F. Atger, La pr??vision du temps ?? moyenne ??ch??ance en france, La M??t??orologie, vol.8, issue.30, pp.61-86, 2000.
DOI : 10.4267/2042/36124

T. L. Bell, A space-time stochastic model of rainfall for satellite remote-sensing studies, Journal of Geophysical Research, vol.12, issue.D8, pp.9631-9643, 1987.
DOI : 10.1029/JD092iD08p09631

H. Bendjoudi and P. Hubert, A propos de la distribution statistique des cumuls pluviométriques annuels. Faut-il en finir avec la normalité ?, pp.617-630, 1998.

H. Bendjoudi, P. Hubert, D. Schertzer, and S. Et-lovejoy, Multifractal point of view on rainfall intensity-duration-frequency, pp.325-323, 1997.

D. Benson, S. W. Wheatcraft, and M. Et-meerschaert, Application of a fractional advection-dispersion equation, Water Resources Research, vol.40, issue.11, pp.1403-1412, 2000.
DOI : 10.1029/2000WR900031

R. Benzi, G. Paladin, G. Parisi, and A. Vulpiani, On the multifractal nature of fully developed turbulence and chaotic systems, Journal of Physics A: Mathematical and General, vol.17, issue.18, pp.3521-3531, 1984.
DOI : 10.1088/0305-4470/17/18/021

J. C. Bertoni, Inondations urbaines en Amérique Latine: réflexions sur le rôle des facteurs de risque, Frontiers in Flood Research: Le point de la recherche sur les crues. Kovacs Coloquium, pp.123-141, 2006.

A. Biaou, De la Meso-échelle à la Micro-échelle: Désagregation spatio-temporelle multifractale des précipitations, p.181, 2004.

M. Bunge, Causality, chance and law, American Scientist, vol.49, pp.432-448, 1961.

G. Cantor, Uber unendliche, lineare Punktmannichfaltigkeiten, Mathematische Annalen, vol.6, issue.244, pp.453-488, 1884.
DOI : 10.1007/978-3-7091-9516-1_4

URL : http://www.digizeitschriften.de/download/PPN235181684_0015/PPN235181684_0015___log5.pdf

A. V. Chechkin, D. Schertzer, A. V. Tur, and V. V. Et-yanovsky, Generalized Fokker- Planck equation for anomalous diffusion, Ukrain Journal Physics, vol.40, issue.5, pp.434-439, 1995.

S. Corrsin, On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence, Journal of Applied Physics, vol.22, issue.4, pp.469-473, 1951.
DOI : 10.1063/1.1699986

A. Crisanti, M. H. Jensen, G. Paladin, and A. Vulpiani, Predictability of velocity and temperature fields in intermittent turbulence, Journal of Physics A: Mathematical and General, vol.26, issue.23, pp.6943-6960, 1993.
DOI : 10.1088/0305-4470/26/23/034

A. Crisanti, M. H. Jensen, A. Vulpiani, and G. Et-paladin, Intermittency and predictability in turbulence, Physical Review Letters, vol.70, issue.2, pp.166-169, 1993.
DOI : 10.1103/PhysRevLett.70.166

A. Davis, A. Marshak, W. Wiscombe, and R. Et-cahalan, Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated, Journal of Geophysical Research, vol.17, issue.4, pp.99-8055, 1994.
DOI : 10.1029/94JD00219

D. Lima and M. I. , Multifractals and the temporal structure of rainfall, p.229, 1998.

R. Deidda, Rainfall downscaling in a space-time multifractal framework, Water Resources Research, vol.12, issue.919, pp.1779-1794, 2000.
DOI : 10.1029/2000WR900038

M. Duncan, S. Lovejoy, F. Fabry, and D. Et-schertzer, Fluctuating radar cross-section of a multifractal distribution of scatterers Proceedings of, 11th International Conference on Precipitation and Clouds, pp.997-1000, 1992.

