Abstract
Numerical modeling of clouds is as old as computers capable of solving discrete versions of the fundamental dynamical equations. With the limited memories and computer power available in the 1960s and 1970s, most modelers employed two-dimensional slab or axisymmetric approximations to study convective dynamics (e.g., Lilly 1962; Ogura and Charney 1962; Orville 1968; Takeda 1971; Wilhelmson and Ogura 1972; Hane 1973; Soong and Ogura 1973; Schlesinger 1973; Soong 1974). The slab models represented the convective growth of infinitely long convective bands forming in environments with or without vertical wind shear, while the axisymmetric simulations were constrained to shearless environments. However, as computer power grew and vector computers were developed (e.g., the CRAY 7600 and the succeeding CRAY computers; Kaufmann and Smarr 1993), it became possible to solve the three-dimensional equations of motion on relatively coarse-mesh grids (e.g., Steiner 1973; Deardorff 1972; Wilhelmson 1974; Schlesinger 1975; Klemp and Wilhelmson 1978b).
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References
Achtemeier, G. L., 1969: Some observations of splitting thunderstorms over Iowa on August 25–26, 1965. Preprints, Sixth Conf. on Severe Local Storms, Chicago, IL, Amer. Meteor. Soc., 89–94.
Adams, J., R. Garcia, B. Gross, J. Hack, D. Haidvogel, and V. Pizzo, 1992: Applications of multigrid software in the atmospheric sciences. Mon. Wea. Rev., 120, 1447–1458.
Adlerman, E. J., K. K. Droegemeier, and R. Davies-Jones, 1999: A numerical simulation of cyclic mesocyclogenesis. J. Atmos. Sci., 56, 2045–2069.
Atkins, N. T., M. L. Weisman, and L. J. Wicker, 1999: The influence of preexisting boundaries on supercell evolution. Mon. Wea. Rev., 127, 2910–2927.
Benoit, R., M. Desgagne, P. Pellerin, S. Pellerin, and Y. Chartier, 1997: The Canadian MC2: A semi-Lagrangian, semi-implicit wideband atmospheric model suited for finescape process studies and simulation. Mon. Wea. Rev., 125, 2382–2415.
Bernardet, L. R., and W. R. Cotton, 1998: Multiscale evolution of a derecho-producing mesoscale convective system. Mon. Wea. Rev., 126, 2991–3015.
Bluestein, H. B., and G. R. Woodall, 1990: Doppler radar analysis of a low-precipitation severe storm. Mon. Wea. Rev., 118, 1640–1664.
Brady, R. H., and E. J. Szoke, 1989: A case study of non-mesocyclone tornado development in northeast Colorado: Similarities to waterspout formation. Mon. Wea. Rev., 117, 843–856.
Brooks, H. E., and R. B. Wilhelmson, 1992: Numerical simulation of a low-precipitation supercell thunderstorm. Meteor. Atmos. Phys., 49, 3–17.
Brooks, H. E., D. J. Stensrud, and J. V. Cortinas Jr., 1993a: The use of mesoscale models to initialize cloud-scale models for convective forecasting. Preprints, 13th Conf. on Weather Analysis and Forecasting, Vienna, VA, Amer. Meteor. Soc., 301–304.
Brooks, H. E., L. J. Wicker, and C. A. Doswell III, 1993b: STORMTIPE: A forecasting experiment using a three-dimensional cloud model. Wea. Forecasting, 8, 352–362.
Brooks, H. E., C. A. Doswell III, and J. Cooper, 1994: On the environ-ments of tornadic and nontornadic mesocyclones. Wea. Forecasting, 9, 606–618.
Brown, R. A., Ed., 1976: The Union City, Oklahoma tornado of 24 May 19973. NOAA Tech. Memo. ERL NSSL-80, National Severe Storms Laboratory, Norman, OK.
Browning, K. A., 1964: Airflow and precipitation trajectories within severe local storms which travel to the right of the winds. J. Atmos. Sci., 21, 634–639.
Brooks, H. E., and R. J. Donaldson Jr., 1963: Airflow structure of a tornadic storm. J. Atmos. Sci., 20, 533–545.
Burgess, D. W., and R. P. Davies-Jones, 1979: Unusual tornadic storms in eastern Oklahoma on 5 December 1975. Mon. Wea. Rev., 107, 451–457.
Burgess, D. W., V. T. Wood, and R. A. Brown, 1982: Mesocyclone evolu-tion statistics. Preprints, 12th Conf. on Severe Local Storms, San Antonio, TX, Amer. Meteor. Soc., 422–424.
Carpenter, R. L., Jr., K. K. Droegemeier, P. R. Woodward, and C. E. Hane, 1990: Application of the Piecewise Parabolic Method (PPM) to meteorological modeling. Mon. Wea. Rev., 118, 586–612.
Chang, C.-Y., and M. Yoshizaki, 1993: Three-dimensional modeling study of squall lines observed in COPT81. J. Atmos. Sci., 50, 161–183.
Charba, J., and Y. Sasaki, 1971: Structure and movement of the severe thunderstorms of 3 April 1964 as revealed from radar and surface mesonetwork data analysis. J. Meteor. Soc. Japan, 49, 191–213.
Chen, C., 1995: Numerical simulations of gravity currents in uniform shear flows. Mon. Wea. Rev., 123, 3240–3253.
