Skip to main content Accessibility help
×
Hostname: page-component-cb9f654ff-hn9fh Total loading time: 0 Render date: 2025-08-22T12:07:45.851Z Has data issue: false hasContentIssue false

14 - Parameterizations of physical processes

Published online by Cambridge University Press:  15 December 2009

Yuh-Lang Lin
Yuh-Lang Lin
Affiliation:
North Carolina State University
Get access

Summary

Reynolds averaging

In the previous two chapters, we have described numerical methods for approximating the primitive equations and the setup for numerical models, such as grid systems, and initial and boundary conditions. As demonstrated in Section 13.5, a mesoscale model may be developed to simulate a simple geophysical fluid system, such as a stratified, inviscid flow over topography. However, in order to apply this type of geophysical fluid dynamics model to simulate mesoscale atmospheric phenomena, some important physical processes, such as boundary layer processes, moist processes, and radiative transfer processes, need to be represented or parameterized in the model.

In order to numerically integrate the governing differential equations in a limited area, a numerical method, such as a finite difference method, spectral method or finite element method, must be used to approximately represent the atmospheric motion and processes by the dependent variables at grid points or elements. The approximations limit the explicit representation of atmospheric motions and processes to a scale smaller than that for the grid interval, truncated wavelength, or finite element. For example, large-scale disturbances may cascade down to mesoscale, then further down to the smallest turbulent eddies responsible for viscous dissipation in the atmosphere. If the subgrid-scale disturbances are not appropriately represented by the grid point values, they may cause nonlinear aliasing and nonlinear numerical instability, as discussed in Chapter 13.

Information

Type
Chapter
Information
Mesoscale Dynamics , pp. 563 - 609
Publisher: Cambridge University Press
Print publication year: 2007

