Cyclolysis: a Diagnosis of Two Extratropical Cyclones

2714 MONTHLY WEATHER REVIEW VOLUME 129

Cyclolysis: A Diagnosis of Two Extratropical Cyclones

WILLIAM E. MORRIS JR.* AND PHILLIP J. SMITH Department of Earth and Atmospheric Sciences, Purdue University West Lafayette, Indiana

(Manuscript received 11 August 2000, in ®nal form 7 May 2001)

ABSTRACT This paper presents a diagnosis of the slow decay of two extratropical cyclones that occurred over the central United States in March and November 1999. Results reveal that vertical superposition of the cyclone and upper- level troughs is not required for cyclone decay to occur. In both cases, decay commenced while the upper-level trough was still upstream from, and thus upper-level cyclonic vorticity was present above, the cyclone. Failure of the upstream tilt in both trough systems to yield cyclone intensi®cation was attributed largely to the advection of cold air, primarily at lower to middle levels, into each cyclone's interior. Also of interest is the fact that latent heat release also contributed to the decay of both cyclones. This latter result was a consequence of the location of the cyclones in the outer portion of their respective heating regions. Finally, more rapid decay of the two cyclones was prevented by middle- and lower-tropospheric adiabatic warming that occurred in the statically stable cyclone interiors.

1. Introduction course, as clouds and precipitation are being formed in the cyclone's ascending motions. This heating acts to Pioneered by nineteenth century work reviewed by enhance the development attributed to the advection Kutzbach (1979) and by the twentieth century contri- processes (e.g., Pauley and Smith 1988; Kuo and Reed butions of Bjerknes (e.g., Bjerkness 1919; Bjerknes and 1988). Solberg 1922), Sutcliffe (e.g., Sutcliffe 1939, 1947), and Petterssen (e.g., Petterssen 1955), a signi®cant body of Uccellini (1990) and Bluestein (1993, 213±214, 290± research has been devoted to understanding the pro- 297) also discuss the advection of stratospheric high- cesses responsible for the genesis of extratropical cy- potential vorticity air over a low-level baroclinic zone clones (hereafter referred to as cyclones). Comprehen- as an alternative mechanism for cyclone development. sive reviews of cyclone studies can be found in Hoskins This high potential vorticity air can act to induce low- (1990), Uccellini (1990), and Bosart (1999). Lupo et al. level cyclonic circulations and/or can enter the tropo- (1992) and Rolfson and Smith (1996) have shown that sphere as a source of absolute vorticity through a fold cyclone development occurs during vertically integrated in the tropopause in the convergent entrance region of horizontal warm air advection and cyclonic vorticity a jet streak (Uccellini et al. 1985). A case study in- advection, usually accompanied by the release of latent volving the interaction between high potential vorticity heat, which typically leads to an increase in surface air from aloft and a low-level baroclinic zone is pre- geostrophic vorticity and a decrease in central sea level sented in Thorncroft and Flocas (1997). pressure. Warm air advection is especially effective In addition to the presence of favorable thermody- when the cyclone lies downstream from a stratospheric namic and dynamic mechanisms, it has also been es- warm pool associated with a stratospheric-level trough tablished that development is favored when certain pre- (Hirschberg and Fritsch 1991), while cyclonic vorticity cursor low-level environmental conditions exist. Smith advection usually occurs in association with an upstream and Tsou (1988) and Smith et al. (1988) discuss the mid- to upper-level trough (Sanders 1986) and a jet presence of low static stability, while Gyakum (1983) streak (Uccellini 1990). Latent heat release occurs, of and Gyakum et al. (1992) discuss the presence of a local surface vorticity maximum as a precursor condition for continued cyclone development. * Current af®liation: ACES Power Marketing LLC, Indianapolis, Indiana. While these, and many more, papers illustrate the progress that has been made in understanding cyclone development, signi®cantly less work has been done to Corresponding author address: Dr. Phillip J. Smith, Department shed light on the processes responsible for cyclone de- of Earth and Atmospheric Sciences, Purdue University, 1397 Civil Engineering Building, West Lafayette, IN 47907-1397. cay. Rolfson and Smith (1996) attempt to alleviate this E-mail: [email protected] de®ciency in cyclolytic research by including a weak-

