1- University of Gonbad Kavous
2- Golestan University
2- Golestan University
Abstract: (592 Views)
Extended Abstract
Introduction and Objective: Clustering time series of precipitation and other hydrological elements by direct use of classic methods such as K-means can be misleading; because there is a time lagged correlation in time series observations that is ignored in classic methods. Periodically correlated time series is a type of non-stationary time series with periodic covariance function. Since, there is periodic behavior in time series observed in hydrology, meteorology, climatology, etc., therefore, the use of periodically correlated time series has attracted the attention of experts in the recent years. Time series data can be studied with two different approaches, time domain and frequency domain. Frequency domain is usually used to identify the structure of time series. In this approach, time series are studied using Fourier transforms that are functions of frequency. Clustering of meteorological stations in terms of percipitation time series provides important information about a geographical area and plays an important role in the water resources management in that area. The main purpose of this research is to calculate the distance between the monthly percipitation of meteorological stations based on the observations of periodically correlated time series in the frequency domain and then use a clustering method to group the meteorological stations. For clustering, the fuzzy clustering method is compared with the usual k-means clustering method.
Material and Methods: In this research, the monthly percipitation time series of 34 meteorological stations of Golestan province were collected in a common period of 15 years from the Regional Water Company of Golestan. Considering that the monthly percipitation values are time-dependent, at first these data were arranged as a time series. Because of the dispersion of percipitation values and the presence of zero values in a number of meteorological stations, the one-to-one transformation was used to stabilize the variance. Since, monthly percipitation data has period of 12 therefore they can be studied as periodically correlated time series. In this research, the clustering of periodically correlated time series of monthly percipitation was done in the spectral domain. First, the distance between the monthly percipitation times series of meteorological stations in the frequency domain was measured based on the periodic multiple correlation coefficient index. Then, based on the calculated distance matrix, clustering was performed by fuzzy method. Moreover, after calculating the distance matrix, clustering was also done using the k-means method. To compare the accuracy of the clustering methods, the mean square error index of monthly percipitation was used and the results were compared. All calculations of this research were done in MINITAB 17 and R 4.3.1 software.
Results: Investigating the seasonal trend for the monthly percipitation time series revealed that there is a period of 12 in all the selected meteorological stations of Golestan province, therefore these data were analyzed based on periodically correlated time series. The distance between meteorological stations was determined based on the periodic multiple correlation index. Then, using 2 methods of fuzzy and k-means clustering, 8 groups were identified for 34 selected meteorological stations in Golestan province. The largest and smallest groups in fuzzy clustering included 8 and 1 stations, respectively, and 7 and 1 meteorological stations in k-means method. Comparing the accuracy of the methods based on the mean square error index showed that the value of this index for fuzzy clustering method was 13.67, while this index was calculated as 165.11 in the k-means method. In this research, it was also found that the accuracy of the spectral domain method along with fuzzy clustering was almost 12 times higher than the spectral domain method based on the k-means method. Moreover, the investigation of the groups in the fuzzy clustering method shows the similarity of the precipitation changes in the meteorological stations assigned in each group, which indicates the accuracy of the spectral domain method along with the fuzzy clustering.
Conclusion: In this research, based on the alternating multiple correlation index the distance between the monthly percipitation time series of 34 meteorological stations in Golestan province was measured in the frequency domain. Then, the selected meteorological stations were clustered in the spectral domain based on fuzzy and k-means clustering methods, and 8 groups were identified in each method. The mean square error index for fuzzy and k-means clustering methods was calculated as 13.67 and 165.11, respectively. These values showed that the accuracy of the fuzzy method for clustering the monthly percipitation time series of the selected meteorological stations is almost 12 times higher than the usual k-means method. The similar trend of changes in monthly percipitation of meteorological stations assigned to each of the clusters shows the considerable efficiency of using the frequency domain method with fuzzy clustering for grouping periodically correlated time series such as monthly percipitation. In addition to the simplicity and accuracy of the clustering method in the frequency domain, the other advantage is considering the periodic structure of time series in clustering. Furthermore, the spectral clustering can be used for time series with unequal length recorded in hydrological studies.
