Schultz, D. M., and C. A. Doswell III, 1999: Conceptual models of upper-level frontogenesis in southwesterly and northwesterly flow. Quart. J. Roy. Meteor. Soc., 125, 2535-2562. (October 1999, Part A) [QJRMS] [HTML] [PDF]

Conceptual Models of
Upper-Level Frontogenesis
in Southwesterly and Northwesterly Flow

David M. Schultz and Charles A. Doswell III

National Severe Storms Laboratory, National Oceanic and Atmospheric Administration, USA

Quarterly Journal of the Royal Meteorological Society
Submitted February 1998; Revised August 1998 and December 1998

22 December 1998

Corresponding author:
Dr. David M. Schultz
NOAA/National Severe Storms Laboratory
1313 Halley Circle
Norman, OK 73069 USA
email: david.schultz@noaa.gov

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  Summary

Vector-frontogenesis diagnostics for the Lagrangian rate of change of the magnitude and direction of the horizontal potential temperature gradient, including tilting due to vertical motion, are derived. These diagnostics are applied to the two cases to examine the maintenance of the potential temperature gradient and the development of cold advection along each upper-level front. The upper-level front in southwesterly (northwesterly) flow was maintained primarily by deformation (tilting) frontogenesis, in agreement with previous research. The increasing cold advection along the upper-level front in both cases was related to an upstream vorticity maximum. For the case in southwesterly flow, the preexisting vorticity maximum approached a downstream equivalent-barotropic upper-level front in a manner similar to an instant occlusion, resulting in cold advection along the length of the upper-level front. For the case in northwesterly flow, an intensifying vorticity maximum concentrated the cold advection in the base of the thermal trough, as warm advection developed upstream.

These two cases are compared to upper-level fronts in previous literature and a climatology of upper-level fronts associated with landfalling cyclones over the eastern North Pacific Ocean. The results indicate that these two cases are typical of early evolutions of upper-level fronts that can occur in southwesterly and northwesterly flow. Therefore, a revised version of the Shapiro conceptual model is presented that more accurately represents the early evolutions exhibited in the present and previous studies.

1  Introduction

1(a)  The Shapiro conceptual model

Despite the Shapiro conceptual model not having been designed to illustrate frontogenesis directly, the schematic has become firmly entrenched in later scientific literature, attesting to its success in describing many of the general features of the migration of an upper-level jet-front system through a larger-scale baroclinic wave. The schematic has been reproduced in review articles on upper-level fronts (e.g., Keyser and Shapiro 1986, Fig. 19; Shapiro and Keyser 1990, Fig. 10.8) and emulated in textbooks (e.g., Carlson 1991, Fig. 15.6; Bluestein 1993, Fig. 2.82). Despite the successes of the Shapiro conceptual model in interpretation of the secondary circulations at different stages in the life cycle of a baroclinic wave, applications of the Shapiro schematic to frontogenesis, however, appear to be an oversimplification of the structural and kinematic complexities inherent in nature (as discussed further below). The present study endeavors to consider some of these complexities.

The Shapiro conceptual model begins with an upper-level front situated within confluent northwesterly flow (e.g., Namias and Clapp 1949), and isentropes are nearly parallel to isohypses (Fig. 1(a)). This phase of the evolution will be referred to hereafter as the equivalent-barotropic stage. Approximately 24 h later, the front evolves to a state where the trough in the isentropes lags the trough in the isohypses, implying geostrophic cold advection along the length of the front (the cold-advection stage; Fig. 1(b)). Later, the trough in the geopotential-height field closes off and becomes more symmetrical (the closed-low stage; Fig. 1(c)), as discussed by Bell and Keyser (1993) and Bell and Bosart (1994), with leading warm advection and trailing cold advection. Finally, the closed low opens up in confluent southwesterly flow and geostrophic warm advection along the length of the front is implied (the warm-advection stage; Fig. 1(d)).

