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Journal of Mountain Science

, Volume 15, Issue 7, pp 1481–1497 | Cite as

A multiscale spatio-temporal framework to regionalize annual precipitation using k-means and self-organizing map technique

  • Kiyoumars Roushangar
  • Farhad Alizadeh
Article
  • 23 Downloads

Abstract

Determination of homogenous precipitation-based regions is a very important task in effective management of water resources. The present study tried to propose an effective precipitation-based regionalization methodology by conjugating both temporal pre-processing and spatial clustering approaches in a way to take advantage of multiscale properties of precipitation time series. Annual precipitation data of 51 years (1960-2010) for 31 rain gauges (RGs) were collected and used in proposed clustering approaches. Discreet wavelet transform (DWT) was used to capture the time-frequency attributes of the time series and multiscale regionalization was performed by using k-means and Self Organizing Maps (SOM) clustering techniques. Daubechies function (db) was selected as mother wavelet to decompose the precipitation time series. Also, proper boundary extensions and decomposition level were applied. Different combinations of the approximation (A) and detail (D) coefficients were used to determine the input dataset as a basis of spatial clustering. The proposed model’s efficiency in spatial clustering stage was verified using three different indexes namely, Silhouette Coefficient (SC), Dunn index and Davis Bouldin index (DB). Results approved superior performance of k-means technique in comparison to SOM. It was also deduced that DWT-based regionalization methodology showed improvements in comparison to historical-based models. Cross mutual information was used to investigate the RGs of cluster 3’s homogeneousness in DWT-k-means approach. Results of non-linear correlation approach verified homogeneity of cluster 3. Verifications based on mean annual precipitation values of rain gauges in each cluster also approved the capability of multiscale approach in precipitation regionalization.

Keywords

Precipitation Discrete wavelet transform (DWT) k-means Self Organizing Map (SOM) Iran 

