Observational Study of a Microburst-Producing Storm Part IV : Fine Scale Analysis 355

Seven teleseismic long period P-wave records from World-Wide Standard SeismographNetwork(WWSSN)are used to infer the source rupture process of the July 23,1978 Lanhsu,eastern Taiwan earthquake through the body-wave iterativedeconvolution method(Kikuchi and Kanamori,1982;1986).Results show that therupture sequence consists of one main event and one largest subevent near thehypocenter determined by Pezzopane and Wesnousky(1989)and numerous smallerones at a distance from the hypocenter.Comparison of the spatial distribution ofmainshock rupture sequence with aftershocks shows that aftershocks are located in thearea which did not break before the occurrence of the above-mentioned events.Thetotal seismic moment of the three largest events is 8.76×10^(26)dyne-cm.


INTRODUCTION
In Part I of this study, Lin et al. (1991) investigated some structural features of a multiple microburst-producing storm, the 5 August 1982 case, in detail using the JAWS (Joint Airport Weather Studies) dual-Doppler data with 0.5 km horizontal grid spacing.Results obtained were then compared to those for the 14 July 1982 case in Part II (Lin and Coover, 1991) of this study TAO Vol.2, No.4 using the 0.5 km grid distance.Vorticity distributions and budgets of these two microburst-producing storms were examined in Part III of the study by Lin and Lapointe (1991) using the Doppler derived winds obtained in Parts I and II mentioned above.
With the aid of JAWS Doppler data, many microburst studies with em phasis on their kinematic structure were reported in the literature; for example, see studies by Wilson et al. (1984), Elmore et al. (1986), Hjelmfelt (1988), Lee et al. (1988), Kessinger et al. (1988) and others.The kinematic structure of the 5 August 1982 case was" studies by Elmore et al. {1986) using the reduced domain (4.5 km x 4. 5 km) centered at microburst Ml.The objective analy sis employed was the Cressman (1959) interpolation scheme with an influence radius equal to the grid spacing of 150 m.They used the 150 m horizontal grid spacing to calculate fields of convergence/divergence and vertical velocity starting from the lowest level near 50 m AGL (above ground level).Results showed that strong downward motion occurred inside the microburst.
In the kinematic study of a microburst, only the first derivative in velocity is required to compute vertical shears, fields of convergence/ divergence, vortic ity and vertical velocity.For this reason, researchers were able to choose much smaller grid spacing, say 250 m or less, to compute those kinematic quanti ties.Hence small-scale features associated with microbursts in the atmospheric boundary layer (ABL) can be resolved, see studies by Wilson et al. (1984), Elmore et al. (1986), Hjelmfelt (1988), etc. Conversely, in the dynamic and thermodynamic study of a micrc:iburst-producing storm using a thermodynamic retrieval method, e.g., Lin et al. (1991), Lin and Coover (1991) and others, first, second and third derivatives in velocity are required to retrieve fields of perturbation pressure and temperature.Consequently, higher quality wind data are needed for the dynamic and thermodynamic study of a microburst storm.This can be achieved by suppressing smaller scale perturbations in the wind field via smoothing or filtering.
As depicted in Part I of this study, our study employed a Barnes (1973) distance-dependent weighting function (instead of a Cressman type weighting) 1 with a 1.75 km scan radius to interpolate data on a grid.The 0.5 km horizontal grid spacing was chosen to be compatible with a 1.75 km scan radius.Hence, small-scale features with wavelength < 3 km wete not resolved in Parts I, II and III of this study.It is of interest to investigate the fine-scale structure of a microburst-producing storm, via a thermodynamic retrieval technique, by reducing the horizontal grid spacing to 0.25 km with a scan radius of 0.875 km.
In this way, mesoscale features with wavelength > 1.5 km can be adequately resolved using the JAWS data mentioned previously.
The purpose of this study in Part IV is to investigate the kinematic, dy namic and thermodynamic properties of the same microburst-producing storm, studied in detail in Part I of this study, using a 0.25 km grid spacing in both horizontal and vertical directions.This multiple microburst-producing storm occurred on 5 August 1982 near Denver, Colorado, In addition to studying the fine-scale structure of the storm, a cross comparison will then be made between the current study using to 0.25 km resolution and the previous study using the 0.5 km resolution.Throughout such a comparison, the structure and internal dynamics of a multiple microburst-producing storm in the ABL can be further understood.