K. Falconer, Fractal Geometry: Mathematical Foundations and Applications., Biometrics, vol.46, issue.3, p.288, 1990.
DOI : 10.2307/2532125

U. Frisch and G. Et-parisi, FULLY DEVELOPED TURBULENCE AND INTERMITTENCY, Course LXXXVIII, p.pp, 1985.
DOI : 10.1111/j.1749-6632.1980.tb29703.x

U. Frisch, P. Sulem, and M. Et-nelkin, A simple dynamical model of intermittent fully developed turbulence, Journal of Fluid Mechanics, vol.81, issue.04, pp.719-724, 1978.
DOI : 10.1103/PhysRevC.15.719

P. Grassberger, Generalized dimensions of strange attractors, Physics Letters A, vol.97, issue.6, pp.227-230, 1983.
DOI : 10.1016/0375-9601(83)90753-3

G. Guillot and T. Et-lebel, Disaggregation of Sahelian mesoscale convective system rain fields: Further developments and validation, Journal of Geophysical Research: Atmospheres, vol.102, issue.1, pp.31533-31551, 1999.
DOI : 10.1029/1999JD900986

V. K. Gupta and E. Et-waymire, A Statistical Analysis of Mesoscale Rainfall as a Random Cascade, Journal of Applied Meteorology, vol.32, issue.2, pp.251-267, 1993.
DOI : 10.1175/1520-0450(1993)032<0251:ASAOMR>2.0.CO;2

V. K. Gupta and E. Et-waymire, Reply, Journal of Applied Meteorology, vol.36, issue.9, p.1304, 1997.
DOI : 10.1175/1520-0450(1997)036<1304:R>2.0.CO;2

H. Hasting and G. Sugihara, Fractals: a user's guide for the natural sciences, p.pp, 1994.

H. G. Hentschel and I. Et-procaccia, The infinite number of generalized dimensions of fractals and strange attractors, Physica D: Nonlinear Phenomena, vol.8, issue.3, pp.435-444, 1983.
DOI : 10.1016/0167-2789(83)90235-X

P. Hubert, Fractals et multifractals appliqués à l'étude de la variabilité temporelle des précipitations Space and time scale variability and interdependencies in hydrological processes, pp.175-181, 1995.

P. Hubert and J. P. Et-carbonnel, Dimensions fractales de l'occurrence de pluie en climat soudano-sahélien, pp.3-10, 1989.

P. Hubert, F. Friggit, and J. P. Et-carbonnel, Multifractal structure of rainfall occurrence in West Africa, New uncertainty concepts in hydrology and water resources, pp.109-113, 1995.
DOI : 10.1017/CBO9780511564482.011

A. N. Kolmogorov, The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.434, issue.1890, pp.301-305, 1941.
DOI : 10.1098/rspa.1991.0075

A. N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, Journal of Fluid Mechanics, vol.30, issue.01, pp.82-85, 1962.
DOI : 10.1017/S0022112062000518

R. Kraichnan, Inertial ranges in two-dimensional turbulence. The Physics of Fluids, pp.1417-1423, 1967.

P. Ladoy, S. Lovejoy, and D. Et-schertzer, Extreme variability of climatological data: scaling and intermittency Non-linear variability in geophysics: scaling and fractals The Netherlands, pp.241-250, 1991.

C. Larnder, Observer problems in multifractals: the example of rain, 1995.

D. Lavallée, Multifractal techniques: analysis and simulation of turbulent fields, 1991.

D. Lavallée, S. Lovejoy, D. Schertzer, and P. Et-ladoy, Nonlinear variability and landscape topography: analysis and simulation, Fractals in geography, pp.158-192, 1993.

D. Lavallée, D. Schertzer, and S. Et-lovejoy, On the determination of the codimension function Scaling, fractals and nonlinear variability in geophysics The Netherlands, pp.99-110, 1991.

C. Leith and R. Et-kraichnan, Predictability of Turbulent Flows, Journal of the Atmospheric Sciences, vol.29, issue.6, pp.1041-1058, 1972.
DOI : 10.1175/1520-0469(1972)029<1041:POTF>2.0.CO;2

M. Lilley, S. Lovejoy, K. Strawbridge, and D. Et-schertzer, 23/9 dimensional anisotropic scaling of passive admixtures using lidar data of aerosols, Physical Review E, vol.70, issue.3, pp.70-71, 2004.
DOI : 10.1103/PhysRevE.70.036307

URL : https://hal.archives-ouvertes.fr/hal-00711731

D. Lilly, Dynamics of rotating thunderstorms Meso-scale meteorology -Theories, observations and models, pp.531-543, 1983.

D. Lilly, Theoretical predictability of small-scale motions Turbulence and predictability in geophysical fluid dynamiczs and climate dynamics, pp.281-289, 1985.

