! modal_aero_coag.F90 !---------------------------------------------------------------------- !BOP ! ! !MODULE: modal_aero_coag --- modal aerosol coagulation ! ! !INTERFACE: module modal_aero_coag ! !USES: use shr_kind_mod, only: r8 => shr_kind_r8 use chem_mods, only: gas_pcnst use modal_aero_data, only: maxd_aspectype implicit none private save ! !PUBLIC MEMBER FUNCTIONS: public modal_aero_coag_sub, modal_aero_coag_init ! !PUBLIC DATA MEMBERS: integer, parameter :: pcnstxx = gas_pcnst #if ( defined MODAL_AERO_7MODE || defined MODAL_AERO_4MODE ) integer, parameter, public :: pair_option_acoag = 3 #elif ( defined MODAL_AERO_3MODE ) integer, parameter, public :: pair_option_acoag = 1 #endif ! specifies pairs of modes for which coagulation is calculated ! 1 -- [aitken-->accum] ! 2 -- [aitken-->accum], and [pcarbon-->accum] ! 3 -- [aitken-->accum], [pcarbon-->accum], ! and [aitken-->pcarbon--(aging)-->accum] ! other -- do no coag integer, parameter, public :: maxpair_acoag = 10 integer, parameter, public :: maxspec_acoag = maxd_aspectype integer, public :: npair_acoag integer, public :: modefrm_acoag(maxpair_acoag) integer, public :: modetoo_acoag(maxpair_acoag) integer, public :: modetooeff_acoag(maxpair_acoag) integer, public :: nspecfrm_acoag(maxpair_acoag) integer, public :: lspecfrm_acoag(maxspec_acoag,maxpair_acoag) integer, public :: lspectoo_acoag(maxspec_acoag,maxpair_acoag) integer :: ip_aitacc, ip_aitpca, ip_pcaacc real(r8) :: fac_m2v_aitage(maxd_aspectype), fac_m2v_pcarbon(maxd_aspectype) ! !DESCRIPTION: This module implements ... ! ! !REVISION HISTORY: ! ! RCE 07.04.13: Adapted from MIRAGE2 code ! !EOP !---------------------------------------------------------------------- !BOC ! list private module data here !EOC !---------------------------------------------------------------------- contains !---------------------------------------------------------------------- !BOP ! !ROUTINE: modal_aero_coag_sub --- ... ! ! !INTERFACE: subroutine modal_aero_coag_sub( & lchnk, ncol, nstep, & loffset, deltat_main, & t, pmid, pdel, & q, & dgncur_a, dgncur_awet, & wetdens_a ) !---------------------------------------------------------------------- ! Authors: R. Easter !---------------------------------------------------------------------- ! !USES: use mo_constants, only: pi use modal_aero_data use modal_aero_gasaerexch, only: n_so4_monolayers_pcage ! soa_equivso4_factor use cam_abortutils, only: endrun use cam_history, only: outfld, fieldname_len use chem_mods, only: adv_mass use constituents, only: pcnst, cnst_name use physconst, only: gravit, mwdry, r_universal use ppgrid, only: pcols, pver use spmd_utils, only: iam, masterproc use ref_pres, only: top_lev => clim_modal_aero_top_lev implicit none ! !PARAMETERS: integer, intent(in) :: lchnk ! chunk identifier integer, intent(in) :: ncol ! number of columns in chunk integer, intent(in) :: nstep ! model step integer, intent(in) :: loffset ! offset applied to modal aero "pointers" real(r8), intent(in) :: deltat_main ! model timestep (s) real(r8), intent(in) :: t(pcols,pver) ! temperature (K) real(r8), intent(in) :: pmid(pcols,pver) ! pressure at model levels (Pa) real(r8), intent(in) :: pdel(pcols,pver) ! pressure thickness of levels (Pa) real(r8), intent(inout) :: q(ncol,pver,pcnstxx) ! tracer mixing ratio (TMR) array ! *** MUST BE mol/mol-air or #/mol-air ! *** NOTE ncol & pcnstxx dimensions real(r8), intent(in) :: dgncur_a(pcols,pver,ntot_amode) ! dry geo. mean dia. (m) of number distrib. real(r8), intent(in) :: dgncur_awet(pcols,pver,ntot_amode) ! wet geo. mean dia. (m) of number distrib. real(r8), intent(in) :: wetdens_a(pcols,pver,ntot_amode) ! density of wet aerosol (kg/m3) ! !DESCRIPTION: ! computes changes due to coagulation involving ! aitken mode (modeptr_aitken) with accumulation mode (modeptr_accum) ! this version will ! compute changes to mass and number, but not to surface area ! calculates coagulation rate coefficients using either ! new CMAQ V4.6 fast method ! older cmaq slow method (direct gauss-hermite quadrature) ! ! !REVISION HISTORY: ! RCE 07.04.15: Adapted from MIRAGE2 code and CMAQ V4.6 code ! !EOP !---------------------------------------------------------------------- !BOC ! local variables ! integer :: i, iok, ipair, ip_aitacc, ip_aitpca, ip_pcaacc, iq integer :: i, iok, ipair, iq integer :: idomode(ntot_amode), iselfcoagdone(ntot_amode) integer :: jfreqcoag, jsoa !MS integer :: k integer :: l, l1, l2, la, lmz, lsfrm, lstoo, lunout integer :: modefrm, modetoo, mait, macc, mpca integer :: n, nfreqcoag integer, save :: nerr = 0 ! number of errors for entire run integer, save :: nerrmax = 9999 ! maximum number of errors before abort integer, parameter :: ldiag1=-1, ldiag2=-1, ldiag3=-1 logical, parameter :: fastcoag_flag = .true. ! selects coag rate-coef method real(r8) :: aircon real(r8) :: deltat, deltatinv_main real(r8) :: dr_so4_monolayers_pcage real(r8) :: dryvol_a(pcols,pver,ntot_amode) real(r8) :: dumexp, dumloss, dumprod real(r8) :: dumsfc_frm_old, dumsfc_frm_new real(r8) :: dum_m2v ! real(r8) :: fac_m2v_aitage(maxd_aspectype), fac_m2v_pcarbon(maxd_aspectype) real(r8) :: fac_volsfc_pcarbon real(r8) :: lnsg_frm, lnsg_too real(r8) :: sg_frm, sg_too real(r8) :: tmpa, tmpb, tmpc, tmpf, tmpg, tmph, tmpn real(r8) :: tmp1, tmp2 real(r8) :: tmp_qold real(r8) :: v2ncur_a_tmp real(r8) :: vol_core, vol_shell real(r8) :: wetdens_frm, wetdens_too, wetdgnum_frm, wetdgnum_too real(r8) :: xbetaij0, xbetaij2i, xbetaij2j, xbetaij3, & xbetaii0, xbetaii2, xbetajj0, xbetajj2 real(r8) :: xferamt, xferfracvol, xferfrac_pcage, xferfrac_max real(r8) :: xnumbconc(ntot_amode) real(r8) :: xnumbconcavg(ntot_amode), xnumbconcnew(ntot_amode) real(r8) :: ybetaij0(maxpair_acoag), ybetaij3(maxpair_acoag) real(r8) :: ybetaii0(maxpair_acoag), ybetajj0(maxpair_acoag) real(r8) :: dqdt(ncol,pver,pcnstxx) ! TMR "dq/dt" array - NOTE dims logical :: dotend(pcnst) ! identifies the species that ! tendencies are computed for real(r8) :: qsrflx(pcols) character(len=fieldname_len) :: tmpname character(len=fieldname_len+3) :: fieldname ! begin ! check if any coagulation pairs exist if (npair_acoag <= 0) return !-------------------------------------------------------------------------------- !!$ if (ldiag1 > 0) then !!$ if (nstep <= 3) then !!$ do i = 1, ncol !!$ if (lonndx(i) /= 37) cycle !!$ if (latndx(i) /= 23) cycle !!$ if (nstep > 3) cycle !!$ write( *, '(/a,i7,i5,2(2x,2i5))' ) & !!$ '*** modal_aero_coag_sub -- nstep, iam, lat, lon, pcols, ncol =', & !!$ nstep, iam, latndx(i), lonndx(i), pcols, ncol !!$ end do !!$ end if !!$! if (ncol /= -999888777) return !!$ if (nstep > 3) call endrun( 'modal_aero_coag_sub -- nstep>3 testing halt' ) !!$ end if ! (ldiag1 > 0) !-------------------------------------------------------------------------------- dotend(:) = .false. dqdt(1:ncol,:,:) = 0.0_r8 lunout = 6 ! ! determine if coagulation will be done on this time-step ! currently coagulation is done every 3 hours ! ! deltat = 3600.0*3.0 deltat = deltat_main nfreqcoag = max( 1, nint( deltat/deltat_main ) ) jfreqcoag = nfreqcoag/2 xferfrac_max = 1.0_r8 - 10.0_r8*epsilon(1.0_r8) ! 