Investigating monthly precipitation variability using a multiscale approach based on ensemble empirical mode decomposition

  • Farhad AlizadehEmail author
  • Kiyoumar Roushangar
  • Jan Adamowski


In environmental and hydrological studies, the issue of variability in precipitation is of great importance, particularly for regions situated in arid and semiarid environments, such as Iran. Since precipitation is extremely complex spatial–temporal process, a time–space framework for rain gauges classification based on rate of information (entropy) can be very useful. The multi-temporal randomness in precipitation time series can be measured by an entropy-based approach. Therefore, an ensemble empirical mode decomposition (EEMD)-based multiscale entropy (EME) approach was implemented to measure and evaluate monthly variability in precipitation and spatially discriminate rain gauges across Iran. Monthly precipitation data spanning 612 months (1960–2010), drawn from rain gauges at 31 stations across Iran, served to verify the proposed model. Given the existence of noise in the time series, a wavelet de-noising approach was applied to remove the corruption of the time series which can influence EME values. An EEMD approach served to decompose the precipitation time series into an intrinsic mode function (IMF), with different periods and specifications, along with residual components. An entropy concept based on the IMFs’ energy and residual sub-series served in calculating the multiscale components’ dispersion. The entropy values of IMFs 1–9 and residual components showed different patterns across rain gauge sites, where IMF 8, IMF 9 and the residual components showed the greatest level of entropy, while IMF 1 showed the greatest variation in entropy among all components. The spatial distribution of EME values showed a downward trend from north to south. A k-means clustering approach based on EME values served to specify the location of rain gauges. On a statistical basis (Davies–Bouldin Index = 0.29, Dunn Index = 3.22 and Silhouette Coefficient Index = 0.64), a clustering number of 5 led to a more precise discrimination of EME-based homogenous areas than did other clustering numbers. An evaluation of the relationships between EME values and latitude/longitude, showed an inverse relationship between EME and longitude and a direct relationship between EME and latitude, though neither was significant.


Precipitation variability Ensemble empirical mode decomposition (EEMD) k-means clustering Entropy 



Authors would like to express their appreciation to the Iran meteorology organization (IRIMO) for data preparation.