Introduction and Objective: Clustering time series of precipitation and other hydrological elements by direct use of classic methods such as K-means can be misleading; because there is a time lagged correlation in time series observations that is ignored in classic methods. Periodically correlated time series is a type of non-stationary time series with periodic covariance function. Since, there is periodic behavior in time series observed in hydrology, meteorology, climatology, etc., therefore, the use of periodically correlated time series has attracted the attention of experts in the recent years. Time series data can be studied with two different approaches, time domain and frequency domain. Frequency domain is usually used to identify the structure of time series. In this approach, time series are studied using Fourier transforms that are functions of frequency. Clustering of meteorological stations in terms of percipitation time series provides important information about a geographical area and plays an important role in the water resources management in that area. The main purpose of this research is to calculate the distance between the monthly percipitation of meteorological stations based on the observations of periodically correlated time series in the frequency domain and then use a clustering method to group the meteorological stations. For clustering, the fuzzy clustering method is compared with the usual k-means clustering method.
Material and Methods: In this research, the monthly percipitation time series of 34 meteorological stations of Golestan province were collected in a common period of 15 years from the Regional Water Company of Golestan. Considering that the monthly percipitation values are time-dependent, at first these data were arranged as a time series. Because of the dispersion of percipitation values and the presence of zero values in a number of meteorological stations, the one-to-one transformation was used to stabilize the variance. Since, monthly percipitation data has period of 12 therefore they can be studied as periodically correlated time series. In this research, the clustering of periodically correlated time series of monthly percipitation was done in the spectral domain. First, the distance between the monthly percipitation times series of meteorological stations in the frequency domain was measured based on the periodic multiple correlation coefficient index. Then, based on the calculated distance matrix, clustering was performed by fuzzy method. Moreover, after calculating the distance matrix, clustering was also done using the k-means method. To compare the accuracy of the clustering methods, the mean square error index of monthly percipitation was used and the results were compared. All calculations of this research were done in MINITAB 17 and R 4.3.1 software.
Results: Investigating the seasonal trend for the monthly percipitation time series revealed that there is a period of 12 in all the selected meteorological stations of Golestan province, therefore these data were analyzed based on periodically correlated time series. The distance between meteorological stations was determined based on the periodic multiple correlation index. Then, using 2 methods of fuzzy and k-means clustering, 8 groups were identified for 34 selected meteorological stations in Golestan province. The largest and smallest groups in fuzzy clustering included 8 and 1 stations, respectively, and 7 and 1 meteorological stations in k-means method. Comparing the accuracy of the methods based on the mean square error index showed that the value of this index for fuzzy clustering method was 13.67, while this index was calculated as 165.11 in the k-means method. In this research, it was also found that the accuracy of the spectral domain method along with fuzzy clustering was almost 12 times higher than the spectral domain method based on the k-means method. Moreover, the investigation of the groups in the fuzzy clustering method shows the similarity of the precipitation changes in the meteorological stations assigned in each group, which indicates the accuracy of the spectral domain method along with the fuzzy clustering.
Conclusion: In this research, based on the alternating multiple correlation index the distance between the monthly percipitation time series of 34 meteorological stations in Golestan province was measured in the frequency domain. Then, the selected meteorological stations were clustered in the spectral domain based on fuzzy and k-means clustering methods, and 8 groups were identified in each method. The mean square error index for fuzzy and k-means clustering methods was calculated as 13.67 and 165.11, respectively. These values showed that the accuracy of the fuzzy method for clustering the monthly percipitation time series of the selected meteorological stations is almost 12 times higher than the usual k-means method. The similar trend of changes in monthly percipitation of meteorological stations assigned to each of the clusters shows the considerable efficiency of using the frequency domain method with fuzzy clustering for grouping periodically correlated time series such as monthly percipitation. In addition to the simplicity and accuracy of the clustering method in the frequency domain, the other advantage is considering the periodic structure of time series in clustering. Furthermore, the spectral clustering can be used for time series with unequal length recorded in hydrological studies.
Keywords: Monthly Percipitation, Seasonal Trend, Fuzzy Clustering, K-means Method, Golestan Province
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