P. Dsd, . Based, . On, and . Technique, 33) is derived from the DSD formulation scaled by radar reflectivity factor, which implies that the rain rate is reconstituted by the reflectivity factor (this is the general case in radar hydrology) This result is analogous to standard regression analyses e.g

. Chapon, R) pairs derived from each single spectra, by considering successively Z and R as the explanatory variable. Fig.3.15 and Fig.3.16 display preliminary evaluations of these two Z-R relationships by comparing reconstituted and observed Z and M 3.67 values. Both of them have good coefficient correlations (>0.9), with 10% underestimation of Z for (3.32) and 10% underestimation of R for (3.33) In order to further evaluate these two climatological Z-R relationships, four criteria (coefficient correlation, bias, Nash coefficient and root mean square deviation) calculated between the estimated and observed rainfall are calculated for the Z = aR b relationships with prefactor (a) ranging from 50 to 350 and exponent (b) ranging from 1, The contours in Fig.3.18 show the statistical criteria as a function of prefactor and exponent, 2008.

. Fig, 18 confirms the good performance of two Z-R relationships regardless their different prefactor and exponent. The Z-R relationship (3.33) produces 10% underestimation of rainfall, which is slightly improved in the (3.32) Except for this underestimation , the other statistical criteria indicate that the relationship (3.33) is slightly better than (3.32) for the rainfall estimation, any case, this example illustrates the impact of the scaling procedure on the prefactor and exponent of the Z-R relationship

A. Of, . Dsd, and . Figure, 12: Illustration of the position of the East-West vertical cross section. -The cross section extends to 120 km from the East to the West

S. Assouline and Y. Mualem, The Similarity of Regional Rainfall: A Dimensionless Model of Drop Size Distribution, Transactions of the ASAE, vol.32, issue.4, pp.1216-1222, 1989.
DOI : 10.13031/2013.31137

D. Atlas and C. W. Ulbrich, Path- and Area-Integrated Rainfall Measurement by Microwave Attenuation in the 1???3 cm Band, Journal of Applied Meteorology, vol.16, issue.12, pp.1322-1331, 1977.
DOI : 10.1175/1520-0450(1977)016<1322:PAAIRM>2.0.CO;2

D. Atlas and C. W. Ulbrich, An Observationally Based Conceptual Model of Warm Oceanic Convective Rain in the Tropics, Journal of Applied Meteorology, vol.39, issue.12, pp.2165-2181, 2000.
DOI : 10.1175/1520-0450(2001)040<2165:AOBCMO>2.0.CO;2

D. Atlas, C. W. Ulbrich, F. D. Marks, R. A. Black, E. Amitai et al., Partitioning tropical oceanic convective and stratiform rains by draft strength, Journal of Geophysical Research: Atmospheres, vol.36, issue.28, pp.2259-2267, 2000.
DOI : 10.1029/1999JD901009

K. V. Beard, Terminal Velocity and Shape of Cloud and Precipitation Drops Aloft, Journal of the Atmospheric Sciences, vol.33, issue.5, pp.851-864, 1976.
DOI : 10.1175/1520-0469(1976)033<0851:TVASOC>2.0.CO;2

K. V. Beard, D. B. Johnson, and D. Baumgardner, Aircraft observations of large raindrops in warm, shallow, convective clouds, Geophysical Research Letters, vol.42, issue.10, pp.991-994, 1986.
DOI : 10.1029/GL013i010p00991

A. C. Best, Empirical formulae for the terminal velocity of water drops falling through the atmosphere, Quarterly Journal of the Royal Meteorological Society, vol.26, issue.329, pp.302-311, 1950.
DOI : 10.1002/qj.49707632905

B. Boudevillain, G. Delrieu, B. Galabertier, L. Bonnifait, L. Bouilloud et al., The C??vennes-Vivarais Mediterranean Hydrometeorological Observatory database, Water Resources Research, vol.103, issue.12, pp.7-701, 2011.
DOI : 10.1029/2010WR010353

