J. Meteor. Res.  2014, Vol. 28 Issue (6): 1137-1154   PDF    
http://dx.doi.org/10.1007/s13351-014-4028-0
The Chinese Meteorological Society
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Article Information

QUAN Wanqing, XU Xin, WANG Yuan. 2014.
Observation of a Straight-Line Wind Case Caused by a Gust Front and Its Associated Fine-Scale Structures
J. Meteor. Res., 28(6): 1137-1154
http://dx.doi.org/10.1007/s13351-014-4028-0

Article History

Received January 25, 2014;
in final form June 20, 2014
Observation of a Straight-Line Wind Case Caused by a Gust Front and Its Associated Fine-Scale Structures
QUAN Wanqing, XU Xin, WANG Yuan     
1 Key Laboratory of Mesoscale Severe Weather of Ministry of Education, School of Atmospheric Sciences, Nanjing University, Nanjing 210093
ABSTRACT:A straight-line wind case was observed in Tianjin on 13 June 2005, which was caused by a gust front from a squall line. Mesoscale analyses based on observations from in-situ surface stations, sounding, and in-situ radar as well as fine-scale analyses based on observation tower data were performed. The mesoscale characteristics of the gust front determined its shape and fine-scale internal structures. Based on the scale and wavelet analyses, the fine-scale structures within the gust front were distinguished from the classical mesoscale structures, and such fine-scale structures were associated with the distribution of straight-line wind zones. A series of cross-frontal fine-scale circulations at the lowest levels of the gust front was discovered, which caused a relatively weak wind zone within the frontal strong wind zone. The downdraft at the rear of the head region of the gust front was more intense than in the classical model, and similar to the microburst, a series of vertical vortices propagated from the rear region to the frontal region. In addition, strong tangential fine-scale instability was detected in the frontal region. Finally, a fine-scale gust front model with straight-line wind zones is presented.
Keywordsstraight-line wind     gust front     fine scale     squall line    
1. Introduction

A gust front is the leading edge of an outflowfrom a thunderstorm(either single or multiple cell), amore complex system such as a squall line(quasi-linearconvective system, QLCS), or other mesoscale convective systems(MCSs). A gust front is often associatedwith strong and damaging winds(straight-line winds) and severe convective weather. This is because it isa type of mesoscale front with a significant pressuregradient across the front line. On the mesoscale(horizontal scale from 2 to 200 km; Orlanski, 1975) and fine-scale(horizontal scale less than 2 km; Orlanski, 1975), and with high-resolution data, strong inconsistency in wind direction, wind speed(both horizontal and vertical), pressure, and temperature is often observed(Shapori, 1985). However, due to limited observations, such a phenomenon has not been recorded toa satisfactory level in China. There have been manystudies published on gust fronts(Wang et al., 2006;Liao et al., 2008), but few on the frontal structure ofgust fronts. Wang et al. (2006)observed an inconsistent pattern within the frontal region of a gust front;however, their analysis lacked in detail, without examination of fine-scale characteristics.

Although the classical structure of a gust frontwas described by Droegemeier and Wilhelmson(1987), later observations have shown different types of gustfronts with different amounts of surges after the headof the gust front. These features also contribute tothe shape of the top of the planetary boundary layer(PBL)(May, 1999) and affect the propagation of gravity waves triggered by the instability from the headof the gust front, and by the range of damaging windzones and the initialization of secondary convectivecells(Weckwerth and Wakimoto, 1992), both of whichare revealed based on examination of fine-scale structures.

The different shapes of gust fronts are to somedegree related to environmental parameters, especiallythe buoyancy and vertical wind shear near the top ofthe PBL. This is because the surge of a gust front iscaused by the backward propagation of the Kelvin-Helmholtz(K-H)wave triggered by the K-H instability at the head of the gust front. The K-H instability isstrongly linked to the environmental Richardson number, which is the ratio of buoyancy and vertical windshear, and for a K-H instability to develop, this ratioshould be not more than 0. 25. The conditions of theenvironment may also contribute to the characteristics of initialized secondary cells along the instability, which affect the intensity of the surface wind.

