Skip to main content
SpringerLink
Log in

Data Assimilation for Numerical Weather Prediction: A Review

  • Chapter
Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications

Abstract

During the last 20 years data assimilation has gradually reached a mature center stage position at both Numerical Weather Prediction centers as well as being at the center of activities at many federal research institutes as well as at many universities.

The research encompasses now activities which involve, beside meteorologists and oceanographers at operational centers or federal research facilities, many in the applied and computational mathematical research communities. Data assimilation or 4-D VAR extends now also to other geosciences fields such as hydrology and geology and results in the publication of an ever increasing number of books and monographs related to the topic.

In this short survey article we provide a brief introduction providing some historical perspective and background, a survey of data assimilation prior to 4-D VAR and basic concepts of data assimilation.

I first proceed to outline the early 4-D VAR stages (1980–1990) and addresses in a succinct manner the period of the 1990s that saw the major developments and the flourishing of all aspects of 4-D VAR both at operational centers and at research Universities and Federal Laboratories. Computational aspects of 4-D Var data assimilation addressing computational burdens as well as ways to alleviate them are briefly outlined.

Brief interludes are provided for each period surveyed allowing the reader to have a better perspective A brief survey of different topics related to state of the art 4-D Var today is then presented and we conclude with what we perceive to be main directions of research and the future of data assimilation and some open problems. We will strive to use the unified notation of Ide et al. (J Meteor Soc Japan 75:181–189, 1997).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aarnes JE (2004) Iterative methods for data assimilation and an application to ocean state modeling. Technical Report, SINTEF Applied Mathematics. Oslo, Norway

    Google Scholar 

  • Akella S, Navon IM (2007) Different approaches to model error formulation in 4D-Var:a study with high resolution advection schemes. In revision process with Tellus

    Google Scholar 

  • Amodei L (1995) Solution approchée pour un problème d’assimilation de données météorologiques avec prise en compte de l’erreur de modèle. Comptes Rendus de l’Académie des Sciences 321, série II: 1087–1094

    Google Scholar 

  • Baker NL, Daley R (2000) Observation and background adjoint sensitivity in the adaptive observation-targeting problem. Q J R Meteorol Soc 126:1431–1454

    Article  Google Scholar 

  • Barkmeijer J et al (1998) Singular vectors and estimates of the analysis-error covariance metric. Q J R Meteorol Soc A:1695–1713

    Google Scholar 

  • Barkmeijer J et al (1999) 3D-Var Hessian singular vectors and their potential use in the ECMWF ensemble prediction system. Q J R Meteorol Soc B:2333–2351

    Google Scholar 

  • Barnes SL (1964) A technique for maximizing details in numerical weather map analysis. J Appl Meteor 3:395–409

    Article  Google Scholar 

  • Bellman RE (1957) Dynamic programming. Princeton University Press, Princeton

    Google Scholar 

  • Bennett AF (2002) Inverse modeling of the ocean and atmosphere. Cambridge University Press, p 256

    Google Scholar 

  • Bergthorsson P, Döös B (1955) Numerical weather map analysis. Tellus 7(3):329–340

    Google Scholar 

  • Berliner LM et al (1999) Statistical design for adaptive weather observations. J Atmos Sci 56:2536–2552

    Article  Google Scholar 

  • Bertsekas DP (1982) Constrained optimization and Lagrange multiplier methods. Addison-Wesley, Tucson, AZ, p 491

    Google Scholar 

  • Berz M et al (eds) (1996) Computational differentiation: techniques, applications, and tools. SIAM, Philadelphia, PA

    Google Scholar 

  • Bischof CH et al (1992) Automatic differentiation of advanced CFD codes for multidisciplinary design. J Comput Syst Eng 3:625–638

    Article  Google Scholar 

  • Bloom SC, Shubert S (1990) The influence of Monte-Carlo estimates of model error growth on the GLA OI assimilation system. In: International symposium on assimilation of observations in meteorology and oceanography. WMO, Geneva, Switzerland, pp 467–470

    Google Scholar 

  • Boer GJ (1984) A spectral analysis of predictability and error in an operational forecast system. Mon Wea Rev 112:1183–1197

    Article  Google Scholar 

  • Bouttier F, Courtier P (1999) Date assimilation concepts and methods. Meteorological Training Lecture Notes, ECMWF, Shinfield Park, Reading

    Google Scholar 

  • Bouttier F, Kelly G (2001) Observing-system experiments in the ECMWF 4D-Var data assimilation system. Q J R Meteorol Soc 127:1469–1488

    Article  Google Scholar 

  • Bratseth A (1986) Statistical interpolation by means of successive corrections. Tellus 38A:439–447

    Google Scholar 

  • Buizza R, Palmer TN (1995) The singular-vector structure of the atmospheric general circulation. J Atmos Sci 529:1434–1456

    Article  Google Scholar 

  • Cacuci DG et al (1980) Sensitivity theory for general systems of nonlinear equations. Nucl Sci Eng 75:88

