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Huw C. Davies

Abstract

A two-component study is undertaken of the classical quasigeostrophic (QG) omega equation. First, a reappraisal is undertaken of extant formulations of the equation’s so-called forcing function. It pinpoints shortcomings of various formulations and prompts consideration of alternative forms. Particular consideration is given to the contribution of flow deformation to the forcing function, and to the role of the advection of the geostrophic flow by the thermal wind (the R vector). The latter is closely related to the Q vector, the horizontal component of the ageostrophic vorticity, and the forcing function itself. The reexamination promotes further examination of the physical interpretation and diagnostic use of the omega equation particularly for assessing richly structured subsynoptic flow features.

Second, consideration is given to the dynamics associated with the equation and its more general utility. It is shown that the R vector is intrinsic to a quasigeostrophic cascade to finer-scaled flow, and that a fundamental feature of the QG omega equation—the in-phase relationship between cloud-diabatic heating and the attendant vertical velocity—has important potential ramifications for the assimilation of data in numerical weather prediction (NWP) models. Finally, it is shown that, in the context of considering NWP model output, mild generalizations of the quasigeostrophic R vector retain interpretative value for flow settings beyond geostrophy and warrant consideration when addressing some contemporary NWP challenges.

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Huw C. Davies

Abstract

Models of wave-CISK are developed that possess a prescribed form for the vertical profile of the diabatic heating due to a cumulus cloud ensemble, and either an explicit or an implicit moisture budget constraint.

A comparison is undertaken of the models that do not have an explicit moisture budget constraint but differ in that the amplitude of the cloud-induced diabatic heating is related to the vertical velocity field at different height levels in the lower troposphere. The comparison reveals the essential equivalence of these models. The neutral eigenmodes demark the transition between stability and instability, and the one associated with the lowest amplitude for the diabatic heating is independent of the height of the forcing level. The only difference between these models is shown to be in the interpretation and specification of the diabatic heating amplitude.

It is further shown that the same neutral eigenmode pertains at the instability-stability boundary for a wave-CISK model with an explicit moisture budget constraint. The results obtained in this case are used to assess the potential for CISK in the tropics by examining the efficiency that the cloud ensemble must exhibit to sustain neutral modes.

Finally, the imposition of an Artificial rigid-lid upper boundary condition is shown to prevent the occurrence of the aforementioned mode and there is a concomitant stabilizing effect upon the flow.

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Huw C. Davies

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Huw C. Davies

Abstract

A brief critical assessment is presented of several lateral boundary schemes currently employed in regional weather prediction models. Simple flow models are used to determine the nature and cause of the primary shortcomings of each of the considered schemes. An awareness of these deficiencies can prove helpful in the implementation and further refinement of these schemes, and also in the interpretation of the resulting prediction errors.

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Huw C. Davies

Abstract

A study is made of the stability properties of certain coupled and decoupled nonlinear diffusion equations. The equations are of the form currently used in many high-resolution models to parameterize the stably stratified boundary layer. It is shown that some parameterization schemes for a decoupled thermal diffusion equation possess an unrealistic instability feature. However, the stability of the schemes is demonstrated in the more natural setting of a coupled, momentum and heat, set of diffusion equations.

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Huw C. Davies

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Sébastien Dirren and Huw C. Davies

Abstract

A theoretical study is undertaken of the relative influence of intermediate-level, near-surface, and tropopause-level perturbations upon flow development and cyclogenesis. The study is based upon two complementary quasigeostrophic models with consideration given to different types of perturbations of Eady-like basic states.

First, the standard linear Eady model is refined to include an interior, vertically localized potential vorticity (PV) wave perturbation, and the wave's influence upon the growth of the boundary waves is examined as a function of its vertical location and its initial phase and amplitude. It is shown that the pseudoresonance arising from the interaction of the interior PV wave with a surface-confined wave is highly transient and comparatively weak. In contrast, a PV wave located at midlevel can have supraexponential sustained impact upon the perturbation growth that results from a combination of its direct forcing effect and its ability to maintain the two Eady edge waves near quadrature for longer, rather than asymptoting to the normal mode setting.

Second, an extended nonlinear configuration is adopted that comprised a baroclinic jetlike basic state of uniform PV perturbed by a localized upper-boundary thermal perturbation or an interior point PV vortex, and the vortex's influence upon the baroclinic growth and cyclogenesis is examined in terms of its vertical and horizontal vertical location. It is shown that the interior perturbation can exert an appreciable and sustained influence upon the growth when it is located on or near the so-called critical surface, and the attendant flow transits smoothly to modal behavior.

The derived results point to the possible influence of low- and midtropospheric perturbations upon cyclone development, and are in accord with and can account for specific aspects of the structure and properties of singular vector (SV) perturbations.

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René Fehlmann and Huw C. Davies

Abstract

A strategy is outlined to explore the contribution of errors in the specification of tropopause-level flow features to the misforecast of individual synoptic and subsynoptic weather systems. The approach is founded upon a potential vorticity (PV) perspective of the flow. It entails the identification of key upper-level PV error elements at the forecast time, their Lagrangian retrodiction back to the initial analysis time in a process incorporating intermittent PV inversion, and a further forward integration starting from the revised initial state. The procedure can yield direct information on the role and strength of upper-level effects, and if the revised “forecast” verifies successfully it can indicate the location and nature of the analysis error.

To illustrate the approach a case study example is provided of a significant misforecast of rapid surface frontal-wave cyclogenesis. A conventional 24-h forecast with a limited-area NWP model failed to capture the low-level cyclone, and the forecast exhibited significant errors in both its low-level and upper-level components of the PV distributions. The revised simulation shadows the analyzed development much more successfully. The result is discussed in the context of the need to improve the initial analysis fields and to devise alternative forecasting strategies.

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Christoph Schär and Huw C. Davies

Abstract

An instability of a cold front possessing a low-level warm-band precursor is examined within an f-plane, quasi- and semigeostrophic framework. The basic frontal state is taken to be two-dimensional and of uniform potential vorticity. Theoretical considerations pinpoint the source and nature of the instability to be a vortex interaction effect acting across the thermal maximum of the warm band. They also reveal that the most unstable mode associated with this flow configuration has a mixed barotropic-baroclinic character and possesses some features (e.g., a wavelength ∼1000 km and a doubling time ∼1½ days) that are akin to surface frontal waves. In addition nonlinear numerical model simulations demonstrate that the frontal wave growth equilibrates rapidly but not before the establishment of a rich mesoscale flow structure.

A brief assessment is presented of the relationship of this diagnosed instability to realized atmospheric flow patterns and to other mechanisms that have been postulated for the growth of frontal waves.

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Huw C. Davies and Marco Didone

Abstract

Consideration is given to the diagnosis and dynamics of synoptic and subsynoptic forecast error from a potential vorticity (PV) perspective. A depiction of the extratropical “forecast minus analysis” PV pattern on a cross-tropopause isentropic surface serves to illustrate characteristic features of the PV-error field, and these features relate both to the instigation, development, and breaking of Rossby waves at the tropopause, and to surface cyclones and anticyclones. An outline is provided of a three-component diagnostic approach for studying PV forecast error. The approach exploits the quintessential PV concepts of quasi conservation, inversion, and attribution, and its essence is illustrated qualitatively by reference to one particular synoptic sequence over the North Atlantic. It also provides a framework for assessing the dynamics of possible mechanisms for generating realized PV-error features. The approach offers a conceptually attractive and diagnostically useful method of analyzing, assessing, and understanding the dynamics of forecast error growth.

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