Chen, C.-H., and H. D. Orville, 1980: Effects of mesoscale convergence on cloud convection. J. Appl. Meteor., 19, 256–274.
Chin, C.-N. S., and R. B. Wilhelmson, 1998: Evolution and structure of tropical squall line elements within a moderate CAPE and strong low-level jet environment. J. Atmos. Sci., 55, 3089–3113.
Chin, C.-N. S., Q. Fu, M. M. Bradley, and C. R. Molenkamp, 1995: Modeling of a tropical squall line in two dimensions: Sensitivity to radiation and comparison with a midlatitude case. J. Atmos. Sci., 52, 3172–3193.
Clark, T. L., 1973: Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci., 30, 857–878.
Clark, T. L., 1977: A small-scale dynamic model using a terrain-follow-ing coordinate transformation. J. Comput. Phys., 24, 186–215.
Clark, T. L., 1979: Numerical simulations with a three-dimensional cloud model: Lateral boundary condition experiments and multicellular severe storm simulations. J. Atmos. Sci., 36, 2191–2215.
Clark, T. L., and R. D. Farley, 1984: Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting: A possible mechanism for gustiness. J. Atmos. Sci., 41, 329–350.
Clark, T. L., W. D. Hall, and J. L. Coen, 1996: Source code documenta-tion for the Clark-Hall cloud-scale model: Code version G3CH01. NCAR Tech. Note NCAR/TN-426+STR, 137 pp. [Available from NCAR Information Service, P.O. Box 3000, Boulder, CO 80307.]
Cotton, W. R., and R. A. Anthes, 1989: Storm and Cloud Dynamics., Academic Press, 883 pp.
Clark, T. L., M. A. Stephens, T. Nehrkorn, and G. J. Tripoli, 1982: The Colorado State University three-dimensional mesoscale model. Part II: An ice phase parameterization. J. Rech. Atmos., 16, 295–320.
Crook, N. A., and M. W. Moncrieff, 1988: The effect of large-scale convergence on the generation and maintenance of deep moist convection. J. Atmos. Sei., 45, 3606–3624.
Crook, N. A., and J. D. Tuttle, 1994: Numerical simulations initialized with radar-derived winds. Part II: Forecasts of three gust-front cases. Mon. Wea. Rev., 122, 1204–1217.
Crook, N. A., and M. L. Weisman, 1998: Comparison of supercell behav-ior in a convective boundary layer with that in horizontally-homogeneous environment. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 253256.
Cullen, M. J. P., 1990: A test of a semi-implicit integration technique for a fully compressible non-hydrostatic model. Quart. J. Roy. Meteor. Soc., 116, 1253–1258.
Davies-Jones, R. P., D. W. Burgess, and M. P. Foster, 1990: Test of helicity as a tornado forecast parameter. Preprints, 16th Conf. on Severe Local Storms, Kananaskis Park, AB, Canada, Amer. Meteor. Soc., 588–592.
Deardorff, J. W., 1972: Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci., 29, 91–115.
Droegemeier, K. K., and R. B. Wilhelmson, 1986: Kelvin-Helmholtz instability in a numerically simulated thunderstorm outflow. Bull. Amer. Meteor. Soc., 67, 416–417.
Droegemeier, K. K., and, 1987: Numerical simulation of thunderstorm outflow dynamics. Part I: Outflow sensitivity experiments and turbulence dynamics. J. Atmos. Sci., 44, 1180–1210.
Droegemeier, K. K., and R. P. Davies-Jones, 1987: Simulation of thunderstorm microbursts with a supercompressible numerical model. Preprints, Fifth Int. Conf. on Numerical Methods in Laminar and Turbulent Flow, Montreal, PQ, Canada, Amer. Meteor. Soc.
Droegemeier, K. K., S. M. Lazarus, and R. Davies-Jones, 1993: The influence of helicity on numerically simulated convective storms. Mon. Wea. Rev., 121, 2005–2029.
Droegemeier, K. K., and Coauthors, 1996a: Realtime numerical prediction of storm-scale weather during VORTEX 95, Part I: Goals and methodology. Preprints, 18th Conf. on Severe Local Storms, San Francisco, CA, Amer. Meteor. Soc., 6–10.
Droegemeier, K. K., and Coauthors, 1996b: The 1996 CAPS spring operational forecasting period—Realtime storm-scale NWP, Part I: Goals and methodology. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., 294–296.
Droegemeier, K. K., and Coauthors, 1999: The explicit numerical prediction of an intense hailstorm using WSR-88D observations: The need for realtime access to Level II data and plans for a prototype acquisition system. Preprints, 15th Int. Conf. on Interactive Information Processing Systems (ZIPS) for Meteorology, Oceanography, and Hydrology, Dallas, TX, Amer. Meteor. Soc., 295–299.
Dudhia, J., 1993: A nonhydrostatic version of the Penn State-NCAR Mesoscale Model: Validation tests and simulations of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121, 1493–1513.
Durran, D. R., 1989: Improving the anelastic approximation. J. Atmos. Sci., 46, 1453–1461.
Durran, D. R., 1990: Reply. J. Atmos. Sci., 47, 1819–1820.
Durran, D. R., 1999: Numerical Methods for Wave Equations in Geophysi-cal Fluid Dynamics., Springer-Verlag, 468 pp.
