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9 - Mesoscale convective systems

Published online by Cambridge University Press:  15 December 2009

Yuh-Lang Lin
Yuh-Lang Lin
Affiliation:
North Carolina State University
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Summary

A mesoscale convective system (MCS) is an organized cluster of thunderstorms, which persists at least for several hours and produces a continguous precipitation area. An MCS may be linear or circular in shape, and is often used to refer to a cluster of thunderstorms that does not satisfy the definition of a mesoscale convective complex (MCC) (Section 9.2). MCSs include squall lines and MCCs in the midlatitudes, and tropical storms (cyclones) and cloud clusters in the tropics. The term mesoscale convective line has also been used to represent a linear form of mesoscale convective systems.

MCSs have a horizontal scale greater than that of an individual thunderstorm, but smaller than the Rossby radius of deformation. The Rossby radius of deformation is defined in (4.2.12) as LR=NLz/f, where Lz is the vertical scale of the motion. In the midlatitudes, LR is approximately 1000km, assuming N=0.01s− 1, Lz=10km, and f=10−4 s− 1. These conditions require the horizontal scale of a MCS to be approximately 100km. Observations have indicated that MCSs have a typical lifetime of 3 hours or more, and their accompaning stratiform clouds may be sustained, or at least remain, for several days. Dynamically, this implies that the Coriolis acceleration is at least comparable to the other terms of the momentum equations, such as the inertial acceleration terms. This gives a time scale of f− 1 (e.g., see Table 1.1), i.e. at least 3h for midlatitude MCSs, which is consistent with observations.

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Mesoscale Dynamics , pp. 322 - 378
Publisher: Cambridge University Press
Print publication year: 2007

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References

Aiyyer, A. R. and Molinari, J., 2003. Evolution of mixed Rossby–gravity waves in idealized MJO environments. J. Atmos. Sci., 60, 2837–55.2.0.CO;2>CrossRefGoogle Scholar
Atallah, E. H. and Bosart, L. F., 2003. The extratropical transition and precipitation distribution of Hurricane Floyd (1999). Mon. Wea. Rev., 131, 1063–81.2.0.CO;2>CrossRefGoogle Scholar
Bergeron, T., 1954. The problem of tropical hurricanes. Quart. J. Roy. Meteor. Soc., 80, 131–64.CrossRefGoogle Scholar
Betts, A. K., 1983. Thermodynamics of mixed stratocumulus layers saturation point budgets. J. Atmos. Sci., 40, 2655–70.2.0.CO;2>CrossRefGoogle Scholar
Bluestein, H. B. and Jain, M. H., 1985. Formation of mesoscale lines of precipitation: Severe squall lines in Oklahoma during the spring. J. Atmos. Sci., 42, 1711–32.2.0.CO;2>CrossRefGoogle Scholar
Bluestein, H. B. and Weisman, M. L., 2000. The interaction of numerically simulated supercells initiated along lines. Mon. Wea. Rev., 128, 3128–49.2.0.CO;2>CrossRefGoogle Scholar
Browning, K. A., 1986. Conceptual models of precipitating systems. Wea. Forecasting, 1, 23–41.Google Scholar
Bryan, G. H. and Fritsch, J. M., 2000. Moist absolute instability: The sixth static stability state. Bull. Amer. Meteor. Soc., 81, 1207–30.2.3.CO;2>CrossRefGoogle Scholar
Camp, J. P. and Montgomery, M. T., 2001. Hurricane maximum intensity: Past and present. Mon. Wea. Rev., 129, 1704–17.2.0.CO;2>CrossRefGoogle Scholar
