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4 - Numerical Methods Used in Cloud Models

Published online by Cambridge University Press:  22 August 2018

Alexander P. Khain  and
Mark Pinsky
Alexander P. Khain
Affiliation:
Hebrew University of Jerusalem
Mark Pinsky
Affiliation:
Hebrew University of Jerusalem
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Summary

Numerical methods applied in atmospheric models in general and in cloud models in particular are described in several books (Marchuk, 1974, 1980; Pielke, 2013; Mesinger and Arakawa, 1976; Durran, 2010). In this chapter we present only a brief overview of the main concepts and approaches. The pivot element of a numerical method is a system of averaged equations that describes several basic processes, among them advection of various quantities by a background wind, diffusion, gravity-inertial waves caused by the interaction of fields of pressure, and velocity in the presence of the Coriolis force, etc. (Sections 4.4 and 4.5). With the help of the splitting-up method (Marchuk, 1974, 1980; Temam, 1977), these processes can be treated successively at each time step, so the solution obtained for one process is used as the initial condition for solving the equations describing the next process. This allows for performing numerical treatment of each particular physical process separately.

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Physical Processes in Clouds and Cloud Modeling , pp. 122 - 150
Publisher: Cambridge University Press
Print publication year: 2018

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References

Arakawa, A., 1966: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part 1. J. Comput. Phys. 1, #1.Google Scholar
Arakawa, A., 1972: Design of the UCLA general circulation model. Numerical simulation of weather and climate. Dept. of Meteorology, Univ. of California, Los Angeles, Tech Rept. 7, p. 116.Google Scholar
Bott, A., 1989: A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes. Mon. Wea. Rev., 117, 1006–1015.Google Scholar
Bryan, K., 1966: A scheme for numerical integration of the equations of motion on an irregular grid free of non-linear instability. Mon. Wea. Rev., 94, 1.Google Scholar
Clark, T.L., 1977: A small scale dynamic model using a terrain following coordinate transformation. J. Comput. Phys., 24, 186–215.Google Scholar
Durran, D.R., 1989: Improving the anelastic approximation. J. Atmos. Sci., 46, 1453–1461.Google Scholar
Durran, D.R., 2010: Numerical methods for fluid dynamics with applications to Geophysics. Springer, p. 515.Google Scholar
Falkovich, A.I., Khain, A.P., and Ginis, I., 1995: Evolution and motion of binary tropical cyclones as revealed by experiments with a coupled atmosphere–ocean movable nested grid model. Mon. Wea. Rev., 123, 1345–1363.2.0.CO;2>CrossRefGoogle Scholar
Ginis, I., Khain, A., and Morosovsky, E., 2004: Effects of large eddies on the structure of the marine boundary layer under strong wind conditions. J. Atmos. Sci., 61, 3049–3063.Google Scholar
Hill, G.E., 1974: Factors controlling the size and spacing of cumulus clouds as revealed by numerical experiments. J. Atmos. Sci., 30, 1672–1690.Google Scholar
Khain, A.P., Lynn, B., and Dudhia, J., 2010: Aerosol effects on intensity of landfalling hurricanes as seen from simulations with WRF model with spectral bin microphysics. J. Atmos. Sci., 67, 365–384.Google Scholar
Khain, A., Lynn, B., and Shpund, J., 2016: High Resolution WRF Simulations of Hurricane Irene: Sensitivity to Aerosols and Choice of Microphysical Schemes. Atmos. Res., 167, 129–145.Google Scholar
Khain, A., Pokrovsky, A., Pinsky, M., Seifert, A., and Phillips, V., 2004: Effects of atmospheric aerosols on deep convective clouds as seen from simulations using a spectral microphysics mixed-phase cumulus cloud model. Part 1: Model description. J. Atmos. Sci., 61, 2963–2982.Google Scholar
Khain, A.P., and Sednev, I., 1996: Simulation of precipitation formation in the Eastern Mediterranean coastal zone using a spectral microphysics cloud ensemble model. Atmos. Res., 43, 77–110.Google Scholar
Khairoutdinov, M.F., and Randall, D.A., 2003: Cloud-resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties and sensitivities. J. Atmos. Sci., 60, 607–625.Google Scholar
Klemp, J.B., and Lilly, D.K., 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci., 35, 78–107.Google Scholar
Klemp, J.B., and Wilhelmson, R., 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070–1096.Google Scholar
Leith, G., 1965: Lagrangian advection in an atmospheric model. WMO-IUGG Symposium on Research and development Aspects of long-range forecasting. Boulder, Colo. WMO Tech. Note 66, 168–176.Google Scholar
