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Volumn 139, Issue 670, 2013, Pages 242-260

On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation

Author keywords

Background error; Correlation functions; Covariance modelling; Diffusion tensor; Ensemble estimation; Ocean data assimilation

Indexed keywords

BACKGROUND ERRORS; CORRELATION FUNCTION; COVARIANCE MODELLING; DIFFUSION TENSOR; OCEAN DATA ASSIMILATION;

EID: 84873309303     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.1955     Document Type: Article
Times cited : (57)

References (74)
  • 2
    • 58049193556 scopus 로고    scopus 로고
    • A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics.
    • Bannister RN. 2008. A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics. Q. J. R. Meteorol. Soc. 134: 1971-1996.
    • (2008) Q. J. R. Meteorol. Soc. , vol.134 , pp. 1971-1996
    • Bannister, R.N.1
  • 3
    • 33749027769 scopus 로고    scopus 로고
    • The use of an ensemble approach to study the background error covariances in a global NWP model
    • Belo Pereira M, Berre L. 2006. The use of an ensemble approach to study the background error covariances in a global NWP model. Mon. Weather Rev. 134: 2466-2489.
    • (2006) Mon. Weather Rev. , vol.134 , pp. 2466-2489
    • Belo Pereira, M.1    Berre, L.2
  • 4
    • 0030523072 scopus 로고    scopus 로고
    • Generalized inversion of a global numerical weather prediction model
    • Bennett AF, Chua BS, Leslie LM. 1996. Generalized inversion of a global numerical weather prediction model. Meteorol. Atmos. Phys. 60: 165-178.
    • (1996) Meteorol. Atmos. Phys. , vol.60 , pp. 165-178
    • Bennett, A.F.1    Chua, B.S.2    Leslie, L.M.3
  • 5
    • 0031510266 scopus 로고    scopus 로고
    • Generalized inversion of a global numerical weather prediction model. II: analysis and implementation.
    • Bennett AF, Chua BS, Leslie LM. 1997. Generalized inversion of a global numerical weather prediction model. II: analysis and implementation. Meteorol. Atmos. Phys. 62: 129-140.
    • (1997) Meteorol. Atmos. Phys. , vol.62 , pp. 129-140
    • Bennett, A.F.1    Chua, B.S.2    Leslie, L.M.3
  • 6
    • 77958479703 scopus 로고    scopus 로고
    • Filtering of background error variances and correlations by local spatial averaging: a review
    • Berre L, Desroziers G. 2010. Filtering of background error variances and correlations by local spatial averaging: a review. Mon. Weather Rev. 138: 3693-3720.
    • (2010) Mon. Weather Rev. , vol.138 , pp. 3693-3720
    • Berre, L.1    Desroziers, G.2
  • 7
    • 77955416144 scopus 로고    scopus 로고
    • Background-error correlation model based on the implicit solution of a diffusion equation
    • Carrier MJ, Ngodock H. 2010. Background-error correlation model based on the implicit solution of a diffusion equation. Ocean Model. 35: 45-53.
    • (2010) Ocean Model. , vol.35 , pp. 45-53
    • Carrier, M.J.1    Ngodock, H.2
  • 8
    • 53149124819 scopus 로고    scopus 로고
    • Non-parametric identification of anisotropic (elliptic) correlations in spatially distributed data sets
    • Chorti A, Hristopulos DT. 2008. Non-parametric identification of anisotropic (elliptic) correlations in spatially distributed data sets. IEEE Trans. Signal Process. 56: 4738-4751.
    • (2008) IEEE Trans. Signal Process. , vol.56 , pp. 4738-4751
    • Chorti, A.1    Hristopulos, D.T.2
  • 9
    • 0001429244 scopus 로고    scopus 로고
    • An inverse ocean modeling system
    • Chua BS, Bennett AF. 2001. An inverse ocean modeling system. Ocean Model. 3: 137-165.
