Water Resources Management

, Volume 30, Issue 12, pp 4399–4413 | Cite as

Wavelet Spectrum and Self-Organizing Maps-Based Approach for Hydrologic Regionalization -a Case Study in the Western United States

  • A. Agarwal
  • R. MaheswaranEmail author
  • J Kurths
  • R. Khosa


Hydrologic regionalization deals with the investigation of homogeneity in watersheds and provides a classification of watersheds for regional analysis. The classification thus obtained can be used as a basis for mapping data from gauged to ungauged sites and can improve extreme event prediction. This paper proposes a wavelet power spectrum (WPS) coupled with the self-organizing map method for clustering hydrologic catchments. The application of this technique is implemented for gauged catchments. As a test case study, monthly streamflow records observed at 117 selected catchments throughout the western United States from 1951 through 2002. Further, based on WPS of each station, catchments are classified into homogeneous clusters, which provides a representative WPS pattern for the streamflow stations in each cluster.


Wavelet power spectrum Regionalization Ungauged catchments K-means technique Self-organizing map 



This research was funded by Deutsche Forschungsgemeinschaft (DFG) (GRK 2043/1) within the graduate research training group “Natural risk in a changing world (NatRiskChange) at the University of Potsdam and the Department of Science and Technology, India, through the INSPIRE Faculty Fellowship held by MaheswaranRathinasamy.


