Height Tendency Research Articles

Dynamical Diagnosis: A Comparison of Quasigeostrophy and Ertel Potential Vorticity

Abstract Advances in computer power, new forecasting challenges, and new diagnostic techniques have brought about changes in the way atmospheric development and vertical motion are diagnosed in an operational setting. Many of these changes, such as improved model skill, model resolution, and ensemble forecasting, have arguably been detrimental to the ability of forecasters to understand and respond to the evolving atmosphere. The use of nondivergent wind in place of geostrophic wind would be a step in the right direction, but the advantages of potential vorticity suggest that its widespread adoption as a diagnostic tool on the west side of the Atlantic is overdue. Ertel potential vorticity (PV), when scaled to be compatible with pseudopotential vorticity, is generally similar to pseudopotential vorticity, so forecasters accustomed to quasigeostrophic reasoning through the height tendency equation can transfer some of their intuition into the Ertel-PV framework. Indeed, many of the differences between pseudopotential vorticity and Ertel potential vorticity are consequences of the choice of definition of quasigeostrophic PV and are not fundamental to the quasigeostrophic system. Thus, at its core, PV thinking is consistent with commonly used quasigeostrophic diagnostic techniques.

Calculated Height Tendencies in Two Southern Hemisphere Blocking and Cyclone Events: The Contribution of Diabatic Heating to Block Intensification

Abstract The Zwack–Okossi vorticity tendency equation was used to calculate 500-hPa height tendencies in two intensifying Southern Hemisphere blocking events. The National Centers for Environmental Prediction–National Center for Atmospheric Research gridded reanalyses were used to make each of these calculations. The block intensification period for each event was associated with a deepening surface cyclone during a 48-h period beginning at 1200 UTC 28 July and 1200 UTC 8 August 1986, respectively. These results demonstrate that the diabatic heating forces height rises through the sensible and latent heating terms in these two Southern Hemisphere blocking events. The sensible heating was the larger contributor, second only to (about the same as) the vorticity advection term in the first (second) event. The vorticity advection term has been shown by several studies to be associated with block intensification.

Lower-Tropospheric Height Tendencies Associated with the Shearwise and Transverse Components of Quasigeostrophic Vertical Motion

Abstract The recent suggestion that lower-tropospheric cyclogenesis is predominantly a result of column stretching associated with the updraft portion of the shearwise quasigeostrophic (QG) vertical motion is quantified through direct calculation of 900-hPa height tendencies via the QG vorticity equation. Comparison of the separate lower-tropospheric height tendencies associated with the shearwise and transverse portions of QG omega in a robust cyclogenesis event demonstrates that the shearwise updraft drives the largest part (>80%) of the cyclogenetic height falls at least through the end of the mature stage of the life cycle. The lower-tropospheric height falls and vorticity production near the sea level pressure minimum of the occluded surface cyclone are driven nearly equally by shearwise and transverse updrafts.

A Quasigeostrophic Analysis of a Meander in the Palamós Canyon: Vertical Velocity, Geopotential Tendency, and a Relocation Technique

The quasigeostrophic geopotential tendency and omega equations are integrated to examine the dynamics of an upper-ocean coastal meander sampled during an intensive survey in the Palamos Canyon (northwestern Mediterranean Sea). Results for dynamic height tendency reveal that the meander is not growing or decaying but is propagating downstream at a velocity of about 4 km day21. This propagation speed implies a problem of synopticity in the field observations, which is solved through a data relocation scheme. The station relocation has important consequences on the magnitude of crucial dynamical variables such as the vertical velocity: maximum values of 20 m day21 before the relocation reduce to 10 m day21 after the relocation. The impact of bottom boundary conditions in the solution of the omega equation is also analyzed. Results indicate that for the stratification encountered during the survey, effects of topographic forcing are negligible above approximately 300 m.

Piecewise Tendency Diagnosis of Weather Regime Transitions

Abstract Piecewise tendency diagnosis (PTD) is extended and employed to study the dynamics of weather regime transitions. Originally developed for adiabatic and inviscid quasigeostrophic flow on a beta plane, PTD partitions local geopotential tendencies into a linear combination of dynamically meaningful source terms within a potential vorticity (PV) framework. Here PTD is amended to account for spherical geometry, diabatic heating, and ageostrophic processes, and is then used to identify the primary mechanisms responsible for Northern Hemisphere weather regime transitions. Height tendency patterns obtained by summing the contributions of individual PTD forcing terms correspond very well to actual height tendencies. Composite PTD analyses reveal that linear PV advections provide the largest dynamical forcing for the weather regime development over the North Pacific. Specifically, linear baroclinic growth provides the primary forcing while barotropic deformation of PV anomalies provides a secondary contrib...