    Google Scholar 

  • Cacuci DG (1981a) Sensitivity theory for nonlinear systems. I: Nonlinear functional analysis approach. J Math Phy 12:2794–2803

    Article  Google Scholar 

  • Cacuci DG (1981b) Sensitivity theory for nonlinear systems. II. Extensions to additional classes of responses. J Math Phy 12:2803–2812

    Article  Google Scholar 

  • Cacuci DG (2003) Sensitivity & uncertainty analysis: A primer, CRC Press, Boca Raton, 1:304

    Google Scholar 

  • Cacuci DG (2004) On the historical evolution of the use of adjoint operators in sensitivity and uncertainty analysis. Sixth Workshop on Adjoint Applications in Dynamic Meteorology, 23–28 May 2004, Acquafredda di Maratea, Basilicata, Italy

    Google Scholar 

  • Cacuci DG et al (2005) Sensitivity and uncertainty analysis. Volume II Applications to Large-Scale Systems, CRC Press, Boca Rotan, p 368

    Google Scholar 

  • Cardinali C et al (2004) Influence matrix diagnostic of a data assimilation system. Q J R Meteorol Soc 130:2767–2786

    Article  Google Scholar 

  • Chapnik B et al (2006) Diagnosis and tuning of observational error statistics in a quasi-operational data assimilation setting. Q J R Meteorol Soc 132:543–565

    Article  Google Scholar 

  • Charney JG et al (1950) Numerical integration of the barotropic vorticity equation. Tellus 2:237–254

    Google Scholar 

  • Charney JG et al (1969) Use of incomplete historical data to infer the present state of the atmosphere. J Atmos Sci 2:1160–1163

    Article  Google Scholar 

  • Cohn SE (1997) An introduction to estimation theory. J Meteorol Soc Jpn 75:257–288

    Google Scholar 

  • Courant R, Hilbert D (1962) Partial differential equations. Methods of Mathematical Physics. Wiley-Interscience, New York

    Google Scholar 

  • Courtier P (1985) Experiments in data assimilation using the adjoint model technique. Workshop on High-Resolution Analysis ECMWF (UK) June

    Google Scholar 

  • Courtier P, Talagrand O (1987) Variational assimilation of meteorological observations with the adjoint equations Part 2. Numerical results. Q J R Meteorol Soc 113:1329–1347

    Article  Google Scholar 

  • Courtier P, Derber J, Errico R, et al (1993) Important literature on the use of adjoint, variational-methods and the Kalman filter in meteorology Tellus A 45A(5):342–357.

    Article  Google Scholar 

  • Courtier P et al (1993) Progress in variational data assimilation at ECMWF. In: Boer GJ (eds) Research activities in atmospheric and oceanic modeling. Report No.181:42

    Google Scholar 

  • Courtier P et al (1994) A strategy for operational implementation of 4D-VAR, using an incremental approach. Q J R Meteorol Soc 120 (519) B JUL:1367–1387

    Article  Google Scholar 

  • Courtier P (1997) Dual formulation of four-dimensional variational assimilation. Q J R Meteorol Soc 123 (544) B:2449–2461

    Google Scholar 

  • Cressman GP (1959) An operational objective analysis system. Mon Wea Rev 87:367–374

    Article  Google Scholar 

  • Daescu DN, Navon IM (2004) Adaptive observations in the context of 4D-Var data assimilation. Meteor Atmos Phys 85:205–226

    Article  Google Scholar 

  • Dalcher A, Kalnay E (1987) Error growth and predictability in operational ECMWF forecasts. Tellus 39A:474–491

    Google Scholar 

  • Daley R, Puri K (1980) Four-dimensional, data assimilation and the slow manifold. Mon Wea Rev 108:85–99

    Article  Google Scholar 

  • Daley R (1991) Atmospheric data analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Daley R (1992a) The effect of serially correlated observation and model error on atmospheric data assimilation. Mon Wea Rev 120:164–177

    Article  Google Scholar 

  • Daley R (1992b) Estimating model-error covariances for application to atmospheric data assimilation. Mon Wea Rev 120:1735–1746

    Article  Google Scholar 

  • Da Silva A et al (1995) Assessing the effects of data selection with DAO’s physical-space statistical analysis system. Proceedings of the second international Symposium on the assimilation of observations in meteorology and Oceanography. Tokyo, Japan

    Google Scholar 

  • Davidson ER (1975) The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of a large real symmetric matrices. J Comput Phys 17: 87–94

    Article  Google Scholar 

  • Davis HE, Turner RE (1977) Updating prediction models by dynamic relaxation. An examination of the technique. Q J R Meteorol Soc 103:225–245

    Article  Google Scholar 

  • Dee D, Silva AD (1998) Data assimilation in the presence of forecast bias. Q J R Meteorol Soc 124:269–295

    Article  Google Scholar 

  • DelSole T, Hou AY (1999) Empirical correction of a dynamical model. Part I: fundamental issues. Mon Wea Rev 127: 2533–2545