    • (2001) Ocean Model. , vol.3 , pp. 137-165
    • Chua, B.S.1    Bennett, A.F.2
  • 10
    • 70149107817 scopus 로고    scopus 로고
    • Ensemble estimation of background-error variances in a three-dimensional variational data assimilation system for the global ocean
    • Daget N, Weaver AT, Balmaseda MA. 2009. Ensemble estimation of background-error variances in a three-dimensional variational data assimilation system for the global ocean. Q. J. R. Meteorol Soc. 135: 1071-1094.
    • (2009) Q. J. R. Meteorol Soc. , vol.135 , pp. 1071-1094
    • Daget, N.1    Weaver, A.T.2    Balmaseda, M.A.3
  • 11
    • 85040897227 scopus 로고
    • Cambridge University Press: Cambridge, UK.
    • Daley R. 1991. Atmospheric Data Analysis. Cambridge University Press: Cambridge, UK.
    • (1991) Atmospheric Data Analysis
    • Daley, R.1
  • 12
    • 84873288462 scopus 로고    scopus 로고
    • Comparison of strategies for the specification of anisotropies in the covariances of a three-dimensional atmospheric data assimilation system'. Office Note 452, National Centers for Environmental Prediction: Camp Springs, MD.
    • De Pondeca MSFV, Purser RJ, Parrish DF, Derber J. 2006. 'Comparison of strategies for the specification of anisotropies in the covariances of a three-dimensional atmospheric data assimilation system'. Office Note 452, National Centers for Environmental Prediction: Camp Springs, MD.
    • (2006)
    • De Pondeca, M.S.F.V.1    Purser, R.J.2    Parrish, D.F.3    Derber, J.4
  • 13
    • 0000092802 scopus 로고
    • A global oceanic data assimilation system
    • Derber JC, Rosati A. 1989. A global oceanic data assimilation system. J. Phys. Oceanogr. 19: 1333-1347.
    • (1989) J. Phys. Oceanogr. , vol.19 , pp. 1333-1347
    • Derber, J.C.1    Rosati, A.2
  • 14
    • 33846304701 scopus 로고    scopus 로고
    • Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system
    • Di Lorenzo E, Moore AM, Arango HG, Cornuelle BD, Miller AJ, Powell B, Chua BS, Bennett AF. 2007. Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system. Ocean Model. 16: 160-187.
    • (2007) Ocean Model. , vol.16 , pp. 160-187
    • Di Lorenzo, E.1    Moore, A.M.2    Arango, H.G.3    Cornuelle, B.D.4    Miller, A.J.5    Powell, B.6    Chua, B.S.7    Bennett, A.F.8
  • 15
    • 43949116618 scopus 로고    scopus 로고
    • An oceanographic three-dimensional variational data assimilation scheme
    • Dobricic S, Pinardi N. 2008. An oceanographic three-dimensional variational data assimilation scheme. Ocean Model. 22: 89-105.
    • (2008) Ocean Model. , vol.22 , pp. 89-105
    • Dobricic, S.1    Pinardi, N.2
  • 16
    • 0028586562 scopus 로고
    • Topex/Poseidon tides estimated using a global inverse model
    • Egbert G, Bennett A, Foreman M. 1994. Topex/Poseidon tides estimated using a global inverse model. J. Geophys. Res. 99: 24821-24852.
    • (1994) J. Geophys. Res. , vol.99 , pp. 24821-24852
    • Egbert, G.1    Bennett, A.2    Foreman, M.3
  • 17
    • 77950160759 scopus 로고    scopus 로고
    • Chemical state estimation for the middle atmosphere by four-dimensional variational data assimilation: system configuration
    • DOI: 10.1029/2009 JD011953.
    • Elbern H, Schwinger J, Botchorishvili R. 2010. Chemical state estimation for the middle atmosphere by four-dimensional variational data assimilation: system configuration. J. Geophys. Res. 115: D06302, DOI: 10.1029/2009 JD011953.
