1. Introduction
Observational studies have shown that the strongest precipitation associated with cold fronts is generally concentrated in a narrow band at the leading edge of the front, referred to as the narrow cold-frontal rainband (NCFR) (Hobbs 1978). The precipitation along an NCFR is often remarkably well organized into what have been called precipitation cores (PCs) and gap regions (GRs) (Hobbs and Biswas 1979; James and Browning 1979; Locatelli et al. 1995; Browning and Roberts 1996). In this paper we describe a successful high-resolution, 3D mesoscale model simulation of an NCFR, and we analyze that simulation to uncover the structure and dynamics associated with the alongfront variability of the NCFR.
The NCFR discussed here passed over Cape Hatteras, North Carolina, during the field phase of the Genesis of Atlantic Lows Experiment (GALE). It was associated with a system that began as a low pressure center over southern Georgia, which then moved northeastward along the eastern seaboard with an accompanying cold front trailing to the south. By 0000 UTC 27 January 1986, the low pressure center had deepened to 998 hPa and was located to the north of Cape Hatteras (Fig. 1). The cold front extended to the south of the low pressure center and a portion of the front passed through the area of coverage of the National Weather Service (NWS) WSR-57 radar located at Cape Hatteras between approximately 0000 and 0200 UTC 27 January 1986. Over the next 6 h the low pressure center deepened to 994 hPa and continued to move to the north with the front extending south.
Martin et al. (1993) have described the development of this system on the synoptic scale, and Locatelli et al. (1995) provide a detailed analysis of the mesoscale structure of the system, including the core–gap structure of the NCFR, using the WSR-57 radar data. Dual-Doppler radar observations, and cloud microphysical retrieval techniques, were applied to this same case by Geerts and Hobbs (1995), and a chemical modeling study of the NCFR was carried out by Barth et al. (1992).
In the following section we describe the techniques that were used to numerically simulate the 27 January 1986 NCFR. In section 3 we compare the results of the numerical simulations with observations. In section 4 we diagnose the 3D frontal structure using the model simulations, and in section 5 we examine the mechanisms responsible for the core–gap structure of the NCFR.
2. Model description and simulation techniques
a. The Penn State–NCAR Mesoscale Model
The numerical model used in this study was the Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR) Mesoscale Model version 5 (MM5). The MM5 is a nonhydrostatic extension of the 3D numerical weather prediction model described by Anthes and Warner (1978) and Dudhia (1993). The model uses a terrain-following sigma (σ) coordinate system and a fully compressible set of primitive equations.
In the form of the MM5 model used here, grid-resolved precipitation and cloud processes are represented explicitly by a set of predictive equations for the distributions of water vapor, cloud water, cloud ice, rainwater, snow, ice nuclei, and graupel (Reisner et al. 1993). Graupel was included since Hobbs and Persson (1982) and Barth and Parsons (1996) showed that it can be a significant hydrometeor in NCFR. Subgrid-scale convection on model domains with horizontal resolutions greater than 6 km was parameterized using the method described by Kain and Fritsch (1990). The planetary boundary layer was parameterized as described by Blackadar (1979) and Zhang and Anthes (1982). The model included surface topography and land use characteristics, as well as sea surface temperatures.
b. The 27 January 1986 numerical simulation
The initial and time-dependent boundary conditions for the model were based on upper-air soundings and surface station reports of wind, temperature, moisture, and sea level pressure. The model was initiated with the National Centers for Environmental Prediction (NCEP) final analysis and then a Cressman scheme was used to integrate the surface and upper-air observations.
The numerical simulation was initialized at 1200 UTC 26 January 1986 using NCEP model data, integrated forward in time for 24 h until 1200 UTC 27 January 1986, on a domain with a horizontal grid spacing of 54 km that contains 82 × 61 grid points and 24 vertical σ levels. This domain is indicated by D1 in Fig. 2. Embedded within this domain was an 18-km horizontal grid-spacing domain (D2 in Fig. 2) with 127 × 100 grid points and two-way interactive boundaries with domain D1. Both of these domains used the Kain–Fritsch cumulus parameterization to resolve subgrid-scale convection.
The results of the 18-km simulation were used to create the initial and time-dependent boundary conditions for the final high-resolution simulation. The high-resolution simulation was initiated at 0000 UTC 27 January 1986 and integrated forward for 9 h until 0900 UTC 27 January. The simulation consists of an outer fixed domain, labeled D3 in Fig. 2, with a horizontal grid spacing of 6 km. Nested within the 6-km resolution domain was a moving inner-nest domain (labeled D4 in Fig. 2), with a horizontal grid spacing of 2 km and a two-way interactive boundary condition with the larger-scale domain D3. Both D3 and D4 contain 100 × 133 grid points. The moving inner domain D4 is shown at its initial (0000 UTC) and final (0900 UTC) positions in Fig. 2. The inner domain D4 was moved at 1-h intervals, 30 min after the hour, in order to remain approximately stationary with respect to the northeasterly moving PC and cold front. The movement of the nest was set up so that the features of interest (the front and PC) would remain well within the high-resolution coverage at all times. Areas of new high-resolution coverage associated with each movement of D4 were almost exclusively in the warm sector, where the flow and thermal structure were essentially uniform.
The model was integrated forward in time using 6-s time steps on the 2-km domain. Model output was stored at 15-min intervals during the entire simulation. In addition, model output was stored at 3-min intervals from 0330 to 0515 UTC, for the purpose of producing highly accurate parcel trajectories.
3. Comparison of model results with observations
a. Overview
The model-simulated sea level pressure, surface temperature, and surface wind fields on the 18-km domain (D2) at 0000 UTC 27 January 1986 (a 12-h forecast) are shown in Fig. 3. As in the observed case (Fig. 1), the model simulation shows a north–south elongated low pressure center just off the East Coast, although the simulated low is 4 hPa weaker and 280 km south of the observed position. Between 30° and 35°N latitude, the simulated position of the cold front is quite close to the observed position, but its orientation is tilted slightly clockwise from that of the observed front. The warm-sector winds are similar in speed and direction to those of the observed case. Although it is not the focus of this study, the model fails to capture the position of the stationary front north of the low center, carrying it well offshore when in fact it remained onshore.