᭧ 2001 American Meteorological Society

Unauthenticated | Downloaded 09/30/21 09:27 AM UTC NOVEMBER 2001 MORRIS AND SMITH 2715 ening cyclone category in their climatological study of cyclone dynamics. They state that vertically integrated horizontal cold air advection and reduced horizontal vorticity advection at the cyclone center led to a decrease in surface geostrophic vorticity tendency and an increase in central sea level pressure during the eight weakening periods they studied. The purpose of this study is to further document the synoptic-scale forcing processes that contribute to cyclolysis by examining two decaying cyclone cases that occurred over the continental United States. Both cases involve cyclones that ®ll during most of their study periods. The diagnostic tool used to examine these cyclolytic processes is the Zwack±Okossi (Z±O) equation, because it quantitatively accounts for the vertically integrated changes of the dynamic and thermal forcing FIG. 1. Total analysis domain (outer grid) and computational processes throughout the troposphere and lower strato- domains [inner grid; see Rolfson and Smith (1996)]. sphere.

2. Data and methodology rameters C and G were chosen to yield a response func- tion (see Fig. 2 in RS) that retains basically no infor- a. Data mation for wavelengths less than 500 km, approximately In this study, observed upper-air and surface data over 38% of the information with wavelengths of 1000 km, the continental United States were utilized. The upper- and approximately 90% for wavelengths of 2000 km. air data, obtained at the standard rawinsonde times of After grids were created for each of the mandatory lev- 0000 and 1200 UTC, included surface pressures, geo- els, the data at the mandatory levels were interpolated potential heights, temperature, wind speeds, and wind linearly in ln(p) to standard 50-hPa isobaric surfaces direction. In addition, sea level pressure at 0000, 0600, from 1050 to 50 hPa. In addition, for levels that occur 1200, and 1800 UTC and 6-h accumulated precipitation below local ground level, winds were set to zero and at 0000 and 1200 UTC were obtained from the surface the hypsometric equation was used with the interpolated data. The data listed above were acquired and formatted temperatures to calculate the geopotential heights. through the Purdue University Weather Processor. De- Heights and temperatures at these levels were calculated tails of the data analysis and computational methods assuming a standard atmosphere lapse rate. summarized below can be found in Rolfson and Smith The diagnostic equation used in this study is the (1996, hereafter referred to as RS). Zwack±Okossi (Z±O) equation. Based on the diagnostic Using a two-pass Barnes objective analysis scheme approach suggested by Sutcliffe (1939, 1947) and later (Barnes 1964, 1973), all mandatory level and surface modi®ed by Petterssen (1955), the Z±O equation relates data were ®t to a 25 ϫ 17 gridpoint polar stereographic changes in surface geostrophic vorticity tendencies to grid (Fig. 1). The grid spacing is 230 km ϫ 230 km on various forcing processes. This paper uses an extension a polar stereographic grid true at 60ЊN. For the appli- of Zwack and Okossi's (1986) quasigeostrophic equa- cation of the Barnes objective analysis scheme, the pa- tion given by Lupo et al. [(1992), their Eq. (11)] as

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

where pl is the near-surface pressure level, pt the upper with ␪ the potential temperature], ␻ the vertical motion pressure level, ␨gl the near-surface geostrophic vorticity, in isobaric coordinates(␻ ϭ dp/dt,) and PD ϭ (pl Ϫ Ϫ1 ␨a the absolute vorticity (␨ ϩ f ), f the Coriolis param- pt) . eter, R the gas constant for dry air, V the horizontal Term A, the dynamic forcing term, represents the in- wind vector, QÇ the diabatic heating/cooling rate per unit ¯uence of vertically integrated horizontal absolute vor- mass, cp the speci®c heat at constant pressure, S the ticity advection on the near-surface geostrophic vorticity ,p), tendency. Terms B, C, and D, the thermal forcing termsץ/␪ץ)(static stability parameter [where S ϭϪ(T/␪

