Modelování syntetických hydrologických řad v systému stanic

Abstract

Based on its applicability and features, two approaches for multivariate time series modelling were discussed. The first, method based Principal Component Analysis is much more simple and direct method, having the advantage of closed form computational processes and therefore holding much smaller computational burden. Its disadvantage is, that it theoretically destroys part of the mutual information that the multivariate data contain, because it preserves only raw mutual correlations between stations but not higher order dependencies. The basis is that it searches for transformation that has been designed based on the covariance matrix, which is a low order statistical characteristic of data. The second, method based on Independent component analysis, theoretically preserves even those higher order dependencies, because it extracts from the data more mutual information and is therefore able to reapply this information to independent univariate synthetic time series that were generated individually. The practical part of this thesis involved construction of the PCA method based multivariate model and evaluation of its performance. Regarding the preservation of the correlation structure the model performed arguably quite well, having total error as a performance measure explained in section 7.4 around 3.40% for the autocorrelation structure of lag 1 of the data set and total error of 7.86% for the cross-correlation structure describing mutual relationships of the multivariate data. In traditional applications of streamflow data the generated time series did not deviate extensively from expected outcomes, making the model's output usable in some classical water management solutions. However, there were some drawback of the model's performance especially in water reservoir operation solutions, where the model produced data that underestimated storage capacity requirements for longer time series.Based on its applicability and features, two approaches for multivariate time series modelling were discussed. The first, method based Principal Component Analysis is much more simple and direct method, having the advantage of closed form computational processes and therefore holding much smaller computational burden. Its disadvantage is, that it theoretically destroys part of the mutual information that the multivariate data contain, because it preserves only raw mutual correlations between stations but not higher order dependencies. The basis is that it searches for transformation that has been designed based on the covariance matrix, which is a low order statistical characteristic of data. The second, method based on Independent component analysis, theoretically preserves even those higher order dependencies, because it extracts from the data more mutual information and is therefore able to reapply this information to independent univariate synthetic time series that were generated individually. The practical part of this thesis involved construction of the PCA method based multivariate model and evaluation of its performance. Regarding the preservation of the correlation structure the model performed arguably quite well, having total error as a performance measure explained in section 7.4 around 3.40% for the autocorrelation structure of lag 1 of the data set and total error of 7.86% for the cross-correlation structure describing mutual relationships of the multivariate data. In traditional applications of streamflow data the generated time series did not deviate extensively from expected outcomes, making the model's output usable in some classical water management solutions. However, there were some drawback of the model's performance especially in water reservoir operation solutions, where the model produced data that underestimated storage capacity requirements for longer time series.