    Article  Google Scholar 

  • Derber JC (1985) The variational four dimensional assimilation of analysis using filtered models as constraints. PhD, Thesis, Univ. of Wisconsin-Madison, p 141

    Google Scholar 

  • Derber JC (1989) A variational continuos assimilation technique. Mon Wea Rev 117: 2437–2446

    Article  Google Scholar 

  • Desroziers G, Ivanov S (2001) Diagnosis and adaptive tuning of information error parameters in a variational assimilation. Q J R Meteorol Soc 127:1433–1452

    Article  Google Scholar 

  • Desroziers G et al (2003) A 4D-Var re-analysis of the FASTEX. Q J R Meteorol Soc 129:1301–1315

    Article  Google Scholar 

  • Ehrendorfer M, Bouttier F (1998) An explicit low-resolution extended Kalman filter: Implementation and preliminary experimentation. Sept, ECMWF Tech Memo No 259

    Google Scholar 

  • Eliassen A (1954) Provisional report on calculation of spatial covariance and autocorrelation of the pressure field, Report # 5. Institute of Weather and Climate Res, Academy of Science, Oslo, p 11

    Google Scholar 

  • Fisher M, Courtier P (1995) Estimating the covariance matrices of analysis and forecast errors in variational data assimilation. ECMWF Tech Memo 220:28

    Google Scholar 

  • Fisher M (1998) Development of a simplified Kalman filter. ECMWF Tech Memo 260:16

    Google Scholar 

  • Fisher M (2003a) Background error covariance modelling M Fisher seminar, Recent developments in data assimilation for atmosphere and ocean. 8–12 September European Centre for Medium-Range Weather Forecasts

    Google Scholar 

  • Fisher M (2003b) Estimation of entropy reduction and degrees of freedom for signal for large variational analysis systems. Technical Memo, ECMWF, Reading, UK, p 397

    Google Scholar 

  • Franke R, Gordon WJ (1983) The structure of optimal interpolation functions. Technical Report, NPS-53-83-0004. Naval Postgraduate School, Monterey, CA

    Google Scholar 

  • Franke R (1988) Statistical interpolation by iteration. Mon Wea Rev 116:961–963

    Article  Google Scholar 

  • Gandin LS (1965) Objective analysis of meteorological fields. Leningrad: Gridromet (in Russian) (1963) English translation by the Israel program for scientific translations, p 242

    Google Scholar 

  • Gauss CF (1809) Theoria motus corporum coelestium in sectionibus conicis solem ambientum Book 2, Section 2, pp 205–224. English translation by Ch. Davis, reprinted 1963 by Dover, New York, p 142

    Google Scholar 

  • Gauthier P, Courtier P (1992) Data assimilation with an extended Kalman filter. ECMWF Workshop on variational assimilation with emphasis on three-dimensional aspects, Shinfield Park, Reading RG2 9AX, UK, p 171–190

    Google Scholar 

  • Gauthier P, Thepaut JN (2001) Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Meteo-France. Mon Wea Rev 129:2089–2102

    Article  Google Scholar 

  • Ghil M et al (l979) Time-continuous assimilation of remote-sounding data and its effect on weather forecasting. Mon Wea Rev 107:l40–l7l

    Google Scholar 

  • Ghil M, Malonotte-Rizzoli P (1991) Data assimilation in meteorology and oceanography. Adv Geophys 33:141–266

    Google Scholar 

  • Ghil M et al (1997) Data assimilation in meteorology and oceanography: Theory and practice. Meteorological Society of Japan and Universal Academy Press, Tokyo, p 496

    Google Scholar 

  • Giering R, Kaminski T (1997) Recipes for adjoint code construction. Technical Report 212, Max-Planck-Institut für Meteorologie

    Google Scholar 

  • Gilchrist B, Cressman GP (1954) An experiment in objective analysis. Tellus 6:309–318

    Article  Google Scholar 

  • Griewank A, Corliss GF (1991) Automatic differentiation of algorithms: theory, implementation, and application. SIAM, Philadelphia, p 353

    Google Scholar 

  • Griewank A (2000) Evaluating derivatives principles and techniques of algorithmic differentiation. Frontiers Appl Math 19:369

    Google Scholar 

  • Griffith AK, Nichols NK (1996) Accounting for model error in data assimilation using adjoint methods. In: Berz M et al (eds) Computational differentiation: Techniques, applications, and tools. SIAM, Philadelphia, PA, pp 195–205

    Google Scholar 

  • Griffith AK (1997) Data assimilation for numerical weather prediction using control theory. The University of Reading, Department of Mathematics, PhD Thesis

    Google Scholar 

  • Griffith AK, Nichols NK (2000) Adjoint methods in data assimilation for estimating model error. Flow Turbul Combust 65:469–488

    Article  Google Scholar 

  • Griffith AK, Martin MJ, Nichols NK (2000) Techniques for treating systematic model error in 3D and 4D data assimilation, in Proceedings of the Third WMO Int. Symposium on Assimilation of Observations in Meterology and Oceanography, World Meteorological Organization, WWRP Report Series No. 2, WMO/TD – 986, pp. 9–12.