Locatelli et al. (1995) show horizontal plots of wind direction and temperature in the cold-frontal region, derived from two orthogonal 300 m above mean sea level (MSL) aircraft passes made at 2213 and 2230 UTC 26 January (see their Fig. 9). Due to the fact that the high-resolution domain is not initialized until 0000 UTC, a meaningful comparison to Locatelli et al.’s observations cannot be made until around 0300 UTC 27 January, when the high-resolution domain has had an opportunity to tighten the frontal boundary and develop realistic precipitation structures at the 2-km scale. The actual data along the two flight tracks on which the Locatelli et al. figure was based have been averaged and are presented as the solid lines in Fig. 4. Corresponding profiles for a 300-m simulated flight track across a representative point on the model-simulated front are shown as dashed lines in Fig. 4. A comparison between the model and observations shows that the model overtightens the thermal gradient at the leading edge of the front but captures the wind shift quite accurately. The stronger thermal gradient suggests that the simulated front should move faster than observed (based on gravity current theory). However, Fig. 5 (which is discussed in more detail below) shows that the simulated depth of the cold air immediately behind the front is lower than observed, which would result in a compensation in the simulated gravity current speed.
Figure 5a (from Fig. 20 of Locatelli et al. 1995) shows the horizontal winds, relative to the motion of a PC, in a vertical cross section oriented perpendicular to the cold front, derived from a dual-Doppler radar analysis. The vertical cross section passes just to the south of a PC. For comparison, a cross section of horizontal wind derived from the MM5 model data is shown in Fig. 5b. The vertical cross section from the model is positioned so that it is oriented perpendicular to the cold front and passes on the southern edge of a typical PC (the model-produced PCs are discussed in more detail in the next section). It can be seen that the model reproduces the observed circulation associated with a PC quite well, although differences can be seen in the strength of the flow in the hydraulic head and aloft. The model-derived structure of the kinematic cold front is also very similar to the observations, with a hydraulic headlike structure at the leading edge of the cold front and a flat postfrontal region. The modeled hydraulic head structure extends to a height of ∼2 km, while the observed structure extended to ∼3 km.
b. Precipitation cores and gap regions
Figure 6a shows the radar reflectivity field associated with the NCFR as observed by the WSR-57 radar at 15-min intervals starting at 0007 UTC on 27 January 1986. The PCs stand out as ellipsoidal-shaped regions of high reflectivity, which are oriented roughly parallel to each other and separated by GRs. Figure 6b shows the corresponding model-generated precipitation mixing ratios on the lowest modeled σ layer (0.995) starting at 0315 UTC. The dashed lines in Fig. 6 indicate the paths followed by the PC. Note that units of radar reflectivity do not vary linearly with precipitation mixing ratio; therefore, the areal extent and the contour intervals in Figs. 6a and 6b cannot be directly compared.
The model-generated precipitation is clearly formed into elliptical PC oriented at an angle to the front. The PCs detected by the radar reflectivity are similarly shaped, but with less regularity than in the model results. The radar observations show that the orientations of the PCs were variable, although most of the stronger PCs were oriented ∼30°–40° counterclockwise from the north (i.e., roughly southeast to northwest). The observed PCs were ∼25–75 km long and ∼10–25 km wide; the modeled PCs are somewhat smaller (∼15–50 km long and ∼5–15 km wide). The PCs in the model simulations exhibit more regularity, with nearly all of the PCs angled at ∼30°–50° from the north.
The observed radar reflectivity field shows that the PCs were separated by GRs, where little precipitation reached the surface. The GRs were about 25 km wide. The model simulations show GRs ∼10–25 km in extent. In the model simulations the PCs moved to the northeast along the cold front at speeds of 15–20 m s−1; radar observations showed that the PCs moved to the northeast at 25 m s−1 (Locatelli et al. 1995).
Overall, the model reproduces the key features of the observed NCFR and its PC–GR substructure, warranting further examination of the structure and dynamics of the simulated NCFR.
4. Frontal structure derived from the model
Since the model simulations of this NCFR agree remarkably well with the observations, we can utilize the model with some confidence to diagnose the detailed structure of the front and the mechanisms responsible for this structure.
a. Thermal structure along the front
From the observed and the modeled precipitation fields, it would seem likely that the cold front would exhibit a structure that is complex but roughly periodic along the length of the front. Some hints of this periodicity can be seen in Fig. 7, which shows the leading edge of the cold front at 30-min intervals from 0330 to 0530 UTC. The frontal positions in Fig. 7 were defined based on the leading edge of strong surface temperature gradient and sharp surface wind shifts. The precipitation mixing ratio on the lowest modeled sigma level (σ = 0.995) at 0330 UTC is also shown in Fig. 7 to highlight the relationship between the precipitation and shape of the leading edge of the cold front.
A more detailed view of the frontal structure near the surface is shown in Fig. 8, which depicts the modeled potential temperatures (θ) and precipitation mixing ratios on the lowest sigma layer at 0500 UTC. The main updrafts along the southern end of the cold front are labeled U1 through U6 in Fig. 8 (this notation will be used throughout the paper to identify key updrafts and will be used as reference points along the cold front).
In Fig. 8 the cold front at the surface is seen to bulge to the east in the GRs, while clefts in the cold front are located where PCs intersect the front. In the warm sector there is little or no horizontal gradient in temperature, except for isolated cold pools associated with convection. The model develops a tight gradient in temperature of ∼1°C km−1 near the surface at the leading edge of the cold front, and this extends ∼10 km to the west. Farther to the rear of the front, the temperature gradients weaken to about 0.03°C km−1.
b. Frontal structure in the vertical
In this section we will show the structures of the NCFR depicted by the model in the three vertical cross sections labeled A–A′ (along a PC), G–G′ (through a GR), and N–N′ (normal to a PC) in Fig. 9. The vertical cross sections depict equivalent potential temperature (θe), the core-relative winds, and rainwater and graupel mixing ratios greater than 0.5 g kg−1.
