Lacunarity, predictability and predictive instability of the daily pluviometric regime in the Iberian Peninsula

Nonlinear Processes in Geophysics

Volumn 14, Issue 2, 2007, Pages 109-121

  Marlincz M D ^a   Lana, X ^a   Burgneno A ^a   Serra, C ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; DATABASE; HYDROLOGICAL REGIME; INSTABILITY; PERSISTENCE; POWER LAW; PRECIPITATION ASSESSMENT; PRECIPITATION INTENSITY; PREDICTION; RAINGAUGE; SPATIAL DISTRIBUTION;

EURASIA; EUROPE; IBERIAN PENINSULA; MEDITERRANEAN COAST [SPAIN]; PORTUGAL; SOUTHERN EUROPE; SPAIN;

EID: 33947257568     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-14-109-2007     Document Type: Article

References (39)

1. Burgueño, A., Martínez, M. D., Lana, X., and Serra, C.: Statistical distributions of the daily rainfall regime in Catalonia (NE Spain) for the years 1950-2000, Int. J. Climatol., 25, 1381-1403, 2005.
2. Diks, C.: Nonlinear Time Series Analysis. Methods and Applications. Nonlinear Time Series and Chaos, vol. 4., World Scientific, London, 1999.
3. Eckmann, J. P., Oliffson, S., Ruelle, D., and Ciliberto, S.: Lyapunov exponents from time series, Phys. Rew. (A), 34(6), 4971-4979, 1986.
4. Fedder, J.: Fractals, Ed. Plenum, New York, USA, 1988.
5. Goltz, C.: Fractal and Chaotic Properties of Earthquakes, in: Lecture Notes in Earth Sciences 77, Springer, Berlin, 1997.
6. Grassberger, P. and Procaccia, I.: Characterization of strange attractors, Phys. Rev. Lett., 50, 346-349, 1983a.
7. Grassberger, P. and Procaccia, I.: Estimation of the Kolmogorov entropy from a chaotic signal, Phys. Rev. (A), 28, 2591-2593, 1983b.
8. Harris, D., Menabde, M., Seed, A., and Austin, G.: Multifractal characterization of rain fields with a strong orographic influence, J. Geophys. Res., 101, 26405-26414, 1996.
9. Hubert, P., Tessier, Y., Lovejoy, S., Shertzer, D., Schmitt, F., Ladoy, P., Carbonnel, J. P., Violette, S., and Desurosne, I.: Multifractals and extreme rainfall events, Geophys. Res. Lett., 20(10), 931-934, 1993.
10. Korvin, G.: Fractal Models in Earth Sciences, Elsevier, Amsterdam, 1992.
11. Lana, X., Martínez, M. D., Serra, C., and Burgueño, A.: Spatial and temporal variability of the daily rainfall regime for Catalonia (NE Spain), 1950-2000, Int. J. Climatol., 24, 613-641, 2004.
12. Lana, X., Martínez, M. D., Posadas, A. M., and Canas, A.: Fractal behaviour of the seismicity in the Southern Iberian Peninsula, Nonlin. Processes Geophys., 12, 353-361, 2005, http://www.nonlin-processes-geophys.net/12/353/ 2005A
13. Lana, X., Martínez, M. D., Burgueño, A., Serra, C., Martín-Vide, J., and Gómez, L.: Distribution of long dry spells in the Iberian Peninsula, years 1951-1990, Int. J. Climatol., 26, 1999-2021, 2006.
14. Lima, M. I. P. and Grasman, J.: Multifractal analysis of 15-min and daily rainfall from a semi-arid region in Portugal, J. Hydrol., 220, 1-11, 1999.
15. Lin, B. and Yang, Z. R.: A suggested lacunarity expression for Sierpinski carpets, J. Phys. A, Math. Gen., 19, L49-L52, 1986.
16. Lovejoy, S. and Mandelbrot, B. B.: Fractal properties of rain and a fractal model, Tellus, 37A, 209-232, 1985.
17. Mandelbrot, B. B.: The Fractal Geometry of Nature, Freemann, San Francisco, USA, 1982.
18. Martínez, M. D., Lana, X., Burgueño, A., and Serra, C.: Spatial and temporal daily rainfall regime in Catalonia (NE Spain) derived from four precipitation indices, years 1950-2000, Int. J. Climatol., 27, 123-138, 2007.