1-eps if (nfreqcoag .gt. 1) then if ( mod(nstep,nfreqcoag) .ne. jfreqcoag ) return end if ! ! set idomode ! idomode(:) = 0 do ipair = 1, npair_acoag idomode(modefrm_acoag(ipair)) = 1 idomode(modetoo_acoag(ipair)) = 1 end do ! ! other init ! macc = modeptr_accum mait = modeptr_aitken mpca = modeptr_pcarbon ! fac_m2v_aitage(:) = 0.0_r8 ! fac_m2v_pcarbon(:) = 0.0_r8 ! if (pair_option_acoag == 3) then ! following ipair definitions MUST BE CONSISTENT with ! the coding in modal_aero_coag_init for pair_option_acoag == 3 ! ip_aitacc = 1 ! ip_pcaacc = 2 ! ip_aitpca = 3 if (mpca > 0 .and. mpca <= ntot_amode) then !MS ! use 1 mol (bi-)sulfate = 65 cm^3 --> 1 molecule = (4.76e-10 m)^3 dr_so4_monolayers_pcage = n_so4_monolayers_pcage * 4.76e-10_r8 fac_volsfc_pcarbon = exp( 2.5_r8*(alnsg_amode(mpca)**2) ) end if ! ipair = ip_aitpca ! do iq = 1, nspecfrm_acoag(ipair) ! lsfrm = lspecfrm_acoag(iq,ipair) ! if (lsfrm == lptr_so4_a_amode(mait)) then ! fac_m2v_aitage(iq) = specmw_so4_amode / specdens_so4_amode ! else if (lsfrm == lptr_nh4_a_amode(mait)) then ! fac_m2v_aitage(iq) = specmw_nh4_amode / specdens_nh4_amode ! else if (lsfrm == lptr_soa_a_amode(mait)) then ! fac_m2v_aitage(iq) = soa_equivso4_factor* & ! (specmw_soa_amode / specdens_soa_amode) ! for soa, the soa_equivso4_factor converts the soa volume into an ! so4(+nh4) volume that has same hygroscopicity contribution as soa ! this allows aging calculations to be done in terms of the amount ! of (equivalent) so4(+nh4) in the shell ! (see modal_aero_gasaerexch) ! end if ! end do ! ! do l = 1, nspec_amode(mpca) ! l2 = lspectype_amode(l,mpca) ! fac_m2v converts (kmol-AP/kmol-air) to (m3-AP/kmol-air) ! [m3-AP/kmol-AP] = [kg-AP/kmol-AP] / [kg-AP/m3-AP] ! fac_m2v_pcarbon(l) = specmw_amode(l2) / specdens_amode(l2) ! end do ! fac_volsfc_pcarbon = exp( 2.5_r8*(alnsg_amode(mpca)**2) ) ! else ! ip_aitacc = -999888777 ! ip_pcaacc = -999888777 ! ip_aitpca = -999888777 ! end if ! ! loop over levels and columns to calc the coagulation ! ! integrate coagulation changes over deltat = nfreqcoag*deltat_main ! then compute tendencies as ! dqdt = (q(t+deltat) - q(t))/deltat_main ! because tendencies are applied (in physics_update) over deltat_main ! deltat = nfreqcoag*deltat_main deltatinv_main = 1.0_r8/(deltat_main*(1.0_r8 + 1.0e-15_r8)) main_k: do k = top_lev, pver main_i: do i = 1, ncol ! air molar density (kmol/m3) aircon = (pmid(i,k)/(r_universal*t(i,k))) ! calculate number conc. (#/m3) for modes doing coagulation do n = 1, ntot_amode if (idomode(n) .gt. 0) then xnumbconc(n) = q(i,k,numptr_amode(n)-loffset)*aircon xnumbconc(n) = max( 0.0_r8, xnumbconc(n) ) end if iselfcoagdone(n) = 0 end do ! ! calculate coagulation rates for each pair ! main_ipair1: do ipair = 1, npair_acoag modefrm = modefrm_acoag(ipair) modetoo = modetoo_acoag(ipair) ! ! compute coagulation rates using cmaq "fast" method ! (based on E. Whitby's approximation approach) ! here subr. arguments are all in mks unit ! call getcoags_wrapper_f( & t(i,k), pmid(i,k), & dgncur_awet(i,k,modefrm), dgncur_awet(i,k,modetoo), & sigmag_amode(modefrm), sigmag_amode(modetoo), & alnsg_amode(modefrm), alnsg_amode(modetoo), & wetdens_a(i,k,modefrm), wetdens_a(i,k,modetoo), & xbetaij0, xbetaij2i, xbetaij2j, xbetaij3, & xbetaii0, xbetaii2, xbetajj0, xbetajj2 ) ! test diagnostics begin -------------------------------------------- !!$ if (ldiag2 > 0) then !!$ if (nstep <= 3) then !!$ if ((lonndx(i) == 37) .and. (latndx(i) == 23)) then !!$ if ((mod(k-1,5) == 0) .or. (k>=23)) then !!$ !!$ wetdgnum_frm = dgncur_awet(i,k,modefrm) !!$ wetdgnum_too = dgncur_awet(i,k,modetoo) !!$ wetdens_frm = wetdens_a(i,k,modefrm) !!$ wetdens_too = wetdens_a(i,k,modetoo) !!$ sg_frm = sigmag_amode(modefrm) !!$ sg_too = sigmag_amode(modetoo) !!$ lnsg_frm = alnsg_amode(modefrm) !!$ lnsg_too = alnsg_amode(modetoo) !!$ !!$ call getcoags_wrapper_f( & !!$ t(i,k), pmid(i,k), & !!$ wetdgnum_frm, wetdgnum_too, & !!$ sg_frm, sg_too, & !!$ lnsg_frm, lnsg_too, & !!$ wetdens_frm, wetdens_too, & !!$ xbetaij0, xbetaij2i, xbetaij2j, xbetaij3, & !!$ xbetaii0, xbetaii2, xbetajj0, xbetajj2 ) !!$ !!$ !!$ write(lunout,9801) !!$ write(lunout,9810) 'nstep,lat,lon,k,ipair ', & !!$ nstep, latndx(i), lonndx(i), k, ipair !!$ write(lunout,9820) 'tk, pmb, aircon, pdel ', & !!$ t(i,k), pmid(i,k)*1.0e-2_r8, aircon, pdel(i,k)*1.0e-2_r8 !!$ write(lunout,9820) 'wetdens-cgs, sg f/t', & !!$ wetdens_frm*1.0e-3_r8, wetdens_too*1.0e-3_r8, & !!$ sg_frm, sg_too !!$ write(lunout,9820) 'dgnwet-um, dgndry-um f/t', & !!$ 1.0e6_r8*wetdgnum_frm, 1.0e6_r8*wetdgnum_too, & !!$ 1.0e6_r8*dgncur_a(i,k,modefrm), 1.0e6_r8*dgncur_a(i,k,modetoo) !!$ write(lunout,9820) 'xbeta ij0, ij3, ii0, jj0', & !!$ xbetaij0, xbetaij3, xbetaii0, xbetajj0 !!$ write(lunout,9820) 'xbeta ij2i & j, ii2, jj2', & !!$ xbetaij2i, xbetaij2j, xbetaii2, xbetajj2 !!$ write(lunout,9820) 'numbii, numbjj, deltat ', & !!$ xnumbconc(modefrm), xnumbconc(modetoo), deltat !!$ write(lunout,9820) 'loss ij3, ii0, jj0 ', & !!$ (xbetaij3*xnumbconc(modetoo)*deltat), & !!$ (xbetaij0*xnumbconc(modetoo)*deltat+ & !!$ xbetaii0*xnumbconc(modefrm)*deltat), & !!$ (xbetajj0*xnumbconc(modetoo)*deltat) !!$ 9801 format( / 72x, 'ACOAG' ) !!$ 9810 format( 'ACOAG ', a, 2i8, 3i7, 3(1pe15.6) ) !!$ 9820 format( 'ACOAG ', a, 4(1pe15.6) ) !!$ 9830 format( 'ACOAG ', a, i1, a, 4(1pe15.6) ) !!$ end if !!$ end if !!$ end if !!$ end if ! (ldiag2 > 0) ! test diagnostics end ---------------------------------------------- ybetaij0(ipair) = xbetaij0 ybetaij3(ipair) = xbetaij3 ybetaii0(ipair) = xbetaii0 ybetajj0(ipair) = xbetajj0 end do main_ipair1 if ( (pair_option_acoag == 1) .or. & (pair_option_acoag == 2) ) then ! ! calculate number and mass changes for pair_option_acoag == 1,2 ! main_ipair2: do ipair = 1, npair_acoag modefrm = modefrm_acoag(ipair) modetoo = modetoo_acoag(ipair) ! calculate number changes ! apply self-coagulation losses only once to a mode (when iselfcoagdone=0) ! first calc change to "too" mode ! next calc change to "frm" mode, using average number conc of "too" if ( (mprognum_amode(modetoo) > 0) .and. & (iselfcoagdone(modetoo) <= 0) ) then iselfcoagdone(modetoo) = 1 tmpn = xnumbconc(modetoo) xnumbconcnew(modetoo) = tmpn/(1.0_r8 + deltat*ybetajj0(ipair)*tmpn) xnumbconcavg(modetoo) = 0.5_r8*(xnumbconcnew(modetoo) + tmpn) lstoo = numptr_amode(modetoo) - loffset q(i,k,lstoo) = xnumbconcnew(modetoo)/aircon dqdt(i,k,lstoo) = (xnumbconcnew(modetoo)-tmpn)*deltatinv_main/aircon end if if ( (mprognum_amode(modefrm) > 0) .and. & (iselfcoagdone(modefrm) <= 0) ) then iselfcoagdone(modefrm) = 1 tmpn = xnumbconc(modefrm) tmpa = deltat*ybetaij0(ipair)*xnumbconcavg(modetoo) tmpb = deltat*ybetaii0(ipair) tmpc = tmpa + tmpb*tmpn if (abs(tmpc) < 0.01_r8) then xnumbconcnew(modefrm) = tmpn*exp(-tmpc) else if (abs(tmpa) < 0.001_r8) then xnumbconcnew(modefrm) = & exp(-tmpa)*tmpn/(1.0_r8 + tmpb*tmpn) else tmpf = tmpb*tmpn/tmpc tmpg = exp(-tmpa) tmph = tmpg*(1.0_r8 - tmpf)/(1.0_r8 - tmpg*tmpf) xnumbconcnew(modefrm) = tmpn*max( 0.0_r8, min( 1.0_r8, tmph ) ) end if xnumbconcavg(modefrm) = 0.5_r8*(xnumbconcnew(modefrm) + tmpn) lsfrm = numptr_amode(modefrm) - loffset q(i,k,lsfrm) = xnumbconcnew(modefrm)/aircon dqdt(i,k,lsfrm) = (xnumbconcnew(modefrm)-tmpn)*deltatinv_main/aircon end if ! calculate mass changes ! xbetaij3*xnumbconc(modetoo) = first order loss rate for modefrm volume ! xferfracvol = fraction of modefrm volume transferred to modetoo over deltat dumloss = ybetaij3(ipair)*xnumbconcavg(modetoo) xferfracvol = 1.0_r8 - exp( -dumloss*deltat ) xferfracvol = max( 0.0_r8, min( xferfrac_max, xferfracvol ) ) do iq = 1, nspecfrm_acoag(ipair) lsfrm = lspecfrm_acoag(iq,ipair) - loffset lstoo = lspectoo_acoag(iq,ipair) - loffset if (lsfrm > 0) then xferamt = q(i,k,lsfrm)*xferfracvol dqdt(i,k,lsfrm) = dqdt(i,k,lsfrm) - xferamt*deltatinv_main q(i,k,lsfrm) = q(i,k,lsfrm) - xferamt if (lstoo > 0) then dqdt(i,k,lstoo) = dqdt(i,k,lstoo) + xferamt*deltatinv_main q(i,k,lstoo) = q(i,k,lstoo) + xferamt