The lowest levels of the gust front structure can beobserved based on the PBL observation towers(Goff, 1976; Zhao et al., 1982)with the height below 500 m. Meanwhile, with the development of Doppler radar, radar data together with sounding data are now helping to provide descriptions of the upper-level structure of gust fronts(Wakimoto, 1982; Uyeda and Zrnic, 1986; Kirsten and Schroeder, 2007). However, in suchstudies, the fine-scale distribution of damaging windsis not delineated well, because the turbulent processis not analyzed down to this level in detail. There isalso a lack of insight into the contribution of turbulentfluctuation and transfer of momentum and energy tothe damaging winds. In-situ Doppler radar measurements are always used in such analyses, but it nevertheless remains challenging to describe the development of meso-fl-scale or fine-scale systems by merelyapplying in-situ radar data. Data from observationtowers can only reach the lower levels of a gust front, and no radar-based velocities can be derived for thispart of the profile because the lowest two elevationsfor Doppler radar are 0. 5(350 m above ground level) and 1. 5(1200 m above ground level), but the heightof the gust front is approximately 600 m. On theother h and , the fine-scale structures within a downburst propagate outwardly near the surface, with themaximum at about 170-300 m(Fujita, 1981). Thusin this paper, only the fine-scale structures within thelowest part of the gust front are analyzed.

In this paper, we analyze a straight-line wind casethat occurred on 13 June 2005 in Tianjin, China. Theevent was caused by a gust front from a squall line. The front happened to pass over a PBL observationtower in Tianjin, thus providing us with valuable datato examine the internal structures of the outflow. Thedata from the observation tower are used to scrutinizethe structure of the gust front, in order to distinguishthe fine-scale structures within the gust front from theclassical mesoscale structures, and to underst and theircharacteristics and causes. The fine-scale structuresdetermine the straight-line wind distribution withinthe traditional strong wind zone. The data used inthe study are described in Section 2. In Section 3, the mesoscale surface observation data are used to examine the environmental conditions to determine howthe gust front formed. The fine-scale tower observations are analyzed in Section 4. Section 5 provides ascale analysis, separates the fine-scale structures fromthe mesoscale structures, and describes the characteristics and causes of these fine-scale structures. Section6 presents a new gust-front model that includes finescale structures. 2. Data and method

Four main sets of data are used in the observational analysis: in-situ surface observations in theBeijing-Tianjin area; the sounding data from Beijngstation(used to represent the soundings at Tianjinstation); in-situ Doppler radar data from Tanggu station; and observation tower data in Tianjin, withper-minute pressure data supplied by an automaticweather station(AWS). Quality check on some of thedata were conducted before further data analysis. 2. 1 In-situ surface station and Doppler radarobservations

In-situ surface observations in the Beijing-Tianjinarea were selected. The closest observation timearound the case was 0900 UTC 13 June 2005. Thetime 0900 UTC was not the st and ard observation timein 2005, and the AWS network was to be established. Thus, the number of stations with observations in thatarea was 20.

The in-situ Doppler radar resides at Tanggu station, 41 km to the southeast of Tianjin station. Theradar provides reflectivity and radial velocity data atelevation angles of 0. 5°, 1. 5°, 2. 4°, 3. 6°, etc., with aninterval of 6 min. 2. 2 Sounding data

Beijing station is the only sounding station withinthe Beijing-Tianjin area. The sounding profile of Beijing station is usually used as a proxy for Tianjin station, together with the surface stationary observationdata of Tianjin. This is because in many cases themid-to-upper atmospheric fields of Beijing and Tianjin are homogeneous(Liu, 2010). In the present case, the wind direction of the Beijing-Tianjin area at both500- and 700-hPa layers was northwest, and Tianjinis to the southeast of Beijing. This means Tianjin isdownstream of Beijing, and the balloon from Beijingwould therefore adequately represent the situation atTianjin in the middle and upper troposphere. Notethat, in this case, we need to use the sounding profilein the morning to represent the atmospheric thermaldynamic field in the afternoon, due to the slow movement of the large-scale systems. 2. 3 Tower observations