Carbone, R. E., 1982. A severe frontal rainband. Part I: Stormwide hydrodynamic structure. J. Atmos. Sci., 39, 258–79.2.0.CO;2>CrossRefGoogle Scholar
Chan, J. C. L. and Williams, R. T., 1987: Analytical and numerical studies of the beta-effect in tropical cyclone motion. Part I: zero mean flow. J. Atmos. Sci., 44, 1257–65.2.0.CO;2>CrossRefGoogle Scholar
Charney, J. G. and Eliassen, A., 1964. On the growth of the hurricane depression. J. Atmos. Sci., 21, 68–75.2.0.CO;2>CrossRefGoogle Scholar
Chow, K. C., Chan, K. L., and Lau, A. K. H.. 2002. Generation of moving spiral bands in tropical cyclones. J. Atmos. Sci., 59, 2930–50.2.0.CO;2>CrossRefGoogle Scholar
Cotton, W. R. and Anthes, R. A., 1989. Storm and Cloud Dynamics. Academic Press.Google Scholar
Crook, N. A. and Moncrieff, M. W., 1988. The effect of large-scale convergence on the generation and maintenance of deep moist convection. J. Atmos. Sci., 45, 3606–24.2.0.CO;2>CrossRefGoogle Scholar
Davis, C. A. and Bosart, L. F., 2002. Numerical simulations of the genesis of Hurricane Diana (1984). Part II: Sensitivity of track and intensity prediction. Mon. Wea. Rev., 130, 1100–24.2.0.CO;2>CrossRefGoogle Scholar
Davis, C. A. and Bosart, L. F., 2003. Baroclinically induced tropical cyclogenesis. Mon. Wea. Rev., 131, 2730–47.2.0.CO;2>CrossRefGoogle Scholar
Dengler, K. and Reeder, M. J., 1997. The effects of convection and baroclinicity on the motion of tropical-cyclone-like vortices. Quart. J. Roy. Meteor. Soc., 123, 699–725.CrossRefGoogle Scholar
DeMaria, M., Mainelli, M., Shay, L. K., Knaff, J. A. and Kaplan, J., 2005. Further improvements to the statistical hurricane intensity prediction scheme (SHIPS). Wea. Forecasting, 20, 531–43.CrossRefGoogle Scholar
Dickinson, M. and Molinari, J., 2002. Mixed Rossby-gravity waves and western Pacific tropical cyclogenesis. Part I: Synoptic evolution. J. Atmos. Sci., 59, 2183–96.2.0.CO;2>CrossRefGoogle Scholar
Elsberry, R. L. (ed.), 1995. Global Perspective of Tropical Cyclones. WMO-/TD No. 693, World Meteor. Org.
Emanuel, K. A., 1986. An air-sea interaction theory for tropical cyclones. Part I: Steady state maintenance. J. Atmos. Sci., 43, 585–604.2.0.CO;2>CrossRefGoogle Scholar
Emanuel, K. A., 1989. The finite-amplitude nature of tropical cyclogenesis. J. Atmos. Sci., 46, 3431–56.2.0.CO;2>CrossRefGoogle Scholar
Emanuel, K. A., 1994. Atmospheric Convection. Oxford University Press.Google Scholar
Emanuel, K. A., 1997. Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 1014–26.2.0.CO;2>CrossRefGoogle Scholar
Emanuel, K. A., 2005. Genesis and maintenance of “Mediterranean hurricanes”. Adv. Geosci., 2, 217–20.CrossRefGoogle Scholar
Emanuel, K. A. and Rotunno, R., 1989. Polar lows as arctic hurricanes. Tellus, 41A, 1–17.CrossRefGoogle Scholar
Fankhauser, J. C., Barnes, G. M., and LeMone, M. A., 1992. Structure of a midlatitude squall line formed in strong unidirectional shear. Mon. Wea. Rev., 120, 237–60.2.0.CO;2>CrossRefGoogle Scholar
Fiorino, M. and Elsberry, R. L., 1989. Some aspects of vortex structure related to tropical cyclone motion. J. Atmos. Sci., 46, 975–90.2.0.CO;2>CrossRefGoogle Scholar
Fritsch, J. M., Murphy, J. D., and Kain, J. S., 1994. Warm core vortex amplification over land. J. Atmos. Sci., 51, 1780–807.2.0.CO;2>CrossRefGoogle Scholar
