Using Hierarchical Clustering in Order to Increase Efficiency of Self-Organizing Feature Map to Identify Hydrological Homogeneous Regions for Flood Estimation

آب و خاک

Article 7, Volume 29, Issue 5, November 2015, Pages 1207-1218   

Document Type: Research Article

DOI: 10.22067/jsw.v29i5.34143

Authors

F. Farsadnia^* ; B. Ghahreman

Ferdowsi University of Mashhad

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. 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

Keywords

Principal component analysis; Regional flood frequency analysis; Hybrid clustering; Linear moments

References

1- Chavoshi S., Azmin Sulaiman W.N., Saghafian B., Sulaiman MD. N.B. and Latifah A.M. 2012. Soft and hard clustering methods for delineation of hydrological homogeneous regions in the southern strip of the Caspian Sea Watershed, Journal of Flood Risk Management, 5 (4): 282–294.

2- Di Prinzio M., Castellarin A., and Toth E. 2011. Data-driven catchment classification: application to the pub problem. Hydrol, Earth System Sci, 15 (6): 1921–1935.

3- Farsadnia F., and Moghaddamnia A. 2014. Regional Flood Frequency Analysis by Self-Organizing Feature Maps and Fuzzy Clustering Approach, Iran-Water Resources Research, 9 (3): 24-36.

4- Farsadnia F., Rostami Kamrood M., Moghaddam Nia A., Modarres R., Bray M.T., Han D., and Sadatinejad, J. 2014. Identification of homogeneous regions for regionalization of watersheds by two-level self-organizing feature maps, Journal of Hydrology, 509: 387–397.

5- Haykin S. 2003. Neural Networks: A Comprehensive Foundation. Fourth Indian Reprint, Pearson Education, Singapore.

6- Hosking J.R.M. 1986. The theory of probability weighted moments. Res. Rep. RC 12210, IBM Research Division, Yorktown Heights, NY.

7- Hosking J.R.M. 1991. Fortran routines for use with the method of L-moments, Version 2, Res. Rep. RC 17097, IBM Research Division, York Town Heights, NY 10598.

8- Hosking J.R.M. and Wallis J.R. 1993. Some statistics useful in regional frequency analysis, Water Resources Research, 29: 271–281.

9- Hosking J.R.M. and Wallis J.R. 1997. Regional frequency analysis: An approach based on L-moments, Cambridge University Press, New York.

10- Kohonen T. 1982. Self-organized formation of topologically correct feature maps, Biological Cybernetics, 43: 59–69.

11- Kohonen T. 2001. Self-Organizing Maps. Springer, Berlin, Germany.

12- Lampinen J. and Oja E. 1992. Clustering properties of hierarchical self-organizing maps, Journal of Mathematical Imaging and Vision, 2: 261–272.

13- Ley R., Casper M.C., Hellebrand H., and Merz R. 2011. Catchment classification by runoff behavior with self-organizing maps (SOM), Hydrology and Earth System Sciences, 15(9): 2947-2962.

14- Lin G. and Wang C. 2006. Performing cluster analysis and discrimination analysis of hydrological factors in one step, Advances in Water Resources, 29: 1573-1585.

15- Niromand H. 1999. Multivariate statistical analysis. Ferdowsi university of Mashhad Press, Mashhad.

16- Roa A.R., and Srinivas V.V. 2008. Regionalization of Watersheds (an approach based on cluster analysis), Speringer.

17- Shamkoueyan H., Ghahraman B., Davary K., and Sarmad M. 2009. Flood frequency analysis using linear moment and flood index method in Khorasan provinces, Journal of Water and Soil, 23(1): 31-43.

18- Vesanto J. and Alhoniemi R. 2000. Clustering of the self organizing map, IEEE Trans. Neural, Netw, 11 (3): 586-600.

19- Vesanto J., Himberg J., Alhoniemi E., and Parhankangas J. 2000. SOFM Toolbox for Matlab 5, Technical Report A57, Neural Networks Research Centre, Helsinki University of Technology, Helsinki, Finland.

20- Ward Jr. 1963. Hierarchical Grouping to Optimize an Objective Function, Journal of the American Statistical Association, 58 (301): 236–244.

21- Wilppu R. 1997. The Visualisation Capability of Self Organizing Maps to Detect Deviation in Distribution Control. TUCS Technical Report No. 153, Turku Centre for Computer Science, Finland.