The observation tower is right on the groundof Tianjin station. The station is located at39°04'29. 26''N, 117°12'20. 51''E, with its surroundingbuildings lower than 10 m. The tower itself is 250-mhigh, with 15 observation levels for the sensors at 5, 10, 20, 30, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, and 250 m. The sensors record temperature, windspeed, wind direction, and relative humidity, with afrequency of 0. 05 Hz(20 s per observation). The localAWS provides pressure data every minute. 2. 4 Calculation of vertical velocity

As vertical velocity data are not directly observable, we need to calculate w from the horizontal velocity(Charba, 1974; Zhao et al., 1982). According tothe Galilean equation,

where C is the average speed of the gust front prop-agation, calculated as the average of the propagationdistance measured from the radar reflectivity chart di-vided by the time. We havewhere Cx and Cy are the average speed of a gust frontin the x and y directions, respectively. Here, we definex as the radial direction and y as the tangential direction. Cx = C cos θ, Cy = C sin θ, and θ is the anglebetween east and x. Subsequently, we havePerforming the integration obtainsBy computational discretization in the vertical direc-tion, the equation becomeswhere i is the number of levels of the tower observation and y is the time series, Δt = 20 is the averagetime interval. 3. Case description3. 1 Synoptic and mesoscale background

As shown in Fig. 1, at 0000 UTC 13 June 2005, upper-level troughs at both 500 and 700 hPa werepresent, with the troughs tilting backward with increasing height, indicating that the system was developing(Wang et al., 2010). The shear line of NW-SE winds at 850 hPa lay between Beijing and Tianjin(Fig. 1a), where the east winds provided a moisturechannel. Tianjin was inside a surface warm zone. Thewhole background was conducive to the developmentof mesoscale convective systems. As seen from thecloud chart at the same time(Fig. 1b), the tail ofa linear convective system was developing right pastBeijing and toward Tianjin, from northwest to south-east. This linear convective system was the squall linefrom where the gust front generated.

Fig. 1. (a)Large-scale environment at 0000 UTC 13 June2005 and (b)satellite IR chart at the same time, with thered square showing the Beijing-Tianjin area.

The sounding data of Tianjin at 0600 UTC provide a thermal profile as shown in Fig. 2. Vertical windshear existed at 925 and 850 hPa. From the surfaceto 850 hPa, the wind shifted anticlockwise, indicatingthe existence of cold advection. From 850 to 500 hPa, the wind shifted clockwise, demonstrating the presence of warm advection. With the lower layers beingcold and the upper layers being relatively warm, it waseasy for convection to be initiated at the boundary ofthe cold flow. However, the CAPE of only 479. 2 Jkg-1 meant that the local buoyancy was weak. Weakinstability with wind shift implied that vertical windshear was the main contributor to the developing convection. The maximum vertical wind shear was 4. 79× 10-3 s-1, with the wind difference from 0 to 6 kmof 26. 79 m s-1, compared to 6. 80 m s-1 from 0 to 2km. This indicates a strong wind shear in the middlelayers, but a rather weak wind shear at the PBL. Itwas observed that main convection happened in themiddle layers, with a maximum vertical velocity of 31m s-1. The θe line shows a thin dry layer between 850 and 700 hPa, and a thick dry layer between 600 and 400 hPa.

Fig. 2. The T-lgp chart for Tianjin at 0600 UTC 13 June 2005. The red line to the far left denotes dew point. Theblue line denotes temperature. The cyan line in the middle denotes θe.

