Observational Study of a Multiple Microburst-Producing Storm Part III: Vorticity Budgets

A vorticity component and budget analysis in thr � e dimension is conducted for the subcloud layer of two microburst-producing storms using dual-Doppler de­ rived winds. This study examines the vorticity associated with a single microburst­ producing storm which occurred on 14 July 1982 and a multiple microburst­ producing storm which occurred on 5 August 1982 in Colorado. Results show that horizontal vorticity centers are coincident with strong hor­ izontal gradients of vertical velocity and with areas of strong vertical shear. These gradients are maximized along the edges of downrushing air and along gust fronts. Regions of high speed low-level winds have a core horizontal vorticity above them. A vorticity budget analysis of the advection, divergence and tilting terms, comprising the vorticity component equations, shows the magnitude of these terms to be greater in the microburst domain than in the storm domain. This indicates that the strongest forcing and advection takes place within small regions of the storms. The diverging outftow of the microburst in both cases weakens any existing positive vorticity in the microburst region (z < 1 km). The differences in storm structure allow examination of the vorticity . of a simple, nearly circular-symmetric microburst and that of a microburst within a complicated How field. This leads to different voricity distributions and


INTRODUCTION
In Part I of this study,  investigated the structure and internal dynamics of a multiple microburst-producing storm in Colorado using dual-Doppler data collected at 1845, 1847 and 1850 MDT (mountain daylight time) on 5 August 1982. The results were then compared to those for the . si�ple case (14 July 1982) in Part II of this study . Fmdmgs TAO Vol.2,No.3 revealed that both misocyclone and horizontal vortex (rotor) play an important role in affecting the structure of a microburst-producing storm.
In the other case study of a micro burst-producing storm, Kessinger et a1. (1988) investigated the subcloud layer of a multicellular storm in Colorado using multiple Doppler derived winds. Their storm produced misocyclones, which are horizontal cyclonic circulation centers with diameters of 2 ,..., 4 km (Fujita, 1985), downbursts, and horizontal vortex circulations. Kessinger et al. (1988) found that the misocyclone characteristics differ from those of mesocyclone by having a vorticity maximum near cloud base instead of at low-levels and that the low-level positive vertical vorticity is weakened by the low-level divergence associated with the microburst. They also pointed out that rotors form along the edge of these misocyclones and storm downdrafts, and propagate away from the storm. These rotors have also been associated with regions of maximum surface winds.
The importance of the rotor in causing damage as well as being an aviation hazard has recently come under more study. The rotor core from the micro burst outflows is associated with lower pressure than its surroundings, which acts to accelerate the surface winds (Waranauskas, 1985). The author suggested that the axis of the rotor and the microburst coincide, thereby linking the rotor as a cause or enhancement of the microburst. Linden and Simpson (1985) stated that the wind shear and downward motion associated with the back of the rotor may be responsible for the danger of flying through a microburst. An additional mechanism for intensifying the leading-edge vortex may be the existence of rotation in the descending air.
The purpose of this study in Part III is to investigate three-dimensional vorticities associated with microbursts. Vorticity budgets for the subcloud layer of two microburst-producing storms described previously in Part I and II will be examined using Doppler derived wind fields. A comparison will be made as to the mechanisms responsible for one storm's vorticity field to that for another storm. The ultimate goal is to better understand the importance of the microburst and its associated structure to the generation of vorticity.

DATA AND ANALYSIS PROCEDURES
The data and analysis procedures for the complex case (5 August 1982) have been detailed in Part I of this study. There were five analysis levels in the vertical ranging from 0.25 to 1.25 km with a horizontal grid spacing of 0.5 km.
Dual-Doppler data at 1845, 1847 and 1850 MDT were objectively analyzed using the horizontal domain of 15 km by 15' k,m. Only those data with a high signal-to-noise ratio were accepted for: analysis.
In the same manner, dual-Doppl e r data for the simple case (14 July 1982) at 1647 and1649 MDT were carefully analyzed over the horizontal domain of 10 km by 10 km using a 0.5 km horizontal grid spacing. The vertical grid spacing varied from 0.25 km for the levels below 1 km to 0.5 km for those above 1 km.
