NOTES and CORRESPONDENCE High-Resolution Airborne Radar Observations of Mammatus

JANUARY 2001 NOTES AND CORRESPONDENCE 159

NOTES AND CORRESPONDENCE

High-Resolution Airborne Radar Observations of Mammatus

NATHANIEL S. WINSTEAD,J.VERLINDE,S.TRACY ARTHUR,FRANCINE JASKIEWICZ, MICHAEL JENSEN,NATASHA MILES, AND DAVID NICOSIA Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

14 January 2000 and 20 June 2000

ABSTRACT High-resolution Doppler radar observations of mammatus clouds coupled with soundings of the preanvil and anvil environments provide a unique opportunity to examine previously reported observations of, and evaluate various hypotheses of, mammatus formation. These observations con®rm the general hypothesis for mammatus formation advanced by Ludlam and Scorer, and provide detail of the cloud interior structure. Speci®cally, the radar observations indicate that mammatus elements are reminiscent of eddy circulations with a weak downdraft core ¯anked by horizontal convergence and divergence at the top and base of the cloud, respectively. Doppler spectral width measurements, however, yielded values of only 2±3 m sϪ1, indicating only weak turbulent motions within individual mammatus elements. Re¯ectivity analyses of mammatus elements indicate a ®rm link to the parent anvil. A dual-Doppler analysis of the parent anvil indicates that the larger-scale environment where the mammatus exist is characterized by the existence of gravity waves or shear overturning. It is hypothesized that these circulations might play a role in the initiation of this particular outbreak of mammatus.

1. Introduction matus clouds. However, studies to verify these hypoth- Mammatus are one of the most striking cloud features eses have been hard to come by. Some studies, such as seen in the atmosphere. Often observed beneath the an- those by Hlad (1944), Martner (1995), and Stith (1995), vils of thunderstorms, these clouds have served as a even presented observations that, on ®rst appearance, visual warning to pilots that turbulence is likely to be seem to bring into question some aspects of the early present (Lankford 1990). Early hypotheses of the pro- hypotheses. Martner presented observations indicating cesses leading to the development of mammatus were that individual clouds have their root deep in the anvil, presented by Wagner (1948), Ludlam and Scorer (1953), while Stith observed positive temperature perturbations and Scorer (1958), and our understanding has not inside the cloud. changed signi®cantly since that time. Three related pro- In this paper, we report results from high-resolution, cesses were identi®ed: subsidence of a cloud interface airborne, radar observations of a large ®eld of mam- layer, fallout of precipitation, and evaporation of pre- matus clouds taken in a severe thunderstorm outbreak cipitation (Scorer 1958). These three processes render during the Veri®cations of the Origins of Rotation in the (stable) subcloud layer slightly unstable and result Tornadoes Experiment (VORTEX95; Rasmussen et al. in downward convection with smooth, usually less 1994). As with several of the previous mammatus stud- sharply outlined, surfaces. In the years since these studies, these observations are from a target of opportunity. ies, additional hypotheses, mostly based on isolated ob- The aircraft was in transit between two severe thun- servational studies, have furthered our understanding of derstorms in the Oklahoma±Texas region when it passed the details of both the environment and structure of beneath a large ®eld of mammatus clouds. The obser- mammatus. Clarke (1962) suggested that gravity waves vations from this single transect are the focus of the produced the vertical motion destabilizing cloud base. study. Martner (1995) provided further evidence that gravity The high spatial resolution within individual mam- waves play an important role in the initiation of mammatus elements, coupled with the along-track mesoscale view offered by the airborne platform and two Cross- chain Linked Atmospheric Sounding System (CLASS) soundings, allow us to evaluate results reported in pre- Corresponding author address: Nathaniel S. Winstead, Space De- partment, Applied Physics Laboratory, The Johns Hopkins Univer- vious papers. In particular, these radar observations are sity, 11100 Johns Hopkins Rd., Laurel, MD 20723. used to examine the different hypotheses presented in E-mail: [email protected] previous studies of mammatus and to address questions