Furthermore, the surface mesoscale analysis(Fig. 3)at 0900 UTC shows a local cyclone with Tianjin atits northeastern edge. To its northwest was a meso-high with convective weather and a cold center. Between the cyclone and the meso-high was the baroclinic zone(Sanders, 1999), with a temperature changereaching 10 K within 30 km. The meso-high stayedbetween two meso-lows, and to their north, a highpressure center existed on a larger scale. All thesemeso-systems formed a deformation field, and a windshift line lay between the converging north wind and southeast wind. The high pressure center and its convective systems moved southwestward and split intotwo cells. The gust front emerged at 0948 UTC(Fig. 4), and it propagated southeastward.

Fig. 3. Mesoscale features of the surface pressure and temperature fields in the Beijing-Tianjin area at 0900 UTC 13June 2005. Blue solid lines are the isobaric lines. Red dashed lines are the isothermal lines. Green dash-dotted lines arethe 3-h pressure change lines. The black dash-dotted line indicates the squall line region. Convective weather associatedwith the meso-high is shown in the radar image as the strong reflectivity zone. The double black line is the wind shiftline. Forty-eight minutes later, the gust front in the radar image is labeled as F.
Fig. 4. Propagation of the gust front re°ectivity line fromradar at the elevation angle of 0. 5°. The dot on the leftdenotes Tianjin station, and the dot on the right denotesTanggu station where the radar is located. The arrow isthe temperature gradient direction of the baroclinic zone at0900 UTC, and the dashed arrow is the actual propagationdirection of the gust front.
3. 2 Radar observation

The radar reflectivity data show that after theconvective system moved into the baroclinic zone, asin Fig. 5, the outflow from the newly split cell emergedat 0948 UTC(Fig. 6), 10. 4 km from Tianjin, and mov-ing toward the southeast with its intensity increas-ing. The outflow passed Tianjin at 1000 UTC(Fig. 5), and then continued to move southeastward, join-ing another outflow and passing Tanggu at 1030 UTC(figure omitted). The outflow's direction of movementwas about 30° to the left of the direction of the tem-perature gradient of the baroclinic zone.

Fig. 5. Radar reflectivity and radial velocity at the elevation angles of(a, b)2. 4°, (c, d)1. 5°, and (e, f)0. 5° at 1000UTC 13 June 2005. T1 and T2 represent Tianjin and Tanggu stations.
Fig. 6. Cross-section of radar radial velocity at(a)0948UTC and (b)1000 UTC. Tianjin station is at a distanceof 43 km.

Figures 5e and 5f show that at the elevation of0. 5°(approximately 350 m above groud level), thegust front was clearly seen as a thin line with a radial velocity couplet. No reflectivity line could be seen atthe elevation of 2. 4°(approximately 1800 m), while thenegative radial velocity meant that the system was tilting toward the radar station, and all parts of the gustfront were within the PBL. At the elevation of 2. 4°(Figs. 5a and 5b), there was neither a line structurenor large radial velocity, but only a weak single celldeveloping, which was not seen before the gust frontpassed. Such a structure means that this weak cellwas triggered by the gust front. In the cross-sectionof the radial velocity at 0948 and 1000 UTC(Fig. 6), the propagation of the outflow from the squall linestructure toward the sea was significant, and tiny circulations above the outflow were around 2 km-onesingle circulation above the head of the outflow and two above the rear part. It should also be pointed outthat a structure with a height of less than 1 km existedahead of the outflow but with an opposite propagationdirection. This was probably a sea-breeze front.

Furthermore, a couplet of radial velocity(Wilson and Schveiberm, 1986)within a thin velocity zeroline(Fig. 7), whose spatial scale was less than 4km, was apparent, which would have evolved intoa meso-vortex. Some similar meso-vortexes were recently observed and analyzed during severe convectivecases(Wakimoto et al., 2006a, b; Atkins and Laurent, 2009a, b). They had fine-scale characteristics thantraditional meso-cyclones.

Fig. 7. Radar radial velocity at the elevation angle of0. 5° at 0954 UTC 13 June 2005. The black square showsthe location of the meso-vortex.