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

André, J. C., DeMoor, G., Lacarcere, P., Therry, G., and Vachat, R. du, 1978. Modeling the 24-hour evolution of the mean and turbulent structures of the planetary boundary layer. J. Atmos. Sci., 35, 1862–83.2.0.CO;2>CrossRefGoogle Scholar
Anthes, R. A., 1977. A cumulus parameterization scheme utilizing a one-dimensional cloud model. Mon. Wea. Rev., 105, 270–86.2.0.CO;2>CrossRefGoogle Scholar
Arakawa, A. and Schubert, W. H., 1974. Interaction of a cumulus cloud ensemble with the large scale environment. Part I. J. Atmos. Sci., 31, 674–701.2.0.CO;2>CrossRefGoogle Scholar
Arking, A. and Grossman, K., 1972. The influence of line shape and band structure on temperatures in planetary atmospheres. J. Atmos. Sci., 29, 937–49.2.0.CO;2>CrossRefGoogle Scholar
Arya, S. P., 2001. Introduction to Micrometeorology. 2nd edn., Academic Press.Google Scholar
Batchelor, G. K., 1967. An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bechtold, P., Bazile, E., Guichard, F., Mascart, P., and Richard, E., 2001. A mass-flux convective scheme for regional and global models. Quart. J. Roy. Meteor. Soc., 127, 869–86.CrossRefGoogle Scholar
Betts, A. K. and Miller, M. J., 1986. A new convective adjustment scheme. Part II. Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc., 112, 693–709.Google Scholar
Betts, A. K. and M. J. Miller, 1993. The Betts-Miller Scheme. In The Representation of Cumulus Convection in Numerical Models, K. A. Emanuel and D. J. Raymond (eds.), Meteor. Monogr., No. 46, Amer. Meteor. Soc., 107–122.
Blackadar, A. K., 1979. High resolution models of the planetary boundary layer. Adv. Environ. Sci. Eng., 1, 50–85.Google Scholar
Businger, J. A., 1973. Turbulent transfer in the atmosphere surface layer. In Workshop in Micrometeorology, Hangen, D. A. (ed.), Amer. Meteor. Soc., Chapter 2.Google Scholar
Chen, S.-H. and Sun, W.-Y., 2002. A one-dimensional time-dependent cloud model, J. Meteor. Soc. Japan, 80, 99–118.CrossRefGoogle Scholar
Chou, M.-D., 1986. Atmospheric solar heating rate in the water vapor bands. J. Clim. Appl. Meteor., 25, 1532–42.2.0.CO;2>CrossRefGoogle Scholar
Chou, M.-D., 1992. A solar radiation model for use in climate studies. J. Atmos. Sci., 49, 762–72.2.0.CO;2>CrossRefGoogle Scholar
Chou, M.-D. and Arking, A., 1980. Computation of infrared cooling rates in the water vapor bands. J. Atmos. Sci., 37, 855–67.2.0.CO;2>CrossRefGoogle Scholar
Chou, M.-D., Lee, K.-T., Tsay, S.-C., and Fu, Q., 1999. Parameterization for cloud longwave scattering for use in atmospheric models. J. Climate, 12, 159–69.CrossRefGoogle Scholar
Cotton, W. R., 1986. Averaging and the parameterization of physical processes in mesoscale models. In Mesoscale Meteorology and Forecasting, P. S. Ray (ed.), Amer. Meteor. Soc., 614–35.
Cotton, W. R., Tripoli, G. J., Rauber, R. M., and Mulvihill, E. A., 1986. Numerical simulation of the effects of varying ice crystal nucleation rates and aggregation processes on orographic snowfall. J. Clim. Appl. Meteor., 25, 1658–80.2.0.CO;2>CrossRefGoogle Scholar
Deardorff, J. W., 1972. Theoretical expression for the countergradient vertical heat flux. J. Geophys. Res., 77, 5900–4.CrossRefGoogle Scholar
Deardorff, J. W., 1974. Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer. Bound.-Layer Meteor., 7, 81–106.CrossRefGoogle Scholar
Driedonks, A. G. M. and Tennekes, H., 1984. Entrainment effects in the well-mixed atmospheric boundary layer. Bound.-Layer Meteor., 30, 75–105.CrossRefGoogle Scholar
Ferrier, B. S., 1994. A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51, 249–80.2.0.CO;2>CrossRefGoogle Scholar
