Structure Analysis and Classification of Precipitation Cells by Fractal Geometry

220JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY, VOL. 12, NO. 2, JUNE 2014Structure Analysis and Classification of PrecipitationCells by Fractal GeometryNafissa Azzaz and Boualem HaddadAbstract- -This paper analyzes the possibility to stratiform conditions, a threshold of Z, or a gradient ofdiscriminate between convective precipitation andvertical reflectivity, or the difference of Z observed abovestratiform precipitation. This study aims to improve the and belowfusion level (or shiny band). The resultsmeasurement of rainfall from teledetection data obtained with these algorithms are not entirely convincing,obtained both on the ground and in space. For this, two because they do not cover all the full diversity of weatherparameters, fractal dimension and fractal lacunarity, conditions'hiO.are considered. To calculate the fractal dimension, weThe work presented in this paper focuses on theuse the approach of box-counting and show that the difference between convective and stratiform cells in radarfractal dimension differs between convectives cells andimages, using fractal dimension and fractal lacunarity.stratiforms ones. And then the fractal lacunarityparameter is calculated by using the sliding boxes2. Databasealgorithm. The study for all the regions shows thatprecipitation cells can be described by differentIn this study, we consider four different weather radarlacunarities whatever the scale of analysis. We deducesites: Dakar (Senegal)， Bordeaux (France)， Melbournethat the two parameters, fractal dimension and fractal (Florida, USA), and State College PA (PennsyIvania, USA).lacunarity, can be used to classify precipitations ir2.1 Region of Dakarconvective regime and stratiform regime.Dakar is the capital of the Republic of Senegal. It isIndex Terms- Convectives cells, fractal dimension,located at the western extremity of Africa, on the narrowfractal lacunarity, radar, stratiforms cells.peninsula of Cape Verde.Being in a tropical semi-desert， Dakar has a1. Introductionmicroclimate of coastal type, influenced by the monsoontrade winds and sea. The hot wet season extends from JuneThe rainfall in general can be characterized by theto October with temperatures of about 27 C and a peak ofconvective regime and stratiform regimel". Convectiveprecipitations in August (250 mm).precipitation is very intense, with a relatively short duration,The radar of Dakar is installed on a tower of 30 mand is very volatile-. In the opposite, stratiform rains are above the sea level at Yoff Airport, in the east of Dakar. Itslow on average, but can persist for hours, leading to angeographical coordinates are 1444' north latitude anaccumulation of significant rainfall24.17° 29' west longitude. It is operated by both the NationalThe classification of precipitations in conveective and Meteorological Office of Senegal and ASECNAstratiform regimes is useful in a variety of meteorology's (Association for the Safety of Air Navigation). This radarapplications. It can help to improve the accuracy of rainfallworks only during storm periods. The average intensity ofrtrieval from teledetetion data obtained both on the rainfalls varies from 300 mm to 1500 mm from Saint Louisground and in spacelShl4.to Cap Skirring"!. The technical characteristics of theMany studies have approached the problem ofweather radar of Dakar are given in Table 1.discrimination between convective precipitation andstratiform precipitation5. Most of the proposed algorithmsTable 1: Characteristics of the: weather radar of Dakar regionconsider a single criterion to identify convective andTechnical characteristicValueDiameter of antenna2.5mManuscript received March 20, 2013; revised May 6, 2013.Transmission frequency5.7 GHzN. Azzaz is with the Laboratory of Images Processing and Radiation,Transmission power250 kW peakFaculty of Electronics and Computer Science, University of Science andTechnology, Algiers， Algeria (Corresponding author e-mail:Spatial resolution1kmx 1kmnafissa_ anl@yahoo.fr).Pulse duration3 usB. Haddad is with the Laboratory of Images Processing and Radiation,Repetition sensitivity-110 dBmFaculty of Electronics and Computer Science. University of Science andBeam wi中国煤化工Technology, Algiers, Algeria (e-mail: h_ boualem@hotmail.com).AntennaDigital Object Identifier: 10.3969/jissn. 