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Richard Rotunno

Abstract

A vertical velocity field is chosen which imitates that of the initial stages of cloud development as simulated numerically by Wilhelmson and Klemp (1978). Given this, an approximate version of the equation for the vertical component of the vorticity is solved. The vertical velocity is assumed to vary with height as sin πz/H where a is the altitude and H is the depth of the domain. At the level of nondivergence (z=H/2), the solutions indicate the development of a vortex pair which then splits into two vortex pairs one moving to the right of the mean wind and the other to the left (as observed in the numerical model). At lower levels, owing to the convergence in the updraft and divergence in the downdraft, the cyclonic/anticyclonic member of the vortex pair in the rightward/leftward moving storm is greatly enhanced. The vorticity maximum is initially on the maximum gradient of vertical velocity. At mid-levels the maximum vorticity migrates with time close to the position of maximum vertical velocity. However, at lower levels, the maximum vorticity migrates with time past the position of maximum vertical velocity and thereafter resides on the vertical velocity gradient separating updraft from downdraft, as observed in a number of case studies. Some general comparisons of the present theory with an observational case study are made.

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Tetsuya Takemi
and
Richard Rotunno

Abstract

Using the newly developed Weather Research and Forecasting (WRF) model, this study investigates the effects of subgrid mixing and numerical filtering in mesoscale cloud simulations by examining the sensitivities to the parameters in turbulence-closure schemes as well as the parameters in the numerical filters. Three-dimensional simulations of squall lines in both no-shear and strong-shear environments have been performed. Using the Smagorinsky or 1.5-order turbulent kinetic energy (TKE) subgrid model with standard values for the model constants and no explicit numerical filter, the solution in the no-shear environment is characterized by many poorly resolved grid-scale cells. In the past, such grid-scale noise was avoided by adding a numerical filter which, however, produces excessive damping of the physical small-scale eddies. Without using such a filter, it was found that by increasing the proportionality constant in the eddy viscosity coefficient in the subgrid turbulence models, the cells become well resolved, but that further increases in the constant overly smooth the cells. Such solution sensitivity is also found in the strong-shear cases. The simulations using the subgrid models with viscosity coefficients 1.5 to 2 times larger than those widely used in other cloud models retain more power in short scales, but without an unwanted buildup of energy; with these optimum values, no numerical filters are required to avoid computational noise. These optimum constants do not depend significantly on grid spacings of O(1 km). Therefore, it is concluded that by using the eddy viscosity formulation appropriate for mesoscale cloud simulations, the use of artificial numerical filters is avoided, and the mixing processes are represented by more physically based turbulence-closure models.

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Tetsuya Takemi
and
Richard Rotunno
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Daniel Keyser
and
Richard Rotunno

Abstract

We review and discuss a difference in interpretation of the role of turbulence in modifying the potential-vorticity distribution in the vicinity of upper-level jet-front systems. In the late 1970s, M. A. Shapiro presented observational evidence that turbulent mixing of heat can result in a positive anomaly of the Ertel potential vorticity on the cyclonic-shear side of upper-level jets near the level of maximum wind. E. F. Danielsen and collaborators disputed this evidence and the accompanying interpretation. They argued that the turbulent mixing of potential vorticity can be described in terms of downgradient diffusion, in the same sense as for a passive chemical tracer. Accordingly, turbulent mixing cannot produce anomalies from initially smooth distributions of potential vorticity. In our view, this dispute stems from differences in the averaging procedures used to analyze turbulent flows, which lead to fundamentally different definitions of potential vorticity. Shapiro defined potential vorticity as the scalar product of the averaged absolute vorticity and the averaged potential-temperature gradient, whereas Danielson et al. defined it, in their analytical framework, as the average of the scalar product of these quantities. We conclude that the positive anomaly of potential vorticity identified by Shapiro is plausible if one accepts the definition of potential vorticity used in his studies. Moreover. we believe Shapiro's alternative to be the only practical option when working with observed or simulated data. Even if Danielsen's alternative could be adopted in practice, we suggest that its utility as a tracer is problematic in view of the questionable validity of the downgradient diffusion of potential vorticity.

