Skip to main content
SpringerLink
Log in
Book cover

Recent Advances in Fluid Dynamics with Environmental Applications pp 139–152Cite as

Rainfall Series Fractality in the Baja California State

  • Conference paper
  • First Online:

Part of the book series: Environmental Science and Engineering ((ENVENG))

Abstract

A fractal analysis of rainfall events registered in Baja California was carried out. Rainfall data from 92 climatological stations distributed along the studied region with at least 30 years of records were used. By studying rainfall series patterns, Hurst exponent values were obtained. The rescalated range method (R/S), box-counting method and the Multifractal Detrended Fluctuation Analysis (MF-DFA) were used, having as a result the Hurst exponent values for different time scales (entire record, 25, 10, and 5 years scales). Data showed that the daily rainfall series tended to present a persistent pattern. The analysis from the Hurst exponent on the previously mentioned time scales showed that, at a lesser time scale, their values increase; thus, the series tended to present a stronger persistent behavior.

This is a preview of subscription content, log in via an institution.

References

  • Akbari A, Friedel M (2014) Forecasting conditional climate-change using a hybrid approach. Environ Modell Softw 52:83–97

    Google Scholar 

  • Amaro IR, Demey JR, Macchiavelli R (2004) Aplicación del análisis R/S de Hurst para estudiar las propiedades fractales de la precipitación en Venezuela. Interciencia 29:617–620

    Google Scholar 

  • Beran J (1994) Statistics for long-memory processes. Monographs on statistics and probability 61. Chapman & Hall, New York

    Google Scholar 

  • Breslin MC, Belward JA (1999) Fractal dimensions for rainfall time series. Math Comput Simul 48:437–446

    Google Scholar 

  • Brunsell N (2010) Amultiscale information theory approach to assess spatial–temporal variability of daily precipitation. J Hydrol 385:165–172

    Google Scholar 

  • Caballero R, Jewson S, Brix A (2002) Long memory in surface air temperature: detection, modeling, and application to weather derivative valuation. Clim Res 21:127–140

    Google Scholar 

  • Capecchi V, Crisci A, Melani S, Morabito M, Politi P (2012) Fractal characterization of rain-gauge networks and precipitations: an application in Central Italy. Atmos Ocean Phys 107:541–546

    Google Scholar 

  • Fluegeman RH Jr, Snow RS (1989) Fractal analysis of long-range paleoclimatic data: oxygen isotope record of pacific core V28-239. PAGEOPH 131:307–313

    Google Scholar 

  • Gallant JC, Moore ID, Hutchinson MF, Gessler P (1994) Estimating fractal dimension of profiles: a comparison of methods. Math Geol 26:455–481

    Google Scholar 

  • Gires A, Tchiguirinskaia I, Schertezer D, Lovejoy S (2012) Influence of the zero rainfall on the assessment of the multifractal parameters. Adv Water Resour 45:13–25

    Google Scholar 

  • Gires A, Tchiguirinskaia I, Schertzer D, Schellart A, Berne A, Lovejoy S (2014) Influence of small scale rainfall variability on standard comparison tools between radar and rain gauge data. Atmos Res 138:125–138

    Google Scholar 

  • Hentschel HG, Procaccia I (1984) Relative diffusion in turbulent media: the fractal dimension of clouds. Phys Rev A 29:1461–1470

    Google Scholar 

  • Hoang CT, Tchiguirinskaia I, SchertzerD Arnaud P, Lavabre J, Lovejoy S (2012) Assessing the high frequency quality of long rainfall series. J Hydrol 438–439:39–51

    Google Scholar 

  • Huai-Hsien H, Puente CE, Cortis A, Fernández JL (2013) An effective inversion strategy for fractal–multifractal encoding of a storm in Boston. J Hydrol 496:205–216

    Google Scholar 

  • Hubert P, Carbonnel JP (1990) Fractal characterization of intertropical precipitations variability and anisotropy. Non-Linear Variab Geophys 3:209–213

    Google Scholar 

  • Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Am Soc Civil Eng 116:770–880

    Google Scholar 

  • Hurst HE (1956) Methods of using long-term storage in reservoirs. Proc Inst Civil Eng 1:516–543

    Google Scholar 

  • Kalauzi A, Cukic M, Millan H, Bonafoni S, Biondi R (2009) Comparison of fractal dimension oscillations and trends of rainfall data from Pastaza Province, Ecuador and Veneto, Italy. Atmos Res 93:673–679