    Google Scholar 

  • Gunzburger MD (2003) Perspectives in flow control and optimization. Advances in design and control. SIAM, Philadelphia, USA

    Google Scholar 

  • Haltiner GJ, Williams RT (1980) Numerical prediction and dynamic meteorology. John Wiley and Sons, New York, p 477

    Google Scholar 

  • Hascoet L, Pascual V (2004) TAPENADE 2.1 user’s guide. Technical report, INRIA, 300:81

    Google Scholar 

  • Hestenes MR (1969) Multiplier and gradient methods. J Opt Theory Appl 4:303–320

    Article  Google Scholar 

  • Hoffmann RN (1986) A four dimensional analysis exactly satisfying equations of motion. Mon Wea Rev 114:388–397

    Article  Google Scholar 

  • Hoke JE, Anthes RA (1976) The initialization of numerical models by a dynamical initialization technique. Mon Wea Rev 194:1551–1556

    Article  Google Scholar 

  • Hollingsworth A, Lonnberg P (1986) The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: the wind field. Tellus 38A:111–136

    Google Scholar 

  • Hollingsworth A et al (2005) The transformation of earth-system observations into information of socio-economic value in GEOSS. Q J R Meteorol Soc 131: 3493–3512.

    Article  Google Scholar 

  • Ide K et al (1997) Unified notation for data assimilation: Operational, sequential and variational. J Meteor Soc Japan 75: 181–189

    Google Scholar 

  • Janiskova M et al (1999) Simplified and regular physical parameterizations for incremental four-dimensional variational assimilation. Mon Wea Rev 127:26–45

    Article  Google Scholar 

  • Janiskova M et al (2002) Linearized radiation and cloud schemes in the ECMWF model: Development and evaluation. Q J R Meteorol Soc 128:1505–1527

    Article  Google Scholar 

  • Kagiwada H et al (1986) Numerical derivatives and nonlinear analysis, Mathematical Concepts and Methods in Science and Engineering. Plenum Press, New York, London

    Google Scholar 

  • Kalnay E et al (2000) Application of the quasi-inverse method to data assimilation. Mon Wea Rev 128: 864–875

    Article  Google Scholar 

  • Kalnay E (2003) Atmospheric modeling, data assimilation and predictability. Cambridge Univ Press, Cambridge, p 341

    Google Scholar 

  • Klinker E et al (2000) The ECMWF operational implementation of four-dimensional variational assimilation. III: Experimental results and diagnostics with operational configuration. Q J R Meteorol Soc 126:1191–1215

    Article  Google Scholar 

  • Krige DG (1951) A statistical approach to some mine valuation problems on the Witwatersrand. J Chem Metal Min Soc South African 52:119–139

    Google Scholar 

  • Langland RH, Baker NL (2004) Estimation of observation impact using the NRL atmospheric variational data assimilation adjoint system. Tellus 56A:189–203

    Google Scholar 

  • Lagrange JL (1760) Essai d’une nouvelle méthode pour déterminer les maxima et les minima des formules indéfinies. Miscellanea Taurinensia, 2 (1762) Oeuvres 1:365–468

    Google Scholar 

  • Lanczos C (1970) The variational principles of mechanics. University of Toronto Press, Toronto

    Google Scholar 

  • Le Dimet FX (1981) Une application des méthodes de contrôle, optimal ‘a l’analyse variationnelle. Rapport Scientifique LAMP, Université Blaise-Pascal, 63170, Aubière Cedex, p 42

    Google Scholar 

  • Le Dimet FX (1982) A general formalism of variational analysis. CIMMS Report, Norman, OK 73091 22:1–34

    Google Scholar 

  • Le Dimet FX et al (1982) Dynamic initialization with filtering of gravity waves. CIMMS Report No.40, Norman, OK 73019, p 12

    Google Scholar 

  • Le Dimet FX, Talagrand O (1986) Variational algorithms for analysis and assimilation of meteorological observations. Tellus 38A: 97–110

    Google Scholar 

  • Le Dimet FX, Navon IM (1988) Variational and optimization methods in meteorology: A review. Tech. Rep. FSU-SCRI-88-144. Florida State University, Tallahassee, Florida, p 83

    Google Scholar 

  • Le Dimet FX et al (1997) Sensitivity analysis in variational data assimilation. J Meteorol Soc Japan 1B:245–255

    Google Scholar 

  • Le Dimet FX et al (2002) Second order information in data assimilation. Mon Wea Rev 130 (3):629–648

    Google Scholar 

  • Lewins J (1965) Importance, the Adjoint Function., Pergamon Press, Oxford.