    • (2010) J. Geophys. Res. , vol.115
    • Elbern, H.1    Schwinger, J.2    Botchorishvili, R.3
  • 18
    • 0033023511 scopus 로고    scopus 로고
    • Construction of correlation functions in two and three dimensions
    • Gaspari G, Cohn S. 1999. Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc. 125: 723-757.
    • (1999) Q. J. R. Meteorol. Soc. , vol.125 , pp. 723-757
    • Gaspari, G.1    Cohn, S.2
  • 20
    • 0033402208 scopus 로고    scopus 로고
    • Correlation functions for atmospheric data analysis
    • Gneiting T. 1999. Correlation functions for atmospheric data analysis. Q. J. R. Meteorol. Soc. 125: 2449-2464.
    • (1999) Q. J. R. Meteorol. Soc. , vol.125 , pp. 2449-2464
    • Gneiting, T.1
  • 21
    • 84873324834 scopus 로고    scopus 로고
    • Matérn cross-covariance functions for multivariate random fields'. Technical Report No. 549, University of Washington, Department of Statistics.
    • Gneiting T, Kleiber W, Schlather M. 2009. 'Matérn cross-covariance functions for multivariate random fields'. Technical Report No. 549, University of Washington, Department of Statistics. http://www.stat.washington.edu/research/reports/2009/tr549.pdf.
    • (2009)
    • Gneiting, T.1    Kleiber, W.2    Schlather, M.3
  • 22
    • 55449138455 scopus 로고    scopus 로고
    • On potentially negative space time covariances obtained as sum of products of marginal ones
    • Gregori P, Porcu E, Mateu J, Sasvári Z. 2008. On potentially negative space time covariances obtained as sum of products of marginal ones. Ann. Inst. Stat. Math. 60: 865-882.
    • (2008) Ann. Inst. Stat. Math. , vol.60 , pp. 865-882
    • Gregori, P.1    Porcu, E.2    Mateu, J.3    Sasvári, Z.4
  • 23
    • 33845770233 scopus 로고    scopus 로고
    • Miscellanea studies in the history of probability and statistics XLIX: on the Matérn correlation family
    • Guttorp P, Gneiting T. 2006. Miscellanea studies in the history of probability and statistics XLIX: on the Matérn correlation family. Biometrika 93: 989-995.
    • (2006) Biometrika , vol.93 , pp. 989-995
    • Guttorp, P.1    Gneiting, T.2
  • 25
    • 0001557950 scopus 로고
    • 'Normal' distribution functions on spheres and the modified Bessel functions
    • Hartman P, Watson GS. 1974. 'Normal' distribution functions on spheres and the modified Bessel functions. Ann. Prob. 2: 593-607.
    • (1974) Ann. Prob. , vol.2 , pp. 593-607
    • Hartman, P.1    Watson, G.S.2
  • 26
    • 0028846284 scopus 로고
    • Recursive filter objective analysis of meteorological fields: applications to NESDIS operational processing
    • Hayden CM, Purser RJ. 1995. Recursive filter objective analysis of meteorological fields: applications to NESDIS operational processing. J. Appl. Meteorol. 34: 3-15.
    • (1995) J. Appl. Meteorol. , vol.34 , pp. 3-15
    • Hayden, C.M.1    Purser, R.J.2
  • 27
    • 23044529084 scopus 로고    scopus 로고
    • New anisotropic covariance models and estimation of aniostropic parameters based on the covariance tensor identity
    • Hristopulos DT. 2002. New anisotropic covariance models and estimation of aniostropic parameters based on the covariance tensor identity. Stoch. Environ. Res. Risk Assess. 16: 43-62.
    • (2002) Stoch. Environ. Res. Risk Assess. , vol.16 , pp. 43-62
    • Hristopulos, D.T.1
  • 28
    • 0346316916 scopus 로고    scopus 로고
    • Spartan Gibbs random field models for geostatistical applications
    • Hristopulos DT. 2003. Spartan Gibbs random field models for geostatistical applications. SIAM J. Sci. Comput. 24: 2125-2162.