DATA AND ANALYSIS PROCEDURES
The synoptic condition for the 5 August 1982 case (the complex case) was presented in Section 2 of Part I. Briefly, the Denver sounding released at 1800 MDT (mountain daylight time) , see Figure 2 in Part I, dispalayed a well mixed boundary layer extending to 1.5 km AGL.The convective condensation level was located at 650 mb with a surface temperature of 30°C.Also, moist conditions prevailed aloft throughout the depth of 4 ,,... ., 7 km.An average mixing ratio value of 6.5 g kg-1 existed within the 3 km thick moist layer.Note the lack of mid-level dry air common to most upper /high plains soundings.The height of the 0° C wet bulb temperature is 2.8 km AGL, indicative of a hail producing storm.
We used the data analysis and reduction procedures, outlined in Part I of this study (Lin et al., 1991) , to process the dual-Doppler data obtained from CP-3 and CP-4.These data were strictly checked to meet the prespecified criterion, i.e., values of reflectivity (Z) must be larger than 5 dBZ.Folded data were collected and ground clutters were removed.Only those data with signal to noise ratio values greater than or equal to 10 dB were accepted for analysis in each slab.All variables within a slab were interpolated onto horizontal grids (42 x 48) with a grid spacing.of0.25 km using a 0.875 km scan radius.There were five equally spaced analysis levels in the.vertical ranging from 0.25 to 1.25 km.

METHODOLOGY
We employed the method suggested by Armijo (1969) to derive the hori zontal wind components from two radial velocity equations, the anelastic conti nuity equation and an empirical formula of terminal fall speed.Vertical veloc ities were computed from the anelastic continuity equation by integrating up-TAO Vol.2, No.4 ward from the surface assuming zero vertical velocity at the surface.Once the three-dimensional winds were obtained, fields of deviation perturbation pres sure and temperature were retrieved from the Doppler derived winds using the three momentum equations (Gal-Chen, 1978).These fields were subjected to momentum checks (Er) to determine the level of confidence before interpreta tion.For detail, see Part I of this study.Values of Er vary from 0.21 to 0.39 with the volume mean of 0.34.

