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    Sea level pressure (in hPa, bold solid lines), θ (in K, thin dashed lines), surface winds (arrows, see legend on figure), regions of model-diagnosed radar echo >4 dBZ averaged between 995 and 700 hPa (shaded regions), and the position of the surface trough (bold dashed line) and arctic front (bold dotted line) at 1900 UTC 6 Mar 1986. The lettered lines mark the position of vertical cross sections referred to in later figures. The bold arrows indicate the distance over which selected variables are averaged along cross section A″A′

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    Vertical cross sections at 1900 UTC 6 Mar 1986 along the lines (a) AA′, (b) BB′, (c) CC′, and (d) AA′ shown in Fig. 1. (a)–(c) The shaded regions are model-diagnosed radar echo >4 dBZ, θe is given in K (solid bold lines), θ is given in K (thin dashed lines), the horizontal winds are shown by arrows where a southerly wind is represented by a northward-pointing arrow (see legend on figure), and T marks the surface trough position. (d) As in (a) but the short dashed lines are contours of the direction from which the wind is blowing (in degrees), the bold dashed line marks the leading edge of the enhanced gradient in θe, and the bold arrows mark the warm-frontal zone of the warm occlusion

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    Vertical cross section at 1900 UTC 6 Mar 1986 along the line A″A′ shown in Fig. 1. Solid lines are contours of vertical velocity (in dPa s−1), and arrows indicate the wind velocity in the cross section plane (see legend for magnitudes). Both fields are averaged over the distance normal to the cross section indicated by the double arrowed line in Fig. 1

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    As in Fig. 3 but where all fields are averaged normal to the cross section. (a) Solid lines (dashed lines) are contours of quasigeostrophic upward (downward) vertical velocity (in dPa s−1); velocities computed assuming dry stability throughout the domain. (b) Solid lines (dashed lines) are contours of smoothed upward (downward) vertical velocity (in dPa s−1). (c) Quasigeostrophic vertical velocities computed assuming moist stability everywhere that the smoothed values of RH shown in (d) exceed 80%. (d) Solid lines are contours of smoothed values of RH. The dashed areas enclose the model diagnosed radar echo >4 dBZ. All fields from the MM5 model

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    Vertical cross section at 1900 UTC 6 Mar 1986 along the line A″A′ shown in Fig. 1. (a) Solid lines (dashed lines) are upward (downward) semigeostrophic vertical velocity (in dPa s−1) assuming dry stability everywhere. (b) As in (a) but assuming moist stability everywhere that the smoothed values of RH shown in Fig. 4d exceed 80%. The shaded areas enclose the model-diagnosed radar echo >4 dBZ

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    Vertical cross section at 1900 UTC 6 Mar 1986 along the line A″A′ shown in Fig. 1. Solid lines are contours of θ (in K), the shading indicates θ gradient (see legend for magnitudes), the bold dashed line indicates the position of the CFA determined from the θe field (taken from Fig. 2a), and the bold solid line indicates the position of the CFA determined from the θ field. The dashed line encloses the model diagnosed radar echo >4 dBZ. See text for an explanation of regions 1 and 2. Lines AB and A′B′ show the approximate locations for which the schematic shown in Fig. 9 is applicable

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    As in Fig. 3 but the shading indicates values of cold θ advection (see legend for magnitudes), and arrows indicate the wind velocity in the plane of the cross section (see legend for magnitudes). The dashed line encloses the model diagnosed radar echo >4 dBZ. Bold arrowed lines are selected streamlines of airflow relative to the storm

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    As in Fig. 3 but solid lines (dashed lines) are positive (negative) contours of pressure gradient (in hPa m−1 × 10−5), where positive values indicate a pressure force to the left. The dotted box shows the location of a smaller section of the cross section used in subsequent figures. The bold solid line, taken from Fig. 6, indicates the position of the CFA derived from the θ gradient. See text for an explanation of the regions indicated by B, C, and D. The shaded areas enclose the model diagnosed radar echo >4 dBZ

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    Schematic showing the relationship between θ and pressure gradient for (a) a tipped-backward baroclinic zone, and (b) a tipped-forward region of localized warming. See text for an explanation of the individual panels

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    As in Fig. 3 but solid lines (dashed lines) are contours of negative (positive) divergence (in s−1 × 10−5). The position of the surface trough is marked by T. Numbered black dots are the starting locations of 5-h back trajectories at 550 and 750 hPa. Refer to the text for an explanation of the regions marked by L, M, and N. The shaded areas enclose the model diagnosed radar echo >4 dBZ

  • View in gallery

    Plan view of 5-h back trajectories of air parcels, relative to the movement of the CFA rainband, along cross section A″A′, and starting at 550 hPa at 1900 UTC from the positions shown in Fig. 10. The following fields are contoured along the trajectories: (a) pressure (in hPa), (b) pressure gradient (in hPa m−1 × 10−5), where positive is a pressure force to the left along A″A′, (c) net force per unit mass along cross section A″A′ (in m s−2 × 10−4) where positive is a force to the left along cross section A″A′, and (d) the horizontal wind speed (in m s−1) along cross section A″A″, where a positive value indicates a wind to the right along the cross section. The small arrows mark the hourly positions of the trajectories, and the shading indicates the position of the CFA baroclinic zone along each trajectory

  • View in gallery

    As in Fig. 11 but for back trajectories starting at 750 hPa. The lighter-shaded area is the axis of the pressure gradient minimum, and the heavier-shaded area is the axis of the pressure gradient maximum. See text for further explanation of the pressure minimum and maximum

  • View in gallery

    Solid lines (dashed lines) are contours of positive (negative) frontogenesis [in K (100 km)−1 h−1], for the smaller region enclosed by the dashed lines along cross section A″A in Fig. 8 produced by (a) horizontal advection by the wind relative to the CFA rainband, (b) vertical advection, (c) confluence, (d) tilting, (e) diabatic, (f) diabatic plus confluence, (g) total of confluence, shear, vertical advection, horizontal advection, tilting, and diabatic, and (h) contours of θe (heavy solid lines in K). The thin solid lines are contours of θ (in K), and the shaded regions show the location of the upper and lower baroclinic zones of the CFA

  • View in gallery

    (Continued)

  • View in gallery

    As in Fig. 3 but the solid lines (dashed lines) are contours of positive (negative) relative vorticity (in s−1 × 10−4). The position of the CFA determined from the θ field is shown by the heavy solid line. The shaded areas enclose the model diagnosed radar echo >4 dBZ

  • View in gallery

    As in Fig. 14 but the solid lines (dashed lines) are contours of positive (negative) Q vector divergence (in s−3 hPa−1). The shaded areas enclose the model diagnosed radar echo >4 dBZ

  • View in gallery

    As in Fig. 3 but (a) the solid lines are contours of water vapor (in g kg−1), the dashed lines are contours of θ (in K), and the vectors indicate winds in the cross section relative to the movement of the rainband (see legend). The position of the CFA determined from the θ field is given by the heavy solid line. (b) As in (a) but the solid lines are contours of θe (in K), and the dashed lines are contours of water vapor (in g kg−1)

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Organization and Structure of Clouds and Precipitation on the Mid-Atlantic Coast of the United States. Part VII: Diagnosis of a Nonconvective Rainband Associated with a Cold Front Aloft

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  • 1 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
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Abstract

A numerical simulation using the Pennsylvania State University–National Center for Atmospheric Research fifth-generation Mesoscale Model (MM5) was run on a rainband associated with a cold front aloft (CFA) in a warm occluded structure on the U.S. east coast. The storm originally developed in the lee of the Rocky Mountains as a Pacific cold front overtook a Rocky Mountain lee trough. This formed a warm-type, occluded structure that was essentially maintained as the storm proceeded to the East Coast.

The CFA was a thermal front and therefore dynamically active. The prominence of the CFA in the equivalent potential temperature field was due primarily to the strong upward transport of water vapor from lower levels in the updraft associated with the CFA. The baroclinic zone was characterized by a tipped-forward lower region, where the CFA coincided with a maximum in potential temperature, and a tipped-backward upper region, where the CFA coincided with the leading (warm-side) edge of a zone of enhanced thermal gradient. The tipped-backward upper region displayed many of the characteristics of a vertically propagating gravity wave. In both of these regions, the potential temperature pattern produced a corresponding change in pressure gradient within the baroclinic zone; the imbalance of forces acting on air parcels as they moved through this pressure gradient produced the convergence in the lower baroclinic zone that was responsible for the CFA rainband.

Neither the dry quasigeostrophic nor dry Sawyer–Eliassen diagnosis resolved the details of the simulated mesoscale lifting associated with the CFA rainband. This is because the baroclinic zone of the CFA was mesoscale and structurally complex.