Although it appears as if the intent of the Shapiro conceptual model was to illustrate the evolution of a jet-front system (e.g., ``t=t<sub>°</sub>'', ``t=t_°+24 h'', etc., in Fig. 1), observational evidence suggests that this schematic evolution typically does not occur exactly in the manner illustrated by Shapiro (1982), particularly over North America. First, cold advection is depicted as maximum at the inflection point in the height field in the cold-advection stage of the Shapiro conceptual model with negligible thermal advection outside of the frontal zone. Nearly all observed upper-level fronts in northwesterly flow in the literature, however, exhibit the strongest cold advection in the base of the thermal trough (Table 1). Weak cold advection, or more typically warm advection, is present along the northwesterly extensions of the fronts (Table 1). Second, as noted by Newton and Carson (1953, p. 325), Newton and Palmén (1963), Cammas and Ramond (1989, p. 2460), Orlanski and Sheldon (1995, Fig. 3, p. 614), and Pyle (1997, pp. 97 and 133), the progression of a jet-front structure from northwesterly flow to the base of the trough to southwesterly flow (Figs. 1(b)-(d)) rarely exists. Since the wind speed within a jet streak is usually much faster than the speed of movement of the jet streak (e.g., Newton and Carson 1953, p. 331; Palmén and Newton 1969, 206-207; Cunningham and Keyser 1996, section 3), the jet-front cannot be tracked as an advective feature of the flow. Oftentimes, as a new jet-front is developing in the downstream southwesterly flow, the upstream jet-front in northwesterly flow remains. A further point is that the reorganization from large-scale diffluence during the cold-advection stage to large-scale confluence during the warm-advection stage (cf. Figs. 1(b),(d)) seems unlikely to occur within the relatively short time period depicted by the Shapiro conceptual model. Finally, the Shapiro conceptual model illustrates the evolution of an upper-level front in northwesterly flow, although as will be shown later in this paper, upper-level fronts in southwesterly flow also may display some similarities (e.g., evolution from equivalent-barotropic to cold-advection stages) to the Shapiro conceptual model at times.

1(b)  Purpose

Section 2 is a derivation of vector frontogenesis, including the vertical-velocity (tilting) terms. Section 3introduces the two cases of upper-level frontogenesis in southwesterly and northwesterly flow, respectively. Then, the changes in the magnitude and direction of the horizontal potential temperature gradient along the two upper-level fronts are diagnosed using vector frontogenesis. Section 4 is a climatology of upper-level fronts associated with landfalling cyclones on the west coast of North America, showing that evolutions similar to that occurring in southwesterly flow are not an uncommon occurrence. Finally, section 5 presents a concluding discussion and a revised conceptual model for the early evolution of southwesterly and northwesterly flow upper-level frontogenesis.

2  Derivation of the two-dimensional vector frontogenesis, including vertical-velocity terms

Conservation of potential temperature in three-dimensional adiabatic flow means that

Terms n₁, n₂, s₁, and s₂ represent similar terms in Keyser et al.'s (1988) derivation. Term n₃ represents tilting scalar frontogenesis due to vertical-velocity gradients acting on the horizontal potential temperature gradient (equivalent to the sum of terms 4 and 8 in Bluestein (1986, p. 181; 1993, p. 253)) and term s₃ represents tilting rotational frontogenesis due to vertical-velocity gradients acting on the horizontal potential temperature gradient.¹ Terms n₃ and s₃ can also be expressed as:

Following Keyser et al. (1988, 764-765), expressions similar to their (2.10a) and (2.10b) result:

3  Case studies

3(a)  Mesoscale-model description

Four-dimensional data assimilation was used throughout the simulation on the 90-km domain and during the first 12 h on the 30-km domain. The assimilation technique (Stauffer and Seaman 1990) employed Newtonian nudging to relax the model simulation to gridded 12-h upper-level and 3-h surface analyses. To create the upper-level analyses, National Meteorological Center (NMC, now known as the National Centers for Environmental Prediction) analyses were interpolated to the model grid. Surface and upper-air observations were then incorporated into the analysis using a Cressman-type analysis scheme (Benjamin and Seaman 1985). After the removal of superadiabatic lapse rates below 500 hPa, the analysis was interpolated to the s-coordinate system, and the integrated mean divergence was removed to avoid the production of spurious gravity waves. Three-hour surface analyses were generated similarly, with first-guess analysis fields provided by linear interpolation of 12-h NMC analyses. Lateral boundary conditions for the 90-km domain were generated by linear interpolation of the 12-h analyses. Throughout this paper, only output from the 90-km domain is displayed.

3(b)  Overview

Unlike other cases of upper-level fronts in southwesterly flow that apparently evolved from a northwesterly flow regime (e.g., Reed 1955; Bosart 1970; Sanders et al. 1991; Pyle 1997, p. 133), this case occurred entirely within southwesterly flow, and will hereafter be referred to as SW. SW was associated with a 500-hPa closed low that moved slowly into the Gulf of Alaska on 11 December 1988 (not shown). NMC analyses (not shown) indicate remnant baroclinity on the southeast side of the closed low in southwesterly flow, with the geopotential-height (hereafter, height) and potential-temperature contours nearly parallel from 0000 UTC 11 December 1988 to 1200 UTC 12 December 1988 (hereafter 12/12) (Fig. 3(a)). Unlike the equivalent-barotropic stage in the Shapiro conceptual model (Fig. 1(a)), however, the upper-level front was strongest in the southwesterly, not the northwesterly, geostrophic flow. The enhanced baroclinity in SW was also associated with a preexisting progressive relative-vorticity (hereafter, vorticity) maximum at the base of the shortwave trough, coincident with the thermal trough at this level (Fig. 3(a)). Twelve hours later (13/00; Fig. 3(b)), the orientation between the isentropes and isohypses implied geostrophic cold advection (potential-temperature advection due to total horizontal wind contoured in thick lines) along much of the length of the 500-hPa front and vorticity. This structure represents the cold-advection stage. Therefore, this case illustrates the same evolution from a nearly equivalent-barotropic stage to a cold-advection stage as in the Shapiro conceptual model (Figs. 1(a),(b)), except in southwesterly, instead of northwesterly, flow. It is curious to note that Hines and Mechoso (1991, Figs. 3-5) simulated a similar structure in their idealized model of primitive-equation upper-level frontogenesis: cold advection along a baroclinic zone developing in southwesterly flow. Further investigation of this case was abandoned because ``This simulated frontogenesis, therefore, has substantial differences with the observed phenomena [as characterized by the Shapiro conceptual model] and will not be analyzed further in this paper'' (Hines and Mechoso 1991, p. 1232).

Satellite imagery for SW (Fig. 4) shows that a comma cloud is associated with the advection of 500-hPa cyclonic vorticity and the polar-front cloud band is associated with the baroclinic zone in southwesterly flow (Fig. 4(a)). As the comma cloud approaches and merges with the polar-front cloud band, the clouds deform owing to the rotation associated with the vorticity maximum (Figs. 4(b),(c)). This evolution is remarkably similar to the instant-occlusion concept reviewed by Schultz and Mass (1993, section 2(d)) and described by, for example, McGinnigle et al. (1988, Fig. 7(a)), Evans et al. (1994), and Bader et al. (1995, section 4.4, Figs. 4.4.3(c) and 4.4.5(c)). In particular, the approach of a shortwave trough (comma cloud) toward a preexisting baroclinic zone in southwesterly flow (polar-front cloud band) epitomizes the instant occlusion. SW is consistent with these previous studies, in that observed instant occlusions tend to occur in confluent large-scale flows that favor merger between the comma cloud and the polar-front cloud band. As has been noted by the above authors, not all cyclone events that occur in southwesterly flow, however, are instant occlusions.