1674-862X.2014.02.016MHCN MH G一AZZAZ et al: Structure Analysis and Classification of Precipitation Cells by Fractal Geometry221Table 2: Characteristics of the weather radar of Bordeaux regionTable 4: Characteristics of the weather radar of State College regionTechnical characracteristicValue .Technical characteristic_ValueType of antennaparabolicParabolicTransmission frequency3 GHzTransmission power500kW peakLatiude positin .40° 55 23" NSpatial resolution1kmx 1 kmLongitude position78° O' 14" wPulse durationSHsElevation758 metersRepetition frequency300 HzBeam width to 3dBBeam width to 3 dB0.93° (to 2850 MH2)2.2 Region of Bordeaux3. Theoretical ConceptsThe city of Bordeaux is located in the south western ofFrance. The Bordeaux radar is located in the Bordeaux- 3.1 Fractal DimensionMerignac airport， whose geographical coordinates areThe concept of fractals was first introduced b;44 49'54" north latitude and 0 41'30" west longitude. It is .Mandelbrot! 1,], as an indicator of surface roughness. Theone of 24 metropolitan France radars. The digital analysisfractal theory has been widely applied to different scientificof the reflectivity of 8 bits (SANAGA) includes dataareas, particularly image processing. It contains informationprocessing and data storagel8. The radar is a part of theabout geometric structures of fractals and can also be usedFrench network (ARAMIS) managed by Meteo-France.for non-fractals. It is a measure to quantize the complexityThe area is almost flat. Table 2 gives the technicalof the geometrical objects. Many approaches were proposedcharacteristics of the radar of Bordeaux.for estimating the fractal dimension of images. In our case,2.3 Region of Melbournewe use the box-counting approach日. This method is basedMelbourne is a city located on the east coast of Florida，on the recovery of the space in which the object is includedUnited States of America. It is situated to the east of in order to calculate the fractal dimension by a gridOrlando, and south of Cape Canaveral. It has a humidconsisting of square (or “boxes") of side 8. The numbersubtropical climate, the typical of the Gulf. and South N(e) represents the number of boxes which are used toAtlantic states, although Melbourne is classified as a humidpave the object. The size of boxes is then defined by:subtropical climate.The radar used is Nexrad WSR-88D type, which workslIn[N(e)]on the coherent Doppler principle.. The geographicalD, = limln(1/ε)(1)position of Melboure radar is 28.109 N, 80.650° W. Itallows to observe the precipitation in the oceanic, lttoral,3.2 Fractal Lacunarityand terrestrial parts'. The Melbourne climate is subtropical,with hot and humid summers and cool winters.Lacunarity is another concept introduced bThe technical characteristics of the weather radar of Mandelbrotlol to quantize the nature of gaps in textureMelbourne are given in Table 3.images. It is inspired from the Latin (lacuna) origin of theEnglish word “lake”, defining a fractal as being“lacunar"2.4 Region of State Collegewhen its gaps tend to be large. If a fractal has large gaps orState College is located in Pennsylvania State, theholes, it has high lacunarityl. Visually different imageseastern of the United States of America. State College issometimes may have similar values for their fractalsituated at an elevation of approximately 1200 feet (370m)dimensions. But lacunarity estimation can help us toabove the sea level. It is surrounded by large tracts ofdistinguish such images.farmland, and an expanse of mountains and forests. StateIt is a measure for spatial heterogeneity. So higherCollege has a humid continental climate. The averagetemperature is- -3.7 C in January and 21.8 C in July. .values of lacunarity implies more heterogeneity, as it meansAnnual precipitation is less than 40 inches (1000 mm), andan object is more homogeneous when the lacunarity islow[13]46.3 inches (118 cm) of snow a year falls in the city.The radar used is Nexrad WSR-88D type called KCCX,There are several methods for calculating the fractalwhich works on the coherent Doppler principle. Its lacunarity in the literature. In our case, we use the methodtechnical characteristics are given in Table 4.of Allain and Cloitre, based on the sliding box algorithm,Table 3: Characteristics of the weather radar of Melbourne regionwhere the lacunarity 1(L) is defined as a function of thescale L byl[l4:ValueDiameter of antenna18.5 mMaximum rotation rateAzimuth 30 s-' Elevation 30° s-'4(L)= :s3(L)(2)Maximum accelerationAzimuth 15 s-' Elevation 15* s-'2(0+1=2+1Mechanical limits-1° to +60"Polarizationhorizontal linearwhere s(L) is中国煤化工、, noted as μ; s20.93° (to 2850 MHz)Antenna gain45 dBzis the variance o:fYHCNM HG2.222JOURNAL OF ELECTRONIC SCIENCE AND TECHNOLOGY, VOL. 12, NO. 2, JUNE 20144. Results and DiscussionTable 5: Fractals dimensions obtained for the four regions.SitesCells typeDD; min; D; maxAs an ilustration, we present the results for the regionDakarStratiform1.477[1.415;1.54]of Dakar (Senegal). Fig. 1 shows an image of convectiveConvective 1 .229[1.147; 1.164]and stratiform cells, taken from Dakar radar, on July 12,BordeauxStratiform1. 