᭧ 2001 American Meteorological Society

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point separation is 400 m in the horizontal and 500 m in the vertical. Each individual radar scan was time± space adjusted with the propagation speed of the storm. A Cressman ®lter (Cressman 1959) was used in the interpolation process with a radius of in¯uence of 500 m in the horizontal and 600 m in the vertical. Horizontal velocities were calculated using Custom Editing and Display of Reduced Information in Cartesian Space software (Mohr and Miller 1983). These horizontal velocities were smoothed using a two-pass, ®ve-point ®lter (Liese 1982), which damped wavelengths up to 1.8 km and eliminated those less than 1.2 km. The vertical velocities were obtained through downward integration of the anelastic continuity equation starting half a grid- point above the last detectable re¯ectivity at cloud top. Following Hildebrand et al. (1996), the vertical velocities were not corrected for hydrometeor fall speed under the assumption that the fall speeds of the mostly ice particles are small. All horizontal velocities are presented as anvil-relative velocities with an anvil- mean wind vector of 15.4 m sϪ1 from 254Њ subtracted. Data from two CLASS radiosonde launches are also presented. Both radiosondes were released from the

FIG. 1. Composite re¯ectivity derived from the ELDORA re¯ec- same location, also indicated in Fig. 1. The ®rst sound- tivities as the NCAR Electra was ¯ying along the anvil containing ing, launched at 2112 UTC, is representative of the pre- the mammatus clouds. The locations of the two CLASS soundings storm environment while the second sounding, launched are indicated by the ϫ. The box on the plot indicates the dual-Doppler at 2144 UTC, passed directly through the anvil of the analysis domain. observed storm. While there is no ®rm evidence that the second sounding passed directly through the mam- that have arisen from aircraft measurements of mammatus ®eld (it passed through the anvil approximately matus. 50 km from the aircraft track), it does pass through the anvil of the same storm and thus is representative of the anvil environment. Comparisons with aircraft as- 2. Data and methods cend±descend temperature pro®les con®rmed that this The radar data analyzed in this study were obtained sounding was representative of the larger anvil region. by the National Center for Atmospheric Research (NCAR) Electra Doppler radar (ELDORA). The design 3. Overview and capabilities of the radar can be found in Hildebrand et al. (1994, 1996). Important to this study is the high On 8 June 1995, a cluster of severe thunderstorms spatial resolution that can be achieved with the ELDORA. over northern Texas and the Oklahoma panhandle were For the case presented here, the VORTEX Convective observed by the ELDORA during VORTEX. These I scanning mode (Wakimoto et al. 1996) was used to storms consisted of a line of convection in the northern collect the data. In this mode, the along-track resolution Texas panhandle and a supercell storm in the Oklahoma (as de®ned by the antenna rotation rate) was approxi- panhandle. The out¯ow anvils of the Texas line merged mately 330 m, with a 150-m gate spacing along the with the Oklahoma storm, creating a mesoscale precip- beam. The crossbeam resolution, in the sweep plane, is itation region of stratiform rain between the two con- approximately 125 m at a distance of 5 km from the vective regions. An extensive ®eld of mammatus clouds radar (where most of the mammatus were observed) and protruded from the base of this anvil between the two 620 m at 25 km from the radar. storms. These mammatus clouds were observed with Re¯ectivity and Doppler velocity measurements ELDORA along the southeastern edge of the anvil as were edited in radar space [using Solo; Oye et al. the Electra ¯ew from the cell in Oklahoma toward the (1995)] to remove ground clutter and sidelobe returns cells in Texas. A photograph (Fig. 2) showing some of before being interpolated onto a Cartesian grid [using these elements was taken from the Electra during this REORDER; Oye (1994)]. Figure 1 shows the location ¯ight leg. of this grid (labeled mesoscale box in Fig. 1) in relation Figure 3 shows re¯ectivity contours on the horizontal to the track of the aircraft and the location of the anvil. slice through the base of the anvil (Z ϭ 7 km), the slope It covers a large section of that region of the anvil in of which is upward toward the south. The southern part which the mammatus clouds were embedded. The grid- of this domain is below cloud. A cut through the domain