For details,.see studies by Lin.and Hughes ( 1 98 7) and . We employed two radial velocity equations, the anelastic continuity equa tion, and an empirical formula of terminal fall speed to obtain the horizontal wind components. The vertical velocity component was computed from the anelastic continuity equation by integrating upward from the surface. Sub sequently, fields of deviation perturbation pressure and temperature were re trieved from the thre� momentum equations using the Doppler derived winds.

METHODOLOGY
The vertical vorticity equation is obtained by taking curl of the equation of motion in vector form. Upon recognizing the small effect the earth's rotation has on the absolute vorticity, one obtains an expression for the relative vorticity along the vertical axis: where and . au au au ) (aa ap aa ap ) +Big( c -+11-+ !."------ax ay az ayaz azay ay az Values of each term in (1)-(3) at every analysis level were determined from the Doppler derived winds using fourth-order finite differencing in horizontal and second-order finite differencing in vertical. The horizontal grid spacing used was 0.5 km, while the vertical grid spacing was 0.25 km.

Complex Case: 5 August 1982
The analyzed vorticity field for 1845 MDT at the 0.5 km level in pre sented on the wind field in Figure 1. This storm is more complicated than the previous case of 14 July 1982 as depicted in Part II of this study. It produced a microburst, Ml (-2, -24), a gust front, northeast through southeast (dashed line) of Ml, and an enhanced downdraft, M2 (-6, -19). The complex inter actions of the flow fields of the enhanced downdraft and Ml combine to create a large elongated region of the two horizontal components of vorticity from { -7, -17) to ( -2, -21). This area corresponds to an area of low pertur ba ti on pressure gradient (see Figure Sa in Part I), and is a feature found in horizontal vortex circulations (Kessinger et al. 1988). A circulation is not found here, but rather, the horizontal vorticity is high. The actual shear then is not ap parent simply by examining the Doppler derived wind field. The microburst  Values of € (Figure la) are overwhelmingly negative in the microburst domain at all levels with a pattern as shown here for 0.5 km. e is positive to the northwest of Ml as depicted in the northwest-southeast cross section (see Figure 2a). Above 0.5 km, €is positive in this northwest quadrant. It is in this region that the divergent outflow of Ml is strongest in the lowest levels.    domain, the elongated region of strong e values mentioned at 1845 MDT' from north of M2, to north of Ml has intensified. A band of strong positive e · v� lues 10 x 10-3 s-1 to 20 x 10-3 s -1 to 15 x 10-3 s-1 lies was southwest to north of Ml. The wind field in this region curves anticyclonically (at 0.5 km) emanating from the high perturbation pressure dome (0.2 'Pb) associated with Ml into a lower pressure region between both Ml and the 'high pressure dome associated with M2 (see Figure Table 3 lists the area mean and standard deviation values for each of the four budget terms in the storm domain. These four terms are horizontal vor ticity advection (HAD), vertical vorticity · adve�tion (VAD), divergence (DIV) and tilting (TILT). At 1845 MDT, a balance must be accomplished between HAD and the combined effect of . DIV and TILT since VAD is small. A balance is not met and by comparing vertical totals (see the last row in Tables 3.... .., 4 for each analysis t. ime), a net increase of e is suggested. By 1847 MDT, the contribution from VAD has increased slightly (level by level) but is still one order of magnitude smaller in the mean than the remaining terms. At this time, HAD and TILT acting positively (source) at low levels overwhelms the loss through DIV. Across each time period, it is apparent that the DIV term is the sole generator of negative e. The remaining terms generate positive e with the strongest gener a tion occurring below 0. 75 km.
In the smaller microburst domain (Table 4), the area mean and standard deviation values are larger than at the storm domain (Table 3). From Figure la it is evident that due to the overwhelming negative e field, HAD would act as a sink as the table indicates. VAD counters by acting as a source. TILT is a source at each time period with maximum contribution occurring at 1847 MDT. The large horizontal gradients of e create a very strong HAD term leading to removal of positive e within the microburst domain over time. VAD and TILT counteract this removal mechanism and dominate at 1845 and 1847 MDT. By 1850 MDT when the e gradient is strongest, DIV acts with VAD and TILT to attempt a balance. As the e field gets stronger, the DIV term especially to the north of M 1 becomes a strong source.