Fujiwhara, S., 1921. The mutual tendency towards symmetry of motion and its application as a principle in meteorology. Quart. J. Roy. Meteor. Soc., 47, 287–93.CrossRefGoogle Scholar
Grady, R. L. and Verlinde, J., 1997. Triple-Doppler analysis of a discretely propagating, long-lived, High Plains squall line. J. Atmos. Sci., 54, 2729–48.2.0.CO;2>CrossRefGoogle Scholar
Gray, W. M., 1968. Global view of the origin of tropical disturbances and storms. Mon. Wea. Rev., 96, 669–700.2.0.CO;2>CrossRefGoogle Scholar
Gray, W. M., 1998. The formation of tropical cyclones. Meteor. Atmos. Phys., 67, 37–69.CrossRefGoogle Scholar
Guinn, T. and Schubert, W. H., 1993. Hurricane spiral bands. J. Atmos. Sci., 50, 3380–404.2.0.CO;2>CrossRefGoogle Scholar
Hendricks, E. A., Montgomery, M. T., and Davis, C. A., 2004. The role of “vortical” hot towers in the formation of tropical cyclone Diana (1984). J. Atmos. Sci., 61, 1209–32.2.0.CO;2>CrossRefGoogle Scholar
Heymsfield, G. M., Halverson, J. B., Simpson, J., Tian, L., and Bui, T. P., 2001. ER-2 Dopper radar investigations of the eyewall of Hurricane Bonnie during the convection and moisture experiment-3. J. Appl. Meteor., 40, 1310–30.2.0.CO;2>CrossRefGoogle Scholar
Hill, C. M. and Lin, Y.-L., 2003. Initiation of a mesoscale convective complex over the Ethiopian Highlands preceding the genesis of Hurricane Alberto (2000). Geophys. Res. Lett., 30, 1232, doi:10.1029/2002GL016655.CrossRefGoogle Scholar
Holland, G. J., 1983. Tropical cyclone motion: environmental interaction plus a beta-effect. J. Atmos. Sci., 40, 328–42.2.0.CO;2>CrossRefGoogle Scholar
Holland, G. J., 1997. The maximum potential intensity of tropical cyclones. J. Atmos. Sci., 54, 2519–41.2.0.CO;2>CrossRefGoogle Scholar
Holland, G. J. and Merrill, R. T., 1984. On the dynamics of tropical cyclone structural changes. Quart. J. Roy. Meteor. Soc., 110, 723–45.CrossRefGoogle Scholar
Houze, R. A. Jr., 1981. Structures of atmospheric precipitation systems – A global survey. Radio Sci., 16, 671–89.CrossRefGoogle Scholar
Houze, R. A. Jr., Rutledge, S. A., Biggerstaff, M. I., and Smull, B. F., 1989. Interpretation of Doppler weather-radar displays in midlatitude mesoscale convective systems. Bull. Amer. Meteor. Soc., 70, 608–19.2.0.CO;2>CrossRefGoogle Scholar
Hsu, H.-H. and Lee, M.-Y., 2005. Topographic effects on the eastward propagation and initiation of the Madden-Julian oscillation. J. Climate, 18, 795–809.CrossRefGoogle Scholar
Jiang, H. and Raymond, D. J., 1995. Simulation of a mature mesoscale convective system using a nonlinear balance model. J. Atmos. Sci., 52, 161–75.2.0.CO;2>CrossRefGoogle Scholar
Johnson, R. H. and Bartels, D. L., 1992. Circulations associated with a mature-to-decaying midlatitude mesoscale convective system. Part II: Upper-level features. Mon. Wea. Rev., 120, 1301–20.2.0.CO;2>CrossRefGoogle Scholar
Jorgensen, D. P., 1984. Mesoscale and convective scale characteristics of mature hurricanes. Part I: Inner core structure of Hurricane Allen (1980). J. Atmos. Sci., 41, 1287–311.2.0.CO;2>CrossRefGoogle Scholar
Kossin, J. P. and Schubert, W. H., 2004. Mesovortices in Hurricane Isabel. Bull. Amer. Meteor. Soc., 85, 151–3.CrossRefGoogle Scholar
Kuo, H.-C., Williams, R.-T., and Chen, J.-H., 1999. A possible mechanism for the eye rotation of typhoon Herb. J. Atmos. Sci., 56, 1659–673.2.0.CO;2>CrossRefGoogle Scholar