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FIG. 2. Photograph from the ELECTRA of the bottom of the anvil containing the mammatus (courtesy W.-C. Lee, NCAR). from south to north ®rst shows the mammatus layer and then the deeper parts of the anvil. Small-scale cellular features, varying in sizes between 1 and 3 km, characterize the mammatus layer. Deeper into the anvil these cellular structures gradually merge into a more uniform re¯ectivity pattern (shown in Fig. 6 later in the paper). Some suggestion of a mesoscale organization in the arrangement of the cells can be seen. The dashed lines in FIG. 3. Horizontal crosssection at Z ϭ 7 km through the anvil Fig. 3 indicate an orientation approximately parallel to showing the mammatus elements. The dashed lines indicate possible axes of organization. Length scales of two mammatus clouds are the mean wind direction, though other orientations may included as a reference and a mean wind vector is shown. North is also be envisioned. up on the image. The mesoscale environment in which the mammatus clouds are embedded is revealed by a dual-Doppler analysis of the parent anvil, shown in Fig. 4. Figure 4a shows relation coef®cient of Ϫ0.7, indicative of downward- the horizontal cross section (Z ϭ 9 km) of vertical ve- propagating waves. locity contours inside the anvil above the mammatus The vertical structure of the re¯ectivity and radial layer with storm-relative wind vectors superimposed. velocity ®elds of a mature mammatus cell can be seen The anvil-relative wind vectors in a vertical cross-sec- in the pseudo±range height indicator (RHI) plots pre- tion (Fig. 4b) reveal strong vertical shear of the hori- sented in Fig. 6. These plots represent the projection of zontal wind (4 ϫ 10Ϫ3 sϪ1 in u, 3.1 ϫ 10Ϫ3 sϪ1 in ␷), the cone scanned by the aft radar onto a vertical plane. with embedded updraft±downdraft circulations. The (The antenna rotates about the long axis of the aircraft vertical velocity pattern is typical of that associated with and is pointing 18.5Њ off the vertical. Therefore, the waves, possibly gravity waves spawned by penetrative radial velocities contain a signi®cant component of the convection upstream or possible shear overturning as- horizontal wind.) A core of strong re¯ectivities extends sociated with the strong vertical shear in the anvil. These down from the uniform parts of the anvil (the original waves have a wavelength of 4±7 km, with maximum anvil base) to the center of the mammatus cloud. Near updraft±downdraft perturbations of approximately 10 m the bottom of the mammatus this core folds back, rem- sϪ1. The analysis extends down to just above the mam- iniscent of the structure of a slow-moving, nonturbulent matus layer, where the vertical velocity perturbations eddy, giving the mammatus cloud a distinctly mush- were on the order of a few meters per second. However, room-shaped appearance. The upward curvature of the there were insuf®cient observations within mammatus high-re¯ectivity core along the outside of the mammatus elements to perform any detailed dual-Doppler analysis element is suggestive of convergence at the base of the there to verify the link between these waves and indi- element with resulting detrainment toward the side with vidual mammatus elements. Figure 4b shows that the a subsequent upward movement along the edge. Though waves are mostly vertically erect and extend from the more dif®cult to interpret due to the scanning plane of anvil base up to the top of the anvil. Moreover, a spectral the radar, the radial velocity image suggests a similar analysis of the vertical velocity measurements from the view of the cloud. Weaker velocities away from the Electra ¯ying below cloud base revealed energy at scales radar, indicative of a downdraft (when the contribution similar to the analyzed waves in the anvil, suggesting of the horizontal wind is included), are present in the that these waves extended to well below cloud base (Fig. center of the mammatus element ¯anked by possible 5). These vertical velocity data were negatively corre- updrafts (stronger radial velocities) at the sides. lated to the altitude-adjusted pressure ®elds with a cor- An expanded view of the base of the anvil (not shown)