Unauthenticated | Downloaded 09/30/21 09:27 AM UTC 2716 MONTHLY WEATHER REVIEW VOLUME 129 correspond to the in¯uence of vertically integrated hor- mation of the ®ltered geostrophic vorticity tendencies izontal temperature advection, diabatic heating, and adi- yields the total Z±O geostrophic vorticity tendency. abatic temperature change, respectively, on the near- Then, sequential overrelaxation was performed to obtain surface geostrophic vorticity tendency. the total Z±O height tendency ®eld, which was then The interior integral in B, C, and D results in greater converted to surface pressure tendencies following the weight being given to temperature change processes lo- RS procedure. For diagnosing the cyclone's decay, val- cated lower in the atmosphere (Rausch and Smith 1996), ues for the geostrophic vorticity tendency for each forc- while the Laplacian operator emphasizes the importance ing term and the total Z±O geostrophic vorticity and of the horizontal distribution of the temperature change pressure tendencies were obtained at the center point of processes (Smith 2000). Further, the adiabatic cooling the cyclone, the grid point with the minimum sea level (warming) that results from the upward (downward) mo- pressure. tion forced by the other three terms often yields values Fourth-order ®nite differencing was used to calculate for term D that are of opposite sign to those of terms the horizontal derivatives at grid points along and within A, B, and C (e.g., Lupo et al. 1992). This opposition the solid box in Fig. 1, while second-order ®nite dif- to the other terms is reduced for smaller static stability ferencing was applied to the grid points along the dashed values. box. To determine vertical derivatives, second-order ®- nite differencing was used. The trapezoidal rule was applied for the vertical integral calculations. b. Diabatic heating and vertical motion Latent heat release, the only diabatic heating considered in this study, was determined from 6-h ac- 3. Synoptic discussion cumulated precipitation values gridded as described a. Case 1: 8±10 March 1999 above. These gridded values were then converted to latent heating values and vertically distributed fol- The case 1 cyclone began as a 1002-hPa low pressure lowing RS. center in eastern Colorado with a southward-extending Vertical motions were determined from a form of the trough at 1200 UTC 8 March (Fig. 2a). Precipitation omega equation given by Tsou and Smith (1990) as had formed ahead of the surface low at this same time. From this point, the cyclone's central pressure increased hPa as the cyclone progressed eastward through 7 ץf 22 ϩ2 (␨ ϩ f ) ␻ٌ .p2 Oklahoma to southern Illinois over the next 24 h (Figsץ ␴[] 2b and 2c). The cyclone's ®nal position at 0000 UTC -RRQÇ 10 March (Fig. 2d) was along the Kentucky±West Vir ץ f (١T) Ϫٌ2 , (2 ´ ١␨ ) ϩٌ2(V ´ ϭ (V p a ␴p ␴pc ginia border, with a sea level pressure value of 1012ץ ␴ ΂΃p hPa. Precipitation continued ahead of the cyclone as it where ␴ is another static stability parameter [␴ ϭ weakened, diminishing to about 0.2 in. (6h)Ϫ1 by the Ϫ(R/P)S]. Sequential overrelaxation was utilized to ®nal map time. compute ␻ using the relaxation criteria and boundary The 850-hPa analysis at 1200 UTC 8 March (Fig. 3a) conditions in RS. shows a closed low height center slightly east of, and a thermal trough over, the surface cyclone. The cyclones c. Computational aspects at both levels are in a similar relative position 12 h later (Fig. 3b), but now the thermal trough lies upstream from The lowest level of the vertical computational domain the surface cyclone. The latter persisted through the last is the near-surface level (pl), not the actual surface level, two map times as the 850-hPa cyclone weakened (Figs. with the highest level being at 50-hPa. The near-surface 3c,d). level is de®ned to be the ®rst pressure level above the During the entire study period the surface low pres- surface divisible by 50. The forcing quantities in Eq. sure center progressed from a position slightly down- (1) were calculated at each level and then integrated to stream from the 500- (Fig. 4) and 200-hPa (Fig. 5) yield geostrophic vorticity tendencies at level pl. The troughs at the initial map time to a position beneath the geostrophic vorticity tendency ®eld for each forcing upper troughs thereafter. The situation at the ®rst map term in Eq. (1) was then ®ltered using a two-dimen- time is particularly interesting because an upstream tilt- sional, fourth-order ®ltering scheme devised by Shapiro ed trough system is often associated with cyclone in- (1970). This Shapiro ®ltering was needed in order to tensi®cation. Weakening is usually associated with the remove subgrid-scale ``noise'' that was introduced dur- vertical superposition of the surface low and the upper- ing the Z±O equation calculations. The response func- level troughs found at the last three map times. The tion for this ®lter (see RS, their Fig. 3) retains essentially decreasing amplitudes of the contour ®elds and the de- zero information at wavelengths less than 1000 km, ap- creasing magnitudes of the 500-hPa vorticity maxima proximately 40% at wavelengths of 1500 km, and ap- suggest that the upper-level trough also weakened dur- proximately 90% at the 2000-km wavelength. The sum- ing the period of study, particularly over the ®nal 24 h.