Corresponding author address: Peter V. Hobbs, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640. Email: phobbs@atmos.washington.edu

Abstract

A numerical simulation using the Pennsylvania State University–National Center for Atmospheric Research fifth-generation Mesoscale Model (MM5) was run on a rainband associated with a cold front aloft (CFA) in a warm occluded structure on the U.S. east coast. The storm originally developed in the lee of the Rocky Mountains as a Pacific cold front overtook a Rocky Mountain lee trough. This formed a warm-type, occluded structure that was essentially maintained as the storm proceeded to the East Coast.

The CFA was a thermal front and therefore dynamically active. The prominence of the CFA in the equivalent potential temperature field was due primarily to the strong upward transport of water vapor from lower levels in the updraft associated with the CFA. The baroclinic zone was characterized by a tipped-forward lower region, where the CFA coincided with a maximum in potential temperature, and a tipped-backward upper region, where the CFA coincided with the leading (warm-side) edge of a zone of enhanced thermal gradient. The tipped-backward upper region displayed many of the characteristics of a vertically propagating gravity wave. In both of these regions, the potential temperature pattern produced a corresponding change in pressure gradient within the baroclinic zone; the imbalance of forces acting on air parcels as they moved through this pressure gradient produced the convergence in the lower baroclinic zone that was responsible for the CFA rainband.

Neither the dry quasigeostrophic nor dry Sawyer–Eliassen diagnosis resolved the details of the simulated mesoscale lifting associated with the CFA rainband. This is because the baroclinic zone of the CFA was mesoscale and structurally complex.

Corresponding author address: Peter V. Hobbs, Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640. Email: phobbs@atmos.washington.edu

1. Introduction

Early in the study of the lifecycle of cyclones, it was suggested that a band of precipitation is located along the “upper cold front” in warm occlusions (see Fig. 4 in Bjerknes and Solberg 1922). Details of the precipitation distribution found in warm occlusions were given by Bergeron (1937, his Fig. 4). As refinements were added to the conceptual model of a warm occlusion (Godske et al. 1957, their Fig. 14.33.1), the original concept of a precipitation band along the upper cold front (or “cold front aloft” as it was also called) was retained. Hobbs et al. (1990, 1996) used the term “cold front aloft”, or CFA, to describe a characteristic type of mid- to lower-tropospheric baroclinic zone within a warm occluded-like structure that develops in the lee of the Rocky Mountains. In this paper, we use the term CFA more generally (and as it was originally used in the mid-twentieth century) to refer to any mid- to lower-tropospheric baroclinic zone in which cold advection above the surface significantly leads that at the surface.

Cold fronts aloft, defined in this general way, are an important component of at least four frontal/cyclone conceptual models that have been discussed in the literature: the warm occlusion model (Godske et al. 1957), the trowal model (Galloway 1958), the split-front model (Browning and Monk 1982), and the Structurally Transformed by Orography Model (STORM; Hobbs et al. 1996). A common feature of these models is that the CFA represents the leading edge of a baroclinic zone that intersects and moves over an underlying layer of increased static stability.1 This layer may be warm-frontal, but it may also be a stable layer connected with other geographically specific phenomena such as the stable moist layer east of a Rocky Mountain lee trough. Consequently, we differentiate CFAs from the upper-level fronts described by Reed and Sanders (1953), Reed (1955) and Keyser and Shapiro (1986), which are defined more by the tropopause-level dynamics associated with their formation than by their interaction with an underlying layer of increased static stability in the lower troposphere. However, there is the possibility of overlap in these two definitions, as demonstrated by the case described by Schultz and Mass (1993) in which an upper-level front was associated with a warm occlusion.

The rainbands associated with a CFA can be composed of precipitation that ranges in intensity from nonconvective to severely convective, depending on the stability structure of the air lifted by the CFA. Examples of nonconvective CFA rainbands can be found in Hobbs and Locatelli (1978), Matejka et al. (1980), Locatelli et al. (1989), and Sienkiewicz et al. (1989). Examples of weakly convective CFA rainbands are described by Browning et al. (1973) and Browning and Monk (1982). Examples of strongly convective CFA rainbands are shown in Kreitzberg and Brown (1970), Businger et al. (1991), Locatelli and Hobbs (1995), and Locatelli et al. (1995, 1998).

The lifting mechanism responsible for the formation of CFA rainbands was thought originally to be the forced lifting of air in the warm sector by the advancing wedge of cold air (Bjerknes and Solberg 1922). This belief held into the late 1950s (Godske et al. 1957). However, with the advent of quasigeostrophic (QG) theory, explanations for the updrafts and rainbands associated with cyclones based on the maintenance of balance between wind and mass fields became more common. By the 1960s, a 2D balance theory that provided a physical link between frontogenesis and vertical motion was well established (Sawyer 1956; Eliassen 1962; hereafter referred to as Sawyer–Eliassen, or S–E, theory). By assuming that cross-front geostrophic balance is maintained, S–E theory quantitatively links the cross-front ageostrophic circulation to geostrophic frontogenesis. Later, Hoskins et al. (1978) showed that, when cast in terms of the divergence of a vector field, the forcing in the familiar QG vertical velocity equation (e.g., Holton 1992) is also directly related to frontogenesis. Thus, the balanced response to frontogenesis was used to explain the upward velocity associated with CFAs (e.g., Locatelli et al. 1995). The updrafts associated with the upper front in the split-front model have been attributed to “synoptic-scale vertical motion” (Mass and Schultz 1993), and “large-scale ascent” (Browning 1990), which implies that the essential mechanism can be explained in terms of balanced flow diagnosis.

Another aspect of CFAs, discussed primarily in the context of the split-front model, is that the airmass transition that accompanies a CFA is often only identifiable in terms of equivalent potential temperature θe or wet-bulb potential temperature θw, rather than potential temperature θ (Browning and Monk 1982). Browning (1990) suggested the upper cold front in the split-front model is better regarded as a “humidity front;” Browning et al. (1997) refer to an upper front as primarily the boundary between dry and moist air. Browning and Roberts (1996) state “we shall use the θw fronts as our definition of cold fronts (for the upper cold front in the split front model)” and that “θw fronts are not necessarily fronts in a dynamical sense.” Grzelak et al. (1994, 1996) refer to a CFA as a boundary between dry and moist air masses, and Mass and Schultz (1993) describe an upper-level humidity front reminiscent of the upper cold front in the split-front model.

The problem with viewing CFAs as only humidity fronts is that the presence of a narrow, nonconvective CFA rainband suggests that uplift is active, but the dynamics required to produce such lifting requires larger density contrasts than those provided by a pure humidity front. Browning and Roberts (1996) allude to this problem when they state that “such θw fronts do tend to be associated with the main cold-frontal precipitation bands,” but they do not attempt to explain how this is possible in a dynamically inactive front.

With the advent of mesoscale models it has become possible to calculate fields such as frontogenesis and QG vertical velocity with temporal and spatial resolutions not possible with conventional data. The goals of this paper are to use a mesoscale model to diagnose the mechanism causing the lifting associated with a CFA rainband, and to diagnose the relationship between the CFA humidity and temperature fields. The East Coast CFA rainband of 6 March 1986 (Locatelli et al. 1989; Sienkiewicz et al. 1989; Steenburgh and Mass 1994), which occurred during the Genesis of Atlantic Lows Experiment field project (GALE; Dirks et al. 1988), was chosen for this study for the following reasons. 1) The CFA had an associated relatively narrow, well-defined rainband. 2) The upward vertical velocity field associated with this rainband was well defined. 3) The rainband was nonconvective, and was due solely to the CFA. 4) The CFA was more clearly defined in θe than in θ. 5) The rainband and its environment were accurately described by observational datasets (including standard and special soundings, digitized National Weather Service (NWS) radars, dual-Doppler radars, a high-resolution surface network, and aircraft data), which allow verification of the model simulation.

The Pennsylvania State University–National Center for Atmospheric Research fifth-generation Mesoscale Model (MM5; Dudhia 1993; Grell et al. 1994) was used to simulate the storm system in which the 6 March rainband developed. Section 2 describes the model simulation and compares it with the observed storm. Section 3 examines the vertical velocity field associated with the simulated rainband from a QG diagnostic perspective. In section 4 we examine the frontal circulation associated with the simulated rainband by means of the 2D semigeostrophic S–E equation. In section 5 we diagnose the origins of the vertical velocity field in terms of the full (unbalanced) wind and mass fields within the frontal zone. In section 6 we calculate frontogenesis in order to gain an understanding of the factors responsible for the maintenance of the frontal structure of the CFA. Section 7 discusses the results presented in this paper, and section 8 summarizes our conclusions.