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FIG. 4. (a) Dual-Doppler analysis at Z ϭ 9 km of vertical velocity. The storm-relative horizontal wind vectors are superimposed. (b) Vertical cross section of vertical velocity within the anvil with storm-relative (z±x) wind vectors superimposed. reveals a broad, uniform re¯ectivity region above a layer 4. Discussion characterized by mammatus elements. Several other mushroom-shaped plumes were also seen, but most of The radial velocity and Doppler spectrum observa- the mammatus clouds were slightly smaller and showed tions presented in section 3 suggest that the mammatus only a core, in many cases sheared to one side like the clouds are slowly descending, low turbulence entities. one to the left of the mushroom-shaped cloud in Fig. These speci®c clouds formed at the base of an anvil 6. These patterns were observed along approximately cloud, the interior of which was characterized by strong 100 km of ¯ight track. Nowhere in this entire set were vertical velocity variations (Fig. 4). Moreover, aircraft mammatus clouds observed to be completely separated measurements below cloud suggest that the vertical var- from the anvil deck above. iations extended some distance below cloud base. There- The variance of the Doppler spectrum (not shown) in fore, these observations suggest that the anvil lower the mammatus element showed no systematic decrease clear air interface was being displaced downward, thus in value from the core toward the bottom edge such as providing a destabilization mechanism. During down- was observed by Martner (1995). However, the view- ward displacements the cloudy air descends moist adi- point of these observations and the wide beam of the abatically and the dry air below cloud base dry adia- ELDORA can partially account for these differences. batically, producing a steepening lapse rate across the The measured values are similar to those reported by cloud boundary. A similar destabilization process was Martner (on the order of 2±3 m sϪ1) and are consistent advanced by Ludlam and Scorer (1953), although they with the weak turbulence encountered in the ¯ight envisioned compensating subsidence around the con- through a mammatus region by Stith (1995). vection as the mechanism producing the initial down-

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FIG. 5. A spectral analysis of Electra in situ vertical velocity measurements underneath the mammatus clouds. This analysis represents 300 points (taken at 1 Hz) from the Electra, which was ¯ying at a speed of 112 m sϪ1 normal to the radar-resolved waves. The peak corresponding to the anvil waves is indicated.

ward forcing. Once destabilized, the developing mam- FIG. 6. Pseudo-RHI plot of (a) re¯ectivity and (b) radial velocity matus cloud no longer depends on the wave for its ex- for a representative mammatus element. This mammatus cloud is istence, but will continue to grow independent of the almost directly above the aircraft ¯ight track. See text for explanation wave. The developing instability results in downward- of arrows. moving cloudy plumes separated by upward-moving clear thermals. In such a situation, one would expect to ture gradients to develop along the edges of an intruding observe dry-adiabatic lapse rates just below and moist- anvil, as required for the Ludlam and Scorer hypothesis. adiabatic lapse rates just above the cloud±clear air in- Thirty minutes later, with the anvil now over the release terface as clear air is displaced upward and cloudy air site, signi®cant differences can be seen in the second is displaced downward. sounding. The air below cloud base (located at ϳ450 Moreover, Ludlam and Scorer also suggested that the evaporation of small precipitation particles in the clear air beneath the anvil might aid in the initiation. Warner (1973) suggested that evaporating precipitation might be suf®cient by itself to trigger the development of mammatus clouds. In this case, one would expect to observe a moistening of the subcloud layer in time. As part of VORTEX, many radiosondes were launched in the area surrounding the greater convective system to characterize the environment in which these storms developed. Of these soundings, two were released from the same site (see Fig. 1 for location) in the general area where the mammatus clouds formed. One radiosonde was released in the clear air ahead of the anvil (Fig. 7, dashed line), and the other into the anvil that produced the mammatus clouds (Fig. 7, solid line). The Electra observed mamma along most of the track shown in Fig. 1; the sounding passing through the anvil was therefore within 50 km from a location with known mammatus clouds. The prestorm sounding reveals a conditionally unstable environment at midlevels with a strong inversion at FIG. 7. Two CLASS soundings for the preanvil environment 750 hPa and signi®cant vertical shear of the horizontal (dashed) and anvil environment (solid). The preanvil sounding was wind, especially in the 500±400-hPa layer. Additionally, taken at 2112 UTC while the anvil sounding was taken at 2144 UTC. midlevel layers are dry, setting the stage for sharp mois- The location where soundings were taken is indicated on Fig. 1.

