SUBROUTINE FLOTT_GWD_RAN(NLON,NLEV,DTIME, pp, pn2, & tt,uu,vv, plevmoy, & zustr,zvstr,d_t, d_u, d_v) !---------------------------------------------------------------------- ! Parametrization of the momentum flux deposition due to a discrete ! number of gravity waves. ! F. Lott ! Version 14, Gaussian distribution of the source ! LMDz model online version ! ADAPTED FOR VENUS / F. LOTT + S. LEBONNOIS ! Version adapted on 03/04/2013: ! - input flux compensated in the deepest layers !--------------------------------------------------------------------- use dimphy USE geometry_mod, only: cell_area, latitude_deg implicit none #include "YOEGWD.h" #include "YOMCST.h" ! 0. DECLARATIONS: ! 0.1 INPUTS INTEGER, intent(in):: NLON, NLEV REAL, intent(in):: DTIME ! Time step of the Physics REAL, intent(in):: pp(NLON, NLEV) ! Pressure at full levels ! VENUS ATTENTION: CP VARIABLE PN2 CALCULE EN AMONT DES PARAMETRISATIONS REAL, intent(in):: pn2(NLON,NLEV) ! N2 (BV^2) at 1/2 levels REAL, intent(in):: TT(NLON, NLEV) ! Temp at full levels REAL, intent(in):: UU(NLON, NLEV) , VV(NLON, NLEV) ! Hor winds at full levels REAL, intent(in) :: plevmoy(NLEV+1) ! press (Pa) at interlayers, at klon/2+1 ! 0.2 OUTPUTS REAL, intent(out):: zustr(NLON), zvstr(NLON) ! Surface Stresses REAL, intent(inout):: d_t(NLON, NLEV) ! Tendency on Temp. REAL, intent(inout):: d_u(NLON, NLEV), d_v(NLON, NLEV) ! Tendencies on winds ! O.3 INTERNAL ARRAYS INTEGER II, LL ! 0.3.0 TIME SCALE OF THE LIFE CYCLE OF THE WAVES PARAMETERIZED REAL DELTAT ! 0.3.1 GRAVITY-WAVES SPECIFICATIONS !VENUS INTEGER, PARAMETER:: NK = 2, NP = 2, NO = 2, NW = NK * NP * NO !Online output: change NO ! INTEGER, PARAMETER:: NK = 1, NP = 2, NO = 11, NW = NK * NP * NO INTEGER JK, JP, JO, JW REAL KMIN, KMAX ! Min and Max horizontal wavenumbers REAL KSTAR ! Min horizontal wavenumber constrained by resolution REAL CMIN, CMAX ! Min and Max absolute ph. vel. REAL CPHA ! absolute PHASE VELOCITY frequency REAL ZK(NW, KLON) ! Horizontal wavenumber amplitude REAL ZP(NW) ! Horizontal wavenumber angle REAL ZO(NW, KLON) ! Absolute frequency ! ! Waves Intr. freq. at the 1/2 lev surrounding the full level REAL ZOM(NW, KLON), ZOP(NW, KLON) ! Wave EP-fluxes at the 2 semi levels surrounding the full level REAL WWM(NW, KLON), WWP(NW, KLON) ! Fluxes X and Y for each waves at 1/2 Levels REAL RUWP(NW, KLON), RVWP(NW, KLON) REAL RUW(KLON, KLEV + 1) ! Flux x at semi levels REAL RVW(KLON, KLEV + 1) ! Flux y at semi levels REAL RUW0(NW, KLON) ! Fluxes at launching level REAL RUWMAX ! Max value INTEGER LAUNCH ! Launching altitude REAL XLAUNCH ! Control the launching altitude ! 0.3.2 PARAMETERS OF WAVES DISSIPATIONS REAL SAT ! saturation parameter REAL RDISS, ZOISEC ! COEFF DE DISSIPATION, SECURITY FOR INTRINSIC FREQ ! 