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FIG. 2. Sea level pressure (hPa, solid) and 6-h precipitation (in., dashed; outer contour, 0.1 in.) at (a) 1200 UTC 8 Mar, (b) 0000 UTC 9 Mar, (c) 1200 UTC 9 Mar, and (d) 0000 UTC 10 Mar 1999.

FIG. 3. As in Fig. 2 but for 850-hPa geopotential height (m, solid) and temperature (ЊC, dashed).

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FIG. 4. As in Fig. 2 but for 500-hPa geopotential height (m, solid) and absolute vorticity (10 Ϫ5 sϪ1, dashed). Cyclone center shown with ®lled dot.

FIG. 5. As in Fig. 2 but for 200-hPa geopotential height (m, solid) and wind speed (kt, dashed). Cyclone center shown with ®lled dot.

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FIG. 6. Sea level pressure (hPa, solid) and 6-h precipitation (in., dashed; center contour, 0.1 in.) at (a) 1200 UTC 19 Nov, (b) 0000 UTC 20 Nov, (c) 1200 UTC 20 Nov, and (d) 0000 UTC 21 Nov 1999.

The weakening 200-hPa trough was accompanied by a thermal trough upstream from the surface cyclone at all moderate to strong jet streak (maximum wind speeds map times (Fig. 7). 50±100 k) that propagated through the trough south of The surface low pressure center was located down- the surface cyclone. stream from the 500- (Fig. 8) and 200-hPa (Fig. 9) troughs until 1200 UTC 20 November, when the two troughs ®nally became superimposed over the surface b. Case 2: 19±21 November 1999 low pressure center. Thus, once again cyclone decay This cyclone originated much like the March cyclone commenced with an upstream tilted wave system. As did, as a low pressure center that began moving out of for the March case, the upper-level troughs for this case the Rocky Mountains. By 1200 UTC 19 November, the weakened as the surface cyclone decayed and as a mod- cyclone center was located in southeastern Minnesota erate 200-hPa jet streak moved south of the cyclone. with a central pressure of 1006-hPa (Fig. 6a). The ab- sence of precipitation contours indicates 6-h totals less 4. Diagnostic results than 0.1 in. everywhere. The cyclone then slowly moved east-northeast into upper Lake Michigan by 0000 UTC In order to quantify the effects of the four forcing 20 November with a 4-hPa pressure increase (Fig. 6b), terms in Eq. (1) on cyclone decay, maps of total Z±O as precipitation increased ahead of the cyclone and tendency ®elds and the four forcing processes, as well ahead of the north±south cold front. The center of the as vertical pro®les at the cyclone center points, are pre- cyclone of interest at this time was smoothed out by the sented. Contributions to cyclone decay or development analysis scheme. The position plotted in Fig. 6b was are revealed by the position of the cyclone center in taken from the National Centers for Environmental Pre- each of the ®elds. diction analysis. By 1200 UTC 20 November, the cyclone's center was positioned north of Lake Huron, with a. Comparison statistics a central sea level pressure of 1013 hPa (Fig. 6c). Light precipitation continued ahead of the cyclone. Finally, The observed sea level pressure tendency ®elds the weakening cyclone moved into northern Quebec by (OBS), computed as a backward 6-h time difference, the last map time (Fig. 6d). The position of the surface are compared with instantaneous Z±O surface pressure cyclone relative to the 850-hPa trough for this case was tendency ®elds, using correlation coef®cients (COR) for similar to that of the March case, with a pronounced pattern comparison and mean absolute values (MAV)

