A Diagnostic Study of an Explosively Developing Extratropical Cyclone and an Associated 500-Hpa Trough Merger

2310 MONTHLY WEATHER REVIEW VOLUME 129

A Diagnostic Study of an Explosively Developing Extratropical Cyclone and an Associated 500-hPa Trough Merger

JENNIFER L. S. STRAHL* AND PHILLIP J. SMITH Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana

(Manuscript received 7 August 2000, in ®nal form 16 March 2001)

ABSTRACT This paper presents a diagnosis of an explosively developing cyclone (1.3 Ber) that occurred in conjunction with a 500-hPa synoptic-scale trough merger over the eastern United States in November 1999. The explosive development occurred in response to cyclonic vorticity and warm air advections that maximized in the 250± 200-hPa layer and latent heat release. Explosive development commenced 12 h before trough merger began and then accelerated through the 12-h merger period. During merger, development was enhanced by increased warm air advection above 300 hPa and reduced adiabatic cooling. Finally, comparison of this case with other explosive cyclogenesis±trough merger cases suggests that at the synoptic scale trough merger is an evolutionary process that requires as little as 12 h to complete and that, although trough merger is not required to initiate explosive cyclogenesis, the occurrence of merger can be expected to increase the development rate.

1. Introduction (1990) suggests that trough mergers are associated with surface cyclogenesis, that this cyclogenesis is often ex- It is well known that inclement weather in midlati- plosive, and that the merger usually occurs 12 to 48 h tudes is often associated with deep extratropical cyclone prior to the time of minimum cyclone central pressure. systems. Therefore, it is not surprising that such systems Of the 21 merger cases they examined, only one was have been extensively researched since the nineteenth associated with a weakening cyclone and only two ex- century (see reviews by Kutzbach 1979; Hoskins 1990; hibited minimum cyclone pressures concurrent with Newton 1990; Uccellini 1990; Bosart 1999; Volkert merger, one an explosive developer, one not. It is this 1999). From all of this it has become clear that extra- latter, rarer circumstance that is the subject of this paper, tropical cyclones evolve in various ways, very often in in which a case of explosive cyclone development that association with baroclinic zones and upstream upper- occurred over the United States in November 1999 in level jet streams and troughs, all of which are under- association with a 500-hPa trough merger is examined. going their own evolution. Note that, as for most of the background trough merger Much contemporary research has focused on the ``ex- studies cited, this paper examines only the synoptic- plosively developing'' variety of extratropical cyclones scale features of the merger. (Sanders and Gyakum 1980; Uccellini 1990), shorter- wave upper-level troughs known as mobile troughs (Sanders 1988; Lefevre and Nielsen-Gammon 1995; 2. Data and methodology Nielson-Gammon and Lefevre 1996), and trough merg- a. Data ers (Lai and Bosart 1988; Gaza and Bosart 1990; Hakim et al. 1995, 1996; Dean and Bosart 1996). Of particular North American surface station reports and rawin- interest relative to the present paper are the relationships sonde reports comprise the data for this case study. For between trough merger and surface cyclogenesis con- the period examined, pertinent variables were extracted tained in the latter papers. from the 0000 and 1200 UTC surface and upper-air The limited climatological study by Gaza and Bosart reports, including pressure, geopotential height, temperature, and wind speed and direction. In addition, sea level pressure at 0000, 0600, 1200, and 1800 UTC and * Current af®liation: SAIC, Monterey, California. 6-h accumulated precipitation amounts from U. S. stations at 0000 and 1200 UTC were retrieved from surface reports. Precipitation data were not available from Ca- Corresponding author address: Prof. Phillip J. Smith, Department of Earth and Atmospheric Sciences, Purdue University, 1397 Civil nadian stations. This, however, did not affect the di- Engineering Building, West Lafayette, IN 47907-1397. agnosis during explosive cyclone development. E-mail: [email protected] Data from all reported levels were interpolated lin-

᭧ 2001 American Meteorological Society

Unauthenticated | Downloaded 10/01/21 04:41 PM UTC SEPTEMBER 2001 STRAHL AND SMITH 2311 early in ln(p) to yield data in 50-hPa intervals from strophic vorticity on an isobaric surface as a function 1050 to 50 hPa. Winds below the ground were set to of explicit dynamic and thermodynamic forcing mech- zero. Geopotential heights were calculated from the anisms at all levels of the atmosphere. Introduced in hypsometric relationship and the interpolated tempera- quasigeostrophic form by Zwack and Okossi (1986), a tures. Below-ground temperatures were calculated as- generalized form of the equation was developed by suming a lapse rate of 6.5ЊCkmϪ1. Lupo et al. (1992), as well as a simpli®ed form, known as the ``extended'' form, appropriate for synoptic-scale diagnoses. This simpli®ed form of the equation neglects b. Surface cyclone dynamics forcing that is largely subsynoptic in space and time. In addition, frictional effects have been neglected due to This study employs the Zwack±Okossi (Z±O) equa- the dif®culty of accurately capturing effects of friction tion as the primary diagnostic tool for assessing cyclone with routine station observations. The resulting extend- dynamics. This equation describes changes in geo- ed Z±O equation is

