********************************************************************* * * * Atmospheric Absorption for Rayleigh, Mie and Ozone. * * * * Created: May-98 * * Author: Aitor Ibarra Ibaibarriaga * * Jose Carlos Gonzalez * * * ********************************************************************* c @T \newpage c @section Source code of {\tt attenu.f} * @text * Copyright $\copyright$ 1998, Aitor Ibarra Ibaibarriaga * @endtext c @code SUBROUTINE attenu(wavelength, height, theta, tr_atmos) C----------------------------------------------------------------------C C RHO (DENSITY) F(UNCTION) C C C C CALCULATES DENSITY (G/CM**3) OF ATMOSPHERE DEPENDING ON HEIGHT (CM) C C (US STANDARD ATMOSPHERE) C C THIS FUNCTION IS CALLED FROM ININKG, UPDATE, CERENE, CERENH C C ARGUMENT: C C ARG = HEIGHT IN CM C C----------------------------------------------------------------------C COMMON /ATMOS/ AATM,BATM,CATM,LAHG,RHOF,LONG,OZ_ABI,AE_ABI DOUBLE PRECISION AATM(5),BATM(5),CATM(5),LAHG(5),RHOF(5),Lm(12) DOUBLE PRECISION H,RT, m,OZ_ABI(48,12),AE_ABI(28,12) DOUBLE PRECISION XR, TOT_OZ, TOT_AE, T_Ray,T_Mie, T_Oz, + RHO_TOT, RHO_FI, RHOFP DOUBLE PRECISION Rcos2, Rsin2 DOUBLE PRECISION x1, x2, x3, x4 DOUBLE PRECISION e1, e2, e3, e4 REAL wavelength, height, theta, tr_atmos real trr, trm, tro REAL LONG(12) c fs: define obervation level double precision obslev INTEGER I,CON_OZ,CON_MI J, ROW DATA OZ_ABI / + 0.2880000D+00,0.5405000D+00,0.7775000D+00,0.1009000D+01, + 0.1241500D+01,0.1480500D+01,0.1750500D+01,0.2085000D+01, + 0.2514500D+01,0.3087500D+01,0.3864500D+01,0.4817500D+01, + 0.5847500D+01,0.6917500D+01,0.8052500D+01,0.9287499D+01, + 0.1068750D+02,0.1231250D+02,0.1415750D+02,0.1617750D+02, + 0.1827250D+02,0.2034750D+02,0.2232750D+02,0.2414750D+02, + 0.2575750D+02,0.2715250D+02,0.2836750D+02,0.2941100D+02, + 0.3031000D+02,0.3109250D+02,0.3176300D+02,0.3232750D+02, + 0.3281200D+02,0.3323200D+02,0.3358350D+02,0.3387750D+02, + 0.3412650D+02,0.3434000D+02,0.3451900D+02,0.3466250D+02, + 0.3477480D+02,0.3486355D+02,0.3493355D+02,0.3498775D+02, + 0.3503010D+02,0.3506360D+02,0.3509020D+02,0.3511185D+02, + 0.2740000D-01,0.5140000D-01,0.7395000D-01,0.9600000D-01, + 0.1181500D+00,0.1409000D+00,0.1666000D+00,0.1984500D+00, + 0.2393500D+00,0.2939500D+00,0.3679500D+00,0.4589500D+00, + 0.5573000D+00,0.6593000D+00,0.7673000D+00,0.8848000D+00, + 0.1017800D+01,0.1172300D+01,0.1348300D+01,0.1540800D+01, + 0.1740300D+01,0.1937800D+01,0.2126300D+01,0.2299800D+01, + 0.2453300D+01,0.2586300D+01,0.2702300D+01,0.2801900D+01, + 0.2887550D+01,0.2962050D+01,0.3025900D+01,0.3079700D+01, + 0.3125850D+01,0.3165850D+01,0.3199350D+01,0.3227400D+01, + 0.3251150D+01,0.3271500D+01,0.3288600D+01,0.3302300D+01, + 0.3312995D+01,0.3321445D+01,0.3328110D+01,0.3333270D+01, + 0.3337305D+01,0.3340500D+01,0.3343035D+01,0.1334510D+01, + 0.2435000D-02,0.4570000D-02,0.6575000D-02,0.8535000D-02, + 0.1050500D-01,0.1253000D-01,0.1481500D-01,0.1764500D-01, + 