E. Lorenz, Deterministic Nonperiodic Flow, Journal of the Atmospheric Sciences, vol.20, issue.2, pp.130-141, 1963.
DOI : 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

E. Lorenz, The predictability of a flow which possesse many scales of motion, Tellus, vol.21, pp.289-307, 1969.

E. Lorenz, The essence of chaos, 1993.

S. Lovejoy and B. B. Et-mandelbrot, Fractal properties of rain, and a fractal model, Tellus A, vol.12, issue.3, pp.209-232, 1985.
DOI : 10.1111/j.1600-0870.1985.tb00423.x

S. Lovejoy and D. Et-schertzer, Generalized Scale Invariance in the Atmosphere and Fractal Models of Rain, Water Resources Research, vol.12, issue.8, pp.1233-1250, 1985.
DOI : 10.1029/WR021i008p01233

S. Lovejoy and D. Et-schertzer, Multifractals, universality classes and satellite and radar measurements of cloud and rain fields, Journal of Geophysical Research, vol.92, issue.D3, pp.95-2021, 1990.
DOI : 10.1029/JD095iD03p02021

S. Lovejoy, D. Schertzer, and K. Et-pflug, Generalized scale invariance and differential rotation in cloud radiances, Physica A: Statistical Mechanics and its Applications, vol.185, issue.1-4, pp.121-128, 1992.
DOI : 10.1016/0378-4371(92)90446-W

S. Lovejoy, D. Schertzer, and J. D. Et-stanway, Direct Evidence of Multifractal Atmospheric Cascades from Planetary Scales down to 1 km, Physical Review Letters, vol.86, issue.22, pp.5200-5203, 2001.
DOI : 10.1103/PhysRevLett.86.5200

S. Lovejoy, D. Schertzer, and A. A. Et-tsonis, Functional Box-Counting and Multiple Elliptical Dimensions in Rain, Science, vol.235, issue.4792, pp.235-1036, 1987.
DOI : 10.1126/science.235.4792.1036

J. Macor, D. Schertzer, and S. Et-lovejoy, M??thodes multifractales appliqu??es ?? la pr??vision de pluie en utilisant des donn??es radar, La Houille Blanche, vol.4, issue.4, pp.1-7, 2007.
DOI : 10.1051/lhb:2007052

J. Macor, D. Schertzer, and S. Et-lovejoy, Rain and Flood Multifractal Nowcasting Using Radar Data. Natural Hazard and Earth System Sciences(Special Issue: Propagation of uncertainty in advanced meteo-hydrological forecast systems) (en préparation), 2007.

B. Mandelbrot, Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, Journal of Fluid Mechanics, vol.15, issue.02, pp.331-358, 1974.
DOI : 10.1063/1.1693226

B. Mandelbrot, A Class of Multinomial Multifractal Measures with Negative (Latent) Values for the ???Dimension??? f(??), Fractals' physical origin and properties, pp.3-29, 1989.
DOI : 10.1007/978-1-4899-3499-4_1

B. B. Mandelbrot, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, Science, vol.156, issue.3775, pp.636-638, 1967.
DOI : 10.1126/science.156.3775.636

B. B. Mandelbrot, Les objects fractals: forme, hasard et dimension, p.288, 1975.

B. B. Mandelbrot, Random Multifractals: Negative Dimensions and the Resulting Limitations of the Thermodynamic Formalism, Proceedings of the royal society of London A, pp.79-88, 1991.
DOI : 10.1098/rspa.1991.0081

B. B. Mandelbrot, Apprenti bétourné, L'irruption des géométries fractales dans les sciences, Académie Européenne Interdisciplinaire des Sciences, pp.15-39, 2006.

D. Marsan, Multifractals espace-temps; dynamique et predicibilité; application aux précipitations, 1998.

D. Marsan, D. Schertzer, and S. Et-lovejoy, Causal space-time multifractal processes: Predictability and forecasting of rain fields, Journal of Geophysical Research: Atmospheres, vol.2, issue.2, pp.26333-26346, 1996.
DOI : 10.1029/96JD01840

D. Marsan, D. Schertzer, and S. Et-lovejoy, Predictability of multifractal processes: the case of turbulence, Fractal and Chaos in Chemical Engineering, CFIC 96. World Scientific, pp.371-384, 1997.

J. Mejia and I. Et-rodriguez-iturbe, On the synthesis of random field sampling from the spectrum: An application to the generation of hydrologic spatial processes, Water Resources Research, vol.49, issue.4, pp.705-711, 1974.
DOI : 10.1029/WR010i004p00705

M. Menabde, D. Harris, A. Seed, G. Austin, and D. Et-stow, Multiscaling properties of rainfall and bounded random cascades, Water Resources Research, vol.11, issue.3, pp.2823-2830, 1997.
DOI : 10.1029/97WR02006

M. Menabde, A. Seed, D. Harris, and G. Et-austin, Self-similar random fields and rainfall simulation, Journal of Geophysical Research: Atmospheres, vol.92, issue.D21, pp.13509-13515, 1997.
DOI : 10.1029/97JD00915

