, in particular a much stronger daytime up-valley wind and nighttime down-valley wind for the plateau configuration. The analysis demonstrates the importance of the exchange of along-valley momentum between the valley atmosphere and its surroundings and of the upper-level pressure gradient in explaining the differences among the cases. Furthermore, differences in the upper-level pressure gradient are shown to be related to the heat exchange of the air above the valley atmosphere with the surroundings, which is related to larger-scale cross-valley circulations.

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Yu Du
and
Richard Rotunno

Abstract

The characteristics of thermally driven diurnally periodic wind signals off the east coast of China are studied using hourly model data for the period June 2006–11 simulated with a mesoscale model. Analysis of these model data indicates low-level diurnally periodic wind signals propagate eastward off the southeast coast, whereas diurnal wind variations off the northeast coast are nearly in phase. It is found that a simple 2D linear land–sea-breeze model with friction can capture this main difference in propagation character with respect to latitude. Idealized simulations using a simplified version of the mesoscale model that includes surface heating and terrain are found to explain certain features not captured by the present linear theory such as the absolute time phase and cross-coast location of the maximum amplitude of the diurnally periodic winds.

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Juerg Schmidli
and
Richard Rotunno

Abstract

The physical mechanisms leading to the formation of diurnal along-valley winds are investigated over idealized three-dimensional topography. The topography used in this study consists of a valley with a horizontal floor enclosed by two isolated mountain ridges on a horizontal plain. A diagnostic equation for the along-valley pressure gradient is developed and used in combination with numerical model simulations to clarify the relative role of various forcing mechanisms such as the valley volume effect, subsidence heating, and surface sensible heat flux effects. The full diurnal cycle is simulated using comprehensive model physics including radiation transfer, land surface processes, and dynamic surface–atmosphere interactions. The authors find that the basic assumption of the valley volume argument of no heat exchange with the free atmosphere seldom holds. Typically, advective and turbulent heat transport reduce the heating of the valley during the day and the cooling of the valley during the night. In addition, dynamically induced valley–plain contrasts in the surface sensible heat flux can play an important role. Nevertheless, the present analysis confirms the importance of the valley volume effect for the formation of the diurnal along-valley winds but also clarifies the role of subsidence heating and the limitations of the valley volume effect argument. In summary, the analysis brings together different ideas of the valley wind into a unified picture.

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Kerry Emanuel
and
Richard Rotunno

Abstract

Extant theoretical work on the steady-state structure and intensity of idealized axisymmetric tropical cyclones relies on the assumption that isentropic surfaces in the storm outflow match those of the unperturbed environment at large distances from the storm’s core. These isentropic surfaces generally lie just above the tropopause, where the vertical temperature structure is approximately isothermal, so it has been assumed that the absolute temperature of the outflow is nearly constant. Here it is shown that this assumption is not justified, at least when applied to storms simulated by a convection-resolving axisymmetric numerical model in which much of the outflow occurs below the ambient tropopause and develops its own stratification, unrelated to that of the unperturbed environment. The authors propose that this stratification is set in the storm’s core by the requirement that the Richardson number remain near its critical value for the onset of small-scale turbulence. This ansatz is tested by calculating the Richardson number in numerically simulated storms, and then showing that the assumption of constant Richardson number determines the variation of the outflow temperature with angular momentum or entropy and thereby sets the low-level radial structure of the storm outside its radius of maximum surface winds. Part II will show that allowing the outflow temperature to vary also allows one to discard an empirical factor that was introduced in previous work on the intensification of tropical cyclones.

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Richard Rotunno
and
Manuela Lehner

Abstract

Observations and models of nocturnal katabatic winds indicate strong low-level stability with much weaker stability aloft. When such winds encounter an embedded depression in an otherwise smooth sloping plane, the flow responds in a manner that is largely describable by the inviscid fluid dynamics of stratified flow. Building on earlier work, the present study presents a series of numerical simulations based on the simplest nontrivial idealization relevant to the observations: the height-independent flow of a two-layer stratified fluid past a two-dimensional valley. Stratified flow past a valley has received much less attention than the related problem of stratified flow past a hill. Hence, the present paper gives a detailed review of existing theory and fills a few gaps along the way. The theory is used as an interpretive guide to an extensive set of numerical simulations. The solutions exhibit a variety of behaviors that depend on the nondimensional input parameters. These behaviors range from complete flow through the valley to valley-flow stagnation to situations involving internal wave breaking, lee waves, and quasi-stationary waves in the valley. A diagram is presented that organizes the solutions into flow regimes as a function of the nondimensional input parameters.