Laing, A. G. and Fritsch, J. M., 1993. Mesoscale convective complexes in Africa. Mon. Wea. Rev., 121, 2254–63.2.0.CO;2>CrossRefGoogle Scholar
Laing, A. G. and Fritsch, J. M., 1997. The global population of mesoscale convective complexes. Quart. J. Meteor. Soc., 123, 389–405.CrossRefGoogle Scholar
Laing, A. G. and Fritsch, J. M., 2000. The large-scale environments of the global populations of mesoscale convective complexes. Mon. Wea. Rev., 128, 2756–76.2.0.CO;2>CrossRefGoogle Scholar
Lilly, D. K., 1979. The dynamical structure and evolution of thunderstorms and squall lines. Ann. Rev. Earth Planet. Sci., 7, 117–71.CrossRefGoogle Scholar
Lin, Y.-L., Robertson, K. E., and Hill, C. M., 2005. Origin and propagation of a disturbance associated with an African easterly wave as a precursor of Hurricane Alberto (2000). Mon. Wea. Rev., 133, 3276–98.CrossRefGoogle Scholar
Lin, Y.-L., Wang, T.-A., and Weglarz, R. P., 1993. Interactions between gravity waves and cold air outflows in a stably stratified uniform flow. J. Atmos. Sci., 50, 3790–816.2.0.CO;2>CrossRefGoogle Scholar
Ludlam, F. H., 1963. Severe local storms: a review. Meteor. Monogr., 5, 1–30.Google Scholar
Madden, R. A. and Julian, P. R. 1994. Observations of the 40–50 day tropical oscillation – A review. Mon. Wea. Rev., 122, 814–37.2.0.CO;2>CrossRefGoogle Scholar
Maddox, R. A., 1980. Mesoscale convective complexes. Bull. Amer. Meteor. Soc., 61, 1374–87.2.0.CO;2>CrossRefGoogle Scholar
Maddox, R. A., 1983. Large-scale meteorological conditions associated with midlatitude mesoscale convective complexes. Mon. Wea. Rev., 111, 1475–93.2.0.CO;2>CrossRefGoogle Scholar
Maddox, R. A., K. W. Howard, D. L. Bartels, and D. M. Rodgers, 1986. Mesoscale convective complexes in the middle latitudes. In Mesoscale Meteorology and Forecasting, P. S. Ray (ed.), Amer. Meteor. Soc., 390–413.
Marks, F. D. Jr., and Houze, R. A. Jr., 1987. Inner-core structure of Hurricane Alicia from airborne Doppler-radar observations. J. Atmos. Sci., 44, 1296–317.2.0.CO;2>CrossRefGoogle Scholar
McBride, J. L., 1995. Tropical cyclone formation. In Global Perspectives on Tropical Cyclones. Elsberry, R. (ed.), World. Meteor. Org., 63–105.Google Scholar
Merrill, R. T., 1988. Characteristics of the upper-tropospheric environmental flow around hurricanes. J. Atmos. Sci., 45, 1665–77.2.0.CO;2>CrossRefGoogle Scholar
Miller, D. and Fritsch, J. M., 1991. Mesoscale convective complexes in the western Pacific region. Mon. Wea. Rev., 119, 2978–92.2.0.CO;2>CrossRefGoogle Scholar
Molinari, J. and Vollaro, D., 2000. Planetary- and synoptic-scale influence on eastern Pacific tropical cyclogenesis. Mon. Wea. Rev., 128, 3296–307.2.0.CO;2>CrossRefGoogle Scholar
Moncrieff, M. W., 1978. The dynamical structure of two-dimensional steady convection in constant vertical shear. Quart. J. Roy. Meteor. Soc., 104, 543–67.CrossRefGoogle Scholar
Montgomery, M. T. and Farrell, B. F., 1992. Polar low dynamics. J. Atmos. Sci., 49, 2484–505.2.0.CO;2>CrossRefGoogle Scholar
Montgomery, M. T. and Farrell, B. F., 1993. Tropical cyclone formation. J. Atmos. Sci., 50, 285–310.2.0.CO;2>CrossRefGoogle Scholar
Neumann, C., 1993. Global overview. In Global Guide to Tropical Cyclone Forecasting. WMO/TD-560, Holland, G. J. (ed.), World Meteor. Org., 3.1–3.46.Google Scholar
Newton, C. W., 1963. Dynamics of severe convective storms. Meteor. Monogr., 5, Amer. Meteor. Soc., 33–58.