    Google Scholar 

  • Lopez P, Moreau E (2005) A convection scheme for data assimilation: Description and initial tests. Q J R Meteorol Soc 131: 409–436

    Article  Google Scholar 

  • Kolmogorov AN (1941) Interpolation and extrapolation of stationary random sequences. Translation by RAND Corporation, memorandum RM-30090-PR, April (1962). Bulletin of the Academy of Sciences, USSR series on Mathematics, p 15

    Google Scholar 

  • Lewis JM, Derber JC (1985) The use of adjoint equations to solve a variational adjustment problem with advective constraints. Tellus 37A: 309–322

    Google Scholar 

  • Lewis JM et al (2006) Dynamic data assimilation: a least squares approach. Cambridge University Press, Cambridge

    Google Scholar 

  • Li Y et al (1993) Variational data assimilation with a semi-implicit semi-Lagrangian global shallow-water equation model and its adjoint. Mon Wea Rev 121:159–169

    Article  Google Scholar 

  • Li Y, Droegemeier KK (1993) The influence of diffusion and associated errors on the adjoint data assimilation technique. Tellus 45A:1–14

    Google Scholar 

  • Li Y et al (1994) 4-D assimilation experiments with a multilevel semi-Lagrangian semi-implicit GCM. Mon Wea Rev.122(5):966–983

    Article  Google Scholar 

  • Lions JL (1968) Contrôle Optimal des Systèmes Gouvernes par des Equations aux Dérivés Partielles. Gauthiers-Villars, Paris

    Google Scholar 

  • Lions JL (1971) Optimal control of systems governed by partial differential equations. Translated by Mitter SK, Springer-Verlag, Berlin-Heidelberg, p 404

    Google Scholar 

  • Lorenc AC (1981) A global three-dimensional multivariate statistical interpolation scheme. Mon Wea Rev 109:701–721

    Article  Google Scholar 

  • Lorenc AC (1986) Analysis-methods for numerical weather prediction. Q J R Meteorol Soc 112 (474):1177–1194

    Article  Google Scholar 

  • Lynch P, Huang XY (1992) Initialization of the HIRLAM model using a digital filter. Mon Wea Rev 120(6):1019–1034

    Article  Google Scholar 

  • Marchuk GI (1958) Numerical calculation of nuclear reactors. Atomizdat, Moskwa, p 162

    Google Scholar 

  • Marchuk GI (1967) Chislennye Metody v Prognoze Pogodi (Numerical Methods in Weather Forecasting). Gidrometeoizdat, Leningrad, p 356

    Google Scholar 

  • Marchuk GI (1974) Numerical solution of the problem of dynamics of atmosphere and ocean (in Russian). Gidrometeoizdat, Leningrad, p 303

    Google Scholar 

  • Martin MJ et al (2001) Estimation of systematic error in an equatorial ocean model using data assimilation. In: Baines MJ (eds) Numerical methods for fluid dynamics VII. ICFD, Oxford, pp 423–430

    Google Scholar 

  • Matsuno T (1966) Numerical integrations of the primitive equations by simulated backward difference scheme. J Meteor Soc Japan 44:76–84

    Google Scholar 

  • McPherson RD (1975) Progress, problems, and prospects in meteorological data assimilation. Bullet Am Meteorol Soc 56 (11):1154–1166

    Article  Google Scholar 

  • Menemenlis D, Chechelnitsky M (2000) Error estimates for an ocean general circulation model from altimeter and acoustic tomography data. Mon Wea Rev 128:763–778

    Article  Google Scholar 

  • Miller RN (1994) Advanced data assimilation in strongly nonlinear dynamical-systems. J Atmospheric Sci 51(8):1037–1056

    Article  Google Scholar 

  • Miller RN, Ghil M, Gauthiez F (1994) Advanced data assimilation in strongly nonlinear dynamical-systems. Atmos Sci 51(8):1037–1056.

    Article  Google Scholar 

  • Mitchell HL, Daley R (1997) Discretization error and signal/error correlation in atmospheric data assimilation, I:All scales resolved. Tellus 49A:32–53

    Google Scholar 

  • Miyakoda K et al (1976) The near-real-time, global, four-dimensional analysis experiment during the GATE period, Part I. J Atmospheric Sci 33 (4):561–591

    Article  Google Scholar 

  • McLaughlin D (2005) Opportunities for enhanced collaboration within the data assimilation community. Q J R Meteorol Soc 131 (613):3683–3693 Part C

    Article  Google Scholar 

  • McLaughlin D, O’Neill A, Derber J, Kamachi M, (2005) Opportunities for enhanced collaboration within the data assimilation community. Q J R Meteorol Soc 131 (613):3683–3693, Part C.