O. Metais and M. Et-lesieur, Statistical Predictability of Decaying Turbulence, Journal of the Atmospheric Sciences, vol.43, issue.9, pp.857-870, 1986.
DOI : 10.1175/1520-0469(1986)043<0857:SPODT>2.0.CO;2

A. S. Monin, Weather Forecasting as a Problem in Physics, American Journal of Physics, vol.42, issue.2, 1972.
DOI : 10.1119/1.1987640

C. Naud, D. Schertzer, and S. Lovejoy, Fractional integration and radiactive transfer in multifractal atmosphères, Stochastic Models in Geosystems, pp.239-267, 1996.

P. Northrop, A clustered spatial-temporal model of rainfall, Proceedings of the royal society of London, pp.1875-1888, 1998.
DOI : 10.1098/rspa.1998.0238

E. Novikov and R. Stewart, Intermittency of turbulence and spectrum of fluctuations in energy dissipation, Izvestiya Akademii Nauk SSSR, Seriya Geofizicheskaya, vol.3, pp.408-412, 1964.

A. Obukhov, Some specific features of atmospheric turbulence, Journal of Geophysical Research, vol.31, issue.no. 9, pp.77-81, 1962.
DOI : 10.1029/JZ067i008p03011

I. Orlanski, A rational subdivision of scale for atmospheric processes, Bulletin American Meteorological Society, vol.56, issue.5, pp.527-530, 1975.

S. Orszag, Analytical theories of turbulence, Journal of Fluid Mechanics, vol.20, issue.02, pp.363-386, 1970.
DOI : 10.1063/1.1761271

T. Over and V. K. Et-gupta, A space-time theory of mesoscale rainfall using random cascades, Journal of Geophysical Research: Atmospheres, vol.33, issue.D21, pp.26319-26331, 1996.
DOI : 10.1029/96JD02033

T. N. Palmer, Predicting uncertainty in forecasts of weather and climate, Reports on Progress in Physics, vol.63, issue.2, pp.71-116, 2000.
DOI : 10.1088/0034-4885/63/2/201

G. Parisi and U. Et-frish, A mulitfractal model of intermittency Turbulence and Predictability in Geophysical Fluid Dynamics and Climate dynamics, pp.84-88, 1985.

G. Peano, Sur une courbe qui remplit toute une aire plane, Mathematische Annalen, vol.26, pp.157-160, 1890.
DOI : 10.1007/978-3-7091-9537-6_6

S. Pecknold, S. Lovejoy, and D. Et-schertzer, The morphology and texture of anisotropic multifractals using generalized scale invariance. Stochastic models in geosystems, IMA Volumes in mathematics and its aplications, pp.269-312, 1996.

S. Pecknold, S. Lovejoy, D. Schertzer, C. Hooge, and J. F. Et-malouin, The simulation of universal multifractal Cellular automata: prospects in astronomy and astrophysics, World Sciences, pp.228-267, 1993.

S. Pecknold, S. Lovejoy, and D. Et-schertzer, The morphology and texture of anisotropic multifractals using generalized scale invariance Stochastic Models in Geosystems, pp.269-311, 1996.

J. Pedlosky, Geophysical fluid dynamics, 1979.

S. Perica and E. Et-foufoula-georgiu, Linkage of scaling and thermodynamic parameters of rainfall: Results from midlatitude mesoscale convective systems, Journal of Geophysical Research: Atmospheres, vol.38, issue.10, pp.7431-7448, 1996.
DOI : 10.1029/95JD02372

K. Pflug, S. Lovejoy, and D. Et-schertzer, Differential Rotation and Cloud Texture: Analysis Using Generalized Scale Invariance, Journal of the Atmospheric Sciences, vol.50, issue.4, pp.538-553, 1993.
DOI : 10.1175/1520-0469(1993)050<0538:DRACTA>2.0.CO;2

W. Press, B. Flannery, S. Teukolsky, and W. Et-vetterling, Numerical recipes in FORTRAN 77, p.pp, 1992.

N. Rebora, L. Ferraris, V. Hardenberg, J. Et-provenzale, and A. , Stochastic downscaling of LAM predictions: an example in the Mediterranean area, Advances in Geosciences, pp.181-185, 2005.
DOI : 10.5194/adgeo-2-181-2005

URL : https://hal.archives-ouvertes.fr/hal-00296873

L. F. Richardson, Weather prediction by numerical processes, p.pp, 1922.

I. Rodriguez-iturbe, D. Cox, and P. S. Et-eagleson, Spatial Modelling of Total Storm Rainfall, Proceedings of the royal society of, pp.27-50, 1986.
DOI : 10.1098/rspa.1986.0002

D. Schertzer and S. Et-lovejoy, Elliptical turbulence in the atmosphere Proceedings of: 4th Symposium on turbulent shear flow, pp.1-11, 1983.