P. Bougeault and C. , The MAP Special Observing Period, Bulletin of the American Meteorological Society, vol.82, issue.3, pp.433-462, 2001.
DOI : 10.1175/1520-0477(2001)082<0433:TMSOP>2.3.CO;2

E. A. Brandes, G. F. Zhang, and J. Vivekanandan, An Evaluation of a Drop Distribution???Based Polarimetric Radar Rainfall Estimator, Journal of Applied Meteorology, vol.42, issue.5, pp.652-660, 2003.
DOI : 10.1175/1520-0450(2003)042<0652:AEOADD>2.0.CO;2

V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar: Principles and Applications, p.27, 2001.
DOI : 10.1017/CBO9780511541094

V. N. Bringi, G. J. Huang, V. Chandrasekar, and E. Gorgucci, A Methodology for Estimating the Parameters of a Gamma Raindrop Size Distribution Model from Polarimetric Radar Data: Application to a Squall-Line Event from the TRMM/Brazil Campaign, Journal of Atmospheric and Oceanic Technology, vol.19, issue.5, pp.633-645, 2002.
DOI : 10.1175/1520-0426(2002)019<0633:AMFETP>2.0.CO;2

I. C. Browne and N. P. Robinson, Cross-polarization of the Radar Melting-Band, Nature, vol.36, issue.4338, pp.1078-1079, 1952.
DOI : 10.1038/1701078b0

Q. Cao and G. F. Zhang, Errors in Estimating Raindrop Size Distribution Parameters Employing Disdrometer and Simulated Raindrop Spectra, Journal of Applied Meteorology and Climatology, vol.48, issue.2, pp.406-425, 2009.
DOI : 10.1175/2008JAMC2026.1

V. Chandrasekar and V. N. Bringi, Simulation of Radar Reflectivity and Surface Measurements of Rainfall, Journal of Atmospheric and Oceanic Technology, vol.4, issue.3, pp.464-478, 1987.
DOI : 10.1175/1520-0426(1987)004<0464:SORRAS>2.0.CO;2

B. Chapon, G. Delrieu, M. Gosset, and B. Boudevillain, Variability of rain drop size distribution and its effect on the Z???R relationship: A case study for intense Mediterranean rainfall, Atmospheric Research, vol.87, issue.1, pp.52-65, 2008.
DOI : 10.1016/j.atmosres.2007.07.003
URL : https://hal.archives-ouvertes.fr/insu-00388072

Y. H. Chu and C. L. Su, An Investigation of the Slope???Shape Relation for Gamma Raindrop Size Distribution, Journal of Applied Meteorology and Climatology, vol.47, issue.10, pp.47-2531, 2008.
DOI : 10.1175/2008JAMC1755.1

G. Delrieu, The Catastrophic Flash-Flood Event of 8???9 September 2002 in the Gard Region, France: A First Case Study for the C??vennes???Vivarais Mediterranean Hydrometeorological Observatory, Journal of Hydrometeorology, vol.6, issue.1, pp.34-52, 2005.
DOI : 10.1175/JHM-400.1

F. Duffourg and V. Ducrocq, Origin of the moisture feeding the Heavy Precipitating Systems over Southeastern France, Natural Hazards and Earth System Science, vol.11, issue.4, pp.1163-1178, 2011.
DOI : 10.5194/nhess-11-1163-2011
URL : https://hal.archives-ouvertes.fr/meteo-00589087

G. Erpul, L. D. Norton, and D. Gabriels, The effect of wind on physical raindrop impact and rainsplash detachment, Transactions of the ASABE, vol.45, issue.6, pp.51-62, 2002.

F. Fabry and I. Zawadzki, The melting layer of precipitation: radar observations and their interpretation, J. Atmos. Sci, vol.52, pp.828-851, 1995.