565[1.560; 1.570]Convective 1. 1 152011.Melbourme1.400[1.381;1.413]Convective .1.082[1.021; 1.125]4.1 Fractal DimensionState College Stratiform1.614[1.602; 1.6251 .Fig. 2 shows the fractal dimension of convective and(KCCX)Convective_ 1.289[.112; 1.4611stratiform cells in region of Dakar.We obtained for stratiform cells an average fractalComecthe celdimension equal to 1.45, while for convective cells anaverage fractal dimension is equal to 1.02. The goodness of0o，fit is given by a correlation coefficient of0.93.Convectire cellsStratiform cellsTable 5 shows the fractals dimensions D, the fractaldimension minimum D;min, and the fractal dimensionmaximum D,max, obtained for the four regions studied.We notice that for all the images studied, the fractaldimension values of stratiform cells are higher than of theconvective ones. It shows that the stratiform cells are moredeformed than the convective cells. As the fractal1020304050607089100dimension varies with the nature of the cells and theSize of boxesprevailing climate in the region considered, we conclude Fig. 3. Fractal lacunarity obtained for convective and stratiformthat the precipitations have a multifractal structure; this cells.result is in good agreement with the literature 5.4.2 Fractal LacunarityFig. 3 represents the lacunarity fractal of convectivecells and stratiform cells obtained for the site of Dakar.It is observed that for all images analyzed, the behavior「Coarectires Cellsof the lacunarity 4(x) resembles a hyperbola. Therefore, weapproach the representations of the fractal lacunarity 4(x)by the following model function L(x):L(x)=ax'+c(3)where a, b, C, and x represent the homogeneity factors,convergence order of L(x), translation term, and boxesizeo, respectively.Table 6 shows the homogeneity factors of lacunaritycurves obtained for the four regions studied. amin and amaxStatfarms Cellssrepresent respectively the minimum and the maximum ofthe homogeneity factors obtained for each studied site.Fig. 1. Convective and stratiform cells obtained from radar imagesWe notice from Fig. 3 that the lacunarity curve ofin Dakar.stratiform cells is below that of the convective cells. We●Stnatem celsthen deduce that the stratiform cells are more homogeneousComectie clllthan the convective cells. The same conclusions areobserved for the other radar sites.Sratiform cellsTable 6: Fractals dimensions obtained for the four regionsFtraclancrmecsona (factors ofamini; Amaxhomogeneity)238..9[221.9; 255.9Convective496.7[489.2; 504.1]Covective clls- -6.42.[- 6.627; -6.22204.9[203.1; 206.6]士市312.4[297.1;327.7]Melbourne二583; 965State中国煤化工-0.956; 0.023]Fig. 2. Fractal dimension obtained for convective and stratiform_Collegecells.MYHCNMH GO63.252_AZZAZ et al: Structure Analysis and Classification of Precipitation Cells by Fractal Geometry223Also, from Table 6, we note that the parameter a of [9] D. B. Wolff, D. A. Marks, E. Amiai, D. s. Silberstein, B., Lconvective cells is greater than that of stratiform cells, .Fisher, A. Tokay, J. Wang, and J. L. Pipitt, “Groundwhatever the study region. This is due to the fact thatvalidation for the tropical rainfall measurement missionconvective cells are less homogeneous than stratiform cells.