Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system

Ocean Modelling

Volumn 16, Issue 3-4, 2007, Pages 160-187

  Di Lorenzo, Emanuele ^a   Moore, Andrew M ^b   Arango, Hernan G ^c   Cornuelle, Bruce D ^d   Miller, Arthur J ^d   Powell, Brian ^b   Chua, Boon S ^e   Bennett, Andrew F ^e  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c RUTGERS UNIVERSITY   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e OREGON STATE UNIVERSITY   (United States)

Author keywords

Adjoint models; Data assimilation; Inverse methods; Ocean models; ROMS; Tangent linear models

Indexed keywords

ALGORITHMS; COASTAL ZONES; COMPUTER SIMULATION; ITERATIVE METHODS; MATHEMATICAL MODELS; OCEAN CURRENTS; WATER WAVES;

BAROCLINIC COASTAL UPWELLING SYSTEM; DATA ASSIMILATION SYSTEM; INVERSE MODELING; REGIONAL OCEAN MODELING SYSTEM;

OCEANOGRAPHY;

DATA ASSIMILATION; INVERSE PROBLEM; UPWELLING;

EID: 33846304701     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2006.08.002     Document Type: Article

References (109)

1. Anderson D.L.T., Sheinbaum J., and Haines K. Data assimilation in ocean models. Reports on Progress in Physics 59 (1996) 1209-1266
2. Arango, H., Moore, A.M., Di Lorenzo, E., Cornuelle, B.D., Miller, A.J., Neilson, D.J., 2003. The ROMS tangent linear and adjoint models: a comprehensive ocean prediction and analysis system. IMCS, Rutgers Tech. Reports. Available online: .
3. Bell M.J., Forbes R.M., and Hines A. Assessment of the FOAM global data assimilation system for real-time operational ocean forecasting. Journal of Marine Systems 25 (2000) 1-22
4. Bennett A.F. Inverse Method in Physical Oceanography (1992), Cambridge University Press 346 pp
5. Bennett A.F. Inverse Modeling of the Ocean and Atmosphere (2002), Cambridge University Press 225 pp
6. Bennett A.F., and Thorburn M.A. The generalized inverse of a nonlinear quasi-geostrophic ocean circulation model. Journal of Physical Oceanography 22 (1992) 213-230
7. Bennett A.F., Chua B.S., Harrison D.E., and McPhaden M.J. Generalized inversion of tropical atmosphere-ocean data and a coupled model of the tropical Pacific. Journal of Climate 11 (1998) 1768-1792
8. Bennett A.F., Chua B.S., Harrison D.E., and McPhaden M.J. Generalized inversion of Tropical Atmosphere-Ocean (TAO) data and a coupled model of the tropical Pacific. Part II: The 1995-96 La Nina and 1997-98 El Nino. Journal of Climate 13 (2000) 2770-2785
9. Bennett A.F., Chua B.S., Ngodock H.E., Harrison D.E., and McPhaden M.J. Generalized inversion of the Gent-Cane model of the tropical Pacific with Tropical Atmosphere-Ocean (TAO) data. Journal of Marine Research 64 (2006) 1-42
10. Bertino, L., Lisæter, K.A., in press. The TOPAZ monitoring and prediction system for the Atlantic and Arctic Oceans. European Operational Oceanography: Present and Future, EuroGOOS Conf. Proc.
11. Chassignet E.P., Hurlburt H.E., Smedstad O.M., Halliwell G.R., Wallcraft A.J., Metzger E.J., Blanton B.O., Lozano C., Rao D.B., Hogan P.J., and Srinivasan A. Generalized vertical coordinates for eddy-resolving global and coastal ocean forecasts. Oceanography 19 (2006) 20-31
12. Chua B.S., and Bennett A.F. An inverse ocean modeling system. Ocean Modelling 3 (2001) 137-165
13. Cornuelle B.D., Chereskin T.K., Niiler P.P., Morris M.Y., and Musgrave D.L. Observations and modeling of a California undercurrent eddy. Journal of Geophysical Research-Oceans 105 (2000) 1227-1243
14. Courtier P. Dual formulation of four-dimensional variational assimilation. Quarterly Journal of the Royal Meteorological Society 123 (1997) 2449-2461
15. Courtier P., Derber J., Errico R., Louis J.F., and Vukicevic T. Important literature on the use of adjoint, variational-methods and the Kalman filter in meteorology. Tellus Series A-Dynamic Meteorology and Oceanography 45A (1993) 342-357