␨ ppplllRQdpÇץ gl 2 (١T ϩϩS␻ dp, (1 ´ ١␨a dp Ϫ PD ٌϪV ´ ϭ PD ϪV tfcp͵ ͵͵ pץ ppp΂΃ tt[] (A) (B) (C) (D)

where pl is the near-surface pressure level, pt the upper stability, S, is combined with vertical motion in this pressure level (50 hPa), ␨gl the near-surface geostrophic term, the opposition to development decreases, and thus vorticity, ␨a the absolute vorticity (␨ ϩ f ), f the Coriolis development is enhanced, for less stable air. parameter, R the dry air gas constant, V the horizontal All data analysis and Z±O equation calculations fol- Ç wind vector, Q the diabatic heating/cooling rate, cp the low the procedures described in Rolfson and Smith speci®c heat at constant pressure, S the static stability (1996). Refer to that paper for details. The analysis do- p), where ␪ is potential main is a 25 by 17 grid with 230-km grid spacing inץ/␪ץ)(parameter (S ϭϪ(T/␪ temperature), ␻ the vertical motion in isobaric coordi- the x and y directions, encompassing the continental United States (Fig. 1). Output is displayed on the 21 by nates (␻ ϭ dp/dt), and PD ϭ 1/(pl Ϫ pt). The dynamic forcing term in (1) is term A, which 13 interior grid shown in Fig. 1. The gridding scheme represents the effect of horizontal vorticity advection on used in translating the sounding data to grid point values the geostrophic relative vorticity tendency. This term is a two-pass Barnes objective analysis (Barnes 1964, describes the adjustment of the mass ®eld to the chang- 1973). Vertical velocities at the grid points were cal- ing wind ®eld as represented by vorticity changes. culated using the omega equation in extended form, Terms B and C represent the effects of horizontal namely, temperature advection and diabatic heating on geo- ץf 22 strophic relative vorticity, respectively. The combined ٌϩ2 (␨ ϩ f ) ␻ p2ץ interior integral and inverse pressure weighting result ΂΃␴ in greater weight being given to temperature changing RRQÇ ץ f processes that occur lower in the troposphere (Rausch 2 2 (١T) Ϫٌ . (2 ´ ١␨a) ϩٌ(V ´ ϭ (V p ␴p ␴pc΂΃pץ and Smith 1996), while the Laplacian operator indicates ␴ the importance of the horizontal distribution (Smith This form of the omega equation is nearly identical in 2000). In contrast to the dynamic forcing, the thermo- form to the quasigeostrophic (QG) omega equation giv- dynamic terms describe the adjustment of the wind ®eld en in Holton (1992, 166±170). The primary differences to the changing mass ®eld. are the inclusion of diabatic heating and reliance on the Term D represents the effect of adiabatic temperature extended equation approach (Tsou et al. 1987). The ex- change on geostrophic vorticity. Upper-level divergence tended equations [(1) and (2)] are the same as the cor- (convergence) patterns initiated by cyclonic (anticy- responding QG equations except that the geostrophic clonic) vorticity advection and nonuniform heating winds and relative vorticity and isobarically constant (cooling) also result in upward (downward) motion. static stability in the latter are replaced by analyzed This upward (downward) motion results in adiabatic winds and vorticity and variable static stability. cooling (warming), which yields vorticity and height Diabatic heating was assumed to be solely latent heat changes that are usually of opposite sign to those of release, calculated from the 6-h precipitation rates. The terms A, B, and C. Therefore, term D often opposes the scheme for vertically distributing the latent heat release development prescribed by the other terms. Since static is described in full in Rolfson and Smith (1996); it yields

Unauthenticated | Downloaded 10/01/21 04:41 PM UTC 2312 MONTHLY WEATHER REVIEW VOLUME 129 heating maxima at or near 700 hPa for grid points in the eastern portion of the United States and Canada. Horizontal derivatives were calculated using fourth-order ®nite differencing at grid points within and along the display domain box of Fig. 1. Second-order ®nite differencing was used to determine the horizontal derivatives at points one grid point out from the indicated box. Vertical derivatives were computed using second- order differencing, and vertical integrals were obtained using the trapezoidal rule. The Z±O computations produce instantaneous geostrophic vorticity tendency values on isobaric surfaces. Subsynoptic-scale noise that occurs in the vorticity tendency calculations was reduced using a Shapiro (1970) ®lter that removes signals at wavelengths less than 1000 km and retains 90% of signals with wavelengths greater FIG. 1. Total computational domain and gridpoint distribution. than 2000 km. The vorticity tendency values were then Display domain indicated by interior box. relaxed to produce height tendencies on the near-surface pressure level. Past 6-h observed sea level pressure 3. Synoptic discussion changes, converted to height change, were used as the The case study commenced at 0000 UTC 1 November lateral boundary condition. Surface pressure tendencies 1999 (Fig. 2). At this time the upper-air ¯ow was char- were obtained from the height tendencies on the near- acterized by two short-wave trough features, one near surface pressure level (usually 950 hPa) using the hyp- the United States±Canada border through Alberta and sometric relationship. the other a closed cyclone at both 500 and 200 hPa in To assess the performance of the Z±O equation, the northeastern Texas, conforming to the initial trough surface pressure tendencies computed as described were merger conditions speci®ed by Gaza and Bosart (1990). compared to the observed sea level pressure tendencies. Both troughs contained pronounced jet streaks east of Observed tendencies are 6-h backward differences in the trough axes with 200-hPa wind speeds in excess of sea level pressure. Correlation coef®cients and mean 45msϪ1. At the surface both wave features were as- absolute values (MAV) over the entire domain were sociated with cyclones, a well-de®ned one to the north calculated for each analysis time in order to quantita- with a 1003-hPa central pressure and a weak, incipient tively compare observed and Z±O ®elds. Correlation 1016-hPa disturbance to the south. It is this latter cy- coef®cients were calculated in order to analyze com- clone that is of primary interest in this study. Note the parability between patterns of the ®elds; MAVs were accumulated precipitation with a 15-mm maximum computed in order to compare magnitudes of the two northeast of the Texas disturbance. ®elds. By 1200 UTC 1 November (Fig. 3), pressures had dropped in both cyclones as they moved eastward, with the lowest sea level pressure reaching 996 and 1014 c. Trough merger diagnosis hPa, respectively. At both 500 and 200 hPa, the Alberta trough began to increase in amplitude as it dipped into Geostrophic absolute vorticity (GAV) at 500 hPa is the Dakotas, and the southern cut-off feature moved to the primary diagnostic tool used to document the syn- the east, with the 200-hPa jets remaining east of the optic-scale wave merger, given by troughs. Central height values decreased at 500 hPa and increased at 200 hPa. The 6-h precipitation totals over 2 -p␾ 15 mm were still located northeast of the southern cyٌ GAV f, (3) ϭϩ clone, which was now located on the Louisiana±Ar- f o kansas border. where ␾ is the geopotential. GAV is an effective tracer Over the next 12 h, the central pressure of the south- of upper-level wave evolution and can reveal subtle ern cyclone continued to decrease to 1009 hPa as it properties about this evolution that may not be seen in drifted into central Mississippi (Fig. 4). The southern the height ®eld. In (3), the two right-hand-side terms 500-hPa trough moved eastward slowly, trailing the sur- are geostrophic relative vorticity (GRV) and Coriolis face low pressure center, as the trough wavelength de- parameter. The Laplacian of the height ®eld required creased and the cut-off low began to open over Mis- for GRV was calculated on the 450-, 500-, and 550-hPa sissippi. The northern trough amplitude continued to levels using fourth-order ®nite differencing. Then the increase as it extended into the central United States by GRV values at each level were averaged to obtain a this analysis time. At 200 hPa, the formerly cut-off layer average GRV. height center was only visible as an open short-wave