R. L. Fornis, H. R. Vermeulen, and J. D. Nieuwenhuis, Kinetic energy???rainfall intensity relationship for Central Cebu, Philippines for soil erosion studies, Journal of Hydrology, vol.300, issue.1-4, pp.20-32, 2005.
DOI : 10.1016/j.jhydrol.2004.04.027

N. I. Fox, TECHNICAL NOTE: The representation of rainfall drop-size distribution and kinetic energy, Hydrology and Earth System Sciences, vol.8, issue.5, pp.1001-1007, 2004.
DOI : 10.5194/hess-8-1001-2004
URL : https://hal.archives-ouvertes.fr/hal-00304977

M. Fujiwara and T. Yanase, Raindrop Z-R relationships in different altitudes, Proc. 13th Radar Meteorology Conf, pp.380-383, 1968.

J. F. Gamache, Microphysical Observations in Summer MONEX Convective and Stratiform Clouds, Monthly Weather Review, vol.118, issue.6, pp.1238-1249, 1990.
DOI : 10.1175/1520-0493(1990)118<1238:MOISMC>2.0.CO;2

A. Godart, S. Anquetin, and E. Leblois, Rainfall regimes associated with banded convection in the C??vennes-Vivarais area, Meteorology and Atmospheric Physics, vol.52, issue.48, pp.25-34, 2009.
DOI : 10.1007/s00703-008-0326-3

E. E. Gossard, D. C. Strauch, D. C. Welsh, and S. Y. Matrosov, Measurements by Clear-Air Doppler Radars, Journal of Atmospheric and Oceanic Technology, vol.9, issue.2, pp.108-119, 1992.
DOI : 10.1175/1520-0426(1992)009<0108:CLPIAR>2.0.CO;2

I. Gultepe and J. A. Milbrandt, Probabilistic Parameterizations of Visibility Using Observations of Rain Precipitation Rate, Relative Humidity, and Visibility, Journal of Applied Meteorology and Climatology, vol.49, issue.1, pp.36-46, 2010.
DOI : 10.1175/2009JAMC1927.1

R. Gunn and G. R. Kinzer, THE TERMINAL VELOCITY OF FALL FOR WATER DROPLETS IN STAGNANT AIR, Journal of Meteorology, vol.6, issue.4, pp.243-248, 1949.
DOI : 10.1175/1520-0469(1949)006<0243:TTVOFF>2.0.CO;2

Z. S. Haddad and D. Rosenfeld, Optimality of empirical Z-R relations, Quarterly Journal of the Royal Meteorological Society, vol.3, issue.93, pp.1283-1293, 1997.
DOI : 10.1002/qj.49712354107

Z. S. Haddad, D. A. Short, S. L. Durden, I. M. Eastwood, S. Hensley et al., A new parametrization of the rain drop size distribution, IEEE Transactions on Geoscience and Remote Sensing, vol.35, issue.3, pp.532-539, 1997.
DOI : 10.1109/36.581961

J. Handwerker and W. Straub, Optimal Determination of Parameters for Gamma-Type Drop Size Distributions Based on Moments, Journal of Atmospheric and Oceanic Technology, vol.28, issue.4, pp.513-529, 2011.
DOI : 10.1175/2010JTECHA1474.1

P. Hazenberg, N. Yu, B. Boudevillain, G. Delrieu, and R. Uijlenhoet, Scaling of raindrop size distributions and classification of radar reflectivity???rain rate relations in intense Mediterranean precipitation, Journal of Hydrology, vol.402, issue.3-4, pp.3-4, 2011.
DOI : 10.1016/j.jhydrol.2011.01.015
URL : https://hal.archives-ouvertes.fr/insu-00648579

J. E. Hooper and A. A. Kippax, The bright band ??? a phenomenon associated with radar echoes from falling rain, Quarterly Journal of the Royal Meteorological Society, vol.1, issue.328, pp.125-132, 1950.
DOI : 10.1002/qj.49707632803

Z. Hu and R. C. Srivastava, Evolution of Raindrop Size Distribution by Coalescence, Breakup, and Evaporation: Theory and Observations, Journal of the Atmospheric Sciences, vol.52, issue.10, pp.1761-1783, 1995.
DOI : 10.1175/1520-0469(1995)052<1761:EORSDB>2.0.CO;2

