Advertisement

Theoretical and Applied Climatology

, Volume 122, Issue 3–4, pp 685–697 | Cite as

A large sample investigation of temporal scale-invariance in rainfall over the tropical urban island of Singapore

  • Pradeep V. Mandapaka
  • Xiaosheng QinEmail author
Original Paper

Abstract

Scaling behavior of rainfall time series is characterized using monofractal, spectral, and multifractal frameworks. The study analyzed temporal scale-invariance of rainfall in the tropical island of Singapore using a large dataset comprising 31 years of hourly and 3 years of 1-min rainfall measurements. First, the rainfall time series is transformed into an occurrence–non-occurrence binary series, and its scaling behavior is analyzed using box-counting analysis. The results indicated that the rainfall support displays fractal structure, but within a limited range of scales. The rainfall support has a fractal dimension (D f ) of 0.56 for scales ranging from 1 min to 1.5 h and a D f of 0.37 from 1.5 h to 1.5 days. The results further showed that the fractal dimension decreases with the increase in the threshold used to define binary series. Spectral analysis carried out on the rainfall time series and the corresponding binary series showed three distinct scaling regimes of 4 min–2 h, 2–24 h, and 24 h–1 month. In all the scaling regimes, the spectral exponents for the rainfall series were smaller than those for the binary series. The study then investigated the presence of multiscaling behavior in rainfall time series using moment scaling analysis. The results confirmed that the rainfall fluctuations display a multiscaling structure, which was modeled in the framework of universal multifractals. The results from this study would not only improve our understanding of the temporal rainfall structure in Singapore and the surrounding Maritime Continent but also help us build and parameterize parsimonious models and statistical downscaling techniques for rainfall in this region.

Keywords

Multifractal Analysis Rainfall Series Spectral Slope Rainfall Time Series Saturation Regime 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This study was supported by Singapores Ministry of Education (MOE) AcRF Tier 2 (M4020182.030) project. The authors appreciate the support from the National Environmental Agency of Singapore for providing rain gauge data.