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FIG. 2. 0000 UTC 1 Nov 1999 (a) sea level pressure (solid, hPa) FIG. 3. As in Fig. 2, except for 1200 UTC 1 Nov 1999. and 6-h accumulated precipitation (dashed, mm), (b) 500-hPa geopotential height (solid, gpm) and absolute vorticity (dashed, 10 Ϫ5 sϪ1), and (c) 200-hPa geopotential height (solid, gpm) and wind speeds (dashed, m sϪ1). experienced by the combined trough system is much like that documented by Gaza and Bosart (1990) and Dean and Bosart (1996). In a similar fashion to the 200- feature over Mississippi. Wind speeds at 200 hPa at this hPa pattern at the prior analysis time, the original cut- time show the southern surface cyclone in the entrance off 500-hPa height center becomes embedded in the region of a 54 m sϪ1 jet streak. Additionally, over 25 circulation of the northern trough, suggesting the be- mm of precipitation fell over the surface cyclone. ginning of a wave merger, but was still visible as a short- By 1200 UTC 2 November (Fig. 5), both 500 and wave feature over Tennessee. Two distinct 500-hPa cy- 200 hPa show a distinct, high-amplitude trough stretch- clonic vorticity centers were still evident at this level, ing into the Gulf of Mexico. The amplitude increase one with the larger-scale trough, and another with the

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FIG. 4. As in Fig. 2, except for 0000 UTC 2 Nov 1999. FIG. 5. As in Fig. 2, except for 1200 UTC 2 Nov 1999. short-wave feature. The 200-hPa height ®eld shows a western New York with a central pressure of 984 hPa. single wave feature extending across the United States. Over the preceding 24-h period, the cyclone had de- Widespread precipitation encircled the surface low pres- veloped explosively at a rate of 1.3 Ber. By 0000 UTC sure center as it traveled along the slopes of the Ap- 3 November (Fig. 6), the 500-hPa trough was a single palachian Mountains. The central pressure decreased to entity with a closed low center and a single cyclonic 1000 hPa, a 12-h decrease of 9 hPa. vorticity maximum, having experienced height falls and Extensive precipitation continued to surround the sur- vorticity increases from 12 h earlier. The fact that the face cyclone by 0000 UTC 3 November (Fig. 6). The two branches of the ¯ow had merged into one, that the greatest accumulations were located directly over the relative vorticity centers of the two branches exceeded surface cyclone, which by this time was located in far 5 ϫ 10Ϫ5 sϪ1, and that the two vorticity centers had

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FIG. 6. As in Fig. 2, except for 0000 UTC 3 Nov 1999. FIG. 7. As in Fig. 2, except for 1200 UTC 3 Nov 1999. become one satis®es the remaining merger criteria of By 1200 UTC 3 November (Fig. 7), the surface cy- Gaza and Bosart (1990). Thus, the synoptic-scale merg- clone, located on the Quebec±Ontario border, had ex- er that began 12 h earlier appears to be completed by perienced a pressure rise to 989 hPa, while the upper- this time. Heights also began to fall at 200 hPa over level heights continued to fall at both 500 and 200 hPa. most of the eastern United States. Trough propagation Furthermore, the upper-level troughs exhibited the neg- at this level continued to be slow. A jet streak at 200 ative tilt seen in Gaza and Bosart (1990), Hakim et al. hPa was located in Quebec, with the cyclone located in (1995), and Dean and Bosart (1996). However, in the the left entrance region. On the back side of the trough present case the negative tilt occurred after surface de- system, a signi®cant digging jet streak was poised to velopment, whereas in the three cited cases it occurred aid in intensifying the upper trough. during surface development.

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Ocean in Figs. 6±8 are artifacts of the objective analysis rather than real features. Fortunately, these analysis ¯aws do not in¯uence the discussion that follows. Figure 9 summarizes the central sea level pressure and track of the southern cyclone. Pressures declined from 0000 UTC 1 November until 0000 UTC 3 No- vember as the cyclone moved ®rst eastward and then northward along the Appalachian Mountains. Explosive development occurred from 0000 UTC 2 November through 0000 UTC 3 November (25 hPa, or 1.3 Ber), with the most rapid pressure decrease occurring during the last 6 h of that period (9 hPa). Although much weaker, this case is in many ways reminiscent of the Cleve- land superbomb case reported by Hakim et al. (1995, 1996). More will be said about this similarity in sub- sequent discussions.

