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ОбложкаAdvanced data assimilation for geosciences: Ecole de Physique des Houches. Special Issue, 28 May-15 June 2012 / ed. by É.Blayo et al. - Oxford: Oxford university press, 2015. - xxiv, 584 p.: ill., tab. - Incl. bibl. ref. - ISBN 978-0-19-872384-4
Шифр: (И/Д-A22) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
List of participants .......................................... xix

Part I  Key lectures ............................................ 1
1  4D-VAR: four-dimensional variational assimilation
   O. TALAGRAND ................................................. 3
   1.1  Introduction ............................................ 5
   1.2  Variational assimilation in the context of statistical
        linear estimation ....................................... 5
   1.3  Minimization methods. The adjoint approach ............. 12
   1.4  Practical implementation ............................... 17
   1.5  Further considerations on variational assimilation ..... 19
   1.6  More on the adjoint method ............................. 23
   1.7  Conclusions ............................................ 25
   References .................................................. 26
2  Four-dimensional variational data assimilation
   A.C. LORENC ................................................. 31
   2.1  4D-Var: background and motivation ...................... 33
   2.2  4D-Var: derivation ..................................... 47
   2.3  4D-Var: advanced aspects ............................... 52
   2.4  4D-Var. coupling with ensembles ........................ 63
   References .................................................. 68
3  Introduction to the Kalman filter
   C. SNYDER ................................................... 75
   3.1  A Bayesian view of data assimilation ................... 77
   3.2  The Kalman filter (I) .................................. 84
   3.3  A closer look at the forecast and update steps ......... 89
   3.4  The Kalman filter (II) ................................. 94
   3.5  Assorted topics ........................................ 96
   3.6  Nonlinearity and non-Gaussianity ...................... 103
   3.7  Basics of the ensemble Kalman filter .................. 106
   3.8  Assorted derivations and identities ................... 118
   References ................................................. 119
4  Smoothers
   E. COSME ................................................... 121
   4.1  Introduction .......................................... 123
   4.2  Smoothing algorithms in a Bayesian framework .......... 124
   4.3  Linear Gaussian smoothers ............................. 127
   4.4  Ensemble smoothers .................................... 131
   4.5  Advantages, drawbacks, and high-dimensional
        applications .......................................... 133
   References ................................................. 135
5  Observation influence diagnostic of a data assimilation
   system
   C. CARDINALI ............................................... 137
   5.1  Introduction .......................................... 139
   5.2  Classical statistical definitions of influence matrix
        and  self-sensitivity ................................. 141
   5.3  Observational influence and self-sensitivity
        for a DA scheme ....................................... 143
   5.4  Results ............................................... 148
   5.5  Conclusions ........................................... 156
   Acknowledgements ........................................... 158
   Appendix 1: Influence matrix calculation in weighted
   regression DA scheme ....................................... 158
   Appendix 2: Approximate calculation of self-sensitivity in
   a large variational analysis system ........................ 160
   References ................................................. 162
6  Observation impact on the short-range forecast
   C. CARDINALI ............................................... 165
   6.1  Introduction .......................................... 167
   6.2  Observational impact on the forecast .................. 168
   6.3  Results ............................................... 173
   6.4  Conclusion ............................................ 178
   Acknowledgements ........................................... 179
   References ................................................. 180

Part II  Specialized lectures ................................. 183
7  Background error covariances: estimation and specification
   L. BERRE ................................................... 185
   7.1  Error equations and their simulation .................. 187
   7.2  Innovation-based estimations .......................... 192
   7.3  Diagnosis of background error covariances ............. 195
   7.4  Modelling and filtering covariances ................... 199
   7.5  Conclusions ........................................... 206
   References ................................................. 206
8  Observation error specifications
   G. DESROZIERS .............................................. 209
   8.1  General framework ..................................... 211
   8.2  Methods for estimating observation error statistics ... 212
   8.3  Diagnosis of observation error variances .............. 219
   8.4  Diagnosis of observation error correlations ........... 219
   8.5  Observation error correlation specification in the