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 2125-2162
    • Hristopulos, D.T.1
  • 29
    • 42649092667 scopus 로고    scopus 로고
    • Analytic properties and covariance functions of a new class of generalized Gibbs random fields
    • Hristopulos DT, Elogne SN. 2007. Analytic properties and covariance functions of a new class of generalized Gibbs random fields. IEEE Trans. Inform. Theory. 53: 4467-4679.
    • (2007) IEEE Trans. Inform. Theory. , vol.53 , pp. 4467-4679
    • Hristopulos, D.T.1    Elogne, S.N.2
  • 31
    • 34248344666 scopus 로고    scopus 로고
    • Retrieval of moisture from simulated GPS slant-path water vapor observations using 3DVAR with anisotropic recursive filter
    • Liu H, Xue M, Purser RJ, Parrish DF. 2007. Retrieval of moisture from simulated GPS slant-path water vapor observations using 3DVAR with anisotropic recursive filter. Mon. Weather Rev. 135: 1506-1521.
    • (2007) Mon. Weather Rev. , vol.135 , pp. 1506-1521
    • Liu, H.1    Xue, M.2    Purser, R.J.3    Parrish, D.F.4
  • 32
    • 68749089503 scopus 로고    scopus 로고
    • Assimilating temperature and salinity profile observations using an anisotropic recursive filter in a coastal ocean model
    • Liu Y, Zhu J, She J, Zhuang S, Fu W, Gao J. 2009. Assimilating temperature and salinity profile observations using an anisotropic recursive filter in a coastal ocean model. Ocean Model. 30: 75-87.
    • (2009) Ocean Model. , vol.30 , pp. 75-87
    • Liu, Y.1    Zhu, J.2    She, J.3    Zhuang, S.4    Fu, W.5    Gao, J.6
  • 33
    • 0027073403 scopus 로고
    • Iterative analysis using covariance functions and filters
    • Lorenc AC. 1992. Iterative analysis using covariance functions and filters. Q. J. R. Meteorol. Soc. 118: 569-591.
    • (1992) Q. J. R. Meteorol. Soc. , vol.118 , pp. 569-591
    • Lorenc, A.C.1
  • 35
    • 34447636957 scopus 로고    scopus 로고
    • Data assimilation in the FOAM operational short-range ocean forecasting system: a description of the scheme and its impact
    • Martin MJ, Hines A, Bell MJ. 2007. Data assimilation in the FOAM operational short-range ocean forecasting system: a description of the scheme and its impact. Q. J. R. Meteorol. Soc. 133: 981-995.
    • (2007) Q. J. R. Meteorol. Soc. , vol.133 , pp. 981-995
    • Martin, M.J.1    Hines, A.2    Bell, M.J.3
  • 36
    • 84862238181 scopus 로고    scopus 로고
    • Importance of using ensemble estimated background error covariances for the quality of atmospheric ozone analyses
    • DOI: 10.1002/qj.971.
    • Massart S, Piacentini P, Pannekouck O. 2012. Importance of using ensemble estimated background error covariances for the quality of atmospheric ozone analyses. Q. J. R. Meteorol. Soc., DOI: 10.1002/qj.971.
    • (2012) Q. J. R. Meteorol. Soc.
    • Massart, S.1    Piacentini, P.2    Pannekouck, O.3
  • 37
    • 0000047608 scopus 로고
    • Oceanographic data interpolation: objective analysis and splines
    • McIntosh P. 1990. Oceanographic data interpolation: objective analysis and splines. J. Geophys. Res. 95: 13529-13541.
    • (1990) J. Geophys. Res. , vol.95 , pp. 13529-13541
    • McIntosh, P.1
  • 38
    • 77957115234 scopus 로고    scopus 로고
    • Representation of correlation functions in variational assimilation using an implicit diffusion operator
    • Mirouze I, Weaver AT. 2010. Representation of correlation functions in variational assimilation using an implicit diffusion operator. Q. J. R. Meteorol. Soc. 136: 1421-1443.