Ageostrophic Forcing in a Height Tendency Equation

The role of the ageostrophic vorticity tendencies in the Zwack‐Okossi vorticity tendency equation has been examined within the context that this term in the equation acts as a correction term for the vorticity tendency or height tendency calculations. In this paper, this term is shown to act as both a response to initial forcing and as a forcing mechanism itself in modulating the initial forcing. Using an earlier methodology for partitioning the wind field and the height field into their divergent and rotational parts, the ageostrophic wind is shown to contain components of both parts. Then, using an omega equation, an ageostrophic vorticity tendency is calculated, which has forcing mechanisms similar to a height tendency equation. This ageostrophic tendency is then used in this height tendency equation and provides for an improved method of calculating the ageostrophic wind rather than simply calculating it as a residual. Two case studies are then examined to demonstrate this point. For both case studies, the calculated height tendencies using the derived ageostrophic winds and those calculated as a residual overestimated the height tendencies, especially at the surface. While the correlation coefficients show that the two methods are comparable at 500 hPa, at the surface there is a notable degree of improvement in the pattern similarity. This resulted in an improved representation of the 500-hPa height tendencies for the onset of the Atlantic blocking event despite marginal improvements in the calculated field overall.

The Role of High- and Low-Frequency Dynamics in Blocking Formation

Time evolutions of prominent blocking flow configurations over the North Pacific and Europe are compared based upon composites for the 30 strongest events observed during 27 recent winter seasons. Fluctuations associated with synoptic-scale migratory eddies have been filtered out before the compositing. A quasi-stationary wave train across the Atlantic is evident during the blocking amplification over Europe, while no counterpart is found to the west of the amplifying blocking over the North Pacific. Correlation between the tropopause-level potential vorticity (PV) and meridional wind velocity associated with the amplifying blocking is found to be negative over Europe in association with the anticyclonic evolution of the low-PV center, but it is almost zero over the North Pacific. Feedback from the synoptic-scale eddies, as evaluated in the form of 250-mb geopotential height tendency due to the eddy vorticity flux convergence, accounts for more than 75% of the observed amplification for the Pacific blocking and less than 45% for the European blocking. This difference is highlighted in two types of ‘‘contour advection with surgery’’ experiments. In one of them PV contours observed four days before the peak blocking time were advected by composite time series of the low-pass-filtered observational wind, and in the other experiment they were advected by the low-pass-filtered wind from which the transient eddy feedback evaluated as above had been removed at every time step. Hence, the latter data should be dominated by low-frequency dynamics. For the European blocking both experiments can reproduce the anticyclonic evolution of low-PV air within a blocking ridge as observed. For the Pacific blocking, in contrast, the observed intrusion of low-PV air into the higher latitudes cannot be reproduced without the transient feedback. Furthermore, in a barotropic model initialized with the composite 250-mb flow observed three days before the peak time, a simulated blocking development over the North Pacific is more sensitive to the insertion of the observed transient feedback than that over Europe. These results suggest that the incoming wave activity flux associated with a quasi-stationary Rossby wave train is of primary importance in the blocking formation over Europe, whereas the forcing by the synoptic-scale transients is indispensable to that over the North Pacific.

A Diagnosis of Two Blocking Events That Occurred Simultaneously in the Midlatitude Northern Hemisphere

Using the Goddard Laboratory for Atmospheres Goddard Earth Observing System-1 analyses, the horizontal distribution of atmospheric forcing processes involved in the growth, maintenance, and decay of two Northern Hemisphere midlatitude blocking anticyclones that occurred simultaneously were examined, with the goal of determining whether there was a dynamic connection between the two cases. The complete form of the Zwack‐ Okossi equation, which is a generalization of the Petterssen‐Sutcliffe development equation, was used as the primary diagnostic tool. The basic analyses were partitioned into their planetary-scale and synoptic-scale components (noninteraction) 500-hPa height tendencies, as well as scale interaction 500-hPa height tendencies. Based on the results of this diagnosis, there was no dynamic connection between these blocking anticyclones. This result agrees with findings of other studies based on a statistical analysis of simultaneous blocking. These results also imply that blocking may be a local phenomenon. The diagnostic results from these blocking events were, in many respects, similar to those of previous studies. However, some key differences were found. For example, it was found here that for both mode 2 blocking events, temperature advection was an important mechanism in block formation. Earlier results showed vorticity advection as the primary atmospheric forcing process in block formation for a mode 1 block. Also, the scalepartitioned results show that upstream cyclones contributed to block formation and intensification in these events directly through the synoptic-scale component, often with the support of the interaction component, of the total forcing. Earlier scale-partitioned results showed that the interaction component of the total forcing was most important in the formation of a mode 1 block.

