A wide cold-frontal rainband and its relationship to frontal topography

Q. J . R. Meteorol. SOC. (1994), 120, pp. 259-275 55 1.5 15.827:551 S77.11

A wide cold-frontal rainband and its relationship to frontal topography

By JOHN D. LOCATELLI, JONATHAN E. MARTIN and PETER V . HOBBS’ University of Washington, USA

(Received 3 February 1993; revised 16 July 1993)

SUMMARY A wide cold-frontal rainband associated with a vigorous surface cold front was investigated using con-

ventional meteorological data and the velocity and reflectivity data from high-resolution Doppler radar. It was found that the movement of the rainband was closely related to the velocity of the frontal surface, and that the substructural features of the rainband corresponded closely with the topographical features of that surface. The evolution of the topography of the frontal surface is described, and some processes that might affect frontal topography, and therefore the structure and movement of rainbands, are examined.

1. INTRODUCTION

Over the past few decades several theories have been proposed to explain the formation of rainbands in extratropical cyclones. These theories include synoptic-scale differential advection (e.g. Harold 1972,1973; Locatelli and Hobbs 1987), various gravity- wave mechanisms (e.g. Lindzen and Tung 1976; Gall et al. 1988) and conditional symmetric instability (CSI) (e.g. Bennetts and Hoskins 1979; Matejka et al. 1980; Emanuel 1983; Parsons and Hobbs 1983; Sanders and Bosart 1985; Moore and Blakely 1988; Knight and Hobbs 1988). In this paper we present, and comment on, observations made with soundings and data from high-resolution dual-Doppler radar that suggest that the pattern and motions of precipitation features associated with a cold front were closely related to the topography of the frontal surface and to the motions of topographical features of that surface.

The case described here concerns a vigorous cold front that formed over and just offshore of the south-eastern United States on 26 and 27 January 1986. The precipitation associated with this front was observed using special facilities that were already in place for the Genesis of Atlantic Lows Experiment (GALE); of particular importance was a dual-Doppler radar pair (CP-3 and CP-4) located at Cape Hatteras, North Carolina (Dirks et al. 1988). A description of this frontal system has been given by Martin et al. (1993). In this paper we present and comment on new observations and analyses of a wide cold-frontal rainband (WCFR) that was associated with this front. We begin by presenting observations of the WCFR, and then show how this rainband, and its internal structure, were related to the topography of the frontal surface. This relationship is then examined in terms of possible mechanisms for generating frontal topography?.

2. THE RAINBAND

A surface cold front passed over Cape Hatteras, North Carolina, at 2 1 0 0 ~ ~ ~ 26 January 1986 (Fig. 1). Four hours after this frontal passage a WCFR passed through a region of dual-Doppler radar coverage adjacent to Cape Hatteras and showed up in the northern lobe of that coverage.

Corresponding author: Atmospheric Sciences Department, University of Washington, Seattle, Washington, USA. t The terms ‘topography’ or ‘topographical features’ in connection with frontal surfaces do not necessarily mean that these features are produced by the topography of the underlying ground.

259

260 J . D. LOCATELLI et al.

1012 mb

Figure 1 . National Meteorological Center’s sea-level pressure analysis at 2100 GMT 26 January 1986. Solid lines are isobars labelled in mb and contoured every 4 mb. Frontal symbols indicate the positions of fronts at

the surface.

Figure 2 shows an expanded view of the region of the dual-Doppler coverage and Fig. 3 the region (90 km x 75 km horizontally by 9 km in height) over which radar reflectivity data were available from the dual-Doppler radars; and from within which three-dimensional wind fields could be derived from the two radars in a volume 90 km x 36 km horizontally by 9 km in height. The insert in Fig. 3 shows the WCFR (defined by the 31 dBZ contour at 1 km altitude) and the surface cold front at approxi- mately 0045 GMT 27 January. The WCFR was located parallel to and 120 km behind the cold front.