D. Schertzer and S. Et-lovejoy, On the dimension of atmospheric motions Turbulence and chaotic phenomena in fluids, pp.505-512, 1984.

D. Schertzer and S. Et-lovejoy, Generalized scale invariance in turbulent phenomena, Physico Chemical Hydrodynamics, vol.6, pp.5-6, 1985.

D. Schertzer and S. Et-lovejoy, The Dimension and Intermittency of Atmospheric Dynamics, Turbulent shear flow, pp.7-33, 1985.
DOI : 10.1007/978-3-642-69996-2_2

D. Schertzer and S. Et-lovejoy, Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, Journal of Geophysical Research, vol.2, issue.D8, pp.9693-9714, 1987.
DOI : 10.1029/JD092iD08p09693

D. Schertzer and S. Et-lovejoy, Singularités anisotropes, divergence des moments en turbulence: invariance d'échelle généralisée et processus multiplicatifs, Annales des Sciences Mathématiques du Québec, vol.11, issue.1, pp.139-181, 1987.

D. Schertzer and S. Et-lovejoy, Generalised scale invariance and multiplicative processes in the atmosphere, Pure and Applied Geophysics PAGEOPH, vol.11, issue.1, pp.57-81, 1989.
DOI : 10.1007/BF00877737

D. Schertzer and S. Et-lovejoy, Nonlinear variability in geophysics: multifractal simulations and analysis Fractals physical origin and properties, pp.49-79, 1989.

D. Schertzer and S. Et-lovejoy, Nonlinear geodynamical variability: multiple singularities, universality and observables Non-linear variability in geophysics: scaling and fractals, pp.41-82, 1991.

D. Schertzer and S. Et-lovejoy, Hard and soft multifractal processes, Physica A: Statistical Mechanics and its Applications, vol.185, issue.1-4, pp.187-194, 1992.
DOI : 10.1016/0378-4371(92)90455-Y

D. Schertzer and S. Et-lovejoy, EGS Richardson AGU Chapman NVAG3 Conference: Nonlinear Variability in Geophysics: scaling and multifractal processes, Nonlinear Processes in Geophysics, vol.1, issue.2/3, pp.77-79, 1994.
DOI : 10.5194/npg-1-77-1994

URL : https://hal.archives-ouvertes.fr/hal-00331025

D. Schertzer and S. Et-lovejoy, Universal Multifractals Do Exist!: Comments on ???A Statistical Analysis of Mesoscale Rainfall as a Random Cascade???, Journal of Applied Meteorology, vol.36, issue.9, pp.1296-1303, 1997.
DOI : 10.1175/1520-0450(1997)036<1296:UMDECO>2.0.CO;2

D. Schertzer and S. Et-lovejoy, Space???time complexity and multifractal predictability, Physica A: Statistical Mechanics and its Applications, vol.338, issue.1-2, pp.173-186, 2004.
DOI : 10.1016/j.physa.2004.04.032

D. Schertzer and S. Et-lovejoy, Uncertainty and predictability in geophysics: Chaos and multifractal insights, State of the Planet, Frontiers and Challenges in Geophysics. AGU, pp.317-334, 2004.
DOI : 10.1029/150GM25

URL : https://hal.archives-ouvertes.fr/hal-00711683

D. Schertzer, M. Larcheveque, V. Duan, V. Yanosvsky, and S. Et-lovejoy, Fractional Fokker???Planck equation for nonlinear stochastic differential equations driven by non-Gaussian L??vy stable noises, Journal of Mathematical Physics, vol.42, issue.1, pp.41-200, 2001.
DOI : 10.1063/1.1318734

D. Schertzer, S. Lovejoy, and P. Hubert, An introduction to stochastic multifractal fields Mathematical problems in environmental science and engineering, Series in Contemporary applied mathematics, pp.106-179, 2002.