2. The MM5 mesoscale model simulation

The MM5 model is a nonhydrostatic, primitive equation model that uses the terrain-following sigma vertical coordinate, and a rectangular grid on a conformal map projection. In version 1 of the MM5, which was used in this study, the physical parameterizations used include a high-resolution PBL scheme (Blackadar 1979), the Kain–Fritsch (1990) cumulus parameterization, and an explicit cloud microphysical scheme (including separate treatment of cloud water, rain, cloud ice, and snow) implemented by Reisner et al. (1993).

The model grid consisted of an outer 54-km domain and an inner 18-km domain. The simulation was initialized at 0000 UTC 6 March 1986 from objective analyses of standard and special field observations, and was run for a period of 21 h. Comparisons of the model simulations to observational analyses from earlier studies are described below.

a. Wind, thermal, and precipitation structure

The 6 March 1986 storm had its origin in the lee of the Rocky Mountains, when a Pacific cold front that traversed the Rockies overtook a lee trough to form a warm occlusion (Locatelli et al. 1989; Sienkiewicz et al. 1989; Steenburgh and Mass 1994). In the STORM model (Hobbs et al. 1996), the warm-frontal circulation of the lee trough can produce a potentially unstable stratification east of the surface location of the trough, due to low θe air that has descended the Rocky Mountains being superimposed over high θe air from the Gulf of Mexico. However, the development of the 6 March 1986 storm was immediately preceded by a strong northerly push of cold dry air through the central United States and over the Gulf of Mexico, and there was little time for a southerly return flow from the Gulf of Mexico to reestablish a moist air mass over the central United States, as commonly occurs after a northerly cold surge in the wintertime (Lanicci and Warner 1997). Consequently, the air was stably stratified along the warm-frontal portion of the occlusion. This stably stratified, warm occluded structure traversed the eastern half of the United States, and led to the development of the nonconvective CFA rainband on the East Coast that is the subject of this study.

Figure 1 shows a surface map from the model simulation valid for 1900 UTC 6 March 1986. Since the model produced prodigious convective precipitation over the Gulf Stream off the U.S. east coast, for clarity only the radar reflectivity from the grid-resolved model precipitation is shown in the Fig. 1. A 40-km-wide nonconvective rainband extends along the East Coast as far south as South Carolina. The model did not produce any convective precipitation from the cumulus parameterization scheme coincident with the rainband, and model soundings taken through the rainband showed no indication of instability. This rainband is located ∼200 km in advance of a surface trough, which can be traced back to the Rocky Mountain lee trough that developed two days earlier. The trough is coincident with an axis of maximum θ. There is no detectable wind shift at the surface that is coincident with the rainband, but there is a cyclonic wind shift along the trough. A comparison of Fig. 1 with a surface analysis of this storm (Fig. 14 from Locatelli et al. 1989) valid for 1800 UTC 6 March shows that the MM5 model simulated the placement of the trough and rainband (rainband R2 in Locatelli et al. 1989) remarkably well. However, the model did not capture the smaller leading rainband, R1, shown in Locatelli et al. (1989). There is an indication of the arctic front in the simulated potential temperature field, where enhanced baroclinity can be seen in a zone extending from west-central Virginia to northern Georgia. In both the observations and the simulations the arctic front has merged with the position of the trough in Virginia.

Figures 2a–c are a series of cross sections valid at 1900 UTC 6 March 1986 along the lines AA′, BB′, and CC′ in Fig. 1. These cross sections show that the storm has the 3D structure of a warm occlusion. Aside from the high values of θe in the lower right hand corner of the cross sections, which resulted from the effects of the warm underlying Gulf Stream water, the familiar θe pattern of a warm occlusion is readily apparent. A region of low θe air extending from the surface trough to 400 hPa is intruding on higher θe air to the east, where the leading edge of the low θe air is tipped forward over the higher θe air from the surface position of the trough (T, in Fig. 2) to about 700 hPa. The CFA and the CFA rainband, which are collocated on the left-hand side of a wedge of high θe air, mark the leading edge of the advancing upper region of low θe air. A heavy dashed line marks the CFA in Fig. 2a. Other examples of this typical θe pattern in warm occlusions or split-fronts can be seen in Hobbs and Locatelli (1978, their Fig. 3), Browning and Monk (1982, their Fig. 2), Locatelli et al. (1989, their Fig. 15), Martin et al. (1990, their Figs. 11 and 16), Kuo et al. (1992, their Fig. 15), and Martin (1998, his Fig. 10). Notice that the occlusion process is further advanced in the northern cross sections. In other words, the CFA has moved farther eastward relative to the surface trough in the more northern sections. This 3D structure is consistent with the CFA overriding a warm front to form a warm occlusion. In this case, the surface trough, which originated as a Rocky Mountain lee trough in the central United States, marks the position of the surface occluded front in a classical warm occlusion. The corresponding “triple point” of the warm occlusion is located close to the Florida–Georgia border (Fig. 1). The arctic front also can be seen in all three cross sections. In the northern cross section (Fig. 2a) it has just crossed the Appalachian crest from the west and reached the surface trough associated with the above-mentioned occluded structure; thus it “shares” that surface pressure trough with the occluded structure. However, it has not yet reached the surface trough in the southernmost cross section (Fig. 2c). A similar situation is depicted in Figs. 14 and 15 of Locatelli et al. (1989).

In terms of the occluded structure discussed above, the cross section along AA′ (Fig. 2a) compares favorably to the time–height cross section shown in Fig. 15 of Locatelli et al. (1989). Both show a similar pattern in θe. In terms of the wind field, a good location for comparison is a vertical column located behind the CFA and ahead of the surface trough (occluded front). Thermal wind considerations imply that there the horizontal wind should veer with height in the lower layers of this column (due to warm advection in the warm-frontal portion of the occlusion), and that there should be backing of the horizontal wind with height in the region behind the CFA (due to cold advection). This is indeed the pattern of the change of horizontal wind with height seen in Fig. 2a (for example, between the surface trough “T” and the rainband), and in Fig. 15 in Locatelli et al. (1989) [in the Wilmington, NC (ILM), 2010 UTC and the Beaufort, NC (MRH), 2020 UTC soundings].

The warm occlusion, while clearly evident in the θe field, is not apparent in the θ field. This is due in part to the fact that the thermal gradient within the warm-frontal zone east of the surface trough is oriented approximately northeast to southwest, whereas, the cross section is oriented perpendicular to the CFA rainband, or northwest to southeast. The warm-frontal zone can be seen more easily in the contours of the horizontal wind direction along cross section AA′ (Fig. 2d). In this figure an upward sloping zone of enhanced veering of the wind with height (marked by the bold arrows) is apparent and marks the zone of enhanced warm advection associated with the warm-frontal zone within the occlusion.

The CFA appears to be embedded in a broad region of left-to-right thermal gradient, which is evident in the right two-thirds of the three cross sections (Figs. 2a, b and c). However, it is difficult to locate a baroclinic zone that corresponds to the CFA defined by θe solely from the θ field in the cross section. This is consistent with some previous descriptions of CFAs as being primarily humidity fronts. However, more detailed analysis, to be presented later in this paper, will show that there is a dynamically significant baroclinic zone associated with the CFA.

b. Vertical velocity structure

In this section, a somewhat shorter portion of the cross section AA′ is used to analyze the CFA. This shorter cross section is along the line A″A′ shown in Fig. 1. All fields are averaged perpendicular to this cross section over a distance indicated by the arrows in Fig. 1, and these averaged values will be shown on the cross section. Averaging is done to remove unrepresentative alongfront perturbations in the displayed quantities.

Figure 3 is a vertical cross section of vertical velocity along the line A″A′ in Fig. 1, which shows contours of vertical velocity and 2D winds relative to the motion of the rainband. The position of the CFA, as determined by the θe field, is located by the heavy dashed line in Fig. 2a. Coincident with the CFA is an 80-km-wide region of ascent, confined between 550 and 800 hPa, with a maximum value of −11 μbar s−1 (∼11 cm s−1). This can be compared to the maximum vertical velocity of 50 cm s−1 for the same rainband derived from dual-Doppler radar measurements (see Fig. 8 in Sienkiewicz et al. 1989), which covered altitudes between 3–6 km (∼800 to 450 hPa) and was ∼25 km wide. The fact that the model overestimated the width of the rainband, and underestimated the vertical velocity, is most likely a consequence of the model resolution (18 km) and parameterized diffusion that strongly damps structures at the 2δx scale.

In addition to the vertical velocity associated with the rainband, there is another region of deep ascent in the model simulation that is located ahead of the rainband. This weaker region of broader lifting is centered at 760 km along the horizontal axis in Fig. 3.