end if end if end do end do main_ipair2 else if (pair_option_acoag == 3) then ! ! calculate number and mass changes for pair_option_acoag == 3 ! ! calculate number changes to accum mode if (mprognum_amode(macc) > 0) then tmpn = xnumbconc(macc) xnumbconcnew(macc) = tmpn/(1.0_r8 + deltat*ybetajj0(ip_aitacc)*tmpn) xnumbconcavg(macc) = 0.5_r8*(xnumbconcnew(macc) + tmpn) lstoo = numptr_amode(macc) - loffset q(i,k,lstoo) = xnumbconcnew(macc)/aircon dqdt(i,k,lstoo) = (xnumbconcnew(macc)-tmpn)*deltatinv_main/aircon end if ! calculate number changes to primary carbon mode modefrm = modeptr_pcarbon if (mprognum_amode(mpca) > 0) then tmpn = xnumbconc(mpca) tmpa = deltat*ybetaij0(ip_pcaacc)*xnumbconcavg(macc) tmpb = deltat*ybetaii0(ip_pcaacc) tmpc = tmpa + tmpb*tmpn if (abs(tmpc) < 0.01_r8) then xnumbconcnew(mpca) = tmpn*exp(-tmpc) else if (abs(tmpa) < 0.001_r8) then xnumbconcnew(mpca) = & exp(-tmpa)*tmpn/(1.0_r8 + tmpb*tmpn) else tmpf = tmpb*tmpn/tmpc tmpg = exp(-tmpa) tmph = tmpg*(1.0_r8 - tmpf)/(1.0_r8 - tmpg*tmpf) xnumbconcnew(mpca) = tmpn*max( 0.0_r8, min( 1.0_r8, tmph ) ) end if xnumbconcavg(mpca) = 0.5_r8*(xnumbconcnew(mpca) + tmpn) lsfrm = numptr_amode(mpca) - loffset q(i,k,lsfrm) = xnumbconcnew(mpca)/aircon dqdt(i,k,lsfrm) = (xnumbconcnew(mpca)-tmpn)*deltatinv_main/aircon end if ! calculate number changes to aitken mode if (mprognum_amode(mait) > 0) then tmpn = xnumbconc(mait) tmpa = deltat*( ybetaij0(ip_aitacc)*xnumbconcavg(macc) & + ybetaij0(ip_aitpca)*xnumbconcavg(mpca) ) tmpb = deltat*ybetaii0(ip_aitacc) tmpc = tmpa + tmpb*tmpn if (abs(tmpc) < 0.01_r8) then xnumbconcnew(mait) = tmpn*exp(-tmpc) else if (abs(tmpa) < 0.001_r8) then xnumbconcnew(mait) = & exp(-tmpa)*tmpn/(1.0_r8 + tmpb*tmpn) else tmpf = tmpb*tmpn/tmpc tmpg = exp(-tmpa) tmph = tmpg*(1.0_r8 - tmpf)/(1.0_r8 - tmpg*tmpf) xnumbconcnew(mait) = tmpn*max( 0.0_r8, min( 1.0_r8, tmph ) ) end if xnumbconcavg(mait) = 0.5_r8*(xnumbconcnew(mait) + tmpn) lsfrm = numptr_amode(mait) - loffset q(i,k,lsfrm) = xnumbconcnew(mait)/aircon dqdt(i,k,lsfrm) = (xnumbconcnew(mait)-tmpn)*deltatinv_main/aircon end if ! calculate mass changes from aitken-->accum direct coagulation and ! aitken-->pcarbon-->accum coagulation/aging ! also calc volume of shell material (so4 & nh4 from aitken-->pcarbon) dumloss = ybetaij3(ip_aitacc)*xnumbconcavg(macc) & + ybetaij3(ip_aitpca)*xnumbconcavg(mpca) tmpa = ybetaij3(ip_aitpca)*xnumbconcavg(mpca)/max( dumloss, 1.0e-37_r8 ) xferfracvol = 1.0_r8 - exp( -dumloss*deltat ) xferfracvol = max( 0.0_r8, min( xferfrac_max, xferfracvol ) ) vol_shell = 0.0_r8 ipair = ip_aitacc do iq = 1, nspecfrm_acoag(ipair) lsfrm = lspecfrm_acoag(iq,ipair) - loffset lstoo = lspectoo_acoag(iq,ipair) - loffset if (lsfrm > 0) then xferamt = q(i,k,lsfrm)*xferfracvol dqdt(i,k,lsfrm) = dqdt(i,k,lsfrm) - xferamt*deltatinv_main q(i,k,lsfrm) = q(i,k,lsfrm) - xferamt if (lstoo > 0) then dqdt(i,k,lstoo) = dqdt(i,k,lstoo) + xferamt*deltatinv_main q(i,k,lstoo) = q(i,k,lstoo) + xferamt end if vol_shell = vol_shell + xferamt*tmpa*fac_m2v_aitage(iq) end if end do ! now calculate aging transfer fraction for pcarbon-->accum ! this duplicates the code in modal_aero_gasaerexch vol_core = 0.0_r8 do l = 1, nspec_amode(mpca) vol_core = vol_core + & q(i,k,lmassptr_amode(l,mpca)-loffset)*fac_m2v_pcarbon(l) end do tmp1 = vol_shell*dgncur_a(i,k,mpca)*fac_volsfc_pcarbon tmp2 = 6.0_r8*dr_so4_monolayers_pcage*vol_core tmp2 = max( tmp2, 0.0_r8 ) if (tmp1 >= tmp2) then xferfrac_pcage = xferfrac_max else xferfrac_pcage = min( tmp1/tmp2, xferfrac_max ) end if ! calculate mass changes from pcarbon-->accum by direct coagulation ! and aging dumloss = ybetaij3(ip_pcaacc)*xnumbconcavg(macc) xferfracvol = 1.0_r8 - exp( -dumloss*deltat ) xferfracvol = xferfracvol + xferfrac_pcage xferfracvol = max( 0.0_r8, min( xferfrac_max, xferfracvol ) ) ipair = ip_pcaacc do iq = 1, nspecfrm_acoag(ipair) lsfrm = lspecfrm_acoag(iq,ipair) - loffset lstoo = lspectoo_acoag(iq,ipair) - loffset if (lsfrm > 0) then xferamt = q(i,k,lsfrm)*xferfracvol dqdt(i,k,lsfrm) = dqdt(i,k,lsfrm) - xferamt*deltatinv_main q(i,k,lsfrm) = q(i,k,lsfrm) - xferamt if (lstoo > 0) then dqdt(i,k,lstoo) = dqdt(i,k,lstoo) + xferamt*deltatinv_main q(i,k,lstoo) = q(i,k,lstoo) + xferamt end if end if end do lsfrm = numptr_amode(mpca) - loffset lstoo = numptr_amode(macc) - loffset if (lsfrm > 0) then xferamt = q(i,k,lsfrm)*xferfrac_pcage dqdt(i,k,lsfrm) = dqdt(i,k,lsfrm) - xferamt*deltatinv_main q(i,k,lsfrm) = q(i,k,lsfrm) - xferamt if (lstoo > 0) then dqdt(i,k,lstoo) = dqdt(i,k,lstoo) + xferamt*deltatinv_main q(i,k,lstoo) = q(i,k,lstoo) + xferamt end if end if else ! (pair_option_acoag /= 1,2,3) then write(lunout,*) '*** modal_aero_coag_sub error' write(lunout,*) ' cannot do _coag_sub error pair_option_acoag =', & pair_option_acoag call endrun( 'modal_aero_coag_sub error' ) end if ! (pair_option_acoag == ...) ! test diagnostics begin -------------------------------------------- !!$ if (ldiag3 > 0) then !!$ if (nstep <= 3) then !!$ if ((lonndx(i) == 37) .and. (latndx(i) == 23)) then !!$ if ((mod(k-1,5) == 0) .or. (k>=23)) then !!$ if (pair_option_acoag == 3) then !!$ write(*,*) !!$ write(lunout,9820) 'xnumbconcavg ait,acc,pca', & !!$ xnumbconcavg(mait), xnumbconcavg(macc), xnumbconcavg(mpca) !!$ write(lunout,9820) 'vshell, core ', & !!$ vol_shell, vol_core !!$ write(lunout,9820) 'dr_mono, dgn ', & !!$ dr_so4_monolayers_pcage, dgncur_a(i,k,mpca) !!$ write(lunout,9820) 'tmp1, tmp2 ', tmp1, tmp2 !!$ write(lunout,9820) 'xferfrac_age ', xferfrac_pcage !!$ end if !!$ !!$ do ipair = 1, npair_acoag !!$ modefrm = modefrm_acoag(ipair) !!$ modetoo = modetoo_acoag(ipair) !!$ if (npair_acoag > 1) then !!$ write(lunout,*) !!$ write(lunout,9810) 'ipair = ', ipair !!$ end if !!$ !!$ do iq = 1, nspecfrm_acoag(ipair) !!$ lsfrm = lspecfrm_acoag(iq,ipair) - loffset !!$ lstoo = lspectoo_acoag(iq,ipair) - loffset !!$ if (lsfrm > 0) then !!$ tmp_qold = q(i,k,lsfrm) - dqdt(i,k,lsfrm)*deltat_main !!$! write(lunout,9820) 'm1 frm dqdt/q0,dqdt,q0/1', & !!$ write(lunout,9830) 'm', iq, & !!$ ' frm dqdt/q0,dqdt,q0/1', & !!$ dqdt(i,k,lsfrm)/tmp_qold, dqdt(i,k,lsfrm), tmp_qold, q(i,k,lsfrm) !!$ end if !!$ if (lstoo > 0) then !!$ tmp_qold = q(i,k,lstoo) - dqdt(i,k,lstoo)*deltat_main !!$ write(lunout,9830) 'm', iq, & !!$ ' too dqdt/q0,dqdt,q0/1', & !!$ dqdt(i,k,lstoo)/tmp_qold, dqdt(i,k,lstoo), tmp_qold, q(i,k,lstoo) !!$ end if !!$ end do ! iq !!$ !!$ lsfrm = numptr_amode(modefrm) - loffset !!$ lstoo = numptr_amode(modetoo) - loffset !!$ if (lsfrm > 0) then !!$ tmp_qold = q(i,k,lsfrm) - dqdt(i,k,lsfrm)*deltat_main !!$ write(lunout,9820) 'n frm dqdt/q0,dqdt,q0/1', & !!$ dqdt(i,k,lsfrm)/tmp_qold, dqdt(i,k,lsfrm), tmp_qold, q(i,k,lsfrm) !!$ end if !!$ if (lstoo > 0) then !!$ tmp_qold = q(i,k,lstoo) - dqdt(i,k,lstoo)*deltat_main !!$ write(lunout,9820) 'n too dqdt/q0,dqdt,q0/1', & !!$ dqdt(i,k,lstoo)/tmp_qold, dqdt(i,k,lstoo), tmp_qold, q(i,k,lstoo) !!$ end if !!$ !!$ end do ! ipair !!$ end if !!$ end if !!$ end if !!$ end if ! (ldiag3 > 0) ! test diagnostics end ---------------------------------------------- end do main_i end do main_k ! set dotend's do ipair = 1, npair_acoag modefrm = modefrm_acoag(ipair) modetoo = modetoo_acoag(ipair) do iq = 1, nspecfrm_acoag(ipair) lsfrm = lspecfrm_acoag(iq,ipair) - loffset lstoo = lspectoo_acoag(iq,ipair) - loffset if (lsfrm > 0) dotend(lsfrm) = .true. if (lstoo > 0) dotend(lstoo) = .true. end do if (mprognum_amode(modefrm) > 0) then lsfrm = numptr_amode(modefrm) - loffset if (lsfrm > 0) dotend(lsfrm) = .true. end if if (mprognum_amode(modetoo) > 0) then lstoo = numptr_amode(modetoo) - loffset if (lstoo > 0) dotend(lstoo) = .true. end if end do ! do history file column-tendency fields do l = loffset+1, pcnst lmz = l - loffset if ( .not. dotend(lmz) ) cycle qsrflx(:) = 0.0_r8 do k = top_lev, pver do i = 1, ncol qsrflx(i) = qsrflx(i) + dqdt(i,k,lmz)*pdel(i,k) end do end do qsrflx(:) = qsrflx(:)*(adv_mass(lmz)/(gravit*mwdry)) fieldname = trim(cnst_name(l)) // '_sfcoag1' call outfld( fieldname, qsrflx, pcols, lchnk ) ! if (( masterproc ) .and. (nstep < 1)) & ! write(*,'(2(a,2x),1p,e11.3)') & ! 