Scale invariance of regional wet and dry durations of rain fields: A diagnostic study

Journal of Geophysical Research: Atmospheres

Volumn 108, Issue 8, 2003, Pages

  Pavlopoulos, Harry ^a   Gupta, Vijay K ^b  

^a ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS   (Greece)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

Dry and wet epoch durations; Intermittence; Scale invariance; Statistical moments; Tail probabilities; Tail quantiles

Indexed keywords

RAINFALL; SPATIAL VARIATION; STATISTICAL ANALYSIS; TEMPORAL VARIATION; TOGA-COARE;

EID: 1642538943     PISSN: 01480227     EISSN: None     Source Type: Journal    
DOI: 10.1029/2002jd002763     Document Type: Article

References (49)

1. Bickel, P. J., and K. A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Holden-Day, Boca Raton, Fla., 1977.
2. Cutler, C. D., A review of the theory and estimation of fractal dimension, in Nonlinear Time Series and Chaos, vol. 1, Dimension Estimation and Models, edited by H. Tong, pp. 1-107, World Sci., River Edge, N. J., 1993.
3. Efron, B., and R. J. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993.
4. Foufoula-Georgiou, E., On scaling theories of space-time rainfall: Some recent results and open problems, in Stochastic Methods in Hydrology: Rainfall, Landforms and Floods, Adv. Ser. Stat. Sci. Appl. Prob., vol. 7, edited by O. E. Barndorff-Nielsen et al., pp. 129- 171, World Sci., River Edge, N. J., 1998.
5. Freidlin, M., and H. Pavlopoulos, On a stochastic model for moisture budget in an Eulerian atmospheric column. Environmetrics, 8, 425-440, 1997.
6. Grabowski, W. W., X. Wu, and M. W Moncrieff, Cloud-resolving modeling of tropical cloud systems during phase III of GATE, part 1: Two-dimensional experiments, J. Atmos. Sci., 53(24), 3684-3709, 1996.
7. Gupta, V. K., and D. R. Dawdy, Physical interpretations of regional variations in the scaling exponents of flood quantiles, in Scale Issues in Hydrological Modelling, edited by J. D. Kalma and M. Sivapalan, pp. 105-119, John Wiley, New York, 1995.
8. Gupta, V. K., and E. C. Waymire, Multiscaling properties of spatial rainfall and river flow distributions, J. of Geophys. Res., 95, 1999-2009, 1990.
9. Gupta, V. K., and E. C. Waymire, A statistical analysis of mesoscale rainfall as a random cascade, J. Appl. Meteorol., 32, 251-267, 1993.
10. Gupta, V K., and E. C. Waymire, Spatial variability and scale invariance in hydrologic regionalization, in Scale Dependence and Scale Invariance in Hydrology, edited by G. Sposito, pp. 88-135, Cambridge Univ. Press, New York, 1998a.
11. Gupta, V. K., and E. C. Waymire, Some mathematical aspects of rainfall, Landforms and floods, in Stochastic Methods in Hydrology: Rainfall, Landforms and Floods, Adv. Ser Stat. Sci. Appl. Prob., vol. 7, edited by O. E. Barndorff-Nielsen et al., pp. 129-171, World Sci., River Edge, N. J., 1998b.
12. Gupta, V. K., O. Mesa, and D. R. Dawdy, Multiscaling theory of flood peaks: Regional quantile analysis, Water Resour. Res., 30(12), 3405-3421, 1994.
13. Gupta, V. K., S. Castro, and T. Over, On scaling exponents of spatial peak flows from rainfall and river network geometry, J. Hydrol, 187, 81-104, 1996.
14. Holley, R., and E. C. Waymire, Multifractal dimensions and scaling exponents for strongly bounded random cascades, Ann. Appl. Prob., 2, 819-845, 1992.
15. Kahane, J. P., and J. Payriere, Sur certaines martingales de Benoit Mandelbrot, Adv. Math., 22, 131-145, 1976.
16. Karr, A. F., Probability, Springer-Verlag, New York, 1993.
17. Kedem, B., and L. S. Chiu, Ara rain rate processes self similar?, Water Resour. Res., 23, 1816-1818, 1987.
18. Kedem, B., and H. Pavlopoulos, On the threshold method for rainfall estimation: Choosing the optimal threshold level, J. Am. Stat. Assoc., 86, 626-633, 1991.
19. Lamperti, J., Semi-stable stochastic processes, Trans. Am. Math. Soc., 104, 62-78, 1962.
20. Lehmann, E. L., Testing Statistical Hypotheses, 2nd ed, John Wiley, New York, 1986.
21. Lovejoy, S., and B. B. Mandelbrot, Fractal properties of rain and a fractal model, Tellus, Ser. A, 37, 209-232, 1985.