0.3.3 BACKGROUND FLOW AT 1/2 LEVELS AND VERTICAL COORDINATE REAL H0bis(KLON, KLEV) ! Characteristic Height of the atmosphere REAL H0 ! Characteristic Height of the atmosphere REAL PR, TR ! Reference Pressure and Temperature REAL ZH(KLON, KLEV + 1) ! Log-pressure altitude (constant H0) REAL ZHbis(KLON, KLEV + 1) ! Log-pressure altitude (varying H) REAL UH(KLON, KLEV + 1), VH(KLON, KLEV + 1) ! Winds at 1/2 levels REAL PH(KLON, KLEV + 1) ! Pressure at 1/2 levels REAL PSEC ! Security to avoid division by 0 pressure REAL BV(KLON, KLEV + 1) ! Brunt Vaisala freq. (BVF) at 1/2 levels REAL BVSEC ! Security to avoid negative BVF ! COSMETICS TO DIAGNOSE EACH WAVES CONTRIBUTION. logical output data output/.false./ ! data output/.true./ ! CAUTION ! IF output is .true. THEN change NO to 10 at least ! character*14 outform character*2 str2 integer ieq ! ON CONSERVE LA MEMOIRE un certain temps AVEC UN SAVE real,save,allocatable :: d_u_sav(:,:),d_v_sav(:,:) LOGICAL firstcall SAVE firstcall DATA firstcall/.true./ REAL ALEAS EXTERNAL ALEAS !----------------------------------------------------------------- ! 1. INITIALISATIONS IF (firstcall) THEN allocate(d_u_sav(NLON,NLEV),d_v_sav(NLON,NLEV)) d_u_sav = 0. d_v_sav = 0. firstcall=.false. ENDIF ! 1.1 Basic parameter ! PARAMETERS CORRESPONDING TO V3: RUWMAX = 0.005 ! Max EP-Flux at Launch altitude (Nominal as Gilli2017) ! RUWMAX = 0.0025 ! Half-nominal ! RUWMAX = 0.01 ! Double-nominal SAT = 0.85 ! Saturation parameter: Sc in (12) RDISS = 0.1 ! Diffusion parameter DELTAT=24.*3600. ! Time scale of the waves (first introduced in 9b) !!!! TESTS ! KMIN = 1.E-5 ! Min horizontal wavenumber (lambda max 628) ! KMIN = 6.3E-6 ! Min horizontal wavenumber (lambda max 1000 km) ! KMIN = 1.2E-6 ! Min horizontal wavenumber (lambda max 5000 km) ! KMAX = 1.E-4 ! Max horizontal wavenumber (lambda min 50 km) !!! TEST Kobs and BestFit Diogo KMIN = 1.E-5 ! Min horizontal wavenumber (lambda max 628) KMAX = 1.E-4 ! Max horizontal wavenumber (lambda min 50 km) !!! TEST GW8 ! KMIN = 1.25E-5 ! Min horizontal wavenumber (lambda max 500 km) ! KMAX = 1.E-4 ! Max horizontal wavenumber (lambda min 50 km) !!! TEST GW9 ! KMIN = 1.E-6 ! Min horizontal wavenumber (lambda max 6000 km) ! KMAX = 2.E-5 ! Max horizontal wavenumber (lambda min 300 km) !!! TEST BestFit GG ! KMIN = 6.3E-6 ! Min horizontal wavenumber (lambda max 1000 km) ! KMAX = 1.E-4 ! Max horizontal wavenumber (lambda min 50 km) !Online output: one value only if (output) then KMIN = 3E-5 KMAX = 3E-5 endif !! CMIN = 1. ! Min phase velocity CMAX = 61. ! Max phase speed velocity TestGW6 ! CMAX= 111. ! TestGW2 ! XLAUNCH=0.6 ! Parameter that control launching altitude XLAUNCH=5e-3 ! Value for top of cloud convective region ! XLAUNCH=2.e-4 ! Value for ~ 70 km? Review this ! PR = 9.2e6 ! Reference pressure ! VENUS!! PR = 5e5 ! Reference pressure ! VENUS: cloud layer TR = 300. ! Reference Temperature ! VENUS: cloud layer H0 = RD * TR / RG ! Characteristic vertical scale height BVSEC = 1.E-5 ! Security to avoid negative BVF PSEC = 1.E-8 ! Security to avoid division by 0 pressure ZOISEC = 1.E-8 ! Security FOR 0 INTRINSIC FREQ IF(DELTAT.LT.DTIME)THEN PRINT *,'GWD RANDO: DELTAT LT DTIME!' STOP ENDIF IF (NLEV < NW) THEN PRINT *, 'YOU WILL HAVE PROBLEM WITH RANDOM NUMBERS' PRINT *, 'FLOTT GWD STOP' STOP 1 ENDIF ! 2. EVALUATION OF THE BACKGROUND FLOW AT SEMI-LEVELS !