    Article  Google Scholar 

  • Nash SG, Sofer A (1996) Linear and Nonlinear Programming. McGraw-Hill, p 692

    Google Scholar 

  • Navon IM (1981) Implementation of a posteriori methods for enforcing conservation of potential enstrophy and mass in discretized shallow-water equations models. Mon Wea Rev 109:946–958

    Article  Google Scholar 

  • Navon IM, De Villiers RD (1983) Combined penalty multiplier optimization methods to enforce integral invariants conservation. Mon Wea Rev 111:1228–1243

    Article  Google Scholar 

  • Navon IM (1986) A review of variational and optimization methods in meteorology. In: Sasaki YK (ed) Festive volume of the international symposium on variational methods in geosciences. Elsevier Science Pub. Co. Developments in Geo-mathematics 5:29–34

    Google Scholar 

  • Navon IM (1987) The Bayliss-Isaacson algorithm and the constraint restoration method are equivalent. Meteorol Atmospheric Phys 13:143–152

    Article  Google Scholar 

  • Navon IM, Zou X (1991) Application of the adjoint model in meteorology. In: Griewank A, Corliss G (eds) Proceedings of the international conference on automatic differentiation of algorithms: Theory, Implementation and Application. SIAM, Philadelphia, PA

    Google Scholar 

  • Navon IM (1992) Numerical experience with limited memory quasi-Newton and truncated Newton methods. In: Phua KH et al (eds) Optimization techniques and applications, Vol 1, World Scientific Publishing Co, Singapore, 1232, p 33–48

    Google Scholar 

  • Navon IM et al (1992a) Variational data assimilation with an adiabatic version of the NMC spectral model. Mon Wea Rev 122:1433–1446

    Article  Google Scholar 

  • Navon IM et al (1992b) Testing for reliability and robustness of optimization codes for large scale optimization problems. In: Phua KH et al (eds) Optimization Techniques and Applications Vol 1. World Scientific Publishing Co, Singapore, 1232, pp 445–480

    Google Scholar 

  • Navon IM et al (2005) The impact of background error on incomplete observations for 4D-Var data assimilation with the FSU GSM. In: Sunderam VS et al (eds) Computational Science-ICCS 2005, LNCS 3515, 2005. Springer Verlag, Heidelberg, pp 837–844

    Google Scholar 

  • Ngodock HE (1996) Data assimilation and sensitivity analysis. Ph D Thesis, LMC-IMAG Laboratory, University Joseph Fourier, Grenoble, France, p 213

    Google Scholar 

  • Nichols NK (2003) Treating model error in 3-D and 4-D data assimilation. Proceedings of the NATO Advanced Study Institute on Data Assimilation for the Earth System, Maratea, Italy

    Google Scholar 

  • Nocedal J (1980) Updating quasi-Newton matrices with limited storage. Math Comput 773–782.

    Google Scholar 

  • Nocedal J, Wright SJ (2006) Numerical optimization. Second Edition, Springer, New York

    Google Scholar 

  • Oblow EM (1983) An automated procedure for sensitivity analysis using computer calculus, Tech Report ORNL/TM-8776, ORNL

    Google Scholar 

  • Panofsky HA (1949) Objective weather-map analysis. J Appl Meteor 6:386–392

    Google Scholar 

  • Park SK, Kalnay E (1999) Application of the quasi-inverse method to storm-scale data assimilation. Abstracts, 5th SIAM Conference on Mathematical and Computational Issues in the Geosciences, 24–27 March, San Antonio, Texas, SIAM, 104

    Google Scholar 

  • Park SK, Zupanski D (2003) Four-dimensional variational data assimilation for mesoscale and storm-scale applications. Meteor Atmos Phys 82:173–208

    Article  Google Scholar 

  • Park SK, Kalnay E (2004) Inverse three-dimensional variational data assimilation for an advection-diffusion problem: Impact of diffusion and hybrid application. Geophys Res Lett, 31:L04102

    Article  Google Scholar 

  • Parrish DF, Derber JC (1992) The National-Meteorological-Centers’ spectral statistical-interpolation analysis system. Mon Wea Rev 120 (8):1747–1763

    Article  Google Scholar 

  • Penenko V, Obratsov NN (1976) A variational initialization method for the fields of the meteorological elements. Meteorol Gidrol 11:1–11

    Google Scholar 

  • Pin et al (1987) ADGEN: An automated adjoin code generator for large-scale sensitivity analysis, Trans. Am Nucl Soc 55:311

    Google Scholar 

  • Pontryagin LS et al (1962) The mathematical theory of optimal processes. John Wiley & Sons, New York

    Google Scholar 

  • Powell MJD (1969) A method for nonlinear constraints in minimization problems. In: Fletcher R(eds) Optimization Chap 19. Academic Press, pp 283–298

    Google Scholar 

  • Pu ZX et al (1997) Sensitivity of forecast errors to initial conditions with a quasi-inverse linear method. Mon Wea Rev Vol 125(10):2479–2503

    Article  Google Scholar 

  • Pu ZX, Kalnay E (1999) Targeting observations with the quasi-inverse linear and adjoint NCEP global models: Performance during FASTEX. Q J R Meteor Soc 125 (561):3329–3337

    Article  Google Scholar 

  • Rabier F, Courtier P (1992) Four-dimensional assimilation in the presence of baroclinic instability. Q J R Meteorol Soc 118:649–672

    Article  Google Scholar 

  • Rabier F et al (1997) Recent experimentation on 4D-Var and first results from a Simplified Kalman Filter. ECMWF Technical Memorandum No 240

    Google Scholar 

  • Rabier F et al (2000) The ECMWF operational implementation of 4D variational assimilation Part I: experimental results with simplified physics. Q J R Meteorol Soc 126:143–1170