0.2128000D-01,0.2613500D-01,0.3272000D-01,0.4081000D-01, + 0.4957000D-01,0.5866000D-01,0.6827000D-01,0.7875500D-01, + 0.9065500D-01,0.1044050D+00,0.1200050D+00,0.1371050D+00, + 0.1548550D+00,0.1724050D+00,0.1891550D+00,0.2045550D+00, + 0.2182050D+00,0.2300550D+00,0.2403600D+00,0.2492200D+00, + 0.2568350D+00,0.2634550D+00,0.2691300D+00,0.2739150D+00, + 0.2780200D+00,0.2815750D+00,0.2845500D+00,0.2870400D+00, + 0.2891500D+00,0.2909600D+00,0.2924750D+00,0.2936900D+00, + 0.2946425D+00,0.2953940D+00,0.2959865D+00,0.2964455D+00, + 0.2968045D+00,0.2970885D+00,0.2973140D+00,0.2974975D+00, + 0.1740000D-03,0.3265000D-03,0.4695000D-03,0.6090000D-03, + 0.7495000D-03,0.8940000D-03,0.1057000D-02,0.1259000D-02, + 0.1518000D-02,0.1863500D-02,0.2332500D-02,0.2909000D-02, + 0.3533000D-02,0.4180500D-02,0.4865000D-02,0.5610500D-02, + 0.6455500D-02,0.7435000D-02,0.8550000D-02,0.9770000D-02, + 0.1103500D-01,0.1229000D-01,0.1348500D-01,0.1458000D-01, + 0.1555100D-01,0.1639550D-01,0.1713150D-01,0.1776300D-01, + 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+ 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 0.0000000D+00,0.0000000D+00,0.0000000D+00,0.0000000D+00, + 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+ 0.1126865D-02,0.1133915D-02,0.1139830D-02,0.1144570D-02, + 0.1148275D-02,0.1151200D-02,0.1153510D-02,0.1155300D-02, + 0.1156700D-02,0.1162205D-02,0.1170990D-02,0.1178145D-02, + 0.9360000D-04,0.1757000D-03,0.2528000D-03,0.3281500D-03, + 0.4038500D-03,0.4816500D-03,0.5694500D-03,0.6784000D-03, + 0.8184000D-03,0.1004900D-02,0.1257900D-02,0.1568900D-02, + 0.1905400D-02,0.2254400D-02,0.2623400D-02,0.3025400D-02, + 0.3480900D-02,0.4008900D-02,0.4609400D-02,0.5266900D-02, + 0.5948400D-02,0.6622900D-02,0.7266400D-02,0.7857900D-02, + 0.8381900D-02,0.8836901D-02,0.9233401D-02,0.9573901D-02, + 0.9866901D-02,0.1012140D-01,0.1033940D-01,0.1052340D-01, + 0.1068140D-01,0.1081840D-01,0.1093290D-01,0.1102855D-01, + 0.1110965D-01,0.1117920D-01,0.1123750D-01,0.1128425D-01, + 0.1132085D-01,0.1134975D-01,0.1137255D-01,0.1139020D-01, + 0.1140400D-01,0.1141492D-01,0.1142358D-01,0.1143063D-01, + 0.2500000D-03,0.4690000D-03,0.6745000D-03,0.8755000D-03, + 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0.4785200E-01,0.4791600E-01,0.4796000E-01,0.4799100E-01, + 0.4801600E-01,0.4803900E-01,0.4806000E-01,0.4807950E-01, + 0.2430000E-01,0.3474000E-01,0.3942000E-01,0.4135500E-01, + 0.4203000E-01,0.4227300E-01,0.4235850E-01,0.4239270E-01, + 0.4241520E-01,0.4243590E-01,0.4245660E-01,0.4247910E-01, + 0.4250970E-01,0.4255920E-01,0.4262310E-01,0.4269240E-01, + 0.4276890E-01,0.4284810E-01,0.4292370E-01,0.4299660E-01, + 0.4306680E-01,0.4312440E-01,0.4316400E-01,0.4319190E-01, + 0.4321440E-01,0.4323510E-01,0.4325400E-01,0.4327155E-01, + 0.2255000E-01,0.3225500E-01,0.3659500E-01,0.3838900E-01, + 0.3901500E-01,0.3924050E-01,0.3931985E-01,0.3935155E-01, + 0.3937240E-01,0.3939160E-01,0.3941080E-01,0.3943165E-01, + 