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Numerical Weather Prediction Basics: Models, Numerical Methods, and Data Assimilation

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Abstract

Numerical weather prediction has become the most important tool for weather forecasting around the world. This chapter provides an overview of the fundamental principles of numerical weather prediction, including the numerical framework of models, numerical methods, physical parameterization, and data assimilation. Historical revolution, the recent development, and future direction are introduced and discussed.

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References

  • A. Arakawa, C. S. Konor, Vertical differencing of the primitive equations based on the Charney–Phillips grid in hybrid σp vertical co-ordinates. Mon. Wea. Rev. 124, 511–528 (1996)

    Article  Google Scholar 

  • A. Arakawa, Adjustment mechanisms in atmospheric motions. J. Meteorol. Soc. Jpn. 75, 155–179 (1997)

    Article  Google Scholar 

  • A. Arakawa, The cumulus parameterization problem: past, present, and future. J. Clim. 17, 2493–2525 (2004)

    Article  Google Scholar 

  • P. Bauer, A. Thorpe, G. Brunet, The quiet revolution of numerical weather prediction. Nature 525, 47–55 (2015)

    Article  Google Scholar 

  • V. Bjerknes, Das Problem der Wettervorhersage betrachtet vomStandpunkt der Mechanik und Physik. Meteorol. Z. 21, 1–7 (1904)

    Google Scholar 

  • F. Bouttier, F. Rabier, The operational implementation of 4D-Var. ECMWF Newsl. 78, 2–5 (1997)

    Google Scholar 

  • G. Brunet et al., Collaboration of the weather and climate communities to advance subseasonal-to-seasonal prediction. Bull. Am. Meteorol. Soc. 91, 1397–1406 (2010)

    Article  Google Scholar 

  • J.G. Charney, R. Fjoertoft, J.V. Neumann, Numerical integration of the barotropic vorticity equation. Tellus 2, 237–254 (1950)

    Article  Google Scholar 

  • F. Chen, J. Dudhia, Coupling an advanced land-surface/hydrology model with the Penn State/NCAR MM5 modeling system. Part I: model description and implementation. Mon. Weather Rev. 129, 569–585 (2001)

    Article  Google Scholar 

  • P. Courtier, O. Talagrand, Variational assimilation of meteorological observations with the adjoint vorticity equations, Part II, numerical results. Quart. J. Roy. Meteor. Soc. 113, 1329–1347 (1987)

    Article  Google Scholar 

  • J. Derber, A variational continuous assimilation technique. Mon. Weather Rev. 117, 2437–2446 (1989)

    Article  Google Scholar 

  • R. Daley, Atmospheric Data Analysis (Cambridge University Press, Cambridge, 1991)

    Google Scholar 

  • D.R. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics (Springer, New York, 1999)

    Book  Google Scholar 

  • M.B. Ek, K.E. Mitchell, Y. Lin, E. Rogers, P. Grunmann, V. Koren, G. Gayno, J.D. Tarpley, Implementation of Noah land surface model advances in the National Centers for Environmental Prediction operational mesoscale Eta model. J. Geophys. Res. 22, 8851 (2003)

    Article  Google Scholar 

  • G. Evensen, Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99, 10143–10162 (1994)

    Article  Google Scholar 

  • T.M. Hamill, C. Snyder, A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Weather Rev. 128, 2905–2919 (2000)

    Article  Google Scholar 

  • M. Hamrud, M. Bonavita, L. Isaksen, EnKF and hybrid gain ensemble data assimilation. Part I: EnKF implementation. Mon. Weather Rev. 143, 4847–4864 (2015)

    Article  Google Scholar 

  • S.Y. Hong, Dudhia, Next-generation numerical weather prediction: bridging parameterization, explicit clouds, and large eddies. Bull. Am. Meteorol. Soc. 93, ES6–ES9 (2012)

    Article  Google Scholar 

  • R.M. Hodur, The naval research laboratory’s coupled ocean/atmosphere mesoscale prediction system (COAMPS). Mon. Weather Rev. 125, 1414–1430 (1997)

    Article  Google Scholar 

  • J. Holton, An introduction to dynamic meteorology. Fourth edition. (Elsevier Academic Press, 2004)

    Google Scholar 

  • P.L. Houtekamer, F. Zhang, Review of the ensemble Kalman filter for atmospheric data assimilation. Mon. Weather Rev. 144, 4489–4452 (2016)

    Article  Google Scholar 

  • R.A. Houze Jr., Cloud Dynamics (Academic, London, 1993)

    Google Scholar 

  • P.A.E.M. Janssen, The Interaction of Ocean Waves and Wind (Cambridge University Press, Cambridge, UK, 2004)

    Book  Google Scholar 

  • H.M. Juang, M. Kanamitsu, The NMC nested regional spectral model. Mon. Weather Rev. 122, 3–26 (1994)

    Article  Google Scholar 

  • E. Kalnay, Atmospheric Modeling, Data Assimilation, and Predictability (Cambridge University Press, 2003)

    Google Scholar 

  • M.F. Khairoutdinov, D.A. Randall, C. DeMott, Simulations of the atmospheric general circulation using a cloud-resolving model as a super- parameterization of physical processes. J. Atmos. Sci. 62, 2136–2154 (2005)

    Article  Google Scholar 

  • D.T. Kleist, K. Ide, An OSSE-based evaluation of hybrid variational-ensemble data assimilation for the NCEP GFS. Part II: 4DEnVar and hybrid variants. Mon. Weather Rev. 143, 452–470 (2015)