    Article  Google Scholar 

  • Rabier F (2005) Overview of global data assimilation developments in numerical weather-prediction centers. Q J R Meteorol Soc 131 (613):215–3233

    Article  Google Scholar 

  • Rall LB (1981) Automatic differentiation: Techniques and applications, Lecture Notes in Computer Science Vol 120. Springer-Verlag, Berlin

    Google Scholar 

  • Richardson LF (1922) Weather prediction by numerical processes. Cambridge University Press. Reprinted by Dover (1965, New York). With a New Introduction by Sydney Chapman, xvi+236

    Google Scholar 

  • Rodgers CD (2000) Inverse methods for atmospheres: theories and practice. World Scientific Publ, Singapore

    Google Scholar 

  • Saha S (1992) Response of the NMC MRF model to systematic error correction within the integration. Mon Wea Rev 120:345–360

    Article  Google Scholar 

  • Sasaki YK (1955) A fundamental study of the numerical prediction based on the variational principle. J Meteor Soc Japan 33:262–275

    Google Scholar 

  • Sasaki YK (1958) An objective analysis based on the variational method. J Meteor Soc Japan 36:77–88

    Google Scholar 

  • Sasaki YK (1969) Proposed inclusion of time-variation terms, observational and theoretical in numerical variational objective analysis. J Meteor Soc Japan 47:115–203

    Google Scholar 

  • Sasaki YK (1970a) Some basic formalisms in numerical variational analysis. Mon Wea Rev 98:857–883

    Google Scholar 

  • Sasaki YK (1970b) Numerical variational analysis formulated under the constraints as determined by long-wave equations as a low-pass filter. Mon Wea Rev 98:884–898

    Article  Google Scholar 

  • Sasaki YK (1970c) Numerical variational analysis with weak constraint and application to the surface analysis of severe storm gust. Mon Wea Rev 98:899–910

    Article  Google Scholar 

  • Sasaki YK (1970d) A theoretical interpretation of anisotropically weighted smoothing on the basis of numerical variational analysis. Mon Wea Rev 99:698–707

    Article  Google Scholar 

  • Seaman RS (1988) Some real data tests of the interpolation accuracy of Bratseth’s successive corrections method. Tellus 40A:173–176

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Sleijpen GLG, HA Van der Vorst, (1996) A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J Matrix Anal Vol 17, Issue 2:401–425

    Google Scholar 

  • Tadjbakhsh IG (1969) Utilization of time-dependent data in running solution of initial value problems. J Appl Meteorol 8(3):389–391

    Article  Google Scholar 

  • Talagrand O, Miyakoda K (1971) Assimilation of past data in dynamical analysis. 2. Tellus 23(4–5):318–327

    Google Scholar 

  • Talagrand O (1981) On the mathematics of data assimilation. Tellus 33 (4):321–339

    Google Scholar 

  • Talagrand O, Courtier P (1987) Variational assimilation of meteorological observations with the adjoint vorticity equation-Part 1. Theory Q J R Meteorol Soc 113:1311–1328

    Article  Google Scholar 

  • Talagrand O (1997) Assimilation of observations, an introduction. J Meteorol Soc Japan 75 (1B) (1997):191–209

    Google Scholar 

  • Tarantola A (1987) Inverse problem theory Methods for data fitting and model parameter estimation. Elsevier, Amsterdam, p 613

    Google Scholar 

  • Thacker WC (1989) The role of Hessian matrix in fitting models to measurements. J Geophys Res 94 (C5):6177–6196

    Article  Google Scholar 

  • Thepaut JN, Moll P (1990) Variational inversion of simulated TOVS radiances using the adjoint technique. Q J R Meteorol Soc:1425–1448

    Google Scholar 

  • Thepaut JN, Courtier P (1991) Four-dimensional variational assimilation using the adjoint of a multilevel primitive-equation model. Q J R Meteorol Soc 117:1225–1254

    Article  Google Scholar 

  • Thepaut JN et al (1993) Variational assimilation of meteorological observations with a multilevel primitive-equation model. Q J R Meteorol Soc 119:153–186

    Article  Google Scholar 

  • Thiébaux HJ, Morone LL (1990) Short-term systematic errors in global forecasts: Their estimation and removal. Tellus 42A:209–229

    Google Scholar 

  • Thompson PD (1969) Reduction of Analysis Error Through Constraints of Dynamical Consistency. J Appl Meteorol 8:738–742

    Article  Google Scholar 

  • Tsyrulnikov MD (2005) Stochastic modelling of model errors: A simulation study. Q J R Meteorol Soc 131, pp 3345–3371

    Article  Google Scholar 

  • Uboldi F, Kamachi M (2000) Time-space weak-constraint data assimilation for nonlinear models. Tellus 52 A:412–421

    Google Scholar 

  • Veerse F, Thepaut JN (1998) Multiple-truncation incremental approach for four-dimensional variational data assimilation. Q J R Meteorol Soc 124:1889–1908