DISCUSSION OF RESULTS
As noted earlier in Section 1, the employment of smaller grid (0.25 km) should provide finer resolution of those events captured at the times of inves tigation.Analyses are conducted by dissecting five horizontal levels separated at 0.25 km intervals for the structural features of those storms present.Indeed, storm features resolved at the 0.5 km grid analysis are significantly more pro nounced than those at the 0.25 km grid analysis and will be discussed later.Additional features of interest also become apparent at the refined scale.Fields of storm-relative wind, reflectivity, vertical velocity along with perturbation pressure and temperature are presented below with distances in kilometers rel ative to the CP-2 radar.In an effort to show the fine-scale structure of motion, the scale of wind vectors displayed at the 0.25 km analyses (Figures la, 2a 7a and lla) is exaggerated by a factor of 2 as compared to that at the 0.5 km analysis.
4.1 Plan View at 0.25 km Figure 1 displays the plain view of the horizontal wind and reflectivity field using both 0.25 and 0.5 km horizontal grid spacings.Similar to the 0.5 km horizontal grid spacing analysis (Figure lb), the 0.25 km analysis (Figure la) also reveals that two microburst events are visible (Ml and M2) and found to be situated near or within the areas of highest reflectivity with values of 45 dB Z or greater.The dominant microburst feature, Ml, is located at (x = -2, y = -23.5).Microburst M2 is located northwest of Ml near (-6, -17.5).The second microburst, M2, is strikingly more visible than as presented at the 0.5 km analysis (see Figure lb).Hence, its center is better defined for 0.25 km resolution than that for 0.5 km resolution.Notice the disagreement in location for M2 between the two analyses.This is attributed to the fact that at the 0.5 km analysis (Figure lb), M2 does not have an apparent diverging outflow from its center, especially in the southeast part of M2.As a result, the location of M2 as shown in Figure lb for 0.5 km resolution is not as accurate as that shown in Figure la for 0.25 km resolution.This point must be kept in mind when the two cases are compared.
The environmental fl.ow at this level is from 220° at 3 ,.., ,, 4 m s-1• A gust front, indicated by the dashed line, is noted at the southeast portion of the grid, which is caused by collision between the Ml eastward divergent outflow bound ary and the cyclonic circulation (inflow) just south of the shear line (Figure la).An additional cyclonic circulation is found to appear to the west-southwest of Ml near (-6.5, -24), a feature which goes unnoticed at the 0.5 km grid datum (Figure lb).The maximum divergence associated with M2 is displaced down wind of its highest reflectivity core and largely due to a coupling between the environmental wind and the Ml outflow boundary.4.2 Plan View at 0.5 km At 0.5 km (Figure 2), both micro bursts Ml and M2 are active, though slightly less pronounced than at 0.25 km, in areas of high reflectivity.Two cyclonic circulations within the vicinity of Ml, one located at (-0.5, -25.5) on the southern edge of the gust front and the other due west in the southwestern portion of the grid domain near (-6.5, -24), remain present and well defined (Figure 2a).However, these circulations are not clearly shown in the 0.5 km horizontal grid spacing (Figure 2h).
The vertical velocity field (Figure 3) indicates values of -3 and -2 m s -1 vertical motion for microbursts Ml and M2, respectively.These values are larger than those of 0.5 km grid resolution (see Figure 6a  the vertical velocity field clearly identifies Ml and M2 as areas of sinking motion.A ring of upward motion is observed to flank both microburst events.Updraft speeds vary from 1 ,... .., 2 m s -1 in the vicinity of micro bursts Ml and M2.The cyclonic circulation due west of Ml near (-6.5, -24) carries an updraft value of 2 m s-1 • The vertical velocity field thus provides credence for all features discussed.Upori examining those parameters discovered thus far, one is led to conclude that a correlation should exist between the vertical velocity and the pressure fields.
The perturbation pressure pattern at this level (Figure 4) displays each microburst event as a relatively high pressure anomaly.This feature is more clearly seen at 0.25 km (not shown) .Low pressure may be fou�d along the gust front and generally surrounds the microburst high pressure regions.The temperature field (Figure 5) is less amplified, but still indicates that each mi croburs� is typified by a cold-core anomaly.A cold temperature value of -1 to -2° C ci ccompanies each micro burst event with a warm pool of air (1 ,...,., 2° C) existent within the central grid domain, consistent with the 0.25 km level and area of strong updrafts (not shown) .Additionally, the cyclonic circulation on the gust front features a relatively cooler region than 0.25 km as upward vertical motion increases� thereby cooling the unsaturated inflow air by dry adiabatic expansion.A cool temperature perturbation of -2°C, located at (-1, -25.5) , corresponds to the gust front cyclone (Figure 2a) , while a value of -1° C accom panies the cyclone in the southwest of the domain near (-6.5, -24) , indicative of dry adiabatic expansion associated with its 2 m s -1 updraft.Note that the temperature pattern depicted in Figure 5 is more pronounce& than that pre sented in Part I (Figure 9a) with 0.5 km grid resolution.Cooler'temperatures are observed in the Ml and M2 domains in both cases.However, relative warm ing found in the areas south of Ml and M2 for 0.25 km resolution (Figure 5) is different from that observed in the 0.5 km case.Such warming is associated with upw -ard motion is those areas (see Figures 3 and 5 for comparison) .

