Nonlinearity and self-similarity of rainfall in time and a stochastic model

Journal of Geophysical Research Atmospheres

Volumn 101, Issue 21, 1996, Pages 26371-26392

  Veneziano, Daniele ^a   Bras, Rafael L ^a   Niemann, Jeffrey D ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVECTIVE STORM; RAINFALL INTENSITY; RAINFALL MODEL; STATISTICAL ANALYSIS; STOCHASTIC MODEL;

EID: 0000234617     PISSN: 01480227     EISSN: None     Source Type: Journal    
DOI: 10.1029/96jd01658     Document Type: Article

References (37)

1. Benzi, R., L. Biferale, A. Crisanti, G. Paladin, M. Vergassola, and A. Vulpiani, A random process for the construction of multiaffine fields, Phys. D, 65, 352-358, 1993.
2. Bracewell, R., The Fourier Transform and Its Applications, McGraw-Hill, New York, 1965.
3. Cox, D. R., Long-range dependence: A review, in Statistics: An Appraisal, edited by H. A. David and H. T. David, pp. 55-74, Iowa State Univ. Press, Ames, 1984.
4. Crane, R. K., Space-time structure of rain rate fields, J. Geophys. Res., 95, 2001-2020, 1990.
5. Davis, A., A. Marshak, W. Wiscombe, and R. Cahalan, Multifractal characteristics of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated, J. Geophys. Res., 99, 8055-8072, 1994.
6. Evertsz, C. J. G., and B. B. Mandelbrot, Multifractal measures, Appendix B, in Chaos and Fractals, edited by H.-O. Peitgen, H. Jurgens, and D. Saupe, Springer-Verlag, New York, 1992.
7. Garcia-Bartual, R., and J. Marco, A stochastic model of the internal structure of convective precipitation in time at a raingauge site, J. Hydrol., 118, 129-142, 1990.
8. Georgakakos, K. P., A. A. Carsteanu, P. L. Sturdevant, and J. A. Cramer, Observation and analysis of midwestern rain rates, J. Appl. Meteorol., 33, 1433-1444, 1994.
9. Gupta, V. K., and E. C. Waymire, Multiscaling properties of spatial rainfall and river flow distributions, J. Geophys. Res., 95, 1999-2009, 1990.
10. Gupta, V. K., and E. C. Waymire, On lognormality and scaling in spatial rainfall averages?, in Non-linear Variability in Geophysics: Scaling and Fractals, edited by D. Schertzer and S. Lovejoy, pp. 175-183, Kluwer Academic, Norwell, Mass., 1991.
11. Gupta, V. K., and E. C. Waymire, A statistical analysis of mesoscale rainfall as a random cascade, J. Appl. Meteorol., 32(2), 251-267, 1993.
12. α spectral density random noise with special reference to flicker noise 1/|f|, Proc. IEEE, 56(3), 251-258, 1968.
13. Holley, R., and E. C. Waymire, Multifractal dimensions and scaling exponents for strongly bounded random cascades, Ann. Appl. Prob., 2, 819-845, 1992.
14. Hubert, P., Y. Tessier, S. Lovejoy, D. Schertzer, F. Schmitt, P. Ladoy, J. P. Carbonnel, S. Violette, and I. Desurosne, Multifractals and extreme rainfall events, Geoph. Res. Lett., 20(10), 931-934, 1993.
15. Kraichnan, R. H., and D. Montgomery, Two-dimensional turbulence, Rep. Prog. Phys., 43, 547-619, 1980.
16. Lesieur, M., and J. Herring, Diffusion of a passive scalar in two-dimensional turbulence, J. Fluid Mech., 161, 77-95, 1985.
17. Lovejoy, S., and B. B. Mandelbrot, Fractal properties of rain, and a fractal model, Tellus, 37(A), 209-232, 1985.
18. Lovejoy, S., and D. Schertzer, Multifractals, universality classes, and satellite and radar measurements of cloud and rain fields, J. Geophys. Res., 95, 2021-2034, 1990.
19. Lovejoy, S., and D. Schertzer, Multifractals and rain, in New Uncertainty Concepts in Hydrology and Water Resources, edited by Z. W. Kunzewicz, Unesco Ser. in Water Sci., Cambridge Univ. Press, New York, 1992.
20. Mandelbrot, B. B., Multifractal measures, especially for the geophysicist, Pure Appl. Geophys., 131, 5, 1989.
21. Marien, J. L., and G. L. Vandewiele, A point rainfall generator with internal storm structure, Water Resour. Res., 22(4), 5231-5238, 1986.
22. Marshak, A., A. Davis, R. Cahalan, and W. Wiscombe, Bounded cascade models as non-stationary multifractals, Phys. Rev. E, 49, 55-69, 1994.
23. Ohsaki, Y., On the significance of phase content in earthquake ground motions, Earthquake Eng. Struct. Dyn., 7, 427-439, 1979.
24. Over, T. M., and V. K. Gupta, Statistical analysis of mesoscale rainfall: Dependence of a random cascade generator on large-scale forcing, J. Appl. Meteorol., 3(12), 1526-1542, 1994.
25. Perica, S., and E. Foufoula-Georgiou, A model for multiscale diaggregation of spatial rainfall based on coupling meteorological and scaling descriptions, J. Geophys. Res., this issue.
26. Rodriguez-Iturbe, I., V. K. Gupta, and E. Waymire, Scale considerations in the modelling of temporal rainfall, Water Resour. Res., 20(11), 1611-1619, 1984.
27. Samorodnitsky, G., and M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall, New York, 1994.
28. Schertzer, D., and S. Lovejoy, Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative processes, J. Geophys. Res., 92, 9693-9714, 1987.
29. Schertzer, D., and S. Lovejoy, Nonlinear geodynamical variability: Multiple singularities, universality and observables, in Non-linear Variability in Geophysics: Scaling and Fractals, edited by D. Schertzer and S. Lovejoy, pp. 41-82, Kluwer Academic, Norwell, Mass., 1991.
30. Sinclair, P. C., Severe storm turbulent velocity and temperature structure, paper presented at the 6th Conference on Aerospace and Areonautical Meteorology, Am. Meteorol. Soc., Boston, Mass., 1974.
31. Sivapalan, M., and E. F. Wood, A multidimensional model of nonstationary space-time rainfall at the catchment scale, Water Resour. Res., 23(7), 1289-1299, 1987.
32. Tessier, Y., S. Lovejoy, and D. Schertzer, Universal multifractals: Theory and observations for rain and clouds, J. Appl. Meteorol., 32(2), 223-250, 1993.
33. Vicsek, T., and A.-L. Barabasi, Multi-affine model for the velocity distribution in fully turbulent flows, J. Phys. A Math. Gen., 24, L845-851, 1991.
34. Waymire, E. C., and V. K. Gupta, The mathematical structure of rainfall representation, 1, A review of stochastic rainfall models, 2, A review of the point processes theory, 3, Some applications of the point process theory to rainfall processes, Water Resour. Res., 17(5), 1261-1294, 1981.
35. Waymire, E. C., V. K. Gupta, and I. Rodriguez-Iturbe, A spectral theory of rainfall intensity at the meso-β scale, Water Resour. Res., 20(10), 1453-1465, 1984.
36. Wilson, J., D. Schertzer, and S. Lovejoy, Continuous multiplicative cascade models of rain and cloud, in Non-linear Variability in Geophysics: Scaling and Fractals, edited by D. Schertzer and S. Lovejoy, pp. 185-207, Kluwer Academic, 1991.
37. Yaglom, A. M., An Introduction to the Theory of Stationary Random Functions, Prentice-Hall, New York, 1962.