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References

  1. Adamowski K, Prokoph A, Adamowski J (2009) Development of a new method of wavelet aided trend detection and estimation. Hydrological Processes 23(18): 2686–2696. https://doi.org/10.1002/hyp.7260 CrossRefGoogle Scholar
  2. Agarwal A, Maheswaran R, Sehgal V, Khos R, Sivakumar B, Bernhofer C (2016) Hydrologic regionalization using waveletbased multiscale entropy method. Journal of Hydrology 538: 22–32. https://doi.org/10.1016/j.jhydrol.2016.03.023 CrossRefGoogle Scholar
  3. Araghi A, Mousavi Baygi M, Adamowski J, Malard J, Nalley D, Hashemnia SM (2014) Using wavelet transforms to estimate surface temperature trends and dominant periodicities in Iran based on gridded reanalysis data. Atmospheric Research 155: 52–72. https://doi.org/10.1016/j.atmosres.2014.11.016 CrossRefGoogle Scholar
  4. Ashraf B, Yazdani R, Mousavi-Baygi M, Bannayan M (2013) Investigation of temporal and spatial climate variability and aridity of Iran. Theoretical and Applied Climatology 118(1): 35–46. https://doi.org/10.1007/s00704-013-1040-8 Google Scholar
  5. Ay M, Kisi O (2015) Investigation of trend analysis of monthly total precipitation by an innovative method. Theoretical and Applied Climatology 120(3–4): 617–629. https://doi.org/10.1007/s0070 CrossRefGoogle Scholar
  6. Beven K (2012) Rainfall-Runoff Modelling: The Primer. 2nd Edition, John Wiley & Sons, Chichester, England. https://doi.org/10.1002/9781119951001 CrossRefGoogle Scholar
  7. Bolshakova N, Azuaje F (2003) Machaon CVE: cluster validation for gene expression data. Bioinformatics 19(18): 2494–2495. https://doi.org/10.1093/bioinformatics/btg356 CrossRefGoogle Scholar
  8. Bruce LM, Koger CH, Jiang L (2002) Dimensionality reduction of hyperspectral data using discrete wavelet transform feature extraction. IEEE Transactions on Geoscience and Remote Sensing. 40(10): 2331–2338. https://doi.org/10.1109/TGRS.2002.804721 CrossRefGoogle Scholar
  9. Brutsaert, W (1982) Evaporation into the Atmosphere. Springer Netherlands. Pp 37–56. https://doi.org/10.1007/978-94-017-1497-6 Google Scholar
  10. Burn DH (1990) An appraisal of the “region of influence” approach to flood frequency analysis. Hydrological Science Journal 35(2) 149–165. https://doi.org/10.1080/02626669009492415 Google Scholar
  11. Chen XY, Chau KW, Busari AO (2015) A comparative study of population-based optimization algorithms for downstream river flow forecasting by a hybrid neural network model. Engineering Application of Artificial Intelligence 46(A): 258–268. https://doi.org/10.1016/j.engappai.2015.09.010 CrossRefGoogle Scholar
  12. Chou CM (2007) Applying multi-resolution analysis to differential hydrological grey models with dual series. Journal of Hydrology 332 (1-2): 174–186. https://doi.org/10.1016/j.jhydrol.2006.06.031 CrossRefGoogle Scholar
  13. Clark PU, Alley RB, Pollard D (1999) Northern hemisphere icesheet influences on global climate change. Science 286: 1104–1111. https://doi.org/10.1126/science.286.5442.1104 CrossRefGoogle Scholar
  14. Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence 1(2): 224–227. https://doi.org/10.1109/TPAMI.1979.4766909 CrossRefGoogle Scholar
  15. Artigas MZ, Elias AG, de Campra PF (2006). Discrete wavelet analysis to assess long-term trends in geomagnetic activity. Physics and Chemistry of the Earth 31 (1-3): 77–80. https://doi.org/10.1016/j.pce.2005.03.009 CrossRefGoogle Scholar
  16. Dinpashoh Y, Fakheri-Fard A, Moghaddam M, et al. (2004). Selection of variables for the purpose of regionalization of Iran’s precipitation climate using multivariate methods. Journal of Hydrology 297: 109–123. https://doi.org/10.1016/j.jhydrol.2004.04.009 CrossRefGoogle Scholar
  17. Domroes M, Kaviani M, Schaefer D (1998) An analysis of regional and intra-annual precipitation variability over Iran using multivariate statistical methods. Theoretical and Applied Climatology 61: 151–159. https://doi.org/10.1007/s007040050060 CrossRefGoogle Scholar