Plan View at 0. 75 km
Structural features are seen to undergo a transition at the 0. 75 km level as attested by the horizontal wind field (Figure 6a) .The environmental fl.ow becomes more dominant in the horizontal plane as the entire wind field for the grid is predominantly southeast or southerly with little horizontal eddy motion.The environmental fl.ow actually begins to dominate the microburst core regions persisting into the 50 dBZ contour.But the M2 outflow boundary becomes replaced by cyclonic motion.Structural changes associated with Ml are less pronounced, although cyclonic turning of the wind becomes apparent to its north.The gust front is not weil defined at this level, but the cyclonic gyration to the south of its presumed position near (-1, -25.5) remains.This feature is  Thus, it appears that this cyclonic circulation extends g:a.ly to 0. 75 km in depth.Each microburst remains intact with respect to V!J:ttical v�locity and carries values of -4 m s-1 (not shown) .Therefore, vertical velocity continues to verify the presence of the microbursts, but it becomes clear that this level is one of transitional change of storm composition.The 0.75 km level may thus be equated to the level of non-divergence for these microburst events.The microburst downdraft does not decelerate greatly due to the effect of the earth's surface, nor is it at a level where mass originates for downward transport since little entrainment occurs into the level nor transport out of the downdraft.The level thus represents an active channel where mass collected from above passes down through the layer to levels below where it may be distributed by horizontal divergence.
The winds at this level are seen to blow parallel to the reflectivity con tours to the northeast of M2 and to the southeast of the cyclonic circulation.Indications are that strong outflow of precipitation cooled air from the high re flectivity core, which occurred at lower levels, is not taking place.Entrainment of dry environmental air from flow towards higher reflectivity values is likewise absent.Therefore, dry air entrainment of environmental air should be occurring at upper levels.Inspection of those levels aloft will undoubtedly provide clues into the structural properties of microburst phenomena.Examination of the 1 km level (Figure 7a) indicates that definite changes have taken place as opposed to the lower levels.The only feature which remains unchanged is the cyclonic circulation south of the presumed surface gust front location near (-1.5, -25.5) .However, this cyclonic feature is not clearly ob served in Figure 7b with 0.5 km resolution.Strong cyclonic motion occurs for both microbursts to the north of their central core regions.Additionally, the strong winds associated with the central grid updrafts found at lower levels are much less amplified.Dry air entrainment begins to occur at 1 km, thereby feed ing the microburst events, as evident by an increase in the crossing angle fl.ow of the environmental air from low to high reflectivity cores associated with the descending precipitation shaft.Additionally, cyclonic curvature becomes estab lished on the north sides of Ml and M2.Vivid finger like protrusions accompany each micro burst event.A finger like appendage is noted in the reflectivity pocket southwest of Ml, an area of 50 dBZ, which curls counter-clockwise up the grid and back towards Mll .Another finger like projection extends down the grid from the extreme northwest corner of the grid, pointing at M2.These finger like appendages act as circulation feeders, which provide abundant tongues of dry environmental air for digestion into microburst core regions.Cyclonic fl.ow around both microburst events is much broader and more pronounced than at lower levels.The cyclonic circulation to the west southwest of Ml, found absent at 0. 75 km, becomes reestablished at this level.A streamline analysis would JAWS S AUG 82 18�5.l<OOkmwell diagram a confluent asymptote connecting the low pressure microburst re gions; which is fed and driven by anticyclonic curvature in the central portion of the domain and just northwest of Ml.Anticyclonic fl.ow is also visible in the southeast portion of the domain.
The vertical velocity field {Figure 8) characterizes each microburst event with downdraft values of -6 m s-1• A semicircle of updraft values (3 m s-1 ) envelopes M2 on its northwestern edge, while updraft values encircling Ml 's northeastern edge are 6 m s-1• The cyclonic gyre due west of Ml near ( -3, -23.5) maintains a downdraft speed of -6 m s-1, but reduces to -2 m s-1 at 0.5 km (Figure 3).Speeds of 3 ,.._, 6 m s-1 accompany the strong updrafts, consistent at all levels, within the central grid region.A strong updraft may also be found south of Ml near (-2.5, -25) with a speed of 6 m s-1• Note that values of w presented in Figure 8 are, in general, 2 ,.., 3 times larger than those with 0.5 km resolution (see Figure 6b in Part I) .This finding is reasonable, since the utilization of 0.25 km grid resolution is able to capture some features associated with fine-scale structure of a microburst-producing storm.As a result, both updrafts and dciwndrafts become stronger as depicted in Figure 8. Figure 9 displays the perturbation pressure pattern for this level where highest pressure is found near the southeast and northwest corners of the do main.The low pressure centers, located at (-3, -23.5) and (-1:5, -25.5), are found near the centers of cyclonic circulation mentioned previously.Mass flow, therefore, is toward the cyclonic center from the surrounding region not associated with the cyclonic gyre, analogous to sedimentary erosion at points of low terrain.
Updraft regions which flank each microburst event maintain high pressure anomalies between 0.1 and 0 . 2 mb.The cyclonic gyre west southwest of Ml near (-6.5, -25) has a -0.l mb low pressure value with a similar high pressure value to its southwest.
The perturbation temperature field {Figure 10) exhibits warm-core anomalies for both microburst regions with surrounding cool air {-1 to -2°C). .