22. Lovejoy, S., and D. Schertzer, Generalized scale invariance in the atmosphere and fractal models of rain, Water Resour. Res., 21(8), 1233-1250, 1985.
23. Lovejoy, S., and D. Schertzer, Multifractals and rain, in New Uncertainty Concepts in Hydrology and Water Resources, edited by Z. W. Kunzewicz, pp. 62-103, Cambridge Univ. Press, New York, 1995.
24. Lowen, S. B., and M. C. Teich, Fractal renewal processes generate 1/f noise, Phys. Rev. E, 47, 992-1001, 1993.
25. Mandelbrot, B. B., Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier, J. Fluid Mech.. 62, 331-358, 1974.
26. Mandelbrot, B. B., The Fractal Geometry of Nature, W. H., Freeman, New York, 1983.
27. Marsan, D., S. Lovejoy, and D. Schertzer, Causal space-time multifractal processes: Predictability and forecasting of rain fields, J. Geophys. Res., 101(D21), 26,333-26,346, 1996.
28. Marshak, A., A. Davis, R. Cahalan, and W. Wiscombe, Bounded cascade models as nonstationary multifractals, Phys. Rev. E, 49(1), 55-69, 1994.
29. Menabde, M., and M. Sivapalan, Linking space-time variability of rainfall and runoff fields: A dynamic approach, Adv. Water Resour., 24, 1001-1014, 2001.
30. Menabde, E., A. W. Seed, D. Harris, and G. L. Austin, Self-similar random fields and rainfall simulation, J. Geophys. Res., 102(D12), 13,509-13,515, 1997a.
31. Menabde, E., D, Harris, A. W. Seed, G. L. Austin, and C. D. Stow, Multiscaling properties of rainfall and bounded random cascades, Water Resour. Res., 33(12); 2823-2830, 1997b.
32. Onof, C., N. Mackay, N. Oh, and H. S. Wheater, An improved rainfall disaggregation technique for GCMs, J. Geophys. Res., 103(D16), 19,577-19,586, 1998.
33. Ossiander, M., and E. C. Waymire, Statistical estimation for multiplicative cascades, Ann. Stat., 28, 1533-1560, 2000.
34. Over, T., and V. K. Gupta, Statistical analysis of meso-scale rainfall: Dependence of a random cascade generator on large-scale forcing, J. Appl. Meteorol., 33(12), 1526-1542, 1994.
35. Over, T., and V. K. Gupta, A space-time theory of mesoscale rainfall using random cascades, J. Geophys. Res., 101, 26,319-26,331, 1996.
36. Pavlopoulos, H., and J. Gritsis, Wet and dry epoch durations of spatially averaged rain rate, their probability distributions and scaling properties, Environ. Ecol. Stat., 6, 351-380, 1999.
37. Pavlopoulos, H., and V. K. Gupta, On the intermittence of rainfields: A space-time approach, Tech. Rep. 143, Dep. of Stat., Athens Univ. of Econ., Athens, 2001.
38. Rao, C. R., Linear Statistical Inference and Its Applications, 2nd ed., John Wileày, 1973.
39. Rohatgi, V. K., An Introduction to Probability Theory and Mathematical Statistics, John Wiley, New York, 1976.
40. Schertzer, D., and S. Lovejoy, Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, J. Geophys. Res., 92(D8), 9693-9714, 1987.
41. Schmitt, F., S. Svannistsem, and A. Barbosa, Modeling of rainfall time series using two-state renewal processes and multifractals, J. Geophys. Res., 103(D18), 181-194, 1998.
42. Short, D. A., P. A. Kucera, B. S. Ferrier, J. C. Gerlach, S. A. Rutledge, and O. W. Thiele, Shipboard radar rainfall patterns within the TOGA/COARE IFA, Bull. Am. Meteorol. Soc., 78, 2817-2836, 1997.
43. Sposito, G., (Ed.), Scale Dependence and Scale Invariance in Hydrology, Cambridge Univ. Press, New York, 1998.
44. Tessier, Y., S. Lovejoy, and D. Schertzer, Universal multifractals: Theory and observations of rain and clouds, J. Appl. Meteorology, 32, 223-250, 1993.
45. Troutman, B. M., and T. M. Over, River flow mass exponents with fractal channel networks and rainfall, Adv. Water Resour., 24(9-10), 967-990, 2001.
46. Troutman, B., and A. V. Vecchia, Estimation of Renyi exponents in random cascades, Bernoulli, 5(2), 191-207, 1999.
47. Waymire, E. C., Scaling limits and self-similarity in precipitation fields, Water Resour. Res., 21(8), 1271-1281, 1985.
48. Waymire, E. C., and S. Williams, Multiplicative cascades: Dimension spectra and dependence, J. Fourier Anal. Appl, 1, 589-609, 1995.
49. Waymire, E. C., and S. Williams, A cascade decomposition theory with applications to Markov and exchangeable cascades, Trans. Am. Math. Soc., 348(2), 585-632, 1996.