4. Trough merger diagnosis The synoptic discussion suggests that the synoptic- scale trough merger occurred over a 12-h period, 1200 UTC 2 November±0000 UTC 3 November, as the 500- hPa southern trough became assimilated into the amplifying northern trough. This process is further examined in this section using GAV ®elds for the period 1200 UTC 2 November±0000 UTC 4 November (Fig. 10). At 1200 UTC 2 November (Fig. 10a) the GAV ®elds associated with the amplifying northern trough and the approaching southern trough are clearly evident, with the northern maximum being about 15% larger than the southern. By the end of the 12-h merger period (0000 UTC 3 November, Fig. 10b) a single prominent GAV maximum is seen. However, note the axis of larger GAV values that extends east±west from Maryland and Del- aware through southern Pennsylvania. A hint of this feature is also seen in the accentuated cyclonic curvature that appears in the same location in the 500-hPa analysis (see Fig. 6b). If this feature represents the southern trough moving northward as it rotates cyclonically around the amplifying northern trough, then it is possible that the two trough features may have experienced a close approach, much as described by Hakim et al. (1996), rather than a complete merger at this time. De- tection of such a close approach for the Cleveland su- FIG. 8. As in Fig. 2, except for 0000 UTC 4 Nov 1999. perbomb case required an examination of a relatively high-resolution (1Њϫ1Њ) analysis set (Hakim et al. 1996). Therefore, con®rmation of this possibility for this The system began to occlude by 0000 UTC 4 No- case would require a similarly higher-resolution analysis vember (Fig. 8), and 12 h later (not shown) the system set. was vertically stacked from the surface to 200 hPa. Both By 1200 UTC 3 November (Fig. 10c), the GAV max- the surface and upper-level cyclones had moved into imum had moved eastward and had assumed the neg- Quebec. The 500-hPa heights continued to fall, while ative tilt evident in the height ®eld. Finally, the GAV sea level pressures leveled off with the lowest value of maximum moved into Quebec by the last map time (Fig. 988 hPa found in south-central Quebec. 10d). These latter GAV ®elds suggest that complete It should be noted that in view of the absence of merger may not have occurred until sometime during upper-air data over the water, the exaggerated troughs this last 12-h period. However, even though the close over the Gulf of Mexico in Figs. 3±6 and the Atlantic approach mentioned above may have occurred, since

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FIG. 9. (a) Cyclone central sea level pressure (hPa), and (b) cyclone track.

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FIG. 10. 500-hPa geostrophic absolute vorticity at (a) 1200 UTC 2 Nov 1999, (b) 0000 UTC 3 Nov 1999, (c) 1200 UTC 3 Nov 1999, and (d) 0000 UTC 4 Nov 1999. the two troughs are ®rst combined into one synoptic- in an upper-level trough that is more intense than the scale GAV maximum at 0000 UTC 3 November, this two precursor troughs, as suggested in Dean and Bo- will be regarded as the time of synoptic-scale merger sart's (1996) climatology. However, this greater inten- completion. sity may not be maintained; for this case, after merger A summary of the intensity change of the troughs the single trough ®rst weakened and then strengthened during merger can be seen in Table 1. At the completion again. of merger (0000 UTC 3 November) the total GAV shows a value that is larger than occurred in the two separate troughs 12 h earlier. This single maximum then de- 5. Surface cyclone dynamics creased before increasing markedly over the last 12 h. a. Comparison of Z±O and observed pressure All of this con®rms that merger can be expected to result tendencies Statistical comparisons of the observed sea level pres- TABLE 1. GAV maxima and 12-h change (⌬A) for the northern, sure changes and Z±O pressure tendencies are presented southern, and merged troughs. Units: 10Ϫ5 sϪ1. in Table 2. These results indicate that the two ®elds Time have correlation coef®cients between 0.80 and 0.93, (UTC)/ with an average correlation of 0.87. This indicates very Date (Nov) Northern (⌬A) Merged (⌬A) Southern good comparability between the patterns of both ®elds. 1200/2 24.7 23.4 To compare the magnitudes of the observed and Z±O 0000/3 (ϩ7.3) 32.0 (ϩ8.6) pressure tendency ®elds the mean over all grid points 1200/3 (Ϫ5.7) 26.3 (Ϫ5.7) of the absolute values of tendencies were calculated. 0000/4 (ϩ19.7) 46.0 (ϩ19.7) The differences between the MAV of each ®eld ranges

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TABLE 2. Mean absolute values [MAV, hPa (12 h)Ϫ1] and correlation coef®cients for each analysis time. Difference represents the per- centage difference between observed and Z±O MAV{[(MAVObs Ϫ

