Numerical Methods Used in Cloud Models

Alexander P. Khain; Mark Pinsky

doi:10.1017/9781139049481.005

4 - Numerical Methods Used in Cloud Models

Published online by Cambridge University Press: 22 August 2018

Alexander P. Khain and

Mark Pinsky

Show author details

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

Book contents

Get access

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.

Information

Type: Chapter
Information: Physical Processes in Clouds and Cloud Modeling , pp. 122 - 150

DOI: https://doi.org/10.1017/9781139049481.005 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

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, #1.10.1016/0021-9991(66)90015-5CrossRef 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, 1006–1015.10.1175/1520-0493(1989)117<1006:APDASO>2.0.CO;22.0.CO;2>CrossRef 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, 1.10.1175/1520-0493(1966)094<0039:ASFNIO>2.3.CO;22.3.CO;2>CrossRef Google Scholar

Clark, T.L., 1977: A small scale dynamic model using a terrain following coordinate transformation. J. Comput. Phys., 24, 186–215.10.1016/0021-9991(77)90057-2CrossRef Google Scholar

Durran, D.R., 1989: Improving the anelastic approximation. J. Atmos. Sci., 46, 1453–1461.10.1175/1520-0469(1989)046<1453:ITAA>2.0.CO;22.0.CO;2>CrossRef Google Scholar

Durran, D.R., 2010: Numerical methods for fluid dynamics with applications to Geophysics. Springer, p. 515.10.1007/978-1-4419-6412-0CrossRef 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>CrossRef Google 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, 3049–3063.10.1175/JAS-3342.1CrossRef 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, 365–384.10.1175/2009JAS3210.1CrossRef 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, 129–145.10.1016/j.atmosres.2015.07.014CrossRef 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, 2963–2982.10.1175/JAS-3350.1CrossRef 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, 77–110.10.1016/S0169-8095(96)00005-1CrossRef 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, 607–625.10.1175/1520-0469(2003)060<0607:CRMOTA>2.0.CO;22.0.CO;2>CrossRef Google Scholar

Klemp, J.B., and Lilly, D.K., 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci., 35, 78–107.10.1175/1520-0469(1978)035<0078:NSOHMW>2.0.CO;22.0.CO;2>CrossRef Google Scholar

Klemp, J.B., and Wilhelmson, R., 1978: The simulation of three-dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070–1096.10.1175/1520-0469(1978)035<1070:TSOTDC>2.0.CO;22.0.CO;2>CrossRef 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.CrossRef Google 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, 44–58.10.1175/MWR-2840.1CrossRef 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, 59–71.10.1175/MWR-2841.1CrossRef 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, 2809–2829.10.1175/MWR-D-15-0368.1CrossRef Google Scholar

Ogura, Y., and Phillips, N.A., 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173–179.10.1175/1520-0469(1962)019<0173:SAODAS>2.0.CO;22.0.CO;2>CrossRef Google Scholar

Orlanski, I., 1976: A simple boundary condition for unbounded hyperbolic flows. J. Comput. Physics, 21, 251–269.10.1016/0021-9991(76)90023-1CrossRef 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, 2064–2086.10.1175/2007JAS2486.1CrossRef 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, 2462–2482.10.1175/JAS3952.1CrossRef Google Scholar

Rood, R.B., 1987: Numerical advection algorithms and their role in atmospheric transport and chemistry models. Rev. Geophys., 25, 71–100.10.1029/RG025i001p00071CrossRef Google Scholar

Skamarock, W.C., 2006: Positive-definite and monotonic limiters for unrestricted-time-step transport scheme. Mon. Wea. Rev., 134, 2241–2250.10.1175/MWR3170.1CrossRef 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, 2109–2127.10.1175/1520-0493(1992)120<2109:TSOTSN>2.0.CO;22.0.CO;2>CrossRef 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.CrossRef Google Scholar

Stull, R.B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, p. 666.10.1007/978-94-009-3027-8CrossRef 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, 97–137.10.1007/s00703-001-0594-7CrossRef Google Scholar

Tapp, M.C., and White, P.W., 1976: A non-hydrostatic mesoscale model. Quart. J. Royal Meteorol. Soc., 102, 277–296.10.1002/qj.49710243202CrossRef 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>CrossRef Google Scholar

Wicker, L.J., and Skamarock, W.C., 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130, 2088–2097.10.1175/1520-0493(2002)130<2088:TSMFEM>2.0.CO;22.0.CO;2>CrossRef Google Scholar

Accessibility standard: Unknown

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the HTML of this chapter is currently unknown and may be updated in the future.