Ogura, Y., and Chen, Y.-L., 1977. A life history of an intense mesoscale convective storm in Oklahoma. J. Atmos. Sci., 34, 1458–76.2.0.CO;2>CrossRefGoogle Scholar
Olsson, P. O. and Cotton, W. R., 1997. Balanced and unbalanced circulations in a primitive equation simulation of a midlatitude MCC. Part II: Analysis of balance. J. Atmos. Sci., 54, 479–97.2.0.CO;2>CrossRefGoogle Scholar
Ooyama, K., 1964. A dynamical model for the study of tropical cyclone development. Geophys. Int., 4, 187–98.Google Scholar
Ooyama, K., 1969. Numerical simulation of the life cycle of tropical cyclones. J. Atmos. Sci., 26, 3–40.2.0.CO;2>CrossRefGoogle Scholar
Ooyama, K., 1982. Conceptual evolution of the theory and modeling of the tropical cyclone. J. Meteor. Soc. Japan, 60, 369–80.CrossRefGoogle Scholar
Palmén, E., 1948. On the formation and structure of tropical cyclones. Geophysics, 3, 26–38.Google Scholar
Parker, M. D. and Johnson, R. H., 2000. Organization modes of midlatitude mesoscale convective systems. Mon. Wea. Rev., 128, 3413–36.2.0.CO;2>CrossRefGoogle Scholar
Parker, M. D. and Johnson, R. H., 2004a. Structures and dynamics of quasi-2D mesoscale convective systems. J. Atmos. Sci., 61, 545–67.2.0.CO;2>CrossRefGoogle Scholar
Parker, M. D. and Johnson, R. H., 2004b. Simulated convective lines with leading precipitation. Part I: Governing dynamics. J. Atmos. Sci., 61, 1637–55.2.0.CO;2>CrossRefGoogle Scholar
Persing, J. and Montgomery, M. T., 2003. Hurricane superintensity. J. Atmos. Sci., 60, 2349–71.2.0.CO;2>CrossRefGoogle Scholar
Rasmussen, E. R., 1979. The polar low as an extratropical CISK disturbance. Quart. J. Roy. Meteor. Soc., 105, 531–49.CrossRefGoogle Scholar
Raymond, D. J. and Jiang, H., 1990. A theory for long-lived mesoscale convective systems. J. Atmos. Sci., 47, 3067–77.2.0.CO;2>CrossRefGoogle Scholar
Redelsperger, J.-L. and Clark, T. L., 1989. The initiation and horizontal scale selection of convection over gently sloping terrain. J. Atmos. Sci., 47, 516–41.2.0.CO;2>CrossRefGoogle Scholar
Reed, R. J., 1979. Cyclogenesis in polar air streams. Mon. Wea. Rev., 107, 38–52.2.0.CO;2>CrossRefGoogle Scholar
Riehl, H., 1948. On the formation of typhoons. J. Meteor., 5, 247–64.2.0.CO;2>CrossRefGoogle Scholar
Riehl, H., 1954. Tropical Meteorology. McGraw-Hill Co.Google Scholar
Ritchie, E. A. and Holland, G. J. 1993. On the interaction of tropical-cyclone scale vortices. II: interacting vortex patches. Quart. J. Roy. Meteor. Soc., 119, 1363–97.CrossRefGoogle Scholar
Ritchie, E. A. and Holland, G. J., 1997. Scale interactions during the formation of Typhoon Irving. Mon. Wea. Rev., 125, 1377–96.2.0.CO;2>CrossRefGoogle Scholar
Rotunno, R. and Emanuel, K. A., 1987. An air-sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axiymmetric numerical model. J. Atmos. Sci., 44, 140–53.2.0.CO;2>CrossRefGoogle Scholar
Rotunno, R., Klemp, J. B., and Weisman, M. L., 1988. A theory for strong, long-lived squall lines. J. Atmos. Sci., 45, 463–85.2.0.CO;2>CrossRefGoogle Scholar