MAVZ±O)/MAVObs] ϫ 100}. MAV MAV Difference Correlation Analysis time Z±O Obs (%) coef®cient 0000 UTC 1 Nov 3.58 6.17 42 0.90 1200 UTC 1 Nov 3.96 4.77 17 0.92 0000 UTC 2 Nov 5.51 6.08 9 0.93 1200 UTC 2 Nov 6.70 5.09 Ϫ32 0.82 0000 UTC 3 Nov 5.72 7.31 22 0.80 1200 UTC 3 Nov 5.66 3.73 Ϫ52 0.85 Case average 5.19 5.53 6 0.87 between a 42% smaller to a 52% larger calculation by the Z±O equation over observed pressure change. For the entire case study, the average difference between observed and Z±O ®elds, however, is only 6%. Fur- thermore, casual examination suggests that Z±O pressure tendencies compare most closely with observed pressure changes around the surface cyclone, the most important portion of the ®eld. Sea level pressure, Z±O pressure tendencies, and observed 6-h pressure change ®elds for the maptimes with the highest (0000 UTC 2 November) and lowest (0000 UTC 3 November) correlations are shown in Figs. 11 and 12, respectively. At both times the Z±O tendency ®elds reasonably re¯ect the negative and positive pressure tendencies corresponding to the cyclone and the following anticyclone. On 2 November (Fig. 11), the beginning of the explosive development period, the surface cyclone was located very close to pressure tendency minimum. As development progressed, however, the surface cyclone moved closer to the zero isopleth (0000 UTC 3 November, Fig. 12). b. Individual forcing mechanisms The contributions of individual, vertically integrated terms in (1) to the total near-surface geostrophic vorticity tendency are represented in Figs. 13±17. While for total ®elds pressure tendencies were displayed in the previous section, individual terms must be represented by vorticity tendencies because appropriate boundary conditions are not available to allow them to be relaxed FIG. 11. 0000 UTC 2 Nov 1999 (a) sea level pressure (hPa), (b) to pressure tendencies. Z±O near-surface pressure tendency [hPa (12 h)Ϫ1], and (c) observed The contribution of horizontal vorticity advection to sea level pressure change over preceding 6 h [hPa (12 h) Ϫ1]. the near-surface geostrophic vorticity tendency is shown in panel (a) of Figs. 13±17. For the early times (Figs. 13a and 14a), the strongest positive tendency maximum cut-off low opened up and the merger process began occurred ahead of the northern trough, while a second- (Fig. 16a), and it remained a single tendency feature as ary tendency maximum was located over the Gulf of merger was completed (Fig. 17a). During the entire pe- Mexico ahead of the cut-off low feature at upper levels. riod, the surface cyclone was persistently located in an Throughout all map times, a negative vorticity tendency area of vorticity increases by integrated vorticity ad- area is seen behind the trough features. At 0000 UTC vection. 2 November (Fig. 15a), a tendency maxima was located Panel (b) of Figs. 13±17 illustrates near-surface geo- ahead of each trough. Over the next 12 h, these maxima strophic vorticity tendencies forced by vertically inte- evolved into one broad positive tendency area as the grated horizontal temperature advection. As with the

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(0000 UTC 3 November, Fig. 17b), negative vorticity tendencies overtook the cyclone from the southwest. The contribution of vertically integrated latent heat release to near-surface geostrophic vorticity tendencies is shown in panel (c) of Figs. 13±17. Maximum vorticity tendencies associated with latent heat release ahead of or over the surface cyclone are seen at most map times. The most notable exception is at 1200 UTC 2 November, when the maximum lagged the cyclone. These maxima coincide with the local precipitation maxima seen in Figs. 2±6a and are generally located no more than two grid points from the surface cyclone during cyclone strengthening (Figs. 13±17c). Panel (d) of Figs. 13±17 shows the effect of vertically integrated adiabatic temperature change on near-surface geostrophic vorticity tendencies. This term generally opposes development forced by the other terms. Therefore, the surface cyclone was consistently within negative vorticity tendencies throughout development. During early development, the negative vorticity tendencies forced by this term strongly resemble the positive tendencies by latent heat release and temperature advection, suggesting that these two terms had dominant in¯uence on the cyclone's upward motions during this period. However, by the last map time the negative adiabatic term values associated with the cyclone were strongly correlated with only the latent heat release term.

c. Forcing at the cyclone center In order to focus on cyclone development, the forcing processes at the cyclone center, qualitatively noted in the previous section, are quantitatively presented in Fig. 18. It is clear from Fig. 18 that the pressure tendency (zopt) was consistently negative and the vorticity tendency (zoto) was consistently positive throughout the case study. The most negative cyclone center Z±O pressure tendencies, Ϫ11.65 and Ϫ11.58 hPa (12 h)Ϫ1, occurred at 0000 and 1200 UTC 2 November, respectively. The combined Z±O pressure fall for the observed explosive development period (0000 UTC 2±3 November) was 23.23 hPa (24 h)Ϫ1, indicating that the Z±O computations prescribe explosive development similar to the observed development (25 hPa pressure decrease). FIG. 12. As in Fig. 11, except for 0000 UTC 3 Nov 1999. The evolution of the individual contributions to the Z±O vorticity tendency is also shown in Fig. 18. As seen in the ®elds over the study domain (Figs. 13±17), the vorticity tendency forced by vorticity advection was vorticity advection term, positive and negative tendency positive at every analysis time, maximizing at the time regions from integrated temperature advection are seen of largest Z±O pressure change, as in Lupo et al. (1992). surrounding the northern trough and the cut-off cyclone The contribution by temperature advection was positive at early analysis times (0000 and 1200 UTC 1 Novem- during the strong development phase (0000 and 1200 ber, Figs. 13b and 14b). The surface cyclone was located UTC 2 November) and negative at analysis times pre- near the zero isopleth in an area of vorticity decreases ceding (1200 UTC 1 November) and at the end of (0000 at 1200 UTC 1 November (Fig. 14b). However, during UTC 3 November) strong development; the change in the strong development phase, the cyclone was in a sign of this term from weaker to stronger development singular area of very high vorticity tendencies (Figs. periods is consistent with the climatological results of 15b and 16b). At the time of minimum surface pressure Rolfson and Smith (1996). Latent heat release was clear-