Height Tendency Diagnostics Using a Generalized Omega Equation, the Vorticity Equation, and a Nonlinear Balance Equation

Abstract Height tendency dynamics are studied with a system consisting of a generalized omega equation, the vorticity equation, and a nonlinear balance equation. By using the first two equations, vorticity tendency is first partitioned into components associated with vorticity advection, thermal advection, friction, diabatic heating, and an ageostrophic tendency term. The nonlinear balance equation is then employed to interpret the vorticity tendency components in terms of height tendencies. The height tendencies due to vorticity advection and friction can be divided into parts associated with the direct forcing and the vertical motions induced by this forcing. This division illustrates the efficiency of vertical motions in smoothing out the vertical gradients in the forcing field. The system is solved over a global domain, but the main emphasis is on an analysis of the “Presidents’ Day cyclone” of February 1979. Although the calculations do not fully capture the observed decrease in the deepening rate of...

Piecewise Tendency Diagnosis of Dynamical Processes Governing the Development of an Upper-Tropospheric Mobile Trough

Abstract The intensification and evolution of midlatitude upper-tropospheric mobile troughs may be viewed in terms of the isentropic advection and deformation of the tropopause potential vorticity gradient. The potential vorticity viewpoint allows one to qualitatively assess observed events in the context of existing theories of mobile trough genesis, such as baroclinic instability or downstream development. In order to quantitatively determine the role of distinct dynamical process, the method of piecewise tendency diagnosis, or PTD, is developed. PTD is an extension of piecewise potential vorticity inversion applied to height tendencies, with the forcing terms in the quasigeostrophic height tendency equation partitioned into potential vorticity advection associated with distinct dynamical processes. A particular case of mobile trough genesis, which occurred during 1–4 December 1980 over North America is diagnosed using PTD. Although about 20% of the intensification of the trough was due to superposition...

The Ohio Valley Wave-Merger Cyclogenesis Event of 25–26 January 1978. Part II: Diagnosis Using Quasigeostrophic Potential Vorticity Inversion

Abstract The dynamical interactions between precursor disturbances during the wave-merger cyclogenesis event of 25–26 January 1978 over eastern North America are diagnosed using quasigeostrophic potential vorticity (QGPV) inversion. This case is characterized by two prominent preexisting upper-level disturbances that induce rapid surface cyclogenesis as they come into close proximity. Static QGPV inversion is used to attribute a particular geopotential height field to the QGPV associated with each precursor disturbance. The full flow is partitioned into the following components: the northern upper precursor, the southern upper precursor, and the background flow. Prognostic QGPV inversion is used to quantify the instantaneous geopotential height tendencies attributable to each of these flow components. The static-inversion results for the upper precursors exhibit the structure of baroclinic vortices with maximum amplitude near the tropopause. During the 48-h period spanning the period of study of this even...

A Forecast and Analyzed Cyclogenesis Event Diagnosed with Potential vorticity

Abstract A cyclone that developed over the eastern United States during December 1992 is investigated using a potential vorticity (PV) framework. Upon partitioning the perturbation PV field (which includes the near-surface potential temperature distribution) into upper-level (UL), low-level (LL), and lower boundary (LB) components, the extent to which particular PV anomalies contribute to the cyclone development is quantified by inverting the PV distribution associated with each component. In addition, the accuracy of a 48–84-h forecast, produced by the CCM2 version of NCAR's Community Climate Model, is assessed. The assessment primarily concerns the 36-h geopotential height tendencies forced at 850 mb by the individual components of the analyzed and forecast PV tendency fields. It is found that the lower boundary (923 mb) thermal wave accompanying the storm is amplified mostly by the winds associated with an upper-level disturbance and that latent heating plays an important, but secondary, role in near-s...

