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High Resolution Observations of a Shallow Cold Front with Density Current Attributes and Topped with Waves
TIMOTHY A. COLEMAN1 AND PATRICK M. GATLIN2
Earth System Science Center, The University of Alabama in Huntsville, Huntsville, AL
KEVIN R. KNUPP
Department of Atmospheric Science, The University of Alabama in Huntsville, Huntsville, AL2
Submitted to the Journal of the Atmospheric Sciences
1 Corresponding author address:
Department of Atmospheric Science, University of Alabama in Huntsville
NSSTC, 320 Sparkman Drive, Huntsville, AL 35805
2 Current affiliation: NASA Marshall Space Flight Center, Huntsville, AL
Very high-resolution Doppler radar analysis and thermal profiles from a profiling radiometer are used to examine a dynamically interesting, shallow cold front. The front was located in a synoptic-scale col region, and exhibited characteristics of a density current, including its forward speed, the presence of a rear-to-front feeder flow, and the presence of an elevated nose near its leading edge. The front was topped by distinct Kelvin-Helmholtz waves that were observed by Doppler radar at a very high-resolution. Utilizing the radiometer and radar measurements, a cross-section of Richardson number was produced along the front.
Numerous studies of the structure and motion of cold fronts have been documented over the past 100 years. Perhaps the earliest study was by Margules (1906). The kinematics of the flow across cold fronts, and the existence of ana- and kata-fronts, was examined later (e.g., Bergeron 1937; Sansom 1951). Regarding the motion of cold fronts, some have concluded that, since many cold fronts have a lifetime of multiple days and are associated with large-scale systems, that the frontal motion is determined by synoptic-scale flow (e.g., Ryan and Wilson 1985; Garratt 1988). However, several authors have also observed that some cold fronts have structure and motion similar to a density current (e.g., Berson 1958; Hobbs and Persson 1982; Carbone 1982; Shapiro et al. 1985; Smith and Reeder 1988; Parsons 1992; Geerts et al. 2006; Karan and Knupp 2006).
It is the purpose of this paper to examine a shallow cold front that moved across the southeastern United States on 4 December 2010. High-resolution Doppler radar analysis, along with thermal and moisture profiles from the microwave profiling radiometer aboard the Mobile Integrated Profiling System (MIPS, Karan and Knupp 2006) at the University of Alabama in Huntsville, indicate that the front exhibited several characteristics of a density current. The forward speed of the front matched that of a density current fairly well. A rear-to-front feeder flow that is typical of density currents (e.g., Goff 1976) was present, and the leading edge of the front had a slightly elevated “nose” (e.g., Simpson 1997). Perhaps most interesting from an observational perspective, distinct Kelvin-Helmholtz billows/waves (e.g., Carbone 1982; Weckwerth and Wakimoto 1992; Simpson 1997) were observed by Doppler radar at a very high-resolution along the top of the frontal surface.
2. Synoptic Overview
As shown in Fig. 1, broad cyclonic flow was present at 500 hPa across the central and eastern United States at 1200 UTC on 4 Dec 2008. Therefore, at least some gradient wind-related speed divergence was likely occurring from the lower Mississippi River Valley northeastward into the northeastern United States. Consequently, a surface cyclone was centered in the eastern Great Lakes, with an inverted trough of low pressure at the surface near the Gulf Coast. This inverted trough was likely associated with the vigorous shortwave trough moving through Arkansas and Louisiana. However, surface anticyclones were located off the North Carolina coast and over the High Plains. This placed the cold front being examined (gray line in Fig. 1) in a “col” region, with very weak synoptic-scale geostrophic flow at the lower levels where the front was located. The typical kinked-isobar structure at the surface along the front was virtually absent along the front from Tennessee into northern Alabama; therefore, front-normal geostrophic winds were also very weak. At 850 hPa (not shown), winds along the front, and for nearly 100 km behind it, were out of the southwest. Therefore, it is likely that the front’s movement was controlled, at least partially, by ageostrophic processes.
3. Detailed analysis of cold front
a. Surface observations of the front
Surface observations of temperature, dewpoint, mean sea level pressure, and wind were recorded at 5-second intervals around the time the front passed over the University of Alabama-Huntsville (UAH, Fig. 2). There was an initial, rapid drop in temperature of 1.9°C in ten minutes between 1430 and 1440 UTC, followed by a drop of 3.1°C between 1440 and 1530 UTC. The drop in dewpoint closely followed that of the temperature, as the air was near saturation at the surface and occasional drizzle and light rain were falling (allowing for excellent observations of air flow using Doppler radar, see Section 3c). The initial pressure rise of 1 hPa (discussed in Section 2a) occurred over a 16-minute period beginning at 1427 UTC. The wind shift and increase in speed was also rapid. Fig. 2c shows u, the component of the ground-relative surface wind in the direction of frontal motion (toward 150 degrees). The change in u is from -2.5 m s-1 (a headwind) at 1424 UTC to 4.1 m s-1 (a tailwind) by 1431 UTC, just after frontal passage at 1430 UTC.
b. Density current attributes
The 12-channel microwave profiling radiometer (MPR) that is part of MIPS provides detailed, one-minute resolution profiles of thermal and moisture data; therefore, time-height sections of material surfaces including potential temperature and equivalent potential temperature are available (Fig. 3). In addition, isentropic lift along the front was producing widespread, light precipitation near the front at low-levels. The precipitation was not heavy enough to bias low-level MPR observations appreciably, yet provided for an excellent dataset from the ARMOR radar, located at the Huntsville airport, 14 km southwest of the MIPS site.
