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David M. Schultz

Abstract

Stonitsch and Markowski perform multiple-Doppler radar analyses of a cold front over Oklahoma and Kansas. Despite their interesting results, their explanations include a number of misconceptions about cold fronts. These misconceptions include the proper interpretation of the frontogenesis function, the role of entrainment versus differential surface sensible heat flux toward weakening the virtual potential temperature gradient across a cold front, a separation of the wind shift from the virtual potential temperature gradient, and the factors that affect the motion of the cold front.

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David M. Schultz

Abstract

Time series of cold fronts from stations in the central United States possess incredible variety. For example, time series of some cold fronts exhibit a sharp temperature decrease coincident with a pressure trough and a distinct wind shift. Other time series exhibit a prefrontal trough and wind shift that precedes the temperature decrease associated with the front by several hours. In early March 2003, two cold fronts passed through Oklahoma City, Oklahoma (OKC), representing each of the above scenarios. The cold front on 4 March was characterized by a coincident sharp wind shift, pressure trough, and a strong temperature decrease of 10°C in 2 min. On the other hand, the cold-frontal passage on 8 March was characterized by a prefrontal wind shift occurring over a 7-h period before the temperature decrease of 10°C in 2 h. Twelve hours before frontal passage at OKC, both fronts had the same magnitude of the horizontal potential temperature gradient and Petterssen frontogenesis. By the time of frontal passage at OKC, the magnitude of the horizontal potential temperature gradient for the 4 March front was double that of the 8 March front, and the frontogenesis was nearly four times as great. The simultaneity of the surface horizontal potential temperature gradient and deformation and convergence maxima (coincident with the wind shift) was primarily responsible for the greater strength of the cold front in OKC on 4 March compared to that on 8 March. Whether a prefrontal wind shift occurred was determined by the timing and location of cyclogenesis in the central United States. On 4 March, a cyclone was adjacent to the slope of the Rocky Mountains and developed on the cold front as it moved through Oklahoma, permitting greater frontogenesis and resulting in a cold-frontal passage at OKC with a simultaneous temperature decrease and wind shift. On 8 March, the cyclone moved eastward through Oklahoma before the arrival of the cold front, resulting in a prefrontal wind shift associated with the northerlies behind the cyclone, followed by the frontal passage. A 2-yr climatology of cold-frontal passages at OKC supports the results from the two cases above, indicating that the timing and location of cyclogenesis was responsible for these two different cold-frontal structures. These results imply that, for situations resembling those of this study, the prefrontal trough is not directly associated with the cold front, but is caused by external processes related to the lee troughing.

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David M. Schultz
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David M. Schultz

Abstract

Despite the popularity of the conveyor-belt model for portraying the airflow through midlatitude cyclones, questions arise as to the path of the cold conveyor belt, the lower-tropospheric airflow poleward of and underneath the warm front. Some studies, beginning with Carlson's analysis of the eastern U.S. cyclone of 5 December 1977, depict the cold conveyor belt moving westward, reaching the northwest quadrant of the storm, turning abruptly anticyclonically, rising to jet level, and departing the cyclone downstream (hereafter, the anticyclonic path). Other studies depict the cold conveyor belt reaching the northwest quadrant, turning cyclonically around the low center, and remaining in the lower troposphere (the cyclonic path). To clarify the path of the cold conveyor belt, the present study reexamines Carlson's analysis of the cold conveyor belt using an observational and mesoscale numerical modeling study of the 5 December 1977 cyclone.

This reexamination raises several previously unappreciated and underappreciated issues. First, airflow in the vicinity of the warm front is shown to be composed of three different airstreams: air-parcel trajectories belonging to the ascending warm conveyor belt, air-parcel trajectories belonging to the cyclonic path of the cold conveyor belt that originate from the lower troposphere, and air-parcel trajectories belonging to the anticyclonic path of the cold conveyor belt that originate within the midtroposphere. Thus, the 5 December 1977 storm consists of a cold conveyor belt with both cyclonic and anticyclonic paths. Second, the anticyclonic path represents a transition between the warm conveyor belt and the cyclonic path of the cold conveyor belt, which widens with height. Third, the anticyclonic path of the cold conveyor belt is related to the depth of the closed circulation associated with the cyclone, which increases as the cyclone deepens and evolves. When the closed circulation is strong and deep, the anticyclonic path of the cold conveyor belt is not apparent and the cyclonic path of the cold conveyor belt dominates. Fourth, Carlson's analysis of the anticyclonic path of the cold conveyor belt was fortuitous because his selection of isentropic surface occurred within the transition zone, whereas, if a slightly colder isentropic surface were selected, the much broader lower-tropospheric cyclonic path would have been evident in his analysis instead. Finally, whereas Carlson concludes that the clouds and precipitation in the cloud head were associated with the anticyclonic path of the cold conveyor belt, results from the model simulation suggest that the clouds and precipitation originated within the ascending warm conveyor belt.