For the purposes of this study, the overall structure of the rainband and its environment are well captured by the model, since the simulated airflow relative to the rainband is very similar to that revealed by the dual-Doppler measurements. The model captures the relative airflow toward the CFA at middle levels, the sudden rise of the air as it encounters the CFA, and the strong relative flow beneath the CFA toward the surface trough.

3. Vertical velocity derived from quasigeostrophic diagnosis of the MM5 model

Quasigeostrophic vertical velocities were computed from the model output on the 54-km domain using the method described by Stoelinga et al. (2000). First, the height and temperature fields were interpolated from the model's sigma coordinate system to pressure levels with a vertical spacing of 30 hPa. A “step-mountain” lower boundary was defined such that the lowest grid point in each column was the lowest point above the ground. Topographic and Ekman conditions were applied at this lower boundary. To remove small-scale variability in the height and temperature fields that is not consistent with QG scaling, a low-pass filter was applied to these fields with 50% attenuation occurring at a wavelength of 300 km, similar to that suggested by Barnes et al. (1996). Using the smoothed pressure-level data, Q vectors (Hoskins et al. 1978) and their divergence were calculated at each grid point, and a simple relaxation method was used to invert the Q-vector form of the omega equation to obtain vertical velocities. The upper boundary condition was defined as zero vertical velocity at 75 hPa, and the lateral boundary conditions were set to a smoothed value of the full vertical velocity.

Figure 4a shows the QG vertical velocity, assuming dry stability, along the averaged cross section A″A′. Figure 4b shows the values of vertical velocity (Fig. 3) smoothed by the same low-pass filter that was applied to the height and temperature fields. Comparing Figs. 4a and b we see that the QG vertical velocity was successful in capturing the broad region of deep ascent located ahead of the CFA rainband, and also the stronger region of vertical velocity associated with the CFA rainband. However the maximum in vertical velocity associated with the CFA rainband was shifted upward, from 700 to 450 hPa in the QG depiction.

Figure 4c shows the QG vertical velocity computed with the effects of moisture included. This was done by first smoothing the relative humidity field using the same low-pass filter that was used to smooth the height and temperature fields (Fig. 4d). Then the computation was performed iteratively, using the dry solution as the first iteration, and the buoyancy frequency was assigned its moist value at locations where the smoothed relative humidity field was greater than 80% and where ascent was diagnosed, and the QG vertical velocity was then recalculated. The process was repeated until convergence was achieved.

The use of moist stability nearly doubles the magnitude of the upward QG vertical velocity associated with the rainband. It also narrows the width of the ascent column to that of the rainband, and moves it closer (both horizontally and vertically) to the location of the vertical velocity maximum from the MM5 simulation (shown in Fig. 4b).

4. Vertical velocity derived from the Sawyer–Eliassen equation using the MM5 model

The ageostrophic frontal circulation along cross section A″A′ was computed with the S–E equation, in a manner similar to the QG computation, except that, because the S–E equation is 2D, only model data that were within the cross section were used to compute the forcing terms in the S–E equation. This technique is similar to that used by Keyser and Carlson (1984) and Trier et al. (1991).

Figure 5a shows the S–E vertical velocity field. The S–E method captures the general region of upward velocity ahead of the CFA. However, unlike the QG method, it does not capture the vertical velocity maximum associated with the rainband simulated by the full MM5 model. The S–E method was also run using the moist stability wherever the relative humidity field (Fig. 4d) exceeded 80%. This result is shown in Fig. 5b. The values of the upward vertical velocities were greater than in the dry stability run, and the S–E moist stability vertical velocity better captured the smoothed vertical velocities (Fig. 4b) associated with the rainband.

Both the QG and S–E vertical velocity fields for conditions of moist stability captured the scale of lifting associated with the CFA rainband depicted in the smoothed vertical velocity fields. As might be expected, the width of the ascent column associated with the rainband was larger in the two balanced solutions than for the nonsmoothed results from the full MM5 model (compare Figs. 4d and 5b to Fig. 3). In section 5, we turn to the full unbalanced model solution to diagnose the forcing of the vertical velocity responsible for the CFA rainband.

5. Vertical velocity generated by the MM5 model simulation

a. Relationship between θ and pressure gradient

It was shown in section 3a that it is difficult to locate a baroclinic zone associated with the CFA strictly from the θ contours in a cross section through the CFA (Fig. 2a). However, if we underlay the horizontal gradient of θ in the cross section along A″A′ (Fig. 6) we can locate a baroclinic zone. A heavy black line in Fig. 6 marks the leading edge of this baroclinic zone. This position is immediately to the west of the location of the CFA as determined by the θe field (marked in Fig. 6 by the heavy dashed line taken from Fig. 2a). This baroclinic zone is divided into two regions. Region 1 corresponds to the upper backward-sloping portion of the CFA and region 2 to the lower forward-sloping portion of the CFA. The gradient of θ within both regions of the baroclinic zone is about 3 K (100 km)−1. This is typical of the gradient of θ in baroclinic zones associated with CFAs on operational upper-level charts and mesoscale model forecasts, which rarely exceeds 5 K (100 km)−1. Shown in Fig. 7 for the same cross section is total temperature advection and the wind vectors relative to the motion of the rainband. It is clear that the baroclinic zone, as defined by the θ gradient, is also a region of cold advection. As such, the CFA is the leading edge of a forward moving cold air mass. In addition, the wind vectors indicate that the forward sloping portion of the CFA is the division between the relative motion of air toward the CFA from the west and east. In particular, the “nose” of the lower sloping portion of the baroclinic zone is associated with the strongest upward movement of the converging air that produced the rainband. From Fig. 6 it can be seen that the location of the CFA, as determined by the θe pattern, is not coincident with the leading edge of the θ gradient; but it is close enough to be a reasonable approximation.

When we plot the contours of the component of the pressure gradient (calculated along constant height surfaces) along the averaged cross section used in Figs. 6 and 7, some pressure gradient patterns can be seen (labeled B, C, and D in Fig. 8) that are associated with the CFA baroclinic zone. The region marked B is composed of contours of pressure gradient that are parallel to and immediately behind the backward tilting portion of the CFA. A forward tilting region of a local minimum in the pressure gradient is indicated by C, and D marks a forward tilting region of a local maximum in the pressure gradient. Both of these features are associated with the forward tilting portion of the CFA.

We present a simple schematic in Fig. 9 that shows how these pressure gradient patterns are related to the θ pattern. In this figure we have ignored the effects of the decrease of density with height, since this would complicate (but not qualitatively change) the conclusions we wish to draw from the figure. Since the upper and lower portions of the baroclinic zones associated with the CFA are each only about 200 hPa high, the density difference between the top and bottom of the separate zones is small.

Figure 9a shows a tipped-back baroclinic zone similar to the one associated with the CFA in region B in Fig. 8. The line AB through the upper baroclinic zone in Fig. 6 shows the approximate location for the schematic in Fig. 9a. Figure 9b shows the relative change of pressure along the line AB resulting from the θ pattern in Fig. 9a. From point B to point b there is no pressure change, since θ is constant at all levels above the line. From point b to point a the pressure rises nonlinearly, because both the depth of the baroclinic zone and the air density within the zone are increasing linearly. Beyond point a on line AB the pressure rises linearly. Shown in Fig. 9c is the resulting change in the pressure gradient along line AB. The final panel in the left hand column (Fig. 9d) shows the resulting contours of pressure gradient in a vertical cross section containing the baroclinic zone in the top panel (Fig. 9a). Notice that the contours of pressure gradient are within and parallel to the baroclinic zone (as in Fig. 8).

Figure 9e shows a tipped-forward zone of maximum θ similar to the one in region C in Fig. 8. The line A′B′ through the lower tipped-forward baroclinic zone in Fig. 6 shows the approximate location for which the schematic in Fig. 9e is applicable. Figure 9f shows the relative change of pressure along the line A′B′ resulting from the θ pattern shown in Fig. 9e. From point A to point a there is no pressure change, because θ is constant at all levels above the line. From point a to point b the pressure decreases nonlinearly, because both the depth of the baroclinic zone and the air density within the zone are increasing linearly. From point b to point c the pressure decreases nonlinearly but with reverse curvature, because the depth of the right half of the baroclinic zone increases linearly and the air density within the right half of the zone decreases linearly. Past point c on line A′B′ the pressure remains constant. Shown in Fig. 9g is the resulting change in the pressure gradient along line A′B′. The final panel in the right hand column (Fig. 9h) shows the resulting contours of pressure gradient in a vertical cross section containing the baroclinic zone in the top panel (Fig. 9e), again assuming the effects of the decrease of density with height can be ignored. Notice that there is a minimum in the pressure gradient corresponding to the maximum in θ. A similar argument can be used to show how a slanted region of a minimum in θ is associated with a maximum in pressure gradient.