Emanuel, K. A., 1994: Atmospheric Convection., Oxford University Press, 580 pp.
Ferrier, B. S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51, 249–280.
Fiedler, B. H., 1994: The thermodynamic speed limit and its violation in axisymmetric numerical simulations of tornado-like vortices. Atmos.—Ocean, 32, 335–339.
Fiedler, B. H., 1995: On modeling tornadoes in isolation from the parent storm. Atmos. Ocean, 33, 501–512.
Fiedler, B. H., 1998: Windspeed limits in numerically-simulated tornadoes with suction vortices. Quart. J. Roy. Meteor. Soc., 124, 2377–2392.
Fiedler, B. H., and R. Rotunno, 1986: A theory for maximum wind speeds in tornado-like vortices. J. Atmos. Sci., 43, 2328–2340.
Finley, C. A., W. R. Cotton, and R. A. Pielke, 1998a: Numerical simulation of two tornadoes produced by a high-precipitation supercell. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 206–209.
Finley, C. A., and, 1998b: Secondary vortex development in a tornado vortex produced by a simulated supercell thunderstorm. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 359–362.
Flora, S. D., 1954: Tornadoes of the United States., University of Oklahoma Press, 194 pp.
Foster, I., 1995: Designing and Building Parallel Programs., Addison-Wesley, 381 pp.
Foster, I., and C. Kesselman, 1999: Computational Grids. The Grid: Blueprint for a New Computing Intrastructure, J. Foster and C. Kesselman, Eds., Morgan Kaufmann Publishers, 15–50.
Fovell, R. G., and P.-H. Tan, 1998: The temporal behavior of numerically simulated multicell-type storms. Part II: The convective cell life cycle and cell regeneration. Mon. Wea. Rev., 126, 551–577.
Fox, D. G., 1972: Numerical simulation of three-dimensional, shape-preserving convective elements. J. Atmos. Sci., 29, 32 2341.
Fox-Rabinovitz, M. S., 1996: Computational dispersion properties of 3D staggered grids for a nonhydrostatic anelastic system. Mon. Wea. Rev., 124, 498–510.
Fujita, T. T., 1971: Proposed mechanisms of suction spots accompanied by tornadoes. Preprints, Seventh Conf. on Severe Local Storms, Kansas City, MO, Amer. Meteor. Soc., 208–213.
Fujita, T. T., and H. Grandoso, 1968: Split of a thunderstorm into anticyclonic and cyclonic storms and their motion as determined from numerical model experiments. J. Atmos. Sci., 25, 416–439.
Gal-Chen, T., 1978: A method for the initialization of the anelastic equations: Implications for matching models with observations. Mon. Wea. Rev., 106, 587–606.
Gao, J., M. Xue, A. Shapiro, and K. K. Droegemeier, 1999: A variational method for the analysis of three-dimensional wind fields from two Doppler radars. Mon. Wea. Rev., 127, 2128–2142.
Gilmore, M., and L. J. Wicker, 1998: The influence of mid-tropospheric dryness on supercell morphology and evolution. Mon. Wea. Rev., 126, 943–958.
Grabowski, W. W., 1998: Toward cloud resolving modeling of large-scale tropical circulations: A simple cloud microphysics parameterization. J. Atmos. Sci., 55, 3283–3298.
Grasso, L. D., and W. R. Cotton, 1995: Numerical simulation of a tornado vortex. J. Atmos. Sci., 52, 1192–1203.
Grasso, L. D., and, 1998: Numerical simulation of the May 15, 1991 Laverne, Oklahoma tornado. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 278–282.
Grasso, L. D., and E. R. Hilgendorf, 2001: Observations of a severe left moving thunderstorm. Wea. Forecasting, 16, 500–511.
Hane, C. E., 1973: The squall line thunderstorm: Numerical experimentation. J. Atmos. Sci., 30, 1672–1690.
Helsdon, J., Jr., and R. D. Farley, 1987: A numerical modeling study of a Montana thunderstorm: 2. Model results versus observations involving electrical aspects. J. Geophys. Res., 92 (D5), 5661–5675.
Hibbard, W., and D. Santek, 1990: The Vis5D system for easy interactive visualization. Proc. Visualization `90, San Francisco, CA, IEEE, 28–35.
Hibbard, W., B. E. Paul, D. A. Santek, C. R. Dyer, A. L. Battaiola, and M.-F. Voidrot-Martinez, 1994: Interactive visualization of earth and space science computations. Computer, 27, 65–72.
Holt, T., and S. Raman, 1988: A review and comparative evaluation of multilevel boundary layer parameterizations for first-order and turbulent kinetic energy closure schemes. Rev. Geophys., 26, 761–780.
Hou, D., E. Kalnay, and K. K. Droegemeier, 2001: Objective verification of the SAMEX ‘88 ensemble forecasts. Mon. Wea. Rev., 129, 73–91.
Houze, R. A., Jr., 1993: Cloud Dynamics., Academic Press, 573 pp.
Houze, R. A., Jr., and P. V. Hobbs, 1982: Organization and structure of precipitating cloud systems. Advances in Geophysics, Vol. 24, Academic Press, 225–315.
Houze, R. A., Jr., W. Schmid, R. G. Fovell, and H.-H. Schiesser, 1993: Hailstorms in Switzerland: Left movers, right movers, and false hooks. Mon. Wea. Rev., 121, 3345–3370.
