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Alan J. Thorpe
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Alan J. Thorpe

Abstract

Ate balanced flow structure of various classic synopitc-scale disturbances is reviewed using the invertibility principle for isentropic potential vorticity (IPV) distributions. Complete solutions are shown for cold and warm core structures of various types. The basic model imagines the tropopause to be the interface between the lower potential vorticity of the troposphere and the approximately six-fold larger value typical of the lower stratosphere. The sensitivity of the structure of the potential temperature variation along the tropopause and at the surface is described. Results are presented in diagrammatic form to allow easy diagnosis of the vortex structure from synoptic data available at perhaps only a few levels. The point is made that upper air IPV and surface potential temperature distributions are often the most crucial in accounting for the balanced flow structure.

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Walter Fernandez and Alan J. Thorpe

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Raymond's (1975) wave-CISK model is applied to several tropical convective storms observed in Venezuela, the eastern Atlantic and West Africa to predict their propagation velocity. Similar calculations are carried out with Moncrieff and Miller's (1976) analytical model for tropical cumulonimbus and squall lines. A comparison of the model predictions with the observed values is made. In some cases the models give good predictions, but not in others. In general, Raymond's model underestimates the propagation speed of the storms, while the Moncrieff-Miller model overestimates it. Raymond's model is poor when the cloud bases are very low. This result indicates that over tropical oceans wave-CISK models cannot give good results unless the mass flux due to the plumes, which is equated to the mass flux across cloud base, is treated in a more realistic way. The Moncrieff-Miller model gives better results if the mean wind component along the direction of motion is used rather than the mid-level wind.

The wave-CISK model and steady-state models of storm motion are then considered in conditions of constant wind shear. In particular, their predictions are compared over a wide range of shear values, using realistic thermodynamic soundings. Despite the obvious differences between the models, it is found that, for Richardson number small (R<1) and very large, they give comparable predictions for the storm velocity. It appears that a very good approximation for the wave-CISK model over the entire R range is to put the storm speed proportional to the shear, plus a constant.

An important conclusion is that the ability of storms to propagate relative to the environmental flow can be reproduced in the linear wave-CISK model and thus may not be a fundamentally nonlinear effect. It is therefore crucial to further examine forcing mechanisms of convective overturning and, in particular, to clarify the relationship between CISK and the implicit forcing involved in the steady model.

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Meral Demirtas and Alan J. Thorpe

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A new method is described to interpret satellite water vapor (WV) imagery in dynamical terms using potential vorticity (PV) concepts. The method involves the identification of mismatches between the WV imagery and a numerical weather prediction model description of the upper-level PV distribution at the analysis time. These mismatches are usually associated with horizontal positioning errors in the tropopause location in the oceanic storm-track region in midlatitudes. The PV distribution is locally modified to minimize this mismatch, and PV inversion is carried out to provide dynamically consistent additional initial data with which to reinitialize the numerical forecast.

One of the advantages of using this method is that it is possible to generate wind and temperature data suitable for inclusion as initial data for numerical weather forecasts. By using PV additional data can be inferred that cannot otherwise be simply derived from the WV data. In this way dynamical concepts add considerable value to the WV imagery, which by themselves would probably not have as significant a forecast impact.

Several examples of the use of this method are given here including cases of otherwise poorly forecast North Atlantic cyclones. In cases where the analysis errors occur at upper levels of the troposphere, the method leads to a significant improvement in the short-range forecast skill. In general, it is useful in highlighting where forecast problems are arising.

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Fred Kucharski and Alan J. Thorpe

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The concept of local extended exergy is here applied to an idealized, dry, and reversible-adiabatic cyclone development. The extended exergy as well as the kinetic energy are decomposed into a mean part, defined by a zonal average, and into a perturbation from the mean. The resulting local energy evolution equations provide an extension of the well-known Lorenz-type available energy equations. A term in the baroclinic conversion rate, connected with static stability anomalies, which is not usually considered, is of significance even in this idealized case study and contributes significantly to the nonlinear equilibration of the baroclinic wave.

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Alain Joly and Alan J. Thorpe

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A methodology suitable for assessing the stability of any time-dependent basic state is presented. The equivalent of the normal modes for steady basic states are the eigenvectors of the resolvent matrix; this matrix incorporates the evolution of the large-scale flow, and growth rates are replaced by amplification rates. This method is applied to the three-dimensional stability of two-dimensional fronts undergoing frontogenesis in the presence of latent heat release in a semigeostrophic model. Disturbances developing in this flow are therefore geostrophically balanced. The concepts are first illustrated in a dry time-dependent uniform shear and potential vorticity flow. At any time during the evolution of the basic flow the stability can be compared to that obtained by assuming that the frontogenesis has, at that instant, ceased. Although differences between the results from the two methods exist, general conclusions as to the scales and structure of the modes are not altered; only large-scale waves are unstable. The situation in moist baroclinic waves is dramatically different. Growth rates are enhanced compared to the steady state analysis, but the possibility for frontal waves on the 1000-km scale to amplify most rapidly depends on the rate of development of the parent wave. Such waves dominate the spectrum only when that rate is slow and then only when the frontal ascent takes on a small cross-frontal width and the vorticity maximum penetrates over a deep layer. The short-wave growth is mostly due to latent heat release in the wave. This heating is shown, in a simplified case, to modify the necessary conditions for instability. It is concluded that shearing deformation does not intrinsically inhibit frontal instability, but paradoxically it greatly favors two-dimensional growth in the early stages due to the more rapid frontogenesis in the presence of latent heating. The role of stretching deformation may be substantially different but is not considered here.