'modal_aero_coag_sub outfld', fieldname, adv_mass(lmz) end do ! l = ... return !EOC end subroutine modal_aero_coag_sub !---------------------------------------------------------------------- !---------------------------------------------------------------------- subroutine modal_aero_coag_init ! ! computes pointers for species transfer during coagulation ! use modal_aero_data use modal_aero_gasaerexch, only: & modefrm_pcage, nspecfrm_pcage, lspecfrm_pcage, lspectoo_pcage, & soa_equivso4_factor use cam_abortutils, only: endrun use cam_history, only: addfld, add_default, fieldname_len, phys_decomp use constituents, only: pcnst, cnst_name use spmd_utils, only: masterproc use phys_control, only: phys_getopts implicit none ! local variables integer :: ipair, iq, iqfrm, iqfrm_aa, iqtoo, iqtoo_aa integer :: jsoa integer :: l, l1, l2, lsfrm, lstoo, lunout integer :: m, mait, mpca, mfrm, mtoo, mtef integer :: nchfrm, nchfrmskip, nchtoo, nchtooskip, nspec character(len=fieldname_len) :: tmpname character(len=fieldname_len+3) :: fieldname character(128) :: long_name character(len=200) :: msg character(8) :: unit logical :: dotend(pcnst) logical :: history_aerosol ! Output the MAM aerosol tendencies !----------------------------------------------------------------------- call phys_getopts( history_aerosol_out = history_aerosol ) lunout = 6 ! ! define "from mode" and "to mode" for each coagulation pairing ! currently just a2-->a1 coagulation ! if (pair_option_acoag == 1) then npair_acoag = 1 modefrm_acoag(1) = modeptr_aitken modetoo_acoag(1) = modeptr_accum modetooeff_acoag(1) = modeptr_accum else if (pair_option_acoag == 2) then npair_acoag = 2 modefrm_acoag(1) = modeptr_aitken modetoo_acoag(1) = modeptr_accum modetooeff_acoag(1) = modeptr_accum modefrm_acoag(2) = modeptr_pcarbon modetoo_acoag(2) = modeptr_accum modetooeff_acoag(2) = modeptr_accum else if (pair_option_acoag == 3) then npair_acoag = 3 modefrm_acoag(1) = modeptr_aitken modetoo_acoag(1) = modeptr_accum modetooeff_acoag(1) = modeptr_accum modefrm_acoag(2) = modeptr_pcarbon modetoo_acoag(2) = modeptr_accum modetooeff_acoag(2) = modeptr_accum modefrm_acoag(3) = modeptr_aitken modetoo_acoag(3) = modeptr_pcarbon modetooeff_acoag(3) = modeptr_accum if (modefrm_pcage <= 0) then write(*,*) '*** modal_aero_coag_init error' write(*,*) ' pair_option_acoag, modefrm_pcage mismatch' write(*,*) ' pair_option_acoag, modefrm_pcage =', & pair_option_acoag, modefrm_pcage call endrun( 'modal_aero_coag_init error' ) end if else npair_acoag = 0 return end if ! ! define species involved in each coagulation pairing ! (include aerosol water) ! aa_ipair: do ipair = 1, npair_acoag mfrm = modefrm_acoag(ipair) mtoo = modetoo_acoag(ipair) mtef = modetooeff_acoag(ipair) if ( (mfrm < 1) .or. (mfrm > ntot_amode) .or. & (mtoo < 1) .or. (mtoo > ntot_amode) .or. & (mtef < 1) .or. (mtef > ntot_amode) ) then write(*,*) '*** modal_aero_coag_init error' write(*,*) ' ipair, ntot_amode =', ipair, ntot_amode write(*,*) ' mfrm, mtoo, mtef =', mfrm, mtoo, mtef call endrun( 'modal_aero_coag_init error' ) end if mtoo = mtef ! effective modetoo if (mfrm < 10) then nchfrmskip = 1 else if (mfrm < 100) then nchfrmskip = 2 else nchfrmskip = 3 end if if (mtoo < 10) then nchtooskip = 1 else if (mtoo < 100) then nchtooskip = 2 else nchtooskip = 3 end if nspec = 0 aa_iqfrm: do iqfrm = 1, nspec_amode(mfrm) lsfrm = lmassptr_amode(iqfrm,mfrm) if ((lsfrm .lt. 1) .or. (lsfrm .gt. pcnst)) cycle aa_iqfrm nchfrm = len( trim( cnst_name(lsfrm) ) ) - nchfrmskip ! find "too" species having same lspectype_amode as the "frm" species ! several species in a mode may have the same lspectype_amode, so also ! use the ordering as a criterion (e.g., 1st <--> 1st, 2nd <--> 2nd) ! AND same cnst_name (except for last 1/2/3 characters which are the mode index) do iqtoo = 1, nspec_amode(mtoo) ! if ( lspectype_amode(iqtoo,mtoo) .eq. & ! lspectype_amode(iqfrm,mfrm) ) then lstoo = lmassptr_amode(iqtoo,mtoo) nchtoo = len( trim( cnst_name(lstoo) ) ) - nchtooskip if (cnst_name(lsfrm)(1:nchfrm) == cnst_name(lstoo)(1:nchtoo)) then exit else lstoo = 0 end if ! end if end do ! iqfrm_aa = 1 ! iqtoo_aa = 1 ! if (iqfrm .gt. nspec_amode(mfrm)) then ! iqfrm_aa = nspec_amode(mfrm) + 1 ! iqtoo_aa = nspec_amode(mtoo) + 1 ! end if ! nsamefrm = 0 ! do iq = iqfrm_aa, iqfrm ! if ( lspectype_amode(iq ,mfrm) .eq. & ! lspectype_amode(iqfrm,mfrm) ) then ! nsamefrm = nsamefrm + 1 ! end if ! end do ! nsametoo = 0 ! lstoo = 0 ! do iqtoo = iqtoo_aa, nspec_amode(mtoo) ! if ( lspectype_amode(iqtoo,mtoo) .eq. & ! lspectype_amode(iqfrm,mfrm) ) then ! nsametoo = nsametoo + 1 ! if (nsametoo .eq. nsamefrm) then ! lstoo = lmassptr_amode(iqtoo,mtoo) ! exit ! end if ! end if ! end do if ((lstoo < 1) .or. (lstoo > pcnst)) lstoo = 0 nspec = nspec + 1 lspecfrm_acoag(nspec,ipair) = lsfrm lspectoo_acoag(nspec,ipair) = lstoo end do aa_iqfrm ! lsfrm = lwaterptr_amode(mfrm) ! if ((lsfrm .ge. 1) .and. (lsfrm .le. pcnst)) then ! lstoo = lwaterptr_amode(mtoo) ! if ((lstoo .lt. 1) .or. (lstoo .gt. pcnst)) lstoo = 0 ! nspec = nspec + 1 ! lspecfrm_acoag(nspec,ipair) = lsfrm ! lspectoo_acoag(nspec,ipair) = lstoo ! end if nspecfrm_acoag(ipair) = nspec end do aa_ipair ! ! output results ! if ( masterproc ) then write(lunout,9310) do ipair = 1, npair_acoag mfrm = modefrm_acoag(ipair) mtoo = modetoo_acoag(ipair) mtef = modetooeff_acoag(ipair) write(lunout,9320) ipair, mfrm, mtoo, mtef do iq = 1, nspecfrm_acoag(ipair) lsfrm = lspecfrm_acoag(iq,ipair) lstoo = lspectoo_acoag(iq,ipair) if (lstoo .gt. 0) then write(lunout,9330) lsfrm, cnst_name(lsfrm), & lstoo, cnst_name(lstoo) else write(lunout,9340) lsfrm, cnst_name(lsfrm) end if end do end do ! ipair = ... write(lunout,*) end if ! ( masterproc ) 9310 format( / 'subr. modal_aero_coag_init' ) 9320 format( 'pair', i3, 5x, 'mode', i3, & ' ---> mode', i3, ' eff', i3 ) 9330 format( 5x, 'spec', i3, '=', a, ' ---> spec', i3, '=', a ) 9340 format( 5x, 'spec', i3, '=', a, ' ---> LOSS' ) ! set following variables that are used in modal_aero_coag_subr ! fac_m2v_aitage(:) = 0.0 fac_m2v_pcarbon(:) = 0.0 if (pair_option_acoag == 3) then ! following ipair definitions MUST BE CONSISTENT with ! the coding in modal_aero_coag_init for pair_option_acoag == 3 ip_aitacc = 1 ip_pcaacc = 2 ip_aitpca = 3 mait = modeptr_aitken mpca = modeptr_pcarbon ipair = ip_aitpca do iq = 1, nspecfrm_acoag(ipair) lsfrm = lspecfrm_acoag(iq,ipair) l2 = -1 do l1 = 1, nspec_amode(mait) if (lmassptr_amode(l1,mait) == lsfrm) then !B l2 = lspectype_amode(l1,mait) l2 = l1 exit end if end do if (l2 <= 0) then write( msg, '(a,5(1x,i12))' ) & 'modal_aero_coag_init error a001 for ipair, iq, lsfrm', & ipair, iq, lsfrm call endrun( msg ) end if if (lsfrm == lptr_so4_a_amode(mait)) then ! fac_m2v_aitage(iq) = specmw_amode(l2) / specdens_amode(l2) fac_m2v_aitage(iq) = specmw_amode(l1,mait) / specdens_amode(l1,mait) else if (lsfrm == lptr_nh4_a_amode(mait)) then ! fac_m2v_aitage(iq) = specmw_amode(l2) / specdens_amode(l2) fac_m2v_aitage(iq) = specmw_amode(l1,mait) / specdens_amode(l1,mait) else do jsoa = 1, nsoa if (lsfrm == lptr2_soa_a_amode(mait,jsoa)) then fac_m2v_aitage(iq) = soa_equivso4_factor(jsoa)* & !