The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

System Identification I

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

Thank you for reading stochastic processes and filtering theory. Maybe you have knowledge that, people have look numerous times for their favorite novels like this stochastic processes and filtering theory, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their computer. stochastic processes and filtering theory is available in our digital library an online access to it is set as public so you can download it instantly. Our digital library saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the stochastic processes and filtering theory is universally compatible with any devices to read.

Stochastic Processes And Filtering Theory

OpenModelica is a unique large-scale integrated open-source Modelicaand FMI-based modeling, simulation, optimization, model-based analysis and development environment. Moreover, the OpenModelica environment provides a number of facilities such as debugging; optimization; visualization and 3D animation; web-based model editing and simulation; scripting from Modelica, Python, Julia, and Matlab; efficient simulation and co-simulation of FMI-based models; compilation for embedded systems; ModelicaUML integration; requirement verification; and generation of parallel code for multi-core architectures. The environment is based on the equation-based object-oriented Modelica language and currently uses the MetaModelica extended version of Modelica for its model compiler implementation. This overview paper gives an up-to-date description of the capabilities of the system, short overviews of used open source symbolic and numeric algorithms with pointers to published literature, tool integration aspects, some lessons learned, and the main vision behind its development.

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The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development

Because of the adverse effect of CO2 from fossil fuel combustion on the earth’s ecosystems, the most cost‐effective method for CO2 capture is an important area of research. The predominant process ...

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A simulation study on the abatement of CO2 emissions by de‐absorption with monoethanolamine

Free oxygen effects in bio-gasification are not well known, apart from the common understanding of oxygen being toxic and inhibitory for anaerobic micro-organisms. Some studies have, however, revealed increased solubilisation of organic matter in the presence of some free oxygen in anaerobic digestion. This article analyses these counterbalancing phenomena with a mathematical modelling approach using the widely accepted biochemical model ADM 1. Aerobic oxidation of soluble carbon and inhibition of obligatory anaerobic organisms are modelled using standard saturation type kinetics. Biomass dependent first order hydrolysis kinetics is used to relate the increased hydrolysis rate with oxygen induced increase in biomass growth. The amended model, ADM 1-Ox (oxygen), has 25 state variables and 22 biochemical processes, presented in matrix form. The computer aided simulation tool AQUASIM 2.1 is used to simulate the developed model. Simulation predictions are evaluated against experimental data obtained using a laboratory batch test array comprising miniature anaerobic bio-reactors of 100 ml total volume each, operated under different initial air headspaces giving rise to the different oxygen loading conditions. The reactors were initially fed with a glucose solution and incubated at 35  for 563 hours. Under the oxygen load conditions of 22, 44 and 88 mg/L, the ADM1-Ox model simulations predicted the experimental methane potentials quite adequately. Both the experimental data and the simulations suggest a linear reduction of methane potential with respect to the increase in oxygen load within this range.

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Oxygen Effects in Anaerobic Digestion

Standard models describing bio-gasication using anaerobic digestion do not include necessary processes to describe digester dynamics under the conditions of oxygen presence. Limited oxygenation in anaerobic digestion can sometimes be benecial. The oxygen eects included anaerobic digestion model, ADM 1Ox, was simulated against experimental data obtained from laboratory scale anaerobic digesters operated under dierent oxygenation conditions. ADM 1-Ox predictions are generally in good agreement with the trends of the experimental data. ADM 1-Ox simulations suggest the existence of an optimum oxygenation level corresponding to a peak methane yield. The positive impact of oxygenation on methane yield is more pronounced at conditions characterized by low hydrolysis rate coecients (slowly degradable feed) and low biomass concentrations. The optimum oxygenation point moves towards zero when the hydrolysis rate coecient and the biomass concentration increase. Accordingly, the impact of oxygenation on methane yield can either be positive or negative depending on the digestion system characteristics. The developed ADM 1-Ox model can therefore be a valuable tool for recognizing suitable operating conditions for achieving the maximum benets from

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Bernt Lie

Papers

The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development

A simulation study on the abatement of CO2 emissions by de‐absorption with monoethanolamine

Oxygen Effects in Anaerobic Digestion

Oxygen Effects in Anaerobic Digestion II

Amine based CO2 capture plant: Dynamic modeling and simulations