Howells, P., R. Rotunno, and R. K. Smith, 1988: A comparative study of atmospheric and laboratory-analogue numerical tornado-vortex models. Quart. J. Roy. Meteor. Soc., 114, 801–822.
Hsie, E. Y., R. D. Farley, and H. D. Orville, 1980: Numerical simulation of ice phase convective cloud seeding. J. Appl. Meteor., 19, 950–977.
Janish, P. R., K. K. Droegemeier, M. Xue, K. Brewster, and J. Levit, 1995: Evaluation of the advanced regional prediction system (ARPS) for storm-scale modeling applications in operational forecasting. Proc. 14th Conf. on Weather Analysis and Forecasting, Dallas, TX, Amer. Meteor. Soc., 224–229.
Johns, R. H., and C. A. Doswell, 1992: Severe local storms forecasting. Wea. Forecasting, 7, 588–612.
Johnson, D. E., P. K. Wang, and J. M. Straka, 1994: A study of microphysical processes in the 2 August 1981 CCOPE super-cell storm. Atmos. Res., 33, 93–123.
Kaufmann, W. J., III, and L. L. Smarr, 1993: Supercomputing and the Transformation of Science., Scientific American Library, 238 pp.
Kay, M. P., and L. J. Wicker, 1998: Numerical simulations of supercell interactions with thermal boundaries. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 246–248.
Keller, D., and B. Vonnegut, 1976: Wind speeds required to drive straws and splinters into wood. J. Appl. Meteor., 59, 899–901.
Kennedy, P. C., N. E. Westcott, and R. W. Scott, 1993: Single-Doppler radar observations of a mini supercell tornadic thunderstorm. Mon. Wea. Rev., 121, 1860–1870.
Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp.
Klemp, J. B., 1987: Dynamics of tornadic thunderstorms. Ann. Rev. Fluid Mech., 19, 369–402.
Klemp, J. B., and R. Wilhelmson, 1978a: The simulation of three-dimen-sional convective storm dynamics. J. Atmos. Sci., 35, 1070 1096.
Klemp, J. B., and, 1978b: Simulations of right- and left-moving storms produced through storm splitting. J. Atmos. Soc., 35, 1097–1110.
Klemp, J. B., and D. R. Durran, 1983: An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon. Wea. Rev., 111, 430–444.
Klemp, J. B., and R. Rotunno, 1983: A study of the tornadic region within a supercell thunderstorm. J. Atmos. Sci., 40, 359–377.
Klemp, J. B., R. B. Wilhelmson, and P. S. Ray, 1981: Observed and numerically simulated structure of a mature supercell thunderstorm. J. Atmos. Sci., 38, 1558–1580.
Klemp, J. B., R. Rotunno, and W. C. Skamarock, 1997: On the propaga-tion of internal bores. J. Fluid Mech., 331, 81–106.
Krueger, S. K., Q. Fu, K. N. Liou, and H.-N. S. Chin, 1995: Improvements of an ice-phase microphysics parameterization for use in numerical simulations of tropical convection. J. Appl. Meteor., 34, 281–287.
Kulie, M. S., and Y.-L. Lin, 1998: The structure and evolution of a numerically simulated high-precipitation supercell thunderstorm. Mon. Wea. Rev., 126, 2090–2116.
Lee, B. D., and R. B. Wilhelmson, 1997a: The numerical simulation of nonsupercell tornadogenesis. Part I: Initiation and evolution of pre-tornadic misocyclone circulations along a dry outflow boundary. J. Atmos. Sci., 54, 32–60.
Lee, B. D., and, 1997b: The numerical simulation of nonsuper-cell tornadogenesis. Part II: Evolution of a family of tornadoes along a weak outflow boundary. J. Atmos. Sci., 54, 2387–2415.
Lemon, L. R., and C. A. Doswell III, 1979: Severe thunderstorm evolution and mesocyclone structure as related to tornadogenesis. Mon. Wea. Rev., 107, 1184–1197.
Lewellen, D. C., W. S. Lewellen, and J. Xia, 2000: The influence of a local swirl ratio on tornado intensification near the surface. J. Atmos. Sci., 57, 527–544.
Lewellen, W. S., 1976: Theoretical models of the tornado vortex. Symp. on Tornadoes: Assessment of Knowledge and Implications for Man, Lubbock, TX, Texas Tech. University, 107–143.
Lewellen, W. S., 1993: Tornado vortex theory. The Tornado: Its Structure, Dynamics, Predictions, and Hazards, Geophys. Monogr., No. 79, Amer. Geophys. Union, 19–40.
Lewellen, W. S., and Y. P. Sheng, 1980: Modeling Tornado Dynamics., U.S. Nuclear Regulatory Commission, NTIS NUREG/CR-2585.
Lewellen, W. S., and D. C. Lewellen, 1997: Large-eddy simulation of a tornado’s interaction with the surface. J. Atmos. Sci., 54, 581–605.
Lilly, D. K., 1962: On the numerical simulation of buoyant convection. Tellus, XIV, 148–172.
Lilly, D. K., 1969: Tornado dynamics. NCAR Manuscript 69–117, 39 pp. [Available from NCAR, P.O. Box 3000, Boulder, CO 80307.]