(specmw_amode(l2) / specdens_amode(l2)) (specmw_amode(l1,mait) / specdens_amode(l1,mait)) end if ! for soa, the soa_equivso4_factor converts the soa volume into an ! so4(+nh4) volume that has same hygroscopicity contribution as soa ! this allows aging calculations to be done in terms of the amount ! of (equivalent) so4(+nh4) in the shell ! (see modal_aero_gasaerexch) end do end if end do do l = 1, nspec_amode(mpca) !B l2 = lspectype_amode(l,mpca) ! fac_m2v converts (kmol-AP/kmol-air) to (m3-AP/kmol-air) ! [m3-AP/kmol-AP] = [kg-AP/kmol-AP] / [kg-AP/m3-AP] ! fac_m2v_pcarbon(l) = specmw_amode(l2) / specdens_amode(l2) fac_m2v_pcarbon(l) = specmw_amode(l,mpca) / specdens_amode(l,mpca) end do else ip_aitacc = -999888777 ip_pcaacc = -999888777 ip_aitpca = -999888777 end if ! ! create history file column-tendency fields ! dotend(:) = .false. do ipair = 1, npair_acoag do iq = 1, nspecfrm_acoag(ipair) l = lspecfrm_acoag(iq,ipair) if ((l > 0) .and. (l <= pcnst)) dotend(l) = .true. l = lspectoo_acoag(iq,ipair) if ((l > 0) .and. (l <= pcnst)) dotend(l) = .true. end do m = modefrm_acoag(ipair) if ((m > 0) .and. (m <= ntot_amode)) then l = numptr_amode(m) if ((l > 0) .and. (l <= pcnst)) dotend(l) = .true. end if m = modetoo_acoag(ipair) if ((m > 0) .and. (m <= ntot_amode)) then l = numptr_amode(m) if ((l > 0) .and. (l <= pcnst)) dotend(l) = .true. end if end do ! ipair = ... if (pair_option_acoag == 3) then do iq = 1, nspecfrm_pcage lsfrm = lspecfrm_pcage(iq) lstoo = lspectoo_pcage(iq) if ((lsfrm > 0) .and. (lsfrm <= pcnst)) then dotend(lsfrm) = .true. if ((lstoo > 0) .and. (lstoo <= pcnst)) then dotend(lstoo) = .true. end if end if end do end if do l = 1, pcnst if ( .not. dotend(l) ) cycle tmpname = cnst_name(l) unit = 'kg/m2/s' do m = 1, ntot_amode if (l == numptr_amode(m)) unit = '#/m2/s' end do fieldname = trim(tmpname) // '_sfcoag1' long_name = trim(tmpname) // ' modal_aero coagulation column tendency' call addfld( fieldname, unit, 1, 'A', long_name, phys_decomp ) if ( history_aerosol ) then call add_default( fieldname, 1, ' ' ) endif if ( masterproc ) write(*,'(3(a,2x))') & 'modal_aero_coag_init addfld', fieldname, unit end do ! l = ... return end subroutine modal_aero_coag_init !---------------------------------------------------------------------- !---------------------------------------------------------------------- subroutine getcoags_wrapper_f( & airtemp, airprs, & dgatk, dgacc, & sgatk, sgacc, & xxlsgat, xxlsgac, & pdensat, pdensac, & betaij0, betaij2i, betaij2j, betaij3, & betaii0, betaii2, betajj0, betajj2 ) use physconst, only: p0 => pstd, & tmelt, & boltz ! ! interface to subr. getcoags ! ! interface code adapted from subr. aeroproc of cmaq v4.6, ! with some of the parameter values from module aero_info_ae4 ! implicit none ! *** arguments real(r8), intent(in) :: airtemp ! air temperature [ k ] real(r8), intent(in) :: airprs ! air pressure in [ pa ] real(r8), intent(in) :: dgatk ! aitken mode geometric mean diameter [m] real(r8), intent(in) :: dgacc ! accumulation mode geometric mean diam [m] real(r8), intent(in) :: sgatk ! aitken mode geometric standard deviation real(r8), intent(in) :: sgacc ! accumulation mode geometric standard deviation real(r8), intent(in) :: xxlsgat ! natural log of geometric standard real(r8), intent(in) :: xxlsgac ! deviations real(r8), intent(in) :: pdensat ! aitken mode particle density [ kg / m**3 ] real(r8), intent(in) :: pdensac ! accumulation mode density [ kg / m**3 ] real(r8), intent(out) :: betaij0, betaij2i, betaij2j, betaij3, & betaii0, betaii2, betajj0, betajj2 ! *** local parameters real(r8) :: t0 ! standard surface temperature (15 deg C) [ k ] real(r8), parameter :: two3 = 2.0_r8/3.0_r8 ! *** local variables real(r8) amu ! atmospheric dynamic viscosity [ kg/m s ] real(r8) sqrt_temp ! square root of ambient temperature real(r8) lamda ! mean free path [ m ] ! *** intramodal coagulation rates [ m**3/s ] ( 0th & 2nd moments ) real(r8) batat( 2 ) ! aitken mode real(r8) bacac( 2 ) ! accumulation mode ! *** intermodal coagulation rates [ m**3/s ] ( 0th & 2nd moments ) real(r8) batac( 2 ) ! aitken to accumulation real(r8) bacat( 2 ) ! accumulation from aitken ! *** intermodal coagulation rate [ m**3/s ] ( 3rd moment ) real(r8) c3ij ! aitken to accumulation ! *** 3rd moment intermodal transfer rate by coagulation real(r8) c30atac ! aitken to accumulation ! *** near continnuum regime (independent of mode) real(r8) knc ! knc = two3 * boltz * airtemp / amu ! *** free molecular regime (depends upon modal density) real(r8) kfmat ! kfmat = sqrt(3.0*boltz*airtemp/pdensat) real(r8) kfmac ! kfmac = sqrt(3.0*boltz*airtemp/pdensac) real(r8) kfmatac ! kfmatac = sqrt( 6.0 * boltz * airtemp / ! ( pdensat + pdensac ) ) real(r8) dumacc2, dumatk2, dumatk3 t0 = tmelt + 15._r8 sqrt_temp = sqrt( airtemp) ! *** calculate mean free path [ m ]: ! 6.6328e-8 is the sea level value given in table i.2.8 ! on page 10 of u.s. standard atmosphere 1962 lamda = 6.6328e-8_r8 * p0 * airtemp / ( t0 * airprs ) ! *** calculate dynamic viscosity [ kg m**-1 s**-1 ]: ! u.s. standard atmosphere 1962 page 14 expression ! for dynamic viscosity is: ! dynamic viscosity = beta * t * sqrt(t) / ( t + s) ! where beta = 1.458e-6 [ kg sec^-1 k**-0.5 ], s = 110.4 [ k ]. amu = 1.458e-6_r8 * airtemp * sqrt_temp / ( airtemp + 110.4_r8 ) ! *** coagulation ! calculate coagulation coefficients using a method dictated by ! the value of fastcoag_flag. if true, the computationally- ! efficient getcoags routine is used. if false, the more intensive ! gauss-hermite numerical quadrature method is used. see section ! 2.1 of bhave et al. (2004) for further discussion. ! *** calculate term used in equation a6 of binkowski & shankar (1995) knc = two3 * boltz * airtemp / amu ! *** calculate terms used in equation a5 of binkowski & shankar (1995) kfmat = sqrt( 3.0_r8 * boltz * airtemp / pdensat ) kfmac = sqrt( 3.0_r8 * boltz * airtemp / pdensac ) kfmatac = sqrt( 6.0_r8 * boltz * airtemp / ( pdensat + pdensac ) ) ! *** transfer of number to accumulation mode from aitken mode is zero bacat(1) = 0.0_r8 ! *** calculate intermodal and intramodal coagulation coefficients ! for zeroth and second moments, and intermodal coagulation ! coefficient for third moment call getcoags( lamda, kfmatac, kfmat, kfmac, knc, & dgatk, dgacc, sgatk, sgacc, & xxlsgat, xxlsgac, & batat(2), batat(1), bacac(2), bacac(1), & batac(2), bacat(2), batac(1), c3ij ) ! convert from the "cmaq" coag rate parameters ! to the "mirage2" parameters dumacc2 = ( (dgacc**2) * exp( 2.0_r8*xxlsgac*xxlsgac ) ) dumatk2 = ( (dgatk**2) * exp( 2.0_r8*xxlsgat*xxlsgat ) ) dumatk3 = ( (dgatk**3) * exp( 4.5_r8*xxlsgat*xxlsgat ) ) betaii0 = max( 0.0_r8, batat(1) ) betajj0 = max( 0.0_r8, bacac(1) ) betaij0 = max( 0.0_r8, batac(1) ) betaij3 = max( 0.0_r8, c3ij / dumatk3 ) betajj2 = max( 0.0_r8, bacac(2) / dumacc2 ) betaii2 = max( 0.0_r8, batat(2) / dumatk2 ) betaij2i = max( 0.0_r8, batac(2) / dumatk2 ) betaij2j = max( 0.0_r8, bacat(2) / dumatk2 ) return end subroutine getcoags_wrapper_f ! ////////////////////////////////////////////////////////////////// ! subroutine getcoags calculates the coagulation rates using a new ! approximate algorithm for the 2nd moment. the 0th and 3rd moments ! are done by analytic expressions from whitby et al. (1991). the ! correction factors are also similar to those from whitby et al. ! (1991), but are derived from the gauss-hermite numerical ! quadratures used by binkowski and roselle (2003). ! ! called from aerostep as: ! call getcoags( lamda, kfmatac, kfmat, kfmac, knc, ! dgat,dgac, sgatk, sgacc, xxlsgat,xxlsgac, ! batat(2), batat(1), bacac(2), bacac(1), ! batac(2), bacat(2), batac(1), c3ij ) ! where all input and outputs are real*8 ! ! revision history: ! fsb 08/25/03 coded by dr. francis s. binkowksi ! ! fsb 08/25/04 added in-line documentation ! ! rce 04/15/2007 ! code taken from cmaq v4.6 code; converted to f90; ! added "intent" to subr arguments; ! renamed "r4" & "r8" variables to "rx4" & "rx8"; ! changed "real*N" declarations to "real(rN)" (N = 4 or 8) ! ! references: ! 