A tight gradient of Yf results from the strong outflow ofMl eastward at low levels   (Figure 3). The most interesting changes for T/ occur within the microburst domain as maximum positive and negative T/ centers pivot around Ml and become oriented northwest to southeast through the center of Ml with positive T/ to the northwest (Figure 3c). The tight horizontal gradient of T/ values along the gust front weakens slightly with time and it appears in cross section (Figure 4) that the slope of the gust front is most shallow at 1850 MDT in fact approaching horizontal above and southeast of Ml. This is to say that negative TJ is being generated and is being spread out to the southeast at lower levels of the storm. Tables 1,... ., 2 show, especially in the microburst domain, that positiv e .,, is being generated above 0.75 km and destroyed below 0.75 km.
The 17 field in Figure 3a has its strongest negative value, -32 x 10-3 s -1 , at this level (0.5 km) just east of Ml. The gust front is closest to Ml at this point. The 'fl field parallels if not defines the location of the gust front with its very tight gradient adjacent to the gust front. Table 5 shows the budget terms for 'fl over the mieroburst domain. It is seen that HAD and VAD and likewise, DIV and TILT act, in general, to oppose each other.  Table 1, it is apparent that � changes very little statistically at the storm domain. The largest changes occur in the microburst domain.
From Figure 5a, two areas of positive � are evident. One area west of Ml (� > 4 x 10-3 s -1) at 0.5 km and the other along the gust front with a maximum (14 x 10-3 s -1 ) associated with the mesocyclonic-like vortex, V, located at the southern end of this gust front at 1845 MDT.
By 184 7 MDT (Figure 5b), the area along the gust front has been split as � is diminished just south of Ml and this continues at 1850 MDT (Figure 5c) .
The mesocyclone-like vortex, V, weakens with time. The area of � greater than 12 X 10-3 s -1 tracks northwestward with time, weakens as it approaches Ml, and merges with the positive � area to the west of Ml.
A west-east cross section (Figure 6) shows that initially the area west of Ml is shallow extending only up to 0.5 km. By 184 7 MDT and continuing at 1850 MDT, this area experiences a spin up of vorticity from the top down. A new misocyclone, Cl, develops here by 1850 MDT with maximum � vorticity (14 x 10-3 s -1) occurring at 1.25 km.
A value 0: f � has a maximum, 14 x 10-3 s -1, in the mesocyclone-like vortex (V) and is positive along the gust front. Another region of positive � values is located west of Ml. The west-east cross section through the micro burst domain in Figure 6a indicates that the positive area west of Ml is a low-level feature, while the area along the gust front extends through several levels and slopes westward with height, i.e., with the updraft in this area. In the column directly above Ml, � is negative below 0. 75 km and positive above although the values are relatively small, i.e., near zero throughout. This signifies that the flow is largely irrotational through the horizontal plane. Table 1 lists the area mean and standard deviation values for each com ponent of vorticity by level for the storm domain. By comparing area mean values of E, T/ and � , it is seen that € and � are predominantly positive over the storm domain with the strongest values above 0.5 km. Conversel y , T/ has Table 5.
TILT.,  negative values at most levels. In the microburst domain (Table 2), E and fJ are predominantly negative in the mean below 0. 75 km ( E) and 0.5 km ( fJ ) , while � continues to be positive throughout with the larger mean values at the higher levels of the microburst domain. The � budget terms in the storm domain for virtually all times were found to be less than those in the microburst domain. Area mean values were typically on the order of 1 x 10-7 s -2 in the storm domain and 1 x 10-6 s-2 in the microburst domain, indicating the many more complex and opposing interactions at he storm domain. Typical values, while being of the same order in both domains, were larger in the microburst domain and extended through more depth. The microburst domain � budget terms are presented in Table 6 for all analysis times. As noted earlier, the last row is a vertical total of the area means of each term. This provides a look at which terms act as a source or sink for �· It can be seen that DIV and TILT become important, especially at 184 7 and 1850 MDT at 0. 75 km to 1.25 km. Both of these terms act positively to generate �. So it appears that the contribution from DIV is critical to the formation and development of the misocyclone.