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FIG. 7. As in Fig. 6 but for 850-hPa geopotential height (m, solid) and temperature (ЊC, dashed).

FIG. 8. As in Fig. 6 but for 550-hPa geopotential height (m, solid) and absolute vorticity (10 Ϫ5 sϪ1, dashed). Cyclone center shown with ®lled dot.

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FIG. 9. As in Fig. 6 but for 200-hPa geopotential height (m, solid) and wind speed (kt, dashed). Cyclone center shown with ®lled dot. averaged over all grid points for magnitude comparison. b. Case 1: 8±10 March 1999 Results for both cases are presented in Table 1. The results show that for both cases the COR values are 1) TOTAL Z±O TENDENCIES generally 0.8 or larger. These high COR values and Maps depicting the Z±O pressure tendency for the visual comparison of the Z±O and OBS ®elds (not ®rst three map times of the March case are shown in shown) suggest good comparability between the two Fig. 10. At the ®rst two times, the decaying cyclone ®elds. MAV values show that, although comparable, the center is found, as expected, in the pressure rise region. Z±O values are on average 25%±30% smaller than the For these two map times the 24-h Z±O pressure change OBS values. Since visual comparison shows that the at the cyclone center is 7.9 hPa, comparable to the ob- two sets of values are usually closer to each other in served central pressure increase of 7 hPa for the 24-h the cyclone domain, these differences are not considered period beginning at 1200 UTC 8 March. At the third to be signi®cant. map time, the cyclone is near the zero line, suggesting a temporary interruption in the cyclone decay process. Con®rmation of this interruption is seen in the hourly

TABLE 1. Correlation coef®cients (COR), and Zwack±Okassi (Z± sea level pressure analyses for this case (not shown). In O) and observed (OBS) mean absolute values (MAV) [hPa (12 h)Ϫ1] these analyses, the central pressure is seen to increase for the Mar and Nov cyclone cases. by 1-hPa from 1200 to 1300 UTC 9 March and then remain constant for the next 3 h before resuming its Time (UTC/day) COR Z±O MAV OBS MAV increase. The cause of this interruption will be examined Mar case in the next section. At each time the cyclone center 1200/8 0.92 3.36 4.29 moves toward the negative pressure tendency center 0000/9 0.82 3.30 5.89 1200/9 0.78 3.98 4.44 over the subsequent 12 h. Avg 0.84 3.55 4.87

Nov case 2) BASIC FORCING PROCESSES 1200/19 0.90 3.08 3.67 0000/20 0.70 2.51 4.20 Fields representing the contributions to the total Z± 1200/20 0.81 2.04 3.39 O surface geostrophic vorticity tendency from vertically Avg 0.80 2.54 3.75 integrated, individual forcing processes are shown in

