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1、MonteCarlosimulationofradiationtransferinopticallyanisotropiccloudsArielCohen(Jerusalem)PieroBruscaglioni(Florence)UlrichG.Oppel(Muenchen)AnatoliG.Borovoi(Tomsk)SergeiM.Prigarin(Novosibirsk)IgorA.Grishin,TatianaB.Zhuravleva(Tomsk)INTASproject“LIDARmultiplescatteringfromcloudsincludingspheric
2、alandnon-sphericalparticles”Themaingoal:todevelopamathematicalmodelandaMonteCarloalgorithmtosimulateradiationtransferinascatteringmediumthatisopticallyanisotropicwithrespecttozenithalangleofthelightbeamMonteCarlosimulationofphotons’trajectoriesinascatteringmediumthatisopticallyanisotropicwit
3、hrespecttozenithalangleStep1.Initialpointr0=(x0,y0,z0)andinitialdirectionω0=(a0,b0,c0),
4、ω0
5、=1,ofaphotonaresimulatedaccordingtothedensityofsources;n=0.Step2.Thephoton'sfree-pathlengthlissimulatedaccordingtotheprobabilitydensityp(l)=σ(cn)exp{-lσ(cn)},l>0,whereσ(c)istheextinctioncoefficientinth
6、edirectionwithcosinecofthezenithangle.Step3.Wesetn=n+1andcalculatethecoordinatesofthenextcollisionpointinthemedium:xn=xn-1+an-1l,yn=yn-1+bn-1l,zn=zn-1+cnl,rn=(xn,yn,zn).Step4.Thetypeofthecollisionissimulated:itisscatteringwithprobabilityq(cn)andabsorptionwithprobability1-q(cn),whereq(c)issin
7、glescatteringalbedointhedirectionwithcosinecofthezenithangle.Thestepsbelowareproducedonlyinthecaseofscattering.Step5.Anewdirectionofthephotonωn=(an,bn,cn)issimulatedaccordingtothephasefunctiong(ωn-1,ωn).Goovertothestep2.Denotethedirectionbeforescatteringbyω?=(a?,b?,c?)andthedirectionaftersca
8、tteringbyω=(a,b,c).First,thevalueofcosinecofthezenithangleissimulated.ForthatweuseadistributionP(c?,c)withrespecttoc?[-1,1]whenthevaluec?isfixed.Thenavariationψoftheazimuthangleissimulated.ForthatweneedtoknowadistributionQ(c?,c,ψ)withrespecttoψ?[-π,π]whenthevaluesc?,carefixed.Thevaluesaandbc
9、anbefoundbyformulasa=[a?cos(ψ)-b?sin(ψ)](1-c2)1/2[1-(c?)2]-1/2,b=[a?sin(ψ)-b?cos(ψ)](1-c2)1/2[1-(c?)2]-1/2.ThusforthemodelofanisotropicscatteringitisnecessarytohavefamiliesofdistributionsP(c?,·),Q(c?,c,·)wherec??[0,1],c?[-1,1].3icecloudmodels3.Parr
