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Daniel Keyser
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Qin Xu and Daniel Keyser

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This paper examines the completeness of the solutions for three-dimensional ageostrophic circulations determined from the quasigeostrophic psi equations (or from the counterpart semigeostrophic psi equations in geostrophic-coordinate space). It is shown that a complete solution should contain two parts: a baroclinic part and a barotropic part. The solution of the psi equations with homogeneous (zero) upper and lower boundary conditions yields only the baroclinic part of the ageostrophic wind field, while the barotropic part can be recovered from the ageostrophic vorticity equation. The barotropic ageostrophic wind field is two-dimensional and nondivergent. It may be subdivided into rotational and harmonic pans, respectively forced by barotropic ageostrophic vorticity and by nonhomogeneous lateral boundary conditions (with nonzero cross-boundary mass flux). Methods for obtaining the complete solution are proposed and examples are given, showing the possible significance of the barotropic ageostrophic wind.

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Daniel Keyser and Richard Rotunno

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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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Daniel Keyser and Michael J. Pecnick

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A two-dimensional primitive equation model of frontogenesis forced by a combination of confluence and horizontal shear is formulated for dry, nearly adiabatic and inviscid conditions. The frontogenetical forcing mechanisms are included by respectively specifying the cross-front and vertical variation of the cross-front geostrophic wind component. The results of three numerical integrations containing confluent forcing are analyzed and discussed in detail. The first is the case of pure confluence, in which the vertical shear of the cross-front geostrophic component is zero. The second and third cases respectively consist of negative and positive vertical shear of the cross-front geostrophic component, which correspond to cold and warm advection at upper levels for the configuration of the alongfront wind component. The above frontogenetical forcing and the resulting frontal structures are related to typical flow patterns occurring within midlatitude baroclinic waves during various stages in their life cycle.

The simulated upper-level frontal structures in the pure confluence and warm advection cases resemble those of previous two-dimensional frontogenesis models. Development is maximized near the tropopause where frontogenetical confluence and convergence are maximized and the frontolytical tilting effects of vertical motions are minimized. Frontogenesis is enhanced throughout the troposphere in the warm advection case relative to the pure confluence case through differential thermal advection by the cyclonically sheared alongfront wind component.

In contrast, in the cold advection case, a well-defined front evolves initially near the tropopause and eventually extends to the midtroposphere. The development is dominated by tilting, as effects associated with the horizontal components of the air motion are frontolytical. The frontogenetical tilting effects are a consequence of a lateral shift of the thermodynamically direct cross-front ageostrophic circulation far enough into the warm air to place the maximum subsidence in the midtroposphere within and to the warm side of the developing frontal zone. Numerous aspects of the above picture are shown to correspond closely to the observational findings of a number of synoptic case studies. A noteworthy result is that tropopause folding is reproduced, in which lower stratospheric air is advected downward to the 700 mb level. This behavior occurs despite the two-dimensional formulation of the model, which does not include the three-dimensional effects of curvature dynamics on the vertical motion field. Finally, several positive feedback mechanisms involving the vertical motion field are postulated and will be examined through a diagnostic analysis of the cross-front ageostrophic circulation in a companion paper.

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Daniel Keyser and Toby N. Carlson

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An elevated mixed layer is a principal component of the conceptual model recently proposed by Carlson and others to explain the evolution of a severe storm environment over the Southern Plains of the United States during springtime. Elevated mixed layers are most likely to be found downwind of strongly heated arid land areas (often plateaus), which favor the growth of a deep mixing layer with high potential temperature. The lower and lateral boundaries of elevated mixed layers are distinctly defined respectively by a statically stable layer, referred to as a lid inversion, and a midlevel front. These boundaries mark the zonesof transition between the airstream defining the elevated mixed layer and other airstreams of differing geographical origin and, consequently, thermodynamic properties.

In this study, the Sawyer-Eliassen secondary circulation equation is used to diagnose the transverse ageostrophic circulations that are associated with the dynamical forcing implied by the above conceptual model of the elevated mixed layer structure. The diagnoses are based upon subjective analyses of the elevated mixed layer identified in the SESAME IV dataset at 2100 GMT 9 May 1979 and upon analytically specified patterns reproducing many of the main features of the subjective analyses. The outcome of the diagnoses indicates that a combination of confluence and anticyclonic shear forces a thermally direct circulation centered in the midlevel front and an indirect cell centered in the upper region of the elevated mixed layer,which results in a zone of rising motion between the cells at the edge of the elevated mixed layer. Additional tests, which compare the ageostrophic circulations derived from analytically specified fields in which the elevated mixed layer structure is defined in detail and in which it is highly smoothed, indicate that the above circulation pattern is enhanced by increased baroclinicity in the midlevel frontal zone and the diminished static stability in the elevated mixed layer.