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cy) at the ®rst two map times is the horizontal temperature advection. Examination of the horizontal temperature advection term reveals that the cyclone center is located well within the negative horizontal temperature advection region at these times (Figs. 11b, 12b). By the last map time (Fig. 13b) the cyclone had moved farther ahead of the negative temperature advection center to a position near the zero isopleth. The interruption to decay discussed earlier is largely due to the decreased magnitude of this term, thus allowing the other terms to nearly balance each other. All three map times display negative contributions by latent heat release to the surface geostrophic vorticity tendency. At all three times, the cyclone center is clearly in the negative latent heat release tendency region (Figs. 11c±13c). These negative values occur despite the fact that the cyclone is in a precipitation, and thus latent heating, region. This can most likely be explained by the Laplacian effect noted by Smith (2000). Smith points out that because the thermal contributions to surface geostrophic vorticity changes depend on the Laplacian of the temperature-changing processes, the horizontal distribution of the thermal process and the location of the cyclone within that distribution are of considerable importance. While in most cases a warming process (such as latent heat release) yields geostrophic vorticity increases, some horizontal warming distributions can yield geostrophic vorticity decreases over at least a portion of the warming region. This is more likely in the outer portion of a warming region. If the cyclone is located in this outer portion, as is the case here (see Figs. 2a±d), then the warming can act to decrease the surface geostrophic vorticity. The adiabatic term contributes to cyclone development at all three times (Figs. 11d±13d), with the largest value occurring at 0000 UTC 9 March.

3) VERTICAL PROFILES In order to understand the contribution of upper levels to cyclone decay, it is useful to examine vertical pro®les of the forcing processes in Eq. (1) at the cyclone center point. Vertical pro®les of horizontal vorticity advection, horizontal temperature advection, and adiabatic temperature change are shown in Fig. 14 for the Fig. 11± 13 map times. Pro®les of latent heat release are excluded because latent heating was small at all levels at the

FIG. 10. The Z±O surface pressure tendency [hPa (12 h)Ϫ1] at (a) cyclone center. The change from positive to negative 1200 UTC 8 Mar, (b) 0000 UTC 8 Mar, and (c) 1200 UTC 9 Mar contribution to cyclone development by the vorticity 1999. Cyclone center shown with ®lled dot. advection term previously noted is shown in Fig. 14 to occur largely because of the change from cyclonic to anticyclonic vorticity advection above 600 hPa. The Figs. 11±13. Horizontal vorticity advection ®rst con- pro®les at the second two times assume a shape much tributes to cyclone development and then to decay, as like that in RS for their weakening cyclone category. the positive geostrophic vorticity tendency contribution The upper-level cyclonic vorticity advection (CVA) at area advances farther downstream from the cyclone cen- the ®rst time corresponds to the surface cyclone's po- ter with time (Figs. 11a±13a). The primary cyclone de- sition downstream from the 500-hPa and 200-hPa cay mechanism (negative geostrophic vorticity tenden- troughs (see Figs. 4 and 5). This pro®le results in the

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FIG. 11. Contributions to the total Z±O near-surface geostrophic vorticity tendency (10 Ϫ9 sϪ2) by (a) horizontal absolute vorticity advection, (b) horizontal temperature advection, (c) latent heat release, and (d) adiabatic temperature change for 1200 UTC 8 Mar 1999. Cyclone center shown with ®lled dot. integrated positive vorticity tendency contribution at the The vertical pro®le of horizontal temperature advec- cyclone center seen in Fig. 11. By 0000 UTC 9 March tion at 1200 UTC 8 March is similar to RS's devel- an anticyclonic vorticity advection (AVA) pro®le is ev- opment pro®les, with low-level warm air advection ident, as the upper wave overtakes the surface cyclone (WAA), low- to midlevel coldair advection (CAA), and and the vorticity maximum moves slightly downstream upper-level WAA, the latter re¯ecting the upstream po- from the surface low. sition of the 200-hPa trough. However, because the CAA

FIG. 12. As in Fig. 11 but for 0000 UTC 9 Mar 1999.

