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Michael J. Pecnick
and
John A. Young

Abstract

The three-dimensional structure and implied dynamics of a strong tropospheric gravity wave event am studied. It is shown that satellite and continuous surface observations reveal the subsynoptic nature of this “wave of depression” to an extent impossible with conventional data. The observations and theory suggest that the gravity wave originated in the upper troposphere near a jet streak, was quasi-hydrostatic and hence relatively nondispersive and long-lived.

The behavior of the wave at upper-tropospheric levels is revealed by sequences of visible and infrared goesynchronous satellite imagery. Quantitative estimates of cloud top temperatures and winds suggest strong subsidence new 300 mb with an isentropic depression as large as 900 m. The upper-level depression and the surface disturbance propagate coherently with a speed of 32 m s−1 indicating that they are part of the same internal gravity wave. The vertical tilt with height is opposite to the propagation direction and thus is consistent with an upper-tropospheric energy source. The negative surface pressure deviation reaches 7 mb and is qualitatively consistent with the field of surface wind divergence.

Theory is applied to estimate and explain gravity wave properties throughout the troposphere: vertical tilt (decreasing upward) as large as 1:9 in the lower troposphere; maximum wave energy at upper levels, with maximum wind deviation ∼ 15 m s−1, horizontal divergence ∼ 4×10−4 s−1, vertical parcel displacement ∼ 1 km, local potential temperature deviations of several degrees, pressure perturbations ∼ 7 mb, and the time to completely establish the wave throughout the troposphere ∼ 4 h. Further improvement in the description may demand development of “solitary” wave theory for deep depression waves in shear flow.

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Daniel Keyser
and
Michael J. Pecnick

Abstract

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
Michael J. Pecnick

Abstract

Diagnoses are presented of the transverse ageostrophic circulation patterns for two cases from a two-dimensional primitive equation model of frontogenesis forced by a combination of confluence and horizontal shear. The cold advection case (the specified alongfront potential temperature gradient results in differential cold advection by the upper-level jet) realistically simulates upper-level frontogenesis in response to tilting by a cross-front gradient of subsidence. The warm advection case features a frontal system spanning the troposphere, which develops in response to differential horizontal advection. The diagnoses are performed by numerically solving three versions of the two-dimensional Sawyer–Eliassen equation for the streamfunction of the transverse ageostrophic circulation. The quasi-geostrophic (QG) and geostrophic momentum (GM) versions are based on the approximation of cross-front geostrophic balance, while the primitive equation (PE) version includes the possibility of an alongfront component of the ageostrophic flow, which is nondivergent. The PE version reduces to the GM version if the alongtront ageostrophic wind component is neglected.

The QG, GM, and PE transverse ageostrophic circulations are compared for the cold and warm advection cases, which are characterized respectively by relatively large and small cross-front geostrophic imbalances. Consequently, the QG and GM circulations underestimate the PE circulation in the cold advection case, and the GM circulation is extremely close to its PE counterpart in the warm advection case. The transverse ageostrophic circulation is then partitioned into components forced by geostrophic confluence and horizontal shear and effects associated with the alongfront ageostrophic flow. In the cold advection case, the latter two forcing mechanisms are shown to be responsible for the frontogenetical midtropospheric configuration of subsidence, which is maximized within and to the warm side of the developing frontal zone. The partitioned ageostrophic circulations also clarify feedback mechanisms in the cold advection case involving the subsidence and upper-level vorticity fields, and involving the transverse ageostrophic circulation and the alongfront ageostrophic flow pattern. Finally, the GM partitioning of the ageostrophic circulation provides a basis for deriving frontogenesis equations for the vorticity and cross-front potential temperature gradient in terms of the net effect of the forcing and response respectively associated with geostrophic confluence and horizontal shear and alongfront ageostrophic flow. The application of these equations to the diagnosis of upper-level frontogenesis in the cold advection case provides an illustrative example.

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Daniel Keyser
and
Michael J. Pecnick

Abstract

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
,
Michael J. Pecnick
, and
M. A. Shapiro

Abstract

Equations are developed for the temporal rates of change of the magnitudes of vector gradients of potential temperature and absolute momentum projected onto vertical planes transverse to straight frontal zones. Subject to restrictions involving two-dimensionality, the temporal rates of change of the magnitudes of gradients of potential temperature and absolute momentum can be partitioned into effects due to the geostrophic and along-front ageostrophic flow (both of which are taken to be nondivergent) and effects due to the divergence and deformation in the cross-front plane associated with the transverse ageostrophic flow. The terms involving the transverse ageostrophic circulation are of the same mathematical form and analogous in a kinematic sense to the divergence and deformation terms involving the horizontal wind field in Petterssen's classic equation for frontogenesis in the potential temperature field.

The proposed form of the frontogenesis equation for the magnitude of the potential temperature gradient in the transverse plane is illustrated with the results of two simulations from an idealized two-dimensional primitive equation model in which upper-level frontogenesis proceeds by quite different mechanisms. For the case in which the along-front variation of potential temperature is zero, geostrophic effects are dominant in the upper troposphere, and are augmented and opposed respectively by ageostrophic vertical deformation in the upper and middle troposphere. The relationship between the horizontal and vertical circulations is consistent with the development of frontal properties that are best defined in the upper troposphere near the tropopause. in contrast, for the case in which the along-front variation of potential temperature results in cold advection by the upper-level jet in the along-front wind component, ageostrophic vertical deformation is strongly dominant in the upper and middle troposphere, where it is opposed weakly by effects associated with both the geostrophic and along-front ageostrophic flow. The relationship between the horizontal and vertical circulations is consistent with the development of frontal properties that are best defined in the upper and middle troposphere. This comparison suggests the possible importance of ageostrophic vertical deformation for the development of mid-tropospheric frontal zones observed in nature in conjunction with amplifying baroclinic waves.

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Ralph A. Petersen
,
Geoffrey J. DiMego
,
James E. Hoke
,
Kenneth E. Mitchell
,
Joseph P. Gerrity
,
Richard L. Wobus
,
Hann-Ming H. Juang
, and
Michael J. Pecnick

Abstract

The final set of changes to NMC's Regional Analysis and Forecast System (RAFS) is described. The changes include modifications to both the forecast model and the analysis model, as well as development of a Regional Data Assimilation System (RDAS). The forecast model changes were developed to correct a number of known deficiencies in the Nested Grid Model (NGM), while the RDAS development will allow the RAFS to take advantage of the new asynoptic data sets soon to be available. Several of the changes were implemented on 7 November 1990. The remaining changes (including the RDAS) are planned for implementation before mid 1991. Results from tests of the revised forecast model and the combined RDAS/NGM system are presented and discussed.

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