------------------------------------------------------------- !Online output if (output) OPEN(11,file="impact-gwno.dat") ! Pressure and Inv of pressure, Temperature / at 1/2 level DO LL = 2, KLEV PH(:, LL) = EXP((LOG(PP(:, LL)) + LOG(PP(:, LL - 1))) / 2.) end DO PH(:, KLEV + 1) = 0. PH(:, 1) = 2. * PP(:, 1) - PH(:, 2) ! Launching altitude DO LL = 1, NLEV IF (plevmoy(LL) / plevmoy(1) > XLAUNCH) LAUNCH = LL ENDDO ! test ! print*,"launch=",LAUNCH ! print*,"launch p,N2=",plevmoy(LAUNCH),pn2(nlon/2+1,LAUNCH) ! Log pressure vert. coordinate DO LL = 1, KLEV + 1 ZH(:, LL) = H0 * LOG(PR / (PH(:, LL) + PSEC)) end DO if (output) then ! altitude above surface ZHbis(:,1) = 0. DO LL = 2, KLEV + 1 H0bis(:, LL-1) = RD * TT(:, LL-1) / RG ZHbis(:, LL) = ZHbis(:, LL-1) & + H0bis(:, LL-1)*(PH(:, LL-1)-PH(:,LL))/PP(:, LL-1) end DO endif ! Winds and BV frequency DO LL = 2, KLEV UH(:, LL) = 0.5 * (UU(:, LL) + UU(:, LL - 1)) ! Zonal wind VH(:, LL) = 0.5 * (VV(:, LL) + VV(:, LL - 1)) ! Meridional wind ! BVSEC: BV Frequency ! VENUS ATTENTION: CP VARIABLE PSTAB CALCULE EN AMONT DES PARAMETRISATIONS BV(:, LL) = MAX(BVSEC,SQRT(pn2(:,LL))) end DO BV(:, 1) = BV(:, 2) UH(:, 1) = 0. VH(:, 1) = 0. BV(:, KLEV + 1) = BV(:, KLEV) UH(:, KLEV + 1) = UU(:, KLEV) VH(:, KLEV + 1) = VV(:, KLEV) ! 3. WAVES CHARACTERISTICS CHOSEN RANDOMLY !------------------------------------------- ! The mod function of here a weird arguments ! are used to produce the waves characteristics ! in a stochastic way !! A REVOIR: !! - utilisation de MOD ou bien de aleas ? !! - distribution gaussienne des CPHA ? (avec signe ZP qui est ajuste apres) JW = 0 DO JP = 1, NP DO JK = 1, NK DO JO = 1, NO JW = JW + 1 ! Angle ZP(JW) = 2. * RPI * REAL(JP - 1) / REAL(NP) DO II = 1, KLON ! Horizontal wavenumber amplitude ! ZK(JW, II) = KMIN + (KMAX - KMIN) * MOD(TT(II, JW) * 100., 1.) ! TN+GG April/June 2020 - "Individual waves are not supposed to occupy ! the entire domain, but only a fraction of it" [Lott+2012]: KSTAR = RPI/SQRT(cell_area(II)) ! KSTAR should be < KMAX... ZK(JW, II) = MAX(KMIN,KSTAR) + (KMAX - MAX(KMIN,KSTAR)) * ALEAS(0.) ! ZK(JW, II) = KMIN + (KMAX - KMIN) * ALEAS(0.) ! Horizontal phase speed ! CPHA = CMIN + (CMAX - CMIN) * MOD(TT(II, JW)**2, 1.) CPHA = CMIN + (CMAX - CMIN) * ALEAS(0.) !Online output: linear if (output) CPHA = CMIN + (CMAX - CMIN) * (JO-1)/(NO-1) ! Intrinsic frequency ZO(JW, II) = CPHA * ZK(JW, II) ! Intrinsic frequency is imposed ZO(JW, II) = ZO(JW, II) & + ZK(JW, II) * COS(ZP(JW)) * UH(II, LAUNCH) & + ZK(JW, II) * SIN(ZP(JW)) * VH(II, LAUNCH) ! Momentum flux at launch lev ! RUW0(JW, II) = RUWMAX / REAL(NW) & RUW0(JW, II) = RUWMAX & ! * MOD(100. * (UU(II, JW)**2 + VV(II, JW)**2), 1.) * ALEAS(0.) !Online output: fixed to max if (output) RUW0(JW, II) = RUWMAX ENDDO end DO end DO end DO ! 4. COMPUTE THE FLUXES !-------------------------- ! 