1. bookVolume 65 (2017): Issue 4 (December 2017)
Journal Details
First Published
28 Mar 2009
Publication timeframe
4 times per year
access type Open Access

A novel fuzzy clustering approach to regionalise watersheds with an automatic determination of optimal number of clusters

Published Online: 07 Nov 2017
Page range: 359 - 365
Received: 13 Jul 2016
Accepted: 02 Dec 2016
Journal Details
First Published
28 Mar 2009
Publication timeframe
4 times per year

One of the most important problems faced in hydrology is the estimation of flood magnitudes and frequencies in ungauged basins. Hydrological regionalisation is used to transfer information from gauged watersheds to ungauged watersheds. However, to obtain reliable results, the watersheds involved must have a similar hydrological behaviour. In this study, two different clustering approaches are used and compared to identify the hydrologically homogeneous regions. Fuzzy C-Means algorithm (FCM), which is widely used for regionalisation studies, needs the calculation of cluster validity indices in order to determine the optimal number of clusters. Fuzzy Minimals algorithm (FM), which presents an advantage compared with others fuzzy clustering algorithms, does not need to know a priori the number of clusters, so cluster validity indices are not used. Regional homogeneity test based on L-moments approach is used to check homogeneity of regions identified by both cluster analysis approaches. The validation of the FM algorithm in deriving homogeneous regions for flood frequency analysis is illustrated through its application to data from the watersheds in Alto Genil (South Spain). According to the results, FM algorithm is recommended for identifying the hydrologically homogeneous regions for regional frequency analysis.


Agarwal, A., Maheswaran, R., Sehgal, V., Khosa, R., Sivakumar, B., Bernhofer, C., 2016. Hydrologic regionalization using wavelet-based multiscale entropy method. J. Hydrol., 538, 22-32.Search in Google Scholar

Arnoldus, H.B.J., 1980. An approximation of the rainfall in the universal soil loss equation. In: De Boodt, M., Gabriels, D. (Eds.), Assesment of Erosion. John Wiley & Sons, Chichester, pp. 127-132Search in Google Scholar

Bargaoui, Z.K., Fortin, V., Bobée, B., Duckstein, L., 1998. A fuzzy approach to the delineation of region of influence for hydrometric stations. Revue des sciences de l'eau 11, 2, 255-282. (In French.)Search in Google Scholar

Basu, B., Srinivas, V.V., 2014. Regional flood frequency analysis using kernel-based fuzzy clustering approach. Water Resour. Res., 50, 4, 3295-3316.10.1002/2012WR012828Open DOISearch in Google Scholar

Basu, B., Srinivas, V.V., 2015. Analytical approach to quantile estimation in regional frequency analysis based on fuzzy framework. J. Hydrol., 524, 30-43.Search in Google Scholar

Bellman, R., Kalaba, R., Zadeh, L.A., 1966. Abstraction and pattern classification. J. Math. Anal. Appl., 2, 581-585.Search in Google Scholar

Bezdek, J.C., 1974. Cluster validity with fuzzy sets. J. Cybernet., 3, 3, 58-73.Search in Google Scholar

Bezdek, J.C., 1981. Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York, 266 p.Search in Google Scholar

Burn, D.H., Zrinji, Z., Kowalchuk, M., 1997. Regionalization of catchments for regional flood frequency analysis. J. Hydrol. Eng., 2, 2, 76-82.Search in Google Scholar

Dikbas, F., Mahmut, F., Cem, K., Gungor, M., 2012. Classification of precipitation series using fuzzy cluster method. Int. J. Climatol., 32, 1596-1603.10.1002/joc.2350Open DOISearch in Google Scholar

Dunn, J.C., 1974. A fuzzy relative of the ISODATA process and its use in detecting compact well separated clusters. J. Cybernet., 3, 3, 32-57.Search in Google Scholar

Flores-Sintas, A., Cadenas, J.M., Martin, F., 1998. A local geometrical properties application to fuzzy clustering. Fuzzy Sets and Systems, 100, 237-248.Search in Google Scholar

Flores-Sintas, A., Cadenas, J.M., Martin, F., 1999. Membership functions in the Fuzzy C-Means algorithm. Fuzzy Sets and Systems, 101, 49-58.Search in Google Scholar

Flores-Sintas, A., Cadenas, J.M., Martin, F., 2000. Partition validity and defuzzification. Fuzzy Sets and Systems, 112, 433-447.Search in Google Scholar

Fournier, F., 1960. Climat et érosion. La relation entre l´érosion du sol par l´eau et les précipitations atmosphériques. [Relationship between soil erosion by water and rainfall]. Presse Universitaire de France, Paris. (In French.)Search in Google Scholar

Fukuyama, Y., Sugeno, M., 1989. A new method of choosing the number of clusters for the fuzzy c-means method. In: Proc. 5th Fuzzy Syst. Symp., pp. 247-250 (In Japanese.)Search in Google Scholar

Gaál, L., Szolgay, J., Lapin, M., Fasko, P., 2009. Hybrid approach to delineation of homogeneous regions for regional precipitation frequency analysis. J. Hydrol. Hydromech., 57, 4, 226-249.Search in Google Scholar

