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  • 1
    Electronic Resource
    Electronic Resource
    Identification of wind stress on shallow water surfaces by optimal smoothing (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 105-119 
    Details
    ISSN: 1436-3259
    Keywords: Kalman filtering ; Optimal smoothing ; Shallow water equations ; Wind stress ; On-line prediction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Using the state space approach, an on-line filter procedure for combined wind stress identification and tidal flow forecasting is developed. The stochastic dynamic approach is based on the linear twodimensional shallow water equations. Using a finite difference scheme, a system representation of the model is obtained. To account for uncertainties, the system is embedded into a stochastic environment. By employing a Kalman filter, the on-line measurements of the water-level available can be used to identify and predict the shallow water flow. Because it takes a certain time before a fluctuation in the wind stress can be noticed in the water-level measurements, an optimal fixed-lag smoother is used to identify the stress.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543285
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  • 2
    Electronic Resource
    Electronic Resource
    Practical aspects of stochastic dynamic tidal modelling (1988)
    Springer
    Stochastic environmental research and risk assessment 2 (1988), S. 137-150 
    Details
    ISSN: 1436-3259
    Keywords: shallow water equations ; Kalman filtering ; data assimilation ; observability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Kalman filtering for stochastic dynamic tidal models, is a hyperbolic filtering problem. The questions of observability and stability of the filter as well as the effects of the finite difference approximation on the filter performance are studied. The degradation of the performance of the filter, in case an erroneous filter model is used, is investigated. In this paper we discuss these various practical aspects of the application of Kalman filtering for tidal flow identification problems. Filters are derived on the basis of the linear shallow water equations. Analytical methods are used to study the performance of the filters under a variety of circumstances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543456
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  • 3
    Electronic Resource
    Electronic Resource
    Stochastic modelling of dispersion in shallow water (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 161-174 
    Details
    ISSN: 1436-3259
    Keywords: advection-diffusion equation ; random walk model ; random flight model ; stochastic differential equation ; Fokker-Planck equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A random walk model to describe the dispersion of pollutants in shallow water is developed. By deriving the Fokker-Planck equation, the model is shown to be consistent with the two-dimensional advection-diffusion equation with space-varying dispersion coefficient and water depth. To improve the behaviour of the model shortly after the deployment of the pollutant, a random flight model is developed too. It is shown that over long simulation periods, this model is again consistent with the advection-diffusion equation. The various numerical aspects of the implementation of the stochastic models are discussed and finally a realistic application to predict the dispersion of a pollutant in the Eastern Scheldt estuary is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543289
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  • 4
    Electronic Resource
    Electronic Resource
    Parameter identification in tidal models with uncertain boundary conditions (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 193-208 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic tidal modeling ; parameter identification ; model calibration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543083
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  • 5
    Electronic Resource
    Electronic Resource
    Tidal flow forecasting using reduced rank square root filters (1997)
    Springer
    Stochastic environmental research and risk assessment 11 (1997), S. 349-368 
    Details
    ISSN: 1436-3259
    Keywords: Data assimilation ; Kalman filter ; Square root filter
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The Kalman filter algorithm can be used for many data assimilation problems. For large systems, that arise from discretizing partial differential equations, the standard algorithm has huge computational and storage requirements. This makes direct use infeasible for many applications. In addition numerical difficulties may arise if due to finite precision computations or approximations of the error covariance the requirement that the error covariance should be positive semi-definite is violated. In this paper an approximation to the Kalman filter algorithm is suggested that solves these problems for many applications. The algorithm is based on a reduced rank approximation of the error covariance using a square root factorization. The use of the factorization ensures that the error covariance matrix remains positive semi-definite at all times, while the smaller rank reduces the number of computations and storage requirements. The number of computations and storage required depend on the problem at hand, but will typically be orders of magnitude smaller than for the full Kalman filter without significant loss of accuracy. The algorithm is applied to a model based on a linearized version of the two-dimensional shallow water equations for the prediction of tides and storm surges. For non-linear models the reduced rank square root algorithm can be extended in a similar way as the extended Kalman filter approach. Moreover, by introducing a finite difference approximation to the Reduced Rank Square Root algorithm it is possible to prevent the use of a tangent linear model for the propagation of the error covariance, which poses a large implementational effort in case an extended kalman filter is used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02427924
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  • 6
    Electronic Resource
    Electronic Resource
    Parameter identification in particle models (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 109-130 
    Details
    ISSN: 1436-3259
    Keywords: Particle models ; transport equations ; parameter identification ; adjoint modelling ; cost function ; gradient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract For the simulation of the transport of dissolved matter particle models can be used. In this paper a technique is developed for the identification of uncertain parameters in these models. This model calibration is formulated as an optimization problem and is solved with a gradient based algorithm. Here adjoint particle tracks are used for the calculation of the gradient of the cost function. The performance of the calibration method is illustrated by simulations and an application to a river Rhine water quality calamity in November 1986.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581420