Schubert, W. H., Hack, J. J., Dias, P. L. Silva, and Fulton, S. R., 1980. Geostrophic adjustment in an axisymmetric vortex. J. Atmos. Sci., 37, 1464–84.2.0.CO;2>CrossRefGoogle Scholar
Schubert, W. H., Montgomery, M. T., Taft, R. K., Guinn, T. A., Fulton, S. R., Kossin, J. P., and Edwards, J. P., 1999. Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes. J. Atmos. Sci., 56, 1197–223.2.0.CO;2>CrossRefGoogle Scholar
Smith, R. K., 1980. Tropical cyclone eye dynamics. J. Atmos. Sci., 37, 1227–32.2.0.CO;2>CrossRefGoogle Scholar
Smith, R. K., 1997. On the theory of CISK. Quart. J. Roy. Meteor. Soc., 123, 407–18.CrossRefGoogle Scholar
Takeda, T., 1971. Numerical simulation of a precipitating system convective cloud: The formation of a “long-lasting” cloud. J. Atmos. Sci., 28, 350–76.2.0.CO;2>CrossRefGoogle Scholar
Thiao, W., R. A. Scofield, and J. Robinson, 1993. The Relationship Between Water Vapor Plumes and Extreme Rainfall Events During the Summer Season, NOAA Technical Report, NESDIS, 67, 69 pp.
Tripoli, G. J. and Cotton, W. R., 1989. Numerical study of an observed orogenic mesoscale convective system. Part I: Simulated genesis and comparison with observations. Mon. Wea. Rev., 117, 273–304.2.0.CO;2>CrossRefGoogle Scholar
Wang, Y., 2002. Vortex Rossby waves in a numerically simulated tropical cyclone. Part I: Overall structure, potential vorticity, and kinetic energy budgets. J. Atmos. Sci., 59, 1213–37.2.0.CO;2>CrossRefGoogle Scholar
Weisman, M. L., and Rotunno, R., 2004. “A theory for strong long-lived squall lines” revisited. J. Atmos. Sci., 61, 361–82.2.0.CO;2>CrossRefGoogle Scholar
Weisman, M. L., Klemp, J. B., and Rotunno, R., 1988. Structure and evolution of numerically simulated squall lines. J. Atmos. Sci., 45, 1990–2013.2.0.CO;2>CrossRefGoogle Scholar
Willoughby, H. E., 1998. Tropical cyclone eye thermodynamics. Mon. Wea. Rev., 126, 3053–67.2.0.CO;2>CrossRefGoogle Scholar
Willoughby, H. E., Marks, F. D., and Feinberg, R. J., 1984. Stationary and moving convective bands in hurricanes. J. Atmos. Sci., 41, 3189–211.2.0.CO;2>CrossRefGoogle Scholar
Wu, C.-C. and Emanuel, K. A., 1993. Interaction of a baroclinic vortex with background shear: Application to hurricane movement. J. Atmos. Sci., 50, 62–76.2.0.CO;2>CrossRefGoogle Scholar
Wu, C.-C. and Kurihara, , 1996. A numerical study of the feedback mechanisms of hurricane-environment interaction on hurricane movement from the potential vorticity perspective. J. Atmos. Sci., 53, 2264–82.2.0.CO;2>CrossRefGoogle Scholar
Xu, Q., 1992. Density currents in shear flows – A two-fluid model. J. Atmos. Sci., 49, 511–24.2.0.CO;2>CrossRefGoogle Scholar
Xue, M., 2000. Density currents in two-layer shear flows. Quart. J. Roy. Met. Soc., 126, 1301–20.CrossRefGoogle Scholar
Zhang, D.-L., Liu, Y., and Yau, M. K., 2002. A multiscale numerical study of Hurricane Andrew (1992). Part V: Inner-core thermodynamics. Mon. Wea. Rev., 130, 2745–63.2.0.CO;2>CrossRefGoogle Scholar
Zipser, E. J., 1977. Mesoscale and convective-scale downdrafts as distinct components of squall-line structure. Mon. Wea. Rev., 105, 1568–89.2.0.CO;2>CrossRefGoogle Scholar

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