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matus-like elements in the ash clouds of volcanoes (Stith 1995). Moreover, these clouds developed in an area characterized by externally forced wave activity. There- fore, it is possible that an external factor such as a contribution of downward momentum from an overlying wave could provide the necessary forcing to modify the local environment suf®ciently to destabilize the anvil by forcing vertical displacements. This might explain the dry-adiabatic clear air and moist-adiabatic cloudy air observations: observations consistent with vertical displacement of the cloud base. The 319-K potential temperature line on the diagram shows the required origin for ascending clear air to offset the negative buoyancy at 500 hPa for a cloud-base parcel with1gkgϪ1 of condensed matter. It reveals that air lifted from about 50 hPa below the level of neutral buoyancy would have approximately the same temperature as the cloudy parcel at the point where it has just evaporated all of its condensed matter. The picture revealed by this analysis is one of a slowly descending cloud near neutral buoyancy relative to the slowly rising clear air environment surrounding it. This picture is consistent with the low radar-observed values of velocity variance in the mammatus clouds. The slow descent of the cloud allows precipitation to fall through the cloud FIG. 8. Close-up of the anvil sounding with an insert of the (a) into the slower descending subsaturated air directly be- cloud layer and (b) conceptual model showing the hypothesized path low the mammatus cloud (evidenced by the moistening of the balloon through the ®eld of mammatus. The ␪e line (long of the subcloud layer between the time of the two sound- dashes) on the sounding is representative of the anvil air just above ings presented in Fig. 7). Evaporation of precipitation the interface. Together with the ␪ line (dotted), the ␪e line represents the path a moist parcel (1 g kgϪ1 of condensed water) would follow below cloud base will produce temperatures between once destabilized. the dry-bulb and the wet-bulb values, which will be less negatively buoyant than the cloud itself, resulting in a fallout front at the leading edge of the cloud (Scorer hPa, at ice saturation) cooled by several degrees while 1958). The convergence along this front leads to hori- moistening at the same time. These changes are con- zontal divergence of this less negatively buoyant air, sistent with precipitation evaporating below cloud base. where it then ascends at the sides of (relative to) the A closer look at the anvil sounding (Fig. 8) reveals downward plume. This view is supported by the detailed it to be absolutely stable in the interior of the anvil. radar observations. Directly above cloud base, however, a moist-adiabatic Figure 9 shows re¯ectivity (panels a and c) and radial lapse rate exists over a 40-hPa layer. The lapse rate in velocity (panels b and d) ®elds of two mammatus ele- the ®rst 30 hPa below cloud base is dry adiabatic, with ments, one overhead (panels a and b) and one off to the the interfacial layer (443±449 hPa) characterized by a side of the aircraft track (panels c and d). A combination small isothermal layer. Although there is no direct ev- of features from these images con®rms the model pre- idence, this arrangement of lapse rates does suggest that sented above. Both of the re¯ectivity images reveal dis- the radiosonde passed through a region of mammatus tinctive upside-down mushroom-shaped appearances. A clouds (in the 410±475-hPa layer), going from an up- stem of high re¯ectivity stretches down the core, con- ward-moving clear air thermal through the side into a necting the mammatus cloud to the uniform anvil above. mammatus cloud (Fig. 8b). Moreover, the isothermal At the base of the mammatus cloud, the core folds back layer at the interface suggests that the interior of the as precipitation-laden air diverges to the sides and is cloud was (slightly) warmer than the environment. This left behind. This view is further supported by the radial observation is in agreement with in situ measurements velocity images. Figure 9d shows general divergence reported by Stith (1995), the analysis of which also (stronger radial velocities toward the radar on the left showed that the mammatus cloud was warmer than its side and weaker on the right side) at the bottom of the environment. However, the sounding gives no infor- cloud, with convergence (weaker radial velocities to- mation about precipitation content, the effect of which ward the radar on the left side and stronger on the right can easily offset the thermal buoyancy. Particles within side) at the stem of the mushroom. The circulation is the parcel contribute to negative buoyancy, their con- completed with the aid of Fig. 9b. In this overhead view, tribution to which can explain the observance of mam- weaker radial velocities in the center of the cloud