  1. 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
  2. Alfonso L, Lobbrecht A, Price R (2010) Information theory-based approach for location of monitoring water level gauges in polders. Water Resour Res. Google Scholar
  3. Amirat Y, Benbouzidb MEH, Wang T, Bacha K, Feld G (2018) EEMD-based notch filter for induction machine bearing faults detection. Appl Acoust 133:202–209CrossRefGoogle Scholar
  4. 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. Atmos Res 155:52–72CrossRefGoogle Scholar
  5. Ashraf B, Yazdani R, Mousavi-Baygi M, Bannayan M (2013) Investigation of temporal and spatial climate variability and aridity of Iran. Theor Appl Climatol 118(1):35–46Google Scholar
  6. Bolshakova N, Azuaje F (2003) Machaon CVE: cluster validation for gene expression data. Bioinformatics 19(18):2494–2495CrossRefGoogle Scholar
  7. Brunsell NA (2010) A multiscale information theory approach to assess spatial-temporal variability of daily precipitation. J Hydrol 385:165–172CrossRefGoogle Scholar
  8. Cazelles B, Chavez M, Berteaux D, Ménard F, Vik JO, Jenouvrier S, Stenseth NC (2008) Wavelet analysis of ecological time series. Oecologia 156(2):287–304CrossRefGoogle Scholar
  9. Cek ME, Ozgoren M, Savaci FA (2009) Continuous time wavelet entropy of auditory evoked potentials. Comput Biol Med 40(1):90–96Google Scholar
  10. Chen PC, Wang YH, You GJY, Wei CC (2017) Comparison of methods for non-stationary hydrologic frequency analysis: case study using annual maximum daily precipitation in Taiwan. J Hydrol 545:197–211CrossRefGoogle Scholar
  11. Clark PU, Alley RB, Pollard D (1999) Northern hemisphere ice-sheet influences on global climate change. Science 286:1104–1111CrossRefGoogle Scholar
  12. Costa M, Goldberger AL, Peng CK (2005) Multiscale entropy analysis of biological signals. Phys Rev E 71:021906CrossRefGoogle Scholar
  13. Darand M, Mansouri-Daneshvar MR (2014) Regionalization of precipitation regimes in Iran using principal component analysis and hierarchical clustering analysis. Environ Process 1(4):517–532CrossRefGoogle Scholar
  14. Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell 1(2):224–227CrossRefGoogle Scholar
  15. Dinpashoh Y, Fakheri-Fard A, Moghaddam M, Jahanbakhsh S, Mirnia M (2004) Selection of variables for the purpose of regionalization of Iran’s precipitation climate using multivariate methods. J Hydrol 297:109–123CrossRefGoogle Scholar
  16. Domroes M, Kaviani M, Schaefer D (1998) An analysis of regional and intra-annual precipitation variability over Iran using multivariate statistical methods. Theor Appl Climatol 61:151–159CrossRefGoogle Scholar
  17. Donoho DH (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41(3):613–617CrossRefGoogle Scholar
  18. Duffy DG (2005) The application of Hilbert–Huang transforms to meteorological data sets. J Atmos Ocean Technol 21:599–611CrossRefGoogle Scholar
  19. Dunn JC (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J Cybern 3(3):32–57CrossRefGoogle Scholar
  20. Elsner J, Tsonis A (1993) Complexity and predictability of hourly precipitation. J Atmos Sci 50:400–405CrossRefGoogle Scholar
  21. Flandrin P, Rilling G, Goncalves P (2004) Empirical mode decomposition as a filter bank. IEEE Signal Process Lett 11:112–114CrossRefGoogle Scholar
  22. Hsu KC, Li ST (2010) Clustering spatial–temporal precipitation data using wavelet transform and self-organizing map neural network. Adv Water Resour 33:190–200CrossRefGoogle Scholar
  23. Huang NE, Shen Z, Long SR, Wu MC et al (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc Math Phys Eng Sci 454(1971):903–995CrossRefGoogle Scholar
  24. Huang NE, Wu Z, Long SR, Arnold KC, Chen X, Blank K (2009) On instantaneous frequency. Adv Adapt Data Anal 1(02):177–229CrossRefGoogle Scholar
  25. Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106:620–630CrossRefGoogle Scholar
  26. Kasturi J, Acharya J, Ramanathan M (2003) An information theoretic approach for analyzing temporal patterns of gene expression. Bioinformatics 19(4):449–458CrossRefGoogle Scholar
  27. Koutsoyiannis D (2005) Uncertainty, entropy, scaling and hydrological stochastics 1 Marginal distributional properties of hydrological processes and state scaling. Hydrol Sci J 50:381–404Google Scholar
  28. Labat D (2005) Recent advances in wavelet analyses: part 1 A review of concepts. J Hydrol 314:275–288CrossRefGoogle Scholar
  29. Lee T, Ouarda TBMJ (2012) An EMD and PCA hybrid approach for separating noise from signal, and signal in climate change detection. Int J Climatol 32(4):624–634CrossRefGoogle Scholar
  30. Li Y, Davis CH (2006) Improved methods for analysis of decadal elevation-change time series over Antarctica. IEEE Trans Geosci Remote Sens 44(10):2687–2697CrossRefGoogle Scholar
  31. Li ZW, Zhang YK (2008) Multi-scale entropy analysis of Mississippi River flow. Stoch Environ Res Risk Assess 22:507–512CrossRefGoogle Scholar
  32. Lin GF, Chen LH (2006) Identification of homogeneous regions for regional frequency analysis using the self-organizing map. J Hydrol 324:1–9CrossRefGoogle Scholar
  33. Lin PF, Feng XL, Liu JJ (2015) Historical trends in surface air temperature estimated by ensemble empirical mode decomposition and least squares linear fitting. Atmos Ocean Sci Lett 8(1):10–16Google Scholar
  34. MacQueen J (1967) Some methods for classification and analysis of multivariate observations. Proc Fifth Berkeley Sympos Math Stat Probab 1:281–297Google Scholar