P. Huet, P. Foin, C. Laurain, and P. Cannard, Retour d'expérience des crues de septembre, p.3, 2002.

A. J. Illingworth and T. M. Blackman, The Need to Represent Raindrop Size Spectra as Normalized Gamma Distributions for the Interpretation of Polarization Radar Observations, Journal of Applied Meteorology, vol.41, issue.3, pp.286-297, 2002.
DOI : 10.1175/1520-0450(2002)041<0286:TNTRRS>2.0.CO;2

J. Jaffrain and A. Berne, Experimental Quantification of the Sampling Uncertainty Associated with Measurements from PARSIVEL Disdrometers, Journal of Hydrometeorology, vol.12, issue.3, pp.352-370, 2011.
DOI : 10.1175/2010JHM1244.1

D. B. Johnson, Raindrop Multiplication by Drop Breakup, Journal of Applied Meteorology, vol.21, issue.7, pp.1048-1052, 1982.
DOI : 10.1175/1520-0450(1982)021<1048:RMBDB>2.0.CO;2

D. B. Johnson, K. V. Beard, and D. Baumgardner, Airborne observations of raindrop size distribution in Hawaiian cloud, Conf. on Cloud Physics, pp.48-51, 1986.

J. Joss and E. G. Gori, Shapes of Raindrop Size Distributions, Journal of Applied Meteorology, vol.17, issue.7, pp.1054-1061, 1978.
DOI : 10.1175/1520-0450(1978)017<1054:SORSD>2.0.CO;2

J. Joss and A. Waldvogel, A method to improve the accuracy of radar-measured amounts of precipitation, Proc. 14th Radar Meteorology Conf, pp.237-238, 1970.

D. S. Kim, M. Maki, and D. I. Lee, Retrieval of Three-Dimensional Raindrop Size Distribution Using X-Band Polarimetric Radar Data, Journal of Atmospheric and Oceanic Technology, vol.27, issue.8, pp.27-1265, 2010.
DOI : 10.1175/2010JTECHA1407.1

P. I. Kinnell, The Problem of Assessing the Erosive Power of Rainfall from Meteorological Observations1, Soil Science Society of America Journal, vol.37, issue.4, pp.617-621, 1973.
DOI : 10.2136/sssaj1973.03615995003700040039x

J. M. Laflen, W. J. Elliot, D. C. Flanagan, C. R. Meyer, and M. A. Nearing, WEPP predicting water erosion using a process-based model, J. Soil Water Conserv, vol.52, issue.2, pp.96-102, 1997.

G. Lee and I. Zawadzki, Variability of Drop Size Distributions: Time-Scale Dependence of the Variability and Its Effects on Rain Estimation, Journal of Applied Meteorology, vol.44, issue.2, pp.241-255, 2005.
DOI : 10.1175/JAM2183.1

G. Lee, I. Zawadzki, W. Szyrmer, D. S. Torres, and R. Uijlenhoet, A General Approach to Double-Moment Normalization of Drop Size Distributions, Journal of Applied Meteorology, vol.43, issue.2, pp.264-281, 2004.
DOI : 10.1175/1520-0450(2004)043<0264:AGATDN>2.0.CO;2

X. Li, C. H. Sui, and K. M. Lau, Dominant Cloud Microphysical Processes in a Tropical Oceanic Convective System: A 2D Cloud Resolving Modeling Study, Monthly Weather Review, vol.130, issue.10, pp.2481-2491, 2002.
DOI : 10.1175/1520-0493(2002)130<2481:DCMPIA>2.0.CO;2

Y. G. Liu, Statistical-theory of the Marshall-Palmer distribution of raindrops, Atmos. Environ. A-GENERAL, vol.27, issue.1 8, pp.15-19, 1993.