Frank, W. M. and J. Molinari, 1993. Convective adjustment. In The Representation of Cumulus Convection in Numerical Models, Emanuel, K. A. and Raymond, D. J. (eds.), Meteor. Monogr., No. 46, Amer. Meteor. Soc., 101–5.CrossRefGoogle Scholar
Fritsch, J. M. and Chappell, C. F., 1980. Numerical prediction of convectively driven mesoscale pressure systems. Part I: Convective parameterization. J. Atmos. Sci., 37, 1722–33.2.0.CO;2>CrossRefGoogle Scholar
Fu, Q. and Liou, K. N., 1992. On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres. J. Atmos. Sci., 49, 2139–56.2.0.CO;2>CrossRefGoogle Scholar
Fu, Q., Liou, K. N., Cribb, M. C., Charlock, T. P., and Grossman, A., 1997. Multiple scattering parameterization in thermal infrared radiative transfer. J. Atmos. Sci., 54, 2799–812.2.0.CO;2>CrossRefGoogle Scholar
Goody, R. M., 1964a. Atmospheric Radiation I: Theoretical Basis. Clarendon Press.Google Scholar
Goody, R. M., 1964b. The transmission of radiation through an inhomogeneous atmosphere. J. Atmos. Sci., 21, 575–81.2.0.CO;2>CrossRefGoogle Scholar
Grell, G. A., 1993. Prognostic evaluation of assumptions used by cumulus parameterization. Mon. Wea. Rev., 121, 764–87.2.0.CO;2>CrossRefGoogle Scholar
Henyey, L. G. and Greenstein, J. L., 1941. Diffuse radiation in the galaxy. Astrophys. J., 93, 70–83.CrossRefGoogle Scholar
Holton, J. R., 2004. Introduction to Dynamic Meteorology. 4th edn., Elsevier Academic Press.Google Scholar
Holtslag, A. A. M. and Moeng, C.-H., 1991. Eddy diffusivity and countergradient transport in the convective atmospheric boundary layer. J. Atmos. Sci., 48, 1690–8.2.0.CO;2>CrossRefGoogle Scholar
Hong, S.-Y. and Pan, H.-L., 1996. Nonlocal boundary layer vertical diffusion in a medium-range forecast model. Mon. Wea. Rev., 124, 2322–39.2.0.CO;2>CrossRefGoogle Scholar
Hong, S.-Y., Dudhia, J., and Chen, S.-H., 2004. A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103–20.2.0.CO;2>CrossRefGoogle Scholar
Kain, J. S., 2004. The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43, 170–81.2.0.CO;2>CrossRefGoogle Scholar
Kain, J. S. and J. M. Fritsch, 1993. Convective parameterization for mesoscale models: The Kain-Fritsch Scheme. In The Representation of Cumulus Convection in Numerical Models, Emanuel, K. A. and Raymond, D. J. (eds.), Meteor. Monogr., No. 46, Amer. Meteor. Soc., 165–70.CrossRefGoogle Scholar
Kessler, E., 1969. On the Distribution and Continuity of Water Substance in Atmospheric Circulations. Meteor. Monogr., No. 32, Amer. Meteor., Soc.CrossRefGoogle Scholar
Kratz, D. P., Chou, M.-D., Yan, M. M.-H., and Ho, C.-H., 1998. Minor trace gas radiative forcing calculations using the k-distribution method with one-parameter scaling. J. Geophys. Res., 103, 31647–56.CrossRefGoogle Scholar
Krishnamurti, T. N., Ramanathan, Y., Pan, H.-L., Pasch, R. J., and Molinari, J., 1980. Cumulus parameterization and rainfall rates I. Mon. Wea. Rev., 108, 465–72.2.0.CO;2>CrossRefGoogle Scholar
Kuo, H.-L., 1965. On formation and intensification of tropical cyclones through latent heat release by cumulus convection. J. Atmos. Sci., 22, 40–63.2.0.CO;2>CrossRefGoogle Scholar
Kuo, H.-L., 1974. Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci., 31, 1232–40.2.0.CO;2>CrossRefGoogle Scholar
Kuo, Y.-H. and Anthes, R. A., 1984. Semiprognostic tests of Kuo-type cumulus parameterization schemes in an extratropical convective system. Mon. Wea. Rev., 112, 1498–509.2.0.CO;2>CrossRefGoogle Scholar
Kurihara, Y., 1973. A scheme of moist convective adjustment. Mon. Wea. Rev., 101, 547–53.2.3.CO;2>CrossRefGoogle Scholar
Lacis, A. A. and Hansen, J. E., 1974. A parameterization for the absorption of solar radiation in the earth's atmosphere. J. Atmos. Sci., 31, 118–33.2.0.CO;2>CrossRefGoogle Scholar