Gabriels, D., 2006. Assessing the modified Fournier Index and the Precipitation Concentration Index for some European countries. In: Boardman, J., Poesen, J. (Eds.): Soil Erosion in Europe. John Wiley & Sons, Chichester, pp. 675-684.Search in Google Scholar

Goyal, M.K., Gupta, V., 2014. Identification of homogeneous rainfall regimes in northeast region of India using Fuzzy Cluster Analysis. Water Resour. Manag., 28, 4491-4511.10.1007/s11269-014-0699-7Open DOISearch in Google Scholar

Goyal, M.K., Sharma, A. 2016. A fuzzy c-means approach regionalization for analysis of meteorological drought homogeneous regions in western India. Nat. Hazards. DOI: 10.1007/s11069-016-2520-9.10.1007/s11069-016-2520-9Open DOISearch in Google Scholar

Hall, M.J., Minns, A.W., 1999. The classification of hydrologically homogeneous regions. Hydrol. Sci. J., 44, 5, 693-704.Search in Google Scholar

Hawkins, R.H., Ward, T.J., Woodward, D.E., Van Mullem, J.A., 2009. Curve number hydrology: state of the practice, Report of ASCE/EWRI Task Committee, American Society of Civil Engineers, Reston, Virginia, USA.Search in Google Scholar

Hosking, J.R.M., Wallis, J.R., 1993. Some statistics useful in regional frequency-analisis. Water Resour. Res., 29, 2, 271-281.10.1029/92WR01980Open DOISearch in Google Scholar

Hosking, J.R.M., Wallis, J.R., 1997. Regional Frequency Analysis: An Approach based on L-Moments. Cambridge University Press, New York.Search in Google Scholar

Isik, S., Singh, V.P., 2008. Hydrologic regionalization of watersheds in Turkey. J. Hydrol. Eng., 13, 824-834.10.1061/(ASCE)1084-0699(2008)13:9(824)Open DOISearch in Google Scholar

Jingyi, Z., Hall, M.J., 2004. Regional flood frequency analysis for the Gan-Ming River basin in China. J. Hydrol., 296, 98-117.Search in Google Scholar

Kumar, R., Goel, N.K., Chatterjee, C., Nayak, P.C., 2015. Regional flood frequency analysis using soft computing techniques. Water Resour. Manage., 29, 1965.Search in Google Scholar

MAGRAMA, 2016. Ministerio de Agricultura, Alimentación y Medio Ambiente. Sistema de Información del Agua. Retrieved from http://www.magrama.gob.es/es/agua/temas/planificacionhidrologica/sia-/ (In Spanish)Search in Google Scholar

Nathan, R.J., McMahon, T.A., 1990. Identification of homogeneous regions for the purposes of regionalization. J. Hydrol., 121, 217-238.Search in Google Scholar

Pal, N.R., Bezdek, J.C., 1995. On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst., 3, 3, 370-379.Search in Google Scholar

Raju, K.S., Nagesh Kumar, D., 2011. Classification of microwatersheds based on morphological characteristics. J. Hydro- Environ. Res., 5, 101-109.Search in Google Scholar

Rao, A.R., Srinivas, V.V., 2006. Regionalization of watersheds by fuzzy cluster analysis. J. Hydrol., 318, 57-79.Search in Google Scholar

Rao, A.R., Srinivas, V.V., 2008. Regionalization of Watersheds: An Approach Based on Cluster Analysis. Water Science and Technology Library Vol. 58. Springer Science & Business Media.Search in Google Scholar

Ross, T.J., 1995. Fuzzy Logic with Engineering Applications, McGraw-Hill, New York. Ruspini, E.H., 1969. A new approach to clustering. Inform. and Control, 15, 22-32.Search in Google Scholar

Smithers, J.C., Schulze, R.E., 2001. A methodology for the estimation of short duration design storms in South Africa using a regional approach based on L-moments. J. Hydrol., 24, 42-52.Search in Google Scholar

Soto, J., Flores-Sintas, A., Paralea-Albaladejo, J., 2008. Improving probabilities in a fuzzy clustering partition. Fuzzy Sets and Systems, 159, 406-421.Search in Google Scholar

Srinivas, V.V., Tripathi, S., Rao, A.R., Govindaraju, R.S., 2008. Regional flood frequency analysis by combining selforganizing feature maps and fuzzy clustering. J. Hydrol., 348, 148-166.Search in Google Scholar

Timón, I., Soto, J., Pérez-Sánchez, H., Cecilia, J.M., 2016. Parallel implementation of fuzzy minimals clustering algorithm. Expert Systems with Applications, 48, 35-41.10.1016/j.eswa.2015.11.011Open DOISearch in Google Scholar

Xie, X.L., Beni, G., 1991. A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell., 13, 8, 841-847.Search in Google Scholar

Zadeh, L.A., 1965. Fuzzy sets. Information and Control, 8, 3, 338-353.10.1016/S0019-9958(65)90241-XOpen DOISearch in Google Scholar

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