The radar reflectivities and the radial velocities (from which the wind fields were derived) were interpolated to a Cartesian grid of 1.5 km X 1.5 km x 0.5 km spacing. Vertical air velocities were derived from the anelastic continuity equation, assuming zero vertical velocity at the ground and at a height of 9 km; the horizontal flow was not adjusted to allow for the upper boundary condition. As in all dual-Doppler analysis, decisions had to be made at each step in the process which affected the derived winds and reflectivities. These decisions included identifying bad data points, deciding which radial data points contributed to the value at a gridpoint when interpolating the radial fields to the Cartesian grid and, when necessary, smoothing the data after each compu- tation. The least number of such decisions is required to derive the reflectivity field, the next smallest to derive the horizontal wind field, and the largest number of decisions is needed to derive the vertical wind field. Consequently, we shall use the reflectivity field

RAINBANDS AND FRONTAL TOPOGRAPHY 261

Figure 2. Map of eastern North Carolina showing the locations of the CP-3 and CP-4 dual-Doppler radar pair. Shaded areas are the regions of dual-Doppler radar coverage. Radiosondes were launched from Morehead

City and Cape Hatteras.

90 60 30 EAST-WEST DISTANCE (km)

E’

D’

I

Figure 3. Radar reflectivity values for the wide cold-frontal rainband (WCFR) at an altitude of 1 krn at 0045 GMT 27 January 1986. The dashed rectangle shows the region over which winds were derived from the dual-Doppler radars. D-D’ and E-E’ are lines along which vertical cross-sections were constructed (see Figs. 5 , 6, 10 and 11). Precipitation cores within the WCFR are designated by X and Y. Sub-bands are the south- north oriented regions defined by the 32-35 dBZ level. The inset shows the rainband (shaded area) relative to

the position of the surface cold front.


as a standard to judge the validity of the derived wind fields, particularly the vertical velocity field.

In common with other WCFRs (e.g. Hobbs et al. 1980), the WCFR depicted in Fig. 3 possessed internal structure. The smallest and strongest elements of this substructure, which we refer to as ‘precipitation cores’ (Hobbs and Locatelli 1978), are denoted by the letters X and Y in Fig. 3; their approximate velocity was 30 m s-’ towards a direction of 13 degrees. We shall refer to the larger, organized elements of the rainband as ‘sub- bands’; these are the south-north oriented regions of precipitation defined by the 33- 35 dBZ level in Fig. 3.

Shown in Fig. 4 are a series of radar reflectivity patterns for the WCFR derived from the National Weather Service’s Cape Hatteras WSR-57 radar. The WCFR comprized sub-bands (labelled, A, B and C in Fig. 4) which, in turn, contained precipitation cores. Sub-band A decreased in strength as sub-band B developed to the east of it. Similarly, sub-band B decreased in strength as sub-band C developed-all within 30 minutes. The net effect of this rapid generation of new sub-bands to the east was that the WCFR (defined as the envelope of reflectivity containing the various sub-bands) propagated eastwards faster than the individual sub-bands or precipitation cores.

5UB SUB 0 31-33 dBZ 0 3335482 35-37 dBZ = >37 dBZ DISTANCE (km) 0 25 50 75 1W 125 150 175 B*ND B*ND BAND

A * * J

SUB SUB SUB BAND BAND

2

Figure 4. Time-lapse development, based on radar reflectivity data, of sub-band A (with respect to precipitation core 1) and of sub-bands B and C (with respect to precipitation core 2). The distance scale applies only

internally to a sub-band.

3. THE STEERING SURFACE OF THE PRECIPITATION CORES AND ITS RELATIONSHIP TO

To determine the ‘steering’ surface of the precipitation cores, that is the level at which the velocity of the wind is the same as that of the precipitation cores (e.g. Carbone 1982), the horizontal velocity of the precipitation cores (obtained from the radar reflectivities) was subtracted from the horizontal winds (derived from the dual-Doppler analysis) at each gridpoint. This was done for twelve vertical cross-sections, located every 3 km in the north-south direction within the dashed rectangular area shown in Fig. 3. As examples of the results so obtained, Figs. 5 and 6 show the speeds of the resulting vectors for vertical cross-sections through lines D-D’ and E-E’ in Fig. 3. Both figures clearly show continuous zones where the differences between the velocities of the precipitation cores and the upper-level winds have minimum values. A line drawn through the centre of this zone of minimum values is therefore representative of the steering line for the precipitation cores. The location of this line in space, derived from all twelve

THE FRONTAL SURFACE


EAST-WEST DISTANCE (km)

Figure 5 . A vertical cross-section along line D-D' in Fig. 3 of the absolute value of the velocity of the winds relative to the velocity of the precipitation cores.

m s-l F 6-8 10

12 14 16

- -

D'

Figure 6 . As for Fig. 5 , but for line E-E' in Fig. 3.