D. Schertzer, S. Lovejoy, and F. Schmitt, Structures in turbulence and multifractal universality, Small scale structures in 3D hydro and MHD turbulence, pp.137-144, 1995.
DOI : 10.1007/BFb0102409

D. Schertzer, S. Lovejoy, F. Schmitt, Y. Chigirinskaya, and D. Et-marsan, Multifractal Cascade Dynamics and Turbulent Intermittency, Fractals, vol.05, issue.03, pp.427-471, 1997.
DOI : 10.1142/S0218348X97000371

D. Schertzer, I. Tchiguirinskaia, J. Macor, and S. Et-lovejoy, Scale problem flooding estimates, Special aspects of urban flood management. Hamburger Wasserbau-Schriftien, pp.53-60, 2007.

R. Stull and D. Et-schertzer, An introduction to boundary layer meteorology Kluwer Academic, 666 pp. Tchiguirinskaia, I Dynamical hierarchical cascade models, multifractal space-time intermittency and lie structure in turbulence, 1988.

S. Woyczynski and . Molchansov, Stochastic Models in Geosystems

I. Tchiguirinskaia, D. Schertzer, and S. Et-lovejoy, Scaling Gyroscopes Cascade: Universal multifractal features of 2-D and 3-D turbulence, Fractals and Chaos in Chemical Engineering. World Scientific, pp.371-384, 1997.

I. Tchiguirinskaia, D. Schertzer, and S. Et-lovejoy, An alternative to Shell-models: More complete and yet simple model of intermittency Advances in Turbulence VII, pp.263-266, 1998.

T. Tél, Fractals, multifractals and thermodynamics: an introductory review, Zeitschrift für Naturforschung A, vol.43, pp.1154-1174, 1988.

H. Tennekes, Karl Popper and the accountability of numerical forecasting, New developments in Predictability, ECMWF Workshop Proceedings, 1991.

Y. Tessier, S. Lovejoy, and D. Et-schertzer, Universal Multifractals: Theory and Observations for Rain and Clouds, Journal of Applied Meteorology, vol.32, issue.2, pp.223-250, 1993.
DOI : 10.1175/1520-0450(1993)032<0223:UMTAOF>2.0.CO;2

P. D. Thompson, Uncertainty of Initial State as a Factor in the Predictability of Large Scale Atmospheric Flow Patterns, Tellus, vol.9, issue.6, pp.275-295, 1957.
DOI : 10.1111/j.2153-3490.1957.tb01885.x

P. Thunis and R. Et-bornstein, Hierarchy of Mesoscale Flow Assumptions and Equations, Journal of the Atmospheric Sciences, vol.53, issue.3, pp.380-397, 1996.
DOI : 10.1175/1520-0469(1996)053<0380:HOMFAA>2.0.CO;2

V. Venugopal, E. Foufoula-georgiu, and V. Et-sapozhnikov, A space-time downscaling model for rainfall, Journal of Geophysical Research: Atmospheres, vol.102, issue.D16, pp.19705-19721, 1999.
DOI : 10.1029/1999JD900338

V. Koch and H. , Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire, Arkiv för Matematik, vol.1, pp.681-704, 1904.

E. Waymire, V. K. Gupta, and I. Et-rodriguez-iturbe, A spectral theory of rainfall intensity at the meso-beta scale, Water Resource Research, vol.20, pp.1483-1465, 1984.

H. Wheater, Spatial-temporal rainfall fields: modelling and statistical aspects, Hydrology and Earth System Sciences, pp.581-601, 2000.
DOI : 10.5194/hess-4-581-2000

URL : https://hal.archives-ouvertes.fr/hal-00304688

P. Willems, A spatial rainfall generator for small spatial scales, Journal of Hydrology, vol.252, issue.1-4, pp.126-144, 2001.
DOI : 10.1016/S0022-1694(01)00446-2

V. Yanosvsky, A. V. Chechkin, D. Schertzer, and A. V. Et-tur, L??vy anomalous diffusion and fractional Fokker???Planck equation, Physica A: Statistical Mechanics and its Applications, vol.282, issue.1-2, pp.13-34, 2000.
DOI : 10.1016/S0378-4371(99)00565-8

R. Benzi, G. Paladin, G. Parisi, and A. Vulpiani, On the multifractal nature of fully developed turbulence and chaotic systems, Journal of Physics A: Mathematical and General, vol.17, issue.18, pp.3521-3531, 1984.
DOI : 10.1088/0305-4470/17/18/021

A. Berne, G. Delrieu, J. D. Creutin, and C. Obled, Temporal and spatial resolution of rainfall measurements required for urban hydrology, Journal of Hydrology, vol.299, issue.3-4, pp.3-4, 2004.
DOI : 10.1016/S0022-1694(04)00363-4

E. Berthier, H. Andrieu, and J. D. Creutin, The role of soil in the generation of urban runoff: development and evaluation of a 2D model, Journal of Hydrology, vol.299, issue.3-4, pp.3-4, 2004.
DOI : 10.1016/S0022-1694(04)00369-5