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FIG. 13. 0000 UTC 1 Nov 1999 contribution to total Z±O near-surface geostrophic vorticity tendency (10 Ϫ9 sϪ2) by (a) horizontal vorticity advection, (b) horizontal temperature advection, (c) latent heat release, and (d) adiabatic temperature change. Surface cyclone position indicated by ®lled circle. ly the dominant intensi®cation mechanism during ex- warm pool of stratospheric air formed behind the surface plosive development (0000 UTC 2±3 November). Cen- cyclone allow for signi®cant warm air advection aloft tral vorticity tendencies by adiabatic temperature change (Hirschberg and Fritsch 1991). At the onset of signi®- consistently opposed the development by the other pro- cant surface development, 0000 UTC 2 November, there cesses. This opposition maximized at 0000 UTC 2 No- was a secondary maximum of warm air advection near vember, the time of maximum Z±O pressure tendency. 800 hPa, a result consistent with those of Lupo et al. Time±pressure cross sections of the physical mech- (1992) and Rolfson and Smith (1996). Cold air advec- anisms responsible for the Z±O vorticity tendencies are tion intruded at lower levels by 0000 UTC 3 November displayed in Fig. 19. These analyses represent values at in a relatively deep layer from 1000 to 400 hPa, which, the cyclone center as it moved across the continent, thus when vertically integrated, forced the vorticity decreases showing the evolution of the forcing mechanisms over due to this term at the cyclone center seen in Fig. 18. the surface cyclone center. The contribution to near- Low-level cold air advection, low-level negative vor- surface geostrophic vorticity increases by horizontal ticity advection, and a decrease in upper-level positive vorticity advection seen in Fig. 18 was a result of cy- vorticity advection all act to terminate the surface in- clonic vorticity advection present throughout much of tensi®cation. the atmosphere above the surface cyclone. Horizontal The Rolfson and Smith (1996) procedure forces latent vorticity advection maximized at the midpoint of the heat release to maximize at or near 700 hPa, as re¯ected explosive development period and typically at 250 hPa in Fig. 19c. Little or no latent heat release took place (Fig. 19a). at the cyclone center at early analysis times, while sig- Horizontal temperature advection (Fig. 19b) at the ni®cant heating occurred later in the event. The pro- cyclone center was typically positive above 500 hPa, nounced heating at 0000 UTC 2 and 3 November was maximizing at the end of explosive development, and a result of the maximum in the heating ®eld occurring if varied between positive and negative values at lower directly over the cyclone center (see Figs. 4a and 6a). levels. Similar to vorticity advection, the maximum At 1200 UTC 2 November, the maximum precipitation warm air advection occurred at 200 hPa. Near the tro- was shifted away from the cyclone center (see Fig. 5a). popause, strong advecting winds and the relatively Finally, the component parts of the adiabatic tem-

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FIG. 14. As in Fig. 13, except for 1200 UTC 1 Nov 1999.

FIG. 15. As in Fig. 13, except for 0000 UTC 2 Nov 1999.

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FIG. 16. As in Fig. 13, except for 1200 UTC 2 Nov 1999.

FIG. 17. As in Fig. 13, except for 0000 UTC 3 Nov 1999.

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FIG. 18. Contributions at the surface cyclone center by horizontal vorticity advection (vadv), horizontal temperature advection (tadv), latent heat release (lath), and adiabatic temperature change (adia), to the total Z±O geostrophic vorticity tendency (zoto, 10Ϫ9 sϪ2) and the resulting Z±O near-surface pressure tendency [zopt, hPa (12 h) Ϫ1]. perature change term are examined in Figs. 19d±f. The motion aloft. During the rest of the development, ver- cross section of vertical motion, ␻, is displayed in Fig. tical motions were upward at all levels over the cyclone 19d. At early analysis times, there was downward mo- center, maximizing in the midtroposphere. Vertical motion in the lower half of the troposphere and upward tion was strongest at the beginning of explosive devel-

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FIG. 19. Time±pressure cross sections of (a) horizontal vorticity advection (10 Ϫ9 sϪ2), (b) horizontal temperature advection (10Ϫ4 KsϪ1), (c) latent heat release (10Ϫ4 KsϪ1), (d) vertical motion (10Ϫ3 hPa sϪ1), (e) static stability (10Ϫ3 KPaϪ1), and (f) adiabatic temperature change (10Ϫ4 KsϪ1). opment (0000 UTC 2 November) at 650 hPa, dimin- with time. Gaza and Bosart (1990) suggest that the latter ished, and then maximized again 24 h later at 550 hPa. is a possible result of trough merger. The shallow layer The static stability S was generally greater than zero, of negative static stability air near the surface at 0000 showed little change with pressure in the troposphere, UTC 3 November occurred when the cyclone was lo- and increased with decreasing pressure in the strato- cated in the Appalachians; thus, that layer represents sphere (Fig. 19e). Further, in contrast to the results of below-ground pressure levels. These two components, Smith and Tsou (1988), tropospheric S values decreased stability and vertical motion, compose the adiabatic