SURFACE ON WHICH THE WINDS HAD A SlMllAR VELOCITY

TO M A T OF THE PRECIPITATION CORES 7

Figure 7. The surface (shaded region) on which the winds had the same velocity as that of the precipitation cores in the wide cold-frontal rainband.

north-south vertical cross-sections, defines the steering surface; this surface is shown in Fig. 7. Notice that the surface is steeper towards the east, but that it also contains smaller regions of even steeper slope towards the south-east.

Martin et al. (1993) showed that a cold-frontal zone existed within the domain of the dual-Doppler regions shown in Fig. 2. To locate this frontal zone more exactly we constructed a vertical, time-space, cross-section of temperature, equivalent potential temperature, 8,, and winds in the region of dual-Doppler radar coverage. This was done using radiosonde data from Cape Hatteras at oo00 and O ~ O O G M T on 27 January 1986, and from Morehead City at oo00 GMT on 27 January 1986. Each sounding was positioned relative to the region of winds obtained from the dual-Doppler radars by ‘advecting the sounding’ at the velocity of the precipitation cores to the time and place where the Doppler winds had been calculated. Shown in Fig. 8 are the positions of the advected soundings relative to the region of dual-Doppler analysis and the rainband. None of these soundings is at a distance greater than 20 km from a corner of the dashed rectangular box in Fig. 8, and the greatest time difference between a sonde launch time and the time at which the winds were derived from the dual-Doppler radars was 45 minutes. Hence, these soundings provide an excellent indication of the strength and position of the frontal zone at these locations, although they cannot match the detailed wind data derived from the dual-Doppler radars.

A vertical cross-section of temperature, equivalent potential temperature and winds along line D-D’ in Fig. 3, derived from the three radiosonde launches, is shown in Fig. 9. The first 90 km of the cross-section corresponds to the east-west length of the dashed box in Fig. 8. A sloping region of relatively high static stability is evident by the vertical gradient of the 8, lines in Fig. 9. In this same region there is a sloping zone of winds, backing with height, that is coincident with a horizontal drop in temperature across the zone. We conclude that this region is the elevated cold-frontal zone and that the top of this zone is the cold-frontal surface, marked by a heavy dashed line in Fig. 9.

We can construct a cold-frontal surface with a spatial detail similar to the steering


MOREHEAD CITY 0000 GMT

NORTH

Figure 8. Locations of the ‘advected soundings’ used to construct the cross-section in Fig. 9 (see text for explanation). Also shown are the radar reflectivities at the surface.

9

8

7

z6 3 I

w ( 3 4

I 3

27 JANUARY 1986 MRH OOOO UTC HAT 0100 UTC HAT 0000

90 60 30 0 EAST-WEST DISTANCE (km)

UTC

Figure 9. A time-space vertical cross-section along line D-D’ in Fig. 3 of equivalent potential temperature, Be, (solid lines, labelled in degrees Kelvin); temperature (dashed lines, labelled in degrees Celsius); and winds (conventional symbols) derived from radiosondes launched from Cape Hatteras (HAT) and Morehead City (MRH). The heavy dashed line is the top of the cold-frontal zone determined from wind shear, temperature

gradient and 0,.

266 J. D. LOCATELLI er al.

surface shown in Figs. 5 to 7 by using the wind field derived from the dual-Doppler measurements to calculate frontogenesis values, as follows. First a cross-section of potential temperature, 8, was drawn from the radiosonde data, then the potential temperature field was transcribed to a grid similar to that on which the winds were derived from the dual-Doppler radars (every 1.5 km in the horizontal and 0.5 km in the vertical). The combined wind and 8-fields were used to compute a field of frontogenesis values, F, defined by the equation

+ - - - - - - - pe( axax ax az ;I( a2 ax az az auae a w a e )

where, x is the west-east direction, u the wind velocity in this direction, and w the vertical air velocity. Since values of 8 were unknown in the south-north direction, y, none of the terms having derivatives of 8 in that direction were included in calculating F. The addition of the vertical velocity terms in (1) served only to create isolated regions of positive and negative frontogenesis adjacent to, and resulting from, the regions of high vertical velocity, in much the same manner as described by Sanders (1955). Hence, for clarity, we shall present the results without the vertical velocity terms.

