Volume 16, Issue 1 (3-2026)
J Watershed Manage Res 2026, 16(1): 121-132 |
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Jandaghi N, Ghare Mahmoodlu M, Azimmohseni M, Khalafi M. (2026). Spectral Clustering of Precipitation Time Series in Golestan Province. J Watershed Manage Res. 16(1), 121-132. doi:10.61882/jwmr.2024.1282
URL: http://jwmr.sanru.ac.ir/article-1-1282-en.html
URL: http://jwmr.sanru.ac.ir/article-1-1282-en.html
1- Department of Rangeland and Watershed Management, Faculty of Agriculture and Natural Resources, University of Gonbad Kavous, Gonbad Kavous, Iran
2- Department of Rangeland and Watershed Management, Faculty of Agriculture and Natural Resources, University of Gonbad Kavous
3- Faculty of Sciences, Department of Statistics, Golestan University, Gorgan, Iran
2- Department of Rangeland and Watershed Management, Faculty of Agriculture and Natural Resources, University of Gonbad Kavous
3- Faculty of Sciences, Department of Statistics, Golestan University, Gorgan, Iran
Abstract: (924 Views)
Extended Abstract
Background: 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. A periodically correlated time series is a type of non-stationary time series with a periodic covariance function. Since there is periodic behavior in time series observed in hydrology, meteorology, climatology, etc., the use of periodically correlated time series has attracted the attention of experts in 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 a time series. In this approach, time series are studied using Fourier transforms, which are functions of frequency. The clustering of meteorological stations in terms of precipitation time series provides important information about a geographical area and plays an important role in water resources management in that area. The main purpose of this research is to calculate the distance between the monthly precipitation 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.
Methods: In this research, the monthly precipitation time series of 34 meteorological stations in Golestan Province were collected over a common period of 15 years from the Regional Water Company of Golestan. Considering that monthly precipitation values are time-dependent, these data were first arranged as a time series. Because of the dispersion of precipitation 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 precipitation data has a period of 12, they can be studied as periodically correlated time series. In this research, the periodically correlated time series of monthly precipitation was clustered in the spectral domain. First, the distance between the monthly precipitation times series of meteorological stations in the frequency domain was measured based on the periodic multiple correlation coefficient index. Then, clustering was performed by a fuzzy method based on the calculated distance matrix. After calculating the distance matrix, clustering was also done using the k-means method. The mean square error index of monthly precipitation was used and the results were compared to compare the accuracy of the clustering methods. All calculations of this research were done in MINITAB 17 and R 4.3.1 software.
Results: Investigating the seasonal trend for the monthly precipitation time series revealed 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 two methods of fuzzy and k-means clustering, eight groups were identified for 34 selected meteorological stations in Golestan Province. The largest and smallest groups in fuzzy clustering included eight and one stations, respectively, and seven and one meteorological stations in the k-means method. Comparing the accuracy of the methods based on the mean square error index showed that the value of this index for the fuzzy clustering method was 13.67, while this index was calculated at 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 precipitation changes in the meteorological stations assigned to each group, which indicates the accuracy of the spectral domain method along with the fuzzy clustering.
Conclusion: In this research, the distance between the monthly percipitation time series of 34 meteorological stations in Golestan Province was measured in the frequency domain based on the alternating multiple correlation index. Then, the selected meteorological stations were clustered in the spectral domain based on fuzzy and k-means clustering methods, and eight groups were identified in each method. The mean square error index for fuzzy and k-means clustering methods was calculated at 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 was almost 12 times higher than the usual k-means method. The similar trend of changes in the monthly precipitation 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 precipitation. In addition to the simplicity and accuracy of the clustering method in the frequency domain, the other advantage is to consider the periodic structure of time series in clustering. Furthermore, spectral clustering can be used for time series with unequal lengths recorded in hydrological studies.
Background: 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. A periodically correlated time series is a type of non-stationary time series with a periodic covariance function. Since there is periodic behavior in time series observed in hydrology, meteorology, climatology, etc., the use of periodically correlated time series has attracted the attention of experts in 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 a time series. In this approach, time series are studied using Fourier transforms, which are functions of frequency. The clustering of meteorological stations in terms of precipitation time series provides important information about a geographical area and plays an important role in water resources management in that area. The main purpose of this research is to calculate the distance between the monthly precipitation 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.
Methods: In this research, the monthly precipitation time series of 34 meteorological stations in Golestan Province were collected over a common period of 15 years from the Regional Water Company of Golestan. Considering that monthly precipitation values are time-dependent, these data were first arranged as a time series. Because of the dispersion of precipitation 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 precipitation data has a period of 12, they can be studied as periodically correlated time series. In this research, the periodically correlated time series of monthly precipitation was clustered in the spectral domain. First, the distance between the monthly precipitation times series of meteorological stations in the frequency domain was measured based on the periodic multiple correlation coefficient index. Then, clustering was performed by a fuzzy method based on the calculated distance matrix. After calculating the distance matrix, clustering was also done using the k-means method. The mean square error index of monthly precipitation was used and the results were compared to compare the accuracy of the clustering methods. All calculations of this research were done in MINITAB 17 and R 4.3.1 software.
Results: Investigating the seasonal trend for the monthly precipitation time series revealed 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 two methods of fuzzy and k-means clustering, eight groups were identified for 34 selected meteorological stations in Golestan Province. The largest and smallest groups in fuzzy clustering included eight and one stations, respectively, and seven and one meteorological stations in the k-means method. Comparing the accuracy of the methods based on the mean square error index showed that the value of this index for the fuzzy clustering method was 13.67, while this index was calculated at 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 precipitation changes in the meteorological stations assigned to each group, which indicates the accuracy of the spectral domain method along with the fuzzy clustering.
Conclusion: In this research, the distance between the monthly percipitation time series of 34 meteorological stations in Golestan Province was measured in the frequency domain based on the alternating multiple correlation index. Then, the selected meteorological stations were clustered in the spectral domain based on fuzzy and k-means clustering methods, and eight groups were identified in each method. The mean square error index for fuzzy and k-means clustering methods was calculated at 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 was almost 12 times higher than the usual k-means method. The similar trend of changes in the monthly precipitation 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 precipitation. In addition to the simplicity and accuracy of the clustering method in the frequency domain, the other advantage is to consider the periodic structure of time series in clustering. Furthermore, spectral clustering can be used for time series with unequal lengths recorded in hydrological studies.
Keywords: Fuzzy Clustering, Golestan Province, K-means Method, Monthly Precipitation, Seasonal Trend
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