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FIG. 13. As in Fig. 11 but for 1200 UTC 9 Mar 1999. is relatively strong through a deep layer, this pro®le increase of 7.6 hPa for these two maptimes is compa- results in the negative contribution to the surface geo- rable to the 6-hPa increase observed over the 24-h pe- strophic vorticity tendency implied in Fig. 12b. By 0000 riod beginning at 0000 UTC 20 November. The pressure UTC 9 March the low levels exhibit a change from tendencies at the ®rst two map times are somewhat sur- WAA to CAA, a transformation that can be con®rmed prising because, as noted earlier, the surface cyclone by comparing the surface cyclone's positions in Figs. center lies downstream from the troughs at both 500 2a,b with the temperature advection implied by the 850- and 200 hPa (compare Fig. 6 with Figs. 8 and 9). At hPa height and temperature ®elds in Figs. 3a,b, and the all times the cyclone propagates toward the Z±O pres- upper-level WAA has weakened signi®cantly. The re- sure tendency minimum. sulting deep CAA above the surface cyclone yields an even stronger negative surface vorticity tendency. The interruption to decay at 1200 UTC 9 March can be 2) BASIC FORCING PROCESSES attributed to WAA from 700±300 hPa, presumably from Contributions from vertically integrated individual the upstream ridge approaching the cyclone from the forcing processes for this case are shown in Figs. 16± west. Finally, the sustaining in¯uence of the adiabatic 18. During the ®rst two map times the vorticity advec- term occurs because of adiabatic warming in the mid- tion term contributes to geostrophic vorticity increases to lower troposphere. Such warming is associated with (Figs. 16a and 17a). The cyclone center is located within downward motions (not shown) in a statically stable the positive vorticity advection area upstream from the atmosphere. advection maximum at both times. By the third map time, the cyclone center is well within the negative vor- c. Case 2: 18±20 November 1999 ticity advection region (Fig. 18a). As for the March case, the temperature advection term plays a critical role in 1) TOTAL Z±O TENDENCIES this cyclone's decay, with negative values occurring at The Z±O pressure tendency ®elds for the ®rst three the cyclone center at all three map times (Figs. 16b± November map times are shown in Fig. 15. At 1200 18b). Also similar to the March case, a contribution to UTC 19 November the cyclone center is near the zero cyclone decay by latent heat release is present at all map pressure tendency contour (Fig. 15a), re¯ecting the near- times for this case, although this forcing term is very zero pressure change at the cyclone center that was ob- small (Figs. 16c±18c). The adiabatic term also makes a served over the previous 7 h (not shown). At the two small contribution, ®rst to decay and then to develop- remaining map times (Figs. 15b and 15c), the cyclone ment, at the ®rst two map times (Figs. 16d and 17d), center is in the positive tendency region, re¯ecting the but then signi®cantly inhibits the decay process at the observed cyclone decay. The combined Z±O pressure third map time (Fig. 18d).

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FIG. 15. As in Fig. 10 but for (a) 1200 UTC 19 Nov 1999; (b) 0000 UTC 20 Nov 1999; and (c) 1200 UTC 20 Nov 1999.

3) VERTICAL PROFILES Vertical pro®les of the signi®cant forcing processes FIG. 14. Vertical pro®les of horizontal absolute vorticity advection for the November case are presented in Fig. 19. The (10Ϫ9 sϪ2, solid), horizontal temperature advection (10 Ϫ4 KsϪ1, vertical pro®les of the horizontal vorticity advection for dashed), and adiabatic temperature change (10Ϫ4 KsϪ1, dotted) at the ®rst two map times depict CVA at every level, with the cyclone center for (a) 1200 UTC 8 Mar, (b) 0000 UTC 9 Mar, and (c) 1200 UTC 9 Mar 1999. a maximum between 200 and 300 hPa, similar to the development pro®les of RS. CVA occurs because the surface low pressure center is located downstream from

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FIG. 16. As in Fig. 11 but for 1200 UTC 19 Nov 1999. the upper-level trough and vorticity maximum (see Figs. the 200-hPa trough. Although such a feature often in- 8 and 9). The last map time depicts a pro®le of AVA dicates development, the cyclone in this case decayed at every level as the upper wave overtakes the surface because of CAA that occurred at all levels below 300 cyclone. hPa. Such advection is con®rmed by comparing the sur- The vertical pro®les for horizontal temperature ad- face cyclone positions (Figs. 6a,b) with the correspond- vection show WAA above 300 hPa at the ®rst two map ing 850-hPa height and temperature ®elds (Figs. 7a,b). times, re¯ecting the cyclone's position downstream from Both of the ®rst two temperature advection pro®les are

FIG. 17. As in Fig. 11 but for 0000 UTC 20 Nov 1999.