1. whitby, e. r., p. h. mcmurry, u. shankar, and f. s. binkowski, ! modal aerosol dynamics modeling, rep. 600/3-91/020, atmospheric ! research and exposure assessment laboratory, ! u.s. environmental protection agency, research triangle park, n.c., ! (ntis pb91-161729/as), 1991 ! ! 2. binkowski, f.s. an u. shankar, the regional particulate matter ! model 1. model decsription and preliminary results, journal of ! geophysical research, 100, d12, pp 26,191-26,209, ! december 20, 1995. ! ! 3. binkowski, f.s. and s.j. roselle, models-3 community ! multiscale air quality (cmaq) model aerosol component 1: ! model description. j. geophys. res., vol 108, no d6, 4183 ! doi:10.1029/2001jd001409, 2003. subroutine getcoags( lamda, kfmatac, kfmat, kfmac, knc, & dgatk, dgacc, sgatk, sgacc, xxlsgat,xxlsgac, & qs11, qn11, qs22, qn22, & qs12, qs21, qn12, qv12 ) implicit none real(r8), intent(in) :: lamda ! mean free path [ m ] ! *** coefficients for free molecular regime real(r8), intent(in) :: kfmat ! aitken mode real(r8), intent(in) :: kfmac ! accumulation mode real(r8), intent(in) :: kfmatac ! aitken to accumulation mode real(r8), intent(in) :: knc ! coefficient for near continnuum regime ! *** modal geometric mean diameters: [ m ] real(r8), intent(in) :: dgatk ! aitken mode real(r8), intent(in) :: dgacc ! accumulation mode ! *** modal geometric standard deviation real(r8), intent(in) :: sgatk ! atken mode real(r8), intent(in) :: sgacc ! accumulation mode ! *** natural log of modal geometric standard deviation real(r8), intent(in) :: xxlsgat ! aitken mode real(r8), intent(in) :: xxlsgac ! accumulation mode ! *** coagulation coefficients real(r8), intent(out) :: qs11, qn11, qs22, qn22, & qs12, qs21, qn12, qv12 integer ibeta, n1, n2a, n2n ! indices for correction factors real(r8) i1fm_at real(r8) i1nc_at real(r8) i1_at real(r8) i1fm_ac real(r8) i1nc_ac real(r8) i1_ac real(r8) i1fm real(r8) i1nc real(r8) i1 real(r8) constii real(r8) kngat, kngac real(r8) one, two, half parameter( one = 1.0_r8, two = 2.0_r8, half = 0.5_r8 ) real(r8) a ! parameter( a = 2.492_r8) parameter( a = 1.246_r8) real(r8) two3rds parameter( two3rds = 2._r8 / 3._r8) real(r8) sqrttwo ! sqrt(two) real(r8) dlgsqt2 ! 1/ln( sqrt( 2 ) ) real(r8) esat01 ! aitken mode exp( log^2( sigmag )/8 ) real(r8) esac01 ! accumulation mode exp( log^2( sigmag )/8 ) real(r8) esat04 real(r8) esac04 real(r8) esat05 real(r8) esac05 real(r8) esat08 real(r8) esac08 real(r8) esat09 real(r8) esac09 real(r8) esat16 real(r8) esac16 real(r8) esat20 real(r8) esac20 real(r8) esat24 real(r8) esac24 real(r8) esat25 real(r8) esac25 real(r8) esat36 real(r8) esac36 real(r8) esat49 real(r8) esat64 real(r8) esac64 real(r8) esat100 real(r8) dgat2, dgac2, dgat3, dgac3 real(r8) sqdgat, sqdgac real(r8) sqdgat5, sqdgac5 real(r8) sqdgat7 real(r8) r, r2, r3, rx4, r5, r6, rx8 real(r8) ri1, ri2, ri3, ri4 real(r8) rat real(r8) coagfm0, coagnc0 real(r8) coagfm3, coagnc3 real(r8) coagfm_at, coagfm_ac real(r8) coagnc_at, coagnc_ac real(r8) coagatat0 real(r8) coagacac0 real(r8) coagatat2 real(r8) coagacac2 real(r8) coagatac0, coagatac3 real(r8) coagatac2 real(r8) coagacat2 real(r8) xm2at, xm3at, xm2ac, xm3ac ! *** correction factors for coagulation rates real(r8), save :: bm0( 10 ) ! m0 intramodal fm - rpm values real(r8), save :: bm0ij( 10, 10, 10 ) ! m0 intermodal fm real(r8), save :: bm3i( 10, 10, 10 ) ! m3 intermodal fm- rpm values real(r8), save :: bm2ii(10) ! m2 intramodal fm real(r8), save :: bm2iitt(10) ! m2 intramodal total real(r8), save :: bm2ij(10,10,10) ! m2 intermodal fm i to j real(r8), save :: bm2ji(10,10,10) ! m2 total intermodal j from i ! *** populate the arrays for the correction factors. ! rpm 0th moment correction factors for unimodal fm coagulation rates data bm0 / & 0.707106785165097_r8, 0.726148960080488_r8, 0.766430744110958_r8, & 0.814106389441342_r8, 0.861679526483207_r8, 0.903600509090092_r8, & 0.936578814219156_r8, 0.960098926735545_r8, 0.975646823342881_r8, & 0.985397173215326_r8 / ! fsb new fm correction factors for m0 intermodal coagulation data (bm0ij ( 1, 1,ibeta), ibeta = 1,10) / & 0.628539_r8, 0.639610_r8, 0.664514_r8, 0.696278_r8, 0.731558_r8, & 0.768211_r8, 0.804480_r8, 0.838830_r8, 0.870024_r8, 0.897248_r8/ data (bm0ij ( 1, 2,ibeta), ibeta = 1,10) / & 0.639178_r8, 0.649966_r8, 0.674432_r8, 0.705794_r8, 0.740642_r8, & 0.776751_r8, 0.812323_r8, 0.845827_r8, 0.876076_r8, 0.902324_r8/ data (bm0ij ( 1, 3,ibeta), ibeta = 1,10) / & 0.663109_r8, 0.673464_r8, 0.697147_r8, 0.727637_r8, 0.761425_r8, & 0.796155_r8, 0.829978_r8, 0.861419_r8, 0.889424_r8, 0.913417_r8/ data (bm0ij ( 1, 4,ibeta), ibeta = 1,10) / & 0.693693_r8, 0.703654_r8, 0.726478_r8, 0.755786_r8, 0.787980_r8, & 0.820626_r8, 0.851898_r8, 0.880459_r8, 0.905465_r8, 0.926552_r8/ data (bm0ij ( 1, 5,ibeta), ibeta = 1,10) / & 0.727803_r8, 0.737349_r8, 0.759140_r8, 0.786870_r8, 0.816901_r8, & 0.846813_r8, 0.874906_r8, 0.900060_r8, 0.921679_r8, 0.939614_r8/ data (bm0ij ( 1, 6,ibeta), ibeta = 1,10) / & 0.763461_r8, 0.772483_r8, 0.792930_r8, 0.818599_r8, 0.845905_r8, & 0.872550_r8, 0.897051_r8, 0.918552_r8, 0.936701_r8, 0.951528_r8/ data (bm0ij ( 1, 7,ibeta), ibeta = 1,10) / & 0.799021_r8, 0.807365_r8, 0.826094_r8, 0.849230_r8, 0.873358_r8, & 0.896406_r8, 0.917161_r8, 0.935031_r8, 0.949868_r8, 0.961828_r8/ data (bm0ij ( 1, 8,ibeta), ibeta = 1,10) / & 0.833004_r8, 0.840514_r8, 0.857192_r8, 0.877446_r8, 0.898147_r8, & 0.917518_r8, 0.934627_r8, 0.949106_r8, 0.960958_r8, 0.970403_r8/ data (bm0ij ( 1, 9,ibeta), ibeta = 1,10) / & 0.864172_r8, 0.870734_r8, 0.885153_r8, 0.902373_r8, 0.919640_r8, & 0.935494_r8, 0.949257_r8, 0.960733_r8, 0.970016_r8, 0.977346_r8/ data (bm0ij ( 1, 10,ibeta), ibeta = 1,10) / & 0.891658_r8, 0.897227_r8, 0.909343_r8, 0.923588_r8, 0.937629_r8, & 0.950307_r8, 0.961151_r8, 0.970082_r8, 0.977236_r8, 0.982844_r8/ data (bm0ij ( 2, 1,ibeta), ibeta = 1,10) / & 0.658724_r8, 0.670587_r8, 0.697539_r8, 0.731890_r8, 0.769467_r8, & 0.807391_r8, 0.843410_r8, 0.875847_r8, 0.903700_r8, 0.926645_r8/ data (bm0ij ( 2, 2,ibeta), ibeta = 1,10) / & 0.667070_r8, 0.678820_r8, 0.705538_r8, 0.739591_r8, 0.776758_r8, & 0.814118_r8, 0.849415_r8, 0.881020_r8, 0.908006_r8, 0.930121_r8/ data (bm0ij ( 2, 3,ibeta), ibeta = 1,10) / & 0.686356_r8, 0.697839_r8, 0.723997_r8, 0.757285_r8, 0.793389_r8, & 0.829313_r8, 0.862835_r8, 0.892459_r8, 0.917432_r8, 0.937663_r8/ data (bm0ij ( 2, 4,ibeta), ibeta = 1,10) / & 0.711425_r8, 0.722572_r8, 0.747941_r8, 0.780055_r8, 0.814518_r8, & 0.848315_r8, 0.879335_r8, 0.906290_r8, 0.928658_r8, 0.946526_r8/ data (bm0ij ( 2, 5,ibeta), ibeta = 1,10) / & 0.739575_r8, 0.750307_r8, 0.774633_r8, 0.805138_r8, 0.837408_r8, & 0.868504_r8, 0.896517_r8, 0.920421_r8, 0.939932_r8, 0.955299_r8/ data (bm0ij ( 2, 6,ibeta), ibeta = 1,10) / & 0.769143_r8, 0.779346_r8, 0.802314_r8, 0.830752_r8, 0.860333_r8, & 0.888300_r8, 