Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T10:45:51.585Z Has data issue: false hasContentIssue false

4 - Model Equations and Numerical Approaches

Published online by Cambridge University Press:  15 May 2017

Guy P. Brasseur  and
Daniel J. Jacob
Guy P. Brasseur
Affiliation:
Max-Planck-Institut für Meteorologie, Hamburg
Daniel J. Jacob
Affiliation:
Harvard University, Massachusetts
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Modeling of Atmospheric Chemistry , pp. 84 - 204
Publisher: Cambridge University Press
Print publication year: 2017

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.)

References

Andrews, D. G., Holton, J. R. and Leong, C. B. (1987) Middle Atmosphere Dynamics, Academic Press, Orlando.Google Scholar
Andrews, D. G. and McIntyre, M. E. (1976) Planetary waves in horizontal and vertical shear: The generalized Eliassen–Palm relation and the mean zonal acceleration, J. Atmos. Sci., 33, 2031–2048.Google Scholar
Andrews, D. G. and McIntyre, M. E. (1978) An exact theory of nonlinear waves on a Lagrangian-mean flow, J. Fluid Mech., 89, 609–646.CrossRefGoogle Scholar
Arakawa, A. and Lamb, V. R. (1977) Computational design of the basic dynamical processes of the UCLA general circulation model, Methods Comput. Phys., 17, 174–265.Google Scholar
Asselin, R. (1972) Frequency filter for time integrations, Mon. Wea. Rev., 100, 487–490.Google Scholar
Banks, P. M. and Kockarts, G. (1973) Aeronomy, Academic Press, New York.Google Scholar
Bishop, C. M. (1995) Neural Networks for Pattern Recognition, Clarendon Press, Oxford.CrossRefGoogle Scholar
Blond, N., Bel, L., and Vautard, R. (2003) Three-dimensional ozone data analysis with an air quality model over the Paris area, J. Geophys. Res, 108 (D23), 4744, doi:10.1029/2003JD003679.Google Scholar
Boughton, B. A., Delarentis, J. M., and Dunn, W. W. (1987) A stochastic model of particle dispersion in the atmosphere, Boundary-Layer Meteorology, 80, 147–163.Google Scholar
Bourke, W. (1974) A multi-level spectral model: I.Formulation and hemispheric integrations, Mon. Wea. Rev., 102, 687–701.2.0.CO;2>CrossRefGoogle Scholar
Boyd, J. (1976) The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat and momentum, J. Atmos. Sci., 33, 2285–2291.Google Scholar
Boyd, J. (1998) Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion. J. Comput. Phys., 143, 283–288.CrossRefGoogle Scholar
Brasseur, G. P. and Solomon, S. (2005) Aeronomy of the Middle Atmosphere: Chemistry and Physics of the Stratosphere and Mesosphere, 3rd edition, Springer, Amsterdam.Google Scholar
Canuto, V. M., Goldman, I., and Hubickyj, O. (1984) A formula for the Shakura–Sunyaev turbulent viscosity parameter, Astrophys. J., 280, L55–L88, doi: 10.1086/184269.CrossRefGoogle Scholar
Chapman, S. and Cowling, T. G. (1970) The Mathematical Theory of Non-uniform Gases, 3rd edition, Cambridge University Press, Cambridge.Google Scholar
Charney, J. G., Fjörtoft, R., and von Neumann, J. (1950) Numerical integration of the barotropic vorticity equation, Tellus, 2, 237–254.Google Scholar
Courant, R. (1943) Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc., 49, 1–23.Google Scholar
Cressie, N. (1993) Statistics for Spatial Data, Wiley, Chichester.CrossRefGoogle Scholar
Cruse, H. (2006) Neural Networks as Cybernetic Systems, 2nd edition, Brains, Mind and Media, Bielefeld.Google Scholar
de Bruyns Kops, S. M., Riley, J. J., and Kosaly, G. (2001) Direct numerical simulation of reacting scalar mixing layers, Phys. Fluids, 13, 5, 1450–1465.Google Scholar