16. Courtier P., Andersson E., Heckley W., Pailleux J., Vasiljevic D., Hamrud M., Hollingsworth A., Rabier E., and Fisher M. The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation. Quarterly Journal of the Royal Meteorological Society 124 (1998) 1783-1807
17. Curchitser E.N., Haidvogel D.B., Hermann A.J., Dobbins E.L., Powell T.M., and Kaplan A. Multi-scale modeling of the North Pacific Ocean: assessment and analysis of simulated basin-scale variability (1996-2003). Journal of Geophysical Research-Oceans (2005) 110
18. De Mey P. Data assimilation at the oceanic mesoscale: a review. Journal of the Meteorological Society of Japan 75 (1997) 415-427
19. De Mey P., and Benkiran M. A multivariate reduced-order optimal interpolation method and its application to the Mediterranean basin-scale circulation. In: Pinardi N., and Woods J.D. (Eds). Ocean Forecasting, Conceptual Basis and Applications (2002), Springer-Verlag, Berlin, Heidelberg, New York 472
20. Derber J., and Bouttier F. A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus Series A-Dynamic Meteorology and Oceanography 51 (1999) 195-221
21. Di Lorenzo E. Seasonal dynamics of the surface circulation in the Southern California Current System. Deep-Sea Research Part II-Topical Studies in Oceanography 50 (2003) 2371-2388
22. Di Lorenzo E., Miller A.J., Neilson D.J., Cornuelle B.D., and Moisan J.R. Modelling observed California Current mesoscale eddies and the ecosystem response. International Journal of Remote Sensing 25 (2004) 1307-1312
23. Di Lorenzo E., Foreman M.G.G., and Crawford W.R. Modelling the generation of Haida Eddies. Deep-Sea Research Part II-Topical Studies in Oceanography 52 (2005) 853-873
24. Di Lorenzo, E., Moore, A.M., Arango, H.G., Cornuelle, B.D., Miller, A.J., in preparation. Weak and strong constraint data assimilation in the inverse regional ocean modeling system (ROMS): sensitivity to error covariance in the Southern California current eddy field. Ocean Modelling.
25. Dobricic, S., Pinardi, N., Adani, M., Bonazzi, A., Fratianni, C., Tonani, M., 2006. Mediterranean forecasting system: an improved assimilation scheme for Sea Level Anomaly and its validation. Quarterly Journal of the Royal Meteorological Society, in press.
26. Dommenget D., and Stammer D. Assessing ENSO simulations and predictions using adjoint ocean state estimation. Journal of Climate 17 (2004) 4301-4315
27. Egbert G.D., and Erofeeva S.Y. Efficient inverse modeling of barotropic ocean tides. Journal of Atmospheric and Oceanic Technology 19 (2002) 183-204
28. Egbert G.D., Bennett A.F., and Foreman M.G.G. Topex/poseidon tides estimated using a global inverse model. Journal of Geophysical Research-Oceans 99 (1994) 24821-24852
29. Eknes M., and Evensen G. Parameter estimation solving a weak constraint variational formulation for an Ekman model. Journal of Geophysical Research-Oceans 102 (1997) 12479-12491
30. Evensen G. Inverse methods and data assimilation in nonlinear ocean models. Physica D 77 (1994) 108-129
31. Ferreira D., Marshall J., and Heimbach P. Estimating eddy stresses by fitting dynamics to observations using a residual-mean ocean circulation model and its adjoint. Journal of Physical Oceanography 35 (2005) 1891-1910
32. Foreman M.G.G., Sutherland G., and Cummins P.F. M-2 tidal dissipation around Vancouver Island: an inverse approach. Continental Shelf Research 24 (2004) 2167-2185
33. Fox D.N., Teague W.J., Barron C.N., Carnes M.R., and Lee C.M. The modular ocean data assimilation system (MODAS). Journal of Atmospheric and Oceanic Technology 19 (2002) 240-252