19. Mazzarella, A.: Multifractal dynamic rainfall processes in Italy, Theor. Appl. Climatol., 63, 73-78, 1999.
20. Mazzarella, A. and Tranfaglia, G.: Fractal characterisation of geophysical measuring networks and its implication for an optimal location of additional stations: an application to a rain-gauge network, Theor. Appl. Climatol., 65, 157-163, 2000.
21. Miranda, J. G. V. and Andrade, R. F. S.: Rescaled range analysis of pluviometric records in Northeast Brazil, Theor. Appl. Climatol., 63, 79-88, 1999.
22. Miranda, J. G. V. and Andrade, R. F. S.: R/S analysis of pluviometrie records: comparison with numerical experiments, Physica A, 295, 38-41, 2001.
23. Miranda, J. G. V., Andrade, R. F. S., da Silva, A. B., Ferreira, C. S., Gonzalez, A. P., and Carrera López, J. L.: Temporal and spatial persistence in rainfall records from Northeast Brazil and Galicia (Spain), Theor. Appl. Climatol., 77, 113-121, 2004.
24. Oliver, M. A. and Webster, R.: Kriging: a method of interpolation for geographical information system, Int. J. Geographical Information Systems, 4(3), 313-332, 1990.
25. Olsson, J., Niemczynowicz, J., and Berndtsson, R.: Fractal analysis of high-resolution rainfall time series, J. Geophys. Res., 98, 23265-23274, 1993.
26. Oñate, J. J.: Fractal analysis of climatic data: annual precipitation records in Spain, Theor. Appl. Climatol, 56, 83-87, 1997.
27. Rodríguez-Iturbe, I., Febres de Power, B., Sharifi, M. B., and Georgakakos, K. P. (1989). Chaos in rainfall, Water Resour. Res., 25, 1667-1675, 1989.
28. Salas, J. D., Kim, S. H., Eykholt, R., Burlando, P., and Green, T. R.: Aggregation and sampling in deterministic chaos: implication for chaos identification in hydrological processes, Nonlin. Processes Geophys., 12, 557-567, 2005, http://www.nonlin-processes-geophys.net/12/557/2005/.
29. Sivakumar, B.: Rainfall dynamics at different temporal scales: A chaotic perspective, Hydrol. Earth Syst. Sci., 5, 645-651, 2001a.
30. Sivakumar, B.: Is a chaotic multi-fractal approach for rainfall possible?, Hydrol. Processes, 15, 943-955, 2001b.
31. Sivakumar, B., Sorooshian, S., Gupta, H. V., and Gao, X.: A chaotic approach to rainfall disaggregation, Water Resour. Res., 37, 61-72, 2001.
32. Stoop, R. and Meier, P. R: Evaluation of Lyapunov exponents and scaling functions from time series, J. Opt. Soc. Am. (B), 5, 1037-1045, 1988.
33. Svensson, C., Olsson, J., and Berndtsson, R.: Multifractal properties of daily rainfall in two different climates, Water Resour. Res., 32, 2463-2472, 1996.
34. Takens, F.: Detecting Strange Attractors in Turbulence, in: Lecture Note in Mathematics, edited by: Rand, D. A. and Young, L. S., Springer, Berlin, 1981.
35. Tessier, Y., Lovejoy, S., Hubert, P., Shertzer, D., and Pecknold, S.: Multifractal analysis and modelling of rainfall and river flows and scaling, causal transfer functions, J. Geophys. Res., 101, 26427-26440, 1996.
36. Turcotte, D. L.: Fractal and Chaos in Geology and Geophysics (2nd edition), Cambridge University Press, 1997.
37. Veneziano, D., Bras, R. L., and Niemann, J. D.: Nonlinearity and self-similarity of rainfall in time and a stochastic model, J. Geophys. Res., 101, 26371-26392, 1996.
38. Whiting, J. P., Lambert, M. F., and Metcalfe, A. V.: Modelling persistence in annual Australian point rainfall, Hydrol. Earth Syst. Sci., 7, 197-211, 2003, http://www.hydrol-earth-syst-sci.net/7/197/2003/.
39. Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A.: Determining Lyapunov exponents from a time series, Physica, 16D, 285-317, 1985.