Dietachmayer, G. S. and Droegemeier, K. K. (1992) Application of continuous dynamic grid adaption techniques to meteorological modelling. Part I: Basic formulation and accuracy, Mon. Wea. Rev., 120, 1675–1706.2.0.CO;2>CrossRefGoogle Scholar
Durran, D. R. (2010) Numerical Methods for Fluid Dynamics, Springer, Amsterdam.CrossRefGoogle Scholar
Eliasen, E., Machenhauer, B., and Rasmussen, E. (1970) On a Numerical Method for Integration of the Hydrodynamical Equations with a Spectral Representation of the Horizontal Fields, Institute of Theoretical Meteorology, University of Copenhagen, Copenhagen.Google Scholar
Enting, I. G. (2000) Green’s function methods of tracer inversion, Geophys. Monograph., 114, 19–31,Google Scholar
Fournier, A., Taylor, M. A., and Tribbia, J. (2004) The spectral element atmosphere model (SEAM): High resolution parallel computation and localized resolution of regional dynamics, Mon. Wea. Rev., 132, 726–748.2.0.CO;2>CrossRefGoogle Scholar
Fritsch, F. N. and Carlson, R. E. (1980) Monotone piecewise cubic interpolation, SIAM J. Numer. Anal., 17, 238–246.Google Scholar
Garcia, R. and Solomon, S. (1983) A numerical model of the zonally averaged dynamical and chemical structure of the middle atmosphere, J. Geophys. Res. 88, 1379–1400.CrossRefGoogle Scholar
Garcia-Menendez, F., Yano, A., Hu, Y., and Odman, M. T. (2010) An adaptive grid version of CMAQ for improving the resolution of plumes, Atmos. Pollut. Res., 1, 239–249.Google Scholar
Gentile, M., Courbin, F., and Meylan, G. (2013) Interpolating point spread function anisotropy, Astronomy & Astrophysics, 549, A1.Google Scholar
Hall, T. M. and Plumb, R. A. (1994) Age of air as a diagnostic of transport, J. Geophys. Res., 99, 1059–1070.Google Scholar
Haltiner, G. J. and Williams, R. T. (1980) Numerical Prediction and Dynamic Meteorology, Wiley, Chichester.Google Scholar
Hubbard, M. E. (2002) Adaptive mesh refinement for three-dimensional off-line tracer advection over the sphere, Int. J. Numer. Methods Fluids, 40, 369–377.Google Scholar
Jablonowski, C. and Williamson, D. L. (2011) The pros and cons of diffusion, filters and fixers in atmospheric general circulation models. In Numerical Techniques for Global Atmospheric Models (Lauritzen, P. H., Jablonowski, C., Taylor, M. A., and Nair, R. D., eds.), Springer-Verlag, Berlin.Google Scholar
Jacob, D. J. (1999) Introduction to Atmospheric Chemistry, Princeton University Press, Princeton, NJ.Google Scholar
Janssen, S., Dumont, G., Fierens, F., and Mensink, C. (2008) Spatial interpolation of air pollution measurements using CORINE land cover data, Atmos. Env., 42, 4884–4903.Google Scholar
Kasahara, A. (1974) Various vertical coordinate systems used for numerical weather prediction, Mon. Wea. Rev., 102, 504–522.Google Scholar
Krige, D. G. (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand, J. Chem., Metal. Mining Soc. South Africa, 52, 119–139.Google Scholar
Langevin, P. (1908) On the theory of Brownian motion, C. R. Acad. Sci. (Paris), 146, 530–533.Google Scholar
Lanser, D. and Verwer, J. G. (1998) Analysis of operator splitting for advection–diffusion–reaction problems from air pollution modeling. CWI Report MAS-R9805.Google Scholar
Lanser, D. and Verwer, J. G. (1999) Analysis of operator splitting for advection–diffusion-reaction problems from air pollution modelling, J. Comput. Appl. Math., 111, 210–216.Google Scholar
Laprise, R. (1992) The resolution of global spectral models. Bull. Amer. Meteor. Soc., 73, 1453–1454.Google Scholar
Lauritzen, P. H., Jablonowski, C., Taylor, M. A., and Nair, R. D. (2011) Numerical Techniques for Global Atmospheric Models, Springer, Amsterdam.Google Scholar