Plan View at 1.25 km
The flow field with reflectivity contours superimposed at 1.25 is shown in Figure 11.The finger like appendages discussed earlier are more numerous and tongue like in resemblance.The finger like appendages associated with the dry air intrusions are broader than 1 km and the crossing angle of environmental air toward the high reflectivity core increases to almost a perpendicular angle.Cyclonic turning of the wind occurs around both microbursts with pronounced cyclonic circulation visible around Ml. Mass is thus noted to spiral inward prior to its descent within the microburst core.Two cyclonic circulations are evident at this level.One is located southwest of Ml near (-3.5, -24), and the other is to the southeast of M2 near (-5, -18.5).These two cyclonic circulations correspond to the misocyclones discussed in Parts I and III of this study.These two misocyclones are better resolved with 0.25 km grid resolution (Figure lla) than those with 0.5 km resolution (Figure llb).In addition, the 0.25 km grid provides much stronger reflectivities (up to 60 dBZ) in the microburst regions.• to the southeast of the domain near (1, -24) is more pronounced than at 1 km and corresponds to the low-level cyclone attached to the southern flank of the surface gust front.A divergence of fl.ow occurs on the southern flowing branch of Ml 's, cyclonic circulation approximately 2 km west of its main core.The westward branch of this split flow feeds into anticyclonic curvature, while the eastern branch continues its cyclonic trek into the feeder tongue just south of Ml.Mass inflow of dry air into Ml is from the southeast, while inflow for M2 occurs from the north.The strength of Ml both absorbs and seemingly blocks the environmental wind, thus forcing M2's circulation to draw its mass field from the north.Unlike Fujita's (1985) description of the misocyclone structure, which de scribed the misocyclone's role as one of a collector of hydrometeors for the microburst to enhance precipitation loading, Lin et al. (1991) proposed that the misocyclones act as pinwheels, which funnel in and efficiently channel dry environmental air for the enhancement of evaporative cooling by ventilating the saturated downdraft.Entrained air is mixed within the downdraft creating evaporative cooling which aids the development of negative buoy�ncy produc tion.Conclusively, circulation enhancement spawned by the misocyclones aids to strengthen microburst affects launched at lower levels.shows that features revealed by 0.25 km resolution {Figure 12a) compare well with those by 0.5 km resolution {Figure 12b).Notice that Ml is located in the downdraft c • olumn with high refiectivities.It is accompanied by the updraft to its east in the vicinity of a microburst gust front (heavy dashed li_ ne).For 0.5 km grid analysis (Figure 12b), the air How is generally from right (east) to left (west), but the 0.25 km grid datum (Figure 12a) reveals a more perturbed field of eddy motion within and around microburst Ml.Spatial variations of vertical velocity ( w) along the same cross section for both 0.25 and 0.5 km spacings are presented in Figure 13.It is seen that micro burst Ml maintains a maximum downdraft speed of -6 m s-1 with cor responding updraft speeds of 2,,..., 4 m s-1 1 km to its east near the gust front (Figure 13a).The maximum downdraft speed is about two times larger than that with 0.5 km resolution (Figure 13b).As noted earlier, the smaller grid spacing (0.25 km) can resolve fine-scale mesoscale features associated with mi crobursts.As a result, much larger values of the updraft and downdraft are discerned.Figure 13 clearly shows that the 0.25 km analysis datum depicts mi croburst features much more vividly and with larger values than those obtained at the 0.5 km analysis.Thus, the vertical velocity display for 0.25 km analysis (Figure 13a) exhibits the overall storm intensity two to three times greater than those for 0.5 km analysis (Figure 13b) .Figure 14 displays the distributions of deviation perturbation pressure (Figure 14a) and temperature {Figure 14b) for the 0.25 km grid analysis.In the lowest layer near the surface, high pressure forms within the microburst in ner core with low pressure to its right (east) and left (west) .As a result, strong horizontal pressure gradients dev: .elop from the center of Ml toward the east and west.Such pressure gradients are necessary to accelerate the diverging outflow from the microburst inner core.These findings are consistent with those for the 0.5 km grid analysis (not shown) except the magnitude is somewhat larger.In the microburst-dominant region, relative cooling (up to -3° C) prevails at low levels.As discussed in Part I of this study, such cooling is mainly caused by evaporation of rain drops embedded within the downdraft column of air.As a result, a diverging outflow from the microburst center is negatively buoy ant at low levels.On the east side of a microburst gust front (heavy dashed line) , relative warming occurs.Such warming is associated with the incoming environmental air from the east, which is warmer than the microburst outflow at low levels.A distinct temperature contrast is evident across the gust front  with warming on its east and cooling on its west.These features are in good agreement with those obtained by using 0.5 km grid spacing (not shown) .