0.3946005E-01,0.3950600E-01,0.3956530E-01,0.3962960E-01, + 0.3970055E-01,0.3977400E-01,0.3984415E-01,0.3991180E-01, + 0.3997695E-01,0.4003040E-01,0.4006715E-01,0.4009305E-01, + 0.4011390E-01,0.4013310E-01,0.4015065E-01,0.4016695E-01, + 0.2130000E-01,0.3044500E-01,0.3455500E-01,0.3625450E-01, + 0.3684700E-01,0.3706050E-01,0.3713575E-01,0.3716575E-01, + 0.3718550E-01,0.3720370E-01,0.3722190E-01,0.3724165E-01, + 0.3726850E-01,0.3731195E-01,0.3736805E-01,0.3742890E-01, + 0.3749605E-01,0.3756555E-01,0.3763190E-01,0.3769590E-01, + 0.3775750E-01,0.3780805E-01,0.3784280E-01,0.3786725E-01, + 0.3788700E-01,0.3790520E-01,0.3792180E-01,0.3793720E-01, + 0.2025000E-01,0.2895000E-01,0.3285000E-01,0.3446250E-01, + 0.3502500E-01,0.3522750E-01,0.3529875E-01,0.3532725E-01, + 0.3534600E-01,0.3536325E-01,0.3538050E-01,0.3539925E-01, + 0.3542475E-01,0.3546600E-01,0.3551925E-01,0.3557700E-01, + 0.3564075E-01,0.3570675E-01,0.3576975E-01,0.3583050E-01, + 0.3588900E-01,0.3593700E-01,0.3597000E-01,0.3599325E-01, + 0.3601200E-01,0.3602925E-01,0.3604500E-01,0.3605960E-01, + 0.1920000E-01,0.2745500E-01,0.3114500E-01,0.3267050E-01, + 0.3320300E-01,0.3339470E-01,0.3346215E-01,0.3348915E-01, + 0.3350690E-01,0.3352320E-01,0.3353950E-01,0.3355725E-01, + 0.3358140E-01,0.3362045E-01,0.3367085E-01,0.3372550E-01, + 0.3378585E-01,0.3384835E-01,0.3390800E-01,0.3396550E-01, + 0.3402090E-01,0.3406635E-01,0.3409760E-01,0.3411965E-01, + 0.3413740E-01,0.3415370E-01,0.3416860E-01,0.3418245E-01 / DATA BATM / 1222.6562D0,1144.9069D0,1305.5948D0,540.1778D0,0.D0 / DATA CATM / 994186.38D0,878153.55D0,636143.04D0,772170.16D0,1.D-9/ DATA LAHG / 2200.0D2,4.0D5,1.0D6,4.0D6,1.0D7 / DATA Lm /3.70D5,3.85D5,4.0D5,4.17D5,4.17D5,4.35D5,5.0D5,5.56D5, + 5.99D5,6.33D5, 6.67D5,7.04D5 / DATA LONG / + 280.0, + 300.0, + 320.0, + 340.0, + 360.0, + 380.0, + 400.0, + 450.0, + 500.0, + 550.0, + 600.0, + 650.0 / DATA PI / 3.141592654D0 / c-- Take same Earth radius as in CORSIKA parameter (rt = 6371315.D2) c-- Scale-height for Exponential density profile parameter (hscale = 7.4d5) *********************************************************************** * * SCATTERING PARAMETERS FOR RAYLEIGH: * * MEAN FREE PATH FOR SCATTERING RAYLEIGH (g/cm^2) PARAMETER (XR=2.970D3) *********************************************************************** c-- Observation level at La Palma parameter (obslev = 2200.d2) T_Ray = 1.0 T_Mie = 1.0 T_Oz = 1.0 c-- Height calculated using an obslev = H(LaPalma) <> 0 c H = -RT + SQRT(RT**2 + (height/COS(theta))**2 + c + (2.0D0*RT*height)) h = -rt + sqrt((rt+obslev)**2 + + ((height-obslev)/cos(theta))**2 + + (2.0d0*(rt+obslev)*(height-obslev))) ROW = AINT(((H+1.)