Lilly, D. K., 1975: Severe storms and storm systems: Scientific back-ground, methods, and critical questions. Pure Appl. Geophys., 113, 713–734.
Lilly, D. K., 1979: The dynamical structure and evolution of thunder-storms and squall lines. Ann. Rev. Earth Planet. Sci., 7, 117–161.
Lilly, D. K., 1990: Numerical prediction of thunderstorms—Has its time come? Quart. J. Roy. Meteor. Soc., 116, 779–797.
Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 1065–1092.
Liu, C. L., and M. W. Moncrieff, 1996: A numerical study of the effects of ambient flow and shear on density currents. Mon. Wea. Rev., 124, 2282–2303.
Lord, S. J., H. E. Willoughby, and J. M. Piotrowicz, 1984: Role of a parameterized ice-phase microphysics in an axisymmetric, nonhydrostatic tropical cyclone model. J. Atmos. Sci., 41, 2836–2848.
Mansell, E. R., 2000: Electrification and lightening in simulated supercell and non-supercell thunderstorms. Ph.D. dissertation, Dept. of Physics, University of Oklahoma, 211 pp.
Markowski, P. M., J. M. Straka, E. N. Rasmussen, and D. O. Blanchard, 1998: Variability of storm-relative helicity during VORTEX. Mon. Wea. Rev., 126, 2959–2971.
McCaul, E. W., Jr., 1987: Observations of the Hurricane Danny tornado outbreak of 16 August 1985. Mon. Wea. Rev., 115, 1206–1223.
McCaul, E. W., Jr., 1993: Observations and simulations of hurricane-spawned tornadic storms. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., No. 79, Amer. Geophys. Union, 119–142.
McCaul, E. W., Jr., and M. L. Weisman, 1996: Simulations of shallow supercell storms in landfalling hurricane environments. Mon. Wea. Rev., 124, 408–429.
Mendez-Nunez, L. R., and J. J. Carroll, 1994: Application of the MacCormack scheme to atmospheric nonhydrostatic models. Mon. Wea. Rev., 122, 984–1000.
Mesinger, F. M., 1977: The forward-backward scheme and its use in a limited-area model. Contrib. Atmos. Phys., 50, 200–210.
Meyers, M. P., P. J. DeMott, and W. R. Cotton, 1992: New primary ice nucleation parameterizations in an explicit cloud model. J. Appl. Meteor., 31, 26–50.
Michalakes, J., 2000: The same-source parallel implementation of MM5. J. Sci. Computing, 8, (1), 5–12.
Moller, A. R., C. A. Doswell, III, M. P. Foster, and G. R. Woodall, 1994: The operational recognition of supercell thunderstorm environments and storm structures. Wea. Forecasting, 9, 327–347.
Moncrieff, M. W., and J. S. A. Green, 1972: The propagation and transfer properties of steady convective overturning in shear. Quart. J. Roy. Meteor. Soc., 98, 336–352.
Ogura, Y., 1963: A review of numerical modeling research on small scale convection in the atmosphere. Severe Local Storms, Meteor. Monogr., No. 27, Amer. Meteor. Soc., 65–75.
Ogura, Y., and J. C. Charney, 1962: A numerical model of thermal convection in the atmosphere. Proc. Int. Symp. Numerical Weather Prediction, Tokyo, Japan, Meteor. Soc. Japan, 431–451.
Ogura, Y., and N. A. Phillips, 1962: Scale analysis of deep and shallow convection in the atmosphere.. J. Atmos. Sci., 19, 173–179.
Ooyama, K. V., 1990: A thermodynamic foundation for modeling the moist atmosphere. J. Atmos. Sci., 47, 2580–2593.
Oreskes, N., K. Shrader-Frechette, and K. Belitz, 1994: Verification, validation, and confirmation of numerical models in the earth sciences. Science, 263, 641–646.
Orville, H. D., 1968: Ambient wind effects on the initiation and development of cumulus clouds over mountains. J. Atmos. Sci., 25, 385–403.
Pandya, R. E., and D. R. Durran, 1996: The influence of convectively generated thermal forcing on the mesoscale circulation around squall lines. J. Atmos. Sci., 53, 2924–2951.
Petch, J. C., 1998: Improved radiative transfer calculations from information provided by bulk microphysical schemes. J. Atmos. Sci., 55, 1846–1858.
Pielke, R. A., and Coauthors, 1992: A comprehensive meteorological modeling system—RAMS. Meteor. Atmos. Phys., 9, 69–91.
Proctor, F. H., 1987: The terminal area simulation system. Volume I: Theoretical formulation. NASA Contractor Rep. 4046, NASA, Washington, DC, 176 pp.
Proctor, F. H., 1988: Numerical simulations of an isolated microburst: Part I: Dynamics and structure. J. Atmos. Sci., 45, 3137–3160.
Purser, R. J., and L. M. Leslie, 1991: Reducing the error in a time-split finite-difference scheme using an incremental technique. Mon. Wea. Rev., 119, 578–585.
Randall, D. A., and B. A. Wielicki, 1997: Measurements, models, and hypotheses in the atmospheric sciences. Bull. Amer. Meteor. Soc., 78, 399–406.
Rasmussen, E. N., J. M. Straka, R. Davies-Jones, C. A. Doswell III, F. H. Carr, M. D. Eilts, and D. R. MacGorman, 1994: Verifications of the Origins of Rotation in Tornadoes Experiment: VORTEX. Bull. Amer. Meteor. Soc., 75, 995–1006.
