F. Farsadnia; B. Ghahreman
Abstract
Introduction: Hydrologic homogeneous group identification is considered both fundamental and applied research in hydrology. Clustering methods are among conventional methods to assess the hydrological homogeneous regions. Recently, Self Organizing feature Map (SOM) method has been applied in some studies. ...
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Introduction: Hydrologic homogeneous group identification is considered both fundamental and applied research in hydrology. Clustering methods are among conventional methods to assess the hydrological homogeneous regions. Recently, Self Organizing feature Map (SOM) method has been applied in some studies. However, the main problem of this method is the interpretation on the output map of this approach. Therefore, SOM is used as input to other clustering algorithms. The aim of this study is to apply a two-level Self-Organizing feature map and Ward hierarchical clustering method to determine the hydrologic homogenous regions in North and Razavi Khorasan provinces.
Materials and Methods: SOM approximates the probability density function of input data through an unsupervised learning algorithm, and is not only an effective method for clustering, but also for the visualization and abstraction of complex data. The algorithm has properties of neighborhood preservation and local resolution of the input space proportional to the data distribution. A SOM consists of two layers: an input layer formed by a set of nodes and an output layer formed by nodes arranged in a two-dimensional grid. In this study we used SOM for visualization and clustering of watersheds based on physiographical data in North and Razavi Khorasan provinces. In the next step, SOM weight vectors were used to classify the units by Ward’s Agglomerative hierarchical clustering (Ward) methods. Ward’s algorithm is a frequently used technique for regionalization studies in hydrology and climatology. It is based on the assumption that if two clusters are merged, the resulting loss of information, or change in the value of objective function, will depend only on the relationship between the two merged clusters and not on the relationships with any other clusters. After the formation of clusters by SOM and Ward, the most frequently applied tests of regional homogeneity based on the theory of L-moments are used to compare and modify the clusters which are formed by clustering algorithms and find the best clustering method to achieve hydrologically homogeneous regions. Two statistical measures are used to form a homogeneous region, (i) discordancy measure and (ii) heterogeneity measure. The discordancy measure, Di, is used to find out unusual sites from the pooling group (i.e., the sites whose at-site sample L moments are markedly different from the other sites). Generally, any site with Di>3 is considered as discordant. The homogeneity of the region is evaluated using homogeneity measures which are based on sample L-moments (LCv, LCs and LCk), respectively. The homogeneity measures are based on the simulation of 500 homogeneous regions with population parameters equal to the regional average sample l-moment ratios. The value of the H-statistic indicates that the region under consideration is acceptably homogeneous when H
B. Ghahraman; K. Davary
Abstract
Due to inadequate flood data it is not always possible to fit a frequency analysis to at-site stations. Reliable results are not always guaranteed by a single clustering algorithm, so a combination of methods may be used. In this research, we considered three clustering algorithms: single linkge, complete ...
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Due to inadequate flood data it is not always possible to fit a frequency analysis to at-site stations. Reliable results are not always guaranteed by a single clustering algorithm, so a combination of methods may be used. In this research, we considered three clustering algorithms: single linkge, complete linkage and Ward (as hierarchial clustering methods), and K-mean (as partitional clustering analysis). Hybrid cluster analysis was tested for up-to-dated of floods data in 68 hydrometric stations in East and NE of Iran. Four cluster validity indices were used to find the optimum number of clusters. Based on the Cophenetic coefficient and average Silhouette width, single linkge, and complete linkage methods were performed well, yet they produced non-consistent clusters (one large and numerous small clusters) which are not amenable for flood frequency analysis. It was shown that hybridization was efficient to form homogeneous regions, however, the usefulness was dependent to the number of classes. Heterogeneity measure of Hosking was negative, due to inter-correlation of floods in the clusters. The hybrid of Ward and K-mean was shown to be the best combination for the region under study. Four homogeneous regions were delineated.