4.1 Vertical velocity at launching altitude to ensure ! the correct value to the imposed fluxes. ! DO JW = 1, NW ! Evaluate intrinsic frequency at launching altitude: ZOP(JW, :) = ZO(JW, :) & - ZK(JW, :) * COS(ZP(JW)) * UH(:, LAUNCH) & - ZK(JW, :) * SIN(ZP(JW)) * VH(:, LAUNCH) ! WW is directly a flux, here, not vertical velocity anymore WWP(JW, :) = RUW0(JW,:) RUWP(JW, :) = COS(ZP(JW)) * SIGN(1., ZOP(JW, :)) * RUW0(JW, :) RVWP(JW, :) = SIN(ZP(JW)) * SIGN(1., ZOP(JW, :)) * RUW0(JW, :) end DO ! 4.2 Initial flux at launching altitude RUW(:, LAUNCH) = 0 RVW(:, LAUNCH) = 0 DO JW = 1, NW RUW(:, LAUNCH) = RUW(:, LAUNCH) + RUWP(JW, :) RVW(:, LAUNCH) = RVW(:, LAUNCH) + RVWP(JW, :) end DO ! 4.3 Loop over altitudes, with passage from one level to the ! next done by i) conserving the EP flux, ii) dissipating ! a little, iii) testing critical levels, and vi) testing ! the breaking. !Online output if (output) then ieq=nlon/2+1 write(str2,'(i2)') NW+2 outform="("//str2//"(E12.4,1X))" WRITE(11,outform) ZH(IEQ, 1) / 1000., ZHbis(IEQ, 1) / 1000., & (ZO(JW, IEQ)/ZK(JW, IEQ)*COS(ZP(JW)), JW = 1, NW) endif DO LL = LAUNCH, KLEV - 1 ! W(KB)ARNING: ALL THE PHYSICS IS HERE (PASSAGE FROM ONE LEVEL ! TO THE NEXT) DO JW = 1, NW ZOM(JW, :) = ZOP(JW, :) WWM(JW, :) = WWP(JW, :) ! Intrinsic Frequency ZOP(JW, :) = ZO(JW, :) - ZK(JW, :) * COS(ZP(JW)) * UH(:, LL + 1) & - ZK(JW, :) * SIN(ZP(JW)) * VH(:, LL + 1) WWP(JW, :) = MIN( & ! No breaking (Eq.6) WWM(JW, :) & ! Dissipation (Eq. 8): * EXP(- RDISS * PR / (PH(:, LL + 1) + PH(:, LL)) & * ((BV(:, LL + 1) + BV(:, LL)) / 2.)**3 & / MAX(ABS(ZOP(JW, :) + ZOM(JW, :)) / 2., ZOISEC)**4 & * ZK(JW, :)**3 * (ZH(:, LL + 1) - ZH(:, LL))), & ! Critical levels (forced to zero if intrinsic frequency changes sign) MAX(0., SIGN(1., ZOP(JW, :) * ZOM(JW, :))) & ! Saturation (Eq. 12) * ABS(ZOP(JW, :))**3 /BV(:, LL+1) & * EXP(-ZH(:, LL + 1)/H0) * SAT**2*KMIN**2/ZK(JW, :)**4) end DO ! END OF W(KB)ARNING ! Evaluate EP-flux from Eq. 7 and ! Give the right orientation to the stress DO JW = 1, NW RUWP(JW, :) = SIGN(1.,ZOP(JW, :))*COS(ZP(JW))*WWP(JW, :) RVWP(JW, :) = SIGN(1.,ZOP(JW, :))*SIN(ZP(JW))*WWP(JW, :) end DO ! RUW(:, LL + 1) = 0. RVW(:, LL + 1) = 0. DO JW = 1, NW RUW(:, LL + 1) = RUW(:, LL + 1) + RUWP(JW, :) RVW(:, LL + 1) = RVW(:, LL + 1) + RVWP(JW, :) end DO !Online output if (output) then do JW=1,NW if(RUWP(JW, IEQ).gt.0.) then RUWP(JW, IEQ) = max(RUWP(JW, IEQ), 1.e-99) else RUWP(JW, IEQ) = min(RUWP(JW, IEQ), -1.e-99) endif enddo WRITE(11,outform) ZH(IEQ, LL+1) / 1000., & ZHbis(IEQ, LL+1) / 1000., & (RUWP(JW, IEQ), JW = 1, NW) endif end DO ! 5 CALCUL DES TENDANCES: !------------------------ ! 5.1 Rectification des flux au sommet et dans les basses couches: ! MODIF SL ! Attention, ici c'est le total sur toutes les ondes... RUW(:, KLEV + 1) = 0. RVW(:, KLEV + 1) = 0. ! Here, big change compared to FLott version: ! We compensate (RUW(:, LAUNCH), ie total emitted upward flux ! over the layers max(1,LAUNCH-3) to LAUNCH-1 DO LL = 1, max(1,LAUNCH-3) RUW(:, LL) = 0. RVW(:, LL) = 0. end DO DO LL = max(2,LAUNCH-2), LAUNCH-1 RUW(:, LL) = RUW(:, LL - 1) + RUW(:, LAUNCH) * & (PH(:,LL)-PH(:,LL-1)) / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3))) RVW(:, LL) = RVW(:, LL - 