A simple model of rain in time: An alternating renewal process of wet and dry states with a fractional (non-Gaussian) rain intensity

Atmospheric Research

Volumn 84, Issue 4, 2007, Pages 291-301

  Bernardara, P ^a,b   De Michele, C ^c   Rosso, R ^c  

^a Universite Paris Est   (France)

^b CENTRE DE LYON VILLEURBANNE   (France)

^c POLITECNICO DI MILANO   (Italy)

Author keywords

Calibration; Fractional Noise; Model; Rainfall; Renewal process; Scale invariance; Spectral density; Validation

Indexed keywords

ATMOSPHERIC DENSITY; ATMOSPHERIC SPECTRA; CLIMATE CHANGE; INVARIANCE; MATHEMATICAL MODELS;

RAIN INTENSITY; RENEWAL PROCESS; SCALE INVARIANCE; SYNOPTIC WEATHER;

RAIN;

CALIBRATION; COUPLING; DATA SET; DRY SEASON; MODEL; PRECIPITATION INTENSITY; RAINFALL; SPECTRAL ANALYSIS; WET SEASON;

EID: 34248348768     PISSN: 01698095     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.atmosres.2006.09.001     Document Type: Article

References (39)

1. Arnaud P., and Lavabre J. Using a stochastic model for generating hourly hyetographs to study extreme rainfall. Hydrological Sciences Journal - Journal Des Sciences Hydrologiques 44 3 (1999) 433-446
2. Arnaud P., and Lavabre J. Coupled rainfall model and discharge model for flood frequency estimation. Water Resources Research 38 6 (2002) 1075
3. Becchi I., and Castelli F. Lettura e archiviazione digitali di registrazioni pluviografiche ad alta risoluzione temporale (1990), Tech.rep. Dep. Of Civil Eng., University of Florence, Italy
4. Beirlant J., Teugels J.L., and Vynckiee P. Practical Analysis of Extreme Values (1996), Leuven University Press
5. Cernesson F., Lavabre J., and Masson J.-M. Stochastic model for generating hourly hyetographs. Atmospheric Research 42 1-4 (1996) 149-161
6. Cowpertwait P.S.P. Further developments of the Neymann-Scott clustered point process for modelling rainfall. Water Resources Research 27 7 (1991) 1431-1438
7. Cowpertwait P.S.P. A generalized point process model for rainfall. Proceedings of the royal society of London A447 (1994) 23-37
8. De Michele C., and Bernardara P. Spectral analysis and modeling of space-time rainfall fields. Atmospheric Research 77 1-4 (2005) 124-136
9. De Michele C., and Salvadori G. A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas. Journal of Geophysical Research, Atmospheres 108 D2 (2003) 4067
10. De Michele C., and Salvadori G. Some hydrological applications of small sample estimators of Generalized Pareto and Extreme Value distributions. Journal of Hydrology 301 1-4 (2005) 37-53
11. Deidda R., Benzi R., and Siccardi F. Multifractal modeling of anomalous scaling laws in rainfall. Water Resources Research 35 6 (1999) 1853-1867
12. Eagleson P.S. Climate, soil and vegetation: 2. the distribution of annual precipitation derived from observed storm sequences. Water Resources Research 14 5 (1978) 713-721
13. Hardy H.H., and Beier R.A. Fractals in reservoir engineering. World Scientific (1994)
14. Hill B.M. A simple general approach to inference about the tail of a distribution. The Annals of Statistics 3 5 (1975) 1163-1174
15. Hubert P., et al. Multifractals and extreme rainfall events. Geophysical Research Letters 20 (1993) 931-934
16. Kottegoda N.T., and Rosso R. Statistics, Probability and Reliability for Civil and Environmental Engineers (1997), McGraw-Hill
17. Lang M., Ouarda T.B.M.J., and Bobee B. Towards operational guidelines for over-threshold modeling. Journal of Hydrology 225 3-4 (1999) 103-117
18. Le Cam L. A Stochastic Description of Precipitation, Fourth Symposium on Mathematical Statistics and Probability (1961), University of California, Berkeley 165-186
19. Malamud B.D., and Turcotte D.L. Self affine time series: measures of weak and strong persistence. Journal of Statistical Planning and Inference 80 (1999) 173-196
20. Menabde M., Harris D., Seed A., Austin G., and Stow D. Multiscaling properties of rainfall and bounded random cascades. Water Resources Research 33 12 (1997) 2823-2830
21. Menabde M., and Sivapalan M. Modeling of rainfall time series and extremes using bounded random cascades. Water Resources Research 36 11 (2000) 3293-3300
22. Olsson J., and Burlando P. Reproduction of temporal scaling by a rectangular pulses rainfall model. Hydrological Processes 16 3 (2002) 611-630
23. Olsson J., Niemczynowicz J., and Berndtsson R. Fractal analysis of high-resolution rainfall time series. Journal of Geophysical Research 98 D12 (1993) 23265-23274
24. Pavlopoulos H., and Gupta V.K. Scale invariance of regional wet and dry duration of rain fields: a diagnostic study. Journal of Geophysical Research 108 D8 (2003) 8387-8401
25. Peters O., and Christensen K. Rain: relaxations in the sky. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 66 3 (2002) 036120-036129
26. Peters O., Hertlein C., and Christensen K. A complexity view of rainfall. Physical Review Letters 88 1 (2002) 018701-018704
27. Pickands J. Statistical inference using extreme order statistics. The Annals of Statistics 3 1 (1975) 119-131
28. Rodriguez-Iturbe I., Febres de Power B., and Valdes J.B. Rectangular pulse point process models for rainfall: analysis of empirical data. Journal of Geophysical Research 92 D8 (1987) 9645-9656
29. Salvadori G., and De Michele C. From Generalized Pareto to Extreme Value laws: scaling properties and derived features. Journal of Geophysical Research 106 D20 (2001) 24,063-24,070
30. Salvadori G., and De Michele C. Statistical characterization of temporal structure of storms. Advances in Water Resources 29 6 (2006) 827-842
31. Schertzer D., and Lovejoy S. Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. Journal of Geophysical Research 92 D8 (1987) 9693-9714
32. Schmitt F., Vannitsem S., and Barbosa A. Modeling of rainfall time series using two-state renewal processes and multifractals. Journal of Geophysical Research 103 D18 (1998) 23181-23193
33. Veneziano D., Bras R.L., and Niemann J.D. Nonlinearity and self-similarity of rainfall in time and a stochastic model. Journal of Geophysical Research 101 D21 (1996) 26371-26392
34. Veneziano D., and Furcolo P. Multifractality of rainfall and scaling of intensity-duration-frequency curves. Water Resources Research 38 12 (2002) 10.1029/2001WR000372
35. Venugopal V., and Foufoula-Georgiou E. Energy decomposition of rainfall in the time-frequency-scale domain using wavelet packets. Journal of Hydrology 187 1-2 (1996) 3-27
36. Venugopal V., Roux S.G., and Foufoula-Georgiou E. Revisiting multifractality of high resolution temporal rainfall using a wavelet-based formalism. Water Resources Research 42 W06D14 (2006) 10.1029/2005WR004489
37. Waymire E., and Gupta V.K. The mathematical structure of rainfall representation: a review of the stochastic rainfall models. Water Resources Research 17 5 (1981) 1261-1272
38. Willems P. Hydrological applications of extreme value analysis. In: Wheater H.a.C.K. (Ed). Hydrology in a Changing Environment (1998), John Wiley & Sons, Chichester 15-25
39. Zawadzky I. Statistical properties of precipitation patterns. Journal of Applied Meteorology 12 (1973) 469-472