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Alain Joly and Alan J. Thorpe

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The stability of the steady two-dimensional horizontal shear front to geostrophic disturbances in the along-front direction is examined within the framework of semi-geostrophic theory. The basic state corresponds to the geostrophic along-front flow at any time during the nonlinear evolution of a two-dimensional Eady wave. The matrix resulting from the stability analysis can be transformed into a weakly nondiagonal form. Its structure shows that the selection of the most unstable along-front wavenumber is independent of the “intensity” of the front. The growth rate is a linear function of this amplitude. The most unstable along-front mode is a modified Eady mode stationary with respect to the front. It draws a fraction of its energy from the shear. For smaller along-front wavelengths, the solution is dominated by propagating modes near the boundaries. These are also baroclinic, with a larger contribution from the basic kinetic energy and much smaller growth rates. It is apparent that the existence of a vorticity maximum at fronts, however large, is not sufficient to produce the observed small scale of frontal waves. Anomalous potential vorticity at the front is necessary to provide a deep zone of large horizontal shear and hence the reduced horizontal scale of waves.

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Ming Xue and Alan J. Thorpe

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A nonhydrostatic numerical model suitable for simulating mesoscale meteorological phenomena is developed and described here. The model is the first to exploit the nonhydrostatic equation system in σ (normalized pressure) coordinates. In addition to the commonly recognized advantages of σ-coordinate models, this model is potentially advantageous in nesting with large-scale σ-coordinate models. The equation system does not support sound waves but it presents the internal gravity waves accurately. External gravity waves are the fastest wave modes in the system that limit the integration time step. However, since short nonhydrostatic external waves are much slower than the speed of shallow-water waves and because fast hydrostatic long waves imposes less severe restriction on the time step when they are resolved by many grid points, a large time step (compared to that determined by the speed of hydrostatic shallow-water waves) can be used when horizontal grid spacing is on the order of 1 km.

The system is solved in a way analogous to the anelastic system in terrain-following height coordinates. The geopotential height perturbation is diagnosed from an elliptic equation. Conventional finite-differencing techniques are used based on Arakawa C grid, The flux-corrected transport (FCT) scheme is included as an option for scalar advection.

The model has been used to study a variety of problems and here the simulations of dry mountain waves are presented. The resists of simulations of the 11 January 1972 Boulder severe downslope windstorm are reported and the wave development mechanism discussed.

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Douglas J. Parker and Alan J. Thorpe

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It is shown here that there exists a regime of balanced frontogenesis that is forced almost entirely by the diabatic hating due to convection at a front. This theory is explored in the context of the two-dimensional semigeostrophic equations with an Eady basic state: convection is parameterized to be dependent on the low-level moisture convergence of the cross-frontal ageostrophic flow, in accordance with recent diagnostic studies. The significant result is that the growth rate of the convective frontal system becomes independent of the total wavelength of the domain once the diabatic heating exceeds a relatively large threshold magnitude. In this regime the frontal zone has a width and structure dependent on the heating magnitude but not on the wavelength. The system is described as “solitary” or “isolated” since the dynamics are self-contained and independent of the far field.

The energetics of the system have a diabatic conversion that is an order of magnitude greater than that due to the large-scale alongfront temperature gradient. The large-scale forcing is, however, necessary as a catalyst in maintaining a weak ageostrophic convergence that allows the convective heating to be triggered. The constraint of alongfront geostrophic balance means that convective forcing alone cannot maintain frontogenesis. It is suggested that the dynamics exhibited by the convectively dominated front may also be important in the study of midlatitude squall lines.

The propagation and dynamics of the front are interpreted in terms of the notion of a “diabatic Rossby wave.”

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Craig H. Bishop and Alan J. Thorpe

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It has been shown that lower tropospheric potential vorticity zones formed during moist deformation frontogenesis will support growing waves if at some time the frontogenesis ceases. In this paper, the ways in which these waves are affected by the frontogenetic process are identified.

Observations show that fronts in the eastern Atlantic commonly feature saturated ascent regions characterized by zero moist potential vorticity. Furthermore, in many cases the horizontal temperature gradient in the lowest one to two kilometers of the atmosphere is rather weak. These features are incorporated in an analytical archetype. The dynamical implications of saturated ascent in conditions of zero moist potential vorticity are represented in the model by assuming that adiabatic temperature changes are precisely balanced by diabatic tendencies. The observed small temperature gradient at low levels is represented in the model by taking it to be zero in the lowest two kilometers. Consequently, the forcing of the low-level moist ageostrophic vortex stretching that strengthens the low-level potential vorticity anomaly is confined to middle and upper levels.

A semianalytical initial value solution for the linear development of waves on the evolving low-level potential vorticity anomaly is obtained. The waves approximately satisfy the inviscid primitive equations whenever the divergent part of the perturbation is negligible relative to the rotational part. The range of nonmodal wave developments supported by the front is summarized using RT phase diagrams. This analysis shows that the most dramatic effects of frontogenesis on frontal wave growth are due to (a) the increase in time of the potential vorticity and hence potential instability of the flow and (b) the increase in time of the alongfront wavelength relative to the width of the strip. An optimally growing streamfunction wave is described. Finally, a diagnostic technique suitable for identifying small amplitude frontal waves in observational data is described.

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