34. Galanti E., Tziperman E., Harrison M., Rosati A., and Sirkes Z. A study of ENSO prediction using a hybrid coupled model and the adjoint method for data assimilation. Monthly Weather Review 131 (2003) 2748-2764
35. Golub G.H., and Van Loan C.F. Matrix Computations (1982), John Hopkins University Press 467 pp
36. Griffin D.A., and Thompson K.R. The adjoint method of data assimilation used operationally for shelf circulation. Journal of Geophysical Research-Oceans 101 (1996) 3457-3477
37. Gunson J.R., and Malanotte-Rizzoli P. Assimilation studies of open-ocean flows. 1. Estimation of initial and boundary conditions. Journal of Geophysical Research-Oceans 101 (1996) 28457-28472
38. Gunson J.R., and Malanotte-Rizzoli P. Assimilation studies of open-ocean flows. 2. Error measures with strongly nonlinear dynamics. Journal of Geophysical Research-Oceans 101 (1996) 28473-28488
39. Haidvogel D.B., Arango H.G., Hedstrom K., Beckmann A., Malanotte-Rizzoli P., and Shchepetkin A.F. Model evaluation experiments in the North Atlantic Basin: simulations in nonlinear terrain-following coordinates. Dynamics of Atmospheres and Oceans 32 (2000) 239-281
40. Haykin S. Adaptive Filter Theory. third ed. (1996), Prentice-Hall, Englewood Cliffs, NJ
41. He R.Y., McGillicuddy D.J., Lynch D.R., Smith K.W., Stock C.A., and Manning J.P. Data assimilative hindcast of the Gulf of Maine coastal circulation. Journal of Geophysical Research-Oceans (2005) 110
42. Hermann A.J., Haidvogel D.B., Dobbins E.L., and Stabeno P.J. Coupling global and regional circulation models in the coastal Gulf of Alaska. Progress in Oceanography 53 (2002) 335-367
43. Hoteit, I., Cornuelle, B.D., in press. Treating strong adjoint sensitivities in tropical eddy-permitting variational data assimilation. Quarterly Journal of the Royal Meteorological Society.
44. Kistler R., Kalnay E., Collins W., Saha S., White G., Woollen J., Chelliah M., Ebisuzaki W., Kanamitsu M., Kousky V., van den Dool H., Jenne R., and Fiorino M. The NCEP-NCAR 50-year reanalysis: Monthly means CD-ROM and documentation. Bulletin of the American Meteorological Society 82 (2001) 247-267
45. Kleeman R., Moore A.M., and Smith N.R. Assimilation of subsurface thermal data into a simple ocean model for the initialization of an intermediate tropical coupled ocean-atmosphere forecast model. Monthly Weather Review 123 (1995) 3103-3113
46. Klinker E., Rabier F., Kelly G., and Mahfouf J.F. The ECMWF operational implementation of four-dimensional variational assimilation. III: Experimental results and diagnostics with operational configuration. Quarterly Journal of the Royal Meteorological Society 126 (2000) 1191-1215
47. Kone V., Machu E., Penven P., Andersen V., Garcon V., Freon P., and Demarcq H. Modeling the primary and secondary productions of the southern Benguela upwelling system: A comparative study through two biogeochemical models. Global Biogeochemical Cycles (2005) 19
48. Kosters F., Kase R., Fleming K., and Wolf D. Denmark strait overflow for last glacial maximum to holocene conditions. Paleoceanography (2004) 19
49. Kurapov A.L., Egbert G.D., Miller R.N., and Allen J.S. Data assimilation in a baroclinic coastal ocean model: ensemble statistics and comparison of methods. Monthly Weather Review 130 (2002) 1009-1025
50. Kurapov A.L., Egbert G.D., Allen J.S., Miller R.N., Erofeeva S.Y., and Kosro P.M. The M-2 internal tide off oregon: inferences from data assimilation. Journal of Physical Oceanography 33 (2003) 1733-1757
51. Lea, D.J., Haine, T.W.N., Gasparovic, R.F., in press. Irminger Sea circulation using variational data assimilation. Quarterly Journal of the Royal Meteorological Society.
52. Lermusiaux P.F.J., and Robinson A.R. Data assimilation via error subspace statistical estimation. Part I: Theory and schemes. Monthly Weather Review 127 (1999) 1385-1407