References

  1. Breslin M, Belward J (1999) Fractal dimensions for rainfall time series. Math Comput Simulat 48 (4):437–446CrossRefGoogle Scholar
  2. Chatterjea K (1998) The impact of tropical rainstorms on sediment and runoff generation from bare and grasscovered surfaces: a plot study from Singapore. Land Degrad Dev 9(2):143–157CrossRefGoogle Scholar
  3. Chatterjea K (2011) Severe wet spells and vulnerability of urban slopes: case of Singapore. Nat Hazards 56(1):1–18CrossRefGoogle Scholar
  4. Chia LS, Foong FS (1991) Climate and weather. In: Tay DBH, Chia L S, Rahman A (eds) The biophysical environment of Singapore. National University of Singapore Press, pp 13–49Google Scholar
  5. De Montera L, Barthès L, Mallet C, Golé P (2009) The effect of rain—no rain intermittency on the estimation of the universal multifractals model parameters. J Hydrometeorol 10(2):493– 506CrossRefGoogle Scholar
  6. Deidda R, Benzi R, Siccardi F (1999) Multifractal modeling of anomalous scaling laws in rainfall. Water Resour Res 35(6):1853–1867CrossRefGoogle Scholar
  7. Deidda R, Badas M, Piga E (2004) Space-time scaling in high intensity tropical ocean global atmosphere coupled ocean-atmosphere response experiment TOGA-COARE storms. Water Resour Res 40(2):W02,506Google Scholar
  8. Falconer K (2004) Fractal geometry: mathematical foundations and applications, WileyGoogle Scholar
  9. Fong M (2012) The weather and climate of Singapore, Meteorological Service Singapore, SingaporeGoogle Scholar
  10. Fraedrich K, Larnder C (1993) Scaling regimes of composite rainfall time series. Tellus 45(4):289–298CrossRefGoogle Scholar
  11. Gan TY, Wang Q, Seneka M (2002) Correlation dimensions of climate subsystems and their geographic variability. J Geophys Res 107(D23):ACL23–1–ACL23–17Google Scholar
  12. Gan TY, Gobena AK, Wang Q (2007) Precipitation of southwestern Canada: wavelet, scaling, multifractal analysis, and teleconnection to climate anomalies. J Geophys Res 112(D10):D10,110CrossRefGoogle Scholar
  13. Gaume E, Mouhous N, Andrieu H (2007) Rainfall stochastic disaggregation models: calibration and validation of a multiplicative cascade model. Adv Water Res 30(5):1301–1319CrossRefGoogle Scholar
  14. Gebremichael M, Vivoni ER, Watts CJ, Rodríguez JC (2007) Submesoscale spatiotemporal variability of North American monsoon rainfall over complex terrain. J Climate 20(9):1751–1773CrossRefGoogle Scholar
  15. Gebremichael M, Krajewski WF, Over T, Takayabu Y, Arkin P, Katayama M (2008) Scaling of tropical rainfall as observed by TRMM precipitation radar. Atmos Res 88(3-4):337–354CrossRefGoogle Scholar
  16. Georgakakos KP, Carsteanu A, Sturdevant-Rees P, Cramer J (1994) Observation and analysis of midwestern rain rates. J Appl Meteorol 33(12):1433–1444CrossRefGoogle Scholar
  17. Ghanmi H, Bargaoui Z, Mallet C (2013) Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate. Hydrol Sci J 58(3):483–497CrossRefGoogle Scholar
  18. Islam S, Bras R, Rodriguez-Iturbe I (1993) A possible explanation for low correlation dimension estimates for the atmosphere. J Appl Meteor 32(2):203–208CrossRefGoogle Scholar
  19. Kiely G, Ivanova K (1999) Multifractal analysis of hourly precipitation. Phys Chem Earth 24(7):781–786CrossRefGoogle Scholar
  20. Licznar P, Łomotowski J, Rupp DE (2011) Random cascade driven rainfall disaggregation for urban hydrology: an evaluation of six models and a new generator. Atmos Res 99(3–4):563–578CrossRefGoogle Scholar
  21. Lovejoy S (1982) Area-perimeter relation for rain and cloud areas. Science 216(4542):185–187CrossRefGoogle Scholar
  22. Lovejoy S, Mandelbrot B (1985) Fractal properties of rain, and a fractal model. Tellus 37(3):209–232CrossRefGoogle Scholar
  23. Lovejoy S, Schertzer D (2007) Scale, scaling and multifractals in geophysics: twenty years on. In: Tsonis A, Elsner J (eds) Nonlinear Dynamics in Geosciences. Springer, New York, pp 311–337CrossRefGoogle Scholar
  24. Lovejoy S, Schertzer D, Tsonis A (1987) Functional box-counting and multiple elliptical dimensions in rain. Science 235(4792):1036–1038CrossRefGoogle Scholar
  25. Lovejoy S, Schertzer D, Allaire V (2008) The remarkable wide range spatial scaling of TRMM precipitation. Atmos Res 90(1):10–32CrossRefGoogle Scholar
  26. Lu Y, Qin XS (2014) Multisite rainfall downscaling and disaggregation in a tropical urban area. J Hydrol 509:55–65CrossRefGoogle Scholar
  27. Mandapaka PV, Qin X (2013) Analysis and characterization of probability distribution and small-scale spatial variability of rainfall in Singapore using a dense gauge network. J Appl Meteor Climatol 52(12):2781–2796CrossRefGoogle Scholar
  28. Mandapaka PV, Lewandowski PA, Eichinger WE, Krajewski WF (2009) Multiscaling analysis of high resolution space-time lidar-rainfall. Nonlinear Process Geophys 16(5):579–598CrossRefGoogle Scholar
  29. Mandapaka PV, Villarini G, Seo BC, Krajewski WF (2010) Effect of radar-rainfall uncertainties on the spatial characterization of rainfall events. J Geophys Res 115(D17):D17,110. doi: 10.1029/2009JD013366 CrossRefGoogle Scholar