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Richard Rotunno
and
Rossella Ferretti

Abstract

Numerical studies by the authors and others of the 1994 Piedmont flood show that the orographically modified flow was a critical element for the production of extraordinary rainfall. To uncover the precise mechanism of orographic rainfall occurring in full-physics MM5 simulations of the 1994 Piedmont flood, the authors carried out simulations with the same real-data initial and boundary conditions, but with the real orography replaced by an idealized one. With excellent agreement between real and idealized orography on the rainfall rate versus time in the Piedmont area, analysis of the idealized-orography simulation provides a clear picture of the model's mechanism of orographically induced rainfall. As noted in previous studies of the 1994 Piedmont case, a moist saturated airflow has a reduced effective static stability and tends to flow over the mountains, while an unsaturated airstream is stable and tries to flow around (toward the left in the Northern Hemisphere). In the 1994 Piedmont case, there was a strong horizontal gradient of moisture; thus the western moist part of the airstream flows over, while the eastern drier part is deflected westward around the obstacle, and so a convergence is produced between the airstreams. This effect is explored using a simple version of MM5 wherein the flow, moisture distribution, and idealized orography are varied within the observed range. Quantitative as well as qualitative rainfall rates and flow features of the full-physics MM5 simulations are captured with the simple model.

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Richard Rotunno
and
Joseph Klemp

Abstract

We examine the rotation and propagation of the supercell-like convection produced by our three-dimensional cloud model. The rotation in the supercell is studied in terms of the conservation of equivalent potential vorticity and V. Bjerknes' first circulation theorem; neither of these have been used previously in this connection, and we find that they significantly contribute to the current level of understanding in this area. Using these we amplify the findings of our previous work in which we found that the source of midlevel rotation is the horizontally oriented vorticity associated with the environmental shear, while the low-level rotation derives from the baroclinic generation of horizontally oriented vorticity along the low-level cold-air boundary. We further demonstrate that these same processes that amplify the low-level rotation also produce the distinctive cloud feature known as the “wall cloud.”

We find that the thunderstorm propagates rightward primarily because of the favorable dynamic vertical pressure gradient that, owing to storm rotation, is always present on the right flank of the updraft. Simulations without precipitation physics demonstrate that this rightward propagation occurs even in the absence of a cold outflow and gust front near the surface.

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Richard Rotunno
and
Maurizio Fantini

Abstract

We investigate B. Farrell's hypothesis that the development of a surface cyclone with the passage of an upper trough, as observed by S. Pettessen and coworkers, may be understood in terms of an initial-value problem on the Eady model. We consider the response of the Eady model to perturbations whose horizontal wavelengths are short enough to ensure their stability, and whose perturbation potential vorticity is zero. We depart from Farrell with the latter condition as it eliminates the continuous spectrum and allows the evolution of the perturbation to be understood solely in terms of the two normal modes of the Eady model—one with maximum amplitude at the upper lid, which propagates eastward with respect to the midlevel flow, and one westward propagating, with maximum amplitude at the lower surface. Imagine an initial upper-level disturbance with no surface perturbation; this is represented by the two Eady modes in combination such that the initial surface perturbation pressure is zero. As the flow evolves out of this initial condition, a pressure disturbance appears at the surface as the two modes propagate past one another. That is, a surface cyclone forms, deepens, and then weakens, as the upper trough passes. This amplification of the surface trough is not due to mere geometrical interference, but rather is the consequence of an energy-exchanging interplay between waves and mean flow. This distinction is emphasized by comparison with a model in which a superficially similar phenomenon occurs, but without such an interplay.

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Yu Du
and
Richard Rotunno

Abstract

The characteristics and mechanisms of diurnal rainfall and winds near the south coast of China are explored using satellite data (CMORPH), long-term hourly WRF Model data (Du model data), a simple 2D linear model, and 2D idealized simulations. Both the CMORPH and Du model data indicate that the diurnal cycle of rainfall has two propagation modes near the coast: onshore and offshore. The diurnally periodic winds (vertical motions) also show a similar propagation feature. Analysis of the rainfall budget indicates that vertically integrated vertical vapor advection plays a key role in the diurnal cycle of rainfall and thus provides a physical connection between winds and rainfall in the diurnal cycle. It was found that a simple 2D linear land–sea breeze model with a background wind can well capture the two propagation modes, which are associated with inertia–gravity waves, in terms of speed and phase. The background wind changes the pattern of the inertia–gravity waves and further affects the diurnal propagation. The effect of the background wind on the diurnal propagation was verified through idealized simulations using a simplified version of the WRF Model that can also capture the diurnal features.

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