On the variational data assimilation problem solving and sensitivity analysis
Tài liệu tham khảo
Ababou, 1994, On the condition number of covariance matrices in kriging, estimation, and simulation of random fields, Math. Geol., 26, 99, 10.1007/BF02065878
Andersson, 1998, The ECMWF implementation of three dimensional variational assimilation (3DVar). Part III: experimental results, Q. J. R. Meteorol. Soc., 124, 1831, 10.1002/qj.49712455004
Arcucci, 2015, On the problem decomposition of scalable 4D-Var data assimilation models, 589
Arcucci, 2016, A scalable numerical algorithm for solving Tikhonov regularization problems, vol. 9574, 45
Baker, 2004, Three-dimensional variational data assimilation system for MM5: implementation and initial results, Mon. Weather Rev., 132, 897, 10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2
Bauera, 2011, Comparing parameter choice methods for regularization of ill-posed problems, Math. Comput. Simul., 81, 1795, 10.1016/j.matcom.2011.01.016
Cacuci, 1981, Sensitivity theory for nonlinear systems. I. Nonlinear functional analysis approach, J. Math. Phys., 22, 2794, 10.1063/1.525186
Cacuci, 2003
Cacuci, 2005, Sensitivity and Uncertainty Analysis, vol. II
Cacuci, 2013
Campagna, 2007, An efficient algorithm for regularization of Laplace transform inversion in real case, J. Comput. Appl. Math., 210, 84, 10.1016/j.cam.2006.10.077
Courtier, 1994, A strategy for operational implementation of 4D-VAR, using an incremental approach, Q. J. R. Meteorol. Soc., 120, 1367, 10.1002/qj.49712051912
Daescu, 2013, Sensitivity analysis in nonlinear variational data assimilation: theoretical aspects and applications
Dahlquist, 1974
D'Amore, 2002, Regularization of a Fourier series method for the Laplace transform inversion with real data, Inverse Probl., 18, 1185, 10.1088/0266-5611/18/4/315
D'Amore, 2011, A parallel three-dimensional variational data assimilation scheme, AIP Conf. Proc., 1389, 1829, 10.1063/1.3636965
D'Amore, 2012, A smoothing spline that approximates Laplace transform functions only known on measurements on the real axis, Inverse Probl., 28
D'Amore, 2013, DD-OceanVar: a domain decomposition fully parallel data assimilation software in Mediterranean sea, Proc. Comput. Sci., 18, 1235, 10.1016/j.procs.2013.05.290
D'Amore, 2014, A scalable variational data assimilation, J. Sci. Comput., 61, 239, 10.1007/s10915-014-9824-2
Dennis, 1996
Dobricic, 2008, An oceanographic three-dimensional variational data assimilation scheme, Ocean Model., 22, 89, 10.1016/j.ocemod.2008.01.004
Ekstrom, 1973, A spectral characterization of the ill conditioning in numerical deconvolution, IEEE Trans. Audio Electroacoust., AU-21, 344, 10.1109/TAU.1973.1162493
Engl, 1996
Errico, 1997, What is an adjoint model, Bull. Am. Meteorol. Soc., 78, 2577, 10.1175/1520-0477(1997)078<2577:WIAAM>2.0.CO;2
Golub, 1979, Generalized cross validation as a method for choosing a good ridge parameter, Technometrics, 21, 215, 10.1080/00401706.1979.10489751
Golub, 1996
Haben, 2011
Hannachi, 2004
Hannachi, 2007, Empirical orthogonal functions and related techniques in atmospheric science: a review, Int. J. Climatol., 1152, 1119, 10.1002/joc.1499
Hansen, 1998, Rank-Deficient and Discrete Ill-Posed Problems, 10.1137/1.9780898719697
Hansen, 2006
Higham, 2002
Hofmann, 1986
Kalnay, 2003
Kostinski, 2000, On the condition number of Gaussian sample covariance matrices, IEEE Trans. Geosci. Remote Sens., 38, 329, 10.1109/36.823928
Lorenz, 1956
Morozov, 1984
Nagy, 2003, Image Deblurring: I can see clearly now, Comput. Sci. Eng., 82, 10.1109/MCISE.2003.1196312
Nichols, 2010, Mathematical concepts in data assimilation
Nocedal, 1997, L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Softw., 23, 550, 10.1145/279232.279236
Rotar, 2012
Wang, 2016, 2D Burgers equation with large Reynolds number using POD/DEIM and calibration, Int. J. Numer. Methods Fluids, 82, 909, 10.1002/fld.4249