K. Beven, Changing ideas in hydrology ??? The case of physically-based models, Journal of Hydrology, vol.105, issue.1-2, pp.157-172, 1989.
DOI : 10.1016/0022-1694(89)90101-7

T. Einfalt, K. Arnbjerg-nielsen, C. Golz, N. E. Jensen, M. Quirmbach et al., Towards a roadmap for use of radar rainfall data in urban drainage, Journal of Hydrology, vol.299, issue.3-4, pp.3-4, 2004.
DOI : 10.1016/S0022-1694(04)00365-8

P. Hubert, I. Tchiguirinskaia, H. Bendjoudi, D. Schertzer, and S. Lovejoy, Multifractal modeling of the Blavet river discharges at Guerledan, Proceedings of the Third Celtic Hydrology Colloquium, pp.47-58, 2002.

D. Labat, A. Mangin, and R. Ababou, Rainfall???runoff relations for karstic springs: multifractal analyses, Journal of Hydrology, vol.256, issue.3-4, pp.176-195, 2002.
DOI : 10.1016/S0022-1694(01)00535-2

D. Lavallée, S. Lovejoy, D. Schertzer, and F. Schmitt, On the Determination of Universal Multifractal Parameters in Turbulence, Topological aspects of the dynamics of fluids and plasmas, pp.463-478, 1992.
DOI : 10.1007/978-94-017-3550-6_27

S. Lovejoy and D. Schertzer, Multifractals and Rain, in New Uncertainty Concepts in Hydrology and Water Resources, pp.62-103, 1995.

S. Lovejoy and D. Schertzer, Multifractals, cloud radiances and rain, Journal of Hydrology, vol.322, issue.1-4, pp.59-88, 2006.
DOI : 10.1016/j.jhydrol.2005.02.042

URL : https://hal.archives-ouvertes.fr/hal-00711639

E. Morin, Y. Enze, U. Shamir, and R. Garti, The characteristic time scale for basin hydrological response using radar data, Journal of Hydrology, vol.252, issue.1-4, pp.1-4, 2001.
DOI : 10.1016/S0022-1694(01)00451-6

C. Obled, J. Wendling, and K. Beven, The sensitivity of hydrological models to spatial rainfall patterns: an evaluation using observed data, Journal of Hydrology, vol.159, issue.1-4, pp.1-4, 1994.
DOI : 10.1016/0022-1694(94)90263-1

G. Pandey, S. Lovejoy, and D. Schertzer, Multifractal analysis of daily river flows including extremes for basins of five to two million square kilometres, one day to 75 years, Journal of Hydrology, vol.208, issue.1-2, pp.62-81, 1998.
DOI : 10.1016/S0022-1694(98)00148-6

G. Parisi and U. Frisch, On the singularity structure of fully developed turbulence, in Turbulence and predictability in geophysical fluid dynamics and climate dynamics

L. F. Richardson, Weather prediction by numerical process, 1922.
DOI : 10.1017/CBO9780511618291

D. Schertzer and S. Lovejoy, On the Dimension of Atmospheric motions, in Turbulence and Chaotic phenomena in Fluids, pp.505-512, 1984.

D. Schertzer and S. Lovejoy, Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes, Journal of Geophysical Research, vol.2, issue.D8, pp.9693-9714, 1987.
DOI : 10.1029/JD092iD08p09693

D. Schertzer and S. Lovejoy, Lecture Notes: Nonlinear Variability in Geophysics 3: Scaling and Mulitfractal Processes in Geophysics, 1993.

G. Sposito, Scale Dependence and Scale Invariance in Hydrology, 1998.
DOI : 10.1017/CBO9780511551864

I. Tchiguirinskaia, P. Hubert, H. Bendjoudi, and D. Schertzer, Multifractal Modeling of River Runoff and Seasonal Periodicity, Preventing & Fighting Hydrological Disasters, 2002.

I. Tchiguirinskaia, D. Schertzer, P. Hubert, H. Bendjoudi, and S. Lovejoy, Multiscaling geophysics and sustainable development, Scales in Hydrology and Water Management, pp.111-137, 2004.

Y. Tessier, S. Lovejoy, P. Hubert, D. Schertzer, and S. Pecknold, Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions, Journal of Geophysical Research: Atmospheres, vol.7, issue.2, pp.31-427, 1996.
DOI : 10.1029/96JD01799

A. M. Yaglom, The influence on the fluctuation in energy dissipation on the shape of turbulent characteristics in the inertial interval, Sov. Phys. Dokl, vol.2, pp.26-30, 1966.