0.913014_r8, 0.933727_r8, 0.950370_r8, 0.963306_r8/ data (bm0ij ( 2, 7,ibeta), ibeta = 1,10) / & 0.798900_r8, 0.808431_r8, 0.829700_r8, 0.855653_r8, 0.882163_r8, & 0.906749_r8, 0.928075_r8, 0.945654_r8, 0.959579_r8, 0.970280_r8/ data (bm0ij ( 2, 8,ibeta), ibeta = 1,10) / & 0.827826_r8, 0.836542_r8, 0.855808_r8, 0.878954_r8, 0.902174_r8, & 0.923316_r8, 0.941345_r8, 0.955989_r8, 0.967450_r8, 0.976174_r8/ data (bm0ij ( 2, 9,ibeta), ibeta = 1,10) / & 0.855068_r8, 0.862856_r8, 0.879900_r8, 0.900068_r8, 0.919956_r8, & 0.937764_r8, 0.952725_r8, 0.964726_r8, 0.974027_r8, 0.981053_r8/ data (bm0ij ( 2, 10,ibeta), ibeta = 1,10) / & 0.879961_r8, 0.886755_r8, 0.901484_r8, 0.918665_r8, 0.935346_r8, & 0.950065_r8, 0.962277_r8, 0.971974_r8, 0.979432_r8, 0.985033_r8/ data (bm0ij ( 3, 1,ibeta), ibeta = 1,10) / & 0.724166_r8, 0.735474_r8, 0.761359_r8, 0.794045_r8, 0.828702_r8, & 0.862061_r8, 0.891995_r8, 0.917385_r8, 0.937959_r8, 0.954036_r8/ data (bm0ij ( 3, 2,ibeta), ibeta = 1,10) / & 0.730416_r8, 0.741780_r8, 0.767647_r8, 0.800116_r8, 0.834344_r8, & 0.867093_r8, 0.896302_r8, 0.920934_r8, 0.940790_r8, 0.956237_r8/ data (bm0ij ( 3, 3,ibeta), ibeta = 1,10) / & 0.745327_r8, 0.756664_r8, 0.782255_r8, 0.814026_r8, 0.847107_r8, & 0.878339_r8, 0.905820_r8, 0.928699_r8, 0.946931_r8, 0.960977_r8/ data (bm0ij ( 3, 4,ibeta), ibeta = 1,10) / & 0.765195_r8, 0.776312_r8, 0.801216_r8, 0.831758_r8, 0.863079_r8, & 0.892159_r8, 0.917319_r8, 0.937939_r8, 0.954145_r8, 0.966486_r8/ data (bm0ij ( 3, 5,ibeta), ibeta = 1,10) / & 0.787632_r8, 0.798347_r8, 0.822165_r8, 0.850985_r8, 0.880049_r8, & 0.906544_r8, 0.929062_r8, 0.947218_r8, 0.961288_r8, 0.971878_r8/ data (bm0ij ( 3, 6,ibeta), ibeta = 1,10) / & 0.811024_r8, 0.821179_r8, 0.843557_r8, 0.870247_r8, 0.896694_r8, & 0.920365_r8, 0.940131_r8, 0.955821_r8, 0.967820_r8, 0.976753_r8/ data (bm0ij ( 3, 7,ibeta), ibeta = 1,10) / & 0.834254_r8, 0.843709_r8, 0.864356_r8, 0.888619_r8, 0.912245_r8, & 0.933019_r8, 0.950084_r8, 0.963438_r8, 0.973530_r8, 0.980973_r8/ data (bm0ij ( 3, 8,ibeta), ibeta = 1,10) / & 0.856531_r8, 0.865176_r8, 0.883881_r8, 0.905544_r8, 0.926290_r8, & 0.944236_r8, 0.958762_r8, 0.969988_r8, 0.978386_r8, 0.984530_r8/ data (bm0ij ( 3, 9,ibeta), ibeta = 1,10) / & 0.877307_r8, 0.885070_r8, 0.901716_r8, 0.920729_r8, 0.938663_r8, & 0.953951_r8, 0.966169_r8, 0.975512_r8, 0.982442_r8, 0.987477_r8/ data (bm0ij ( 3, 10,ibeta), ibeta = 1,10) / & 0.896234_r8, 0.903082_r8, 0.917645_r8, 0.934069_r8, 0.949354_r8, & 0.962222_r8, 0.972396_r8, 0.980107_r8, 0.985788_r8, 0.989894_r8/ data (bm0ij ( 4, 1,ibeta), ibeta = 1,10) / & 0.799294_r8, 0.809144_r8, 0.831293_r8, 0.858395_r8, 0.885897_r8, & 0.911031_r8, 0.932406_r8, 0.949642_r8, 0.963001_r8, 0.973062_r8/ data (bm0ij ( 4, 2,ibeta), ibeta = 1,10) / & 0.804239_r8, 0.814102_r8, 0.836169_r8, 0.862984_r8, 0.890003_r8, & 0.914535_r8, 0.935274_r8, 0.951910_r8, 0.964748_r8, 0.974381_r8/ data (bm0ij ( 4, 3,ibeta), ibeta = 1,10) / & 0.815910_r8, 0.825708_r8, 0.847403_r8, 0.873389_r8, 0.899185_r8, & 0.922275_r8, 0.941543_r8, 0.956826_r8, 0.968507_r8, 0.977204_r8/ data (bm0ij ( 4, 4,ibeta), ibeta = 1,10) / & 0.831348_r8, 0.840892_r8, 0.861793_r8, 0.886428_r8, 0.910463_r8, & 0.931614_r8, 0.948993_r8, 0.962593_r8, 0.972872_r8, 0.980456_r8/ data (bm0ij ( 4, 5,ibeta), ibeta = 1,10) / & 0.848597_r8, 0.857693_r8, 0.877402_r8, 0.900265_r8, 0.922180_r8, & 0.941134_r8, 0.956464_r8, 0.968298_r8, 0.977143_r8, 0.983611_r8/ data (bm0ij ( 4, 6,ibeta), ibeta = 1,10) / & 0.866271_r8, 0.874764_r8, 0.892984_r8, 0.913796_r8, 0.933407_r8, & 0.950088_r8, 0.963380_r8, 0.973512_r8, 0.981006_r8, 0.986440_r8/ data (bm0ij ( 4, 7,ibeta), ibeta = 1,10) / & 0.883430_r8, 0.891216_r8, 0.907762_r8, 0.926388_r8, 0.943660_r8, & 0.958127_r8, 0.969499_r8, 0.978070_r8, 0.984351_r8, 0.988872_r8/ data (bm0ij ( 4, 8,ibeta), ibeta = 1,10) / & 0.899483_r8, 0.906505_r8, 0.921294_r8, 0.937719_r8, 0.952729_r8, & 0.965131_r8, 0.974762_r8, 0.981950_r8, 0.987175_r8, 0.990912_r8/ data (bm0ij ( 4, 9,ibeta), ibeta = 1,10) / & 0.914096_r8, 0.920337_r8, 0.933373_r8, 0.947677_r8, 0.960579_r8, & 0.971111_r8, 0.979206_r8, 0.985196_r8, 0.989520_r8, 0.992597_r8/ data (bm0ij ( 4, 10,ibeta), ibeta = 1,10) / & 0.927122_r8, 0.932597_r8, 0.943952_r8, 0.956277_r8, 0.967268_r8, & 0.976147_r8, 0.982912_r8, 0.987882_r8, 0.991450_r8, 0.993976_r8/ data (bm0ij ( 5, 1,ibeta), ibeta = 1,10) / & 0.865049_r8, 0.872851_r8, 0.889900_r8, 0.909907_r8, 0.929290_r8, & 0.946205_r8, 0.959991_r8, 0.970706_r8, 0.978764_r8, 0.984692_r8/ data (bm0ij ( 5, 2,ibeta), ibeta = 1,10) / & 0.868989_r8, 0.876713_r8, 0.893538_r8, 0.913173_r8, 0.932080_r8, & 0.948484_r8, 0.961785_r8, 0.972080_r8, 0.979796_r8, 0.985457_r8/ data (bm0ij ( 5, 3,ibeta), ibeta = 1,10) / & 0.878010_r8, 0.885524_r8, 0.901756_r8, 0.920464_r8, 0.938235_r8, & 0.953461_r8, 0.965672_r8, 0.975037_r8, 0.982005_r8, 0.987085_r8/ data (bm0ij ( 5, 4,ibeta), ibeta = 1,10) / & 0.889534_r8, 0.896698_r8, 0.912012_r8, 0.929395_r8, 0.945647_r8, & 0.959366_r8, 0.970227_r8, 0.978469_r8, 0.984547_r8, 0.988950_r8/ data (bm0ij ( 5, 5,ibeta), ibeta = 1,10) / & 0.902033_r8, 0.908713_r8, 0.922848_r8, 0.938648_r8, 0.953186_r8, & 0.965278_r8, 0.974729_r8, 0.981824_r8, 0.987013_r8, 0.990746_r8/ data (bm0ij ( 5, 6,ibeta), ibeta = 1,10) / & 0.914496_r8, 0.920599_r8, 0.933389_r8, 0.947485_r8, 0.960262_r8, & 0.970743_r8, 0.978839_r8, 0.984858_r8, 0.989225_r8, 0.992348_r8/ data (bm0ij ( 5, 7,ibeta), ibeta = 1,10) / & 0.926281_r8, 0.931761_r8, 0.943142_r8, 0.955526_r8, 0.966600_r8, & 0.975573_r8, 0.982431_r8, 0.987485_r8, 0.991128_r8, 0.993718_r8/ data (bm0ij ( 5, 8,ibeta), ibeta = 1,10) / & 0.937029_r8, 0.941877_r8, 0.951868_r8, 0.962615_r8, 0.972112_r8, & 0.979723_r8, 0.985488_r8, 0.989705_r8, 0.992725_r8, 0.994863_r8/ data (bm0ij ( 5, 9,ibeta), ibeta = 1,10) / & 0.946580_r8, 0.950819_r8, 0.959494_r8, 0.968732_r8, 0.976811_r8, & 0.983226_r8, 0.988047_r8, 0.991550_r8, 0.994047_r8, 0.995806_r8/ data (bm0ij ( 5, 10,ibeta), ibeta = 1,10) / & 0.954909_r8, 0.958581_r8, 0.966049_r8, 0.973933_r8, 0.980766_r8, & 0.986149_r8, 0.990166_r8, 0.993070_r8, 0.995130_r8, 0.996577_r8/ data (bm0ij ( 6, 1,ibeta), ibeta = 1,10) / & 0.914182_r8, 0.919824_r8, 0.931832_r8, 0.945387_r8, 0.957999_r8, & 0.968606_r8, 0.976982_r8, 0.983331_r8, 0.988013_r8, 0.991407_r8/ data (bm0ij ( 6, 2,ibeta), ibeta = 1,10) / & 0.917139_r8, 0.922665_r8, 0.934395_r8, 0.947580_r8, 0.959792_r8, & 0.970017_r8, 0.978062_r8, 0.984138_r8, 0.988609_r8, 0.991843_r8/ data (bm0ij ( 6, 3,ibeta), ibeta = 1,10) / & 0.923742_r8, 0.928990_r8, 0.940064_r8, 0.952396_r8, 0.963699_r8, & 0.973070_r8, 0.980381_r8, 0.985866_r8, 0.989878_r8, 0.992768_r8/ data (bm0ij ( 6, 4,ibeta), ibeta = 1,10) / & 0.931870_r8, 0.936743_r8, 0.946941_r8, 0.958162_r8, 0.968318_r8, & 0.976640_r8, 0.983069_r8, 0.987853_r8, 0.991330_r8, 0.993822_r8/ data (bm0ij ( 6, 5,ibeta), ibeta = 1,10) / & 0.940376_r8, 0.944807_r8, 0.954004_r8, 0.963999_r8, 0.972928_r8, & 0.980162_r8, 0.985695_r8, 0.989779_r8, 0.992729_r8, 0.994833_r8/ data (bm0ij ( 6, 6,ibeta), ibeta = 1,10) / & 0.948597_r8, 0.952555_r8, 0.960703_r8, 0.969454_r8, 0.977181_r8, & 0.983373_r8, 0.988067_r8, 0.991507_r8, 0.993977_r8, 0.995730_r8/ data (bm0ij ( 6, 7,ibeta), ibeta = 1,10) / & 0.956167_r8, 0.959648_r8, 0.966763_r8, 0.974326_r8, 0.980933_r8, & 0.986177_r8, 0.990121_r8, 0.992993_r8, 0.995045_r8, 0.996495_r8/ data (bm0ij ( 6, 8,ibeta), ibeta = 1,10) / & 0.962913_r8, 0.965937_r8, 0.972080_r8, 0.978552_r8, 0.984153_r8, & 0.988563_r8, 0.991857_r8, 0.994242_r8, 0.995938_r8, 0.997133_r8/ data (bm0ij ( 6, 9,ibeta), ibeta = 1,10) / & 