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Daniel Keyser and Michael J. Pecnick

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The development of frontal zones is examined in a two-dimensional primitive equation model of frontogenesis formulated for dry, nearly adiabatic and inviscid conditions. The model results are interpreted in the context of the general problem of determining the dynamical properties of cold and warm fronts. The central hypothesis (attributable to Eliassen) is that cold and warm fronts may be distinguished by the orientation of the cross-front thermal wind component and the sense of the associated along-front temperature variation. Three simulations comprising confluent forcing (geostrophic contraction in the cross-front direction) and differing initial specifications of the along-front potential temperature gradient are examined in detail. In the first simulation, referred to as the pure confluence case, the along-front potential temperature gradient is set to zero, establishing a control for specifying along-front potential temperature variations respectively characteristic of cold and warm fronts in the latter two simulations. These simulations are referred to as the cold and warm advection cases, reflecting the initial sense of the potential temperature advection in the along-front direction at low levels in the model atmosphere.

Whereas the frontal zone in the pure confluence case is relatively shallow, the frontal zone in the cold advection case is better defined and occupies a deeper extent of the lower troposphere. The associated transverse ageostrophic circulations are centered within the frontal zones and are thermodynamically direct in both cases, but the circulation is significantly stronger in the cold advection case. The frontal zone in the warm advection case is quite shallow and the associated cross-front potential temperature gradient is rather weak, although the low-level vorticity and convergence are well defined. In contrast to the previous two cases, the vertical circulation, although thermodynamically direct, is centered sufficiently far into the cold air for the upward branch to be situated in the baroclinic region within and to the cold side of the surface frontal zone. A comparative analysis of the evolution of the three frontal zones performed with the prognostic equations for cross-front potential temperature gradient and relative vorticity and with diagnostic equations for the vertical circulation leads to the identification of frontogenetical feedbacks involving the convergence field and its dynamical forcing. This analysis further reveals frontogenetical and frontolytical roles for along-front potential temperature variations respectively characteristic of the cold and warm advection cases, a consequence of the correspondence of the frontal zones with regions of cyclonic relative vorticity.

Evidence is presented to support the contention that the basic frontal structures identified in the three simulations are compatible with recent classifications of frontal features found in idealized three-dimensional simulations of the evolution of baroclinic waves to finite amplitude. This proposed compatibility suggests that the two-dimensional model formulation considered in this study may be capable of abstracting essential dynamical properties of the frontogenetical environment associated with growing baroclinic disturbances in idealized three-dimensional models and perhaps in nature.

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Daniel Keyser and M. A. Shapiro

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This article presents a review of upper-level fronts with the intent of synthesizing observational and modeling studies into a conceptual and dynamical description of these fronts and their evolution relative to the life cycle of midlatitude baroclinic waves. The discussion begins by tracing present-day concepts concerning the structure of upper-level frontal systems, which are based on composite analyses of radiosonde and aircraft data, from their origins in the pioneering analyses of upper-air data in the 1930s. Perspectives from scales both smaller and larger than upper-level frontal systems are provided respectively by considering the effects of turbulent processes on frontal structure and dynamics and by relating variations in frontal structure to the evolution of the baroclinic waves that provide the dynamical environment for upper-level frontogenesis.

The dynamics of upper-level fronts are shown to comprise the interactions between the primary (geostrophic) and secondary (ageostrophic) circulations. To elucidate the mechanisms and feedbacks contributing to the evolution of upper-level fronts in relation to their setting within baroclinic waves, the two-dimensional theory of forced secondary circulations in the cross-front plane developed by Sawyer and Eliassen is presented and interpreted, and theoretical and numerical examples of the formation of upper-level fronts in idealized two-dimensional flows are reviewed. In the three-dimensional case, the presence of along-front ageostrophic circulations superimposed upon the cross-front ageostrophic circulations treated by the two-dimensional theory is discussed in terms of the gradient wind. The relative contribution of the along-front ageostrophic circulation to upper-level frontogenesis is considered in the context of the results from three-dimensional β-plane channel models of baroclinic wave growth.

Directions for future observational, diagnostic and theoretical investigation are identified, including the scale interactions between upper-level fronts, their environmental baroclinic waves and related low-level cyclones, and between upper-level fronts and mesoscale convective systems. The review concludes with a discussion of the potential role of recent innovations in remote-sensing technology and trends in numerical weather prediction using mesoscale models in motivating continuing interest and future advances in frontal research.