A cross section along a PC is shown in Fig. 10. This cross section is located to the south of the main core-producing updraft. The front resembles the structure of a gravity current (also called density current), which is common for an NCFR (Hobbs and Persson 1982; Carbone 1982), but without a pronounced head in the thermal structure at the leading edge. The alignment of this cross section is similar to that of Fig. 5 and, as in Fig. 5, we can see a weak hydraulic headlike structure in the wind field on the scale of ∼10 km. The updraft that produced the PC is on the right of Fig. 10, where warm-sector air is lifted over the advancing cold air. The plane of the cross section does not pass through the core of the updraft, which extends to ∼500 hPa. The θe = 312 K contour roughly approximates the frontal surface and extends to ∼800 hPa, with lower θe values below; this value of θe will be used for later comparisons.
The cross section normal to the PC is shown in Fig. 11. Convergence and lifting are seen to the north of the PC, with subsidence downwind (to the left). The convergence is a result of low-level horizontal pressure gradients (to be discussed later). When a weak pressure gradient is superimposed on the northerly postfrontal wind field, convergence occurs upwind and divergence downwind of the pressure perturbations under the PC. The convergence acts to lift cooler postfrontal air and further enhance the surface pressure perturbation, as seen in the values of the lifted θe under the PC (Fig. 11). This lifting along the length of the PC can be attributed partially to the process described by Miller (1978) for a cumulonimbus system, where precipitation loading and diabatic cooling led to increased surface pressure and, therefore, increased convergence and lifting beneath the heaviest precipitation. However, in the present case, the precipitation fell to the rear of the cold front, where the increased convergence and lifting produced by the precipitation acted on cold stable postfrontal air, which was not lifted sufficiently to produce significant precipitation. The main source of precipitation was at the leading edge of the front, where warm-sector air fed the main updraft.
From the cross section normal to the PC (Fig. 11) we see that the θe surfaces beneath the PC are higher than they are to either the north or south, showing that the elevated θe value along the PC in Fig. 10 is actually a narrow ridge. The θe = 312 K surface, which can be used to characterize the frontal surface, is as low as 950 hPa to the north of the PC and 875 hPa to the south. The maximum height of the θe = 312 K surface is reached at the transition from upward to downward vertical velocity. Since θe is conserved in moist processes, the elevated minima in θe is due primarily to vertical transport, which agrees with the symmetry in θe seen at the transition in vertical velocity.
The cross section through a GR is shown in Fig. 12. This cross section highlights key structural differences between the GR and the PC. In Fig. 12, the θe = 312 K surface extends from the surface at the leading edge of the front to 875 hPa at 30 km behind the front. Consequently, the frontal surface is, on average, 100 hPa lower in the GR than in the PC. However, like a PC, the GR resembles a gravity current. As in the case of the PC, the front in the GR does not have a pronounced head, although a weak rotor circulation is seen in the cross section. The GR produces little precipitation at the front, as air that is lifted over the leading edge of the front does not become convectively unstable. The region of graupel seen in Fig. 12 between 750 and 450 hPa is associated with the PC to the south of this cross section (i.e., it has been advected at upper levels from the PC associated with updraft U3).
c. Pressure structure along the front
The postfrontal surface pressure pattern can be described as recurring couplets of low and high pressure centers with a tight pressure gradient between the pressure centers. The low pressure centers are located to the north of the PC and the high pressure centers are under, and to the south of, the PC. One such pressure couplet can be seen in Fig. 13. Each pressure couplet is separated from the adjacent couplets by weaker pressure gradients. Figure 13a shows sea level pressure, and Fig. 13b shows θ values on the lowest σ surface. Figures 13a and 13b also show PC-relative back trajectories for 20 air parcels starting along the cold front in the vicinity of updraft U3.
The surface pressure in the low pressure centers is lower after the cold-frontal passage, as seen in Fig. 13a. This cannot be explained by the expected low-level temperature structure, which would indicate higher postfrontal pressures (relative to the warm sector). The nonhydrostatic (vertical acceleration) and water loading contributions to the surface pressure were examined (not shown) and found to be small compared to the hydrostatic contribution (i.e., the virtual temperature structure aloft). The unusual postfrontal low-level pressure structure is linked to a gravity wave response to the convective updrafts from the environmental flow aloft, resulting in warming and subsidence aloft as well as increases in pressure under the PC due to the melting and evaporation of hydrometeors. The effects of these features will be discussed in the following sections.
5. Mechanisms for the core–gap structure
a. Horizontal shear instability
Horizontal shear instability (HSI) has been proposed as a mechanism for the core–gap structure of precipitation along the NCFR (Matejka 1980; Hobbs and Persson 1982). In this theory, the shear of horizontal wind across the cold front leads to a wave disturbance on the frontal surface, resulting in regions of enhanced convergence and divergence along the cold front. The vorticity distribution, which in an idealized scenario would initially be a uniform strip along the undisturbed front, accumulates into regularly spaced centers of enhanced vorticity. This mechanism has been demonstrated in numerical simulations of gravity currents in the presence of shear, but only in a dry environment (e.g., Lee and Wilhelmson 1997). The applicability of this mechanism to sharp cold fronts with moist updrafts (i.e., to the NCFR) is still an open question. Moore (1985) claimed that the environment of a typical NCFR would in fact be stable to HSI, but showed that HSI combined with absolute instability to parcel ascent (N2 < 0) within the shear zone could produce unstable (growing) modes with elliptically shaped updrafts. He hypothesized that such modes may be an explanation for regularly spaced elliptically shaped PCs within a NCFR. One weakness of Moore’s hypothesis is that in some observed cases of NCFR that exhibited core–gap structure, the prefrontal environment was either neutral or absolutely stable to parcel ascent (Hobbs and Persson 1982; Carbone 1982). Also, Moore’s idealized scenario did not include any density contrast, just a shear zone, which calls into question its applicability to fronts. In any event, the question of whether or not the core–gap structure of NCFR is due to HSI is an open question.