From the wind profile right across Tanggu radarstation, we can obtain the vertical kinetic structure ofthe gust front(Fig. 8). The height of the gust frontwas approximately 600 m, and right above the headof the gust front there existed a weak wind zone, from1200 m to around 3000 m. This suggests the existence of a vertical circulation above the head of thegust front that may be associated with sub-generatedconvective cells.

Fig. 8. The vertical profile of wind at Tanggu radar station. The yellow line denotes the gust front and the redline is the relative low-speed line.
3. 3 Tower observation

We use the tower observation data from 0955 to1030 UTC because during this period, the entire structure of the gust front, as well as the possible secondarysystems, passed over the tower. In order to examinethe different scales of structure within the gust front and the associated wind speed and secondary systems, we ran a pair of moving averages on different timescales on the observation data: one was a 5-min moving average(Fig. 9), and the other was a 1-min movingaverage(Fig. 10). To obtain the chosen pair of movingaverages, we first ran four sets of moving averages(1, 2, 5, and 10 min)on the original observational data. The original data contained too much turbulence, especially for the fine scale. The mesoscale structureswere preserved well in the 5-min moving averaging, while the 10-min average only retained a basic frontlike feature. The 1- and 2-min averaged data containedfine-scale structures that were not shown in the classical gust front conceptual model, and the 1-min resultswere more clear.

Fig. 9. The 5-min moving average of tower observations of(a)pressure, (b)potential temperature, (c)horizontal windspeed, (d)wind direction, (e)vertical velocity, (f)radial velocity, (g)radial horizontal vorticity, (h)tangential velocity, and (i)tangential horizontal vorticity.
Fig. 10. As in Fig. 10, but for the 1-min moving average of tower observations

Figure 9 shows that the 5-min average provided awhole head range of the gust front. The strong windzone split into two: one near the potential temperaturegradient zone and the other mostly at the end of thehead. The difference between the kinetic front and the thermal front also became distinguishable. Thesurface pressure increased through the whole potentialtemperature gradient zone, reaching a maximum rightafter the front, but with no significant pressure jump. The wind direction shifted with the kinetic front. Thevertical velocity was arranged in the form of a series ofcouplets, with the first and strongest updraft betweenthe kinetic and thermal fronts, while the most intensedowndraft at the rear of the head region. The radialvelocity within the head region was stratified, with theupper layer toward the front and the lower layer awayfrom the front, indicating the existence of backflow, and the height of the backflow layer increased towardthe back of the head, and then stayed the same afterthe head. The tangential velocity also showed stratification, but was only significant within the head region. This suggests that the direction of the backflow wasnot just parallel to the propagation route of the gustfront, but lay at various angles. Although the back-flow region in both the radial velocity and tangentialvelocity fields overlapped perfectly, there was no windspeed jump at the boundary of the backflow and themain flow, albeit the strong wind zones were mainlyrelated to the maximum radial velocity zones. Bothradial and tangential horizontal vorticity fields reachedtheir maximum around the velocity boundary, and themaximum regions were shaped as a single continuousbelt.

Figure 10 shows that the 1-min average was theonly way to truly observe the pressure jump, whichwas in the thermal gradient zone. The horizontal vorticity was clearly a series of small circulations from theback of the head to the front, and the vertical velocityat the back of the head was much greater than that atthe front. The maximum wind speed was also contributed by the downdraft at the end of the gust fronthead, with vertical velocity couplets being more significant. This was more like the near-surface structurein a moving downburst, in that the fine-scale circulations in the bottom layer of the outflow tended towardthe propagation direction of the downburst, while theywere depressed in the opposite direction(Fujita, 1981). It is also important to note that the surge part in theclassical model of a gust front's structure was barelyapparent, even at the finest scale systems observedfrom the gust front. Therefore, we can say that, in thiscase, the surge was not su°ciently significant, and thestrong wind zone was trapped in a single head of thegust front. The intensity of the gust front downdraftwas relatively larger compared to the calculated velocity from the thermal gradient. In the classical modelof a gust front, the intensity of the downdraft at therear of the head section is due to that of the updraft atthe front, resulting from the frontal thermal gradient. Thus, other factors would affect the downdraft intensity. In this case, the downburst-like structure shouldbe considered. 4. Observation analysis4. 1 K-H wave and its propagation