  35. McMahon TA, Kiem AS, Peel MC, Jordan PW, Pegram GG (2008) A new approach to stochastically generating six-monthly rainfall sequences based on empirical mode decomposition. J Hydrometeorol 9(6):1377–1389CrossRefGoogle Scholar
  36. Mishra AK, Özger M, Singh VP (2009) An entropy-based investigation into the variability of precipitation. J Hydrol 370:139–154CrossRefGoogle Scholar
  37. Modarres R (2006) Regional precipitation climates of Iran. J Hydrol N Z 45(1):13–27Google Scholar
  38. Modarres R, Sarhadi A (2008) Rainfall trends analysis of Iran in the last half of the twentieth century. J Geophys Res 114:D03101Google Scholar
  39. Murtagh F, Hernández-Pajares M (1995) The Kohonen self-organizing feature map method: an assessment. J Classif 12:165–190CrossRefGoogle Scholar
  40. Nagarajan R (2010) Drought assessment. Springer, New York, p 383CrossRefGoogle Scholar
  41. Nourani V, Andalib G, Sadikoglu F, Sharghi E (2017) Cascade-based multi-scale AI approach for modeling rainfall-runoff process. Hydrol Res 49(4):1191–1207CrossRefGoogle Scholar
  42. Nourani V, Roushangar K, Andalib G (2018) An inverse method for watershed change detection using hybrid conceptual and artificial intelligence approaches. J Hydrol 562:371–384CrossRefGoogle Scholar
  43. Rao AR, Srinivas VV (2008) Regionalization of watersheds: an approach based on cluster analysis, vol 58. Springer, New YorkGoogle Scholar
  44. Raziei T (2017) A precipitation regionalization and regime for Iran based on multivariate analysis. Theor Appl Climatol 131(3–4):1429–1448Google Scholar
  45. Raziei T, Bordi I, Pereira LS (2008) A precipitation-based regionalization for Western Iran and regional drought variability. Hydrol Earth Syst Sci 12:1309–1321CrossRefGoogle Scholar
  46. Rokach L, Maimon O (2005) Clustering methods. Data mining and knowledge discovery handbook. Springer, New York, pp 321–352CrossRefGoogle Scholar
  47. Roushangar K, Alizadeh F (2018a) Identifying complexity of annual precipitation variation in Iran during 1960–2010 based on information theory and discrete wavelet transform. Stoch Environ Res Risk Assess 32(5):1205–1223CrossRefGoogle Scholar
  48. Roushangar K, Alizadeh F (2018b) Scenario-based prediction of short-term river stage-discharge process using wavelet-EEMD-based relevance vector machine. J Hydroinform 21(1):56–76CrossRefGoogle Scholar
  49. 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. Envrion Res 165:176–192CrossRefGoogle Scholar
  50. Saboohi R, Soltani S, Khodagholi M (2012) Trend analysis of temperature parameters in Iran. Theor Appl Climatol 109:529–547CrossRefGoogle Scholar
  51. Sang YF (2012) Wavelet entropy-based investigation into the daily precipitation variability in the Yangtze River Delta, China, with rapid urbanizations. Theor Appl Climatol 111:361–370CrossRefGoogle Scholar
  52. Sang YF, Wang D, Wu JC, Zhu QP, Wang L (2009) The relation between periods’ identification and noises in hydrologic series data. J Hydrol 368:165–177CrossRefGoogle Scholar
  53. Sang YF, Wang D, Wu JC, Zhu QP, Wang L (2011) Wavelet-based analysis on the complexity of hydrologic series data under multi-temporal scales. Entropy 13:195–210CrossRefGoogle Scholar
  54. Soltani S, Modarres R, Eslamian SS (2007) The use of time series modelling for the determination of rainfall climates of Iran. Int J Climatol 27:819–829CrossRefGoogle Scholar
  55. Tabari H, Talaee HP (2011) Temporal variability of precipitation over Iran: 1966–2005. J Hydrol 396:313–320CrossRefGoogle Scholar
  56. Teegavarapu RSV, Aly A, Pathak CH, Ahlquist J, Fuelberg H, Hood J (2017) Infilling missing precipitation records using variants of spatial interpolation and data-driven methods: use of optimal weighting parameters and nearest neighbour-based corrections. Int J Climatol 38(2):776–793CrossRefGoogle Scholar
  57. Villarini G, Denniston RF (2016) Contribution of tropical cyclones to extreme rainfall in Australia. Int J Climatol 36(2):1019–1025CrossRefGoogle Scholar
  58. Wang WC, Chau KW, Xu DM, Chen XY (2015) Improving forecasting accuracy of annual runoff time series using ARIMA based on EEMD decomposition. Water Resour Manag 29(8):2655–2675CrossRefGoogle Scholar
  59. Weather and Climate Information (2015) Weather and climate: Iran, average monthly Rainfall, sunshine, temperature, humidity and wind speed. World Weather and Climate InformationGoogle Scholar
  60. Wu Z, Huang NE (2004) A study of the characteristics of white noise using the empirical mode decomposition method. Proc R Soc Lond 460A:1597–1611CrossRefGoogle Scholar
  61. Wu Z, Huang NE, Wallace JM, Smoliak BV, Chen X (2011) On the time-varying trend in global-mean surface temperature. Clim Dyn 37:759–773CrossRefGoogle Scholar
  62. Xie LA, Pietrafesa LJ, Wu K (2002) Interannual and decadal variability of landfalling tropical cyclones in the southeast coastal states of the United States. Adv Atmos Sci 19(4):677–686CrossRefGoogle Scholar
  63. Zhang YC (1991) Complexity and 1/f noise: a phase space approach. J Phys I Fr 1:971–977CrossRefGoogle Scholar
  64. Zhang W, Villarini G (2017) Heavy precipitation is highly sensitive to the magnitude of future warming. Clim Change 145(1–2):249–257CrossRefGoogle Scholar

Copyright information

© The International Society of Paddy and Water Environment Engineering 2019

Authors and Affiliations

  1. 1.Department of Water Resources Engineering, Faculty of Civil EngineeringUniversity of TabrizTabrizIran
  2. 2.Department of Bioresource EngineeringMcGill UniversitySte. Anne de BellevueCanada

Personalised recommendations