In attempting to ascertain the extent to which HSI can explain the core–gap structure seen in the model simulation, our approach is to compare the frontal structure in the present case to known structural features that occur in either a pure HSI scenario or in Moore’s combined shear–convective instability mode. Figure 14a shows the vorticity pattern near the surface at 0500 UTC 27 January, 5 h into the high-resolution simulation. Note that, although there is some variability in vorticity along the front, it is still essentially a continuous strip of approximately uniform vorticity. This is contrasted with the HSI scenario, in which the vorticity accumulates into definite centers, with little or no vorticity between the centers (see, e.g., Fig. 9 of Lee and Wilhelmson 1997). Higher above the surface (Fig. 14b), the vorticity does become organized into separate regions, but they do not appear as circular vorticity centers (or vortices). Rather, they appear as elongated vorticity strips (or shear zones). In favor of Moore’s hypothesis, the vorticity pattern at 1.5 km above the surface correlates very closely with the vertical velocity pattern at that level (Fig. 14b), suggesting that vertical stretching of vorticity is an important contribution to the vorticity at this level. The same mechanism is a key component of Moore’s hypothesis. Finally, the surface convergence pattern (Fig. 14c) is characterized by a continuous strip of approximately uniform convergence along the leading edge of the front. In addition, the convergence pattern displays enhanced values at the clefts (where the main updrafts tend to be located), as well as additional lines of convergence that protrude back into the cold air, immediately north of the elliptical PCs. This pattern is quite different from that seen in the HSI scenario [e.g., Fig. 7b of Lee and Wilhelmson (1997)] or the combined shear–convective instability scenario [as inferred from Fig. 13b of Moore (1985)]. In both of those cases, the convergence pattern is clearly organized into unconnected, or very weakly connected, elliptical cells oriented clockwise from the large-scale front.
In summary, a comparison between the vorticity and convergence structures in the present case, and that of either the HSI scenario or the combined shear convective instability, reveals some similarities but also some key differences. This finding, combined with the fact that shear instability has not been demonstrated to be a dominant mechanism for alongfront variability in realistic cold fronts with moist ascent, precludes us from attributing the core–gap structure in the present case to shear instability, although we cannot eliminate it as a possibility. We leave open the possibility that the interaction of HSI with density current dynamics, surface friction, latent heating and cooling, gravity waves, large-scale frontogenesis, etc., may lead to a mode of organization that is fundamentally linked to HSI but is unlike the structures that have been seen in the previously cited idealized studies.
b. Convectively induced gravity waves
Strong isolated low pressure centers are seen in the model simulation directly to the north of the PCs. (e.g., Fig. 13a). These are believed to be due to trapped gravity waves in the lee of the PCs. The updrafts associated with PCs along the NCFR act as barriers to the southerly midlevel (∼3–10 km) flow by vertically advecting low-momentum air into that flow, analogous to isolated mountain peaks, and thereby trigger gravity waves (Kuettner et al. 1987). These waves produce subsidence, a warm anomaly aloft, and a hydrostatic pressure minimum at the surface.
The Froude number can be used to classify the responses expected from density-stratified flow past 3D obstacles. The Froude number for the 27 January 1986 case ranged from ∼0.5 to 1.2, depending on the assumed height of the “obstacle.” Numerical modeling results of flow around isolated mountain peaks (Smith 1980; Smolarkiewicz and Rotunno 1989) indicate that at low Froude numbers (Fr ≃ 1) gravity waves begin as strong subsidence in the lee of the obstacle, followed by several vertical oscillations. The gravity waves emanate from the obstacle as V-shaped regions of alternating downward and upward air motions. At low Froude numbers, the flow is expected to partially diverge horizontally around an obstacle.
The Scorer parameter (Scorer 1949) can be used to determine whether the environment is conducive to the development of trapped lee waves. The general condition for the existence of trapped lee waves is that there must exist a reflecting layer (above the trapped waves) in which l2 < k2, where l is the Scorer parameter and k is the horizontal wavenumber of the gravity waves. Examination of the Scorer parameter in the warm sector environment at the location of the cold front (not shown) revealed a trapping layer at a height of approximately 6.5 km. The horizontal wavenumber (k) was estimated as 4.2 × 10−4 m−1 and was obtained from the wavelength of the disturbance seen in Figs. 15 and 16 (to be discussed below). In summary, both the Froude number and the Scorer parameter indicate that the environmental conditions on 27 January were conducive to the formation of trapped gravity waves.
We will now examine the model results for evidence of gravity waves. Figure 15a shows the vertical velocity field on a horizontal plane at a height of 4.5 km. The label U3 in Fig. 15 marks the position of the forcing updraft of interest near the surface. This level was chosen to best show the vertical velocity of the gravity wave produced by updraft U3. The gravity waves are seen to align with the PC-relative flow at the mid- and upper levels. As expected, the resulting oscillations form V-shaped regions of downward and upward motion directly downwind of the forcing updraft. The vertical velocities are stronger in the western branches of the V-shaped region, possibly due to the asymmetry of the forcing updraft. The initial subsidence region extends over the frontal zone to the northeast of the main updraft.
Figure 15b shows relative streamlines at a height of 3.5 km. The flow separates around the updraft and does not converge downwind of the obstacle. This is consistent with previous modeling studies of gravity wave flow forced by an isolated mountain barrier in similar Froude number flow regimes (Smith 1980; Smolarkiewicz and Rotunno 1989).