/1.0E5)) *********************************************************************** * * LARGE ZENITH ANGLE FACTOR (AIR MASS): c fs : air mass factor = path_lenght(za) / path_lenght(vertical) c at point of emission of cherenkov photon c => pure geometric correction on c absorption lenght measured at vertical height [km^-1] c-- c ma = (1.D0/H)*(SQRT((RT*COS(theta))**2+(2*RT*H)+H**2)- c + (RT*COS(theta))) c-- c mb = (1.d0/(h-obslev)) * c & ( -(rt+obslev)*cos(theta) c & +sqrt( (rt+h)**2 - ((rt+obslev)*sin(theta))**2) ) c-- c-- Air mass "m" calcualted using a one-exponential density c-- profile for the atmosphere, rho = rho_0 exp(-h/Hs) c-- with Hs = hscale = 7.4 km Rcos2 = rt * cos(theta)**2 Rsin2 = rt * sin(theta)**2 x1 = sqrt((2. * obslev + Rcos2) / (2. * hscale)) x2 = sqrt((2. * h + Rcos2) / (2. * hscale)) x3 = sqrt((2. * obslev + rt) / (2. * hscale)) x4 = sqrt((2. * h + rt) / (2. * hscale)) e1 = derfc(x1) e2 = derfc(x2) e3 = derfc(x3) e4 = derfc(x4) m = exp(-Rsin2 / (2. * hscale)) * ((e1 - e2) / (e3 - e4)) ********************************************************************** * * RAYLEIGH SCATTERING RHOTOT = 0.0 do 11 i=1,5 RHOF(i) = 0 11 continue DO 91 I=2,5 IF ( H .LT. LAHG(I) ) THEN RHOTOT = RHOTOT + + BATM(I-1)*(EXP(-LAHG(I-1)/CATM(I-1) ) - + EXP(-H/CATM(I-1))) GOTO 92 ELSE RHOTOT = RHOTOT + + BATM(I-1)*(EXP(-LAHG(I-1)/CATM(I-1) ) - + EXP(-LAHG(I)/CATM(I-1))) ENDIF 91 CONTINUE 92 RHO_FI = m*RHOTOT T_Ray = EXP(-(RHO_FI/XR)*(400.D0/wavelength)**4) *************************************************************************** * * * MIE ABSORPTION: WE USE FOR HEIGHTS LOWER THAN 10 Km AN EXACT FORMULA* * FOR THE AEROSOL DENSITY, AND WE USE A TABLE FOR HIGHTS HIGHER THAN * * 10 Km. WE TAKE THE TABLE FROM THE ALTERMAN ARTICLE. * *************************************************************************** *************************************************************************** * * * MIE SCATTERING PARAMETERS * Hm = 1.2D5 *************************************************************************** IF (ROW.GT.27) THEN ROW=28 ENDIF CON_MI = 2 1001 IF (ABS(LONG(CON_MI)-wavelength).LT.0.01) THEN TOT_AE =AE_ABI(ROW,CON_MI) ELSEIF (LONG(CON_MI).GT.wavelength) THEN A = (AE_ABI(ROW,CON_MI)-AE_ABI(ROW,CON_MI-1))/ + (LONG(CON_MI) - LONG(CON_MI-1)) B = AE_ABI(ROW,CON_MI) - (A*LONG(CON_MI)) TOT_AE = A*wavelength + B ELSE CON_MI = CON_MI +1 GOTO 1001 ENDIF T_Mie = EXP(-(m*TOT_AE)) *********************************************************************** * * * OZONE ABSORPTION: We used the Elterman table. * * * *********************************************************************** IF (ROW.GT.47) THEN ROW = 47 ENDIF CON_OZ = 2 2001 IF (LONG(CON_OZ).GT.wavelength) THEN A = (OZ_ABI(ROW,CON_OZ)-OZ_ABI(ROW,CON_OZ-1))/ + (LONG(CON_OZ) - LONG(CON_OZ-1)) B = OZ_ABI(ROW,CON_OZ) - (A*LONG(CON_OZ)) TOT_OZ = (A* wavelength)+B ELSEIF (ABS(LONG(CON_OZ)-wavelength).LT.0.01) THEN TOT_OZ = OZ_ABI(ROW,CON_OZ) ELSE CON_OZ = CON_OZ + 1 GOTO 2001 ENDIF T_Oz = EXP(-(m*TOT_OZ)) ************************************************************************ * * * TOTAL TRANSMISSION OF THE ATMOSPHERE: (RAYLEIGH + MIE + OZONE) * ************************************************************************ tr_atmos = T_Ray*T_Mie*T_Oz RETURN END c @endcode c EOF