    Article  Google Scholar 

  • Veerse F (1999) Variable-storage quasi-Newton operators as inverse forecast/analysis error covariance matrices in data assimilation. INRIA Technical Report 3685 Theme 4, p 28

    Google Scholar 

  • Vidard PA et al (2000) 4-D variational data analysis with imperfect model. Flow Turbul Combust 65:489–504

    Article  Google Scholar 

  • Wang Z et al (1992) The second order adjoint analysis: Theory and application. Meteorol and Atmos Phy 50:3–20

    Article  Google Scholar 

  • Wang Z, (1993) Variational Data Assimilation with 2-D Shallow Water Equations and 3-D FSU Global Spectral Models, Ph.D. Dissertation, Department of Mathematics, College of Arts and Sciences, The Florida State University, 235 pp.

    Google Scholar 

  • Wang Z et al (1993) The adjoint truncated Newton algorithm for large-scale unconstrained optimization. Tech Rep FSU-SCRI-92-170, Florida State University, Tallahassee, Florida, p 44

    Google Scholar 

  • Wang Z et al (1995) A truncated Newton optimization algorithm in meteorology applications with analytic hessian vector products. Comput Opt Appl 4:241–262

    Article  Google Scholar 

  • Wang Z et al (1997) Application of a new adjoint Newton algorithm to the 3-D ARPS storm scale model using simulated data. Mon Wea Rev 125 (10):2460–2478

    Google Scholar 

  • Wang Z et al (1998) The adjoint Newton algorithm for large-scale unconstrained optimization in meteorology applications. Comput Opt Appl 10:283–320

    Article  Google Scholar 

  • Wergen W (1992) Effect of model errors in variational assimilation. Tellus 44 A:297–313

    Google Scholar 

  • Wiener N (1949) Extrapolation, interpolation and smoothing of stationary time series with engineering applications. M.I.T. Press, Cambridge, MA, p 163

    Google Scholar 

  • Wigner EP (1945) Effects of small perturbations on pile period. Chicago Rep, CP-G 3048

    Google Scholar 

  • Xu L et al (2005) Development of NAVDAS-AR: formulation and initial tests of the linear problem. Tellus 57A:546–559

    Google Scholar 

  • Yaglom A (1962) An Introduction to the theory of stationary random functions. Dover, New York

    Google Scholar 

  • Yang W et al (1996) A new Hessian preconditioning method applied to variational data assimilation experiments using adiabatic version of NASA/GEOS-1 GCM. Mon Wea Rev 124 (5):1000–1017

    Google Scholar 

  • Zhu K et al (1994) Variational data assimilation with a variable resolution finite-element shallow-water equations model. Mon Wea Rev 122 (5):946–965

    Google Scholar 

  • Zhu J, Kamachi M (2000) An adaptive variational method for data assimilation with imperfect models. Tellus 52 A:265–279

    Google Scholar 

  • Zou X et al (1992) Incomplete observations and control of gravity waves in variational data assimilation. Tellus 44A:273–296

    Google Scholar 

  • Zou X et al (1993) Numerical experience with limited-memory quasi-Newton methods and truncated Newton methods. SIAM J Num Opt 3:582–608

    Article  Google Scholar 

  • Zou J et al (1995) Sequential open-boundary control by data assimilation in a limited area model. Mon Wea Rev 123 No. 9:2899–2909

    Article  Google Scholar 

  • Zupanski M (1993) Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon Wea Rev 121:2396–2408

    Article  Google Scholar 

  • Zupanski D (1997) A general weak constraint applicable to operational 4DVAR data assimilation systems. Mon Wea Rev 125:2274–2292

    Article  Google Scholar 

  • Zupanski M, Kalnay E (1999) Principles of data assimilation. In: Browning KA, Gurney RJ (eds) Global energy and water cycles. Cambridge Univ Press, Cambridge, pp 48–54

    Google Scholar 

  • Zupanski D, Zupanski M, Rogers E, et al. (2002) Fine-resolution 4DVAR data assimilation for the Great Plains tornado outbreak of 3 May 1999 Weather and Forecasting 17(3):506–525.

    Google Scholar 

  • Zupanski M et al (2005) CIRA/CSU four- dimensional variational data assimilation system. Mon Wea Rev 123:829–843

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Scientific Computing, The Florida State University, Tallahassee, Florida 32306-4120, USA

    Ionel M. Navon

Authors
  1. Ionel M. Navon
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. Environmental Science & Engineering, Ewha Womans University, 11-1 Daehyun-dong, Seoul, Seodaemun-gu, Seoul 120-750, Republic of Korea

    Seon K. Park (Prof.) (Prof.)

  2. Naval Research Laboratory, 7 Grace Hopper Avenue Stop 2, Monterey, CA 93943-5502, USA

    Liang Xu Dr.

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Navon, I.M. (2009). Data Assimilation for Numerical Weather Prediction: A Review. In: Park, S.K., Xu, L. (eds) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71056-1_2

Download citation

Publish with us

Policies and ethics

Search

Navigation