    Google Scholar 

  • Kantelhardt JW, Rybski D, Zschiegner SA, Braun P, Koscielny-Bunde E, Livina V, Havlin S, Bunde A (2003) Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods. Phys A 330:240–245

    Google Scholar 

  • Koutsoyiannis D, Paschalis A, Theodoratos N (2011) Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields. J Hydrol 398:91–100

    Google Scholar 

  • Lanza LG, Gallant J (2006) Fractals and similarity approaches in hydrology. Encycl Hydrol Sci 123–133

    Google Scholar 

  • Lombardo V, Volpi E, Koutsoyiannis D (2012) Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades. Hydrol Sci J 57:1052–1066

    Google Scholar 

  • López Lambraño AA (2012) Tesis de Doctorado en Facultad de Ingeniería, Universidad Autónoma de Querétaro

    Google Scholar 

  • Lovejoy S, Mandelbrot B (1985) Fractal properties of rain and a fractal model. Tellus 37A:209–232

    Google Scholar 

  • Lovejoy S, Pinel J, Schertzer D (2012) The global space–time cascade structure of precipitation: satellites, gridded gauges and reanalyses. Adv Wat Resour 45:37–50

    Google Scholar 

  • Lovejoy S, Schertzer D, Tsonis AA (1987) Functional box-counting and multiple elliptical dimensions in rain. Science 235:1036–1038

    Google Scholar 

  • Lovejoy S, Schertzer D (1990) Multifractals, universality classes and satellite and radar measurements of cloud and rain fields. J Geophys Res 95:2021–2034

    Google Scholar 

  • Lovejoy S, Schertzer D (2006) Multifractals, cloud radiances and rain. J Hydrol 322:59–88

    Google Scholar 

  • Malamud BD, Turcotte DL (1999) Self-affine time series: measures of weak and strong persistence. J Stat Plan Inf 80:173–196

    Google Scholar 

  • Malinowski SR, Lecrerc MY, Baumgardner D (1993) Fractal analysis of high-resolution cloud droplet measurements. J Atmos Sci 397–413

    Google Scholar 

  • Mandelbrot BB (1972) Statistical methodology for nonperiodic cycles: from the covariance to R/S analysis. Ann Econ Soc Meas 1(3):259–290

    Google Scholar 

  • Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636–638

    Google Scholar 

  • Millan H, Rodriguez J, Ghanbarian-Alavijeh B, Biondi R, Llerena G (2011) Temporal complexity of daily precipitation records from different atmospheric environments: chaotic and Lévy stable parameters. Atmos Res 101:879–892

    Google Scholar 

  • Movahed S, Jafari G, Ghasemi F, Rahvar S, Rahimi M (2006) Multifractal detrended fluctuation analysis of sunspot time series. J Stat Mech-Theory E P02003:1–17

    Google Scholar 

  • Nunes S, Romani L, Avila A, TrainaJr C, de Sousa EPM, Traina AJM (2011) Fractal-based analysis to identify trend changes in multiple climate time series. J Inf Data Manag 2:51–57

    Google Scholar 

  • Oñate JJ (1997) Fractal analysis of climatic data: annual precipitation records in Spain. Theoret Appl Climatol 56(1–2):83–87

    Google Scholar 

  • Peñate I, Martín-González JM, Rodríguez G, Cianca A (2013) Scaling properties of rainfall and desert dust in the Canary Islands. Nonlinear Process Geophys 20:1079–1094

    Google Scholar 

  • Peters O, Hertlein C, Christensen K (2002) A complexity view of rainfall. Phys Rev Lett 88:1–4

    Google Scholar 

  • Pinel J, Lovejoy S, Schertzer D (2014) The horizontal space–time scaling and cascade structure of the atmosphere and satellite radiances. Atmos Res 140–141:95–114

    Google Scholar 

  • Rangarajan G, Sant D (2004) Fractal dimensional analysis of Indian climatic dynamics. Chaos Solitons Fractals 19:285–291

    Google Scholar 

  • Rehman S (2009) Study of Saudi Arabian climatic conditions using Hurst. Chaos Solitons Fractals 39:499–509

    Google Scholar 

  • Schepers HE, van Beek JHGM, Bassingthwaighte JB (1992) Four methods to estimate the fractal dimension from self-affine signals. IEEE Eng Med Biol 11:57–64

    Google Scholar 

  • Schertzer D, Tchiguirinskaia I, Lovejoy S, Hubert P (2010) No monsters, no miracles: in nonlinear sciences hydrology is not an outlier! Hydrol Sci J—Journal des Sciences Hydrologiques 55:965–979

