ISSN ：1674-2370
CN ：32-1785/TV
| Citation: | Jacques GOLDER, Maminirina JOELSON, Marie-Christine NEEL, Liliana DI PIETRO. 2014: A time fractional model to represent rainfall process. Water Science and Engineering, 7(1): 32-40. doi: 10.3882/j.issn.1674-2370.2014.01.004
|
|
Cadavid, A. C., Lawrence, J. K., and Ruzmaikin, A. A. 1999. Anomalous diffusion of solar magnetic elements. The Astrophysical Journal,521(2), 844-850. [doi: 10.1086/307573]
|
|
Cho, H. K., Boxman, K. P., and North, G. R. 2004. A comparison of Gamma and lognormal distributions for characterizing satellite rain rates from the tropical rainfall measuring mission. Journal of Applied Meteorology, 43(11), 1586-1597. [doi: 10.1175/JAM2165.1]
|
|
de Lima, M. I. P., and Grasman, J. 1999. Multifractal analysis of 15-minute and daily rainfall from a semi-arid region in Portugal. Journal of Hydrology,220(1-2), 1-11.
|
|
Delrieu, G., Nicol, J., Yates, E., Kirstetter, P. E., Creutin, J. D., Anquetin, S., Obled, C., Saulnier, G. M., Ducrocq, V. Gaume, E., et al. 2005. The catastrophic flash-flood event of 8-9 September 2002 in the Gard region, France: A first case study for the Cévennes-Vivarais Mediterranean Hydrometeorological Observatory. Journal of Hydrometeorology,6(1), 34-52. [doi: 10.1175/JHM-400.1]
|
|
Gajda, J., and Magdziarz, M. 2010. Fractional Fokker-Planck equation with tempered α-stable waiting times: Langevin picture and computer simulation. Physical Review E, Statistical, Nonlinear, and Soft Matter Pgysics, 82(1 Pt 1) , 011117. [doi: 10.1103/PhysRevE.82.011117]
|
|
Gaume, E., Mouhous, N., and Andrieu, H. 2007. Rainfall stochastic disaggregation models: Calibration and validation of a multiplicative cascade model. Advances in Water Resources, 30(5), 1301-1319.
|
|
Gupta, V. K., and Waymire, E. C. 1993. A statistical analysis of mesoscale rainfall as a random cascade. Journal of Applied Meteorology, 32(2), 251-267. [doi:10.1175/1520-0450(1993)032<0251: ASAOMR>2.0.CO;2]
|
|
Hurst, H. E. 1951. Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770-799.
|
|
Joelson, M., and Néel, M. C. 2008. On alpha stable distribution of wind driven water surface wave slope. Chaos: An Interdisciplinary Journal of Nonlinear Science, 18(3), 033117. [doi: 10.1063/1.2955742].
|
|
Kahane, J. P. 1974. Sur le modèle de turbulence de Benoit Mandelbrot. Comptes Rendus hebdomadaires des Séances de l’Académies des Sciences, Série A,278, 621-623. (in French)
|
|
Klemes, V. 1974. The Hurst phenomenon: A puzzle? Water Resources Research, 10(4), 675-688. [doi: 10.1029/WR010i004p00675]
|
|
Koutrouvelis, I. A. 1980. Regression-type estimation of the parameters of stable laws. Journal of the American Statistical Association, 75(372), 918-928.
|
|
Koutrouvelis, I. A. 1981. An iterative procedure for the estimation of the parameters of stable laws. Communication in Statistics-Simulation and Computation, 10(1), 17-28. [doi:10.1080/ 03610918108812189]
|
|
Kundu, P. K., and Bell, T. L. 2006. Space-time scaling behavior of rain statistics in a stochastic fractional diffusion model. Journal of Hydrology, 322(1-4), 49-58. [doi:10.1016/ j.jhydrol.2005.02.031]
|
|
Kundu, P. K., and Travis, J. E. 2013. A stochastic fractional dynamics model of rainfall statistics. Geophysical Research Abstracts, 15, EGU2013-1491.
|
|
Magdziarz, M., Weron, A., and Weron, K. 2007. Fractional Fokker-Planck dynamics: Stochastic representation and computer simulation. Physical Review E, 75(1), 016708. [doi: 10.1103/PhysRevE.75.016708]
|
|
Magdziarz, M. 2009. Black scholes formula in subdiffusive regime. Journal of Statistical Physics, 136(3), 553-564. [doi: 10.1007/s10955-009-9791-4]
|
|
McCulloch, J. H. 1986. Simple Consistent Estimators of Stable Distribution Parameters. Communications in Statistics-Simulation and Computation, 15(4), 1109-1136.
|
|
MandelBrot, B. B. 1974. Intermittent turbulence in self-similar cascades: Divergence of higher moments and dimension of the carrier. Journal of Fluid Mechanics, 62(2), 331-358.
|
|
Marani, M. 2005. Non-power-law-scale properties of rainfall in space and time. Water Resources Research, 41(8), W08413. [doi: 10.1029/2004WR003822]
|
|
Metzler, R., Barkai, E., and Klafter, J. 1999. Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker Planck equation approach. Physical Review Letters, 82, 3563-3567. [doi:10.1103/ PhysRevLett.82.3563]
|
|
Metzler, R., and Klafter, J. 2000. The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Physical Reports, 339, 1-77. [doi: 10.1016/S0370-1573(00)00070-3]
|
|
Olsson, J. 1995. Limits and characteristics of the multifractal behaviour of a high-resolution rainfall time series. Nonlinear Processes in Geophysics, 2(1), 23-29. [doi: 10.5194/npg-2-23-1995]
|
|
Olsson, J., and Burlando, P. 2002. Reproduction of temporal scaling by a rectangular pulses rainfall model. Hydrological Processes, 16(3), 611-630. [doi: 10.1002/hyp.307]
|
|
Paschalis, A., Molnar, P., and Burlando, P. 2012. Temporal dependence structure in weights in a multiplicative cascade model for precipitation. Water Resources Research, 48(1), W01501. [doi:10.1029/ 2011WR010679]
|
|
Perica, S., and Foufoula-Georgiou, E. 1996. Model for multiscale disaggregation of spatial rainfall based on coupling meteorological and scaling descriptions. Journal of Geophysical Research: Atmospheres, 101(D21), 26347-26361. [doi: 10.1029/96JD01870]
|
|
Peyriere, J. 1974. Turbulence et dimension de Hausdorff. Comptes Rendus hebdomadaires des Séances de l’Académies des Sciences, Série A,278, 567-569. (in French)
|
|
Schertzer, D., and Lovejoy, S. 1987. Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. Journal of Geophysical Research: Atmospheres, 92(D8). 9693-9714. [doi: 10.1029/JD092iD08p09693]
|
|
Veneziano, D., Bras, R. L., and Niemann, J. L. 1996. Nonlinearity and self-similarity of rainfall in time and a stochastic model. Journal of Geophysical Research: Atmospheres, 101(D21), 26371-26392. [doi: 10.1029/96JD01658]
|
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