J. S. Marshall and W. M. Palmer, THE DISTRIBUTION OF RAINDROPS WITH SIZE, Journal of Meteorology, vol.5, issue.4, pp.165-166, 1948.
DOI : 10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2

M. Duncan, S. Lovejoy, F. Fabry, and D. Schertzer, ? Fluctuating radar cross-section of a multifractal distribution of scatterers, Proc. 11 Int. Conf. on Precipitation and Clouds, pp.997-1000, 1992.

L. F. Richardson, ? Weather prediction by numerical processes, 1922.

A. N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, Journal of Fluid Mechanics, vol.30, issue.01, pp.82-85, 1962.
DOI : 10.1017/S0022112062000518

E. A. Novikov and R. Steward, ? Intermittency of turbulence and spectrum of fluctuations in energy dissipation, Izv.Akad. Nauk SSSR, Ser. Geofiz, vol.3, pp.408-412, 1964.

A. M. Yaglom, ? The influence of fluctuations in energy dissipation on the shape of turbulent characteristics in the inertial interval, Sov. Phys. Dokl, vol.2, pp.26-30, 1966.

B. Mandelbrot, Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, Journal of Fluid Mechanics, vol.15, issue.02, pp.331-358, 1974.
DOI : 10.1063/1.1693226

U. Frish, P. L. Sulem, and M. Nelkin, A simple dynamical model of intermittent fully developed turbulence, Journal of Fluid Mechanics, vol.81, issue.04, pp.719-724, 1978.
DOI : 10.1103/PhysRevC.15.719

D. Schertzer and S. Lovejoy, ? On the dimension of atmospheric motions. Turbulence and chaotic phenomena in fluids, pp.505-512, 1984.

E. Levitch and E. Tzvetkov, Helical inverse cascade in three-dimensional turbulence as a fundamental dominant mechanism in mesoscale atmospheric phenomena, Physics Reports, vol.128, issue.1, pp.1-37, 1985.
DOI : 10.1016/0370-1573(85)90036-5

A. Bialas and R. Pechanski, Moments of rapidity distributions as a measure of short-range fluctuations in high-energy collisions, Nuclear Physics B, vol.273, issue.3-4, pp.703-718, 1986.
DOI : 10.1016/0550-3213(86)90386-X

G. Parisi and U. Frish, ? A multifractal model of intermittency. Turbulence and predictability in geophysical fluid dynamics and climatic dynamics, pp.84-88, 1985.

D. Schertzer and S. Lovejoy, ? Physical modelling and analysis of rain and clouds by anisotropic scaling of multiplicative processes, J. Geophys.Res, issue.D8, pp.92-9693, 1987.

S. Lovejoy and D. Schertzer, Multifractals, universality classes and satellite and radar measurements of cloud and rain fields, Journal of Geophysical Research, vol.92, issue.D3, pp.95-2021, 1990.
DOI : 10.1029/JD095iD03p02021

D. Schertzer and S. Lovejoy, EGS Richardson AGU Chapman NVAG3 Conference: Nonlinear Variability in Geophysics: scaling and multifractal processes, Nonlinear Processes in Geophysics, vol.1, issue.2/3, pp.77-79, 1994.
DOI : 10.5194/npg-1-77-1994

URL : https://hal.archives-ouvertes.fr/hal-00331025

M. I. De-lima, ? Multifractal and temporal structure of rainfall, 1998.

D. Lavallée, S. Lovejoy, D. Schertzer, and P. Ladoy, ? Nonlinear variability and landscape topography: analysis and simulation. Fractals in geography, pp.171-205, 1993.

P. Ladoy, F. Schmitt, D. Schertzer, and S. Lovejoy, ? Variabilité temporelle multifractale des observations pluviométriques à Nîmes, C. R. Acad. Sci. Paris, pp.317-775, 1993.

D. Schertzer and S. Lovejoy, ?Nonlinear variability in Geophysics: multifractal simulations and analysis. Fractal's physical origin and properties, pp.49-79, 1988.

D. Schertzer and S. Lovejoy, ?Nonlinear geodynamical variability: multiple singularities, universality and observables. Nonlinear variability in Geophysics: scaling and fractals, pp.41-829, 1991.

D. Marsan, ? Multifractals espace-temps, dynamique et prédicibilité; application aux précipitations, 1998.

A. Biaou, ? De la meso-échelle à la micro-échelle : disagregation spatio-temporelle multifractale des précipitations, 2004.