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Roger K. Smith

Abstract

The problem of explaining the surface pressure rise in simple balanced models of fronts, discussed at length by Sutcliffe, is reexamined. It is shown that air mass models for steadily translating fronts (including the Margules' front) are dynamically consistent, except along a vertical line above the surface front, only if there is vertical motion (subsidence for a cold front, ascent for a warm front) in the warm air that overlies the cold air. In this case, the local post-frontal pressure rise in a model cold front and the pre-frontal pressure fall in a model warm front can be attributed to advection. However, the presence of the vertical motion is a limiting factor in the applicability of such models.

The analysis resolves an apparent inconsistency between the surface pressure changes computed in Boussinesq models and the prediction of a theorem of Brunt.

Irrespective of the Boussinesq approximation, it is shown that, in the model, the surface pressure change at any fixed location bears no relation to the variation of surface pressure normal to the front at any given instant. This would imply that it is inappropriate to infer space cross-sections of pressure from observed time series at a single station, even for a steadily translating front. The result highlights a further limitation of balanced air mass models when applied to fronts in the atmosphere.

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Roger K. Smith

Abstract

The cyclostrophic and hydrostatic adjustment of simple one-layer and multilayer vortex flows to the local removal and/or redistribution of mass and angular momentum are studied, and a detailed physical interpretation of the dynamics of adjustment is given for the one-layer model. The calculations provide insight into possible responses of tropical cyclones to modification by cloud seeding and facilitate an appraisal of the Simpson-Malkus modification hypothesis.

Calculations for two- and three-layer models show that the maximum tangential velocity is increased whether or not mass transfer takes place predominantly inside or outside the radius at which the maximum occurs, and the central surface pressure decreases due to subsidence at one or both interface levels. However, the magnitude of these effects are comparatively small in relation to the strengths of the induced meridional circulation and corresponding changes in tangential wind speed outside the core, at, or beyond, the radii at which mass transfer occurs. Moreover, the estimated maximum change in tangential wind speed that might be produced in a tropical cyclone by following the seeding procedure suggested by Simpson and Malkus is small compared with observed natural variations.

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Roger K. Smith and Wolfgang Ulrich

Abstract

An analytical theory is presented for the motion of an initially symmetric barotropic vortex on a beta-plane at rest, the prototype problem in the theory of tropical cyclone motion. In the case of vortices with parameter values appropriate to tropical cyclones, the theory shows excellent agreement with equivalent numerical model calculations for a period of between one and two days. In particular, the vortex track and the evolution of vortex asymmetries, the so-called beta gyres, are accurately predicted. The calculations provide further insight into dynamics of tropical cyclone motion in general and provide a firmer basis for interpreting the numerical solutions in particular. They are relevant also to the important problem of designing more appropriate “bogus” vortices for the initialization of dynamically based tropical cyclone forecast models.

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Hongyan Zhu and Roger K. Smith

Abstract

The minimal three-dimensional tropical cyclone model developed by Zhu et al. is used to explore the role of shallow convection, precipitation-cooled downdrafts, and the vertical transport of momentum by deep convection on the dynamics of tropical cyclone intensification. The model is formulated in σ coordinates and has three vertical levels, one characterizing a shallow boundary layer, and the other two representing the upper and lower troposphere, respectively. It has three options for treating cumulus convection on the subgrid scale and a simple scheme for the explicit release of latent heat on the grid scale.

In the model, as in reality, shallow convection transports air with low moist static energy from the lower troposphere to the boundary layer, stabilizing the atmosphere not only to itself, but also to deep convection. Also it moistens and cools the lower troposphere. For realistic parameter values, the stabilization in the vortex core region is the primary effect: it reduces the deep convective mass flux and therefore the rate of heating and drying in the troposphere. This reduced heating, together with the direct cooling of the lower troposphere by shallow convection, diminishes the buoyancy in the vortex core and thereby the vortex intensification rate.

The effects of precipitation-cooled downdrafts depend on the closure scheme chosen for deep convection. In the two closures in which the deep cloud mass flux depends on the degree of convective instability, the downdrafts do not change the total mass flux of air that subsides into the boundary layer, but they carry air with a lower moist static energy into this layer than does subsidence outside downdrafts. As a result they decrease the rate of intensification during the early development stage. Nevertheless, by reducing the deep convective mass flux and the drying effect of compensating subsidence, they enable grid scale saturation, and therefore rapid intensification, to occur earlier than in calculations where they are excluded. In the closure in which the deep cloud mass flux depends on the mass convergence in the boundary layer, downdrafts reduce the gestation period and increase the intensification rate.