Almost all gust fronts will trigger K-H wave fromthe head. Assuming that the gust front is two-dimensional, we can obtain the wavelength of the K-Hwave by

and the velocity by the results of which are presented in Table. 1. As thehead of a gust front is roughly 3/4 of the K-H wave-length, the length of the head was calculated as 1763m, and the period as approximately 10 min.
Table 1. Parameters of the K-H wave
4. 2 Environmental parameters

We know from the observations that the K-H wavein this case was restrained. As the head section of agust front is formed by the K-H wave, the propagationof the K-H wave being opposite to the gust front's direction of movement is the cause of the surge of thegust front. In the current particular case, the surgesection was hard to recognize, but the head sectionwas obvious. Using the observed propagation speed and the propagation time of the head section, the calculated length of the head section was 2499 m, whichwas longer than the head length based on the K-Hwave calculation. As K-H instability is sure to occur inevery gust front case(Mueller and Carbone, 1987), thereason for this long head without a surge was the lackof a proper K-H wave propagation; the main reasonfor this was the environment, because K-H instabilitycan only develop when the environmental Richardsonnumber(Ri)is less than 0. 25. Ri is the partition of theenvironmental buoyancy to vertical wind shear. In thiscase, from Fig. 3, we know that although the buoyancy was rather weak and the total vertical wind shearwas strong enough that convection developed, the low-level vertical wind shear was much weaker. Note thatthe entire gust front was within the PBL. Based on thesounding data from surface to 850 hPa(approximately1500 m), Ri was calculated. The Ri was 0. 32, suggesting that no further K-H wave propagated backward toform the surge. 4. 3 Gust front intensity

The intensity of the gust front is shown by thedata presented in Table 2. We can see that the intensity of the gust front was not very high, with a shallower thermal gradient and a lower propagation speedthan in most cases(Moncriff and Liu, 1999). Nevertheless, this gust front still caused severe wind damage, suggesting that the mesoscale features were notthe critical part. The horizontal wind speed caused bya classical mesoscale gust front should be proportionalto the intensity of the gust front itself, as the momentum transfer is caused by the frontal pressure gradient. A weak gust front cannot provide enough momentumtransfer to cause strong damaging winds solely fromits head circulation. Thus, finer-scale structures musthave been involved.

Table 2. The intensity of the gust front and related parameters
4. 4 Scale analysis

As gust fronts can be cataloged into fi or flmesoscale systems, we first presume that all factors related to the gust front are mesoscale structures, meaning that they should have a Rossby number of 1. TheRossby number(Ro)is calculated as

which represents a comparison between the inertialforce and the Coriolis force. If Ro ≤ 1, the Coriolis force cannot be ignored, i. e., the rotation of theearth is significant and the system is of large or mesoscale. If Ro > 1, the Coriolis force can be ignored and the system is fine scale.

We should also note another non-dimensionalnumber, the Froude number(Fr), which is

and represents the partition of the inertial force and gravity. A mesoscale system always has an Fr number that approximately equals 1. In the case of a gustfront, Fr is more or less around 1.

Therefore, if we presume both Ro and Fr are equalto 1, we can calculate the characteristic length of thegust front by

Putting L back into Eq. (8), we can obtain thecharacteristic velocity U of the gust front, which indicates the maximum wind speed that the gust frontcan lead to. For the present case, the results are listedin Table 3.
Table 3. Characteristics of the gust front

The calculated value of U is less than the actual horizontal velocity, meaning that the actual wind, partly due to the gust front itself, was also affected bysome fine-scale structures. Based on the definition of Orlanski(1975), with L = 2 km as the shortest characteristic length of the mesoscale structure, if Ro = 1, then U2km should be 5. 33 m s-1 according to Eq. (8), comparable to the real horizontal velocity of 7. 66 ms-1(obtained by sustrating U from Ur). This resultsuggests that the affecting finer-scale structure had acharacteristic length of 2 km, which was approximatelythe length of the head section of the gust front.