Lin, H.-M., Wang, P.-K., and Schlesinger, B. E., 2005. Three-dimensional nonhydrostatic simulations of summer thunderstorms in the humid subtropics versus High Plains. Atmos. Res., 78, Issue 1, 103–45.CrossRefGoogle Scholar
Lin, Y.-L., Farley, R. D., and Orville, H. D., 1983. Bulk parameterization of the snow field in a cloud model. J. Clim. Appl. Meteor., 22, 1065–92.2.0.CO;2>CrossRefGoogle Scholar
Liou, K.-N., 1992. Radiation and Cloud Processes in the Atmosphere. Oxford University Press.Google Scholar
Liou, K.-N., 2002. An Introduction to Atmospheric Radiation. 2nd edn., Academic Press, New York.Google Scholar
Liou, K.-N. and Ou, S. C. S., 1981. Parameterization of infrared radiative transfer in cloudy atmosphere. J. Atmos. Sci., 38, 2707–16.2.0.CO;2>CrossRefGoogle Scholar
Lord, S. J., Willoughby, H. E., and Piotrowicz, J. M., 1984. Role of a parameterized ice-phase microphysics in an axisymmetric, nonhydrostatic tropical cyclone model. J. Atmos. Sci., 41, 2836–48.2.0.CO;2>CrossRefGoogle Scholar
Manabe, S., Smogorinski, J., and Strickler, R. F., 1965. Simulated climatology of a general circulation model with a hydrological cycle. Mon. Wea. Rev., 93, 769–98.2.3.CO;2>CrossRefGoogle Scholar
Marshall, J. S. and Palmer, W. M., 1948. The distribution of raindrops with size. J. Meteor., 5, 165–6.2.0.CO;2>CrossRefGoogle Scholar
Mason, P. J., 1994. Large-eddy simulations: A critical review of the technique. Quart. J. Roy. Meteor. Soc., 120, 1–26.CrossRefGoogle Scholar
McNider, R. T. and Pielke, R. A., 1981. Diurnal boundary-layer development over sloping terrain. J. Atmos. Sci., 38, 2198–212.2.0.CO;2>CrossRefGoogle Scholar
Mellor, G. L. and Yamada, T., 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31, 1791–806.2.0.CO;2>CrossRefGoogle Scholar
Meyers, M. P., Walko, R. L., Harrington, J. Y., and Cotton, W. R., 1997. New RAMS cloud microphysics parameterization. Part II: The two-moment scheme. Atmos. Res., 45, 3–39.CrossRefGoogle Scholar
Milbrandt, J. A. and Yau, M. K., 2005. A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter. J. Atmos. Sci., 62, 3051–64.CrossRefGoogle Scholar
Miyakoda, K., Smagorinski, J., Strickler, R. F., and Hembree, G. D., 1969. Experimental extended predictions with a nine-level hemispheric model. Mon. Wea. Rev., 97, 1–76.2.3.CO;2>CrossRefGoogle Scholar
Mlawer, E. J., Taubman, S. J., Brown, P. D., Iacono, M. J., and Clough, S. A., 1997. Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, D14, 16663–82.CrossRefGoogle Scholar
Molinari, J., 1993. An overview of cumulus parameterization in mesoscale models. In The Representation of Cumulus Convection in Numerical Models, Emanuel, K. A. and Raymond, D. J. (eds.), Meteor. Monogr., No. 46, Amer. Meteor. Soc., 155–8.CrossRefGoogle Scholar
Morrison, H. and Pinto, J. O., 2005. Mesoscale modeling of springtime arctic mixed-phase stratiform clouds using a new two-moment bulk microphysics scheme. J. Atmos. Sci., 62, 3683–704.CrossRefGoogle Scholar
Oke, T. R., 1987. Boundary Layer Climates. 2nd edn., Methuen.Google Scholar
Ooyama, V. K., 1982. Conceptual evolution of the theory and modeling of the tropical cyclone. J. Meteor. Soc. Japan, 60, 369–79.CrossRefGoogle Scholar
Orville, H. D. and Kopp, F. J., 1977. Numerical simulation of the history of a hailstorm. J. Atmos. Sci., 34, 1596–618.2.0.CO;2>CrossRefGoogle Scholar
Perkey, D. J. and C. W. Kreitzberg, 1993. A method of parameterizing cumulus transports in a mesoscale primitive equation model: The sequential plume scheme. In The Representation of Cumulus Convection in Numerical Models, Emanuel, K. A. and Raymond, D. J. (eds.), Meteor. Monogr., No. 46, Amer. Meteor. Soc., 171–7.CrossRefGoogle Scholar
