Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate

Abstract The scale invariance of rainfall series in the Tunis area, Tunisia (semi-arid Mediterranean climate) is studied in a mono-fractal framework by applying the box counting method to four series of observations, each about 2.5 years in length, based on a time resolution of 5 min. In addition, a single series of daily rainfall records for the period 1873–2009 was analysed. Three self-similar structures were identified: micro-scale (5 min to 2 d) with fractal dimension 0.44, meso-scale (2 d to one week) and synoptic-scale (one week to eight months) with fractal dimension 0.9. Interpretation of these findings suggests that only the micro-scale and transition to saturation are consistent, while the high fractal dimension relating to the synoptic scale might be affected by the tendency to saturation. A sensitivity analysis of the estimated fractal dimension was performed using daily rainfall data by varying the series length, as well as the intensity threshold for the detection of rain. Editor Z.W. Kundzewicz; Associate editor S. Grimaldi Citation Ghanmi, H., Bargaoui, Z., and Mallet, C., 2013. Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate. Hydrological Sciences Journal, 58 (3), 483–497.

[1]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[2]  H. Guibert,et al.  Caractérisation du climat dans quatre terroirs en région soudano-sahélienne du Nord-Cameroun et conséquences pour l'agriculture , 2003 .

[3]  Pierre Hubert,et al.  Dimensions fractales de l'occurrence de pluie en climat soudano-sahélien , 1989 .

[4]  Daniel Schertzer,et al.  Extrêmes et multifractals en hydrologie : résultats, validations et perspectives , 2006 .

[5]  François G. Schmitt,et al.  Modeling of rainfall time series using two-state renewal processes and multifractals , 1998 .

[6]  V. Iacobellis,et al.  Multiscaling pulse representation of temporal rainfall , 2002 .

[7]  S. Kohnová,et al.  Estimation of IDF curves of extreme rainfall by simple scaling in Slovakia , 2009 .

[8]  P. Hubert,et al.  Interprétation multifractale des courbes intensité-durée-fréquence des précipitations , 1997 .

[9]  I. Orlanski.  A rational subdivision of scales for atmospheric processes , 1975 .

[10]  R. Rosso,et al.  Analytical derivation of rain intensity–duration–area–frequency relationships from event maxima , 2011 .

[11]  L. Barthès,et al.  Multifractal analysis of African monsoon rain fields, taking into account the zero rain-rate problem , 2010 .

[12]  L. Barthès,et al.  The Effect of Rain–No Rain Intermittency on the Estimation of the Universal Multifractals Model Parameters , 2009 .

[13]  P. Hubert,et al.  New Uncertainty Concepts in Hydrology and Water Resources: Multifractal structure of rainfall occurrence in West Africa , 1995 .

[14]  W. Briggs.  Statistical Methods in the Atmospheric Sciences , 2007 .

[15]  A. Langousis,et al.  Intensity‐duration‐frequency curves from scaling representations of rainfall , 2007 .

[16]  A. Langousis,et al.  Multifractal rainfall extremes: Theoretical analysis and practical estimation , 2009 .

[17]  Intensity-duration-area-frequency functions for precipitation in a multifractal framework , 2004 .

[18]  L. H. Cammeraat,et al.  Space and time scale variability and interdependencies in hydrological processes , 1998 .

[19]  Ronny Berndtsson,et al.  Fractal Analysis of High-Resolution Rainfall Time Series , 1993 .

[20]  A. Langousis,et al.  Marginal methods of intensity‐duration‐frequency estimation in scaling and nonscaling rainfall , 2007 .

[21]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[22]  Merab Menabde,et al.  Multiaffine random field model of rainfall , 1999 .

[23]  H. Isnard.  La répartition saisonnière des pluies en Algérie , 1950 .

[24]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[25]  R. Pielke.  Mesoscale Meteorological Modeling , 1984 .

[26]  M. D. Lima,et al.  Investigating the multifractality of point precipitation in the Madeira archipelago , 2009 .

[27]  Ronny Berndtsson,et al.  An analysis of the rainfall time structure by box counting—some practical implications , 1992 .

[28]  N. T. Kottegoda,et al.  IDAF (intensity-duration-area frequency) curves of extreme storm rainfall: a scaling approach. , 2002, Water science and technology : a journal of the International Association on Water Pollution Research.

[29]  L. Barthès,et al.  Multiscaling properties of rain in the time domain, taking into account rain support biases , 2011 .

[30]  J. Lavergnat,et al.  A Stochastic Raindrop Time Distribution Model , 1998 .

[31]  Edward C. Waymire,et al.  A statistical analysis of mesoscale rainfall as a random cascade , 1993 .

[32]  D. Schertzer,et al.  Functional Box-Counting and Multiple Elliptical Dimensions in Rain , 1987, Science.

[33]  R. Forthofer,et al.  Rank Correlation Methods , 1981 .

[34]  Angelbert Biaou.  De la méso-échelle à la micro-échelle : désagrégation spatio-temporelle multifractale des précipitations , 2004 .

[35]  S. Lovejoy.  Area-Perimeter Relation for Rain and Cloud Areas , 1982, Science.

[36]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[37]  P. Hubert.  La prédétermination des crues , 2005 .

[38]  Benoit B. Mandelbrot,et al.  Les objets fractals : forme, hasard et dimension , 1989 .

[39]  Shaun Lovejoy,et al.  Universal Multifractals: Theory and Observations for Rain and Clouds , 1993 .