Figure 16a shows a vertical cross section of θ, and the vertical velocity along the line X–X′ in Fig. 15. Figure 16b is the same as Fig. 16a except that wind vectors in the plane of the cross section are shown in place of θ. The transition between northerly low-level flow and southeasterly mid- and upper-level flow is clearly evident. The forcing updraft (U3) is seen in the lower-left corner of Fig. 16a, with vertical velocities of up to 8 m s−1. The trapped gravity wave response is seen directly downwind, with a subsidence of 4 m s−1 followed by upward velocities of 3 m s−1, with a wavelength of ∼20 km. After the initial wave, the vertical motion decreases rapidly to ∼1 m s−1. As expected, the vertical velocity and wave amplitude decay with height above the trapping level, which is at 6.5 km.
Dual-Doppler radar studies of this NCFR by Geerts and Hobbs (1995) support the existence of gravity waves along the front. Their Figs. 6 and 7 show alongfront cross sections of vertical velocity and radar reflectivities several hours prior to our numerical simulation. The figures depict a strong updraft of ∼7 m s−1 followed by several vertical oscillations of ∼5 m s−1. The observations of Geerts and Hobbs can be compared to the cross sections shown in Figs. 16a and 16b, although the latter are aligned with the midlevel winds and the center of the gravity wave oscillations. A weaker pattern of vertical motion is seen aloft with similar wavelengths (Fig. 16).
An examination of the vertical temperature profiles in Fig. 17 shows that the gravity waves can have a pronounced effect on convection. The figure shows a model-generated sounding taken in the warm sector directly ahead of a GR along the cold front (solid line). A second sounding was taken in a GR to the rear of the leading edge of the cold front. The locations of the soundings in the warm sector and GR are indicated in Fig. 14c as W and G, respectively. Since the GR sounding is essentially the same as the warm-sector sounding below 750 hPa and above 350 hPa (Fig. 17), where there is little influence from the gravity wave, it is shown in Fig. 17 only where it differs from the warm-sector sounding. Neither sounding is shown in the lowest 100 hPa where they penetrate the frontal zone. Between 350 and 750 hPa we can see the effect of the gravity wave in inducing warming over the GR, which is as much as ∼3°–4°C warmer than the warm-sector sounding.
The long-dashed line in Fig. 17 shows the temperature profile of a parcel that is lifted from the mixed region at the leading edge of the cold front. The chosen moist adiabat is consistent with the temperature profiles seen in the main updrafts along the front, indicating that the choice of parcels is reasonable and is typical of the convection occurring along the front. It can be seen that convection in the GR will be reduced, since air parcels will be less buoyant as they rise into the warmer environment than if they rose outside of the GR. Consequently, parcels in the GR generally do not rise above 700 hPa, whereas the updrafts in the PC generally extended to above 500 hPa.
To examine further the effects of gravity waves on convection along the front, we will now show vertical cross sections through the region of tight horizontal temperature gradient (∼0.5° km−1) at the leading edge of the cold front. The positions of two such cross sections are shown in Fig. 18 (lines ABCD and EFGH), along with the frontal zone, PC, and updraft positions. Figures 19 and 20 are composite cross sections, showing vertical velocity and θ, along the lines ABCD and EFGH, respectively, in Fig. 18. Each cross section is composed of three segments, with each segment parallel to the surface cold front. The segments are positioned within or to the west of the frontal zone, which tilts westward with height. The cross section in Fig. 19 extends from the southernmost updraft U1, northward along the front to the updraft U3. The cross section in Fig. 20 extends from the updraft U3, northward along the front to updraft U6. In the vicinity of U3, the two cross sections are parallel. Together these two figures detail the updraft and θ structure along ∼100 km of the cold front.
We will consider first the updraft structure shown in Fig. 20. The southernmost updraft in this figure is U3. To its north is a large region of subsidence and warming at midlevels above the next GR. Updraft U4 attempts to form in the GR but does not go on to produce a PC. Updraft U5 extends to ∼10 km but does not trigger a gravity wave at this level, possibly because it impinged on the tropopause. Updraft U6 forms ∼10 km to the north of updraft U5. The relative proximity of the two updrafts is presumably due to the lack of subsidence and warming aloft between them. In addition to the subsidence aloft producing widespread warming (2–8 km above MSL), the effects of diabatic cooling produce low-level subsidence (2–4 km above MSL) to the south (left) of the updrafts that produce PC. The diabatically cooled subsidence can be distinguished from the subsidence produced by the gravity wave by the higher θ values in the subsidence region, indicating cooling.
Similar structures to those shown in Fig. 20 can be seen in the southern cross section shown in Fig. 19. Most notably, the subsidence associated with U1 appears to suppress convection over a region extending 40 km to the north, as in the case of updraft U2.
The effect of the subsidence to the north of updraft U3 appeared to suppress the formation of a new PC over at least the next hour (not shown). In the absence of mid- and upper-level subsidence to the north of updraft 5, a new updraft forms within minutes in the narrow gap (∼10 km) between updrafts 5 and 6. This is consistent with the observations of Locatelli et al. (1995) who noted that new PC formation generally takes place in the larger GRs, while existing PCs can exist in close proximity.
In light of the above discussion, we propose that gravity waves can act to regulate the core–gap structure of NCFR. Subsidence and warming aloft can suppress the formation of convection along the front, thereby creating a GR. The strongest subsidence is located close to the PC that triggers the gravity wave. The amplitude of the gravity wave diminishes thereafter, permitting PCs to form farther downwind. If a gravity wave dies out (as in the case of updraft 5), a new PC can form in close proximity to existing updrafts.
The simulated cold front at the surface forms a bulge–cleft structure (Fig. 7), similar to that seen in tank experiments of gravity currents (Simpson 1969, 1972). Simpson proposed that this structure is the result of small-scale convection associated with the head of a gravity current, where low-density fluid is overridden by higher-density fluid. This vertical stratification creates a convective instability, in which the lower-density fluid rises through the leading edge of the gravity current and creates a cleft. Regions of the gravity current where fluid is not rising continue to move forward unobstructed to form bulges.