Consideration of the total two-dimensional gradient in (1) helps to define maximum values of F in regions with poorly defined horizontal gradients but with well-defined vertical gradients (i.e. in regions where the frontal surface is nearly horizontal). An examination of (1) revealed that two terms produced large frontogenesis values, namely d8/dz and au/dz, which represent the static stability and the vertical wind shear. The first of these, a8/az, is well resolved by the sonde data, and the second, du/az , is well resolved by the dual-Doppler data. Combination of these two data-sets provides a much better resolution of the frontogenesis field than might be expected from the rather poor resolution of the thermodynamic data.

Shown in Fig. 10 are the values of F in an east-west vertical cross-section through line D-D‘ in Fig. 3. This cross-section of F is similar to all the other cross-sections of F that we derived (twelve in all) within the region where winds were derived from the dual- Doppler radar data. Figure 10 shows a zone of positive frontogenesis, the shape and the coherency of which suggests that this is the cold-frontal zone; the top of this zone is marked by a heavy dash-dot line in Fig. 10. Except for the isolated maxima located at a distance of 20 km, the location of the cold-frontal zone derived in this way is consistent with those derived from the wind speeds relating to the cores and from the soundings (see Figs. 5 and 9).

Shown in Fig. 11 is a vertical cross-section, along line D-D’ of Fig. 3, of the two- dimensional winds in the plane of the cross-section relative to the speed of the precipitation cores. The heavy solid line in Fig. 11 is the intersection with the vertical cross- section through D-D’ of the surface on which the winds move with a velocity similar to that of the precipitation cores, as depicted in Fig. 7. This line divides the cross-section into an upper region of rising westward airflow and a lower region of sinking eastward airflow. The rising westward airflow has a region of maximum vertical velocity, near distance of 15 km; this region also showed a strong maximum in the radar reflectivity field. Also shown in Fig. 11 are the positions of the cold-frontal surface from Fig. 9 (heavy dashed line) and Fig. 10 (heavy dash-dot line): all three lines are similar in shape and position. Similar comparisons for the whole region in which winds were derived from the dual-Doppler radars showed similar correspondence between these three lines.


‘i - L‘

I I I I I I I I


Frontogenesis Values (F) (OK km-‘ s”)

< -0.0001 7 -

I- -I n 0.0001 -0.0003 -

0.0003-0.0005

D’

Figure 10. Frontogenesis values across the rainband, in a vertical cross-section along line D-D’ in Fig. 3, at 0045 GMT 27 January 1986. The heavy dash-dot line is the top of the layer of positive frontogenesis.


D’

Figure 11. Vector airflow relative to the velocity of the precipitation cores, in a vertical cross-section along line D-D’ in Fig. 3, at 0045 GMT 27 January 1986. The heavy dash-dot line is at the top of the layer of positive frontogenesis (from Fig. 10); the heavy dashed line is the top of the layer defined by wind shear, temperature gradient and Oe (from Fig. 9); and the heavy solid line shows the region along which the winds derived from the dual-Doppler radars were closest to the velocity of the precipitation cores (i.e. the steering surface for the

precipitation cores).

268 J. D. LOCATELLI et al.

We conclude from the results presented in this section that the steering surface for the precipitation cores is similar to (if not the same as) the frontal surface (as determined independently from frontogenesis calculations and thermodynamic analysis). This con- clusion is supported by the data shown in Fig. 11, where it can be seen that the steering surface separates two distinct airmasses, corresponding to the warm and cold sides of the cold front, and shows the proper relative flow of these airmasses (i.e. warm air flows upwards along the surface relative to the cold airmass beneath).

4. RELATIONSHIP OF THE PRECIPITATION FEATURES IN THE RAINBAND TO THE TOPOGRAPHY OF THE FRONTAL SURFACE

Since we have hypothesized that the steering surface for the precipitation cores is also the frontal surface, the detailed topography of the steering surface derived from the dual-Doppler radar data (see, for example, Fig. 7) reflects the topography of the frontal surface. We shall now show that there is a correspondence between the undulations of the frontal surface derived in this way, the vertical velocity fields, and the intensity of the precipitation in the WCFR.

The cold-frontal surface depicted in Fig. 7 is shown again in Fig. 12(a). Figure 12 (b) shows three vertical cross-sections through the rainband oriented in the east-west direction. Pronounced regions of higher radar reflectivity are located at the eastern portion of each cross-section, where fallstreaks of precipitation particles were descending from aloft. Comparison of Fig. 12(a) and Fig. 12(b) shows that the WCFR formed in that region where the slope of the cold-frontal surface was steep. Also, the steeper the slope of the cold-frontal surface the stronger the fallstreaks. All of the other cross- sections through the rainband that were investigated showed the same correspondence between radar reflectivity, fallstreak strength, and the steepness of the cold-frontal surface.