  30. Mandelbrot BB (1983) The fractal geometry of nature, Times BooksGoogle Scholar
  31. Mascaro G, Deidda R, Hellies M (2013) On the nature of rainfall intermittency as revealed by different metrics and sampling approaches. Hydrol Earth Syst Sci 17(1):355–369. doi: 10.5194/hess-17-355-2013 CrossRefGoogle Scholar
  32. Mascaro G, Vivoni ER, Gochis DJ, Watts CJ, Rodriguez JC (2014) Temporal downscaling and statistical analysis of rainfall across a topographic transect in Northwest Mexico. J Appl Meteor 53(4):910–927. doi: 10.1175/JAMC-D-13-0330.1 CrossRefGoogle Scholar
  33. Molini A, Katul GG, Porporato A (2009) Revisiting rainfall clustering and intermittency across different climatic regimes. Water Resour Res 45:W11,403Google Scholar
  34. Nykanen D (2008) Linkages between orographic forcing and the scaling properties of convective rainfall in mountainous regions. J Hydrometeorol 9(3):327–347CrossRefGoogle Scholar
  35. Nykanen D, Harris D (2003) Orographic influences on the multiscale statistical properties of precipitation. J Geophys Res 108(D8):8381CrossRefGoogle Scholar
  36. Olsson J (1995) Limits and characteristics of the multifractal behavior of a high-resolution rainfall time series. NPG 2(1):23–29Google Scholar
  37. Olsson J, Niemczynowicz J, Berndtsson R, Larson M (1992) An analysis of the rainfall time structure by box counting—some practical implications. J Hydrol 137(1):261–277CrossRefGoogle Scholar
  38. Olsson J, Niemczynowicz J, Berndtsson R (1993) Fractal analysis of high-resolution rainfall time series. J Geophys Res 98(D12):23,265–23,274CrossRefGoogle Scholar
  39. Over T, Gupta V (1996) A space-time theory of mesoscale rainfall using random cascades. J Geophys Res 101(26):319–26,331Google Scholar
  40. Pathirana A, Herath S, Yamada T (2003) Estimating rainfall distributions at high temporal resolutions using a multifractal model. Hydrol Earth Syst Sci 7:668–679CrossRefGoogle Scholar
  41. Purdy J, Harris D, Austin G, Seed A, Gray W (2001) A case study of orographic rainfall processes incorporating multiscaling characterization techniques. J Geophys Res 106(D8):7837– 7845CrossRefGoogle Scholar
  42. Renyi A (1970) Probability theory. Amsterdam, North-HollandGoogle Scholar
  43. Rubalcaba J (1997) Fractal analysis of climatic data: annual precipitation records in Spain. Theor Appl Climatol 56(1-2):83–87CrossRefGoogle Scholar
  44. Rysman JF, Verrier S, Lemaître Y, Moreau E (2013) Space-time variability of the rainfall over the Western Mediterranean region: a statistical analysisGoogle Scholar
  45. Schertzer D, Lovejoy S (1987) Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J Geophys Res 92(D8):9693–9714CrossRefGoogle Scholar
  46. Schertzer D, Lovejoy S (1997) Universal multifractals do exist!: Comments on “a statistical analysis of mesoscale rainfall as a random cascade”. J Appl Meteorol 36(9):1296–1303CrossRefGoogle Scholar
  47. Schmitt F, Vannitsem S, Barbosa A (1998) Modeling of rainfall time series using two-state renewal processes and multifractals. J Geophys Res 103(D18):23,181–23,193CrossRefGoogle Scholar
  48. Sivakumar B (2000a) Fractal analysis of rainfall observed in two different climatic regions. Hydrol Sci J 45(5):727–738CrossRefGoogle Scholar
  49. Sivakumar B (2000b) A preliminary investigation on the scaling behaviour of rainfall observed in two different climates. Hydrol Sci J 45(2):203–219CrossRefGoogle Scholar
  50. Svensson C, Olsson J, Berndtsson R (1996) Multifractal properties of daily rainfall in two different climates. Water Resour Res 32(8):2463–2472CrossRefGoogle Scholar
  51. Tessier Y, Lovejoy S, Schertzer D (1993) Universal multifractals: theory and observations for rain and clouds. J Appl Meteorol 32(2):223–250CrossRefGoogle Scholar
  52. Venugopal V, Foufoula-Georgiou E, Sapozhnikov V (1999) Evidence of dynamic scaling in space-time rainfall. J Geophys Res 104(D24):31,599–31,610CrossRefGoogle Scholar
  53. Venugopal V, Roux S, Foufoula-Georgiou E, Arneodo A (2006) Revisiting multifractality of high-resolution temporal rainfall using a wavelet-based formalism. Water Resour Res 42(6)Google Scholar
  54. Verrier S, Mallet C, Barthès L (2011) Multiscaling properties of rain in the time domain, taking into account rain support biases. J Geophys Res 116(D20):D20,119. doi: 10.1029/2011JD015719 CrossRefGoogle Scholar
  55. Watts IEM (1955) Rainfall of Singapore island. Singapore J Trop Geo 7:1–71Google Scholar
  56. Yonghe L, Kexin Z, Wanchang Z, Yuehong S, Hongqin P, Jinming F (2013) Multifractal analysis of 1-min summer rainfall time series from a monsoonal watershed in eastern China. Theor Appl Climatol 111(1-2):37–50. doi: 10.1007/s00704-012-0627-9 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.School of Civil and Environmental EngineeringNanyang Technological UniversityNanyangSingapore

Personalised recommendations