53. Levin J.C., Haidvogel D.B., Chua B., Bennett A.F., and Iskandarani M. Euler-Lagrange equations for the spectral element shallow water system. Ocean Modelling 12 (2006) 348-377
54. Lorenc A.C. Development of an operational variational assimilation scheme. Journal of the Meteorological Society of Japan 75 (1997) 339-346
55. Lorenc A.C. Modelling of error covariances by 4D-Var data assimilation. Quarterly Journal of the Royal Meteorological Society 129 (2003) 3167-3182
56. Lorenc A.C., Bell R.S., and Macpherson B. The meteorological-office analysis correction data assimilation scheme. Quarterly Journal of the Royal Meteorological Society 117 (1991) 59-89
57. Luong B., Blum J., and Verron J. A variational method for the resolution of a data assimilation problem in oceanography. Inverse Problems 14 (1998) 979-997
58. Lyard F.H. Data assimilation in a wave equation: a variational representer approach for the Grenoble tidal model. Journal of Computational Physics 149 (1999) 1-31
59. Lynch D.R., and Hannah C.G. Inverse model for limited-area hindcasts on the continental shelf. Journal of Atmospheric and Oceanic Technology 18 (2001) 962-981
60. Lynch D.R., and Naimie C.E. Hindcasting the Georges Bank circulation, Part II: wind-band inversion. Continental Shelf Research 22 (2002) 2191-2224
61. Lynch D.R., Naimie C.E., and Hannah C.G. Hindcasting the Georges bank circulation. Part I: Detiding. Continental Shelf Research 18 (1998) 607-639
62. Mahfouf J.F., and Rabier F. The ECMWF operational implementation of four-dimensional variational assimilation. II: Experimental results with improved physics. Quarterly Journal of the Royal Meteorological Society 126 (2000) 1171-1190
63. Malanotte-Rizzoli P. Modern Approach to Data Assimilation in Ocean Modeling. Oceanography Series vol. 61 (1996), Elsevier 455 pp
64. Malanotte-Rizzoli P., Hedstrom K., Arango H., and Haidvogel D.B. Water mass pathways between the subtropical and tropical ocean in a climatological simulation of the North Atlantic ocean circulation. Dynamics of Atmospheres and Oceans 32 (2000) 331-371
65. Marchesiello P., McWilliams J.C., and Shchepetkin A. Equilibrium structure and dynamics of the California Current System. Journal of Physical Oceanography 33 (2003) 753-783
66. Marotzke J., Giering R., Zhang K.Q., Stammer D., Hill C., and Lee T. Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport sensitivity. Journal of Geophysical Research-Oceans 104 (1999) 29529-29547
67. Marshall J., Adcroft A., Hill C., Perelman L., and Heisey C. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. Journal of Geophysical Research-Oceans 102 (1997) 5753-5766
68. Miller A.J., and Cornuelle B.D. Forecasts from fits of frontal fluctuations. Dynamics of Atmospheres and Oceans 29 (1999) 305-333
69. Miller R.N., Carter E.F., and Blue S.T. Data assimilation into nonlinear stochastic models. Tellus Series A-Dynamic Meteorology and Oceanography 51 (1999) 167-194
70. Miller A.J., Di Lorenzo E., Neilson D.J., Cornuelle B.D., and Moisan J.R. Modeling CalCOFI observations during El Nino: fitting physics and biology. California Cooperative Oceanic Fisheries Investigations Reports 41 (2000) 87-97
71. Miller A.J., Di Lorenzo E., Neilson D.J., Kim H.J., Capotondi A., Alexander M.A., Bograd S.J., Schwing F.B., Mendelssohn R., Hedstrom K., and Musgrave D.L. Interdecadal changes in mesoscale eddy variance in the Gulf of Alaska circulation: possible implications for the Steller sea lion ecline. Atmosphere-Ocean 43 (2005) 231-240
72. Mooers C.N.K. Coastal Ocean Prediction. Estuarine Series vol. 56 (1999), American Geophysical Union 523 pp