In the following section we will use trajectory analysis to show how the convergence field associated with the CFA is related to the pressure gradient field.

b. Trajectory analysis

In the following trajectory analysis the x axis is taken to be perpendicular to the CFA, pointing toward warmer air (in other words, along the cross section A″A′, pointing to the right). The y axis is taken to be into the page when viewing a cross section along the line A″A′. Figure 10 shows the horizontal divergence (∂u/∂x + ∂υ/∂y) in the averaged cross section A″A′. The areas of convergence marked L, M, and N are associated with the warm-frontal portion of the occlusion, the surface trough or occluded front, and the CFA, respectively. Since the CFA is approximately 2D in the region of cross section A″A′, the convergence in region N is due primarily to the term ∂u/∂x. To diagnose the cause of this region of enhanced convergence, we will look at the forces acting on individual air parcels that arrive within the region of convergence associated with the CFA. A series of seven backward 5-h trajectories starting at 1900 UTC 6 March (located by the numbered black circles in Fig. 10) was computed for two locations, one series at 750 hPa and the other at 550 hPa. The series at 550 hPa is initiated within the region of convergence associated with the upper tipped-backward portion of the CFA, which did not contribute to the formation of the rainband. The series of backward trajectories at 750 hPa, located at the “nose” of the CFA, is initiated in the region of convergence that contributed to the formation of the rainband.

Figures 11 and 12 show contours of various fields along the trajectories using the following format. The double-arrowed line in the upper right-hand corner is along cross section A″A′. Therefore, the x-axis is along the arrow pointing toward A′. The numbers (1–7) in these figures indicate the starting positions for the backward trajectories, and the small arrows along each trajectory indicate the hourly locations. Contours are drawn from the value of the field at the hourly position. Note that the values at the starting points of the trajectories differ from the values in the cross section A″A′, since they are point values, whereas the cross section shows values averaged along lines perpendicular to the cross section. The trajectories are plotted relative to the velocity of the rainband in the x direction along the cross section A″A′. In Fig. 11 the position of the baroclinic zone is indicated by the shaded region. This region was defined by the points at which each trajectory passed into or out of the baroclinic zone. The position of the baroclinic zone was located along the true 3D trajectory of the parcel and not on the 2D projection of the parcel trajectory onto the cross section A″A′.

Figure 11a shows the contours of pressure along the trajectories that start at 550 hPa. Air parcels along trajectories numbered 5–7 rise the entire 5 h and pass into and out of the baroclinic zone. Air parcels along trajectories 1–4 initially subside, then rise while passing into the baroclinic zone, and terminate within the baroclinic zone on cross section A″A′ at 1900 UTC. It should be noted that the baroclinic zone slopes downward toward positive x and, in the vicinity of the baroclinic zone, the surface on which the contours are defined slopes downward toward negative y, due to the fact that the trajectories are rising there. Therefore, although the line A″A′ is perpendicular to the baroclinic zone in a horizontal plane (as in Fig. 1), it is not perpendicular to the intersection of the baroclinic zone with the sloping trajectory surface (as seen in Fig. 11).

Figure 11b shows the x component of pressure gradient along the trajectories. One pattern that is clear is the decreasing contours of equal pressure gradient that are parallel to and lie within the baroclinic zone. This is consistent with the pattern of pressure gradient shown in Fig. 8 and demonstrates that the baroclinic zone and the resultant pressure gradient field are consistent over the time period of the 5-h backward trajectories. Notice that as the air parcels traverse the baroclinic zone, and the farther through the baroclinic zone the parcels travel, the stronger is the pressure gradient force (directed toward the left; a positive pressure gradient in the x direction results in a force toward the negative x direction, that is, to the left). The x component of net force per unit mass is the sum of the x components of the pressure gradient and Coriolis forces. This net force per unit mass on parcels along the trajectories is contoured in Fig. 11c. Just before all parcels enter the baroclinic zone, the x component of net force is near zero (i.e., υ is close to the geostrophic value). As all parcels continue into the baroclinic zone and the region of increasing pressure gradient, they experience a net force to the left. Therefore, υ becomes subgeostrophic in the baroclinic zone. The net force to the left decelerates the x component of the wind u. The longer the parcels experience this force to the left, the greater the deceleration in u. The effects of this differential deceleration on the parcels can be seen in Fig. 11d, where contours of u along the trajectories are plotted. Notice that at the time parcel 7 enters the baroclinic zone, its u value is ∼3 m s−1 faster than that of parcel 1 at the time parcel 1 entered the baroclinic zone. If these values did not change as the parcels traverse the baroclinic zone, the resulting effect would be divergence at 1900 UTC at 550 hPa (the termination points of the trajectories). However, the differential deceleration acting on the parcels as they traverse the baroclinic zone results in the u value of parcel 7 being ∼3 m s−1 slower than that of parcel 1 at the termination of the trajectories. This reversal in the relative values of u between parcels, results in convergence at 550 hPa and produces the vertical velocity associated with the CFA in this region.

We now turn to the 750-hPa level where the convergence resulted in the formation of the CFA rainband. Figure 12a shows the pressure along backward trajectories that start at 750 hPa. In Fig. 12 the axis of the minimum pressure gradient (C in Fig. 8) is indicated by the lightly shaded area and the axis of maximum pressure gradient (D in Fig. 8) is indicated by the heavily shaded area. The axis of minimum pressure gradient is located at the leading edge of the tipped-forward section of the baroclinic zone.

Air parcels along all of the trajectories rise during the five hours, with the fastest rising parcel (trajectory 3) located just to the right of the pressure gradient minimum (light shaded line). Figure 12b depicts the x component of pressure gradient along the trajectories. During the 5-h period, parcels along trajectories 1 and 2 undergo only a slight change in pressure gradient as they travel parallel to the axis of minimum pressure gradient. Parcels along trajectories 4, 5, 6, and 7 experience the greatest change in pressure gradient as they move toward the rainband (in the negative x direction) into the region of maximum pressure gradient. Figure 12c depicts the x component of net force along the trajectories. For the first few hours, the air parcel along trajectory 2 is slightly subgeostrophic, and for the last few hours it is slightly supergeostrophic. However, the net change in u for the parcel (Fig. 12d) is a decrease of only about 1 m s−1 (from 17.3 to 16.5 m s−1). In contrast, trajectories 4–7 (once they move into the increasing pressure gradients associated with the pressure gradient maximum) become subgeostrophic, and the associated net force in the x direction results in a decrease in their u velocity. In contrast to the parcel along trajectory 2, u for the parcel along trajectory 5 decreases by ∼4 m s−1. Consequently, the difference in u between trajectories 2 and 5 starts at 1400 UTC with a value of ∼4 m s−1 and ends at 1900 UTC with a value of ∼7 m s−1. If parcels 2 and 5 simply moved together, maintaining their initial u values, there would have still been convergence along the x direction when they arrived at the line A″A′, because of the initial difference in their u values. However, the trajectories of the air parcels through the pressure gradient pattern described above, and the differential effects on the u values of the parcels, increase the convergence within a smaller region.

6. Frontogenesis

In the preceding section we described how air parcels moving through changing pressure gradients associated with the tipped-forward and tipped-backward sections of the baroclinic zone, and the differential accelerations the parcels experienced as they traversed the changing pressure gradients, result in enhanced convergence and upward air motions that produce the CFA rainband. In this section, the 2D frontogenesis equation is used to examine how the baroclinic zone was maintained at forecast hour 19 (1900 UTC 6 March).

As noted previously, there are two regions of temperature gradient associated with the CFA at model hour 19: the lower, tipped-forward baroclinic zone, and the upper, tipped-back baroclinic zone. The flow patterns (relative to the rainband) in the vicinities of these two regions are quite different, as seen by the two groups of streamlines shown in the cross section A″A′ (Fig. 7). In the lower baroclinic zone the flow is primarily vertical, whereas, in the upper baroclinic zone the flow is primarily horizontal. It was confirmed from examination of hourly cross sections along line A″A′ during the period between hours 15–21 (not shown) that the CFA and its associated rainband had an approximately fixed structure, and all parts of the CFA moved to the right at a speed that is within 2 m s−1 of the rainband speed (13 m s−1). Therefore, the CFA thermal gradients and relative flow at hour 19 (Fig. 7) can be assumed to be approximately steady state. As such, it is clear from Fig. 7 that in both the upper and lower regions of the CFA, air parcels flow through the baroclinic zone. In other words, neither the upper nor lower baroclinic zones that comprise the CFA are acting as material boundaries, which is contrary to the classical concept of a front. This picture raises the issue of how these baroclinic zones are maintained as air parcels pass through them. This issue will be addressed with a 2D frontogenesis analysis.