Next, the wavelet method was used to filter theobservation data, in order to separate structural wavesof different timescales, similar to a direct scale analysis. The result is presented in Fig. 11. The significant signals and their corresponding timescales canbe identified. The base wave represents the 10-minaverage, and the high-frequency waves represent thedifferent timescales from 5 min to turbulence of lessthan 1 min. We calculated the magnitude of the filtered signals of vertical velocity and associated errors. The magnitude of the 1-min moving average signal wasroughly the same as the error. Thus, the filter longerthan the 1-min moving average could be consideredvalid. Furthermore, we can see the front region withthe amplitude of the wave increased, and fewer structures existing and affecting the base wave mostly atthe front and the back of the head. The lack-of-surgefeature was also apparent in the analysis result.

Fig. 11. Wavelet analysis of the case(s). The base wave(α4)is about the 10-min average, while d4, d3, d2, and d1 in(c){(f)are the 5-, 2-, 1-min, and less than 1-min average, respectively.

We then calculated the turbulence flux to seewhether all fine-scale structures were turbulencebased. The result is shown in Fig. 12. We can seethat most of the turbulence-affected area was aroundthe frontal zone around 1203 UTC, whose intensitywas much greater than that around the back of thehead around 1210 UTC, although the classical modelshows that the back of the head is related to turbulence shattering. Moreover, the turbulence flux hadcouplets, indicating the existence of a coherent structure. Such structures are related to turbulence vorticesthat might cause an increasing of the fine-scale verticalvelocity by tilting and intensifying the wind speed.

Fig. 12. The turbulence flux(v'w')of different time-scales:(a)1, (b)2, (c)5, and (d)10 min. The numbers onthe right indicate the levels at which the tower observationsare available.
4. 5 The fine-scale instability

The reason why the non-turbulent fine-scalestructures distribute more at the frontal zone of thehead is due to the fine-scale instability. The fine-scaleinstability is the instability from the systems on a spatial scale of less than 2 km. The instability was calculated based on moving-average results of the towerobservations. As stated in the scale analysis section4. 3, the 5- and 10-min moving averages provided themesoscale or coarser scale structures, while the 1- and 2-min moving averages provided the structures withhorizontal scales of less than 2 km, i. e., fine scale. As the tower is static, the structures of a gust frontpassing directly over the tower would be free from thegust front propagation effect. Removing the high frequency perturbation components would also removethe acoustic wave.

To calculate the fine-scale instability, the equations of perturbation are first examined, which arewritten as

where u is tangential to the propagation direction ofthe gust front, and v is radial. By separating the radial and tangential parts from the equations and calculating the momentum and kinetic perturbation, wecan obtain the distribution of perturbation within thehead region. As our focus is on the fine-scale instability, we use the 1-min data to perform the calculation and the results are shown in Figs. 13 and 14. Figure 13 shows that the tangential perturbation tends to propagate more in the rear part of the head, stretchingbackward and out of the head region. Although themomentum transfix seems to be complex, the kineticenergy transfix only concentrates on a belt from thecirculation belt in the head up to a higher backwardregion. The perturbation tends to propagate to theleft of the gust front, with nearly no energy transfix tothe right. While the radial perturbation is weaker and mainly within the head, it overlaps with the internalhorizontal vorticity maximum regions, which meansthat the radial perturbation is mainly due to the finescale internal circulations, and is the cause of the vertical instability and high-frequency waves within thehead region.