Our model simulations do not support the application of Simpson’s theory to the NCFR discussed in this paper, because bulges and clefts were present even though the cold front did not override warm-sector air (Fig. 10). Updrafts may have played some role in restraining the forward motion of clefts by advecting parcels upward with lower horizontal momentum, but they are unlikely to have formed by the frictionally induced instability mechanism postulated by Simpson. As we will show below, the bulge–cleft structure appeared to form predominately in response to organized pressure perturbations along the front associated with the convectively generated trapped gravity waves.
We are primarily interested in the first oscillation of the gravity wave, since it has the largest effect on the vertical temperature and pressure structure and occurs over the frontal zone. The maximum in θ (Fig. 16a) lags behind the phase of the vertical motion by 90°, as expected for a gravity wave. The region of warming aloft produced by the wave is up to 4°C warmer than the ambient air. This results in an isolated core of lower surface pressure beneath the region of subsidence, where the pressure is several hPa lower than in the warm sector and there is a horizontal pressure difference of 4 hPa across the updraft. As mentioned previously, this is almost entirely hydrostatically generated.
The effects of the complex pressure pattern can be seen by examining trajectories of parcels in the region of the front (Figs. 13a and 13b). Trajectories 1–10 are terminated just behind the advancing cold front, and trajectories 11–20 are terminated 2 km (one horizontal grid space) to the east in the warm sector ahead of the front. Trajectories 6 and 16 mark the approximate center of a cleft in the front. To the north and south of this point the front can be seen to bulge to the east. The distinction between the prefrontal and postfrontal air masses is evident in the trajectories, as well as in the pressure and temperature fields. The trajectories show uniform core-relative southeasterly flow in the warm sector and a sharp transition to northerly flow behind the front. The cleft–bulge structure of the front is also evident in the trajectories, as is the influence of the pressure field on the motion of the air parcels.
As a parcel approaches a pressure couplet from the north, it first encounters the low pressure center and is accelerated inward (to the west). As it passes to the south of the low pressure center, it travels against the pressure gradient and is therefore decelerated. As the parcel passes the high pressure center, it moves at a lower speed and is strongly affected by an outwardly directed pressure gradient force from the high pressure center and is, therefore, accelerated to the east. This westward acceleration, deceleration, and then eastward acceleration creates the cleft structure along the front. As a parcel passes on to the next couplet, it is weakly accelerated to the east as it leaves the influence of the high pressure and then to the west as it approaches the low pressure center of the next couplet. This more gradual shift from high to low pressure produces smooth bulges along the front.
The above discussion has focused on the surface flow pattern as a response to the surface pressure pattern associated with the combined effects of the front and trapped gravity waves. This approach was taken in the interest of conceptual simplicity, given the complexity of trapped gravity waves superimposed on a highly three-dimensional frontal structure. However, it should be noted that it is more correct to describe the surface flow and pressure patterns as mutually interacting components of the gravity wave structure, superimposed on the frontal structure.
c. Orientation of the precipitation cores
In section 3 we showed that the model simulations reproduce fairly well the sizes and orientations of the PC observed by radar. We will now use the model to explore the mechanism for the orientation of the PC.
Model results for a typical PC at 0500 UTC are shown in Fig. 21. Depicted are the PC-relative winds, vertical air velocity, and precipitation mixing ratios at heights of 1–4 km. At heights ≥2 km (Figs. 21a–c), where there is significant precipitation, the plume of precipitation is seen to be clearly aligned with the PC-relative winds. At heights ≥3 km (Figs. 21a and 21b), where graupel is the dominant form of precipitation, there is significant downwind transport of precipitation that is enhanced by the relatively slow fall speed of graupel (compared to the fall speed of rainwater lower down). At heights <3 km (Figs. 21c and 21d), where rain is the main form of precipitation, the PC is located close to the updraft. This suggests that the slower falling graupel contributes to the elliptical elongation of the PC. Similar results were found for a PC to the north of the one shown in Fig. 21.
To verify that the downwind transport of precipitation is a significant factor in the distribution of precipitation into elongated PCs, hydrometeor trajectories were calculated from the model. Figure 22 shows a vertical cross section of precipitation particle trajectories over a 15-min period from 0500 to 0515 UTC. The trajectories are labeled from 1 to 10, and the precipitation was “released” in the center of the updraft at 50-hPa intervals from 900 to 450 hPa. The trajectories are projected onto the plane of the cross section that runs parallel to the PC. The location of the cross section is shown in Fig. 21d as the line T–T′. The trajectories were terminated when the precipitation reached the lowest σ level. It can be seen that particles initiated in the rainwater regions (labeled 1–5) fall close to the updraft, forming a strong core of precipitation. These trajectories highlight the shift to northwesterly winds in the postfrontal region. Particles initiating above the freezing level (labeled 6–10) travel ∼20 km toward the northwest over a 15-min period, creating the extension of the PC to the rear of the front.
From these modeling results, and detailed analyses of other PCs generated in the numerical simulation, we conclude that the advection of precipitation by the PC-relative winds is primarily responsible for the distribution of precipitation into elliptically shaped PCs oriented at an angle to the NCFR. Since PCs in NCFR generally move toward the northeast along a front at speeds of ∼10–40 m s−1 (Hobbs and Biswas 1979; James and Browning 1979; Locatelli et al. 1995; Browning and Roberts 1996), the PC-relative wind field can depart significantly from the actual wind field; it is the PC-relative wind field that determines the distribution of precipitation.