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FIG. 18. As in Fig. 11 but for 1200 UTC 20 Nov 1999. similar to RS's weakening cyclone pro®le. By 1200 does AVA prevail. Failure of the early CVA to yield UTC 20 November, the pro®le shows a nearly complete development is attributed to CAA at middle and lower reversal, with upper-level CAA, midlevel WAA, and levels. Only at the decay interruption time for the March lower-level CAA. The largest contribution to decay oc- case does CAA fail to be signi®cant. A secondary, al- curs at this time (cf. Figs. 16b±18b). though at some map times signi®cant, contribution to Figure 19 con®rms the small adiabatic temperature decay is made by latent heat release. In both cases this change seen at the ®rst two map times shown in Figs. appears to occur because the cyclones are located in the 16d and 17d. These small values occur because of weak outer fringes of their respective latent heat release re- vertical motions (not shown). The positive contribution gions, where Laplacian values that are the same sign as to development made at the third time results from stron- the heating may be located, as suggested by Smith ger downward motions and corresponding adiabatic (2000). warming below 200 hPa in a statically stable atmo- The predominant mechanism that opposes cyclone sphere. decay, and thus sustains the cyclone, is adiabatic warming, which occurs as a result of downward motions in a statically stable atmosphere. d. Case comparison

The purpose of this section is to compare the forcing 5. Summary and conclusions mechanisms that contribute to cyclone decay in both the March and November cases. Although differences exist Two cyclones that experienced cyclolysis over the in magnitude and in many of the details of the forcing continental Unites States have been diagnosed using an mechanisms, comparison of the horizontal distributions ``extended'' form of the Zwack±Okossi equation. The (Figs. 11±13 and 16±18) and vertical pro®les (Figs. 14 Z±O surface pressure tendency for each map time was and 19) shows that the decay of both cyclones occurs compared to the backward 6-h observed sea level pres- in association with a very similar set of physical pro- sure change at each diagnosis time. The comparisons cesses. Both cases reveal that cyclone decay does not between the two ®elds at all map times and for both require that the upper-level troughs ®rst become super- cases were very good, as suggested by correlation co- imposed above the surface cyclone. Rather, upstream ef®cients ranging from 0.70 to 0.92 (average ϭ 0.82) tilt in the system may still be present. In both cases this and magnitudes generally within about 35% of each results in a contribution to development by CVA, largely other. at middle and upper levels, early in the decay process. It is clear from this study that vertical superposition Only after the upper trough overtakes and the vorticity of the upper-level troughs and the surface cyclone is maximum moves downstream from the surface cyclone not required for cyclone decay to occur. In both of the

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cases studied, cyclone decay commenced while the upper-level troughs were still upstream from the surface cyclone. As a result, upper-level vorticity advection, which was initially cyclonic, did not play a role in cyclone decay until later in the cyclone's evolution, after the upper-level troughs overtook the cyclone. Failure of upstream tilt in the trough system, which is often favorable for development, to yield cyclone intensi®cation was attributed largely to the advection of lower- to middle-level cold air into the cyclone interior. Only at 1200 UTC 9 March, when the case 1 cyclone was experi- encing a temporary interruption to its decay, was warm air advection prevalent through most of the troposphere over the cyclone center. Latent heat release also contributed to cyclone decay, despite the fact that heating was present. This was apparently a consequence of the cyclone center being located in the outer portion of the heating region, where the Laplacian can be of the same sign as the heating. Finally, more rapid decay of the cyclone was prevented by the adiabatic warming that was present in response to the weak lower- to middle- level subsidence that prevailed in the statically stable cyclone interior.

Acknowledgments. Thanks are extended to Dayton Vincent, Robert Oglesby, and two anonymous reviewers for their very helpful comments on this work.

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