Fig. 13. The tangential perturbation of 1-min average data:(a)momentum and (b)kinetic energy.
Fig. 14. The radial perturbation of 1-min average data:(a)momentum and (b)kinetic energy.
5. Discussion

From the observation analysis presented in thispaper, we can provide a fine-scale structural model ofthe studied gust front; in particular, this is a model ofthe gust front without a surge. Figure 15a is the st and ard gust front model(based on tower observations atTianjin on 22 June 2004; Quan, 2013), which shows asimilar internal pattern as the case in this paper, withonly a more buoyant environment, in which the surgesection of the gust front is obvious. The fine-scale circulation at the low levels of the head propagates fromthe end of the head, both forward to the frontal zone and backward. The forward propagation creates aseries of positive radial horizontal vorticities, and thebackward propagation creates a series of negative ones, similar to the circulations generated by the backflow. The frontal zone shows a distinguishable gravity current pattern, while a shallow updraft rising betweenthe kinetic and thermal fronts runs past the thermalfront and merges with the main updraft behind thethermal front, and the two updrafts are different inintensity. Because of this, a negative radial horizontal vorticity forms between the two updrafts, wherethe relative minimum wind speed occurs within thestrong wind zone. The surge is caused by the K-Hwave's backward propagation and duplicates the pattern of the head, and only the intensity is weaker.

Fig. 15. Fine-scale structural model of a gust front:(a)st and ard gust front with a surge and (b)gust front without asurge. The straight-line wind zone in(b)is shattered.

Figure 15b provides the structure when the gustfront lacks a surge part, due to environmental lowvertical wind shear that prevents the propagation ofthe K-H wave. As the energy cannot propagate out, it intensifies the downdraft at the rear of the head, which provides a semi-downburst structure(Jarvi et al., 2007), thus increasing the wind speed at the rearpart and the internal circulation. Furthermore, as thesemi-downburst is more affected by the turbulence, the straight-line wind zone is more shattered. On theother h and , as the downdraft intensity increases, thewhole circulation at the head is also magnified, meaning that the updraft before the head is also intensified. With the strong mid-level vertical wind shear, a subgenerated convective cell develops, and the downdraftfrom the cell also contributes to the downdraft at therear of the head. 6. Conclusions

In this study, the mesoscale background and meso- and fine-scale internal structures of a gust frontwere examined. The distribution and intensity of thestraight-line wind zones were associated with all of thestructures, yet their functions differed. The synopticscale and mesoscale surface and sounding observationscould barely capture the gust front itself, but succeeded in providing the background that may havedetermined the possible relevant systems and propagation pattern of the gust front and its mesoscale shape. Environmental parameters, especially Ri, determinedthe propagation of the K-H wave. As the momentum and energy failed to propagate out, they intensified atthe rear of the head section of the gust front and produced stronger horizontal winds than a classical gustfront.

By using scale analysis, the fine-scale structureswere separated from the mesoscale structures. Someof these structures, as they generated the convectivecell, could be identified from radar observations, butmore detailed structures were revealed by the towerobservations.

Beside the classical mesoscale structures within agust front, which were shown based on the 5-min averaged data, the fine-scale structures were also revealedfrom the 1-min averaged observations, and these finescale structures were strongly affected by turbulencebut were not dominated by r and om effects. A minor updraft existed between the kinetic and thermalfronts, generating a relatively negative radial circulation with the main updraft after the thermal front dueto the low intensity of the minor updraft. The horizontal wind speed reduced at the location of this negativecirculation, and thus split the straight-line wind zoneinto two. As the flow formed, the head downdraftsat the back of the head triggered formed a series ofcirculations propagating forward and backward. Theforward-propagating circulations were positive and thebackward circulations were negative; plus, they weresimilar to the structures generated in a downburst asthe flow reached the surface, and some of them wereeven identified as downbursts. This suggests the general existence of intense horizontal wind shear at theback of the head of the gust front.

With the calculation of fine-scale instability, thetendency of instability propagating tangentially wasobserved, which was significant with the time scale of1 min(whose spatial scale, according to the propagation speed, was roughly less than 1 km). The modelof Weckwerth and Wakimoto(1992)on the tangentialpropagation within a gust front concerns the generation of new cells of fl-mesoscale, while the observationof tangential instability in the present study was ofa finer scale. Such a phenomenon will be discussedin more detail in a numerical simulation study of thesame case in future.

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