1) + RVW(:, LAUNCH) * & (PH(:,LL)-PH(:,LL-1)) / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3))) end DO ! This way, the total flux from GW is zero, but there is a net transport ! (upward) that should be compensated by circulation ! and induce additional friction at the surface !Online output if (output) then DO LL = 1, KLEV - 1 WRITE(11,*) ZHbis(IEQ, LL)/1000.,RUW(IEQ,LL) end DO CLOSE(11) stop endif ! AR-1 RECURSIVE FORMULA (13) IN VERSION 4 DO LL = 1, KLEV d_u(:, LL) = RG * (RUW(:, LL + 1) - RUW(:, LL)) & / (PH(:, LL + 1) - PH(:, LL)) * DTIME d_v(:, LL) = RG * (RVW(:, LL + 1) - RVW(:, LL)) & / (PH(:, LL + 1) - PH(:, LL)) * DTIME ENDDO d_t = 0. ! ON CONSERVE LA MEMOIRE un certain temps AVEC UN SAVE d_u = DTIME/DELTAT/REAL(NW) * d_u + (1.-DTIME/DELTAT) * d_u_sav d_v = DTIME/DELTAT/REAL(NW) * d_v + (1.-DTIME/DELTAT) * d_v_sav d_u_sav = d_u d_v_sav = d_v ! Cosmetic: evaluation of the cumulated stress ZUSTR(:) = 0. ZVSTR(:) = 0. DO LL = 1, KLEV ZUSTR(:) = ZUSTR(:) + D_U(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL)) ZVSTR(:) = ZVSTR(:) + D_V(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL)) ENDDO END SUBROUTINE FLOTT_GWD_RAN !=================================================================== !=================================================================== !=================================================================== !=================================================================== FUNCTION ALEAS (R) !***BEGIN PROLOGUE ALEAS !***PURPOSE Generate a uniformly distributed random number. !***LIBRARY SLATEC (FNLIB) !***CATEGORY L6A21 !***TYPE SINGLE PRECISION (ALEAS-S) !***KEYWORDS FNLIB, ALEAS NUMBER, SPECIAL FUNCTIONS, UNIFORM !***AUTHOR Fullerton, W., (LANL) !***DESCRIPTION ! ! This pseudo-random number generator is portable among a wide ! variety of computers. RAND(R) undoubtedly is not as good as many ! readily available installation dependent versions, and so this ! routine is not recommended for widespread usage. Its redeeming ! feature is that the exact same random numbers (to within final round- ! off error) can be generated from machine to machine. Thus, programs ! that make use of random numbers can be easily transported to and ! checked in a new environment. ! ! The random numbers are generated by the linear congruential ! method described, e.g., by Knuth in Seminumerical Methods (p.9), ! Addison-Wesley, 1969. Given the I-th number of a pseudo-random ! sequence, the I+1 -st number is generated from ! X(I+1) = (A*X(I) + C) MOD M, ! where here M = 2**22 = 4194304, C = 1731 and several suitable values ! of the multiplier A are discussed below. Both the multiplier A and ! random number X are represented in double precision as two 11-bit ! words. The constants are chosen so that the period is the maximum ! possible, 4194304. ! ! In order that the same numbers be generated from machine to ! machine, it is necessary that 23-bit integers be reducible modulo ! 