M. Maki, T. D. Keenan, Y. Sasaki, and K. Nakamura, Characteristics of the Raindrop Size Distribution in Tropical Continental Squall Lines Observed in Darwin, Australia, Journal of Applied Meteorology, vol.40, issue.8, pp.1393-1412, 2001.
DOI : 10.1175/1520-0450(2001)040<1393:COTRSD>2.0.CO;2

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

B. E. Martner, S. E. Yuter, A. B. White, S. Y. Matrosov, D. E. Kingsmill et al., Raindrop Size Distributions and Rain Characteristics in California Coastal Rainfall for Periods with and without a Radar Bright Band, Journal of Hydrometeorology, vol.9, issue.3, pp.408-425, 2008.
DOI : 10.1175/2007JHM924.1

Y. Mihara, 1951: Raindrops and soil erosion, Bulletin of the National Institute of Agricultural Sciences, pp.48-51

D. N. Moisseev and V. Chandrasekar, Examination of the mu-Lambda relation suggested for drop size distribution parameters, J. Atmos. Oceanic Technol, vol.241, issue.5 9, pp.847-855, 2007.

A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, McGraw-Hill Series in Probability and Statistics, p.40, 1974.

R. P. Morgan, The European Soil Erosion Model (EUROSEM): a dynamic approach for predicting sediment transport from fields and small catchments, Earth Surface Processes and Landforms, vol.3, issue.6, pp.527-544, 1998.
DOI : 10.1002/(SICI)1096-9837(199806)23:6<527::AID-ESP868>3.0.CO;2-5

E. Morin, W. F. Krajewski, D. C. Goodrich, X. Gao, and S. Sorooshian, Estimating Rainfall Intensities from Weather Radar Data: The Scale-Dependency Problem, Journal of Hydrometeorology, vol.4, issue.5, pp.782-797, 2003.
DOI : 10.1175/1525-7541(2003)004<0782:ERIFWR>2.0.CO;2

Y. Mualem and S. Assouline, Mathematical Model for Rain Drop Distribution and Rainfall Kinetic Energy, Transactions of the ASAE, vol.29, issue.2, pp.494-500, 1986.
DOI : 10.13031/2013.30179

O. Nuissier, V. Ducrocq, D. Ricard, C. Lebeaupin, and S. Anquetin, A numerical study of three catastrophic precipitating events over southern France. I: Numerical framework and synoptic ingredients, Quarterly Journal of the Royal Meteorological Society, vol.72, issue.630, pp.111-130, 2008.
DOI : 10.1002/qj.200
URL : https://hal.archives-ouvertes.fr/meteo-00260840

M. L. Parry, O. F. Canziani, J. P. Palutikof, P. J. Van-der-linden, and C. E. Hanson, Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, pp.976-116, 2007.

P. J. Petrocchi and K. J. Banis, Computer analysis of raindrop disdrometers spectral data acquired during the 1979 SESAME project. 19th Radar Meteor, pp.490-492, 1980.

J. M. Porrà, D. S. Torres, and J. D. Creutin, Modeling of drop size distribution and its applications to rainfall measurements from radar Stochastic methods in hydrology: Rain, landforms and floods, pp.73-84, 1998.

M. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, Computer Journal, vol.7, issue.45, pp.155-162, 1964.

S. Pradier, M. Chong, and F. Roux, Characteristics of some frontal stratiform precipitation events south of the Alpine chain during MAP, Meteorol. Atmos. Phys, vol.87, pp.197-218, 2004.

O. Pujol, J. F. Georgis, M. Chong, and F. Roux, Dynamics and microphysics of orographic precipitation during MAP IOP3, Quart. J. Roy. Meteor. Soc, vol.131, issue.611, pp.2795-2819, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00023212

R. M. Rauber, K. V. Beard, and B. M. Andrews, A mechanism for giant raindrop formation in warm, shallow, convective clouds, J. Atmos. Sci, vol.48, pp.1791-1797, 1991.

D. Rosenfeld and I. M. Lensky, Spaceborne sensed insights into precipitation formation processes in continental and maritime clouds, Bull. Amer. Meteor. Soc, vol.79, pp.2457-2476, 1998.