  18. Dong X, Nyren P, Patton B, et al. (2008) Wavelets for agriculture and biology: a tutorial with applications and outlook. Bioscience 58(5): 445–453. https://doi.org/10.1641/B580512 CrossRefGoogle Scholar
  19. Dunn JC (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. Journal of Cybernetics 3(3): 32–57. https://doi.org/10.1080/01969727308546046 CrossRefGoogle Scholar
  20. Eagleson PS (1970) Dynamic Hydrology. McGraw Hill, New York.Google Scholar
  21. Farajzadeh J, Alizadeh F (2018) A hybrid linear-nonlinear approach to predict the monthly rainfall over the Urmia Lake watershed using Wavelet-SARIMAX-LSSVM conjugated model. Journal of Hydroinformatics 20(1) 246–262. https://doi.org/10.2166/hydro.2017.013 CrossRefGoogle Scholar
  22. Farge M (1992) Wavelet transforms and their applications to turbulence, Annual Review of Fluid Mechanics 24: 395–457. https://doi.org/10.1146/annurev.fl.24.010192.002143 Google Scholar
  23. Grossmann A, Morlet J (1984) Decomposition of Hardy function into square integrable Wavelets of constant shape. Journal of Mathematical Analysis and Applications 5: 723–736. https://doi.org/10.1137/0515056 Google Scholar
  24. Halkidi M, Batistakis Y, Vazirgiannis M (2001) On clustering validation techniques. Journal of Intelligent Information Systems 17 (2-3): 107–145. https://doi.org/10.1023/A:1012801612483 CrossRefGoogle Scholar
  25. Hall MJ, Minns AW (1999) The classification of hydrologically homogeneous regions. Hydrological Science Journal 44(5): 693–704. https://doi.org/10.1080/02626669909492268 CrossRefGoogle Scholar
  26. Hsu KC, Li ST (2010) Clustering spatial-temporal precipitation data using wavelet transform and self-organizing map neural network. Advances in Water Resources 33: 190–200. https://doi.org/10.1016/j.advwatres.2009.11.005 CrossRefGoogle Scholar
  27. Hulme M, Osborn TJ, Johns TC (1998) Precipitation sensitivity to global warming: comparison of observations with HadCM2 simulations. Geophysical Research Letter 25(17): 3379–3382. https://doi.org/10.1029/98GL02562 CrossRefGoogle Scholar
  28. Kallache M, Rust HW, Kropp J (2005) Trend assessment: applications for hydrology and climate research. Nonlinear Processes in Geophysics 12(2): 201–210. https://doi.org/10.5194/npg-12-201-2005 CrossRefGoogle Scholar
  29. Kasturi J, Acharya J, Ramanathan M (2003) An information theoretic approach for analyzing temporal patterns of gene expression. Bioinformatics 19(4): 449–458. https://doi.org/10.1093/bioinformatics/btg020 CrossRefGoogle Scholar
  30. Kendall C, McDonnell JJ (1999) Isotope Tracers in Catchment Hydrology. 1st Edition. Elsevier Science, Netherland. eBook ISBN: 9780080929156Google Scholar
  31. Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biological Cybernetics 43: 59–69. https://doi.org/10.1007/BF00337288 CrossRefGoogle Scholar
  32. Kraskov A, Stögbauer H, Andrzejak RG, et al. (2005) Hierarchical Clustering Based on Mutual Information. Europhysics Letters 70(2): 278–288.CrossRefGoogle Scholar
  33. Kumar, P. and Foufoula GE (1993) Multicomponent decomposition of spatial rainfall fields, 1. Segregation of large-and small-scale features using wavelet transforms. Water Resources Research 29(8): 2515–2532. https://doi.org/10.1029/93WR00548 Google Scholar
  34. Lauzon N, Anctil F, Baxter CW (2006) Clustering of heterogeneous precipitation fields for the assessment and possible improvement of lump neural network models for streamflow forecasts. Hydrological Earth System Sciences 10: 485–494. https://doi.org/10.5194/hess-10-485-2006 CrossRefGoogle Scholar
  35. Lin GF, Chen LH (2006) Identification of homogeneous regions for regional frequency analysis using the self-organizing map. Journal of Hydrology 324 (1-4): 1–9. https://doi.org/10.1016/j.jhydrol.2005.09.009 CrossRefGoogle Scholar
  36. Liong SY, Lim WH, Kojiri T, Hori T (2000) Advance flood forecasting for flood stricken Bangladesh with a fuzzy reasoning method. Hydrological Processes 14(3): 431–48. https://doi.org/10.1002/(SICI)1099-1085(20000228) CrossRefGoogle Scholar
  37. Mallat SG (1998) A Wavelet Tour of Signal Processing. Second edition. Academic Press, San Diego.Google Scholar