Vertical Cross Section
Based on the results presented above, we found that analyses with differ ent grid resolution have revealed the delicate nature of micro burst phenomena.In particular, the 0.25 km grid analysis often provides better resolution of those relevant features of microbursts as compared to those with 0.5 km resolution.As noted earlier, the 0.25 km grid analysis can resolve mesoscale feature with wavelength > 1.5 km, while the 0 .5 km analysis can only resolve those with wavelength> 3 km.

CONCLUSIONS
Case studies • of•microburst-producing storms, conducted in Parts I and II of this study; hav� established the diversity of the microburst phenomena and the role played' . .by •the misocyclone with each \ndividual storm.With the aid of 0.25 km grid spacing, we reexamined the 5 August 1982 case at 1845 MDT.Results show that structural features of a microburst-producing storm become more .visibleand readily identifiable.In particular, vertical velocities increase 2 •,.., 3 times at the 0.25 km grid analysis than those with 0.5 km resolution.However, the overall pattern of vertical velocity between the two analyses remains essentially the same.Magnitudes of deviation perturbation pressure and temperature for the 0.25 km analysis are found to be somewhat larger than those for the 0.5 km analysis.However, the differences are relatively small compared to those for vertical velocity mentioned early.
Examination of both analysis data sets has provided useful knowledge toward understanding the phenomena of a microburst-producing storm in the ABL.It was discovered that several features undetected at the 0.5 km grid spac ing became vividly apparent at the 0.25 km grid datum.Furthermore, most features found became strikingly more apparent, both in magnitude and appear ance than those reported in Part I of this study.When the data quality and resolution are adequate, a thermodynamic retrieval method can be employed to study some fine-scale structures of mesoscale disturbances in the ABL, includ ing three-dimensional winds, pressure and temperature perturbations within a convective system, with success.
A elm ow ledge me nb.

�
Figure9displays the perturbation pressure pattern for this level where highest pressure is found near the southeast and northwest corners of the do main.The low pressure centers, located at(-3, -23.5) and (-1:5, -25.5), are found near the centers of cyclonic circulation mentioned previously.Mass flow, therefore, is toward the cyclonic center from the surrounding region not associated with the cyclonic gyre, analogous to sedimentary erosion at points of low terrain.Updraft regions which flank each microburst event maintain high pressure anomalies between 0.1 and 0 . 2 mb.The cyclonic gyre west southwest of Ml near (-6.5, -25) has a -0.l mb low pressure value with a similar high pressure value to its southwest.The perturbation temperature field {Figure 10) exhibits warm-core anomalies for both microburst regions with surrounding cool air {-1 to -2°C).The cold anomalies are believed, in part, resultant from dry adiabatic expan sion of the lower level environmental air being channeled aloft within updraft areas.Similarly, cold temperature anomaly values associated with M2 vary between -1 and -2° C. Temperatures along the supposed gust front location . r;-:-:;-,.�o);:::_ , \-:-:-:: : : : /a .

Figure 12
Figure12displays the west-east cross section of the wind field with reflec tivity contours superimposed for both 0.25 and 0.5 km grid spacings.This cross

Fig. 13 .
Fig. 13.As in Figure 12 except for vertical velocity.co ntour interval is 1 m s -1 • Negative values are shaded,

Fig. 14 .
Fig. 14.The west-east cross section similar to Figure 12 showing (a) deviation perturba tion pressure (PJ) and (b) deviation perturbation temperature (T�d) with 0.25 km grid resolution.Contour intervals for PJ and T�d are 10 Pa (0. 1 mb) and 1°c, respectively.Negative values are shaded.
The authors wish to thank the National Center for Atmospheric Research { NC AR ) for providing the dual-D op pier data and technical assistance.We are grateful to John Coover, Paul Lapointe and William McNamee for their help throughout the course of this study.This research was partially supported by the Division of Atmospheric Sciences, National Science Foundation, under Grant ATM-8312172-01.B. T. Regan was supported by the Air Force Institute of Technology.