Since the front entering north Alabama was located in a low-level synoptic-scale col, with a very small synoptic-scale pressure gradient below 500 m AGL (Section 2), the synoptic-scale flow likely played little role in the motion of the front. It appears that the cold front was moving at least partially as a density current, based on several observations, primarily from MPR and ARMOR radar data. The leading edge of the cold front was rather shallow, as indicated by RHI Doppler velocity scans roughly normal to the front (Figs. 4 and 5) and MPR time-height sections of equivalent potential temperature (Fig. 3). A vertical section of Doppler velocity (Vr, Fig. 5) shows that the cold front exhibited a sharp wind shift at its leading edge and was only about 500 m deep at a point 15 km behind the leading edge of the frontal surface. The Vr data shows a raised “head” (e.g., Goff 1976; Simpson 1997, see Fig. 6a) region about 1 km wide, and about 600 m high, within 3 km of the surface front. MPR e time-height sections (Fig. 3a, b) indicate that there was also a “nose” at the front due to surface friction, causing the leading edge of the front (at a height of 120 m AGL) to pass over the MPR site about 3 minutes before the surface front. Research has shown that the ratio of the height of the nose to the height of the gravity current head should be between 0.1 and 0.2 (e.g., Keulegan 1957; Lawson 1971; Simpson 1997), and the ratio in this case is 0.2, within theoretical limits. There is also a “feeder flow” behind the front, indicated by the enhanced inbound Vr 10-20 km behind the front (Figs. 4b, 5a). Despite the slow movement of the front (around 6 m s-1), Doppler radar indicated winds only 17 km behind the front were as high as 11 m s-1. Surface data from the KHSV ASOS (located less than 1 km from the ARMOR radar) and from UAH indicate wind speeds of 8 to 10 m s-1 after frontal passage. All of these features (the raised head, nose, and feeder flow) are consistent with density current dynamics illustrated in Fig. 6a (e.g., Simpson 1997, Goff 1976).
The observed motion of the front near the ARMOR and MIPS sites in Huntsville was from 330 degrees at 5.8 m s-1. Comparing the movement of the cold front to that of a density current, we use the following (from Seitter 1986):
Here, k represents the modified Froude number (Seitter 1986), that may vary from 0.7 to 1.1 in atmospheric density currents (Seitter 1986; Wakimoto 1982). p is the change in surface pressure, w is the density of the warm air the density current is moving in to, and U is the component of the mean background wind in the direction of density current motion, ahead of the density current. In this case, w = 1.17 kg m-3, and p = 1 hPa (the initial pressure surge in the minutes after frontal passage). The component of the background wind in the direction of the front U was determined to be -4.8 m s-1, using a VAD analysis at 1330 UTC, well ahead of the front, and RHI velocity data just ahead of the front. Assuming 0.7 < k < 1.1, the speed of a density current V would range from 3.5 to 7.0 m s-1, depending on the Froude number k. Therefore, the observed motion of 5.8 m s-1 falls close to the middle of this range, supporting the idea that the cold front is, at least near its leading edge, moving as a density current when it passes Huntsville (with k = 0.95).
c. Waves on frontal surface
Perhaps the most notable features in these observations are the wave-like undulations on the top of the frontal surface. These appear to mainly be Kelvin-Helmholtz billows (e.g., Simpson 1997), similar to those shown in many other studies of density currents (e.g., Carbone 1982; Weckwerth and Wakimoto 1992, Fig. 6b). As shown in Fig. 5b, these waves are associated with the extreme vertical shear created by the cold air moving from rear to front underneath the density current surface, and the warm air flowing isentropically up and over the density current.
The vertical wind shear near the frontal surface was very large, as indicated by ARMOR Doppler radar RHI imagery (Fig. 5a). The radar was not pointed in a plane perfectly normal to the frontal surface (the RHI was toward 360 degrees azimuth, while the front was approaching from 330 degrees), but it is close enough to reveal spectacular detail of the wind shear and waves along the front. As an example of the extreme wind shear, at a range of 3.8 km from the radar, or about 1.3 km behind the surface front (the surface front was at a range of only 2.5 km), inbound radial velocities (northerly winds) up to 7.7 m s-1 were indicated by radar at a height of 200 m AGL in the cold air. However, outbound radial velocities up to 8.3 m s-1 were indicated at the same range above the frontal surface, at a height of only 750 m AGL. Vertical shear of the horizontal wind near the sloped frontal surface ranged from 0.04 to 0.10 s-1 at least 25 km behind the intersection of the front with the ground.