    • (2010) Q. J. R. Meteorol. Soc. , vol.136 , pp. 1421-1443
    • Mirouze, I.1    Weaver, A.T.2
  • 39
    • 79951863325 scopus 로고    scopus 로고
    • The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems. I: System overview and formulation.
    • Moore AM, Arango HG, Broquet G, Powell BS, Weaver AT, Zavala-Garay J. 2011. The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems. I: System overview and formulation. Prog. Oceanogr. 91: 50-73.
    • (2011) Prog. Oceanogr. , vol.91 , pp. 50-73
    • Moore, A.M.1    Arango, H.G.2    Broquet, G.3    Powell, B.S.4    Weaver, A.T.5    Zavala-Garay, J.6
  • 41
    • 6444232760 scopus 로고    scopus 로고
    • Efficient implementation of covariance multiplication for data assimilation with the representer method
    • Ngodock HE. 2005. Efficient implementation of covariance multiplication for data assimilation with the representer method. Ocean Model. 8: 237-251.
    • (2005) Ocean Model. , vol.8 , pp. 237-251
    • Ngodock, H.E.1
  • 42
    • 33745999511 scopus 로고    scopus 로고
    • Spatial modelling using a new class of nonstationary covariance functions
    • Paciorek CJ, Schervish MJ. 2006. Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17: 483-506.
    • (2006) Environmetrics , vol.17 , pp. 483-506
    • Paciorek, C.J.1    Schervish, M.J.2
  • 43
    • 70350778485 scopus 로고    scopus 로고
    • Heterogeneous correlation modeling based on the wavelet diagonal assumption and on the diffusion operator
    • Pannekoucke O. 2009. Heterogeneous correlation modeling based on the wavelet diagonal assumption and on the diffusion operator. Mon. Weather Rev. 131: 2995-3012.
    • (2009) Mon. Weather Rev. , vol.131 , pp. 2995-3012
    • Pannekoucke, O.1
  • 44
    • 57349186760 scopus 로고    scopus 로고
    • Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation
    • Pannekoucke O, Massart S. 2008. Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation. Q. J. R. Meteorol. Soc. 134: 1425-1438.
    • (2008) Q. J. R. Meteorol. Soc. , vol.134 , pp. 1425-1438
    • Pannekoucke, O.1    Massart, S.2
  • 45
    • 44349153459 scopus 로고    scopus 로고
    • Background-error correlation length-scale estimates and their sampling statistics
    • Pannekoucke O, Berre L, Desroziers G. 2008. Background-error correlation length-scale estimates and their sampling statistics. Q. J. R. Meteorol. Soc. 134: 497-508.
    • (2008) Q. J. R. Meteorol. Soc. , vol.134 , pp. 497-508
    • Pannekoucke, O.1    Berre, L.2    Desroziers, G.3
  • 46
    • 84873301513 scopus 로고    scopus 로고
    • A geometrical approach to the synthesis of smooth anisotropic covariance operators for data assimilation'. Office Note 447, National Centers for Environmental Prediction: Camp Springs, MD.
    • Purser RJ. 2005. 'A geometrical approach to the synthesis of smooth anisotropic covariance operators for data assimilation'. Office Note 447, National Centers for Environmental Prediction: Camp Springs, MD.
    • (2005)
    • Purser, R.J.1
  • 47
    • 84873324299 scopus 로고    scopus 로고
    • Normalization of the diffusive filters that represent the inhomogeneous covariance operators of variational assimilation, using asymptotic expansions and techniques of non-Euclidean geometry. Part I: Analytic solutions for symmetrical configurations and the validation of practical algorithms'. Office Note 456, National Centers for Environmental Prediction: Camp Springs, MD.