Development of a Rapidly Deepening Extratropical Cyclone over Land. Part I: Kinematic Aspects

Abstract The relatively rare case of an explosive land cyclone that occurred on I5–17 November 1989 over the United States and Canada is investigated to determine the physical mechanisms responsible for its development. Hourly surface and 12-h upper-air data are analyzed for this storm for the 36-h period beginning on 0000 UTC 15 November. The system appears to develop through favorable positioning of the surface low with respect to a 5OO-hPa short-wave trough and 250-hPa jet streak and yields the greatest deepening of 13 hPa in 12 h. Through an analysis of the terms in the quasigeostrophic height tendency equation, quasigeostrophic theory is deemed to be qualitatively inaccurate in diagnosing the development of this system. The performance of the National Meteorological Center's (currently known as the National Centers for Environmental Prediction) operational models is viewed, and errors in model forecasts of surface low position and intensity are attributed in large part to faulty initialization. A com...

The Balanced Dynamical Nature of a Rapidly Intensifying Oceanic Cyclone

Abstract Aided with a numerical simulation, the authors diagnose the synoptic-scale evolution of an intense extratropical cyclone over the western Atlantic Ocean from the perspective of balanced dynamics using potential vorticity inversion techniques. The authors show that even during the period of largest growth rate, early in the life cycle, the balance equations capture much of the nondivergent wind, irrotational wind, and height tendency fields. The structure of the cyclone evolves from a maximum amplitude at the tropopause to a maximum amplitude at the surface as the system moves offshore. The vertical phase structure remains slightly upshear tilted throughout (less than one-quarter wavelength). Cyclogenesis is interpreted in terms of a baroclinic wave propagating through a varying basic state, in which surface development is rapid because of the sudden response of the wave structure to a changing environment. The mature cyclone structure strongly resembles cases of continental cyclones except that t...

An examination of pressure tendency mechanisms in an idealized simulation of extratropical cyclogenesis

A numerical simulation of idealized Type-A extratropical cyclogenesis is used to examine pressure tendency mechanisms following a surface low center through its evolution. It is found that horizontal density advection, which maximizes near a developing tropopause undulation (potential vorticity anomaly), is the primary mechanism by which the density and hydrostatic pressure is reduced in the column above the developing surface low center. The density and pressure tendencies associated with horizontal velocity divergence and vertical mass divergence are an order of magnitude larger than the horizontal advective tendencies but are of opposite sign and tend to offset each other. The residual tendencies that result from combining the horizontal velocity divergence and vertical mass divergence are associated with positive density and pressure tendencies that generally oppose but do not counteract the negative tendencies produced by upper-level horizontal advection until late in the evolution of the cyclone. However, this residual divergence is the primary mechanism for the generation of the upstream low density warm pool over the low portion of the tropopause undulation that is later advected over the surface low. In general, these results are consistent with historical as well as more recent studies that suggest the importance of tropopause-level temperature advection in the promotion of the observed height tendency patterns accompanying the superposition of tropopause- and ground-based potential vorticity anomalies during Type B cyclogenesis. From a hydrostatic tendency perspective, it is concluded that baroclinic instability is a process whereby low density, warm air especially above the tropopause that has formed owing to divergence and vertical motion effects is advected downstream and over low-level baroclinic zones and nascent cyclones. In this framework, Type B is distinguished from Type A cyclogenesis by the existence of an initial reservoir of low density, warm air above a tropopause undulation prior to surface cyclogenesis. DOI: 10.1034/j.1600-0870.1995.00117.x

Planetary and synoptic-scale interactions during the life cycle of a mid-latitude blocking anticyclone over the North Atlantic

The formation of a blocking anticyclone over the North Atlantic has been examined over its entire life-CyCle using the Zwack-Okossi (Z-O) equation as the diagnostic tool. This blocking anticyclone occurred in late October and early November of 1985. The data used were provided by the NASA Goddard Laboratory for Atmospheres on a global 2.O degree latitude by 2.5 degree longitudinal grid. The horizontal distribution of the atmospheric forcing mechanisms that were important to 500 mb block formation, maintenance and decay were examined. A scale-partitioned form of the Z-O equation was then used to examine the relative importance of forcing on the planetary and synoptic scales, and their interactions. As seen in previous studies, the results presented here show that upper tropospheric anticyclonic vorticity advection was the most important contributor to block formation and maintenance. However, adiabatic warming, and vorticity tilting were also important at various times during the block lifetime. In association with precursor surface cyclogenesis, the 300 mb jet streak in the downstream (upstream) from a long-wave trough (ridge) amplified significantly. This strengthening of the jet streak enhanced the anti-cyclonic vorticity advection field that aided the amplification of a 500 mb short-wave ridge. Tile partitioned height tendency results demonstrate that the interactions between the planetary and sn,noptic-scale through vorticity advection was the most important contributor to block formation. Planetary-scale, synoptic-scale. and their interactions contributed weakly to the maintenance of the blocking anticyclone with the advection of synoptic-scale vorticity by the planetary-scale flow playing a more important role. Planetary-scale decay ofthe long-wave ridge contributed to the demise of this blocking event.