73. Moore A.M. Data assimilation in a quasi-geostrophic open-ocean model of the Gulf-stream region using the adjoint method. Journal of Physical Oceanography 21 (1991) 398-427
74. Moore A.M., Arango H.G., Di Lorenzo E., Cornuelle B.D., Miller A.J., and Neilson D.J. A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Modelling 7 (2004) 227-258
75. Morrow R., and DeMey P. Adjoint assimilation of altimetric, surface drifter, and hydrographic data in a quasi-geostrophic model of the Azores Current. Journal of Geophysical Research-Oceans 100 (1995) 25007-25025
76. Muccino J.C., Hubele N.F., and Bennett A.F. Significance testing for variational assimilation. Quarterly Journal of the Royal Meteorological Society 130 (2004) 1815-1838
77. Muccino, J., Arango, H.G., Bennett, A., Cornuelle, B., Chua, B., Di Lorenzo, E., Egbert, G.D., Haidvogel, D., Levin, J.C., Luo, H., Miller, A.J., Moore, A.M., Zaron, E.D., 2006. The inverse ocean modelling system. II: Applications. Journal of Atmospheric and Ocean Technology, submitted for publication.
78. Ngodock H.E., Chua B.S., and Bennett A.E. Generalized inverse of a reduced gravity primitive equation ocean model and Tropical Atmosphere-Ocean data. Monthly Weather Review 128 (2000) 1757-1777
79. Parrish D.F., Derber J.C., Purser R.J., Wu W.S., and Pu Z.X. The NCEP global analysis system: recent improvements and future plans. Journal of the Meteorological Society of Japan 75 (1997) 359-365
80. Penven P., Echevin V., Pasapera J., Colas F., and Tam J. Average circulation, seasonal cycle, and mesoscale dynamics of the Peru Current system: a modeling approach. Journal of Geophysical Research-Oceans 110 (2005)
81. Pinardi N., Allen I., Demirov E., De Mey P., Korres G., Lascaratos A., Le Traon P.Y., Maillard C., Manzella G., and Tziavos C. The Mediterranean ocean forecasting system: first phase of implementation (1998-2001). Annales Geophysicae 21 (2003) 3-20
82. Rabier F., and Courtier P. 4-Dimensional assimilation in the presence of Baroclinic instability. Quarterly Journal of the Royal Meteorological Society 118 (1992) 649-672
83. Ricci S., Weaver A.T., Vialard J., and Rogel P. Incorporating state-dependent temperature-salinity constraints in the background error covariance of variational ocean data assimilation. Monthly Weather Review 133 (2005) 317-338
84. Robertson R., Beckmann A., and Hellmer H. M-2 tidal dynamics in the Ross Sea. Antarctic Science 15 (2003) 41-46
85. Robinson, A.R., 1999. Forecasting and simulating coastal ocean processes and variabilities with the Harvard Ocean Prediction System, in Coastal Ocean Prediction. Coastal Estuarine Studies M.C.N.K., Ed., AGU, 100.
86. Robinson A.R., and Walstad L.J. The Harvard open ocean model - calibration and application to dynamic process, forecasting, and data assimilation studies. Applied Numerical Mathematics 3 (1987) 89-131
87. Rosmond T., and Xu L. Development of NAVDAS-AR: non-linear formulation and outer loop tests. Tellus Series A-Dynamic Meteorology and Oceanography 58 (2006) 45-58
88. Schroter J., Seiler U., and Wenzel M. Variational assimilation of Geosat data into an eddy-resolving model of the Gulf-stream extension area. Journal of Physical Oceanography 23 (1993) 925-953
89. Scott R.K., Allen J.S., Egbert G.D., and Miller R.N. Assimilation of surface current measurements in a coastal ocean model. Journal of Physical Oceanography 30 (2000) 2359-2378
90. Seiler U. Estimation of open boundary-conditions with the adjoint method. Journal of Geophysical Research-Oceans 98 (1993) 22855-22870
91. Shchepetkin A.F., and McWilliams J.C. The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modelling 9 (2005) 347-404
92. She J., and Klinck J.M. Flow near submarine canyons driven by constant winds. Journal of Geophysical Research-Oceans 105 (2000) 28671-28694