    Article  Google Scholar 

  • S.-J. Lin, A finite-volume integration method for computing pressure gradient forces in general vertical coordinates. Q. J. R. Meteorol. Soc. 13, 1749–1762 (1997)

    Google Scholar 

  • S.J. Lin, R.B. Rood, Multidimensional flux-form semi-Lagrangian transport scheme. Mon. Weather Rev. 124, 2046–2070 (1996)

    Article  Google Scholar 

  • K.-N. Liou, An Introduction to Atmospheric Radiation (Academic, London, 1980)

    Google Scholar 

  • A.C. Lorenc, Analysis methods for numerical weather prediction. Q. J. R. Meteorol. Soc. 112, 1177–1194 (1986)

    Article  Google Scholar 

  • P. Lynch, The origins of computer weather prediction and climate modeling. J. Comput. Phys. 227, 3431–3444 (2008)

    Article  Google Scholar 

  • T. Miyoshi et al., “Big Data Assimilation” revolutionizing severe weather prediction. Bull. Am. Meteorol. Soc. 97, 1347–1354 (2016)

    Article  Google Scholar 

  • E. Ott et al., A local ensemble Kalman filter for atmospheric data assimilation. Tellus 56A, 415–428 (2004)

    Article  Google Scholar 

  • D.F. Parrish, J.C. Derber, The National Meteorological Center’s spectral statistical interpolation analysis system. Mon. Weather Rev. 120, 1747–1763 (1992)

    Article  Google Scholar 

  • S.G. Penny, The hybrid local ensemble transform Kalman filter. Mon. Weather Rev. 142, 2139–2149 (2014)

    Article  Google Scholar 

  • T.N. Palmer, P.D. Williams, Introduction: stochastic physics and climate modelling. Phil. Trans. R. Soc. A 366, 2421–2427 (2008)

    Google Scholar 

  • R.A. Pielke Sr., Mesoscale meteorological modelling. Second edition (Academic Press, 2002)

    Google Scholar 

  • L.F. Richardson, Weather Prediction by Numerical Process (Cambridge University Press, Cambridge, UK, 1922)

    Google Scholar 

  • A.J. Robert, A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations. J. Meteorol. Soc. Jpn. 60, 319–324 (1982)

    Article  Google Scholar 

  • A.J. Simmons, A. Hollingsworth, Some aspects of the improvement in skill of numerical weather prediction. Q. J. R. Meteorol. Soc. 128, 647–677 (2002)

    Article  Google Scholar 

  • W.C. Skamarock, J.B. Klemp, J. Dudhia, D.O. Gill, M. Barker, K.G. Duda, X.Y. Huang, W. Wang, J.G. Powers, A description of the advanced research WRF version 3. NCAR Tech. Note, NCAR/TN-475+STR, 113 pp. (2008)

    Google Scholar 

  • D.J. Stensrud, Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models (Cambridge University Press, Cambridge, UK, 2007)

    Book  Google Scholar 

  • G.L. Stephens, The parameterization of radiation for numerical weather prediction and climate models. Mon. Weather Rev. 112, 826–867 (1984)

    Article  Google Scholar 

  • J.M. Straka, Cloud and Precipitation Microphysics: Principles and Parameterization (Cambridge University Press, Cambridge, UK, 2009)

    Book  Google Scholar 

  • R.B. Stull, An Introduction to Boundary Layer Meteorology (Kluwer Academic Publishers, Dordrecht, 1988)

    Book  Google Scholar 

  • O. Talagrand, Assimilation of observations, an introduction. J. Met. Soc. Jpn. Spec. Issue 75(1B), 191–209 (1997)

    Article  Google Scholar 

  • M. Teixeira, The physics of orographic gravity wave drag. Front. Phys. 2, 43 (2014)

    Article  Google Scholar 

  • M. Tiedtke, The general problem of parameterization. ECMWF Lecture Note (1984), http://www.ecmwf.int/en/learning/education-material/introductory-lectures-nwp

  • M.K. Tippett, J.L. Anderson, C.H. Bishop, T.M. Hamill, J.S. Whitaker, Ensemble square-root filters. Mon. Weather Rev. 131, 1485–1490 (2003)

    Article  Google Scholar 

  • H.L. Tolman, User manual and system documentation of WAVEWATCH III version 4.18. NOAA/NWS/NCEP/MMAB Technical Note 316, 194 pp. (2014)

    Google Scholar 

  • X. Wang, D. Parrish, D. Kleist, J. Whitaker, GSI 3DVarbased ensemble-variational hybrid data assimilation for NCEP global forecast system: single-resolution experiments. Mon. Weather Rev. 141, 4098–4117 (2013)

    Article  Google Scholar 

  • T. Warner, Numerical Weather and Climate Prediction (Cambridge Press, Cambridge, UK, 2011)

    Google Scholar 

  • D.L. Williamson, The evolution of dynamical cores for global atmospheric models. J. Meteorol. Soc. Jpn. B 85, 241–269 (2007)

    Article  Google Scholar 

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Correspondence to Zhaoxia Pu .

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Pu, Z., Kalnay, E. (2019). Numerical Weather Prediction Basics: Models, Numerical Methods, and Data Assimilation. In: Duan, Q., Pappenberger, F., Wood, A., Cloke, H., Schaake, J. (eds) Handbook of Hydrometeorological Ensemble Forecasting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39925-1_11

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