Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

Part B: Sensitivity Analysis in Nonlinear Variational Data Assimilation: Theoretical Aspects and Applications

Author(s): Dacian N. Daescu and Ionel M. Navon

Pp: 276-300 (25)

DOI: 10.2174/9781608057788113010012

* (Excluding Mailing and Handling)

Abstract

This chapter presents the mathematical framework to evaluate the sensitivity of a model forecast aspect to the input parameters of a nonlinear four-dimensional variational data assimilation system (4D-Var DAS): observations, prior state (background) estimate, and the error covariance specification. A fundamental relationship is established between the forecast sensitivity with respect to the information vector and the sensitivity with respect to the DAS representation of the information error covariance. Adjoint modeling is used to obtain first- and second-order derivative information and a reduced-order approach is formulated to alleviate the computational cost associated with the sensitivity estimation. Numerical results from idealized 4D-Var experiments performed with a global shallow water model are used to illustrate the theoretical concepts.


Keywords: Estimation theory, atmospheric data assimilation, error statistics, sensitivity analysis, adjoint model, large-scale optimization, Hessian matrix, second-order derivative information, order reduction, variational data assimilation, background estimate, error covariance, DAS representation, shallow water model, error statistics, information-redundancy, suboptimal weighting, a priori estimates, data thinning, super-obbing.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 1351 and `b`.`banner_from_date` <= 1739834419 and `b`.`banner_to_date` >= 1739834419 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.03msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 1351
      • 3: 1739834419
      • 4: 1739834419
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='39185d93843a02e7e0406ebf4c0601a2'
      180μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    20Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        FLb8L368PyMsGmHi965K8S6dEQKbbCQjhHSvx18Z
        uc_cart_id
        39185d93843a02e7e0406ebf4c0601a2
        _previous
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        _flash
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        PHPDEBUGBAR_STACK_DATA
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        path_info
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        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
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        request_headers
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-17 23:20:19GET/chapter/59861121822