The 2-D frontogenesis equation can be written
i1520-0493-130-2-278-e1
where the x axis is taken to be along the cross section, positive to the right, and θx is the left-to-right component of the gradient of θ. Each of the terms on the right-hand side of (1) contribute to local (Eulerian) frontogenesis. They will be referred to, respectively, as the contributions due to horizontal advection along the cross section, horizontal advection into the cross section, confluence, shear, vertical advection, tilting, and diabatic heating. Although frontogenesis is usually defined in terms of the Lagrangian time rate of change of temperature gradient, it is cast here in Eulerian form, which is more useful for steady-state situations. As noted above, to create an approximately steady-state situation, the velocity field must be considered in the frame of reference of the moving rainband. Cross section A″A′ is perpendicular to the rainband but fixed relative to the ground, and the rainband moves with a speed of 13 m s−1 along the cross section and 25 m s−1 into the cross section. These velocity components are subtracted from the u and υ velocities in the horizontal advection terms so that (1) is applied in the rainband-relative frame of reference.

Figure 13a shows total horizontal advection [i.e., the sum of the first two terms on the right-hand side of (1)]. Because the CFA frontal zone is approximately 2D, there is very little advection of θx along the front (into the cross section A″A′). Therefore, most of what is seen in Fig. 13a is due to cross-front advection. Because there is very little thermal gradient in the alongfront direction, the shear frontogenesis term is very small and therefore not shown, although it is included in the total frontogenesis (Fig. 13g).

Consistent with the three upper streamlines shown in Fig. 7, which are primarily horizontal, it is not surprising that horizontal advection of θx (Fig. 13a) is an important contributor to local frontogenesis ahead of the upper part of the CFA baroclinic zone, whereas, vertical advection (Fig. 13b) is not. There is a strong couplet of horizontal advection (negative to the left and positive to the right) straddling the upper baroclinic zone (Fig. 13a). There is a similar (but weaker and narrower) couplet of confluent frontogenesis in approximately the same location (Fig. 13c). These terms alone would tend to move the baroclinic zone downstream (to the right) in the relative reference frame, but they are counteracted by tilting frontogenesis (Fig. 13d), which supplies an opposing couplet of frontogenesis (positive to the left and negative to the right) straddling the upper baroclinic zone. The diabatic term (Fig. 13e) is zero in the region of the upper baroclinic zone. The net result for the upper baroclinic zone (Fig. 13g) is a roughly steady-state situation, with a few regions of primarily positive frontogenesis within the zone that indicate the thermal gradient is strengthening at those locations. In many ways, the upper baroclinic zone displays characteristics of a vertically propagating gravity wave, rather than a frontal zone in the classical sense. This issue will be addressed in more detail in section 7.

The lower, forward-tipped baroclinic zone is dominated by upward rather than horizontal flow (in the context of the vertically stretched cross section displayed in Fig. 7). Consequently, vertical advection (Fig. 13b) contributes strongly to local frontolysis underneath the baroclinic zone and to local frontogenesis above. Because the streamlines through the baroclinic zone (Fig. 7) are tipped forward slightly, vertical advection is slightly counteracted by horizontal advection. To maintain the baroclinic zone, the advective effect is approximately balanced by confluent frontogenesis (Fig. 13c) on the forward side of the baroclinic zone. Frontogenesis due to tilting (Fig. 13d) and diabatic heating (Fig. 13e) produces very large dipoles (note the doubled contour interval in Figs. 13d and 13e) straddling the vertical velocity maximum associated with the rainband. When added together (Fig. 13g), these dipoles largely cancel each other. The extent to which they cancel each other, assuming a saturated environment, is determined by the moist stability (i.e., the vertical gradient of θe). In a moist neutral environment, local cooling due to vertical advection of θ is exactly canceled by diabatic heating, therefore, tilting frontogenesis is exactly canceled by diabatic frontogenesis. In a moist stable environment, local cooling due to vertical advection of θ exceeds diabatic heating; therefore, tilting frontogenesis exceeds diabatic frontogenesis. Above and to the right of the baroclinic zone, the θe distribution (Fig. 13h) indicates a moist stable environment, and therefore diabatic frontogenesis does not completely cancel tilting frontogenesis. However, within the lower baroclinic zone, the air is saturated and the approximately vertical contours of θe (Fig. 13h) indicate a moist neutral environment. Therefore, there is near cancellation between tilting and diabatic frontogenesis.

To summarize, the salient features in the frontogenetical analysis of the lower, tipped-forward baroclinic zone indicate an approximate steady-state situation in which parcels pass upward into the baroclinic zone. To maintain the baroclinic zone against the effects of advection, confluent frontogenesis acts to increase the horizontal gradient of θ following a parcel.

7. Discussion

a. QG diagnosis

In section 3 we showed that the dry QG diagnosis was able to capture the broad division between upward vertical velocity ahead of the CFA and downward vertical velocity behind it, and the moist diagnosis was able to resolve the vertical velocity structure that produced the CFA rainband defined by the smoothed vertical velocity field (compare Figs. 4a and 4c to Fig. 4b). However, two issues warrant further discussion.

The first issue is that the dry solution overemphasizes upward motion in the upper troposphere (between 400 and 500 hPa) compared to the full vertical velocity. Although the moist solution shows a more realistic midtropospheric ascent column, it too overemphasizes upward motion in the upper troposphere. To explore this discrepancy, we will now examine the field of relative vorticity (smoothed to the same degree as the QG input fields) in the same cross section in which the QG diagnosis was displayed in section 3. Quasigeostrophic theory is valid when the Rossby number is much less than unity; one measure of the Rossby number is the ratio of relative to planetary vorticity (ζ/f). The values of the relative vorticity in Fig. 14 are scaled by 1 × 10−4, or approximately f, so that this is effectively a plot of Rossby number. Large Rossby numbers (>0.5) prevail in the entire upper-left quadrant of the plot. Thus, in this region strict QG assumptions are not met. To help determine if the region of large Rossby number at ∼400 hPa is important, we examine the forcing term in the QG ω-equation (i.e., the divergence of Q vectors) along cross section A″A′. The distribution of the forcing term shown in Fig. 15 (smoothed to the same degree as the QG input fields) indicates that the strongest forcing occurs in the same location where QG theory is least valid, namely, in the upper troposphere in the left half of the cross section. We hypothesize that regions where the flow is acting most strongly to develop imbalance are also regions where nearly instantaneous restoration of balance is not occurring. Therefore, in this cross section, the validity of the QG vertical velocity solution is weakest where the QG vertical velocity diagnosis (both the moist and dry methods) produce the largest values, namely in the upper troposphere.

The second issue is that even if the moist solution produces a reasonable ascent column at the location of the rainband, this demonstrates only that QG dynamics are consistent with the simulated rainband in a diagnostic rather than a prognostic sense. This distinction is important because the moist solution is obviously strongly influenced by the relative humidity distribution, particularly the location of the 80% RH threshold used to switch on the moist stability. In spite of smoothing the relative humidity field with the same low-pass filter that was used to smooth the height and temperature fields (Fig. 4d), the region of relative humidity greater than 80% associated with the CFA rainband is about 100-km wide. When this region of rainband-scale relative humidity is used to define the region of moist ascent, and therefore to enhance the response to the forcing, the result is a narrow region of lifting on the scale of the CFA. However, in addressing the question of whether the CFA rainband can be explained by balanced dynamics in a prognostic sense, it is not clear that using the moisture field developed from the full MM5 model run (even if smoothed) is the appropriate moisture field to apply in the QG diagnosis; this is because that moisture field has been produced by the time-integrated effects of all processes, balanced and unbalanced.

Another approach would be to use moist stability everywhere that the diagnosis produces ascent, similar to the assumption made by Emanuel (1985) in his analytical frontal study using the S–E equation. We attempted this in both the QG and S–E solutions, but this approach did not produce the expected narrowing of the ascent seen in Emanuel's study. In our study, the only way we were able to narrow the ascent column, in both the QG and S–E solutions, was to use the actual, narrow column of moist air as an “on switch” for moist stability.