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  • 7
    Electronic Resource
    Electronic Resource
    Identification of shallow sea models (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 637-665 
    Details
    ISSN: 0271-2091
    Keywords: Tidal models ; Maximum likelihood ; Modelling uncertain boundaries ; Parameter estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we consider a parameter estimation procedure for shallow sea models. The method is formulated as a minimization problem. An adjoint model is used to calculate the gradient of the criterion which is to be minimized. In order to obtain a robust estimation method, the uncertainty of the open boundary conditions can be taken into acoount by allowing random noise inputs to act on the open boundaries. This method avoids the possibility that boundary errors are interpreted by the estimation procedure as parameter fluctuations. We apply the parameter estimation method to identify a shallow sea model of the entire European continental shelf. First, a space-varying bottom friction coefficient is estimated simultaneously with the depth. The second application is the estimation of the parameterization of the wind stress coefficient as a function of the wind velocity. Finally, an uncertain open boundary condition is included. It is shown that in this case the parameter estimation procedure does become more robust and produces more realistic estimates. Furthermore, an estimate of the open boundary conditions is also obtained.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170802
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  • 8
    Electronic Resource
    Electronic Resource
    Data assimilation for non-linear tidal models (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 1097-1112 
    Details
    ISSN: 0271-2091
    Keywords: Data assimilation ; Kalman filtering ; Shallow water equations ; Water level measurements On-line prediction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A data assimilation procedure to incorporate measurements into a non-linear tidal model by using Kalman-filtering techniques is developed. The Kalman filter is based on the two-dimensional shallow water equations. To account for the inaccuracies, these equations are embedded into a stochastic environment by introducing a coloured system noise process into the momentum equations. The continuity equation is assumed to be perfect. The deterministic part of the equations is discretized using an ADI method, the stochastic part using the Euler scheme. Assuming that the system noise is less spatially variable than the underlying water wave process, this stochastic part can be approximated on a coarser grid than the grid used to approximate the deterministic part. A Chandrasekhar-type filter algorithm is employed to obtain the constant-gain extended Kalman filter for weakly non-linear systems. The capabilities of the filter are illustrated by applying it to the assimilation of water level measurements into a tidal model of the North Sea.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110804
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  • 9
    Electronic Resource
    Electronic Resource
    Adaptive harmonic analysis (1991)
    Springer
    Ocean dynamics 44 (1991), S. 91-106 
    Details
    ISSN: 1616-7228
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Description / Table of Contents: Zusammenfassung In diesem Artikel beschreiben wir eine neue Methode zur harmonischen Analyse der Gezeiten. Aus verschiedenen Gründen sind die harmonischen Konstanten nicht wirklich konstant, sondern sie variieren mit der Zeit. Deshalb führen, wir einen stochastischen Prozeß ein, um das zeitvariable Verhalten dieser harmonischen Parameter zu modellieren. Außerdem führen wir auch einen möglichst zeitvariablen stochastischen Prozeß bei den Messungen ein, um Meßfehler zu modellieren, weil die vorhandenen Messungen nicht perfekt sind. Bei der Anwendung eines Kalmanfilters zur rekursiven Beurteilung der harmonischen Parameter können diese Wertungen sich ändernden Bedingungen laufend angepaßt werden. Die angepaßte harmonische Analyse kann man für die Berechnung der astronomischen Gezeiten benutzen, oder, weil das Kalmanfilter auch die Kovarianz des Bewertungsfehlers liefert, um einen quantitativen Einblick in die Auflösung von Gezeitenkonstanten zu gewinnen.
    Notes: Summary In this paper we describe a new approach to the harmonic analysis of the tide. For a number of reasons the harmonic “constants” are not really constant but vary slowly in time. Therefore, we introduce a narrow-band noise process to model the time-varying behaviour of these harmonic parameters. Furthermore, since the measurements available are not perfect, we also introduce a, possibly time-varying, measurement noise process to model the errors associated with the measurement process. By employing a Kalman filter to estimate the harmonic parameters recursively, the estimates can be adapted contineously to chaning conditions. The adaptive harmonic analysis can be used for the on-line prediction of the astronomical tide or, since the Kalman filter also produces the covariance of the estimation error, to gain quantitative insight into the resolution of tidal constituents.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02226429
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  • 10
    Electronic Resource
    Electronic Resource
    Assimilation of ERS-1 altimeter data in a tidal model of the continental shelf (1994)
    Springer
    Ocean dynamics 46 (1994), S. 285-319 
    Details
    ISSN: 1616-7228
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden ERS-1 Altimeter Daten zum Kalibrieren eines Gezeitenmodells des Europäischen Kontinentalschelfs benutzt. Das Verfahren der Datenassimilation zur Bestimmung der unbekannten Modellparameter beruht auf der adjungierten Methode. Die Aufgabe ist ein großskaliges Optimierungsproblem, das mit einem Gradientenverfahren gelöst wird. Zur Gradientenbestimmung benutzt man die Lösung des adjungierten Problems. Neben den Daten von ERS-1 werden wahlweise noch Beobachtungen von Küstenpegeln assimiliert.
    Notes: Summary In this paper ERS-1 altimeter data are used for the calibration of a tidal model of the European Continental Shelf. The data assimilation procedure to estimate the uncertain parameters in the model is based on the adjoint method. Here the estimation problem is formulated as a large scale optimization problem, that is solved with a gradient based optimization method. The gradient is determined efficiently by using the solution of the adjoint problem. The data assimilation procedure is applied by using the ERS-1 data with and without other measurement information from water level stations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02226308
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