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George H. Bryan
and
Richard Rotunno

Abstract

An axisymmetric numerical model is used to evaluate the maximum possible intensity of tropical cyclones. As compared with traditionally formulated nonhydrostatic models, this new model has improved mass and energy conservation in saturated conditions. In comparison with the axisymmetric model developed by Rotunno and Emanuel, the new model produces weaker cyclones (by ∼10%, in terms of maximum azimuthal velocity); the difference is attributable to several approximations in the Rotunno–Emanuel model. Then, using a single specification for initial conditions (with a sea surface temperature of 26°C), the authors conduct model sensitivity tests to determine the sensitivity of maximum azimuthal velocity (υ max) to uncertain aspects of the modeling system. For fixed mixing lengths in the turbulence parameterization, a converged value of υ max is achieved for radial grid spacing of order 1 km and vertical grid spacing of order 250 m. The fall velocity of condensate (Vt ) changes υ max by up to 60%, and the largest υ max occurs for pseudoadiabatic thermodynamics (i.e., for Vt > 10 m s−1). The sensitivity of υ max to the ratio of surface exchange coefficients for entropy and momentum (CE /CD ) matches the theoretical result, υ max ∼ (CE /CD )1/2, for nearly inviscid flow, but simulations with increasing turbulence intensity show less dependence on CE /CD ; this result suggests that the effect of CE /CD is less important than has been argued previously. The authors find that υ max is most sensitive to the intensity of turbulence in the radial direction. However, some settings, such as inviscid flow, yield clearly unnatural structures; for example, υ max exceeds 110 m s−1, despite a maximum observed intensity of ∼70 m s−1 for this environment. The authors show that turbulence in the radial direction limits maximum axisymmetric intensity by weakening the radial gradients of angular momentum (which prevents environmental air from being drawn to small radius) and of entropy (which is consistent with weaker intensity by consideration of thermal wind balance). It is also argued that future studies should consider parameterized turbulence as an important factor in simulated tropical cyclone intensity.

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Mario Marcello Miglietta
and
Richard Rotunno

Abstract

In two recent papers, the authors reported on numerical simulations of conditionally unstable flows past an idealized mesoscale mountain ridge. These idealized simulations, which were performed with a three-dimensional, explicitly cloud-resolving model, allowed the investigation of simulated precipitation characteristics as a function of the prescribed environment. The numerical solutions were carried out for a uniform wind flowing past a bell-shaped ridge and using an idealized unstable sounding with prescribed values of the relevant parameters.

In the present work the application of these theoretical results to observed cases of orographically forced convective rainfall including the Big Thompson flood (1976, Colorado), the Oahu flood (1974, Hawaii), and the Gard flood (2002, France) is reported. Specifically, numerical simulations have been carried out using observed and idealized soundings relevant to these cases but with idealized topography. It is found that using the observed soundings, but with idealized constant-wind profiles, the simulated rain rates fit reasonably well within the previous theoretically derived parameter space for intense orographic convective rainfall. However, in order to reproduce larger rainfall rates, in closer agreement with observations, in the first two cases it was necessary to initialize the sounding with a wind profile characterized by low-level flow toward the mountain with weak flow aloft (as observed for the across-mountain wind component). For the Gard case, the situation was more complex and it is found unlikely that the situation can be reduced to a simple two-dimensional problem.

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F. Zhang
,
Chris Snyder
, and
Richard Rotunno

Abstract

A mesoscale model is used here to investigate the possible sources of forecast error for the 24–25 January 2000 snowstorm along the east coast of the United States. The primary focus is the quantitative precipitation forecast out to lead times of 36 h. The success of the present high-resolution control forecast shows that the storm could have been well forecasted with conventional data in real time. Various experiments suggest that insufficient model grid resolution and errors in the initial conditions both contributed significantly to problems in the forecast. Other experiments, motivated by the possibility that the forecast errors arose from the operational analysis poorly fitting one or two key soundings, test the effects of withholding single soundings from the control initial conditions. While no single sounding results in forecast changes that are more than a small fraction of the error in the operational forecast, these experiments do reveal that the detailed mesoscale distribution of precipitation in the 24- or 36-h forecast can be significantly altered even by such small changes in the initial conditions. The experiments also reveal that the forecast changes arise from the rapid growth of error at scales below 500 km in association with moist processes. The results presented emphasize the difficulty of forecasting precipitation relative to, say, surface pressure and suggest that the predictability of mesoscale precipitation features in cases of the type studied here may be limited to less than 2–3 days.

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Richard Rotunno
and
Jian-Wen Bao

Abstract

It is universally agreed that cyclogenesis in midlatitudes occurs through baroclinic conversion of the potential energy available from an initial state. The mechanical process by which that conversion takes place is a perennial subject of discussion. At least as far back as the 1950s, it was recognized that in any practical forecast problem, the initial condition is influential. Observational research continues to confirm the prevalence of tropopause-level perturbations preceding surface cyclogenesis. The observations also suggest that the growing disturbances have time-varying vertical structures. Relating these observations to the classical linear theory of baroclinic instability is not immediately obvious since, in the latter, the precise form of the initial condition is not important, and the theory predicts cyclogenesis with a fixed-in-time vertical structure. These differences between theory and observations are but a few of the many that have been recognized and treated in modified theories of baroclinic instability. We attempt herein to draw a closer connection between the modified theories and observations by performing a case study using a hierarchy of models of decreasing complexity.

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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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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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