The airflow depicted in Fig. 11 suggests that there should be a correlation between the steepness of the frontal surface and the vertical air velocity. Shown in Fig. 12(c) are vertical air velocities derived from the dual-Doppler radar data. Since these fields require more smoothing than any of the other derived fields, it is not possible to compare individual cross-sections of vertical air velocities at 3 km intervals with the frontal undulations and radar reflectivity fields. However, we can see from Fig. 12(c) that the velocities were greater towards the south-east end of the dual-Doppler region; and that is where the radar reflectivity was greatest (Figs. 12(a, b)). A comparison of Fig. 12(a) and Fig. 12(c) shows that the steeper the slope of the frontal surface, the greater the vertical velocity of the air in the upper regions of the fallstreaks. Since precipitation is the manifestation of the vertical velocity of saturated air, this explains why the radar reflectivity and the fallstreaks had greater intensity in the regions of greater frontal slope.

5. SOME MECHANISMS THAT MIGHT AFFECT FRONTAL TOPOGRAPHY

In the previous section we showed that the wide cold-frontal rainband (WCFR) was associated with steeper regions on the cold-frontal surface, and that the regions of heaviest precipitation within the rainband (i.e. the precipitation cores) were associated with still smaller scale and even steeper slopes of the frontal surface. This could be due either to the frontal topography determining the precipitation intensity or to the precipitation intensity determining the frontal topography. The latter might occur owing to cooling of the air by the evaporation of precipitation particles. However, it can be


9 1 8 l 7

9 8 7

1

I 9, VERTICAL ' VELOCITY 8 I (m/s)

0.2-0.4

-(0.2-0.4) Y

Figure 12. (a) The hatched surface shows the steering surface for the precipitation cores in the wide cold- frontal rainband (WCFR); this is also the cold-frontal surface (see text). Radar reflectivities at 1 km are also shown. (b) Radar reflectivities of the WCFR on three vertical planes. (c) Vertical air velocities in the WCFR

on two vertical planes. All the data are for 0045 GMT 27 January 1986.


deduced from Figs. 5 , 6 , and 7 that the cold column behind the front would have had to deepen by about 800 m as a result of the greater precipitation intensity associated with core Y (which was only 5 to 7 dBZ more intense than the weakest portions of the WCFR). Further, this change in height would have had to occur in about 30 minutes and, most important, would have depended on the stationarity of the precipitation core relative to the air beneath the cold-frontal zone. However, the precipitation cores moved at 30 m s-’ (at 13 degrees), northwards along the WCFR, while the air beneath the frontal zone moved southwards. Therefore, any evaporative cooling from the precipitation was spread over much larger an area than that of the undulations of the frontal surface. Therefore, we conclude that it was the frontal topography that affected the precipitation intensity, rather than the other way round. In this section, we examine some processes that could affect the slope of a frontal surface.

The possible role of slantwise convection in the formation of rainbands in extratropical cyclones has been investigated extensively in the past decade (e.g. Bennetts and Hoskins 1979; Emanuel 1983; Thorpe and Emanuel 1985). Since this process may have a bearing on the dynamical interpretation of the observations presented here, we discuss the possibilities briefly below, in so far as they relate to this case-study.

In a two-dimensional slantwise neutral atmosphere, lines of pseudo-angular momen- tum, M (M = V + fx, where V is the geostrophic wind along the front, f the Coriolis parameter, and x a cross-front coordinate that is positive towards the warm air) and equivalent potential temperature lines, 8,, are parallel (Bennetts and Hoskins 1979). M- surfaces were calculated from the detailed dual-Doppler wind field. In the vicinity of the frontal surface, the M-surfaces were generally parallel to the 8, isopleths. However, since 8, was derived from the sounding data and was therefore not as finely resolved as the M-surfaces, small areas of weak conditional symmetric instability (CSI) were not discernable from a comparison of the fields of 8, and M. Nevertheless, for the case described in this paper, the combined thermodynamic and dual-Doppler radar wind data indicated that the atmosphere appeared to be slantwise neutral in the ascending air above the frontal surface. Also, the frontal surface was characterized by parallel M- and 8,- lines. Thus, displaced warm air should have ascended, with least resistance, along the frontal surface itself. As can be seen from Fig. 11, the air that moved upwards and westwards relative to the frontal surface did, in fact, move parallel to that surface. This was found to be generally true throughout the region in which winds were derived from the dual-Doppler radar data. This observation is consistent with Emanuel’s (1988) suggestion that frontal precipitation regions are likely to be characterized by a slantwise neutral atmosphere.