The other case is the upper-level front associated with the Experiment on Rapidly Intensifying Cyclones over the Atlantic (ERICA) Intensive Observing Period (IOP) 2 cyclone on 13-14 December 1988 over central North America. Because the upper-level front intensified in northwesterly upper-level flow, this case will hereafter be referred to as NW. The ERICA IOP 2 cyclone and its upper-level features have been discussed previously by Sanders (1990), Roebber (1993), Lackmann et al. (1997), Hakim (1997, section 5.1), and Reed and Albright (1997). At 13/00 (Fig. 5(a)), as well as 12 and 24 h previous (not shown), much of the frontal zone was characterized by weak cold advection, with the strongest cold advection on the equatorward side of the front and near the intensifying vorticity maximum. Lackmann et al. (1997) determined that tilting of horizontal vorticity into the vertical by differential subsidence across the upper-level front was responsible for the formation and intensification of this vorticity maximum, which would later be associated with the ERICA IOP 2 cyclogenesis. By 13/12, however, warm advection was occurring along much of the length of the upper-level front (Fig. 5(b)). Unlike in SW, where cold advection occurred along the length of the front, the cold advection in NW was limited to the base of the thermal trough (cf. Figs. 3(b) and 5(b)) associated with the ``compacting'' vorticity maximum (Lackmann et al. 1997). A compacting vorticity maximum is one that undergoes an increase in isotropy during its evolution (i.e., the length of the major axis of the vorticity maximum decreases relative to that of the minor axis) (Lackmann et al. 1997, p. 2731). Therefore, NW, as well as other similar events from the literature discussed previously, indicate significant along-front variability in thermal advection as the upper-level front reaches maturation, in contrast to the depicted cold advection dominating the entire length of the front in the Shapiro conceptual model (Fig. 1(b)).

It is apparent that significant differences exist between the early stages in the evolutions of the two cases of upper-level frontogenesis discussed presently, SW and NW (Figs. 3 and 5, respectively). In particular, the evolution from the equivalent-barotropic stage to cold-advection stage in SW occurred in southwesterly, not northwesterly flow. Also, NW experienced significant along-front variation in the sign of the thermal advection, with cold advection at the leading edge of the vorticity maximum and warm advection along the northwestern portion, rather than cold advection along the length of the front as portrayed in the Shapiro conceptual model (Fig. 1). It might be argued that cases exhibiting these same evolutions may be relatively uncommon, or alternatively, it may be that the Shapiro conceptual model applies best to cases in a limited geographical area (e.g., over North America). As will be shown in section 4, evolutions similar to SW are commonly associated with North Pacific cyclones landfalling on the west coast of North America, which, in turn, resemble cases throughout the Northern Hemisphere; we have already observed that many cases of upper-level fronts in the literature are similar to NW. Therefore, we believe our results based on these two cases to be of some generality.

3(c)  Vector-frontogenesis diagnostics

This hypothesis is confirmed by examining 500-hPa -F_n and its components (divergence, deformation, and vertical-tilting) for SW and NW.³ At 12/12 for SW, the divergence term was consistently smaller than the deformation term, which was positive along much of the front (cf. Figs. 8(a),(b)). Figure 8(c) supports the interpretation from Fig. 6(a) that the ascent along the front was unfavorable for frontogenesis through tilting, as negative tilting frontogenesis occurred along the length of the front. As a result, the total scalar frontogenesis was positive along much of the length of the front, primarily supported by deformation (Figs. 8(b),(d)). At 13/00, the divergence term was once again small compared to the deformation term (cf. Figs. 9(a),(b)). Tilting resulted in frontolysis along the front so that the total frontogenesis was primarily a result of the deformation term (Figs. 9(b),(c),(d)), a result consistent with other cases of upper-level frontogenesis in southwesterly flow (e.g., Bosart 1970).