Redelsperger, J. L., and G. Sommeria, 1986: Three-dimensional simulation of a convective storm: Sensitivity studies on sub-grid parameterization and spatial resolution. J. Atmos. Sei., 22, 2619–2635.
Richardson, Y. P., 1999: The influence of horizontal variations in vertical shear and low-level moisture on numerically simulated convective storms. Ph.D. dissertation, University of Oklahoma, 236 pp.
Richardson, Y. P., K. K. Drogemeier, and R. P. Davies-Jones, 1998: A study of the horizontally-varying vertical shear and CAPE on numerical simulated convective storms. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 249–251.
Rotunno, R., 1984: An investigation of a three-dimensional asymmetric vortex. J. Atmos. Sci., 41, 283–298.
Rotunno, R., 1993: Supercell thunderstorm modeling and theory. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., No. 79, Amer. Geophys. Union, 57–73.
Rotunno, R., and J. B. Klemp, 1982: The influence of the shear-induced pressure gradient on thunderstorm motion. J. Atmos. Sci., 42, 271–292.
Rotunno, R., and, 1985: On the rotation and propagation of simulated supercell thunderstorms. Mon. Wea. Rev., 110, 136151.
Rotunno, R., and M. L. Weisman, 1988: A theory for strong, long-lived squall lines. J. Atmos. Sci., 45, 463–485.
Rutledge, S. A., and P. V. Hobbs, 1983: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. Part VIII: A model for the “seeder-feeder” process in warm-frontal rainbands. J. Atmos. Sci., 40, 1185–1206.
Sathye, A., G. Bassett, K. Droegemeier, M. Xue, and K. Brewster, 1996: Experiences using high performance computing for operational storm scale weather prediction. Concurrency: Practice and Experience, 8, 731–740.
Sathye, A., G. M. Xue, G. Bassett, and K. Droegemeier, 1997: Parallel weather modeling with the advanced regional prediction system. Parallel Computing, 23, 2243–2256.
Saunders, C. P., and S. L. Peck, 1998: Laboratory studies of the influence of the rime accretion rate on charge transfer during crystal/graupel collisions. J. Geophys. Res., 103, 13 9491–3956.
Schiavone, J. A., and T. V. Papathomas, 1990: Visualizing meteo- rological data. Bull. Amer. Meteor. Soc., 71, 1012–1020.
Schlesinger, R. E., 1973: A numerical model of deep moist convection. Part I: Comparative experiments for variable ambient moisture and wind shear. J. Atmos. Sci., 30, 835–856.
Schlesinger, R. E., 1975: A three-dimensional numerical model of an isolated deep convective cloud: Preliminary results. J. Atmos. Sci., 35, 2268–2273.
Schlesinger, R. E., 1978: Nonlinear eddy-viscosity turbulence parameterization in anelastic three-dimensional flow: Some mathematical aspects. J. Atmos. Sci., 35, 2268–2273.
Schlesinger, R. E., 1980: A three-dimensional numerical model of an isolated deep thunderstorm. Part II: Dynamics of updraft splitting and mesovortex couplet evolution. J. Atmos. Sci., 37, 395–490.
Sherman, W. R., A. B. Craig, M. P. Baker, and C. Bushell, 1997: Scientific visualization, The Computer Science and Engineering Handbook, A. B. Tucker Jr., Ed., CRC Press, 820–846.
Skamarock, W. C., and J. B. Klemp, 1992: The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon. Wea. Rev., 120, 2109–2127.
Skamarock, W. C., and, 1993: Adaptive grid refinement for two-dimensional and three-dimensional nonhydrostatic atmospheric flow. Mon. Wea. Rev., 121, 788–804.
Skamarock, W. C., and, 1994: Efficiency and accuracy of the Klemp-Wilhelmson time-splitting technique. Mon. Wea. Rev., 122, 2623–2630.
Skamarock, W. C., M. L. Weisman, and J. B. Klemp, 1994: Three-dimensional evolution of simulated long-lived squall lines. J. Atmos. Sci., 51, 2563–2584.
Skamarock, W. C., P. K. Smolarkiewicz, and J. B. Klemp, 1997: Precondi-tioned conjugate-residual solvers for Helmholtz equations in nonhydrostatic models. Mon. Wea. Rev., 125, 587–599.
Smolarkiewicz, P. K., V. Grubisic, and L. G. Margolin, 1997: On forward-in-time differencing for fluids: Stopping criteria for iterative solutions of anelastic pressure equations. Mon. Wea. Rev., 125, 647–654.
Snow, J. T., and R. L. Pauley, 1984: On a thermodynamic method for estimating maximum tornado wind speeds. J. Climate Appl. Meteor., 23, 1465–1468.
Soong, S.-T., 1974: Numerical simulation of warm rain development in an axisymmetric cloud model. J. Atmos. Sci., 31, 1262–1285.
Soong, S.-T., and Y. Ogura, 1973: A comparison between axi-symmetric and slab-symmetric cumulus cloud models. J. Atmos. Sci., 30, 879–883.
Steiner, J. T., 1973: A three-dimensional model of cumulus cloud development. J. Atmos. Sci., 30, 414–434.