Pielke, R. A., 2002. Mesoscale Meteorological Modeling. Academic Press.Google Scholar
Raymond, D. J., 1994. Cumulus convection and the Madden-Julian oscillation of the tropical troposphere. Physica D, 77, 1–22.CrossRefGoogle Scholar
Raymond, D. J. and K. A. Emanuel, 1993. The Kuo Cumulus Parameterization. In The Representation of Cumulus Convection in Numerical Models, Emanuel, K. A. and Raymond, D. J. (eds.), Meteor. Monogr., No. 46, Amer. Meteor. Soc., 145–7.CrossRefGoogle Scholar
Reisner, J., Rasmussen, R. M., and Bruintjes, R. T., 1998. Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc., 124, 1071–107.CrossRefGoogle Scholar
Reynolds, O., 1895. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Roy. Soc. London, A174, 935–82.Google Scholar
Rodgers, C. D., 1967. The use of emissivity in atmospheric radiation calculations. Quart. J. Roy. Meteor. Soc., 93, 43–54.CrossRefGoogle Scholar
Rothman, L. S., Gamache, R. R., Goldman, A., Brown, L. R., Toth, R. A., Pickett, H. M., Poynter, R. L., Flaud, J.-M., Camy-Peyret, C., Barbe, A., Husson, N., Rinsland, C. P., and Smith, M. A. H., 1987. The HITRAN database: 1986 edition. Appl. Opt., 26, 4058–97.CrossRefGoogle ScholarPubMed
Rutledge, S. A. and Hobbs, P. V., 1984. The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. XII: A diagnostic modeling study of precipitation development in narrow cold-frontal rainbands. J. Atmos. Sci., 41, 2949–72.2.0.CO;2>CrossRefGoogle Scholar
Seaman, N. L., 1999. Cumulus parameterization. COMET Faculty Course on Numerical Weather Prediction. June 7–11, NCAR, Boulder, CO.
Seifert, A. and Beheng, K. D., 2006. A two-moment cloud microphysics parameterization for mixed-phase clouds. Part I: Model description. Meteor. Atmos. Phys., 92, 45–66.CrossRefGoogle Scholar
Stephens, G. L., 1978a and b. Radiative properties of extended water clouds. Parts I and II. J. Atmos. Sci., 35, 2111–32.2.0.CO;2>CrossRefGoogle Scholar
Stephens, G. L., 1984. The parameterization of radiation for numerical weather prediction and climate models. Mon. Wea. Rev., 112, 826–67.2.0.CO;2>CrossRefGoogle Scholar
Stephens, G. L., Gabriel, P. M., and Partain, P. T., 2001. Parameterization of atmospheric radiative transfer. Part I: Validity of simple models. J. Atmos. Sci., 58, 3391–409.2.0.CO;2>CrossRefGoogle Scholar
Stull, R. B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers.CrossRefGoogle Scholar
Sun, W.-Y. and Chang, C.-Z., 1986. Diffusion model for a convective layer. Part I: Numerical simulation of convective boundary layer. Clim. Appl. Meteor., 25, 1445–53.2.0.CO;2>CrossRefGoogle Scholar
Tao, W.-K., Simpson, J., Baker, D., Braun, S., Chou, M.-D., Ferrier, B., Johnson, D., Khain, A., Lang, S., Lynn, B., Shie, C.-L., Starr, D., Sui, C.-H., Wang, Y., and Wetzel, P., 2003. Microphysics, radiation, and surface processes in the Goddard Cumulus Ensemble (GCE) model. Meteor. Atmos. Phys., 82, 97–137.CrossRefGoogle Scholar
Troen, I. and Mahrt, L., 1986. A simple model of the atmospheric boundary layer: Sensitivity to surface evaporation. Bound.-Layer Meteor., 37, 129–48.CrossRefGoogle Scholar
Tsay, S.-C., Stamnes, K., and Jayaweera, K., 1989. Radiative energy budget in the cloudy and hazy arctic. J. Atmos. Sci., 46, 1002–18.2.0.CO;2>CrossRefGoogle Scholar
Wyngaard, J. C. and Brost, R. A., 1984. Top-down and bottom-up diffusion of a scalar in the convective boundary layer. J. Atmos. Sci., 41, 102–12.2.0.CO;2>CrossRefGoogle Scholar

Accessibility standard: Unknown

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

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×