A third approach, and perhaps the most rigorous, would be to run a prognostic QG model, initialized at some earlier time, to examine if QG dynamics not only produce ascent in about the right location, but also produce the narrow column of moist air that feeds back into the narrowing of the ascent column itself.

b. Sawyer–Eliassen diagnosis

Application of the S–E equation to real (or simulated) 3D datasets for the purpose of diagnosing vertical velocity introduces both a potential improvement and a potential degradation over 3D QG diagnosis. The improvement comes from the greater accuracy of S–E over QG, which allows for a more realistic response to frontal forcing in the presence of baroclinity. The degradation comes from the assumption of two-dimensionality, which may be questionable, even for fronts that appear approximately 2D in terms of their thermal and precipitation structure. In the present application, the 2D dry S–E equation performed worse than the QG dry solution (compare Figs. 4a and 5a), most likely due to a lack of two-dimensionality in the forcing terms and/or the terms that affect the response. In the moist solutions the patterns are comparable (see Figs. 4c and 5b), and differences can be attributed to the reasons stated above for the dry solution. Therefore, it should not always be assumed that the semigeostrophic (but 2D) S–E equation is an improvement over the QG ω-equation for the diagnosis of vertical velocity in real fronts, even if they appear to be approximately 2D. More may be lost from the 2D assumption than is gained from the retention of additional terms in the diagnostic equation.

c. Model-generated vertical velocity

In section 5 we examined the full (unfiltered) vertical velocity associated with the CFA. As discussed by Bluestein (1986), it is clear that the actual spatial scale of the lifting associated with most fronts, whether they are surface-based or forced aloft in occluded-like structures, is mesoscale, but only in the cross-front direction. Stoelinga et al. (2000) proposed the term frontal scale to refer specifically to the scale of front-related features and dynamics that are mesoscale in the cross-front direction but synoptic-scale in the alongfront direction.

We have shown that the θ structure in the CFA baroclinic zone led to the frontal-scale spatial pattern of rapidly changing pressure gradient depicted in Fig. 8. From the trajectory analysis presented in section 5, we showed that the actual, narrow region of convergence at the CFA resulted from the different cross-front horizontal velocities that air parcels obtained by the differential forces acting on them as they moved through these changing pressure gradients. It is not clear to what extent these results represent a fundamentally different dynamical mechanism than what is qualitatively implied by QG or S–E theory, namely, that a secondary (vertical/ageostrophic) circulation develops to restore thermal wind balance that is being perturbed by geostrophic frontogenesis. Perhaps the qualitative understanding provided by these theories is correct, but a higher order balance than geostrophy is required to obtain a more accurate quantitative result at the frontal scale.

d. Frontal maintenance

The frontogenetical analysis was performed in an Eulerian framework moving with the rainband, to exploit the roughly steady-state nature of the CFA. An examination of the CFA in this framework showed that, contrary to the traditional idea of a front as essentially a material boundary, both the upper, tipped-back baroclinic zone, and the lower, tipped-forward baroclinic zone, did not act as material boundaries: air parcels clearly flowed through both boundaries.

The upper baroclinic zone was a narrow (∼100 km wide) region of baroclinity embedded in a broader (∼400 km wide) region of weaker baroclinity. In many ways, the narrow upper baroclinic zone displayed some characteristics of a vertically propagating gravity wave: air flowed through the feature primarily horizontally, with vertical velocity in quadrature with potential temperature perturbations. A calculation of the horizontal phase speed of a gravity wave with horizontal and vertical wavelength similar to that of the upward–downward vertical velocity couplet seen in the model simulation, and the environmental buoyancy frequency yielded values very close to the relative flow through the upper narrow baroclinic zone (6 m s−1 compared to 7 m s−1). If this simulated feature was a gravity wave, it is more likely that it was produced by the rainband than by orographic effects, since its structure remains tied to the rainband and the attendant frontal structure for several hours as it moves away from the mountains. The vigorous (though nonconvective) ascent associated with the CFA rainband may have forced a gravity wave response, similar to that produced in the stratosphere by deep tropospheric convection. This interpretation does not preclude the presence of a baroclinic zone of frontal origin above 600 hPa in the model simulation. Such a baroclinic zone was clearly seen in the observations. In the model simulation the baroclinic zone of frontal origin cannot be separated from the gravity wave.

The lower, tipped-forward part of the CFA did not act as a “material” surface, since parcels moved (primarily vertically) through this baroclinic zone. However, we do not interpret this feature as a gravity wave, because the atmosphere was at (or close to) saturation and nearly moist neutrally stable, with a column of vigorous upright ascent within the baroclinic zone. The lower, tipped-forward portion of the CFA, which was much more directly involved in the formation and maintenance of the rainband, was a frontal baroclinic zone.

e. The CFA: A humidity or a potential temperature boundary?

As discussed in section 1, CFAs have been classified as both θ- and humidity-fronts. The difficulty with classifying a CFA as purely a humidity front is that it cannot explain the narrow rainband that accompanies a CFA. As shown in section 5, the narrow rainband is the result of pressure gradient forces produced by the baroclinic zones. In the storm described in this paper, the location of the CFA was more evident in the θe field than the θ field (see Fig. 2a). In fact, without a careful analysis of the θ field (see Figs. 6 and 7), the CFA appeared to be embedded in a region of general cooling. This might suggest that it be classified as a humidity front. However, in section 5 we showed that there was indeed a baroclinic zone associated with the CFA [of ∼3 K (100 km)−1 and about 100-km wide] that was dynamically active in the development of the vertical velocity associated with the CFA rainband. Moreover, we showed in section 6 that the baroclinic zone was frontogenetically active. Therefore, the CFA discussed in this paper cannot be classified simply as a humidity front. Regular studies of CFAs on operational charts and daily mesoscale model forecasts show that the thermal discontinuity associated with the CFA for the case discussed in this paper is not atypical. Therefore, in general, CFAs (regardless of whether they are associated with classical warm occlusions, split fronts, trowals, or STORM-type systems) are not simply humidity fronts.

To understand why the CFA was prominent in the θe field we need to look at the separate fields that comprise it, namely, the water vapor and θ fields. These two averaged fields at model hour 19 are shown in Fig. 16a (in a cross-section along the line A′A″ in Fig. 1) along with the airflow in the cross-section relative to the motion of the CFA rainband (vectors) and the position of the CFA (solid heavy line) determined from the θ field. Figure 16b shows the θe field for the same cross-section superimposed on the water vapor field. These fields, while calculated at model hour 19, are the result of several hours of air movement prior to model hour 19. Therefore, they can help illuminate the origin of the θe pattern that so clearly shows a CFA.

Both above and below the nose of the CFA (i.e., at ∼600 hPa and ∼800 hPa), the θe-defined front is clearly located ahead of the θ-defined front. In both these regions, the leading edge of the θe gradient is associated more with the left side of a prominent plume in water vapor than it is with a change in the θ gradient. This plume in the water vapor field is likely the result of upward transport of water vapor from lower levels by the ascent associated with the CFA. This transport of water vapor is responsible for the prominence of the CFA in the θe field. However, although the water vapor field was instrumental in producing the strong CFA pattern in the θe field, it was the dynamics associated with the CFA baroclinic zone that forced the lifting necessary to produce the θe field.

8. Conclusions

A numerical simulation using the MM5 model was run on a cold front aloft (CFA) and an associated rainband situated over the U.S. east coast on 6 March 1986. The CFA was part of a warm occluded structure, which originated in the lee of the Rocky Mountains when a Pacific cold front overtook a lee trough. From the MM5 model simulation we have arrived at the following principal conclusions.

  • Quasigeostrophic diagnosis with dry stability everywhere recovered the large-scale pattern of the full vertical velocity structure associated with the CFA rainband, but not the ascent associated with the rainband itself. QG diagnosis using moist stability in regions of saturated ascent also recovered the narrow (∼100 km wide) ascent region associated with the CFA rainband. The success of the moist method was due to the strong influence of the narrow region of moist stability in enhancing the response to the dynamic forcing. Problems with the QG diagnosis occurred in the upper troposphere where Rossby number was large.
  • Sawyer–Eliassen 2D diagnosis with dry stability did a poorer job of recovering the vertical velocity associated with the CFA rainband than the dry QG diagnosis, probably due to the lack of two-dimensionality in the front and its environment. Moist S–E diagnosis (using moist stability in regions of saturated ascent) performed well in capturing the ascent associated with the CFA rainband, for the same reason that the moist QG method performed well.
  • The frontal-scale vertical velocity ahead of the CFA resulted from the convergence caused by the differential acceleration of air parcels as they moved through characteristic pressure gradient patterns associated with the two distinct portions of the CFA: an upper, backward-sloping portion characterized by an increase in the eastward thermal gradient, and a lower, forward-sloping portion characterized by a minimum in potential temperature.
  • Examination of frontogenesis within an Eulerian framework moving with the rainband showed that the upper, tipped-back portion of the CFA baroclinic zone did not act as a material surface. Parcels passed through this baroclinic zone, with frontogenesis due to tilting counteracting horizontal advection and (to a lesser extent) confluent frontogenesis. In many ways, this upper baroclinic zone behaved like a vertically propagating gravity wave.
  • The lower, tipped-forward baroclinic zone also did not act as a material surface. It was characterized by parcels traveling primarily vertically (upward) through this zone, with the front being maintained by a balance between advection (primarily vertical) and confluent frontogenesis.
  • The prominence of the CFA in the θe field was due mainly to the strong upward transport of water vapor from lower levels in the updraft produced by the CFA.
  • In spite of the prominence of the CFA in the θe field compared to the θ field, the CFA was a cold (thermal) front.