Straka, J. M., R. B. Wilhelmson, L. J. Wicker, J. R. Anderson, and K. K. Droegemeier, 1993: Numerical solutions of a non-linear density current: A benchmark solution and comparisons. Int. J. Num. Meth. Fluids, 17, 1–22.
Sun, J., and N. A. Crook, 1996: Comparison of thermodynamic retrieval by the adjoint method with the traditional retrieval method. Mon. Wea. Rev., 124, 308–324.
Sun, J., and, 1997: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint: Model development and simulated data experiments. Mon. Wea. Rev., 125, 1642–1661.
Takahashi, T., 1984: Thunderstorm electrification—A numerical study. J. Atmos. Sci., 41, 2541–2558.
Takahashi, T., 1987: Determination of lightning origins in a thunderstorm model. J. Meteor. Soc. Japan, 65, 777–794.
Takahashi, T., 1988: Long-lasting trade-wind showers in a three-dimen-sional model. J. Atmos. Sci., 45, 3333–3353.
Takeda, T., 1971: Numerical simulation of a precipitating convective cloud: The formation of a “long-lasting” cloud. J. Atmos. Sci., 28, 350–376.
Tanguay, M., A. Robert, and R. Laprise, 1990: A semi-implicit semi-Lagrangian fully compressible regional forecast model. Mon. Wea. Rev., 118, 1970–1980.
Tao, W.-K., and J. Simpson, 1993: Goddard cumulus ensemble model. Part I: Model Description. TAO, 4, 35–72.
Tao, W.-K., S. Lang, J. Simpson, C.-H. Sui, B. Ferrier, and M.-D. Chou, 1996: Mechanisms of cloud-radiation interaction in the tropics and midlatitudes. J. Atmos. Sci., 53, 2624–2651.
Tapp, M. C., and P. W. White, 1976: A non-hydrostatic mesoscale model. Quart. J. Roy. Meteor. Soc., 102, 277–296.
Trapp, R. J., and B. H. Fiedler, 1995: Tornado-like vortexgenesis in a simplified numerical model. J. Atmos. Sci., 52, 3757–3778.
Trapp, R. J., E. D. Mitchell, G. A. Tipton, D. W. Effertz, A. I. Watson, D. L. Andra Jr., and M. A. Magsig, 1999: Descending and nondescending tornadic vortex signatures detected by WSR88Ds. Wea. Forecasting, 14, 625–639.
Tremback, C. J., J. Powell, W. R. Cotton, and R. A. Pielke, 1987: The forward-in-time upstream advection scheme: Extension to higher orders. Mon. Wea. Rev., 115, 540–555.
Trier, S. B., and D. B. Parsons, 1995: Updraft dynamics within a numerically simulated subtropical rainband. Mon. Wea. Rev., 123, 39–58.
Tripoli, G. J., 1992: A nonhydrostatic mesoscale model designed to simulate scale interaction. Mon. Wea. Rev., 120, 1342–1359.
Tripoli, G. J., and W. R. Cotton, 1981: The use of ice-liquid water potential temperature as a thermodynamic variable in deep atmospheric models. Mon. Wea. Rev., 109, 1094–1102.
Tripoli, G. J., and, 1989: Numerical study of an observed mesoscale convective system. Part I: Simulated genesis and comparison with observations. Mon. Wea. Rev., 117, 273–304.
Tufte, E. R., 1997: Visual Explanations., Graphics Press, 157 pp.
Wakimoto, R. M., and J. W. Wilson, 1989: Non-supercell tornadoes. Mon. Wea. Rev., 117, 1113–1140.
Walko, R. L., 1988: Plausibility of substantial dry adiabatic subsi- dence in a tornado core. J. Atmos. Sci., 45, 2251–2267.
Walko, R. L., 1993: Tornado spin-up beneath a convective cell: Required basic structure of the near-field boundary layer winds. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., No. 79, Amer. Geophys. Union, 89–95.
Wang, D., M. Xue, V. C. Wong, and K. K. Droegemeier, 1996: Prediction and simulation of convective storms during VORTEX `95. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., 301–303.
Ward, N. B., 1972: The exploration of certain laboratory features of tornado dynamics using a laboratory model. J. Atmos. Sci., 29, 1194–1204.
Weisman, M. L., 1993: The genesis of severe, long-lived bow echos. J. Atmos. Sci., 50, 645–670.
Weisman, M. L., and J. B. Kiemp, 1982: The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Wea. Rev., 110, 504–520.
Weisman, M. L., and, 1984: The structure and classification of numerically simulated convective storms in directionally varying wind shears. Mon. Wea. Rev., 112, 2479–2498.
Weisman, M. L., and H. B. Bluestein, 1985: Dynamics of numerically simulated LP storms. Preprints, 14th Goof on Severe Local Storms, Indianapolis, IN, Amer. Meteor. Soc., 267–270.
Weisman, M. L., J. B. Kiemp, and R. Rotunno, 1988: Structure and evolution of numerically simulated squall lines. J. Atmos. Sci., 45, 1990–2013.
Weisman, M. L., W. C. Skamarock, and J. B. Klemp, 1997: The resolution dependence of explicitly modeled convective systems. Mon. Wea. Rev., 125, 527–548.
Wicker, L. J., 1996: The role of near surface wind shear on low-level mesocyclone generation and tornadoes. Preprints, 18th Conf on Severe Local Storms, San Francisco, CA, Amer. Meteor. Soc., 115–119.