As a consequence of the reexamination of the 5 December 1977 storm using air-parcel trajectories, this paper clarifies the structure of and terminology associated with the cold conveyor belt. It is speculated that cyclones with well-defined warm fronts will have a sharp demarcation between the cyclonic and anticyclonic paths of the cold conveyor belt. In contrast, cyclones with weaker warm fronts will have a broad transition zone between the two paths. Finally, the implications of this research for forecasting warm-frontal precipitation amount and type are discussed.

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David M. Schultz

Abstract

The conceptual model of a classical surface-based cold front consists of a sharp temperature decrease coincident with a pressure trough and a distinct wind shift at the surface. Many cold fronts, however, do not conform to this model—time series at a single surface station may possess a pressure trough and wind shift in the warm air preceding the cold front (hereafter called a prefrontal trough and prefrontal wind shift, respectively). Although many authors have recognized these prefrontal features previously, a review of the responsible mechanisms has not been performed to date. This paper presents such a review. Ten disparate mechanisms with different frontal structures have been identified from the previous literature. These mechanisms include those external to the front (i.e., those not directly associated with the cold front itself): synoptic-scale forcing, interaction with lee troughs/drylines, interaction with fronts in the mid- and upper troposphere, and frontogenesis associated with inhomogeneities in the prefrontal air. Mechanisms internal to the front (i.e., those directly associated with the structure and dynamics of the front) include the following: surface friction, frontogenesis acting on alongfront temperature gradients, moist processes, descent of air, ascent of air at the front, and generation of prefrontal bores/gravity waves. Given the gaps in our knowledge of the structure, evolution, and dynamics of surface cold fronts, this paper closes with an admonition for improving the links between theory, observations, and modeling to advance understanding and develop better conceptual models of cold fronts, with the goal of improving both scientific understanding and operational forecasting.

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David M. Schultz and Frederick Sanders

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Previous studies have shown that 500-hPa mobile trough births (or genesis) occur preferentially in northwesterly flow during upper-level frontogenesis, and that cold advection assists in, and is a product of, mobile trough intensification. This study focuses on the synoptic environments and thermal-advection patterns of upper-level fronts associated with mobile trough births in northwesterly flow. A climatology of 186 such events, derived from an earlier study by Sanders, shows that most births tend to occur within uniform or diffluent flow and that most tend to be associated with relatively weaker 500-hPa thermal advection. Most mobile trough births in diffluence, however, tend to be associated with increasing 500-hPa cold advection, typically indicated by a cyclonic rotation of isentropes, whereas, most mobile trough births in confluence tend to be associated with weaker 500-hPa thermal advection.

Two cases of upper-level frontogenesis associated with mobile trough genesis—one in diffluence and one in confluence—are compared to determine the processes acting to produce the differing thermal-advection patterns at 500 hPa. A thermal-advection tendency equation is developed and shows that the magnitude of the temperature advection can be changed by accelerating the advecting wind speed or by changing the temperature gradient (i.e., vector frontogenesis). The latter can be accomplished either by changing the magnitude of the temperature gradient (the frontogenetical component F n, also known as scalar frontogenesis) or by rotating the direction of the temperature gradient relative to the flow (the rotational component F s). The dominant processes acting on F n for the diffluence and confluence cases are tilting and deformation frontogenesis, respectively. The dominant process acting on F s for the diffluence case is rotation of the isentropes due to the vorticity term, whereas rotation of the isentropes due to the vorticity and tilting terms are both important for the confluence case. The rotational component of frontogenesis is cyclonic downstream of the vorticity maximum for both cases, favoring increasing cold advection downstream of the vorticity maximum. For both cases, the rate of rotation of the isentropes at a point due to horizontal advection is large and that due to vertical advection is negligible. Since advection can only transport the existing isentrope angle and cannot change the isentrope angle, the rotational component of frontogenesis normalized by the temperature gradient is the only term that can increase the isentrope angle following the flow. This term dominates in the diffluence case but is small in the confluence case. This diagnosis suggests the following reasoning. In diffluent flow, the vorticity associated with the incipient trough is compacted into a more circular shape and intensifies. The potent vorticity maximum leads to robust isentrope rotation. In confluent flow, however, the vorticity is deformed into an elongated maximum, inhibiting both strong isentrope rotation and increasing cold advection. Thus, the rotational frontogenesis component explains the rotation of the isentropes that is responsible for the differing thermal-advection patterns.