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FIG. 9. (a) Re¯ectivity and (b) radial velocity ®elds of a mammatus element directly overhead of the radar. (c) Re¯ectivity and (d) radial velocity off to the side of the radar.

¯anked by stronger velocities are indicative of a down- anvil environments provided a unique opportunity to draft in the center. The radial velocity ®elds reveal an reinterpret previously reported observations of, and (slowly) overturning eddy structure, consistent with the evaluate various hypotheses of, mammatus formation. observations reported here and with what was proposed Observations presented con®rm the general hypothesis by Ludlam and Scorer. Critical in this model is the sup- for mammatus formation advanced by Ludlam and Scor- ply of condensed matter, for that is what sustains the er (1953), and provide detail of the cloud interior struc- negative buoyancy. ture. In spite of the lack of direct evidence, a case was However, this model does not support the detrainment presented that the anvil penetrated by the radiosonde hypothesis advanced by Emanuel (1981). Emanuel hy- was characterized by mammatus clouds. This sounding pothesized that the mammatus cloud mixes the entrained revealed a cloudy layer slightly warmer than its sur- air homogeneously through the cloud, and that the mam- roundings, similar to what Stith (1995) found. However, matus elements may separate completely from the parent with the contribution of precipitation loading to the neg- anvil. The re¯ectivity structures presented (Figs. 6 and ative buoyancy, the cloud would be negatively buoyant. 9) clearly reveal organized, inhomogeneous mixing. An analysis of the sounding and radar data suggests that Furthermore, there were no observations of mammatus the clouds remain only marginally negatively buoyant, elements separated from the parent anvil. in their immediate environment, which consists of clear air lifted from below. The low velocity variances reported in this and other (Martner 1995; Stith 1995) stud- 5. Conclusions ies are consistent with such a slowly descending entity. High-resolution Doppler radar observations of mam- This study adds further evidence that either gravity matus clouds and a dual-Doppler analysis of the over- wave activity or shear overturning in the environment/ lying anvil coupled with soundings of the preanvil and parent cloud may play a role in the initiation (Clarke