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Daniel Keyser and Richard A. Anthes

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The mesoscale numerical model of the planetary boundary layer (PBL), which Lavoie applied to lake-effect snowstorm and to airflow over the Hawaiian Islands, is modified and utilized to assess the feasibility of producing short-range real-data forecasts of low-level flow patterns. The dry model atmosphere comprises three layers. A parameterized surface layer of fixed depth (50 m) follows the variable terrain and allows vertical fluxes of heat and momentum to affect the flow in the overlying PBL or “mixed layer.” The horizontal wind velocity and potential temperature, both prognostic variables, are assumed to be independent of height in the mixed layer. The height of the top of the mixed layer is an additional prognostic variable. A parameterized stable layer, characterized by a vertically constant potential temperature lapse rate, overlies the mixed layer. Synoptic-scale patterns of pressure and potential temperature are specified at the top of this uppermost layer as upper boundary conditions. Energy-conserving parameterizations for the entrainment of heat and momentum from the upper stable layer into the mixed layer and for convective adjustment are introduced. The simplifications in the atmospheric structure provide for considerable computational efficiency while preserving a high degree of physical realism under the assumed conditions of a well-mixed PBL.

Experiments with a cross-section version of the model are performed for a domain containing a smoothed Appalachian terrain profile and adjacent coastal waters in order to economically assess the model's response to variable terrain, differential heating and differential roughness at the coast. The terrain profile produces a perturbation in the quasi-steady-state westerly flow pattern that exhibits subsidence and higher wind speeds over a ridge in qualitative agreement with mountain-wave theory. While differential roughness causes subsidence at the coast, differential heating engenders a maximum of upward motion around 40 km inland that is considered to be a crude representation of a sea breeze superimposed on the westerly flow. The results of the cross-section experiments are used to aid in interpreting a real-data simulation of the daytime PBL over the Middle Atlantic States on 16 October 1973. The model resolves a lee trough in the flow east of the Appalachians, a surface pressure trough in eastern Virginia and eastern North Carolina, and realistic vertical motion patterns along the coastal regions and the Chesapeake Bay. Verification statistics are provided for the sea level pressure and surface potential temperature patterns.

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Daniel Keyser and Richard A. Anthes

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The energetics of Eady's (1949) model of baroclinic instability are used to express the wavenumber-dependent disturbance growth rate in terms of upward and northward fluxes of heat and momentum. This formulation leads to simple physical interpretations for the existence of the wavelength of maximum growth rate and the shortwave cutoff.

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Richard A. Anthes and Daniel Keyser

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Thirty–two 24 h forecasts have been run over western Europe and the eastern United States using a six-layer, 60 km mesh primitive equation model. The forecasts show considerable skill in forecasting cyclogenesis over the Mediterranean and the United States in spite of the inadvertent neglect of surface friction over half of the domain. The average 24 h S 1score for sea level pressure is 39.1 compared to an average of 45.9 for Fleet Numerical Weather Central's operational model and 73.4 for persistence.

The initialization scheme is based on an objective analysis of the horizontal wind field. Following the wind analysis, we infer geopotential and temperature from the rotational part of the wind with a nonlinear form of the balance equation. We present detailed results from one initial analysis and error statistics from 30 analyses occurring from December 1977 through April 1978. Typical root-mean-square (rms) differences between first-guess and balanced analyses of geopotential and temperature are ∼20 m and 2°C, while rms vector differences between analyzed and balanced winds are ∼5 m s–1

Three forecasts are discussed in detail. The first is a case of cyclogenesis in the Gulf of Genoa that was forecast well by the model. The second is a forecast of the intense Ohio blizzard of 26 January 1978, which was also reasonably successful. The structure of the model planetary boundary layer (PBL) in the second forecast is studied with the aid of a one-dimensional, second-order closure PBL model. The third forecast greatly overpredicted the intensity of a cyclone along the southern coast of the United States. Latent heating and the parameterization of cumulus convection were dominant factors in producing this fictitious intensification. In the latter two cases the sensitivity of the model's 24 h forecast of cyclogenesis to surface friction and parameterization of cumulus convection is established.

A major conclusion from this study is that significant improvements in 24 h sea level pressure forecasts were obtained from a model with high horizontal resolution, even though the vertical resolution was coarse and the physics in the model was simple. It appears likely that further increases in forecast accuracy are possible by refining the vertical resolution and improving the physics.

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