Bennetts and Hoskins (1979) suggested that if a region is initially slightly con- ditionally symmetrically unstable, symmetric instability will be released, resulting in thermally direct, slantwise circulation cells. Particularly intense circulations will distort M-and 8,-surfaces and produce local regions of purely inertial and purely gravitational instability. Less intense circulations could distort M- and 8,-lines in the manner shown schematically in Fig. 13. Thus, theoretically, it is possible to generate local variations in the steepness of the M- and O,-surfaces while simultaneously rendering a region neutral to CSI. Bennetts and Hoskins demonstrated how this might occur in the warm air above a cold-frontal zone. As a consequence, rainbands generated by this mechanism would move backwards with respect to the front (Knight and Hobbs 1988). Thorpe and Rotunno (1989) suggested that it was not possible to provide a clear description of how (or even if) the neutral states observed by Emanuel (1988) were formed as a result of symmetric motions. They suggested that down-gradient mixing of potential vorticity by turbulent motions associated with symmetric circulations might act to break up large continuous

RAINBANDS AND FRONTAL TOPOGRAPHY 27 1

t

- Initial position of Be or M surface

--- Position of Be or M surface after roll circulation

Horizontal distance (x) + Figure 13. Schematic illustration of the effect of CSI roll circulations on the configuration of a hypothetical conserved quantity. The solid line indicates the initial position of a hypothetical M or Be isopleth and the

dashed line indicates its position after displacement by the circulation.

regions of slantwise instability into smaller discontinuous regions which, when viewed from a synoptic-scale perspective, might give the impression that the previously slantwise unstable environment had become neutral. Thorpe and Clough (1991) provided observational evidence for the bending of M-. and 8,-surfaces near a frontal zone; however, they did not show that the release of CSI was the responsible mechanism. Since frontal zones are characterized by large slantwise stability, they are unlikely places for the occurrence of symmetric circulations. Therefore, it is unlikely that CSI theory can account for the undulations within the frontal zone described in this paper. We do not know if the apparent slantwise neutrality in the westward-flowing warm air above the cold front was due to distortion of M- and 8,-surfaces and their subsequent realignment by symmetric circulations. However, our observations are consistent with apparent slantwise neutrality in the warm air.

Gall ef a f . (1988) proposed a mechanism for the formation of frontal topographical features. In their theory, vertically-propagating, standing gravity waves, generated by the unbalanced accelerations initiated during frontogenesis, are trapped between the ground and the frontal surface. The horizontal distance between the waves, which is proportional to the vertical wavelength of the standing wave and also depends on the along-front wind speed and ambient static stability, was of the order of 50 km in Gall et af.’s model simulations. The associated pattern of convergence produces a progressive steepening of the isentropes in the frontal zone (Fig. 14) and therefore of the frontal surface. This results in the formation of ‘steps’ on the frontal surface with a horizontal spacing similar to the horizontal wavelength of the waves. Since these trapped gravity waves move relative to the cold air, they could be horizontally stationary with respect to the frontal surface; in that case, the steps on the front would also have no movement relative to the frontal surface. This is consistent with our observations that the steps on the frontal surface, the WCFR, the sub-bands and the precipitation cores, all moved at a speed close to that of the frontal surface. Gall ef a f . also discuss the presence of a concentrated downdraught located in the cold air under the steepening portion of the front. Interestingly, in the case described in the present paper, there was a concentrated


Figure 14. Schematic showing the effect of a vertically propagating standing gravity wave on a frontal surface. Arrows indicate the sense of the secondary circulation produced by the wave. Solid lines are isentropes

(contours of the frontal surface). Adapted from Gall el al. (1988).

downdraught under the steepest part of the front (Fig. 11). Gall et al. suggested that localized frontogenesis might occur in regions of frontal steepening, as in fact we observed (Fig. 10). Hence, this mechanism appears to explain some of our observations, at least qualitatively; quantitative comparison is not possible because Gall et al. considered only the dry case. However, a word of caution is necessary. Gall et al. reported that the intensity of the gravity waves was dependent on the horizontal and vertical grid spacing; this indicates that their appearance in the model could have been due to the lack of a sufficiently high numerical resolution.

