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.
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References
Abbott, M.B. 1979: Computational Hydraulics. Pitman: London
Brummelhuis, P.G.J. ten.; De Jong, B.; Heemink, A.W. 1984: On-line prediction of water-levels in an estuary using Kalman filters. Proceedings of the 4th Int. Symp. on Stochastic Hydraulic. Urbana-Champaign, 153–166
Brummelhuis, P.G.J. Ten.; De Jong, B.; Heemink, A.W. 1988: A stochastic dynamic approach to predict water-levels in estuaries. J. of Hydraulic Engineering (to appear)
Budgell, W.P.; Unny, T.E. 1980: A stochastic-deterministic model for predicting tides in branched estuaries. Proceedings of the 3rd Int. Symp. on Stochastic Hydraulics. Tokyo, 485–496
Budgell, W.P. 1986: Nonlinear data assimilation for shallow water equations in branched channels. J. of Geophysical Research. 91, 633–644
Goodson, R.E.; Klein, R.E. 1970: Definition and some results for distributed system observability. IEEE Trans. Autom. Control. 15, 165–174
Goodson, R.E.; Klein, R.E. 1971: Authors reply to: comments on a definition and some results for distributed system observability. IEEE Trans. Autom. Control. 16, 106
Heemink, A.W. 1986: Storm surge prediction using Kalman filtering. Ph. D. Thesis, University Twente (also appeared as: Rijkswaterstaat Communications No. 46, Rijkswaterstaat, The Hague, 1986)
Heemink, A.W.; De Jong, B. 1982: The use of Kalman-Bucy filters in forecasting the water-levels in the Dutch coastal area. Proceedings of the 4th Int. Conf. on Finite Elements in Water Resour. Berlin: Springer-Verlag, 557–566
Jazwinski, A.H. 1970: Stochastic processes and filtering theory. New York: Academic Press
Kwakernaak, H.; Sivan, R. 1972: Linear optimal control systems. New York: Wiley-Interscience
Liggett, J.A.; Cunge, J.A. 1975: Numerical methods of solution of the unsteady flow equations. In: Mahmoed, K.; Yevjevich, V. (eds.) Unsteady flow in open channels. Water Resour. Publications. Fort Collins, 89–182
Maybeck, P.S. 1979: Stochastic models, estimation and control. I. New York: Academic Press
Miller, R.N. 1986: Toward the application of the Kalman-Bucy filter to regional open ocean modelling. J. of Physical Oceanography. 16, 72–86
Parrish, D.F.; Cohn, S.E. 1985: A Kalman filter for two-dimensional shallow water model: formulation and preliminary experiments. National Meteorological Center, Office Note 304, DC 20233, Washington
Ritchmyer, R.W.; Morton, K.W. 1967: Difference methods for initial value problems. New York: Wiley-Interscience
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Heemink, A.W. Practical aspects of stochastic dynamic tidal modelling. Stochastic Hydrol Hydraul 2, 137–150 (1988). https://doi.org/10.1007/BF01543456
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DOI: https://doi.org/10.1007/BF01543456