D. Rosenfeld and C. W. Ulbrich, Cloud microphysical properties, processes, and rainfall estimation opportunities, Meteorological Monographs, vol.30, issue.15, pp.237-237, 2003.
DOI : 10.1175/0065-9401(2003)030<0237:cmppar>2.0.co;2

C. Salles, Analyse microphysical de la pluie au sol: mesures par spectro-pluviometre optique et methods stattistiques d'analyse spectrale et de simulation numerique, p.33, 1995.

C. Salles and J. D. Creutin, Instrumental uncertainties in Z-R relationships and raindrop fall velocities, J. Appl. Meteorol, vol.42, pp.279-290, 2003.

C. Salles, J. Poesen, and D. Torres, Kinetic energy of rain and its functional relationship with intensity, J. Hydrol, vol.257, issue.120, pp.256-270, 2002.

D. M. Schultz, Understanding Utah winter storms: The intermountain precipitation experiment, Bull. Amer. Meteor. Soc, vol.83, issue.2, pp.189-210, 2002.

C. Schumacher and R. A. Houze, Stratiform rain in the tropics as seen by the TRMM precipitation radar, J. Climate, issue.11, pp.16-1739, 2003.

R. S. Sekhon and R. C. Srivastava, Snow size spectra and radar reflectivity, J. Atmos. Sci, vol.27, issue.9, pp.299-307, 1970.
DOI : 10.1175/1520-0469(1970)027<0299:sssarr>2.0.co;2

S. Torres, D. , J. M. Porrà, and J. D. Creutin, A general formulation for raindrop size distribution, J. Appl. Meteorol, vol.33, issue.9, pp.1494-1502, 1994.

S. Torres, D. , J. M. Porrà, and J. D. Creutin, Experimental evidence of a general description for raindrop size distribution properties, J. Geophys. Res., [Atmos.], vol.103, issue.9, pp.1785-1797, 1998.

S. Torres, D. , C. Salles, J. D. Creutin, and G. Delrieu, Quantification of soil detachment by raindrop impact : performance of classical formulae of kinetic energy in Mediterranean storms. Erosion and sediment transport monitoring programs in river basin, pp.115-124, 1992.

S. Sharma, M. Konwar, D. K. Sarma, M. C. Kalapureddy, and A. R. Jain, Characteristics of rain integral parameters during tropical convective, transition, and stratiform rain at Gadanki and its application in rain retrieval, J. Appl. Meteor. Climatol, vol.48, pp.1245-1266, 2009.

J. A. Smith, E. Hui, M. Steiner, M. L. Baeck, W. F. Krajewski et al., Variability of rainfall rate and raindrop size distributions in heavy rain, Water Resour. Res, vol.45, issue.4, pp.4-430, 2009.

P. L. Smith, Comments on " an investigation of the slope-shape relation for gamma raindrop size distribution, J. Appl. Meteor. Climatol, vol.481, issue.9 9, pp.1994-199510, 2009.

R. B. Smith, The influence of mountains on the atmosphere, Adv. Geophys, vol.21, issue.3, pp.87-230, 1979.

M. Steiner and J. A. Smith, Reflectivity, rain rate, and kinetic energy flux relationships based on raindrop spectra, J. Appl. Meteorol, vol.39, issue.119, pp.1923-1940, 2000.
DOI : 10.1175/1520-0450(2000)039<1923:rrrake>2.0.co;2

M. Steiner, J. A. Smith, and R. Uijlenhoet, A microphysical interpretation of radar reflectivity-rain rate relationships, J. Atmos. Sci, issue.10, pp.61-1114, 2004.

J. Testud, S. Oury, R. A. Black, P. Amayenc, and X. K. Dou, The concept of " normalized " distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing, J. Appl. Meteorol, vol.40, issue.40, pp.1118-1140, 2001.

A. Tokay and D. A. Short, Evidence from tropical raindrop spectra of the origin of rain from stratiform versus convective clouds, J. Appl. Meteorol, vol.35, issue.11, pp.355-371, 1996.