Some of the wave undulations may be explained by sudden isentropic lifting in the statically stable environment above the front, creating internal gravity waves. Indeed, a wave reflecting mechanism, such as that associated with curvature in the wind profile (e.g., Nappo 2002), was in place due to the northerly jet shown in the RHI scan between 2.25 and 3 km AGL. However, the waves are also consistent with Kelvin-Helmholtz billows. A vertical cross-section of Richardson number (Ri) was computed to determine the likelihood of Kelvin-Helmholtz (K-H) instability. The Richardson number is given by
where N is the Brunt-Vaisala frequency (representing static stability), and u is the component of the wind speed in the vertical plane of interest (in this case, the cold front). The flow is considered unstable due to shear when Ri < 0.25; indicative of Kelvin-Helmholtz (K-H) instability. Given the known motion (direction and speed) of the front, and assuming that its thermodynamic profile was approximately steady- state, a time-to-space conversion (TSC) of the form
was used to convert the time-height sections of potential temperature from the MPR and Brunt-Vaisala frequency N into a vertical cross-section of N at 1423 UTC. Since the ARMOR Vr data (Fig. 5a) provides a close approximation of u and du/dz in the same vertical cross-section at 1423 UTC, the two datasets were combined to calculate Ri in the vertical plane of the RHI velocity scan shown in Fig. 5a. The results of this calculation are shown in Fig. 6b. The data are somewhat noisy due to necessary smoothing (the RHI and TSC thermodynamic data were not on the same grid). However, since only areas where Ri < 0.25 (areas of K-H instability) are shaded in Fig. 5b, it is obvious that a fairly extensive area of K-H instability was present, especially near the leading edge of the front. K-H instability also extended along the sloping frontal surface well behind the front’s intersection with the ground. Therefore, the wave features observed in Doppler velocity RHI images were likely K-H waves.
4. Summary and Conclusions
A detailed and visually illustrative dataset was gathered as a well-defined, shallow cold front moved through northern Alabama on 4 Dec 2008. This dataset included high-resolution thermal profiles from an MPR, and both PPI and RHI Doppler velocity scans nearly normal to the front. Given the lack of a significant low-level geostrophic wind component normal to the cold front examined in this paper (the front over northern Alabama was located in a col region), and given that observations show that the front contained a raised head, an elevated nose, and rear-to-front feeder flow, it is valid to assume that the front was behaving, at least at its leading edge, very similar to a density current. The forward speed of the front was also found to be consistent with that of a density current.
Distinct waves are seen very clearly atop the front in RHI scans of Vr taken nearly normal to the front. Time-to-space conversion of MPR-derived stability data, combined with the RHI velocity data, allowed for a rather unique analysis of the Richardson number along the front. This analysis showed a fairly large area near the leading edge of the front where Ri < 0.25, indicating K-H instability, and a shallower layer of this instability extended along the top of the frontal surface, well behind the front’s intersection with the ground. This indicates that the waves were likely K-H billows atop the front. This is also consistent with the density current nature of the cold front.
The authors wish to thank the reviewers, whose comments always improve a manuscript. This research was funded by the National Science Foundation (NSF award AGS-1110622).
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Figure 1. Analysis at 12 UTC 4 Dec 2008. a) MSL pressure (hPa) and surface winds. Gray curve indicates position of surface cold front. b) 500 hPa geopotential heights and station plots. Square in panel a shows location of Huntsville, Alabama.
Figure 2. Surface time series at UAH of a) temperature and dewpoint (C); b) MSL pressure (hPa); c) component of wind in direction of frontal movement (solid line, m s-1)
Figure 3. Time-height sections from UAH Microwave Profiling Radiometer on 4 Dec 2008 of equivalent potential temperature (e,K). a) 12-hour time-height section showing entire frontal passage. b) Zoom-in on frontal passage around 1430 UTC, illustrating “nose” of cold air protruding ahead of surface front near 250 m AGL.
Figure 4. 0.7° elevation PPI scan of a) reflectivity (dBZ) and b) radial velocity (m s-1) from the ARMOR radar at 1331 UTC. The cold front is clearly visible in both panels. Note the enhanced inbound Vr behind the front, indicative of low-level feeder flow.
Figure 5. a) RHI scan of radial velocity (m s-1) from ARMOR at 0 degrees azimuth at 1423 UTC 4 Dec 2008; b) Cross-section of Richardson number (Ri) along same axis as in a), based on the shear of ARMOR radial velocity and time-to-space conversion of MPR potential temperature.
Figure 6. a) Schematic cross-section of density current showing raised head, nose, and feeder flow (after Goff 1976). b) Schematic showing flow in a density current containing Kelvin-Helmholtz billows (Carbone 1982).
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