Lynn, B., and Khain, A., 2007: Utilization of spectral bin microphysics and bulk parameterization schemes to simulate the cloud structure and precipitation in a mesoscale rain event. J. Geophys. Res. 112, D22205.CrossRefGoogle Scholar
Lynn, B., Khain, A., Dudhia, J., Rosenfeld, D., Pokrovsky, A., and Seifert, A., 2005a: Spectral (bin) microphysics coupled with a mesoscale model (MM5). Part 1. Model description and first results. Mon. Wea. Rev., 133, 44–58.Google Scholar
Lynn, B., Khain, A., Dudhia, J., Rosenfeld, D., Pokrovsky, A., and Seifert, A., 2005b: Spectral (bin) microphysics coupled with a mesoscale model (MM5). Part 2: Simulation of a CaPe rain event with squall line. Mon. Wea. Rev., 133, 59–71.Google Scholar
Marchuk, G.I., 1974: Numerical methods in weather prediction. Academic Press, p. 277.Google Scholar
Marchuk, G.I., 1980: Methods of computational mathematics (in Russian). Nauka Press, p. 536.Google Scholar
Mesinger, F., and Arakawa, A., 1976: Numerical methods used in atmospheric models. 1, GARP Publication Series, 17. WMO.Google Scholar
Morrison, H., Jensen, A.A., Harrington, J.Y., and Milbrandt, J.A., 2016: Advection of coupled hydrometeor quantities in bulk cloud microphysics schemes. Mon. Wea.Rev., 144, 2809–2829.Google Scholar
Ogura, Y., and Phillips, N.A., 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173–179.Google Scholar
Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. Comput. Physics, 21, 251–269.Google Scholar
Pielke, R.A., 2013: Mesoscale meteorological modeling, Third Edition. Academic Press, p. 722.Google Scholar
Pinsky, M., Khain, A., Magaritz, L., and Sterkin, A., 2008: Simulation of droplet size distributions and drizzle formation using a new trajectory ensemble model of cloud topped boundary layer. Part 1: Model description and first results in non-mixing limit. J. Atmos. Sci., 65, 2064–2086.Google Scholar
Pinsky, M.B., Khain, A.P., and Shapiro, M., 2007: Collisions of cloud droplets in a turbulent flow. Part 4: Droplet hydrodynamic interaction. J. Atmos. Sci., 64, 2462–2482.Google Scholar
Rood, R.B., 1987: Numerical advection algorithms and their role in atmospheric transport and chemistry models. Rev. Geophys., 25, 71–100.Google Scholar
Skamarock, W.C., 2006: Positive-definite and monotonic limiters for unrestricted-time-step transport scheme. Mon. Wea. Rev., 134, 2241–2250.Google Scholar
Skamarock, W.C., and Klemp, J.B., 1992: The Stability of Time-Split Numerical Methods for the Hydrostatic and the Nonhydrostatic Elastic Equations. Mon. Wea. Rev., 120, 2109–2127.Google Scholar
Skamarock, W.C., Klemp, J.B., Dudhia, J., Gill, D.O., Barker, D.M., Wang, W., and , J.G, 2005a: A Description of the Advanced Research WRF Version 2. Powers, NCAR Technical Note.Google Scholar
Skamarock, W.C., Klemp, J.B., Dudhia, J., Gill, D.O., Barker, D.M., Wang, W., and Powers, J.G., 2005b: A Description of the Advanced Research WRF Version 2, NCAR, Boulder, Colorado.Google Scholar
Skamarock, W.C., Klemp, J.B., Dudhia, J., Gill, D.O., Barker, D.M., Duda, M.G., Huang, X-Y., Wang, W., and Powers, J.G., 2008: A Description of the advanced research WRF version 3. NCAR Technical Note. Boulder, Colorado.Google Scholar
Smolarkiewicz, P.K., and Grell, G.A., 1990: A class of monotone interpolation schemes. J. Comp. Phys., 101, 431–440.CrossRefGoogle Scholar
Stull, R.B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, p. 666.Google Scholar
Tao, W.-K, Simpson, J., Baker, D., Braun, S., Chou, M., Ferrier, B., Johnson, D., Khain, A., Lang, S., Lynn, B., Shie, C., Starr, D., Sui, C-h., Wang, Y., and Wetzel, P., 2003: Microphysics, radiation and surface processes in the Goddard Cumulus Ensemble (GCE) model. Meteorol. Atmos. Phys., 82, 97–137.Google Scholar
Tapp, M.C., and White, P.W., 1976: A non-hydrostatic mesoscale model. Quart. J. Royal Meteorol. Soc., 102, 277–296.Google Scholar
Temam, R., 1977: Theory and Numerical Analysis of the Navier-Stokes Equations. North-Holland, p. 465.Google Scholar
Tripoli, G.I., and Cotton, W.R., 1982: The Colorado State University three-dimensional cloud/mesoscale model-1982. Part 1: General theoretical framework and sensitivity experiments. J. de Rech. Atmos., 16, 185–220.Google Scholar
Wicker, L.J., and Skamarock, W.C., 1998: A time splitting scheme for the elastic equations incorporating second-order Runge-Kutta time differencing. Mon. Wea. Rev., 126, 1992–1999.2.0.CO;2>CrossRefGoogle Scholar
Wicker, L.J., and Skamarock, W.C., 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 2088–2097.Google Scholar

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