The situation was quite different for NW. At 13/00, the divergence term was smaller than the deformation term, and both were negative along the equatorward side of the front (Figs. 10(a),(b)). Tilting, on the other hand, was positive along much of the front, and dominant along the northwest extent of the front (Figs. 10(c),(d)) in the region of active frontogenesis. This confirms our hypothesis from Fig. 7(a) and the conclusion of Lackmann et al. (1997) that descent along the front results in frontogenesis through tilting. At 13/12, divergent and deformation frontolysis dominated along the poleward side of the front, maximized in the base of the thermal trough and along the northwest extent of the front (Figs. 11(a),(b)). Even though tilting frontogenesis was positive along the length of the front, it was not large enough to offset the negative deformation frontogenesis, with the result that the total scalar frontogenesis was negative, maximized at the base of the thermal trough (Figs. 11(c),(d)).

That the tilting frontogenesis for NW was maximum upstream of the strongest cold advection in a region of warm advection, particularly at 13/12, was noted in an earlier similar case study by Sanders et al. (1991, pp. 1339, 1364-1365). For SW, despite the presence of cold advection and confluence, frontogenetical tilting along the upper-level front did not occur (i.e., the Shapiro effect did not seem to be operating in SW). Uccellini et al. (1985, p. 978) and Pyle (1997, section 7.1) emphasized the importance of along-flow contributions to the vertical circulations around upper-level jet-fronts. This research, therefore, underscores the point made by these previous authors that two-dimensional conceptualizations of jet-front circulations can be difficult to apply to the real atmosphere in regions of curved flow.

We next examine 500-hPa F_s and its components for SW and NW. At 12/12 for SW, the vorticity term in F_s was largest along the vorticity maximum, with the deformation term negative along the northeastern extent of the front (Figs. 12(a),(b)). Positive F_s implies cyclonic rotation of the isentropes, consistent with positive vorticity in that area. Tilting led to negative F_s, anticyclonic rotation of the isentropes, which favored eastward migration of the thermal trough (Fig. 12(c)). Total F_s was a maximum in the base of the thermal trough (Fig. 12(d)), due primarily to the vorticity term (Fig. 12(a)). It was this feature that resulted in the cyclonic rotation of the isentropes relative to the flow field, thereby initiating cold advection along the front in the base of the thermal trough (see footnote 3). At 13/00 after the onset of cold advection, patterns similar to that at 12/12 existed along the front. The dominant term was the vorticity term, maximum along the length of the front (Figs. 13(a),(d)). The deformation and vertical terms were smaller and negative (Figs. 13(b),(c)). Total F_s was thus positive along most of the length of the front (Fig. 13(d)), consistent with the cyclonic rotation of the isentropes leading to cold advection along the length of the front.

For NW at 13/00, the vorticity term was positive along the front (Fig. 14(a)) and the deformation term was negative along the upstream part of the front (Fig. 14(b)), as opposed to the downstream part of the front in SW (Fig. 12(b)). With the negative contribution from the vertical term (Fig. 14(c)), the total F_s was positive at the leading downstream edge of the front (Fig. 14(d)), thereby implying that the rotation of isentropes leading to cold advection occurred here, as opposed to the upstream edge of the front in SW. This pattern was repeated and intensified at 13/12 (Fig. 15). The vorticity term dominated (Fig. 15(a)), but was offset by the deformation term along the northwest extension of the front upstream (Fig. 15(b)). Tilting was weak or negative such that the total F_s implied cyclonic rotation of the isentropes occurring in the base of the thermal trough (Figs. 15(c),(d)), in agreement with the region of cold advection in Fig. 5(b).

To examine these results further, we employed the methodology of Keyser et al. (1989) and Loughe et al. (1995) to calculate the divergent and rotational wind explicitly. Calculations of vector frontogenesis using these wind components (not shown) illustrate that the 500-hPa rotational wind was primarily responsible for the 500-hPa rotational frontogenesis, resulting in the transition to cold advection along the front. Also, the contribution of the divergent wind field to frontogenesis at 500 hPa is small. This confirms our earlier results using the vector-frontogenesis diagnostics on the total wind field.

