As is well known, numerical models are far from perfect. Time series of real-world observations are increasingly valuable as they provide information of what is actually happening in nature as compared to the results obtained from the numerical models. The observations help us to understand nature better and provide us with better forecasts.
Data mining is concerned with searching for the valuable information from large data sets. New approaches emerging in this area are not limited to traditional methods.
Chaos theory is one such new research field. Chaotic time series generate quite irregular and broadband power spectra. However, chaotic systems can be generated also from deterministic systems with low number of degrees of freedom. With the development of insights into chaos theory, state space reconstruction using embedding techniques, and dynamics reconstruction by families of local models, this approach provides a tool for the time series analysis and the short-term prediction of such systems.
So far most of the research in this area has been based on scalar chaos analysis. Multivariate time series analysis is a quite new and attractive area. For systems polluted by noise, there is no doubt that multivariate time series techniques can give better information than do standard scalar analyse. In this study, a multidimensional technique has been implemented and employed in a test on the Lorenz model and a data assimilation problem. The multivariate technique gives better result than scalar analysis in both cases.
MIKE 21 is a widely used deterministic modelling system for two-dimensional unsteady flow, such as occur in lakes and coastal areas. Data assimilation is an approach which combines observations with the operation of a numerical model. In this study, a data assimilation based on a multivariate chaotic technique has been implemented. The state space is reconstructed based on the MIKE 21 modelling results on finite difference grid points. The error prediction is carried out on the basis of the reconstruction of the dynamics using a local model. Three kinds of noise were introduced into the model, namely from boundary conditions, resistance coefficients, and wind force terms. This data assimilation method gives very reasonable results, comparable with those obtained using Kalman filtering techniques, and it is most likely that this technique will be extended into other areas. The chaotic error prediction technique built in this study has proved successful and provides a new approach to the problem of data assimilation.
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