Acknowledgments

This research was supported by Grant ATM-9106235 from the Mesoscale Dynamic Meteorology Program (program manager: Stephen Nelson), Atmospheric Research Division, National Science Foundation.

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Fig. 1.
Fig. 1.

Sea level pressure (in hPa, bold solid lines), θ (in K, thin dashed lines), surface winds (arrows, see legend on figure), regions of model-diagnosed radar echo >4 dBZ averaged between 995 and 700 hPa (shaded regions), and the position of the surface trough (bold dashed line) and arctic front (bold dotted line) at 1900 UTC 6 Mar 1986. The lettered lines mark the position of vertical cross sections referred to in later figures. The bold arrows indicate the distance over which selected variables are averaged along cross section A″A′

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 2.
Fig. 2.

Vertical cross sections at 1900 UTC 6 Mar 1986 along the lines (a) AA′, (b) BB′, (c) CC′, and (d) AA′ shown in Fig. 1. (a)–(c) The shaded regions are model-diagnosed radar echo >4 dBZ, θe is given in K (solid bold lines), θ is given in K (thin dashed lines), the horizontal winds are shown by arrows where a southerly wind is represented by a northward-pointing arrow (see legend on figure), and T marks the surface trough position. (d) As in (a) but the short dashed lines are contours of the direction from which the wind is blowing (in degrees), the bold dashed line marks the leading edge of the enhanced gradient in θe, and the bold arrows mark the warm-frontal zone of the warm occlusion

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 3.
Fig. 3.

Vertical cross section at 1900 UTC 6 Mar 1986 along the line A″A′ shown in Fig. 1. Solid lines are contours of vertical velocity (in dPa s−1), and arrows indicate the wind velocity in the cross section plane (see legend for magnitudes). Both fields are averaged over the distance normal to the cross section indicated by the double arrowed line in Fig. 1

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 4.
Fig. 4.

As in Fig. 3 but where all fields are averaged normal to the cross section. (a) Solid lines (dashed lines) are contours of quasigeostrophic upward (downward) vertical velocity (in dPa s−1); velocities computed assuming dry stability throughout the domain. (b) Solid lines (dashed lines) are contours of smoothed upward (downward) vertical velocity (in dPa s−1). (c) Quasigeostrophic vertical velocities computed assuming moist stability everywhere that the smoothed values of RH shown in (d) exceed 80%. (d) Solid lines are contours of smoothed values of RH. The dashed areas enclose the model diagnosed radar echo >4 dBZ. All fields from the MM5 model

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 5.
Fig. 5.

Vertical cross section at 1900 UTC 6 Mar 1986 along the line A″A′ shown in Fig. 1. (a) Solid lines (dashed lines) are upward (downward) semigeostrophic vertical velocity (in dPa s−1) assuming dry stability everywhere. (b) As in (a) but assuming moist stability everywhere that the smoothed values of RH shown in Fig. 4d exceed 80%. The shaded areas enclose the model-diagnosed radar echo >4 dBZ

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 6.
Fig. 6.

Vertical cross section at 1900 UTC 6 Mar 1986 along the line A″A′ shown in Fig. 1. Solid lines are contours of θ (in K), the shading indicates θ gradient (see legend for magnitudes), the bold dashed line indicates the position of the CFA determined from the θe field (taken from Fig. 2a), and the bold solid line indicates the position of the CFA determined from the θ field. The dashed line encloses the model diagnosed radar echo >4 dBZ. See text for an explanation of regions 1 and 2. Lines AB and A′B′ show the approximate locations for which the schematic shown in Fig. 9 is applicable

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 7.
Fig. 7.

As in Fig. 3 but the shading indicates values of cold θ advection (see legend for magnitudes), and arrows indicate the wind velocity in the plane of the cross section (see legend for magnitudes). The dashed line encloses the model diagnosed radar echo >4 dBZ. Bold arrowed lines are selected streamlines of airflow relative to the storm

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 8.
Fig. 8.

As in Fig. 3 but solid lines (dashed lines) are positive (negative) contours of pressure gradient (in hPa m−1 × 10−5), where positive values indicate a pressure force to the left. The dotted box shows the location of a smaller section of the cross section used in subsequent figures. The bold solid line, taken from Fig. 6, indicates the position of the CFA derived from the θ gradient. See text for an explanation of the regions indicated by B, C, and D. The shaded areas enclose the model diagnosed radar echo >4 dBZ

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 9.
Fig. 9.

Schematic showing the relationship between θ and pressure gradient for (a) a tipped-backward baroclinic zone, and (b) a tipped-forward region of localized warming. See text for an explanation of the individual panels

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 10.
Fig. 10.

As in Fig. 3 but solid lines (dashed lines) are contours of negative (positive) divergence (in s−1 × 10−5). The position of the surface trough is marked by T. Numbered black dots are the starting locations of 5-h back trajectories at 550 and 750 hPa. Refer to the text for an explanation of the regions marked by L, M, and N. The shaded areas enclose the model diagnosed radar echo >4 dBZ

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 11.
Fig. 11.

Plan view of 5-h back trajectories of air parcels, relative to the movement of the CFA rainband, along cross section A″A′, and starting at 550 hPa at 1900 UTC from the positions shown in Fig. 10. The following fields are contoured along the trajectories: (a) pressure (in hPa), (b) pressure gradient (in hPa m−1 × 10−5), where positive is a pressure force to the left along A″A′, (c) net force per unit mass along cross section A″A′ (in m s−2 × 10−4) where positive is a force to the left along cross section A″A′, and (d) the horizontal wind speed (in m s−1) along cross section A″A″, where a positive value indicates a wind to the right along the cross section. The small arrows mark the hourly positions of the trajectories, and the shading indicates the position of the CFA baroclinic zone along each trajectory

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 12.
Fig. 12.

As in Fig. 11 but for back trajectories starting at 750 hPa. The lighter-shaded area is the axis of the pressure gradient minimum, and the heavier-shaded area is the axis of the pressure gradient maximum. See text for further explanation of the pressure minimum and maximum

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 13.
Fig. 13.

Solid lines (dashed lines) are contours of positive (negative) frontogenesis [in K (100 km)−1 h−1], for the smaller region enclosed by the dashed lines along cross section A″A in Fig. 8 produced by (a) horizontal advection by the wind relative to the CFA rainband, (b) vertical advection, (c) confluence, (d) tilting, (e) diabatic, (f) diabatic plus confluence, (g) total of confluence, shear, vertical advection, horizontal advection, tilting, and diabatic, and (h) contours of θe (heavy solid lines in K). The thin solid lines are contours of θ (in K), and the shaded regions show the location of the upper and lower baroclinic zones of the CFA

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 14.
Fig. 14.

As in Fig. 3 but the solid lines (dashed lines) are contours of positive (negative) relative vorticity (in s−1 × 10−4). The position of the CFA determined from the θ field is shown by the heavy solid line. The shaded areas enclose the model diagnosed radar echo >4 dBZ

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 15.
Fig. 15.

As in Fig. 14 but the solid lines (dashed lines) are contours of positive (negative) Q vector divergence (in s−3 hPa−1). The shaded areas enclose the model diagnosed radar echo >4 dBZ

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

Fig. 16.
Fig. 16.

As in Fig. 3 but (a) the solid lines are contours of water vapor (in g kg−1), the dashed lines are contours of θ (in K), and the vectors indicate winds in the cross section relative to the movement of the rainband (see legend). The position of the CFA determined from the θ field is given by the heavy solid line. (b) As in (a) but the solid lines are contours of θe (in K), and the dashed lines are contours of water vapor (in g kg−1)

Citation: Monthly Weather Review 130, 2; 10.1175/1520-0493(2002)130<0278:OASOCA>2.0.CO;2

1

Browning and collaborators use the term “upper cold front” instead of “cold front aloft,” but these should be interchangeable. Also, they do not explicitly state that an underlying stable layer is important for the formation of the upper cold front in their split-front model. However, examination of cross sections that are presented as examples of the split-front model [e.g., Fig. 2 in Browning and Monk (1982)] show that the upper front is indeed bounded underneath by a layer of enhanced static stability. They do not discuss this stable layer, and it is therefore unclear whether it is warm-frontal in origin (as in a standard warm occlusion) or some nonfrontal feature within the warm sector.

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