        assimilation .......................................... 221
   8.6  Conclusion ............................................ 226
   References ................................................. 227
9  Brrors. A posteriori diagnostics
   O. TALAGRAND ............................................... 229
   9.1  Introduction .......................................... 231
   9.2  Reminder on statistical linear estimation ............. 231
   9.3  Objective evaluation of assimilation algorithms ....... 235
   9.4  Estimation of the statistics of data errors ........... 237
   9.5  Diagnostics of internal consistency ................... 238
   9.6  Diagnostics of optimality of assimilation
        algorithms ............................................ 250
   9.7  Conclusions ........................................... 252
   Acknowledgements ........................................... 253
   References ................................................. 253
10 Error dynamics in ensemble Kalman-filter systems:
   localization
   P. HOUTEKAMER .............................................  255
   10.1 Motivation ............................................ 257
   10.2 Estimation of scalars and matrices .................... 257
   10.3 Assimilation of one observation ....................... 258
   10.4 Experiments with the Lorenz III model ................. 260
   10.5 Discussion ............................................ 264
   References ................................................. 264
11 Short-range error statistics in an ensemble Kalman
   filter
   P. HOUTEKAMER .............................................. 267
   11.1 Introduction .......................................... 269
   11.2 Experimental environment .............................. 270
   11.3 Horizontal correlations ............................... 271
   11.4 vertical correlations ................................. 273
   11.5 Temporal correlations ................................. 275
   11.6 Stratospheric wind analysis ........................... 276
   11.7 Discussion ............................................ 277
   References ................................................. 278
12 Error dynamics in ensemble Kalman filter systems: system
   error
   P. HOUTEKAMER .............................................. 279
   12.1 Introduction .......................................... 281
   12.2 Monte Carlo methods ................................... 281
   12.3 Review of model error ................................. 282
   12.4 Review of data-assimilation error ..................... 284
   12.5 Evidence of bias ...................................... 285
   12.6 Evidence of horizontal error correlations ............. 286
   12.7 Discussion ............................................ 287
   References ................................................. 288
13 Particle filters for the geosciences
   P.J. VAN LEEUWEN ........................................... 291
   13.1 Introduction .......................................... 293
   13.2 A simple particle filter based on importance
        sampling .............................................. 294
   13.3 Reducing the variance in the weights .................. 298
   13.4 The proposal density .................................. 300
   13.5 Conclusions ........................................... 316
   References ................................................. 318
14 Second-order methods for error propagation in variational
   data assimilation
   F.-X. LE DIMET, I. GEJADZE, and V. SHUTYAEV ................ 319
   14.1 Introduction .......................................... 321
   14.2 Variational methods ................................... 322
   14.3 Second-order methods .................................. 325
   14.4 Sensitivity with respect to sources ................... 329
   14.5 Stochastic methods .................................... 334
   14.6 Covariances of the optimal solution error ............. 335
   14.7 Effective inverse Hessian (EIH) method ................ 338
   14.8 Numerical examples .................................... 341
   14.9 Conclusions ........................................... 346
   Acknowledgements ........................................... 347
   References ................................................. 347
15 Adjoints by automatic differentiation
   L. HASCOËT ................................................. 349
   15.1 Introduction .......................................... 351
   15.2 Elements of AD ........................................ 351
   15.3 Application of adjoint AD to data assimilation ........ 359
   15.4 Improving the adjoint AD code ......................... 362
   15.5 AD tools .............................................. 364
   15.6 Conclusion ............................................ 366
   References ................................................. 368
16 Assimilation of images
   A. VIDARD, O. TITAUD ....................................... 371
   16.1 Motivations ........................................... 373
   16.2 Images: level(s) of interpretation .................... 375
   16.3 Current use of images in data assimilation: pseudo
        observation ........................................... 377
   16.4 Direct assimilation of images ......................... 382
   References ................................................. 391
17 Multigrid algorithms and local mesh refinement methods
   in the context of variational data assimilation