Horizontal variations of � at 1.25 km for all three analysis times are pre sented in Figure 7. Two misocyclones are evident; Cl is located to the west to southwest of Ml, while C2 is located to the immediate east to northeast of M2. Centers of the misocyclones coincide with the maxima of � vorticity. For misocydone Cl, values of � increase from 8x10-3 to 12 x 10-3 s -1 with a max imum of 12 x 10-3 s-1 at 1850 MDT ( Figure 7c). Vertical vorticity advection (VAD) and divergence (DIV) terms contribute positive � at this level. On the other hand, misocyclone C2 begins to develop at 184 7 MDT (Figure 7b) reach ing the maximum intensity by 1850 MDT (Figure 7c). The circulation center coincides with a maximum value of 12 x 10-3 s -1 • As discussed in Part I of Ta ble 6. Same as Table 5 (Figure 8c) are relatively smaller than those of horizontal components in most areas. In the inner core region of the micro burst, � is very small indicative of the diverging flow in this region as depicted in the study by Lin and Hughes (1987).

Vol.2, No.3
A north-south cross section along line GH in Figure Sa showing spatial variations of vorticities is presented in Figure 9. Note that a rotor (vortex circulation), located at (y = -15.5; z = 0.75), is apparent in the wind field on the micro burst side of the gust front (Figure 9a). Its position coincides with a maximum value of E ( 18 x 10-3 s -1 ) . On the .south side of the micro burst, the rotor is non-existent although the fl.ow field does show a circulation, but it is not closed. Notice that the horizontal outflow to the north of M is going against the environmental flow, whil� the outflow to the south is almost in the same direction as the environmental flow. For the TJ field (Figure 9b), large positive values (up to 10-2 s-1) occur in the region south of M ( y = -19.5; z = 0.75). Values of T/ are relatively small over the north region. The vertical vorticity component (Figure 9c), in general, is much smaller than the horizontal components in the layer below 1 km. In this microburst-dominat1ng layer, the horizontal diverging flow prevails and vorticity vectors are nearly horizontal.
Figure lOa depicts horizontal vorticity vectors at 0.75 km. Notice that a vortex ring surrounds the microburst center (M) indicative of the strong shear in this region. The field of perturbation pressure (P�) in relation to horizontal vorticity vectors at 0. 75 km is illustrated in Figure !Ob. It is evident that the vortex ring lies in a region of low pressure which serves to accelerate the wind. Likewise, the rotor itself is within the low pressure region as viewed in the north-south cross section (Figure 9d). Parsons et al. (1987), Droegemeier and Wilhelmson (1987) and Kessinger et al. (1988) also suggested that these vortex circulations could be partly responsible for the observed high surface winds.
The vortices studied by Kessinger et al. (1988) move away from the storm center. They hypothesized that variations in the strength of the downdraft may create separate centers of horizontal vorticity which then move down and away from the storm. The existence of vortices can be inferred from Figure 9 on either side of the microburst. The vorticity centers are more evident in southwest-northeast cross section (not shown). Time resolution does not allow tracking of these vorticity centers, but some movement down and outward can be inferred between 1647 MDT northeast of the microburst. This apparent movement could be a establishment or a development of vorticity lower and further away as opposed to actual movement.
In order to determine typical magnitudes of the three vorticity compo nents, area means and standard deviations were computed over the full storm domain and the microburst domain, see a box in Figure 8. Findings are pre sented in Table 7. A comparison of standard deviations in the table shows that the E and TJ components are the dominant components at every level. Mean values of E are positively large in the layer between 0.5 km and 1.5 km, while mean values of T/ are negative from the surface to 2 km. The rotor, which af-  fects the vorticity field at levels between 0.5 km and 1 km, and the predominant northerly flow to the northeast produce strong positive values for the e area means at these levels. The values for 77 and � are more varied, positively and negatively, and hence their areal means are smaller than that of e.