(TRMM)," Journal of Atmos. Ocean. Tech, vol. 31, no.1, pp.On the other hand, we know that the lacunarity is low[10] B. B. Mandelbrot, The Fractal Geometry of Nature, New51- 55, 2005.when the texture is fine while it is high for a coarseYork: W. H. Freeman and Company, 1983, pp.45- 47.texturel' .We then deduce that the stratiform cells have a finer[11]K. I. Kilic and R. H. Abiyev, “Exploiting the synergybetween fractal dimension and lacunarity for improvedtexture than the convective cells.texture recognition," Signal Processing, vol. 91, no. 10, Pp.2332- 2344, 2011.5. Conclusions[12] S. Lovejoy and D. Schertzer, “Multifractals, Universalityclasses and satellite and radar measurement of cloud and rainfields," Journal of Geophysical Research, vol. 95, pp.recognition of cells types of precipitation by combining2021- -2034, Feb. 1990.fractal measures and lacunarity measures. In the literature, [13] K. Falconer, Fractal Geometry. Mathematical Foundationsthe lacunarity and fractal dimension were always studiedand Applications, Chichester: John Wiley & Sons, 1990, pp.288.separately.In this study, we showed that the fractal dimension and[14] C. Allain and M. Cloitre,“Characterizing the lacunarity ofthe fractal lacunarity are powerful discriminators betweenrandom and deterministic fractal sets," Physical Review A, .vol. 44, pp. 3552- -3558, Sep. 1991.stratiform cells and convective cells. We also demonstrated[15] D. Schertzer and S. Lovejoy, “Hard and soft multifractalthat the stratiforms cells are more homogeneous and moreprocesses," Physical Review A, vol. 185, pp. 187- 194, Jun.distorted than convectives cells whatever the prevailing1992.climate.The calculation methods used in this paper, based on16] A. Zaia, R. Eleonori, P. Maponi, R. Rossi, and R. Murri,“Medical imaging and osteoporosis: fractal's lacunarityfractal geometry, could become an important complementanalysis of trabecular bone in MR images," in Proc. of theto conventional techniques currently used in radar imaging18th IEEE Symposium on Computer- Based Medical Systems,for the identification and evaluation of rainfall. It canDublin, 2005, pp. 1063 -7125.improve weather forecasts in the medium and long term.[17] B. Olalla, “Analysis of the basic dispersion and overallmechanisms of mineral fllers in polymers: influence theReferencesrheology and structure of the matrix,” Ph.D. dissertation,Jean Monnet University, Saint Etienne, France, 20101] R. A. Houze, Jr, Cloud Dynamics, San Diego: AcademicPress, 1993, pp.570- -573.Nafissa Azzaz was born in Algiers, Algeria[2] F. Tridon, J. Van Baelen, and Y. Pointin, “Identification ofin 1984. She received the bachelor degree inconvective and stratiform areas towards improvedelectronic telecommunication engineeringprecipitation estimation with a local area X-band radar, infrom the University of Science andProc. of the 6th European Conf. on Radar in MeteorologyTechnology Houari Boumediene, Algeria inand Hydrology, Sibiu, 2010, pp. 219- 225.2007, and the M.S. degree in electronics;3] J. Simpson, R. F Adler, and G North,“A proposed tropicalrainfall measurement mission (TRMM) satellite," Bull. Am.option atmospheric radiation from the sameMeteorol, vol. 69, pp. 278 -295, Mar. 1998.university in 2010. She is currently pursuing[4] N.E.1Anagnostou,“A convectiv/stratiform precipitationthe Ph.D. degree with Radiation and Image Processing Laboratory,classification algorithm for volume scanning weather radaraculty of Electronics and Computer Science, Universityobservations," Meteorological Applications, vol. 11, no. 4, pp. Science and Technology. Her research interests include fractal and :291- 300, 2004.multifractal theory, image processing, and meteorogical5] F. Mesnard, O. Pujol, H. Sauvageot, C. Costes, N. Bon, andJ. applicationsArtis,“Discrimination between convective and stratiformprecipitation in radar-observed rainfield using fuzzy logic,"Boualem Haddad was born in Tizi-ouzou,presented at the 5th European Conf. on Radar in meteorologyAlgeria in 1957. He got his bachelor degreeand Hydrology, Helsinki, 2008.in telecommunications engineering from the[6] C. w. Ulbrich and D. Atlas, “On the separation of tropicalNational Polytechnic School (Algeria) inconvective and stratiform rains,” Journal of Applied1982, magister degree in applied electronicsMeteorology, vol. 41, no. 2, pp. 188- 195, 2002.in 1991, and Ph.D. degree in atmospheric7] A. Nzeukou and H. Sauvageot, "Distribution of rainfallradiation in 2000 both from the University ofparameters near the coasts of France and Senegal," JournalSciences and Technology of Algiers. He hasofApplied Meteorologvol. 41, no.1, pp.69- 82, 2002.been a teacher since 1984. From 1996 to[8] H.Sauvageot and G Despaux, “SANAGA: A digital1999, he was the assistant director of education and pedagogy. Heacquisition and visualization of radar data for the validity of has been a professor with the University of Sciences andsatellite precipitation estimates," Standby Climate Satellite, Technology of A中国煤化τber of Radiationvol.31, no. 1, pp.51- 55, 1990.and Image ProcessYHCNMH G