A. Tokay, R. Wolff, P. Bashor, and O. Dursun, On the measurement errors of the Joss- Waldvogel disdrometer, 31st Int. Conf. on Radar Meteorology, pp.437-440, 2003.

R. Uijlenhoet, J. A. Smith, and M. Steiner, The microphysical structure of extreme precipitation as inferred from ground-based raindrop spectra, J. Atmos. Sci, vol.60, issue.40, pp.1220-1238, 2003.

R. Uijlenhoet, M. Steiner, and J. A. Smith, Variability of raindrop size distributions in a squall line and implications for radar rainfall estimation, J. Hydrometeor, vol.4, issue.12, pp.43-61, 2003.

R. Uijlenhoet and J. N. Stricker, A consistent rainfall parameterization based on the exponential raindrop size distribution, J. Hydrol, vol.218, pp.3-4, 1999.

C. Ulbrich, Natural variations in the analytical form of the raindrop size distribution, J. Climate Appl. Meteor, vol.22, issue.62, pp.1764-1775, 1983.

C. W. Ulbrich, The effects of drop size distribution truncation on rainfall integral parameters and empirical relations, J. Climate Appl. Meteor, vol.24, issue.6, pp.580-590, 1985.

C. W. Ulbrich, 1992: Effects of drop-size-distribution truncation on computer-simulations of dual-measurement radar methods, J. Appl. Meteorol, issue.7, pp.31-689

C. W. Ulbrich, Radar properties of tropical rain found from disdrometer data at Arecibo, Puerto Rico. The 29th Conference on Radar Meteorology, p.20, 1999.

A. I. Van-dijk, A. G. Meesters, J. Schellekens, and L. A. , A two-parameter exponential rainfall depth-intensity distribution applied to runoff and erosion modelling, J. Hydrol, vol.300, pp.155-171, 2005.

B. Vié, O. Nuissier, and D. V. , 2011: Cloud-resolving ensemble simulations of heavy precipitating events : uncertainty on initial conditions and lateral boundary conditions, Mon. Wea. Rev, vol.139, pp.403-423

B. Vincendon, V. Ducrocq, O. Nuissier, and B. Vié, 2011: Perturbation of convectionpermitting NWP forecasts for flash-flood ensemble forecasting, Nat. Hazards Earth Syst. Sci, vol.11, issue.92, pp.1529-1544

R. M. Wakimoto and V. N. Bringi, Dual-polarization observations of microbursts associated with intense convection: The 20 july storm during mist project, Mon. Wea. Rev, vol.116, pp.1521-1539, 1988.

A. Waldvogel, The No jump of raindrop spectra, J. Atmos. Sci, vol.31, issue.11, pp.1067-1078, 1974.

A. Waldvogel, W. Henrich, and L. Mosimann, New insight into the coupling between snow spectra and raindrop size distributions, 26th Int. Conference on Radar Meteorology, pp.602-604, 1993.

P. T. Willis, 1984: Functional fits to some observed drop size distributions and parameterization of rain, J. Atmos. Sci, vol.41, issue.9, pp.1648-1661

P. T. Willis and P. Tattelman, Drop-size distributions associated with intense rainfall, J. Appl. Meteorol, vol.28, issue.1, pp.3-15, 1989.
DOI : 10.1175/1520-0450(1989)028<0003:dsdawi>2.0.co;2

S. E. Yuter, D. E. Kingsmill, L. B. Nance, and M. L. Mang, Observations of precipitation size and fall speed characteristics within coexisting rain and wet snow, J. Appl. Meteor. Climatol, issue.10, pp.45-1450, 2006.

I. Zawadzki, M. De-agostinho, and . Antonio, Equilibrium raindrop size distributions in tropical rain, J. Atmos. Sci, vol.45, pp.3452-3459, 1988.

G. F. Zhang, J. Vivekanandan, E. A. Brandes, R. Meneghini, and T. Kozu, The shapeslope relation in observed gamma raindrop size distributions: Statistical error or useful information?, J. Atmos. Oceanic Technol, vol.20, issue.8, pp.1106-1119, 2003.