2**11 exactly, that 23-bit integers be added exactly, and that 11-bit ! integers be multiplied exactly. Furthermore, if the restart option ! is used (where R is between 0 and 1), then the product R*2**22 = ! R*4194304 must be correct to the nearest integer. ! ! The first four random numbers should be .0004127026, ! .6750836372, .1614754200, and .9086198807. The tenth random number ! is .5527787209, and the hundredth is .3600893021 . The thousandth ! number should be .2176990509 . ! ! In order to generate several effectively independent sequences ! with the same generator, it is necessary to know the random number ! for several widely spaced calls. The I-th random number times 2**22, ! where I=K*P/8 and P is the period of the sequence (P = 2**22), is ! still of the form L*P/8. In particular we find the I-th random ! number multiplied by 2**22 is given by ! I = 0 1*P/8 2*P/8 3*P/8 4*P/8 5*P/8 6*P/8 7*P/8 8*P/8 ! RAND= 0 5*P/8 2*P/8 7*P/8 4*P/8 1*P/8 6*P/8 3*P/8 0 ! Thus the 4*P/8 = 2097152 random number is 2097152/2**22. ! ! Several multipliers have been subjected to the spectral test ! (see Knuth, p. 82). Four suitable multipliers roughly in order of ! goodness according to the spectral test are ! 3146757 = 1536*2048 + 1029 = 2**21 + 2**20 + 2**10 + 5 ! 2098181 = 1024*2048 + 1029 = 2**21 + 2**10 + 5 ! 3146245 = 1536*2048 + 517 = 2**21 + 2**20 + 2**9 + 5 ! 2776669 = 1355*2048 + 1629 = 5**9 + 7**7 + 1 ! ! In the table below LOG10(NU(I)) gives roughly the number of ! random decimal digits in the random numbers considered I at a time. ! C is the primary measure of goodness. In both cases bigger is better. ! ! LOG10 NU(I) C(I) ! A I=2 I=3 I=4 I=5 I=2 I=3 I=4 I=5 ! ! 3146757 3.3 2.0 1.6 1.3 3.1 1.3 4.6 2.6 ! 2098181 3.3 2.0 1.6 1.2 3.2 1.3 4.6 1.7 ! 3146245 3.3 2.2 1.5 1.1 3.2 4.2 1.1 0.4 ! 2776669 3.3 2.1 1.6 1.3 2.5 2.0 1.9 2.6 ! Best ! Possible 3.3 2.3 1.7 1.4 3.6 5.9 9.7 14.9 ! ! Input Argument -- ! R If R=0., the next random number of the sequence is generated. ! If R .LT. 0., the last generated number will be returned for ! possible use in a restart procedure. ! If R .GT. 0., the sequence of random numbers will start with ! the seed R mod 1. This seed is also returned as the value of ! RAND provided the arithmetic is done exactly. ! ! Output Value -- ! RAND a pseudo-random number between 0. and 1. ! !***REFERENCES (NONE) !***ROUTINES CALLED (NONE) !***REVISION HISTORY (YYMMDD) ! 770401 DATE WRITTEN ! 890531 Changed all specific intrinsics to generic. (WRB) ! 890531 REVISION DATE from Version 3.2 ! 891214 Prologue converted to Version 4.0 format. (BAB) !***END PROLOGUE RAND SAVE IA1, IA0, IA1MA0, IC, IX1, IX0 DATA IA1, IA0, IA1MA0 /1536, 1029, 507/ DATA IC /1731/ DATA IX1, IX0 /0, 0/ !***FIRST EXECUTABLE STATEMENT RAND ! ! A*X = 2**22*IA1*IX1 + 2**11*(IA1*IX1 + (IA1-IA0)*(IX0-IX1) ! + IA0*IX0) + IA0*IX0 ! IF (R.EQ.0.) THEN IY0 = IA0*IX0 IY1 = IA1*IX1 + IA1MA0*(IX0-IX1) + IY0 IY0 = IY0 + IC IX0 = MOD (IY0, 2048) IY1 = IY1 + (IY0-IX0)/2048 IX1 = MOD (IY1, 2048) ENDIF IF (R.GT.0.) THEN IX1 = MOD(R,1.)*4194304. + 0.5 IX0 = MOD (IX1, 2048) IX1 = (IX1-IX0)/2048 ENDIF ALEAS = IX1*2048 + IX0 ALEAS = ALEAS / 4194304. RETURN END