Hessian-based covariance approximations in variational data assimilation

被引：6

作者：

Gejadze, Igor Yu. ^{[1
]}

Shutyaev, Victor P. ^{[2
,3
]}

Le Dimet, Francois-Xavier ^{[4
]}

机构：

[1] IRSTEA Montpellier, UMR G EAU, 361 Rue JF Breton,BP 5095, F-34196 Montpellier, France

[2] Russian Acad Sci, Inst Numer Math, Gubkina 8, Moscow 119333, Russia

[3] RAS, Inst Marine Hydrophys, Fed State Budget Sci Inst, Kapitanskaya 2, Sevastopol 299011, Russia

[4] Univ Grenoble Alpes, BP 51, F-38051 Grenoble 9, France

来源：

RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING | 2018年 / 33卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

Variational data assimilation; optimality system; Hessian; estimation error covariance; ERROR COVARIANCES; METEOROLOGICAL OBSERVATIONS; OPERATIONAL IMPLEMENTATION;

D O I：

10.1515/rnam-2018-0003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of variational data assimilation (estimation) for a nonlinear model is considered in general operator formulation. Hessian-based methods are presented to compute the estimation error covariances. The importance of dynamic formulation and the role of the Hessian and its inverse are discussed.

引用

页码：25 / 39

页数：15

共 50 条

[1] Hessian-based model reduction for large-scale data assimilation problems
Bashir, Omar
Ghattas, Omar
Hill, Judith
van Bloemen Waanders, Bart
Willcox, Karen
COMPUTATIONAL SCIENCE - ICCS 2007, PT 1, PROCEEDINGS, 2007, 4487 : 1010 - +
[2] Analysis error covariance versus posterior covariance in variational data assimilation
Gejadze, I. Yu.
Shutyaev, V.
Le Dimet, F. -X.
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, 2013, 139 (676) : 1826 - 1841
[3] Adjoint to the Hessian derivative and error covariances in variational data assimilation
Shutyaev, V. P.
Gejadze, I. Yu.
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2011, 26 (02) : 179 - 188
[4] Efficient Ensemble Covariance Localization in Variational Data Assimilation
Bishop, Craig H.
Hodyss, Daniel
Steinle, Peter
Sims, Holly
Clayton, Adam M.
Lorenc, Andrew C.
Barker, Dale M.
Buehner, Mark
MONTHLY WEATHER REVIEW, 2011, 139 (02) : 573 - 580
[5] Understanding Hessian-based density scoring
Raundahl, Jakob
Loog, Marco
Nielsen, Mads
DIGITAL MAMMOGRAPHY, PROCEEDINGS, 2006, 4046 : 447 - 452
[6] Forecast sensitivity to the observation error covariance in variational data assimilation
Daescu, Dacian N.
ICCS 2010 - INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE, PROCEEDINGS, 2010, 1 (01): : 1271 - 1279
[7] An evaluation of methods for normalizing diffusion-based covariance operators in variational data assimilation
Weaver, Anthony T.
Chrust, Marcin
Menetrier, Benjamin
Piacentini, Andrea
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, 2021, 147 (734) : 289 - 320
[8] Hessian-based optimization of constrained quantum control
Dalgaard, Mogens
Motzoi, Felix
Jensen, Jesper Hasseriis Mohr
Sherson, Jacob
PHYSICAL REVIEW A, 2020, 102 (04)
[9] New bounds on the condition number of the Hessian of the preconditioned variational data assimilation problem
Tabeart, Jemima M.
Dance, Sarah L.
Lawless, Amos S.
Nichols, Nancy K.
Waller, Joanne A.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2022, 29 (01)
[10] Optimal Voronoi Tessellations with Hessian-based Anisotropy
Budninskiy, Max
Liu, Beibei
de Goes, Fernando
Tong, Yiying
Alliez, Pierre
Desbrun, Mathieu
ACM TRANSACTIONS ON GRAPHICS, 2016, 35 (06):

← 1 2 3 4 5 →