Convective momentum transport as represented in the model weakens both the primary and secondary circulations of the vortex. However, it does not significantly reduce the maximum intensity attained after the period of rapid development. The weakening of the secondary circulation impedes vortex development and significantly prolongs the gestation period.

Where possible the results are compared with those found in other studies.

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Michael J. Reeder and Roger K. Smith

Abstract

We examine air parcel trajectories in the two-dimensional model for a cold front by Reeder and Smith. These are found to be in close agreement with trajectories deduced from analyses of summertime “cool changes” in southeastern Australia, adding further support to the applicability of the numerical model to this kind of cold front. The favorable comparison points also to the dynamical consistency of the conceptual model for the cool change, which has evolved from the analysis of data from observational experiments.

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Gerald L. Thomsen and Roger K. Smith

Abstract

The importance of the boundary layer parameterization in the numerical prediction of low-level convergence lines over northeastern Australia is investigated. High-resolution simulations of convergence lines observed in one event during the 2002 Gulf Lines Experiment are carried out using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). Calculations using five different parameterizations are compared with observations to determine the optimum scheme for capturing these lines. The schemes that give the best agreement with the observations are the three that include a representation of countergradient fluxes and a surface layer scheme based on Monin–Obukhov theory. One of these, the Medium-Range Forecast scheme, is slightly better than the other two, based on its ability to predict the surface pressure distribution. The findings are important for the design of mesoscale forecasting systems for the arid regions of Australia and elsewhere.

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Hongyan Zhu, Wolfgang Ulrich, and Roger K. Smith

Abstract

The interaction between a tropical cyclone and the ocean is investigated using a minimal three-dimensional tropical cyclone model coupled with a two-layer ocean model. Two representations for entrainment into the ocean mixed layer are compared: one based on the assumption that the velocity scale for entrainment is the surface friction velocity, the other on the assumption that this scale is the magnitude of the mean velocity difference across the base of the mixed layer. It is shown that the magnitude and distribution of the ocean cooling depends strongly on the method for representing entrainment velocity. The method based on the surface friction velocity is more effective in reducing the heat flux from the ocean to the storm in the inner-core region and leads to a greater reduction of the tropical cyclone intensity.

With ocean coupling, the surface heat flux is reduced in the inner core, mainly in the rear-right quadrant relative to the track, which is toward the northwest. As a result, the potential temperature distribution in the core region is more asymmetric in the coupled model, with a higher value in the northern sector than in the southern sector. The region of convergence in the lower troposphere in the coupled experiments is rotated counterclockwise from the rear (or southeastern) sector of the inner core to the eastern part, apparently in response to the change in the temperature distribution in the middle troposphere. In addition, the region of strong upward motion in the middle troposphere shifts also counterclockwise from the rear-right quadrant to the front-right quadrant. These changes are accompanied with changes in the divergence pattern that are mainly in the lower troposphere rather than in the boundary layer.

The presence of ocean coupling has little influence on the track of the model cyclones, unlike the case in some previous studies.

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Hongyan Zhu, Roger K. Smith, and Wolfgang Ulrich

Abstract

A minimal 3D numerical model designed for basic studies of tropical cyclone behavior is described. The model is formulated in σ coordinates on an f or β plane and has three vertical levels, one characterizing a shallow boundary layer and the other two representing the upper and lower troposphere, respectively. It has three options for treating cumulus convection on the subgrid scale and a simple scheme for the explicit release of latent heat on the grid scale. The subgrid-scale schemes are based on the mass-flux models suggested by Arakawa and Ooyama in the late 1960s, but modified to include the effects of precipitation-cooled downdrafts. They differ from one another in the closure that determines the cloud-base mass flux. One closure is based on the assumption of boundary layer quasi-equilibrium proposed by Raymond and Emanuel.

It is shown that a realistic hurricane-like vortex develops from a moderate strength initial vortex, even when the initial environment is slightly stable to deep convection. This is true for all three cumulus schemes as well as in the case where only the explicit release of latent heat is included. In all cases there is a period of gestation during which the boundary layer moisture in the inner core region increases on account of surface moisture fluxes, followed by a period of rapid deepening. Precipitation from the convection scheme dominates the explicit precipitation in the early stages of development, but this situation is reversed as the vortex matures. These findings are similar to those of Baik et al., who used the Betts–Miller parameterization scheme in an axisymmetric model with 11 levels in the vertical. The most striking difference between the model results using different convection schemes is the length of the gestation period, whereas the maximum intensity attained is similar for the three schemes. The calculations suggest the hypothesis that the period of rapid development in tropical cyclones is accompanied by a change in the character of deep convection in the inner core region from buoyantly driven, predominantly upright convection to slantwise forced moist ascent.

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Michael T. Montgomery and Roger K. Smith
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