Lin, J. C. (2012) Lagrangian modeling of the atmosphere: An introduction. In Lagrangian Modeling of the Atmosphere (Lin, J., Brunner, D., Gerbig, C., et al., eds.), American Meteorological Union, Washington, DC.Google Scholar
Lin, J. C., Gerbig, C., Wofsy, S. C., et al. (2003) A near-field tool for simulating the upstream influence of atmospheric observations: The Stochastic Time-Inverted Lagrangian Transport (STILT) model, J. Geophys. Res., 108(D16), 4493, doi:10.1029/202JD003161.Google Scholar
Lin, J. S. and Hildemann, L. (1996) Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities, Atmos. Environ., 30(2), 239–254.Google Scholar
Lin, S.-J. and Rood, R. B. (1996) Multidimensional flux-form semi-Lagrangian scheme, Mon. Wea. Rev., 124, 2046–2070.Google Scholar
Liu, S. C., McAfee, J. R., and Cicerone, R. J. (1982) Radon-222 and tropospheric vertical transport, J. Geophys. Res., 89, 7291–7297.Google Scholar
Luhar, A. K. (2012) Lagrangian particle modeling of dispersion in light winds. Lagrangian Modeling of the Atmosphere (Lin, J., Brunner, D., Gerbig, C., et al., eds.), American Meteorological Union, Washington, DC.Google Scholar
Matheron, G. (1962) Traité de géostatistique appliquée. Editions Technip, Paris.Google Scholar
McWilliams, J. (2006) Fundamentals of Geophysical Fluid Dynamics, Cambridge University Press, Cambridge.Google Scholar
Mesinger, F. (1984) A blocking technique for representation of mountains in atmospheric models. Riv. Meteor. Aeronautica, 44, 195–202.Google Scholar
Moler, C. (2004) Numerical Computing with MATLAB, Society for Industrial and Applied Mathematics, Philadelphia, PA.Google Scholar
Neufeld, Z. and Hernandez-Garcia, E. (2010) Chemical and Biological Processes in Fluid Dynamics, Imperial College Press, London.Google Scholar
Odman, M. T., Mathur, R., Alapaty, K., et al. (1997) Nested and adaptive grids for multiscale air quality modeling. In Next Generation Environmental Models and Computational Methods (Delic, G. and Wheeler, M. F., eds.), Society for Industrial and Applied Mathematics, Philadelphia, PA.Google Scholar
Odman, M. T., Khan, M. N., Srivastava, R. K., and McRae, D. S. (2002) Initial application of the adaptive grid air pollution model. In Air Pollution Modeling and Its Applications (Borrego, C. and Schayes, G., eds.), Kluwer Academic/Plenum Publishers, New York.Google Scholar
Orszag, S. A. (1970) Transform method for the calculation of vector-coupled sums: Application to the spectral form of the vorticity equation, J. Atmos. Sci., 27, 890–895.2.0.CO;2>CrossRefGoogle Scholar
Pasquill, F. (1971) Atmospheric dispersion of pollutants, Q. J. Roy. Meteor. Soc., 97, 369–395.CrossRefGoogle Scholar
Patera, A. T. (1984) A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Compute. Phys., 54, 468–488.Google Scholar
Phillips, N. A. (1957) A coordinate system having some special advantages for numerical forecasting, J. Meteor. 14, 184–185.Google Scholar
Prather, M. J. (2007) Lifetimes and time-scales in atmospheric chemistry. Phil. Trans. R. Soc. A, 365, 1705–1726, doi: 10.1098/rsta.2007.2040.CrossRefGoogle ScholarPubMed
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007) Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge.Google Scholar
Qaddouri, A. (2008) Optimized Schwarz methods with the Yin–Yang grid for shallow water equations. In Domain Decomposition Methods in Science and Engineering (Langer, U., Discacciati, M., Keyes, D. E., Widlund, O., and Zulehner, W., eds.) Springer, New York.Google Scholar
Reynolds, O. (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistances in parallel channels. Phil. Trans. Roy. Soc. London, 174, 935–982.Google Scholar
