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.
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.
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Heemink, A., de Jong, B. & Prins, H. Adaptive harmonic analysis. Deutsche Hydrographische Zeitschrift 44, 91–106 (1991). https://doi.org/10.1007/BF02226429
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DOI: https://doi.org/10.1007/BF02226429