A Study of the Development of Extratropical Cyclones with an Analytic Model. Part II: Sensitivity to Tropospheric Structure and Analysis of Height Tendency Dynamics

Abstract An analytic quasigeostrophic model is used to examine the sensitivity of type B cyclogenesis to the vertical structure of the troposphere given a particular stratospheric temperature configuration. It is found that there is an optimal tropospheric configuration that produces the largest negative height tendency at the center of the 1000-mb model cyclone. Based on the response of the 1000-mb height tendencies, altering the baroclinicity in the model planetary boundary layer (PBL) does not significantly affect the instantaneous quasigeostrophic dynamics of the deep atmosphere. Rather, the PBL temperature anomalies affect the development of lower-tropospheric model lows by hydrostatically shifting or steering the cyclone centers to locations beneath more (or less) favorable deep atmospheric quasigeostrophic conditions for development. Diagnostic analyses of three individual stratospheric-tropospheric model configurations are also performed to examine the dynamics that drive the height (pressure) ten...

On Understanding Height Tendency

Abstract Top-down height tendency reasoning is explained and examined. This approach uses the assumption of a stratospheric level of insignificant dynamics (LID)—where height and pressure tendencies are considered negligible—to simplify the understanding of cyclone-scale hydrostatic height (pressure) tendency in the troposphere. Quasigeostrophic analytic model results confirm the existence of such a LID for scales less than approximately 5000 km. An examination of a height tendency equation with the LID assumption shows that there must be net integrated local warming (cooling) between the LID and any level below the LID where heights are falling (rising). The local temperature tendency, which from the thermodynamic equation results from advection, diabatic heating, and the product of vertical motion and static stability, reflects the combined actions of all thermodynamic and dynamic processes that together promote hydrostatic height change in isobaric coordinates. In particular, the important dynamic effe...

On the Interpretation of Geopotential Height Tendency Equations

Abstract The conceptual model for height tendency presented by Hirschberg and Fritsch directly links upper-level virtual temperature tendency with low-level height tendency, overlooking the essential dynamics of mass divergence. An analysis of the complete height tendency equation shows that upper-level virtual temperature change car only indirectly induce low-level height change by driving ageostrophic circulations. To avoid misconceptions about middle- and lower-tropospheric height tendency, the dynamics of height tendency are reviewed.

A Study of the Influence of Satellite Data on GLA Analyses over the Atlantic Ocean during a Period of Blocking Anticyclone Development

This paper presents a statistical diagnosis of the differences between two Goddard Laboratory for Atmospheres analysis representations of temperature and wind speed, one containing satellite data influences (SAT analyses) and one without (NOSAT analyses), for a case of oceanic blocking anticyclone development. Results, obtained using area means and standard deviations of the two fields and correlation coefficients and root-mean-square differences between the two fields, indicate that the inclusion of satellite data can have significant impact on ocean-domain analyses. This is especially evident if one examines higher-order fields that represent gradients in the basic variable fields or contain covariances between two different variables (e.g., advections). More specifically, the inclusion of satellite data resulted in a cold (warm) temperature bias at low (high) levels and weaker temperature gradients, stronger winds, weaker vertical wind shears, and a warm-air advection bias at most levels. The SAT analyses also exhibited larger standard deviations than the NOSAT for wind speed, relative vorticity, vorticity advection, temperature advection, and 500-mb height tendencies, suggesting that for this case the spatial variability of the circulation features were enhanced by the inclusion of satellite data. Even so, since height tendencies forced by vorticity and temperature advection were less sensitive to the addition of satellite data than were the advection quantities themselves, the dynamics of the blocking system was apparently less influenced by the presence of satellite data than was the structure of the system.