   L. DEBREU, E. NEVEU, E. SIMON, and F.-X. LE DIMET .......... 395
   17.1 Structure of the variational data assimilation
        problem ............................................... 397
   17.2 Multigrid methods and application to variational
        data assimilation ..................................... 400
   17.3 Data assimilation and local mesh refinement ........... 405
   17.4 Coupling the two approaches ........................... 409
   17.5 Conclusions and perspectives .......................... 410
   References ................................................. 411
18 Selected topics in multiscale data assimilation
   M. BOCQUET, L. WU, F. CHEVALLIER, and M.R. KOOKHAN ......... 413
   18.1 Introduction .......................................... 415
   18.2 Bayesian multiscale analysis .......................... 415
   18.3 Application to Bayesian control space design .......... 422
   18.4 Empirical multiscale statistics ....................... 427
   18.5 Conclusion ............................................ 430
   References ................................................. 431
19 Data assimilation in meteorology
   F. RABIER and M. FISHER .................................... 433
   19.1 Transforming data ..................................... 435
   19.2 Comparing data and models ............................. 439
   19.3 Thinning the dataset .................................. 444
   19.4 Filtering the analysis ................................ 447
   19.5 Nonlinearities and non-Gaussian densities in
        variational data assimilation ......................... 449
   19.6 Parallel algorithms for 4D-Var ........................ 453
   19.7 Conclusion ............................................ 456
   References ................................................. 457
20 An introduction to inverse modelling and parameter
   estimation for atmosphere and ocean sciences
   M. BOCQUET ................................................. 461
   20.1 Introduction .......................................... 463
   20.2 Bayesian approach to inverse problems ................. 463
   20.3 Alternative approaches ................................ 473
   20.4 Estimation of second-order statistics ................. 479
   20.5 Inverse modelling in atmospheric and ocean
        sciences: a selection ................................. 489
   20.6 Conclusion ............................................ 493
   Acknowledgements ........................................... 493
   References ................................................. 493
21 Greenhouse gas flux inversion
   F. CHEVALLIER .............................................. 497
   21.1 Introduction .......................................... 499
   21.2 Observations .......................................... 499
   21.3 Uncertainties ......................................... 500
   21.4 Methods ............................................... 501
   21.5 Conclusion ............................................ 502
   References ................................................. 503
22 Data assimilation in atmospheric chemistry and air
   quality
   H. ELBERN, E. FRIESE, L. NIERADZIK, and J. SCHWINGER ....... 507
   22.1 Introduction .......................................... 509
   22.2 Advanced chemistry data assimilation .................. 513
   22.3 A posteriori validation in atmospheric chemistry ...... 518
   22.4 Tropospheric chemical data assimilation ............... 520
   22.5 Aerosol data assimilation ............................. 523
   References ................................................. 528
23 Combining models and data in large-scale oceanography:
   examples from the consortium for Estimating the
   Circulation and Climate of the Ocean (ECCO)
   I. FUKUMORI ................................................ 535
   23.1 Introduction .......................................... 537
   23.2 Physical consistency .................................. 537
   23.3 ECCO products ......................................... 539
   23.4 Examples of ECCO applications ......................... 540
   23.5 Practical considerations in employing advanced
        estimation methods .................................... 544
   23.6 Summary ............................................... 550
   Acknowledgements ........................................... 551
   References ................................................. 551
24 Data assimilation in coastal oceanography: IS4DVAR
   in the Regional Ocean Modelling System (ROMS)
   J. ZAVALA-GARAY, J. WILKIN, and J. LEVIN ................... 555
   24.1 The Regional Ocean Modelling System and the IS4DVAR
        data assimilation algorithm ........................... 557
   24.2 ROMS IS4DVAR in a quasi-geostrophic domain:
        the East Australia Current ............................ 560
   24.3 ROMS IS4DVAR in a complex coastal domain:
        the Middle Atlantic Bight ............................. 564
   References ................................................. 573
25 Data assimilation in glaciology
   B. BONAN, M. NODET, O. OZENDA, and C. RITZ ................. 577
   25.1 Introduction .......................................... 579
   25.2 Ice-sheet model ....................................... 579
   25.3 Adjoint method and adjoint model ...................... 581
   25.4 Numerical results for twin experiments ................ 582
   References ................................................. 584

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