Robert, A. (1969) The integration of a spectral model of the atmosphere by the implicit method. Proceedings of the WMO/IUGG Symposium on NWP. Japan Meteorological Society, Tokyo.Google Scholar
Seinfeld, J. H. and Pandis, S. N. (2006) Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd edition, Wiley, New York.Google Scholar
Shapiro, R. (1970) Smoothing, filtering and boundary effects, Rev. Geophys. Spac. Phys., 8, 2, 359–387.Google Scholar
Shapiro, R. (1975) Linear filtering, Math. Comput., 29, 1094–1097.Google Scholar
Shepard, D. (1968) A two-dimensional interpolation function for irregularly-space data. In Proceedings of the 1968 ACM National Conference, doi:10.1145/800186.810616.Google Scholar
Shuman, F. G. (1957) Numerical methods for weather prediction, II: Smoothing and filtering, Mon. Wea. Rev., 85, 357–361.Google Scholar
Skamarock, W. C. and Klemp, J. B. (1993) Adaptive grid refinement for two-dimensional and three-dimensional nonhydrostatic atmospheric flow, Mon. Wea. Rev., 121, 788–804.2.0.CO;2>CrossRefGoogle Scholar
Sportisse, B. (2000) An analysis of operator splitting techniques in the stiff case, J. Comput. Phys., 161, 140–168, doi: 10.1006/jcph.2000.6495.Google Scholar
Sportisse, B. (2010) Fundamentals in Air Pollution, Springer, Amsterdam.Google Scholar
Srivastava, R. K., McRae, D. S., and Odman, M. T. (2000) An adaptive grid algorithm for air-quality modeling, J. Comput. Phys., 165, 437–472, doi: 10.1006/jcph.2000.6620.Google Scholar
Steyn, D. G. and Rao, S. T. (2010) Air pollution modeling and its application. In Proceedings of the 30th NATO/SPS International Technical Meeting on Air Pollution Modelling and Its Application, Springer, New York.Google Scholar
Stockie, J. M. (2011) The mathematics of atmospheric dispersion modeling, SIAM Rev., 53 (2) 349–372.CrossRefGoogle Scholar
Stohl, A. (1998) Computation, accuracy and applications of trajectories: A review and bibliography, Atmos. Environ., 32, 6, 947–966.Google Scholar
Stohl, A., Forster, C., Frank, A., Seibert, P., and Wotawa, G. (2005) Technical note: The Lagrangian particle dispersion model FLEXPART version 6.2, Atmos. Chem. Phys., 5, 2461–2474.Google Scholar
Strang, G. (1968) On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5, 3, 506–517.Google Scholar
Thomson, D. J. (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows, J. Fluid. Mech., 180, 529–556.Google Scholar
Tomlin, A. S., Berzins, M., Ware, J., Smith, J., and Pilling, M. J. (1997) On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources, Atmos. Environ., 31, 2945–2959.Google Scholar
Vandeven, H (1991) Family of spectral filters for discontinuous problems. J. Sci. Comput., 6, 159–192.Google Scholar
Warner, T. T. (2011) Numerical Weather and Climate Prediction, Cambridge University Press, Cambridge.Google Scholar
Washington, W. M., Buja, L., and Craig, A. (2009) The computational future for climate and Earth system models: On the path to petaflop and beyond, Phil. Trans. R. Soc. A, 367, 833–846.Google Scholar
Williamson, D. L. and Laprise, R. (1998) Numerical approximations for global atmospheric general circulation models. In Numerical Modelling of the Global Atmosphere for Climate Prediction (Mote, P. and O’Neill, A., eds.), Kluwer Academic Publishers, Dordrecht.Google Scholar
Wilson, J. D. and Sawford, B. L. (1996) Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere, Boundary-Layer Meteorology, 78, 191–210.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@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
×