Application of optimization methods to the problem of mathematical simulation of atmospheric processes and environment

Marchuk, G. I.; Penenko, Vladimir

doi:10.1007/bfb0004167

Cited by 39 publications

(29 citation statements)

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“…2.3) were studied by Pontryagin et al (1962); Lions (1968Lions ( , 1988) (see also Agoshkov and Marchuk, 1993;Blayo et al, 1998;Glowinski and Lions, 1994;Kurzhanskii and Khapalov, 1991;Le Dimet and Talagrand, 1986;Marchuk and Penenko, 1978;Marchuk et al, 1996;Navon, 1995;Sasaki, 1970, and others).…”

Section: Statement Of the Problemmentioning

confidence: 98%

On deterministic error analysis in variational data assimilation

Dimet

Shutyaev

2005

Nonlin. Processes Geophys.

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Abstract. The problem of variational data assimilation for a nonlinear evolution model is considered to identify the initial condition. The equation for the error of the optimal initialvalue function through the errors of the input data is derived, based on the Hessian of the misfit functional and the second order adjoint techniques. The fundamental control functions are introduced to be used for error analysis. The sensitivity of the optimal solution to the input data (observation and model errors, background errors) is studied using the singular vectors of the specific response operators in the error equation. The relation between "quality of the model" and "quality of the prediction" via data assimilation is discussed.

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Section: Statement Of the Problemmentioning

confidence: 98%

On deterministic error analysis in variational data assimilation

Dimet

Shutyaev

2005

Nonlin. Processes Geophys.

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“…The algorithms and the results of calculations carried out for the adjoint sensitivity functions were presented at the Joint UITAM/IUGG International Symposium on Monsoon dynamics in Delhi (1977) [16]. The development of methods for environmental problems was continued in [14,15]. A detailed description of the variational methods for the construction of numerical models, sensitivity theory methods, and organisation of numerical modelling for the atmosphere, ocean and transport of pollutants were given in [18].…”

Section: Introductionmentioning

confidence: 99%

Discrete-analytical methods for the implementation of variational principles in environmental applications

Penenko

Tsvetova

2009

Journal of Computational and Applied Mathematics

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a r t i c l e i n f o MSC: 58E30 76R99 49Q12 81T80 65M06 65M32 65N99 65K10 Keywords: Variational principle Convection-diffusion Monotonic scheme Discrete-analytical approximation Numerical environment modelling Adjoint sensitivity problem Direct and inverse modelling a b s t r a c tA new method of constructing numerical schemes on the base of a variational principle for models including convection-diffusion operators is proposed. An original element is the use of analytical solutions of local adjoint problems formulated for the operators of convectiondiffusion within the framework of the splitting technique. This results in numerical schemes which are absolutely stable, monotonic, transportive, and differentiable with respect to the state functions and parameters of the model. Artificial numerical diffusion is avoided due to the analytical solutions. The variational technique provides strong consistency between the numerical schemes of the main and adjoint problems. A theoretical study of the new class of schemes is given. The quality of the numerical approximations is demonstrated by an example of the non-linear Burgers equation. These new schemes enhance our variational methodology of environmental modelling. As one of the environmental applications, an inverse problem of risk assessment for Lake Baikal is presented.

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“…The use of the theory of adjoint equations was an important step in this direction (LIONS, 1968;MARCHUK, 1995, MARCHUK et al 1996. Beginning with well-known works (PENENKO 1976;MARCHUK and PENENKO 1978;LE DIMET and TALA-GRAND, 1986), adjoint equations have been used extensively by many researchers to investigate and numerically solve data assimilation problems and to calculate the gradient of the functional (AGOSHKOV and MARCHUK, 1993;MARCHUK and ZALESNY, 1993;MARCHUK and SHUTYAEV, 1994;WENZEL et al 2001;COURTIER et al 1998;SHUTYAEV, 2001;BENNETT, 2002;AGOSHKOV et al, 2005, 2008, ZALESNY and RUSAKOV, 2007BLUM et al, 2008;ZALESNY and GUSEV, 2009;NAVON, 2009). Currently, growing interest is being aroused by four-dimensional data assimilation (4DVAR), which uses forward and adjoint models for observational data assimilation not at a concrete moment in time but rather in a specified time interval (BLUM et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics

Agoshkov

Zalesny

2011

Pure Appl. Geophys.

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Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.

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Application of optimization methods to the problem of mathematical simulation of atmospheric processes and environment

Cited by 39 publications

References 1 publication

On deterministic error analysis in variational data assimilation

On deterministic error analysis in variational data assimilation

Discrete-analytical methods for the implementation of variational principles in environmental applications

Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics

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