    • Purser RJ. 2008a. 'Normalization of the diffusive filters that represent the inhomogeneous covariance operators of variational assimilation, using asymptotic expansions and techniques of non-Euclidean geometry. Part I: Analytic solutions for symmetrical configurations and the validation of practical algorithms'. Office Note 456, National Centers for Environmental Prediction: Camp Springs, MD.
    • (2008)
    • Purser, R.J.1
  • 48
    • 84873281117 scopus 로고    scopus 로고
    • Normalization of the diffusive filters that represent the inhomogeneous covariance operators of variational assimilation, using asymptotic expansions and techniques of non-Euclidean geometry. Part II: Riemannian geometry and the generic parametrix expansion method'. Office Note 457, National Centers for Environmental Prediction: Camp Springs, MD.
    • Purser RJ. 2008b. 'Normalization of the diffusive filters that represent the inhomogeneous covariance operators of variational assimilation, using asymptotic expansions and techniques of non-Euclidean geometry. Part II: Riemannian geometry and the generic parametrix expansion method'. Office Note 457, National Centers for Environmental Prediction: Camp Springs, MD.
    • (2008)
    • Purser, R.J.1
  • 49
    • 0038293594 scopus 로고    scopus 로고
    • Numerical aspects of the application of recursive filters to variational statistical analysis. Part I: Spatially homogeneous and isotropic Gaussian covariances.
    • Purser RJ, Wu WS, Parrish DF, Roberts NM. 2003a. Numerical aspects of the application of recursive filters to variational statistical analysis. Part I: Spatially homogeneous and isotropic Gaussian covariances. Mon. Weather Rev. 131: 1524-1535.
    • (2003) Mon. Weather Rev. , vol.131 , pp. 1524-1535
    • Purser, R.J.1    Wu, W.S.2    Parrish, D.F.3    Roberts, N.M.4
  • 50
    • 0141682980 scopus 로고    scopus 로고
    • Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: Spatially inhomogeneous and anisotropic general covariances.
    • Purser RJ, Wu WS, Parrish DF, Roberts NM. 2003b. Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: Spatially inhomogeneous and anisotropic general covariances. Mon. Weather Rev. 131: 1536-1548.
    • (2003) Mon. Weather Rev. , vol.131 , pp. 1536-1548
    • Purser, R.J.1    Wu, W.S.2    Parrish, D.F.3    Roberts, N.M.4
  • 51
    • 84866165805 scopus 로고    scopus 로고
    • Heterogeneous filtering of ensemble-based background-error variances
    • DOI:10.1002/qj.1890.
    • Raynaud L, Pannekoucke O. 2012. Heterogeneous filtering of ensemble-based background-error variances. Q. J. R. Meteorol. Soc., DOI:10.1002/qj.1890.
    • (2012) Q. J. R. Meteorol. Soc.
    • Raynaud, L.1    Pannekoucke, O.2
  • 52
    • 48649095711 scopus 로고    scopus 로고
    • Objective filtering of ensemble-based background-error variances
    • Raynaud L, Berre L, Desroziers G. 2009. Objective filtering of ensemble-based background-error variances. Q. J. R. Meteorol. Soc. 134: 1003-1014.
    • (2009) Q. J. R. Meteorol. Soc. , vol.134 , pp. 1003-1014
    • Raynaud, L.1    Berre, L.2    Desroziers, G.3
  • 54
    • 84873321153 scopus 로고    scopus 로고
    • Ensemble-based background error covariance implementations using spatial recursive filters in NCEP's grid-point statistical interpolation system'. Office Note 459, National Centers for Environmental Prediction: Camp Springs, MD.
    • Sato Y, De Pondeca MSFV, Purser RJ, Parrish DF. 2009. 'Ensemble-based background error covariance implementations using spatial recursive filters in NCEP's grid-point statistical interpolation system'. Office Note 459, National Centers for Environmental Prediction: Camp Springs, MD.