Finally, it should be noted that the processes discussed above are, in principle, two- dimensional, whereas undulations on the frontal surface are three-dimensional. Detailed examination of mechanisms for the undulations would require a high-resolution, three- dimensional numerical model.

6. CONCLUSIONS

In this paper we have presented observational evidence that the steering surface for the precipitation cores that constituted a wide cold-frontal rainband was identical with the frontal surface. Therefore, by relating dual-Doppler radar measurements of upper- level winds to the motions of various precipitation cores (as described in section 3), we can derive the detailed topography of a frontal surface. Shown in Fig. 15 is a summary of the relationship of the topography of the frontal surface, derived in this manner, to the precipitation pattern. It can be seen that the steepest regions of the frontal surface were associated with the heaviest precipitation (i.e. the precipitation cores), the next


frontal surface motion

0 Type of slope responsible for the rainband

Type of slope responsible for the sub-bands = Type of slope responsible for the precipitation cores

Figure 15. The connections between the slope (different shadings) and motion of the cold-frontal surface, the upward air motions (black and hatched arrows), and the structure and intensity of the wide cold-frontal

rainband. Based on dual-Doppler radar data for 0045 GMT 27 January 1986.

steepest with more moderate precipitation (i.e. the sub-bands), and a region of the frontal surface with somewhat less steepness defines the boundary of the rainband itself. The simple interpretation of these observations is that the warm air flowing towards the frontal surface (black and hatched flat arrows in Fig. 15) was lifted at a rate proportional to the steepness of the frontal surface. This implies that the front acted as a barrier to the warmer air ahead of it. The 8, pattern in Fig. 9 shows that a parcel of warm air moving towards the cold air beneath the frontal surface could not easily have penetrated this surface, because the potential temperature differences would have forced it to rise. In other words, the frontal surface represents a thermodynamic barrier. The speed of the wind in the east-west direction, eastward of the dashed rectangle in Fig. 3, was computed from the 0000 GMT 27 January National Meteorological Center’s nested grid model initialization using a weighted average of the three closest 700mb model data points. When this speed was subtracted from the speed of the frontal surface in the same direction, it produced a relative wind speed of 3 m s-* towards the frontal surface. The resulting vertical velocity was calculated in a vertical cross-section along line D-D’ in Fig. 3 by assuming that

w = -u,. Vhf (2)

where, or is the relative air velocity toward the front and Vhf the frontal slope. This assumes that the lifting of the air was due entirely to flow over the frontal surface. This gave an updraught speed of 0.2 m s-’, compared to a maximum updraught of less than 0.5 m s-l computed from the dual-Doppler radar data for the same region. We consider this to be a reasonable agreement and support of our contention that the frontal surface acted as a barrier over which the warm air rose with a vertical velocity proportional to the steepness of the frontal surface.


It follows from the above arguments that we can estimate the rates of change of the undulations on the frontal surface by noting the rates of change of the resulting reflectivity pattern (as shown, for example, in Fig. 4). If this interpretation is correct, the timescale for local changes in the steepness of the cold-frontal surface, which resulted in changes in the sub-bands, must have been of the order of 30 minutes, since it was over this timescale that the sub-bands grew and died. However, the envelope of the sub-band- scale undulations lasted for a matter of hours, as indicated by the lifetime of the wide cold-frontal rainband.

These findings indicate that the distribution and intensity of precipitation associated with cold fronts may depend on the detailed topography of the cold-frontal surface. If this is the case, increased attention should be paid to understanding the mechanisms responsible for producing and modifying undulations in frontal surfaces.

ACKNOWLEDGEMENTS

This research was funded by a series of grants from the National Science Foundation (NSF) the latest of which is ATM-9106235. The CP-3 and CP-4 radars were operated by NCAR, which is funded by NSF. This paper was written while one of us (P.V.H.) was on study leave at FISBAT-CNR, Bologna, Italy.

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Dirks, R., Kuettner, J. P. and

Emanuel, K. A. Moore, J.

Gall, R. L., Williams, R. T. and

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Hobbs. P. V., Mateika, T. J.,

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Locatelli, J. D. and Hobbs, P. V.

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A wide cold-frontal rainband and its relationship to frontal topography