Diagnosis of these cases supports the results from the climatology indicating a strong relationship between the synoptic environment and the upper-tropospheric thermal-advection pattern. Nevertheless, current conceptual models of upper-level frontogenesis do not fully explain the variety of these features in the real atmosphere. In particular, mobile trough genesis and its associated upper-level frontogenesis can occur in weak 500-hPa thermal-advection patterns, in contrast to the confluence and cold advection that have been previously identified as important to upper-level frontal intensification. This result provides further support for the possibility that generation and intensification of mobile troughs can occur by barotropic processes.

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Carl M. Thomas and David M. Schultz

Abstract

Climatologies of fronts, airmass boundaries, and airstream boundaries can be calculated using automated approaches on gridded data. Such approaches may require choices to define a front, including a quantity (or quantities) to diagnose the front, a mathematical function(s) that operates upon the quantity to produce a diagnostic field, a level(s) at which the field is calculated, and a minimum threshold(s) in the magnitude of the field. To understand how resulting climatologies depend upon these choices using a consistent dataset, ERA-Interim reanalyses from 1979 to 2016 are used to construct global monthly climatologies for various definitions of fronts and airstream boundaries from potential temperature, equivalent potential temperature, water vapor mixing ratio, and wind, including gradients, thermal front parameter, frontogenesis, and asymptotic contraction rate at the surface and 850 hPa. Maps of automated fronts are similar to manual analyses when about 10% of the map is identified as a front. Definitions of fronts that use potential temperature or frontogenesis produce climatologies similar to those of manually analyzed fronts with maxima along the major storm tracks and their seasonal migrations. In contrast, definitions that use equivalent potential temperature or the thermal front parameter produce fewer fronts at higher latitudes and more fronts at lower latitudes, more akin to airmass boundaries than fronts. Although surface fronts defined by thermodynamic quantities are more infrequent over the oceans than at 850 hPa, they are more frequent when using metrics that include the wind field (e.g., frontogenesis, asymptotic contraction rate).

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Robert A. Cohen and David M. Schultz
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John W. Nielsen-Gammon and David M. Schultz

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Robert A. Cohen and David M. Schultz

Abstract

Although a kinematic framework for diagnosing frontogenesis exists in the form of the Petterssen frontogenesis function and its vector generalization, a similar framework for diagnosing airstream boundaries (e.g., drylines, lee troughs) has not been constructed. This paper presents such a framework, beginning with a kinematic expression for the rate of change of the separation vector between two adjacent air parcels. The maximum growth rate of the separation vector is called the instantaneous dilatation rate and its orientation is called the axis of dilatation. Similarly, a maximum decay rate is called the instantaneous contraction rate and its orientation is called the axis of contraction. These expressions are related to the vector frontogenesis function, in that the growth rate of the separation vector corresponds with the scalar frontogenesis function, and the rotation rate of the separation vector corresponds with the rotational component of the vector frontogenesis function.

Because vorticity can rotate air-parcel pairs out of regions of deformation, the instantaneous dilatation and contraction rates and axes may not be appropriate diagnostics of airstream boundaries for fluid flows in general. Rather, the growth rate and orientation of an airstream boundary may correspond better to the so-called asymptotic contraction rate and the asymptotic axis of dilatation, respectively. Expressions for the asymptotic dilatation and contraction rates, as well as their orientations, the asymptotic dilatation and contraction axes, are derived. The asymptotic dilatation rate is related to the Lyapunov exponent for the flow. In addition, a fluid-trapping diagnostic is derived to distinguish among adjacent parcels being pulled apart, being pushed together, or trapped in an eddy. Finally, these diagnostics are applied to simple, idealized, steady-state flows and a nonsteady idealized vortex in nondivergent, diffluent flow to show their utility for determining the character of air-parcel trajectories and airstream boundaries.

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