    • (2009)
    • Sato, Y.1    De Pondeca, M.S.F.V.2    Purser, R.J.3    Parrish, D.F.4
  • 55
    • 0000977456 scopus 로고
    • Variational assimilation of XBT data. Part II: Sensitivity studies and use of smoothing constraints.
    • Sheinbaum J, Anderson DLT. 1990. Variational assimilation of XBT data. Part II: Sensitivity studies and use of smoothing constraints. J. Phys. Oceanogr. 20: 689-704.
    • (1990) J. Phys. Oceanogr. , vol.20 , pp. 689-704
    • Sheinbaum, J.1    Anderson, D.L.T.2
  • 57
    • 0011798552 scopus 로고
    • Statistical properties of the contours of random surfaces
    • Swerling P. 1962. Statistical properties of the contours of random surfaces. IRE Trans. Inform. Theory IT-8: 315-321.
    • (1962) IRE Trans. Inform. Theory , vol.IT-8 , pp. 315-321
    • Swerling, P.1
  • 58
    • 0001169449 scopus 로고
    • Fitting models to inadequate data by enforcing spatial and temporal smoothness
    • Thacker WC. 1988. Fitting models to inadequate data by enforcing spatial and temporal smoothness. J. Geophys. Res. 93: 10655-10665.
    • (1988) J. Geophys. Res. , vol.93 , pp. 10655-10665
    • Thacker, W.C.1
  • 59
    • 0041117168 scopus 로고
    • 'Vector splines on the sphere, with application to the estimation of vorticity and divergence from discrete, noisy data'
    • In, eds). Birkhäuser: Basel;
    • Wahba G. 1982. 'Vector splines on the sphere, with application to the estimation of vorticity and divergence from discrete, noisy data'. In Multivariate Approximation Theory II, Schempp W, Zeller K (eds). Birkhäuser: Basel; 407-429.
    • (1982) Multivariate Approximation Theory II , pp. 407-429
    • Wahba, G.1    Schempp, W.2    Zeller, K.3
  • 60
    • 0000681041 scopus 로고
    • Some new mathematical methods for variational objective analysis using splines and cross-validation
    • Wahba G, Wendelberger J. 1980. Some new mathematical methods for variational objective analysis using splines and cross-validation. Mon. Weather Rev. 108: 36-57.
    • (1980) Mon. Weather Rev. , vol.108 , pp. 36-57
    • Wahba, G.1    Wendelberger, J.2
  • 61
    • 62749149846 scopus 로고    scopus 로고
    • A hybrid ETKF-3DVAR data assimilation scheme for the WRF model. Part I: Observing system simulation experiment.
    • Wang X, Barker DM, Synder C, Hamill TM. 2008. A hybrid ETKF-3DVAR data assimilation scheme for the WRF model. Part I: Observing system simulation experiment. Mon. Weather Rev. 136: 5116-5131.
    • (2008) Mon. Weather Rev. , vol.136 , pp. 5116-5131
    • Wang, X.1    Barker, D.M.2    Synder, C.3    Hamill, T.M.4
  • 62
    • 0035390475 scopus 로고    scopus 로고
    • Correlation modelling on the sphere using a generalized diffusion equation
    • Weaver AT, Courtier P. 2001. Correlation modelling on the sphere using a generalized diffusion equation. Q. J. R. Meteorol. Soc. 127: 1815-1846.
    • (2001) Q. J. R. Meteorol. Soc. , vol.127 , pp. 1815-1846
    • Weaver, A.T.1    Courtier, P.2
  • 64
    • 0042031463 scopus 로고    scopus 로고
    • Three- and four-dimensional variational assimilation with an ocean general circulation model of the tropical Pacific Ocean. Part 1: Formulation, internal diagnostics and consistency checks.
    • Weaver AT, Vialard J, Anderson DLT. 2003. Three- and four-dimensional variational assimilation with an ocean general circulation model of the tropical Pacific Ocean. Part 1: Formulation, internal diagnostics and consistency checks. Mon. Weather Rev. 131: 1360-1378.