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TABLE 3. Cyclone central sea level pressure during explosive de- difference occurs in the time of maximum 500-hPa in- velopment (ps, hPa) and 500-hPa trough merger beginning (MB) and tensity. Hakim et al. (1995) identify maximum 500-hPa completion (MC) dates for 1) this study and for case studies reported by 2) Gaza and Bosart (1990), 3) Hakim et al. (1995), and 4) Dean intensity for the Cleveland superbomb case at 1200 UTC and Bosart (1996). 25 January, 24 h before the time of minimum cyclone pressure. In contrast, maximum 500-hPa intensity for 1) Time (UTC)/ 2) Time (UTC)/ Date (Nov 1999) ps Date (Feb 1976) ps the present case occurred at 0000 UTC 4 November, 24 h after the time of minimum cyclone pressure. 00/02 1009 00/01 1007 Returning to the Z±O results previously discussed, 06/02 1003 12/01 MB 1000 12/02 MB 1000 00/02 MC 986 one can explore the extent to which trough merger in- 18/02 993 12/01 964 ¯uenced the cyclone's dynamics. Focusing on the trough 00/03 MC 984 merger subperiod during which the cyclone underwent 3) Time (UTC)/ 4) Time (UTC)/ its strongest development (1200 UTC 2 November± Date (Jan 1978)* ps Date (Jan 1978)** ps 0000 UTC 3 November), it is apparent that the inten- 18/25 994 00/08 1005 sifying upper trough (see Figs. 10a and 10b and Table 00/26 MB 983 00/09 A/B MB 994 1) was accompanied by some reduction in cyclonic vor- 06/26 962 12/09 A/B MC, A/B/C MB 974 ticity advection but an increase in warm air advection 12/26 MC 955 00/10 A/B/C MC 964 above 300 hPa (see Figs. 19a and 19b). The former may 12/10 956 have been caused by the late intensi®cation of the upper * Refers to Hakim et al.'s (1995) cyclone C. trough, while the latter may have occurred as the stron- ** A, B, C refer to three troughs identi®ed in Dean and Bosart ger stratospheric warm pool that would be expected in (1996). the stronger northern trough extended southward with the trough as it merged with the southern trough. Failure of either advection term to force sea level pressure term. The cross section of this term (Fig. 19f) is very changes that approach those of the Cleveland super- much like that of ␻. Therefore, early analysis times bomb may have occurred because of 1) the advection show adiabatic warming at lower levels and adiabatic of anticyclonic vorticity and cold air into the maturing cooling aloft, while at the remaining times adiabatic cyclone below 500 hPa, and 2) the exceptionally strong cooling that maximized in the midtroposphere prevails. northern trough that occurred in the Cleveland superbomb case. 6. Cyclogenesis and trough merger The increased cyclone development observed during this period was forced by an increased latent heat release A summary of cyclone central pressure during ex- contribution and a decreased magnitude of the adiabatic plosive development and 500-hPa trough merger dates contribution. Comparison of Figs. 16c and 17c reveals for this study and for case studies reported by Gaza and that the former occurred because of a change in the Bosart (1980), Hakim et al. (1995), and Dean and Bosart position of the cyclone center relative to the latent heat- (1996) is given in Table 3. Trough merger is viewed as ing term maximum, not to an increase in the maximum an evolutionary process. The beginning of the process itself. In view of the fact that the latent heating in¯uence at the synoptic scale (MB) is judged to occur, when, in maximized before merger began, it is dif®cult to credit the opinion of the present authors, one trough becomes the merger process to this term's positive contribution. embedded in the circulation of the other trough. This The decreased adiabatic contribution occurred despite occurs in the present case at 1200 UTC 2 November, the fact that the magnitude of the upward motion in- as the southern trough becomes embedded in the south- creased, an increase that was not completely offset by westerly ¯ow of the northern trough. The process is the tropospheric static stability reduction noted in the judged to be completed at the synoptic scale (MC) when previous section. This suggests that the increased adi- a single vorticity center appears. abatic cooling at 0000 UTC 3 November (see Fig. 19f) From this summary one sees that the synoptic-scale assumed a more uniform horizontal distribution around merger was completed 12 h before minimum cyclone the surface cyclone, thus reducing the Laplacian of the pressure was reached in two of the four cases and at quantity and the magnitude of the adiabatic Z±O term the same time as minimum cyclone pressure in the other (see Figs. 16d and 17d). This is illustrated by the 500- two cases, this study and the Cleveland superbomb (Ha- hPa vertical motion ®elds at 0000 UTC 2 November, kim et al. 1995). Further, while these cases reveal that 12 h before merger began, and 0000 UTC 3 November, trough merger was not essential to initiate explosive when merger was completed, in Fig. 20. Although weak- development, merger invariably was associated with er upward vertical motions are in the cyclone region on more rapid pressure decreases during at least a portion 3 November, the difference between the two times is of the 12-h merger period. not suf®cient to account for the substantial decrease in A further comparison of this case and the Cleveland the adiabatic term from 2 to 3 November seen in Fig. superbomb, which are similar in their synoptic evolution 18. Of greater signi®cance is the reduced gradient and but very different in intensity, reveals that a signi®cant curvature in the upward motion ®eld at the latter time.

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Texas trough, experienced a 24-h period (0000 UTC 2 November±0000 UTC 3 November; see Fig. 9a) of explosive development (25 hPa or 1.3 Ber) as it moved northward along the Appalachian Mountains (see Fig. 9b). Explosive development began 12 h before trough merger began and continued until merger was completed. Using the Zwack±Okossi (Z±O) equation (Zwack and Okossi 1986; Lupo et al. 1992) as the diagnostic tool, the explosive development was seen to occur in response to cyclonic vorticity and warm air advections, both of which maximized in the 250±200- hPa layer and prevailed throughout much of the troposphere, and latent heat release, which was the largest contributor to the explosive development (see Figs. 18 and 19a±c). This latter result is very much like that found in the land case reported by Lupo et al. (1992). Explosive development ceased as anticyclonic vorticity and cold air advected into the cyclone center below 500 hPa. The roles played by the various synoptic-scale forcing mechanisms during and at the end of explosive development are consistent with the climatological results of Rolfson and Smith (1996). The only cyclone development forcing term ®elds that appeared to be positively in¯uenced (i.e., resulted in values that enhanced cyclone development) by the merger were increased warm air advection above 300 hPa and reduced adiabatic cooling. Failure of the surface cyclone to react as strongly to the trough merger as did the cases documented by Hakim et al. (1995) and Dean and Bosart (1996) was at least partially due to the early FIG. 20. 500-hPa vertical motion (10Ϫ3 hPa sϪ1) at (a) 0000 UTC introduction of the anticyclonic vorticity and cold air 2 Nov 1999 and (b) 0000 UTC 3 Nov 1999. Surface cyclone position below 500 hPa mentioned above. indicated by ®lled circle. Finally, comparison of this case with those reported by Gaza and Bosart (1990), Hakim et al. (1995), and This, in turn, is consistent with the increased wavelength Dean and Bosart (1996), leads to the following conclu- of the merged wave compared with the premerged sions (see Table 3). southern wave, thus extending the upward motions as- 1) Trough merger can be viewed as an evolutionary sociated with the merged wave more uniformly over the process that commences when one trough becomes cyclone domain. embedded in the circulation of another trough and ends when the two synoptic-scale vorticity maxima 7. Summary and conclusions combine into one. When viewed at the synoptic scale, the approximate period of the merger process, A case of explosive cyclone development that oc- at least for these four cases, is a relatively fast (on curred over the eastern United States in November 1999 synoptic timescales) 12 h. If examined with a higher- in association with a 500-hPa synoptic-scale trough resolution analysis, the two vorticity centers could merger is examined. Using geopotential height and geo- survive longer, thus extending the merger process. strophic absolute vorticity (Holton 1992, 164±165; Ha- 2) Trough merger is not required to initiate explosive kim et al. 1995) as the diagnostic parameters, merger cyclogenesis. However, results for the four cases was judged to occur over a 12-h period (1200 UTC 12 summarized in Table 3 suggest that if merger does November±0000 UTC 3 November; see Figs. 5 and 6b occur, the rate of explosive development could in- and 10a and 10b) as a trough that was propagating east- crease, sometimes markedly, during the merger pe- ward near the United States±Canada border ampli®ed riod. into the midwest and Great Lakes states and joined with a trough moving northeastward out of Texas. Trough merger and postmerger periods were marked ®rst by trough intensi®cation followed by an intensity oscilla- REFERENCES tion (see Table 1). Barnes, S. L., 1964: A technique for maximizing details in numerical The cyclone of interest, originally associated with the weather map analysis. J. Appl. Meteor., 3, 396±409.