Early observations of NCFR often focused on the angle that the PC formed with the synoptic-scale front (Hobbs and Biswas 1979; James and Browning 1979). Our modeling results suggest that the orientation of the PC is not primarily related to the orientation of the cold front; instead, the orientation of the PC is the result of its interaction with the larger-scale winds. Hence, it is not surprising that PCs can be oriented in a variety of ways, including southeast to northwest (Locatelli et al. 1995, and the present paper), northeast to southwest orientation (Hobbs and Biswas 1979; James and Browning 1979; Locatelli et al. 1995), and circular PCs (Locatelli et al. 1995).
d. Application of gravity current theory
Using the average cross section, there was some uncertainty in how far behind the leading edge of the front to take the pressure perturbation. Thus, ΔP is estimated to be between 0.6 and 1.5 hPa. The density of the warm air is 1.18 kg m−3, and VW was found to be −6 m s−1. These numbers yield a calculated speed of V = 5.6–8.9 m s−1. The actual ground-relative frontal speed (VGR) in the simulation was 8 m s−1, and the actual ground-relative warm air speed perpendicular to the front (VW) was −6 m s−1, yielding V = 14 m s−1. Thus, the gravity current calculation, when applied to alongfront averaged quantities, significantly underestimates the speed of the front relative to the warm air.
However, it was also found that the calculated gravity current speed provides a good estimate at particular locations along the front, where the frontal structure appears to behave locally like a 2D gravity current. For example, at a location immediately south of the cleft associated with updraft U3 in Fig. 9, the ground-relative speed of the front perpendicular to its orientation at that location (i.e., the local value of VGR) was estimated to be 15.5 m s−1, and the local value of VW was 5 m s−1, yielding an actual value of V = 10.5 m s−1. Meanwhile, the pressure perturbation behind the front was estimated (from Fig. 13a) to be 2.2 hPa, yielding a calculated gravity current speed of V = 10.9 m s−1, in close agreement with the actual speed.
In summary, parts of the front behave locally like a gravity current, traveling at the theoretical gravity current speed in a direction perpendicular to the local orientation of the front, but the motion of the front as a whole is not well described by the gravity current speed calculated from alongfront averaged quantities.
6. Conclusions
In this paper we have described a 3D numerical model simulation of an observed NCFR. The synoptic environment of the NCFR was generally well reproduced by the model, although there were some differences in the position of the surface low pressure center and stationary front north of the low center. Comparison with radar and aircraft observations demonstrated that the simulation captured the key features of the finescale cold frontal structure. In particular, the model produced precipitation cores on the order of 40 km in length that were rotated counterclockwise from the synoptic-scale front, consistent with the observations.
An examination of the environment for this case showed that it was susceptible to the formation of trapped gravity waves. The model simulations show that the convection associated with each PC triggers a gravity wave that resembles airflow over an isolated mountain peak. The gravity waves are V shaped and aligned with their apexes oriented slightly counterclockwise to the cold front, with the eastward branch of the initial wave extending over the cold front. The first and strongest oscillation of each gravity wave consists of downward motion, which produces a region of warming aloft and a GR. The next (weaker) upward oscillation of the gravity wave creates favorable conditions for convection farther north. In this way, the precipitation on the cold front is organized into a series of PCs separated by gaps. We have shown also that the trapped gravity waves had a significant effect on the structure of the front through their associated pressure perturbations at the surface, which deformed the front into bulges and clefts similar to those seen in gravity currents.
The model simulations also show that the elliptical shapes and the orientations of the PCs are due to the advection of precipitation by the PC-relative winds. This was verified by examining the trajectories of the hydrometeors, which showed that the precipitation was carried backward from the updrafts on the front to form trailing elliptically shaped PCs.
Horizontal shear instability (HSI) has been proposed as a mechanism leading to the core–gap structure of NCFR, and this mechanism was investigated in the present case by means of comparison with the convergence and vorticity patterns seen in published examples of HSI along a density current interface (Lee and Wilhelmson 1997) and shear–convective instability modes in an idealized shear zone that is unstable to parcel ascent (Moore 1985). The comparisons revealed some similarities but also some key differences. This finding, combined with the fact that shear instability has not been demonstrated to be a dominant mechanism for alongfront variability in realistic cold fronts with moist ascent, precludes us from attributing the core–gap structure in the present case to shear instability, although it cannot be eliminated as a possibility. We leave open the possibility that the interaction of HSI with density current dynamics, surface friction, latent heating and cooling, gravity waves, large-scale frontogenesis, etc., may lead to a mode of organization that is fundamentally linked to HSI but is unlike the structures that have been seen in the previously cited idealized studies.
Gravity current theory was used to examine both the synoptic-scale movement of the NCFR and the movement of the PCs along the front. It was found that parts of the front behave locally like a gravity current, traveling at the theoretical gravity current speed in a direction perpendicular to the local orientation of the front, but the motion of the front as a whole is not well described by the gravity current speed calculated from quantities averaged along the length of the front.
Acknowledgments
This research was supported by the Mesoscale Dynamics Program, Atmospheric Research Division, National Science Foundation under Grants ATM-9106235 and ATM-9632580.
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Surface analysis valid at 0000 UTC 27 Jan 1986. Solid lines are isobars, contoured every 2 hPa. Frontal symbols and station plots follow standard plotting conventions.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Model domain configuration. Positions of observed fronts and low pressure center (L) at 0000 UTC 27 Jan 1986 are taken from Fig. 1. Coarsest model domain is labeled D1, and nested model domains are labeled D2, D3, and D4. Domain D4 shown at 0000 UTC (left innermost box) and 0900 UTC 27 Jan 1986 (right innermost box).
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Sea level pressure (solid, contoured every 2 hPa), surface temperature (dashed, contoured every 2°C), and surface wind vectors (velocity scale shown at lower left) from the model (domain D2) at 0000 UTC 27 Jan 1986. Fronts analyzed subjectively from data in figure.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Comparison of observed (2230 UTC 26 Jan 1986) and modeled (0300 27 Jan 1986) profiles of (a) wind direction and (b) temperature along a horizontal line perpendicular to the front at a height of 300 m above ground level (AGL).