The same results hold for the microburst domain with the exception that the 17 component is strongest at levels between 0.75 km and 1 km. Comparing across the domains, one finds the maximum positive and maximum negative values of each component over the grid, which illustrates the significance of the presence of the microburst, i.e., these values occur in the microburst domain predominantly. Table 8  Since the area means for each component of the E, 17 and � are at least one order of magnitude smaller than their standard deviations at each level, Table 8.   Table 8 reveals that HAD is the largest of all the terms for E and rJ budgets with VAD and TILT being the next higher terms, respectively. Term DIV is the smallest of all terms for all three components. TILT dominates the VAD term in the � budget and has the strongest typical value of all term within the t budget at 0. 75 km. It was shown earlier that the €-component of vorticity was the strongest component and, therefore, its budget has the strongest terms of all three directions. The last row in Table 8 represents the vertical total of the area means for €w ith HAD, VAD and TILT being nearly equal. HAD and TILT play opposite roles as source and sink for TJ as do VAD and DIV but to a lesser degree. It appears that the advection terms are nearly balanced by the divergence and tilting terms for this direction. The final budget, �, indicates that VAD is the source, while the other terms are all acting to decrease positive �· Table 9 lists the area means and standard deviations for the microburst domain budget terms. As expected, the typical magnitudes (standard devia tions) are larger in the micro burst domain as compared to those in the storm domain for each term at virtually every level. The hierarchy of significance remains as in the storm domain as HAD, VAD , TILT and DIV for the E and TJ budgets. The t budget again has VAD and TILT being very close in magnitude. The vertically totaled area means are .found in the last row of Table 9.
Note that HAD acts to decrease (sink) €, while the remaining terms provide a source of positive e. VAD and TILT have the largest totals, but the deficit attributed to HAD cuts the source due to VAD in half. The positive contribu tions from DIV and TILT are roughly five and six times, respectively, those at the storm domain. This points out the significance of the microburst flow field towards the generation of e. The TJ budget, on the other hand, shows (via the vertical total row) the same trend as at the storm domain. That is, HAD and VAD are sources of rJ, while DIV and TILT are sinks. The largest change occurs with VAD and DIV between domains. VAD develops to become the dominant source term and DIV increases fourfold to virtually match TILT as a sink. Ye t again, the sources remain due to HAD and VAD. For the �-component, VAD and TILT dominate the budget terms with VAD the source and TILT the sink. · The decrease in HAD seems to indicate that the horizontal gradients of t are weaker on average than the vertical gradients. Furthermore, as VAD is acting to bring positive � values lower into the storm, TILT appears to singlehandedly spin down the positive values. Note that terms VAD and TILT have the same order of magnitude, but opposite sign throughout .the whole boundary layer.

CONCLUSIONS
Budgets for each vorticity component were assessed at every analysis level from the Doppler derived winds and their derivatives. In addition, spatial vari ations of three vorticity components were computed throughout the boundary layer.
Results show that horizontal vorticity centers were found in regions of strong horizontal gradients of vertical velocity and in areas with large vertical shear of the horizontal winds. The simple case had a nearly circular-symmetric microburst with a vortex ring surrounding the microburst down fl.ow. This ring descended from 0.75 km at 16 47 MDT to 0.5 km at 1649 MDT. The effect was to create increased surface winds southwest and northeast along the gust fronts as the ring descended. The complex case showed the evolution of a misocyclone. A positive value of vertical vorticity was generated from top down similar to that reported in Kessinger et al. (1988).
Vorticity budget analyses reveal the magnitude of each term in the budget TAO Vol.2, No.3 equation to be greater in the micro burst domain than in the storm domain. This indicates that the strongest forcing and advection occurred within small regions of the storms. The existence of the microburst enhanced the magnitude of the vorticity components in the near micro burst region of the storm. This was true for both cases and for each component of vorticity.
The differences in storm structure allow examination of the vorticity of a microburst embedded within a relatively simple flow field and that of a mi croburst within a complicated flow field. This resulted in different vorticity distributions and budgets.
Further study is needed to determine why the rotors develop in some cases are not in others. With sufficient time resoluti�n, the propagation of these vortices and rotors may be studied. The solenoidal term, although believed to be small, may contribute in the head of the gust front. This may be important in the formation of the rotor.