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ÐÐ, 1973: Mesoscale objective map analysis using weighted time of cyclone concepts. Extratropical Cyclones: The Erik PalmeÂn series observations. NOAA Tech. Memo. ERL NSSL-62, 60 pp. Memorial Volume, C. W. Newton and E. O. Holopainen, Eds., Bosart, L. F., 1999: Observed cyclone life cycles. The Life Cycles of Amer. Meteor. Soc., 1±18. Extratropical Cyclones, M. A. Shapiro and S. Gronas, Eds., Nielsen-Gammon, J. W., and R. J. Lefevre, 1996: Piecewise tendency Amer. Meteor. Soc., 187±213. diagnosis of dynamical processes governing the development of Dean, D. B., and L. F. Bosart, 1996: Northern Hemisphere 500-hPa an upper-tropospheric mobile trough. J. Atmos. Sci., 53, 3120± trough merger and fracture: A climatology and case study. Mon. 3142. Wea. Rev., 124, 2644±2671. Rausch, R. L. M., and P. J. Smith, 1996: A diagnosis of a model- Gaza, R. S., and L. F. Bosart, 1990: Trough merger characteristics simulated explosively developing extratropical cyclone. Mon. over North America. Wea. Forecasting, 5, 314±331. Wea. Rev., 124, 875±904. Hakim, G. J., L. F. Bosart, and D. Keyser, 1995: The Ohio Valley Rolfson, D. M., and P. J. Smith, 1996: A composite diagnosis of wave-merger cyclogenesis event of 25±26 January 1978. Part I: synoptic-scale extratropical cyclone development over the Unit- Multiscale case study. Mon. Wea. Rev., 123, 2663±2692. ed States. Mon. Wea. Rev., 124, 1084±1099. ÐÐ, D. Keyser, and L. F. Bosart, 1996: The Ohio Valley wave- Sanders, F., 1988: Life history of mobile troughs in the upper west- merger cyclogenesis event of 25±26 January 1978. Part II: Di- erlies. Mon. Wea. Rev., 116, 2629±2648. agnosis using quasigeostrophic potential vorticity inversion. ÐÐ, and J. R. Gyakum, 1980: Synoptic-dynamic climatology of the Mon. Wea. Rev., 124, 2176±2205. ``bomb.'' Mon. Wea. Rev., 108, 1589±1606. Hirschberg, P. A., and J. M. Fritsch, 1991: Tropopause undulations Shapiro, R., 1970: Smoothing, ®ltering, and boundary effects. Rev. and the development of extratropical cyclones. Part II: Diag- Geophys., 8, 359±387. nostic analysis and conceptual model. Mon. Wea. Rev., 119, 518± Smith, P. J., 2000: The importance of the horizontal distribution of 550. heating during extratropical cyclone development. Mon. Wea. Rev., 128, 3692±3694. Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3d ed. ÐÐ, and C.-H. Tsou, 1988: Static stability variations during the Academic Press, 511 pp. development of an intense extratropical cyclone. Mon. Wea. Hoskins, B. J., 1990: Theory of extratropical cyclones. Extratropical Rev., 116, 1245±1250. Cyclones: The Eric PalmeÂn Memorial Volume, C. W. Newton Tsou, C.-H., P. J. Smith, and P. M. Pauley, 1987: A comparison of and E. O. Holopainen, Eds., Amer. Meteor. Soc., 64±80. adiabatic and diabatic forcing in an intense extratropical cyclone Kutzbach, G., 1979: The Thermal Theory of Cyclones: A History of system. Mon. Wea. Rev., 115, 763±786. Meteorological Thought in the Nineteenth Century. Amer. Me- Uccellini, L. W., 1990: Processes contributing to the rapid devel- teor. Soc., 254 pp. opment of extratropical cyclones. Extratropical Cyclones: The Lai, C.-C., and L. F. Bosart, 1988: A case study of trough merger in Erik PalmeÂn Memorial Volume, C. W. Newton and E. O. Hol- split westerly ¯ow. Mon. Wea. Rev., 116, 1838±1856. opainen, Eds., Amer. Meteor. Soc., 81±105. Lefevre, R. J., and J. W. Nielsen-Gammon, 1995: An objective cli- Volkert, H., 1999: Components of the Norwegian cyclone model: matology of mobile troughs in the Northern Hemisphere. Tellus, Observations and theoretical ideas in Europe prior to 1920. The 47A, 638±655. Life Cycles of Extratropical Cyclones, M. A. Shapiro and S. Lupo, A. R., P. J. Smith, and P. Zwack, 1992: A diagnosis of the Gronas, Eds., Amer. Meteor. Soc., 15±28. explosive development of two extratropical cyclones. Mon. Wea. Zwack, P., and B. Okossi, 1986: A new method for solving the qua- Rev., 120, 1490±1523. sigeostrophic omega equation by incorporating surface pressure Newton, C. W., 1990: Erik PalmeÂn's contributions to the development tendency data. Mon. Wea. Rev., 114, 655±666.

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