93. Smedstad O.M., Hurlburt H.E., Metzger E.J., Rhodes R.C., Shriver J.F., Wallcraft A.J., and Kara A.B. An operational Eddy resolving 1/16 degrees global ocean nowcast/forecast system. Journal of Marine Systems 40 (2003) 341-361
94. Stammer D., Wunsch C., Giering R., Eckert C., Heimbach P., Marotzke J., Adcroft A., Hill C.N., and Marshall J. Volume, heat, and freshwater transports of the global ocean circulation 1993-2000, estimated from a general circulation model constrained by World Ocean Circulation Experiment (WOCE) data. Journal of Geophysical Research-Oceans (2003) 108
95. Stammer D., Ueyoshi K., Kohl A., Large W.G., Josey S.A., and Wunsch C. Estimating air-sea fluxes of heat, freshwater, and momentum through global ocean data assimilation. Journal of Geophysical Research-Oceans 109 (2004)
96. Taillandier V., Echevin V., Mortier L., and Devenon J.L. Controlling boundary conditions with a four-dimensional variational data-assimilation method in a non-stratified open coastal model. Ocean Dynamics 54 (2004) 284-298
97. Talagrand O., and Courtier P. Variational assimilation of meteorological observations with the adjoint vorticity equation. 1. Theory. Quarterly Journal of the Royal Meteorological Society 113 (1987) 1311-1328
98. Thepaut J.N., and Courtier P. 4-Dimensional variational data assimilation using the adjoint of a multilevel primitive-equation model. Quarterly Journal of the Royal Meteorological Society 117 (1991) 1225-1254
99. Tziperman E., Thacker W.C., Long R.B., and Hwang S.M. Oceanic data-analysis using a general-circulation model. 1. Simulations. Journal of Physical Oceanography 22 (1992) 1434-1457
100. Tziperman E., Thacker W.C., Long R.B., Hwang S.M., and Rintoul S.R. Oceanic data-analysis using a general-circulation model. 2. A North-Atlantic model. Journal of Physical Oceanography 22 (1992) 1458-1485
101. Uboldi F., and Kamachi M. Time-space weak-constraint data assimilation for nonlinear models. Tellus Series A-Dynamic Meteorology and Oceanography 52 (2000) 412-421
102. Vialard J., Weaver A.T., Anderson D.L.T., and Delecluse P. Three- and four-dimensional variational assimilation with a general circulation model of the tropical Pacific Ocean. Part II: Physical validation. Monthly Weather Review 131 (2003) 1379-1395
103. Warner J.C., Geyer W.R., and Lerczak J.A. Numerical modeling of an estuary: a comprehensive skill assessment. Journal of Geophysical Research-Oceans 110 (2005)
104. Weaver A., and Courtier P. Correlation modelling on the sphere using a generalized diffusion equation. Quarterly Journal of the Royal Meteorological Society 127 (2001) 1815-1846
105. Weaver A.T., Vialard J., and Anderson D.L.T. Three- and four-dimensional variational assimilation with a general circulation model of the tropical Pacific Ocean. Part I: Formulation, internal diagnostics, and consistency checks. Monthly Weather Review 131 (2003) 1360-1378
106. Wilkin J.L., Arango H.G., Haidvogel D.B., Lichtenwalner C.S., Glenn S.M., and Hedstrom K.S. A regional ocean modeling system for the long-term ecosystem observatory. Journal of Geophysical Research-Oceans 110 (2005)
107. Wunsch C. The Ocean Circulation Inverse Problem (1996), Cambridge University Press 422 pp
108. Zou X., Liu H., Derber J., Sela J.G., Treadon R., Navon I.M., and Wang B. Four-dimensional variational data assimilation with a diabatic version of the NCEP global spectral model: system development and preliminary results. Quarterly Journal of the Royal Meteorological Society 127 (2001) 1095-1122
109. Zupanski M., Zupanski D., Vukicevic T., Eis K., and Haar T.I.V. CIRA/CSU four-dimensional variational data assimilation system. Monthly Weather Review 133 (2005) 829-843