    • (2003) Mon. Weather Rev. , vol.131 , pp. 1360-1378
    • Weaver, A.T.1    Vialard, J.2    Anderson, D.L.T.3
  • 65
    • 0027842160 scopus 로고
    • Some remarks on spatial correlation function models
    • Weber RO, Talkner P. 1993. Some remarks on spatial correlation function models. Mon. Weather Rev. 121: 2611-2617.
    • (1993) Mon. Weather Rev. , vol.121 , pp. 2611-2617
    • Weber, R.O.1    Talkner, P.2
  • 66
    • 0001760833 scopus 로고
    • On stationary processes in the plane
    • Whittle P. 1954. On stationary processes in the plane. Biometrika 41: 434-449.
    • (1954) Biometrika , vol.41 , pp. 434-449
    • Whittle, P.1
  • 67
    • 0008976275 scopus 로고
    • Stochastic processes in several dimensions
    • Whittle P. 1963. Stochastic processes in several dimensions. Bull. Inst. Int. Statist. 40: 974-994.
    • (1963) Bull. Inst. Int. Statist. , vol.40 , pp. 974-994
    • Whittle, P.1
  • 68
    • 0036968196 scopus 로고    scopus 로고
    • Three-dimensional variational analysis with spatially inhomogeneous covariances
    • Wu WS, Purser RJ, Parrish DF. 2002. Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Weather Rev. 130: 2905-2916.
    • (2002) Mon. Weather Rev. , vol.130 , pp. 2905-2916
    • Wu, W.S.1    Purser, R.J.2    Parrish, D.F.3
  • 69
    • 15944426807 scopus 로고    scopus 로고
    • Representations of inverse covariances by differential operators
    • Xu Q. 2005. Representations of inverse covariances by differential operators. Adv. Atmos. Sci. 22: 181-198.
    • (2005) Adv. Atmos. Sci. , vol.22 , pp. 181-198
    • Xu, Q.1
  • 71
    • 84857097690 scopus 로고    scopus 로고
    • On the renormalization of the covariance operators
    • Yaremchuk M, Carrier M. 2012. On the renormalization of the covariance operators. Mon. Weather Rev. 140: 637-649.
    • (2012) Mon. Weather Rev. , vol.140 , pp. 637-649
    • Yaremchuk, M.1    Carrier, M.2
  • 72
    • 80055099999 scopus 로고    scopus 로고
    • On the correlation functions associated with polynomials of the diffusion operator
    • Yaremchuk M, Smith S. 2011. On the correlation functions associated with polynomials of the diffusion operator. Q. J. R. Meteorol. Soc. 137: 1927-1932.
    • (2011) Q. J. R. Meteorol. Soc. , vol.137 , pp. 1927-1932
    • Yaremchuk, M.1    Smith, S.2
  • 73
    • 79959634821 scopus 로고    scopus 로고
    • A hybrid background-error covariance model for assimilating glider data into a coastal ocean model
    • Yaremchuk M, Nechaev D, Pan C. 2011. A hybrid background-error covariance model for assimilating glider data into a coastal ocean model. Mon. Weather Rev. 139: 1879-1890.
    • (2011) Mon. Weather Rev. , vol.139 , pp. 1879-1890
    • Yaremchuk, M.1    Nechaev, D.2    Pan, C.3
  • 74
    • 68749101978 scopus 로고    scopus 로고
    • Baroclinic tidal generation in the Kauai Channel inferred from high-frequency radio Doppler current meters
    • Zaron ED, Chavanne C, Egbert GD, Flament P. 2009. Baroclinic tidal generation in the Kauai Channel inferred from high-frequency radio Doppler current meters. Dyn. Atmos. Oceans 48: 93-120.
    • (2009) Dyn. Atmos. Oceans , vol.48 , pp. 93-120
    • Zaron, E.D.1    Chavanne, C.2    Egbert, G.D.3    Flament, P.4


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