  38. Mishra AK, Özger M, Singh VP (2009) An entropy-based investigation into the variability of precipitation. Journal of Hydrology 370: 139–154. https://doi.org/10.1016/j.jhydrol.2009.03.006 CrossRefGoogle Scholar
  39. Modarres, R., 2006. “Regional precipitation climates of Iran.” Journal of Hydrology (NZ) 45 (1): 13–27.Google Scholar
  40. Modarres R, Sarhadi A (2008) Rainfall trends analysis of Iran in the last half of the twentieth century. Journal of Geophysical Research 114: D03101. https://doi.org/10.1029/2008JD010707 Google Scholar
  41. Murtagh F, Hernández-Pajares M (1995) The Kohonen selforganizing feature map method: an assessment. Journal of Classification 12: 165–190. https://doi.org/10.1007/BF03040854 CrossRefGoogle Scholar
  42. Nagarajan R (2010) Drought Assessment. Springer Science & Business Media. p. 383.CrossRefGoogle Scholar
  43. Nalley D, Adamowski J, Khalil B (2012) Using discrete wavelet transforms to analyze trends in streamflow and precipitation in Quebec and Ontario (1954-2008). Journal of Hydrology 475: 204–228. https://doi.org/10.1016/j.jhydrol.2012.09.049 CrossRefGoogle Scholar
  44. Nourani V, Parhizkar M (2013) Conjunction of SOM-based feature extraction method and hybrid wavelet-ANN approach for rainfall-runoff modeling. Journal of Hydroinformatics 15(3): 829–848. https://doi.org/10.2166/hydro.2013.141 CrossRefGoogle Scholar
  45. Nourani V, Taghi Alami M, Vousoughi Daneshivar F (2015) Wavelet-entropy data pre-processing approach for ANNbased Groundwater Level Modeling. Journal of Hydrology 524: 255–269. https://doi.org/10.1016/j.jhydrol.2015.02.048 CrossRefGoogle Scholar
  46. Partal T (2010) Wavelet transform-based analysis of periodicities and trends of Sakarya basin (Turkey) streamflow data River Research and Applications 26 (6): 695–711. https://doi.org/10.1002/rra.1264 Google Scholar
  47. Popivanov I, Miller RJ (2002) Similarity search over time-series data using wavelets. In: Proceedings 18th International Conference on Data Engineering pp 212–221.CrossRefGoogle Scholar
  48. Rao AR, Srinivas VV (2008) Regionalization of Watersheds: an Approach Based on Cluster Analysis. vol. 58. Springer Science & Business Media.Google Scholar
  49. Raziei T (2017) A precipitation regionalization and regime for Iran based on multivariate analysis. Theoretical and Applied Climatology 1–20. https://doi.org/10.1007/s00704-017-2065-1 Google Scholar
  50. Raziei T, Bordi I, Pereira LS (2008). A precipitation-based regionalization for Western Iran and regional drought variability. Hydrological Earth System Sciences 12: 1309–1321. https://doi.org/10.5194/hess-12-1309-2008 CrossRefGoogle Scholar
  51. Raziei T, Daryabari J, Bordi I, Pereira LS (2014). Spatial patterns and temporal trends of precipitation in Iran. Theoretical and Applied Climatology 15(3–4): 531–540. https://doi.org/10.1007/s00704-013-0919-8 CrossRefGoogle Scholar
  52. Rokach L, Maimon O (2005) Clustering methods. In: Data Mining and Knowledge Discovery Handbook. Springer, New York, USA, pp 321–352.CrossRefGoogle Scholar
  53. Roushangar K, Alizadeh F, Adamowski J (2018) Exploring the effects of climatic variables on monthly precipitation variation using a continuous wavelet-based multiscale entropy approach. Environmental research 165: 176–192. https://doi.org/10.1016/j.envres.2018.04.017 CrossRefGoogle Scholar
  54. Saboohi R, Soltani S, Khodagholi M (2012) Trend analysis of temperature parameters in Iran. Theoretical and Applied Climatology 109: 529–547. https://doi.org/10.1007/s00704-012-0590-5 CrossRefGoogle Scholar
  55. She D, Xia J, Zhu L, et al. (2016) Changes of rainfall and its possible reasons in the Nansi Lake Basin, China. Stochastic Environmental Research and Risk Assessment 30(4): 1099–1113. https://doi.org/10.1007/s00477-015-1176-4 CrossRefGoogle Scholar
  56. She DX, Xia J, Zhang D, et al. (2014) Regional extreme dry spell frequency analysis using L-moments method in the middle reach of Yellow River Basin, China. Hydrological Processes 28: 4694–4707. https://doi.org/10.1002/hyp.9930 CrossRefGoogle Scholar