    Google Scholar 

  • Schertzer D, Lovejoy S (1987) Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J Geophys Res 92:9693–9714

    Google Scholar 

  • Selvam AM (2010) Universal inverse power law distribution for fractal fluctuations in dynamical systems: applications for predictability of inter—annual variability of Indian and USA region rainfall. Cornell University Library, pp 1–28

    Google Scholar 

  • Sivakumar B (2000) A preliminary investigation on the scaling behavior of rainfall observed in two different climates. Hydrol Sci J 45:203–219

    Google Scholar 

  • Svanidze GG (1980) Mathematical modeling of hydrologic series. Water Resources Publications, USA, pp 847–848

    Google Scholar 

  • Tao K, Barros A (2010) Using fractal downscaling of satellite precipitation products for hydrometeorological applications. J Atmos Ocean Technol 27:409–427

    Google Scholar 

  • Turcotte D (1994) Fractal theory and estimation of extreme floods. J Res Nail Inst Stand Technol 99:377–389

    Google Scholar 

  • Valdez-Cepeda R, Hernandez-Ramirez D, Mendoza B, Valdes-Galicia J, Maravilla D (2003) Fractality of monthly extreme minimum temperature. Fractals 11:137–144

    Google Scholar 

  • Velásquez MA, Medina G, Sánchez I, Oleschko K, Ruiz JA, Korvin G (2013) Spatial variability of the hurst exponent for the daily scale rainfall series in the State of Zacatecas, Mexico. Am Meteorol Soc 52:2771–2780

    Google Scholar 

  • Venugopal V, Foufola-Georgiuo E, Sapozhnikov V (1999) Evidence of dynamic scaling in space-time rainfall. J Geophys Res 104:31599–31610

    Google Scholar 

  • Verrier S, de Montera L, Barthès L, Mallet C (2010) Multifractal analysis of African monsoon rain fields, taking into account the zero rain-rate problem. J Hydrol 389:111–120

    Google Scholar 

  • Xu J, Chen Y, Li W, Liu Z, Tang J, Wei C (2015) Understanding temporal and spatial complexity of precipitation distribution in Xinjiang, China. Theor Appl Climatol 1–13

    Google Scholar 

  • Yuval, Broday DM (2010) Studying the time scale dependence of environmental variables predictability using fractal analysis. Environ Sci Technol 44:4629–4634

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Ingeniería, Universidad Autónoma de Baja California (UABC), Km. 103 Carretera Tijuana—Ensenada, C.P. 22860, Mexicali, BC, Mexico

    A. López-Lambraño

  2. Instituto Mexicano de Tecnología del Agua, Paseo Cuauhnahuac 8532, Progreso, 62550, Jiutepec, Morelos, Mexico

    C. Fuentes

  3. Escuela de Ingenierías y Arquitectura, Facultad de Ingeniería Civil, Universidad Pontificia Bolivariana-Seccional Montería, Km. 8 vía a Cereté, Montería, Córdoba, Colombia

    A. López-Ramos

  4. Instituto Tecnológico de Querétaro, Ciencias Básicas. Av. Tecnológico S/N, Centro, 76000, Santiago de Querétaro, Qro, Mexico

    M. Pliego-Díaz

  5. Universidad del Norte, Km. 5 Vía Puerto Colombia, Barranquilla, Colombia

    M. López-L

Authors
  1. A. López-Lambraño
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Fuentes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. López-Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Pliego-Díaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. López-L
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. López-Lambraño .

Editor information

Editors and Affiliations

  1. Instituto Nacional de Investigaciones Nucleares, Ocoyoacac, Mexico

    Jaime Klapp

  2. Departamento de Ciencias Básicas, UAM Azcapotzalco, Mexico City, Mexico

    Leonardo Di G. Sigalotti

  3. SEPI ESIME Azcapotzalco, Instituto Politécnico Nacional, Mexico City, Mexico

    Abraham Medina

  4. SEPI ESIME Azcapotzalco, Instituto Politécnico Nacional, Mexico City, Mexico

    Abel López

  5. Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Gerardo Ruiz-Chavarría

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

López-Lambraño, A., Fuentes, C., López-Ramos, A., Pliego-Díaz, M., López-L, M. (2016). Rainfall Series Fractality in the Baja California State. In: Klapp, J., Sigalotti, L.D.G., Medina, A., López, A., Ruiz-Chavarría, G. (eds) Recent Advances in Fluid Dynamics with Environmental Applications. Environmental Science and Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-27965-7_11

Download citation

Publish with us

Policies and ethics

Search

Navigation