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
(a) Vertical cross section showing horizontal winds relative to the motion of the precipitation cores derived from dual-Doppler radar analysis. The length of each arrow is proportional to the relative wind velocity at the origin of each arrow. The heavy line is the kinematic cold front. Adapted from Locatelli et al. (1995). (b) As in (a) but from MM5 model simulation at 0500 UTC 27 Jan 1986.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Time series showing the movement of precipitation cores (shaded regions) on the NCFR on 27 Jan 1986: (a) observed and (b) simulated by the MM5 model. (a) Precipitation intensity is indicated by the radar reflectivity; (b) precipitation is depicted by the precipitation mixing ratio. The dashed lines indicate the motions of the precipitation cores. Both (a) and (b) have the same horizontal scale, but the eastward movement of the PCs have been expanded by 40 km per time step to avoid overlaps in the time series.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Frontal positions from the model at 0330 through 0530 UTC 27 Jan 1986 (thicker lines). Precipitation mixing ratio on the σ = 0.995 surface at 0330 UTC are shown by the contours (lighter lines) at 0.5 g kg−1 intervals.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
MM5 model simulations of the potential temperature θ (shading, see key) and precipitation mixing ratio (contours, in 0.5 g kg−1 interval) shown on the σ = 0.995 surface at 0500 UTC 27 Jan 1986. Positions of the updrafts discussed in the text are labeled U1–U6.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Magnified view of Fig. 8 around the region of updraft U3.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Vertical cross section from MM5 model along line A–A′ in Fig. 9 at 0500 UTC 27 Jan 1986 showing equivalent potential temperature θe (K), graupel mixing ratio greater than 0.5 g kg−1 (dark shading), rainwater mixing ratio greater than 0.5 g kg−1 (light shading), and winds relative to the precipitation cores in the plane of the cross section. The length of each arrow is proportional to the relative wind velocity at the origin of each arrow. The location where this cross section intersects the line N–N′ in Fig. 9 is shown as the vertical line labeled N.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
As for Fig. 10 but along the line N–N′ in Fig. 9. The location where this cross section intersects the line A–A′ in Fig. 9 is shown as the vertical line labeled A.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
As for Fig. 10 but along line G–G′ in Fig. 9.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
(a) Relative back trajectories from the MM5 model terminating on the σ = 0.995 surface at 0500 UTC 27 Jan 1986. The arrow heads on the trajectories are at 3-min intervals. The width of the trajectories indicates height in σ units (see inset key). Sea level pressure (solid contours, 0.25-hPa interval) and precipitation mixing ratio (shading, see key) are shown on the lowest σ surface. Updrafts are labeled as in Fig. 8. (b) As in (a) except θ (solid contours, 1 K intervals) is shown in place of sea level pressure.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Horizontal plots from the MM5 model at 0500 UTC: (a) absolute vorticity (shading) and wind vectors (velocity scale at lower right) at 50 m AGL; (b) absolute vorticity (shading) and vertical velocity (contoured every 1 m s−1; solid is upward, dashed is downward, zero contour is suppressed) at 1.5 km AGL; and (c) mixing ratio (shaded), divergence (contoured every 10−4 s−1; solid is convergence, dashed is divergence, zero contour is suppressed), and wind vectors [velocity scale same as in (a)] at 50 m AGL. Vorticity shading scale applies to both (a) and (b); mixing ratio scale applies to (c). Updrafts U3–U6 indicated by heavy dots.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
MM5 model results for (a) vertical air velocity at a height of 4.5 km MSL (solid and dashed lines indicate updrafts and downdrafts, respectively; contours are labeled in cm s−1) and (b) PC-relative horizontal streamlines at 3.5 km MSL and surface frontal position at 0500 UTC Jan 27 1986. The frontal position on the surface is indicated by the standard symbols. Updrafts are labeled as in Fig. 8.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
(a) MM5 model results in vertical cross sections along line X–X′ in Fig. 15 showing the vertical air velocity (shading, see key; arrows indicate upward or downward motion) and θ (solid lines). (b) As in (a) but arrows indicate PC-relative winds in the plane of the cross section. The length of each arrow is proportional to the relative wind velocity at the origin of each arrow.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Skew T–logp diagram showing MM5 model soundings in the warm sector (solid line) and in a gap region to the rear of the leading edge of a cold front (short-dashed line), and a parcel trajectory (long-dashed line) at 0500 UTC 27 Jan 1986. The location of the warm-sector and gap-region soundings are indicated by W and G, respectively, in Fig. 14c.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Horizontal plot at 0500 UTC 27 Jan showing MM5 model results for the frontal zone at the surface (light shading) and regions where the precipitation mixing ratio >0.5 g kg−1 on the σ = 0.995 surface (darker shading) for (a) the southernmost portion of the high-resolution model domain and (b) a portion of the front to the north. Updrafts are designated as in Fig. 8.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Vertical cross section along the front and along line ABCD in Fig. 18a at 0500 UTC 27 Jan 1986 from the MM5 model. Shown are the vertical air velocity (shading, see key; arrows indicate upward or downward motion) and θ (solid lines). Updrafts labeled as in Fig. 8. See text for a detailed explanation.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
As for Fig. 19 but along line EFGH in Fig. 18b.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
MM5 model results at heights of (a) 4 km, (b) 3 km, (c) 2 km, and (d) 1 km for the airflow relative to a precipitation core (vectors), vertical air velocity (contours labeled in m s−1; dashed lines and negative values indicate downdrafts), and precipitation mixing ratio (shading, see key). The updrafts are labeled as in Fig. 8.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
Vertical cross section along line T–T′ in Fig. 21 (d) from the MM5 model simulations showing graupel (solid lines; labeled in g kg−1) and rainwater mixing ratio (dashed lines; labeled in g kg−1). The heavier lines show hydrometeor trajectories released at 0500 UTC with arrowheads at 3-min intervals.
Citation: Journal of the Atmospheric Sciences 56, 9; 10.1175/1520-0469(1999)056<1175:NMOPCO>2.0.CO;2