  57. Soltani S, Modarres R, Eslamian SS (2007) The use of time series modelling for the determination of rainfall climates of Iran. International Journal of Climatology 27: 819–829. https://doi.org/10.1002/joc.1427 CrossRefGoogle Scholar
  58. Su H, Liu Q, Li J (2011) Alleviating border effects in wavelet transforms for nonlinear time-varying signal analysis.” Advances in Electrical and Computer Engineering 11(3): 55–60. https://doi.org/10.4316/AECE.2011.03009 CrossRefGoogle Scholar
  59. Tabari H, Talaee PH (2011) Temporal variability of precipitation over Iran: 1966–2005. Journal of Hydrology 396: 313–320. https://doi.org/10.1016/j.jhydrol.2010.11.034 CrossRefGoogle Scholar
  60. Teegavarapu RSV (2017) Climate Variability and Changes in Precipitation Extremes and Characteristics. In: Kolokytha E, Oishi S, Teegavarapu R (eds.) Sustainable Water Resources Planning and Management Under Climate Change. Springer, Singapore. https://doi.org/10.1007/978-981-10-2051-3_1
  61. Teegavarapu RSV, Aly A, Pathak CH, et al. (2017) Infilling missing precipitation records using variants of spatial interpolation and data-driven methods: use of optimal weighting parameters and nearest neighbour-based corrections. International Journal of Climatology. https://doi.org/10.1002/joc.5209 Google Scholar
  62. Trenberth KE, Dai A, Rasmussen RM, et al. (2003) The changing character of precipitation. Bulletin of American Meteorological Society 84(9): 1205–1217. https://doi.org/10.1175/BAMS-84-9-1205 CrossRefGoogle Scholar
  63. Villarini G, Denniston RF (2016) Contribution of tropical cyclones to extreme rainfall in Australia. International Journal of Climatology 36(2): 1019–1025. https://doi.org/10.1002/joc.4393 CrossRefGoogle Scholar
  64. Vonesch C, Blu T, Unser M (2007) Generalized Daubechies wavelet families. IEEE Transactions on Signal Processing 55(9): 4415–4429. https://doi.org/10.1109/TSP.2007.896255 CrossRefGoogle Scholar
  65. Wang S, Zhang X, Liu Z, et al. (2013). Trend analysis of precipitation in the Jinsha River Basin in China. Journal of Hydrometeorological 14(1): 290–303. https://doi.org/10.1175/JHM-D-12-033.1 CrossRefGoogle Scholar
  66. Wang WC, Chau KW, Xu DM, et al. (2015) Improving forecasting accuracy of annual runoff time series using ARIMA based on EEMD decomposition. Water Resources Management 29 (8): 2655–2675. https://doi.org/10.1007/s11269-015-0962-6 CrossRefGoogle Scholar
  67. Weather and Climate Information. (2015) Weather and Climate: Iran, average monthly Rainfall, Sunshine, Temperature, Humidity and Wind Speed. World Weather and Climate Information.Google Scholar
  68. Wu Y, Li W, Zhou J, et al. (2013) Temperature and precipitation variations at two meteorological stations on eastern slope of Gongga Mountain, SW China in the past two decades. 10(3): 370–377. https://doi.org/10.1007/s11629-013-2328-y Google Scholar
  69. Xia L, Song X, Fu N, et al. (2017) Impacts of precipitation variation and soil and water conservation measures on runoff and sediment yield in the Loess Plateau Gully Region, China. Journal of Mountain Science. 14(10): 2028–2041. https://doi.org/10.1007/s11629-016-4173-2 CrossRefGoogle Scholar
  70. Xin W, Zichu X, Shiyin L, et al. (2005) Modeling the roles of precipitation increasing in glacier systems responding to climate warming. Journal of Mountain Science 2(4): 306–312. https://doi.org/10.1007/BF02918403 CrossRefGoogle Scholar
  71. Zhang Q, Xiao M, Singh VP, Li F (2012) Regionalization and spatial changing properties of droughts across the Pearl River basin, China. Journal of Hydrology 472-473(23): 355–366. https://doi.org/10.1016/j.jhydrol.2012.09.054 CrossRefGoogle Scholar
  72. Zhang W, Villarini G (2017) Heavy precipitation is highly sensitive to the magnitude of future warming. Climate Change 145(1–2): 249–257. https://doi.org/10.1007/s10584-017-2079-9 CrossRefGoogle Scholar

Copyright information

© Science Press, Institute of Mountain Hazards and Environment, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Water Resources Engineering, Faculty of Civil EngineeringUniversity of TabrizTabrizIran

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