4  Climatology of upper-level fronts over the eastern North Pacific Ocean

Of the 19-30 winter (DJF) cyclones per year that made landfall on the west coast of North America during the six-year period of our climatology, 44% occurred in southwesterly flow versus 14% in northwesterly flow (Table 2), consistent with the wintertime-averaged southwesterly jet stream over the eastern North Pacific Ocean (e.g., Sanders 1988, Fig. 7; Bluestein 1993, Fig. 1.72(a); Lackmann et al. 1996, Fig. 1). With regard to the thermal evolution of the baroclinic zone, the largest percentage (49%) was characterized by weak thermal advection, indicating relatively old, nearly equivalent-barotropic systems, characteristic of cyclones at the end of their evolutions over the eastern North Pacific Ocean. The second largest group (23%) comprised those events that underwent the change from equivalent barotropic to cold advection.

Those 23% (35 events in total) that evolved from a state of equivalent barotropy to a state of cold advection were then examined separately (Table 3). Of these 35 events, 63% occurred in southwesterly flow, or 15% of the total of 149 cyclones. Of the 66 events that occurred in southwesterly flow (Table 2), 33% (22/66) evolved from equivalent barotropy to cold advection (not shown). This is in comparison to the 29% (6/21) of the northwesterly flow cases and the 28% (5/18) of the zonal flow cases that underwent this evolution (not shown). Since the evolution from equivalent barotropic to cold advection occurs at roughly the same rate regardless of flow type, it seems that the predominance of southwesterly flow fronts that evolve from equivalent barotropic to cold advection is favored in this area owing to the climatological tendency for southwesterly flow, rather than some inherent tendency for cold advection to develop from an initial state of equivalent barotropy, preferentially, in southwesterly versus northwesterly or zonal flow. Results from Tables 2 and 3 indicate, therefore, that the SW evolution displayed in Fig. 3, although not the only upper-level-frontal evolution possible in southwesterly flow, is relatively common on the west coast of North America.

It should be noted that this evolution in southwesterly flow from nearly equivalent barotropic to cold advection is not necessarily limited to over the eastern North Pacific Ocean. We would expect similar evolutions to SW to be common in regions where relatively old, nearly equivalent-barotropic systems traverse regions of climatological southwesterly flow (e.g., the eastern North Atlantic Ocean). Indeed, similar evolutions elsewhere have been documented in the literature: Bjerknes (1951, Figs. 11, 12, and 14), McGinnigle et al. (1988, Fig. 7), and Cammas and Ramond (1989, their case JS2, Figs. 2(a) and 19).

Additionally, M. Sinclair (1998, personal communication) has performed composite analyses of cyclogenesis in different large-scale flows over the western South Pacific Ocean. For a composite of cyclones that develop in the equatorward entrance region of an upper-level jet streak (his classification E; Sinclair and Revell 1999), the 500-hPa thermal evolution resembles that of SW, whereas for a composite of cyclones that develop in the diffluent exit region of an upstream upper-level jet streak (his classification U; Sinclair and Revell 1999), the 500-hPa thermal evolution resembles that of NW. These results are consistent with those presented in this paper.

5  Concluding discussion

5(a)  Revised conceptual model

In contrast, Fig. 16(b) presents the schematic evolution of an upper-level front in northwesterly flow over North America. Initial cold advection along the length of the front becomes concentrated in the base of the thermal trough in conjunction with an intensifying and compacting vorticity maximum in northwesterly flow. Upstream of the thermal trough, warm advection is typically occurring in the northwesterly flow, indicating substantial along-front variation in thermal advection, in contrast to the Shapiro conceptual model.