Wicker, L. J., 1998: The role of low-level shear, mid-level shear, and CAPE in low-level mesocyclone generation. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 222–225.
Wicker, L. J., and R. B. Wilhelmson, 1995: Simulation and analysis of tornado development and decay within a three-dimensional supercell thunderstorm. J. Atmos. Sci., 52, 2675–2703.
Wicker, L. J., and W. C. Skamarock, 1998: A time-splitting scheme for the elastic equations incorporating second-order Runge–Kutta time differencing. Mon. Wea. Rev., 126, 1992–1999.
Wicker, L. J., M. P. Kay, and M. P. Foster, 1997: STORMTIPE-95: A convective storm forecast experiment. Wea. Forecasting, 12, 427–436.
Wilhelmson, R. B., 1974: The life cycle of a thunderstorm in three dimensions. J. Atmos. Sci., 31, 1629–1651.
Wicker, L. J., 1977: On the thermodynamic equation for deep convection. Mon. Wea. Rev., 105, 545–549.
Wicker, L. J., and Y. Ogura, 1972: The pressure perturbation and the numerical modeling of a cloud. J. Atmos. Sci., 29, 1295–1307.
Wicker, L. J., and J. B. Klemp, 1978: A three-dimensional numerical simulation of splitting that leads to long-lived storms. J. Atmos. Sci., 35, 1974–1986.
Wicker, L. J., and, 1981: A three-dimensional numerical simula-tion of splitting severe storms on 3 April 1964. J. Atmos. Sci., 38, 1581–1600.
Wicker, L. J., and C.-S. Chen, 1982: A simulation of the development of successive cells along a cold outflow boundary. J. Atmos. Sci., 39, 1466–1483.
L. J. Wicker, H. E. Brooks, and C. Shaw, 1989: The display of modeled storms. Preprints, Fifth Int. Conf on Interactive and Information Processing Systems for Meteorology, Oceanography, and Hydrology, Anaheim, CA, Amer. Meteor. Soc., 166–171.
Wicker, L. J., and Coauthors, 1990: A study of the evolution of a numerically modeled severe storm. Int. J. Supercomputing Appl., 4, 20–36.
Wicker, L. J., D. P. Wojtowicz, C. Shaw, J. Hagedorn, and S. Koch, 1995: NCSA PATHFINDER: Probing ATmospHeric Flows in an INtegrated and Distributed EnviRonment. Visualization Techniques in Space and Atmospheric Sciences, E. P. Szuszczewicz and J. H. Bredekamp, Eds., NASA, 289–296.
Wicker, L. J., and Coauthors, 1996: Visualization of storm and tornado development for an OMNIMAX film and for the CAVE. Preprints, 12th Int. Conf. on Interactive Information and Processing Systems for Meteorology, Oceanography, and Hydrology, Atlanta, GA, Amer. Meteor. Soc., 135–138.
Xue, M., K. K. Droegemeier, V. Wong, A. Shapiro, and K. Brewster, 1995: ARPS User’s Guide. CAPS, 375 pp. [Available from Center for Analysis and Prediction of Storms, University of Oklahoma, Sarkeys Energy Center, Room 1110, 100 East Boyd Street, Norman, OK 73019 or online at http://wwwcaps.ou.edu/ARPS/.]
Xue, M., K. K. and Coauthors, 1996a: Realtime numerical prediction of storm-scale weather during VORTEX 95, Part II: Operations summary and example predictions. Preprints, 18th Conf on Severe Local Storms, San Francisco, CA, Amer. Meteor. Soc., 178–182.
Xue, M., K. K. and Coauthors, 1996b: The 1996 CAPS spring operational forecasting period—Realtime storm-scale NWP, Part II: Operational summary and sample cases. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., 297–300.
Xue, M., K. K. Q. Xu, and K. K. Droegemeier, 1997: A theoretical and numerical study of density currents in non-constant shear flows. J. Atmos. Sci., 54, 1998–2019.
K. K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multiscale nonhydro- static atmospheric simulation and prediction tool. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161–193.
K. K. Droegemeier, A. Shapiro, K. Brewster, F. Carr, D. Weber, Y. Liu, and D.-H. Wang, 2001: The Advanced Regional Prediction System (ARPS)—A multiscale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications. Meteor. Atmos. Phys., 76, 134–165.
Yang, M.-J., and R. A. Houze Jr., 1995: Sensitivity of squall line rear inflow to ice microphysics and environmental humidity. Mon. Wea. Rev., 123, 3175–3193.
Zhang, D.-L., H.-R. Chang, N. L. Seaman, T. T. Warner, and J. M. Fritsch, 1986: A two-way interactive nesting procedure with variable terrain resolution. Mon. Wea. Rev., 114, 1330–1339.
Ziegler, C. L., T. J. Lee, and R. A. Pielke Sr., 1997: Convective initiation at the dryline: A modeling study. Mon. Wea. Rev., 125, 1001–1026.
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Wilhelmson, R.B., Wicker, L.J. (2001). Numerical Modeling of Severe Local Storms. In: Doswell, C.A. (eds) Severe Convective Storms. Meteorological Monographs. American Meteorological Society, Boston, MA. https://doi.org/10.1007/978-1-935704-06-5_4
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