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1962; Martner 1995), and possibly development, of Emanuel, K. A., 1981: A similarity theory for unsaturated downdrafts mammatus clouds. It is postulated that wave activity in within clouds. J. Atmos. Sci., 38, 1541±1557. Hildebrand, P. H., C. A. Walther, C. L. Frush, J. Testud, and F.Baudin, the atmosphere may provide a different mechanism to 1994: The ELDORA/ASTRAIA airborne Doppler weather radar: produce the necessary destabilization, which was hy- Goals, design, and ®rst ®eld tests. Proc. IEEE, 82, 1873±1890. pothesized by Ludlam and Scorer to come from com- , and Coauthors, 1996: The ELDORA/ASTRAIA airborne Dopp- pensating subsidence. However, wave activity should be ler weather radar: High-resolution observations from TOGA COARE. Bull. Amer. Meteor. Soc., 77, 213±232. considered a suf®cient rather than a necessary condition. Hlad, C. J., Jr., 1944: Stability tendency and mammatocumulus Pilots are instructed that mammatus clouds serve as clouds. Bull. Amer. Meteor. Soc., 25, 327±331. a visual warning of turbulence, likely based on the ob- Lankford, T. T., 1990: The Pilot's Guide to Weather Reports, Fore- servations of Hlad (1944) who experienced signi®cant casts, and Flight Planning. TAB Books, 383 pp. turbulence ¯ying through a mammatus cloud. This Leise, J. A., 1982: A multi-dimensional, scale-telescoped ®lter and data extension package. NOAA Tech. Memo. ERL WPL-82, 19 warning has been questioned by Stith (1995) because pp. [Available from NOAA/ETL, 325 Broadway, Boulder, CO of recent observations (Martner 1995; Stith 1995). At 80303.] ®rst sight, the observations presented here would sup- Ludlam, F. H., and R. S. Scorer, 1953: Convection in the atmosphere. port Stith's doubts. However, the observation of wave Quart. J. Roy. Meteor. Soc., 79, 317±341. activity with ϩ10msϪ1 perturbations in the anvil, and Martner, B. E., 1995: Doppler radar observations of mammatus. Mon. Wea. Rev., 123, 3115±3121. reports from observers on the aircraft indicating a very Mohr, C. G., and L. J. Miller, 1983: CEDRICÐA software package bumpy ride, suggest that there is reason for caution. for Cartesian space editing, synthesis and display of radar ®elds Even though the interior circulations of a mammatus under interactive control. Preprints, 21st Conf. on Radar Me- cloud may not be very turbulent, the environment in teorology, Edmonton, AB, Canada, Amer. Meteor. Soc., 569± which mammatus clouds occur may indeed be turbulent, 574. Oye, R., 1994: REORDER: A program for gridding radar data. Field and provide an uncomfortable ride for passengers. Observing Facility, National Center for Atmospheric Research, 20 pp. [Available from Atmospheric Technology Division, Acknowledgments. The authors would like to thank NCAR, P.O. Box 3000, Boulder, CO 80307.] Dr. Roger Wakimoto for suggesting the case and Dr. , C. Meuller, and S. Smith, 1995: Software for radar translation, Wen-Chau Lee for giving us the data. We also thank visualization, editing, and interpolation. Preprints, 27th Conf. on Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 359±361. David Dowell for helping with construction of Fig. 1 Rasmussen, E. N., J. M. Straka, R. Davies-Jones, C. A. Doswell III, and Drs. John Clark, Dennis Lamb, and Alistair Fraser F. H. Carr, M. D. Eilts, and D. R. MacGorman, 1994: Veri®cation for many enjoyable discussions. Comments by Dr. Jeff of the Origins of Rotation in Tornadoes Experiment: VORTEX. Stith and other anonymous reviewers greatly improved Bull. Amer. Meteor. Soc., 75, 995±1006. the manuscript. Scorer, R. S., 1958: Dynamics of mamma. Sci. Prog., 46, 75±82. Stith, J. L., 1995: In situ measurements and observations of cumu- lonimbus mamma. Mon. Wea. Rev., 123, 907±914. REFERENCES Wagner, F., 1948: Mammatusform als Anzeichen Absinkbewegung in Wolkluft. Ann. Meteor., 1, 336. Clarke, R. H., 1962: Pressure oscillations and fallout downdraughts. Wakimoto, R. M., W.-C. Lee, H. B. Bluestein, C.-H. Liu, and P. H. Quart. J. Roy. Meteor. Soc., 88, 459±469. Hildebrand, 1996: ELDORA observations during VORTEX 95. Cressman, G. P., 1959: An operational objective analysis scheme. Bull. Amer. Meteor. Soc., 77, 1465±1481. Mon. Wea. Rev., 87, 367±374. Warner, C., 1973: Measurements of mamma. Weather, 28, 394±397.

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