5(b)  Thermal advection along upper-level fronts

A mechanism for the onset of cold advection along upper-level fronts was suggested previously by Rotunno et al. (1994, 3390-3391) and discussed further in Keyser (1998). Based on their analysis of normal-mode cyclogenesis in a baroclinic primitive-equation channel model, Rotunno et al. (1994) hypothesized that the transition to along-front cold advection in the confluent jet-entrance region (the Shapiro effect) was due to the subsidence along the upper-level front bringing down higher potential-temperature air from aloft, thereby implying a horizontal rotation of the isentropes. This mechanism would appear to implicate the vertical tilting term in F_s, s₃ in (11b), in contrast to our results that implicate the vorticity term in F_s in both SW and NW. In fact, the tilting term in both SW and NW acted in the opposite direction (anticyclonic rotation of the isentropes) than what was observed to occur (cyclonic rotation of the isentropes) (Figs. 12(c), 13(c), 14(c), and 15(c)).

Furthermore, since SW and NW are similar to other observed cases (as discussed in sections 1(a) and 4), the hypothesis advanced by Rotunno et al. (1994) that tilting is responsible for the onset of cold advection may not be applicable for most cases of observed upper-level frontogenesis. A possible interpretation of this discrepancy may be related to the developing midtropospheric potential-vorticity maximum (Rotunno et al. 1994, Fig. 12(b)). Their configuration is similar to that in NW, where the intensifying vorticity maximum resulted in cyclonic rotational frontogenesis. It therefore seems likely that the primitive-equation simulation presented by Rotunno et al. (1994) could be reinterpreted in terms of the diagnostics presented in this paper: frontogenetical tilting leads to midtropospheric vorticity generation which results in rotation of the isentropes relative to the flow, resulting in cold advection.

We also note that the evolution shown in Rotunno et al. (1994) more closely resembles NW than SW, a point made previously by Lackmann et al. (1997, 2755-2756). Whereas tilting of vorticity greatly intensified a weak vorticity maximum in NW, SW possessed a preexisting vorticity maximum that did not change intensity substantially. Idealized normal-mode model experiments by their nature must generate vorticity maxima from a basic state with very small initial disturbances. This comparison has already been noted by Keyser and Shapiro (1986, p. 494), who state, ``Although realistic reproductions of upper-level and surface fronts are found in the context of baroclinic instability theory, they arise as a consequence of upper-level wave amplification and low-level cyclogenesis, rather than appearing in advance of these processes.'' As we have shown here, the evolution of upper-level fronts is intimately related to vorticity maxima preexisting (SW) or developing concomitantly with the upper-level front (NW). The large-scale flow, therefore, acts to position the upper-level fronts and the vorticity maxima into an appropriate configuration.

5(c)  Future research

  Acknowledgments

This research was conducted while the first author was a National Research Council Postdoctoral Research Associate at the National Severe Storms Laboratory.

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  Tables

  Table Captions

Table 2: Climatology of upper-level fronts associated with cyclones making landfall on the west coast of North America between 35^°N and 60^°N in December, January, and February for the six winters 1988-89 through 1993-94. Percentages may not add up to 100% due to round-off of decimal values.

Table 3: Climatology of equivalent-barotropic stage to cold-advection stage events from Table 2.

  Figure Captions

Footnotes:

¹ A similar expression for ``tilting scalar frontogenesis'' in an x-z plane, involving v_ag, the ageostrophic cross-front wind, can be found in Keyser et al. (1986, (2.12)).

² Strictly speaking, the rotational frontogenesis does not describe the time rate of change of the angle between isohypses and isotherms, as the height field, as well as the thermal field, will be altered by the relative vorticity, deformation, and tilting terms. Rigorous resolution of this discrepancy, however, would involve inversion techniques, the methodology for which has not matured. Nevertheless, our results suggest that the rotation of the isohypses by the vorticity is a secondary effect, at least in the cases presented here.

³ We present -F_n rather than F_n in order that regions of positive -F_n represent regions of positive frontogenesis, according to (5a).

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