  1. Agarwal A (2015) Hydrologic regionalization using wavelet-based multiscale entropy technique. Dissertation, Indian Institute of Technology DelhiGoogle Scholar
  2. Agarwal A, Maheswaran R, Sehgal V, Khosa R, Sivakumar B, Bernhofer C (2016) Hydrologic regionalization using wavelet-based multiscale entropy method. J Hydrol 538:22–32CrossRefGoogle Scholar
  3. Allende TC, Mendoza ME, and Lopez GE, Morales-Manilla L (2009) Hydrogeographical regionalization: an approach for evaluating the effects of land cover change in watersheds. A case study in the Cuitzeo Lake Watershed, Central Mexico. Water Resour Manag 23(12):2587–2603Google Scholar
  4. Atiem IA, Harmancioğlu NB (2006) Assessment of Regional Floods Using L-Moments Approach: The Case of the River Nile. Water Resour Manag 20(5):723–747CrossRefGoogle Scholar
  5. Bloschl G, Sivapalan M (1995) Scale issues in hydrological modeling: a review. Hydrol Process 9(3–4):251–290CrossRefGoogle Scholar
  6. Bock AR, Hay LE, McCabe GJ, Markstrom SL, Atkinson RD (2015) Parameter regionalization of a monthly water balance model for the conterminous United States. Hydrol Earth SystSc 12:10023–10066CrossRefGoogle Scholar
  7. Céréghino R, Park YS (2009) Review of the self-organizing map approach in water resources: a commentary. Environ Modell & Softw 24(8):945–947CrossRefGoogle Scholar
  8. Chen Y, Qin B, Liu T, Liu Y, Li S (2010) The Comparison of SOM and K-means for Text Clustering. Comput Inform Sci 3(2):268CrossRefGoogle Scholar
  9. Chen LH, Lin GF, Hsu CW (2011) Development of Design Hyetographs for Ungauged Sites Using an Approach Combining PCA, SOM and Kriging Methods. Water Resour Manag 25(8):1995–2013CrossRefGoogle Scholar
  10. Coelho AC, Labadie JW, Fontane DG (2012) Multicriteria decision support system for regionalization of integrated water resources management. Water Resour Manag 26(5):1325–1346CrossRefGoogle Scholar
  11. Cutore P, Cristaudo G, Campisano A, Modica C, Cancelliere A, Rossi G (2007) Regional Models for the Estimation of Streamflow Series in Ungauged Basins. Water Resour Manag 21(5):789–800CrossRefGoogle Scholar
  12. Daubechies I (1992) Ten lectures on wavelets, Philadelphia: Society for industrial and applied mathematics (Vol. 61):198–202Google Scholar
  13. Devito K, Creed I, Gan T, Mendoza C, Petrone R, Silins U, Smerdon B (2005) A framework for broad-scale classification of hydrologic response units on the Boreal Plain: is topography the last thing to consider? Hydrol Process (19):1705–1714Google Scholar
  14. Dunn JC (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters (73):32–57Google Scholar
  15. Franchini M, Suppo M (1996) Regional analysis of flow duration curves for a limestone region. Water Resour Manag 10(3): 199–218Google Scholar
  16. Giri BK, Mitra C, Panigrahi PK, Iyengar AS (2014) Multi-scale dynamics of glow discharge plasma through wavelets: Self-similar behavior to neutral turbulence and dissipation. Chaos 24(4):0431–0435CrossRefGoogle Scholar
  17. Goyal MK, Gupta V (2014) Identification of homogeneous rainfall regimes in Northeast Region of India using fuzzy cluster analysis. Water Resour Manag 28(13):4491–4511CrossRefGoogle Scholar
  18. Haykin S, Lippmann R (1994) Neural networks, a comprehensive foundation. Int J Neural Syst 5(4):363–364CrossRefGoogle Scholar
  19. Kisi O (2011) Wavelet regression model as an alternative to neural networks for river stage forecasting. Water Resour Manag 25(2):579–600CrossRefGoogle Scholar
  20. Kohonen T (2012) Self-organization and associative memory (Vol. 8). Springer-Verlag New York Inc, New YorkGoogle Scholar
  21. Labat D (2005) Recent advances in wavelet analyses: part 1. A review of concepts. J Hydrol 314(1):275–288CrossRefGoogle Scholar
  22. Lakhanpal A (2015) Statistical downscaling of GCM outputs using wavelet based model. Dissertation, Indian Institute of Technology DelhiGoogle Scholar
  23. Latt ZZ, Wittenberg H, Urban B (2015) Clustering hydrological homogeneous regions and neural network based index flood estimation for ungauged catchments: an Example of the Chindwin River in Myanmar. Water Resour Manag 29(3):913–928CrossRefGoogle Scholar
  24. Lin GF, Chen LH (2006) Identification of homogeneous regions for regional frequency analysis using the self-organizing map. J Hydrol 324(1):1–9CrossRefGoogle Scholar
  25. Maheswaran R, Khosa R (2012) Wavelet–Volterra coupled model for monthly stream flow forecasting. J Hydrol (450):320–335Google Scholar
  26. Manning CD, Raghavan P, Schutze H (2008) Introduction to Information Retrieval. In: Cambridge University press, Cambridge, England pp 450–416Google Scholar
  27. Mehta R, Jain SK (2009) optimal operation of a multi-purpose reservoir using neuro-fuzzy technique. Water Resour Manag 23:509–529Google Scholar
  28. Morissette L, Chartier S (2013) The k-means clustering technique: General considerations and implementation in Mathematica. Tutor Quant Methods Psychol 9(1):15–24Google Scholar
  29. Nourani V, Komasi M, Mano A (2009) A multivariate ANN-wavelet approach for rainfall–runoff modeling. Water ResourManag 23(14):2877–2894Google Scholar
  30. Rao AR, Srinivas V (2008) Regionalization of watersheds: an approach based on cluster analysis. Springer Netherlands. doi: 10.1007/978-1-4020-6852-2
  31. Razavi T, Coulibaly P (2013) Streamflow prediction in ungauged basins: Review of regionalization methods. J Hydrol Eng 18(8):958–975CrossRefGoogle Scholar
  32. Saco P, Kumar P (2000) Coherent modes in multiscale variability of streamflow over the United States. Water Resour Res 36(4):1049–1067CrossRefGoogle Scholar
  33. Saf B (2009) Regional flood frequency analysis using L-moments for the West Mediterranean region of Turkey. Water ResourManag 23(3):531–551Google Scholar
  34. Sahay RR, Srivastava A (2014) Predicting monsoon floods in rivers embedding wavelet transform, genetic algorithm and neural network. Water Resour Manag 28(2):301–317CrossRefGoogle Scholar
  35. Sang YF (2013) Improved wavelet modeling framework for hydrologic time series forecasting. Water Resour Manag 27(8):2807–2821CrossRefGoogle Scholar
  36. Sehgal V, Sahay RR, Chatterjee C (2014a) Effect of utilization of discrete wavelet components on flood forecasting performance of wavelet based ANFIS models. Water Resour Manag 28(6):1733–1749CrossRefGoogle Scholar
  37. Sehgal V, Tiwari MK, Chatterjee C (2014b) Wavelet bootstrap multiple linear regression based hybrid modeling for daily River discharge forecasting. Water ResourManag 28(10): 2793–2811Google Scholar
  38. Shahapurkar SS, Sundareshan MK (2004) Comparison of self-organizing map with k-means hierarchical clustering for bioinformatics applications. Neural Netw, Int Joint Conference 2:1221–1226Google Scholar
  39. Sivakumar B, Singh VP (2012) Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework. Hydrol Earth Syst Sc 16(11):4119–4131CrossRefGoogle Scholar
  40. Sivakumar B, Woldemeskel FM (2015) A network-based analysis of spatial rainfall connections. Enviro Modell & Soft 69:55–62CrossRefGoogle Scholar
  41. Sivakumar B, Singh VP, Berndtsson R, Khan SK (2013) Catchment classification framework in hydrology: challenges and directions. J Hydrol Eng 20(1):A4014002CrossRefGoogle Scholar
  42. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. B Am Meteorol Soc 79(1):61–78CrossRefGoogle Scholar
  43. Vandewiele GL, CY X, Huybrechts W (1991) Regionalisation of physically-based water balance models in Belgium. Application to ungauged catchments. Water Resour Manag 5(3):199–208CrossRefGoogle Scholar
  44. Zhou HC, Peng Y, Liang GH (2008) The research of monthly discharge predictor-corrector model based on wavelet decomposition. Water ResourManag 22(1):217–227Google Scholar
  45. Zoppou C, Neilsen O, Zhang L (2002) Regionalization of daily stream flow in Australia using wavelets and k-means analysis Tech. Rep., Australian National University. Available from

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • A. Agarwal
    • 1
    • 2
    • 3
  • R. Maheswaran
    • 4
    • 5
    Email author
  • J Kurths
    • 1
    • 2
  • R. Khosa
    • 3
  1. 1.Institute of Earth and Environmental ScienceUniversity of PotsdamPotsdamGermany
  2. 2.Postdam Institute for Climate Impact Research, ResearchPotsdamGermany
  3. 3.Water Resource EngineeringIndian Institute of TechnologyDelhiIndia
  4. 4.MVGR College of EngineeringVizianagaramIndia
  5. 5.Saint Anthony Falls LaboratoryUniversity of MinnesotaMinneapolisUSA

Personalised recommendations