0.968787_r8, 0.971391_r8, 0.976651_r8, 0.982148_r8, 0.986869_r8, & 0.990560_r8, 0.993301_r8, 0.995275_r8, 0.996675_r8, 0.997657_r8/ data (bm0ij ( 6, 10,ibeta), ibeta = 1,10) / & 0.973822_r8, 0.976047_r8, 0.980523_r8, 0.985170_r8, 0.989134_r8, & 0.992215_r8, 0.994491_r8, 0.996124_r8, 0.997277_r8, 0.998085_r8/ data (bm0ij ( 7, 1,ibeta), ibeta = 1,10) / & 0.947410_r8, 0.951207_r8, 0.959119_r8, 0.967781_r8, 0.975592_r8, & 0.981981_r8, 0.986915_r8, 0.990590_r8, 0.993266_r8, 0.995187_r8/ data (bm0ij ( 7, 2,ibeta), ibeta = 1,10) / & 0.949477_r8, 0.953161_r8, 0.960824_r8, 0.969187_r8, 0.976702_r8, & 0.982831_r8, 0.987550_r8, 0.991057_r8, 0.993606_r8, 0.995434_r8/ data (bm0ij ( 7, 3,ibeta), ibeta = 1,10) / & 0.954008_r8, 0.957438_r8, 0.964537_r8, 0.972232_r8, 0.979095_r8, & 0.984653_r8, 0.988907_r8, 0.992053_r8, 0.994330_r8, 0.995958_r8/ data (bm0ij ( 7, 4,ibeta), ibeta = 1,10) / & 0.959431_r8, 0.962539_r8, 0.968935_r8, 0.975808_r8, 0.981882_r8, & 0.986759_r8, 0.990466_r8, 0.993190_r8, 0.995153_r8, 0.996552_r8/ data (bm0ij ( 7, 5,ibeta), ibeta = 1,10) / & 0.964932_r8, 0.967693_r8, 0.973342_r8, 0.979355_r8, 0.984620_r8, & 0.988812_r8, 0.991974_r8, 0.994285_r8, 0.995943_r8, 0.997119_r8/ data (bm0ij ( 7, 6,ibeta), ibeta = 1,10) / & 0.970101_r8, 0.972517_r8, 0.977428_r8, 0.982612_r8, 0.987110_r8, & 0.990663_r8, 0.993326_r8, 0.995261_r8, 0.996644_r8, 0.997621_r8/ data (bm0ij ( 7, 7,ibeta), ibeta = 1,10) / & 0.974746_r8, 0.976834_r8, 0.981055_r8, 0.985475_r8, 0.989280_r8, & 0.992265_r8, 0.994488_r8, 0.996097_r8, 0.997241_r8, 0.998048_r8/ data (bm0ij ( 7, 8,ibeta), ibeta = 1,10) / & 0.978804_r8, 0.980591_r8, 0.984187_r8, 0.987927_r8, 0.991124_r8, & 0.993617_r8, 0.995464_r8, 0.996795_r8, 0.997739_r8, 0.998403_r8/ data (bm0ij ( 7, 9,ibeta), ibeta = 1,10) / & 0.982280_r8, 0.983799_r8, 0.986844_r8, 0.989991_r8, 0.992667_r8, & 0.994742_r8, 0.996273_r8, 0.997372_r8, 0.998149_r8, 0.998695_r8/ data (bm0ij ( 7, 10,ibeta), ibeta = 1,10) / & 0.985218_r8, 0.986503_r8, 0.989071_r8, 0.991711_r8, 0.993945_r8, & 0.995669_r8, 0.996937_r8, 0.997844_r8, 0.998484_r8, 0.998932_r8/ data (bm0ij ( 8, 1,ibeta), ibeta = 1,10) / & 0.968507_r8, 0.970935_r8, 0.975916_r8, 0.981248_r8, 0.985947_r8, & 0.989716_r8, 0.992580_r8, 0.994689_r8, 0.996210_r8, 0.997297_r8/ data (bm0ij ( 8, 2,ibeta), ibeta = 1,10) / & 0.969870_r8, 0.972210_r8, 0.977002_r8, 0.982119_r8, 0.986619_r8, & 0.990219_r8, 0.992951_r8, 0.994958_r8, 0.996405_r8, 0.997437_r8/ data (bm0ij ( 8, 3,ibeta), ibeta = 1,10) / & 0.972820_r8, 0.974963_r8, 0.979339_r8, 0.983988_r8, 0.988054_r8, & 0.991292_r8, 0.993738_r8, 0.995529_r8, 0.996817_r8, 0.997734_r8/ data (bm0ij ( 8, 4,ibeta), ibeta = 1,10) / & 0.976280_r8, 0.978186_r8, 0.982060_r8, 0.986151_r8, 0.989706_r8, & 0.992520_r8, 0.994636_r8, 0.996179_r8, 0.997284_r8, 0.998069_r8/ data (bm0ij ( 8, 5,ibeta), ibeta = 1,10) / & 0.979711_r8, 0.981372_r8, 0.984735_r8, 0.988263_r8, 0.991309_r8, & 0.993706_r8, 0.995499_r8, 0.996801_r8, 0.997730_r8, 0.998389_r8/ data (bm0ij ( 8, 6,ibeta), ibeta = 1,10) / & 0.982863_r8, 0.984292_r8, 0.987172_r8, 0.990174_r8, 0.992750_r8, & 0.994766_r8, 0.996266_r8, 0.997352_r8, 0.998125_r8, 0.998670_r8/ data (bm0ij ( 8, 7,ibeta), ibeta = 1,10) / & 0.985642_r8, 0.986858_r8, 0.989301_r8, 0.991834_r8, 0.993994_r8, & 0.995676_r8, 0.996923_r8, 0.997822_r8, 0.998460_r8, 0.998910_r8/ data (bm0ij ( 8, 8,ibeta), ibeta = 1,10) / & 0.988029_r8, 0.989058_r8, 0.991116_r8, 0.993240_r8, 0.995043_r8, & 0.996440_r8, 0.997472_r8, 0.998214_r8, 0.998739_r8, 0.999108_r8/ data (bm0ij ( 8, 9,ibeta), ibeta = 1,10) / & 0.990046_r8, 0.990912_r8, 0.992640_r8, 0.994415_r8, 0.995914_r8, & 0.997073_r8, 0.997925_r8, 0.998536_r8, 0.998968_r8, 0.999271_r8/ data (bm0ij ( 8, 10,ibeta), ibeta = 1,10) / & 0.991732_r8, 0.992459_r8, 0.993906_r8, 0.995386_r8, 0.996633_r8, & 0.997592_r8, 0.998296_r8, 0.998799_r8, 0.999154_r8, 0.999403_r8/ data (bm0ij ( 9, 1,ibeta), ibeta = 1,10) / & 0.981392_r8, 0.982893_r8, 0.985938_r8, 0.989146_r8, 0.991928_r8, & 0.994129_r8, 0.995783_r8, 0.996991_r8, 0.997857_r8, 0.998473_r8/ data (bm0ij ( 9, 2,ibeta), ibeta = 1,10) / & 0.982254_r8, 0.983693_r8, 0.986608_r8, 0.989673_r8, 0.992328_r8, & 0.994424_r8, 0.995998_r8, 0.997146_r8, 0.997969_r8, 0.998553_r8/ data (bm0ij ( 9, 3,ibeta), ibeta = 1,10) / & 0.984104_r8, 0.985407_r8, 0.988040_r8, 0.990798_r8, 0.993178_r8, & 0.995052_r8, 0.996454_r8, 0.997474_r8, 0.998204_r8, 0.998722_r8/ data (bm0ij ( 9, 4,ibeta), ibeta = 1,10) / & 0.986243_r8, 0.987386_r8, 0.989687_r8, 0.992087_r8, 0.994149_r8, & 0.995765_r8, 0.996971_r8, 0.997846_r8, 0.998470_r8, 0.998913_r8/ data (bm0ij ( 9, 5,ibeta), ibeta = 1,10) / & 0.988332_r8, 0.989313_r8, 0.991284_r8, 0.993332_r8, 0.995082_r8, & 0.996449_r8, 0.997465_r8, 0.998200_r8, 0.998723_r8, 0.999093_r8/ data (bm0ij ( 9, 6,ibeta), ibeta = 1,10) / & 0.990220_r8, 0.991053_r8, 0.992721_r8, 0.994445_r8, 0.995914_r8, & 0.997056_r8, 0.997902_r8, 0.998513_r8, 0.998947_r8, 0.999253_r8/ data (bm0ij ( 9, 7,ibeta), ibeta = 1,10) / & 0.991859_r8, 0.992561_r8, 0.993961_r8, 0.995403_r8, 0.996626_r8, & 0.997574_r8, 0.998274_r8, 0.998778_r8, 0.999136_r8, 0.999387_r8/ data (bm0ij ( 9, 8,ibeta), ibeta = 1,10) / & 0.993250_r8, 0.993837_r8, 0.995007_r8, 0.996208_r8, 0.997223_r8, & 0.998007_r8, 0.998584_r8, 0.998999_r8, 0.999293_r8, 0.999499_r8/ data (bm0ij ( 9, 9,ibeta), ibeta = 1,10) / & 0.994413_r8, 0.994903_r8, 0.995878_r8, 0.996876_r8, 0.997716_r8, & 0.998363_r8, 0.998839_r8, 0.999180_r8, 0.999421_r8, 0.999591_r8/ data (bm0ij ( 9, 10,ibeta), ibeta = 1,10) / & 0.995376_r8, 0.995785_r8, 0.996597_r8, 0.997425_r8, 0.998121_r8, & 0.998655_r8, 0.999048_r8, 0.999328_r8, 0.999526_r8, 0.999665_r8/ data (bm0ij ( 10, 1,ibeta), ibeta = 1,10) / & 0.989082_r8, 0.989991_r8, 0.991819_r8, 0.993723_r8, 0.995357_r8, & 0.996637_r8, 0.997592_r8, 0.998286_r8, 0.998781_r8, 0.999132_r8/ data (bm0ij ( 10, 2,ibeta), ibeta = 1,10) / & 0.989613_r8, 0.990480_r8, 0.992224_r8, 0.994039_r8, 0.995594_r8, & 0.996810_r8, 0.997717_r8, 0.998375_r8, 0.998845_r8, 0.999178_r8/ data (bm0ij ( 10, 3,ibeta), ibeta = 1,10) / & 0.990744_r8, 0.991523_r8, 0.993086_r8, 0.994708_r8, 0.996094_r8, & 0.997176_r8, 0.997981_r8, 0.998564_r8, 0.998980_r8, 0.999274_r8/ data (bm0ij ( 10, 4,ibeta), ibeta = 1,10) / & 0.992041_r8, 0.992716_r8, 0.994070_r8, 0.995470_r8, 0.996662_r8, & 0.997591_r8, 0.998280_r8, 0.998778_r8, 0.999133_r8, 0.999383_r8/ data (bm0ij ( 10, 5,ibeta), ibeta = 1,10) / & 0.993292_r8, 0.993867_r8, 0.995015_r8, 0.996199_r8, 0.997205_r8, & 0.997985_r8, 0.998564_r8, 0.998981_r8, 0.999277_r8, 0.999487_r8/ data (bm0ij ( 10, 6,ibeta), ibeta = 1,10) / & 0.994411_r8, 0.994894_r8, 0.995857_r8, 0.996847_r8, 0.997685_r8, & 0.998334_r8, 0.998814_r8, 0.999159_r8, 0.999404_r8, 0.999577_r8/ data (bm0ij ( 10, 7,ibeta), ibeta = 1,10) / & 0.995373_r8, 0.995776_r8, 0.996577_r8, 0.997400_r8, 0.998094_r8, & 0.998630_r8, 0.999026_r8, 0.999310_r8, 0.999512_r8, 0.999654_r8/ data (bm0ij ( 10, 8,ibeta), ibeta = 1,10) / & 0.996181_r8, 0.996516_r8, 0.997181_r8, 0.997861_r8, 0.998435_r8, & 0.998877_r8, 0.999202_r8, 0.999435_r8, 0.999601_r8, 0.999717_r8/ data (bm0ij ( 10, 9,ibeta), ibeta = 1,10) / & 0.996851_r8, 0.997128_r8, 0.997680_r8, 0.998242_r8, 0.998715_r8, & 0.999079_r8, 0.999346_r8, 0.999538_r8, 0.999673_r8, 0.999769_r8/ data (bm0ij ( 10, 10,ibeta), ibeta = 1,10) / & 0.997402_r8, 0.997632_r8, 0.998089_r8, 0.998554_r8, 0.998945_r8, & 0.999244_r8, 0.999464_r8, 0.999622_r8, 0.999733_r8, 0.999811_r8/ ! rpm.... 3rd moment nuclei mode corr. fac. for bimodal fm coag rate data (bm3i( 1, 1,ibeta ), ibeta=1,10)/ & 0.70708_r8,0.71681_r8,0.73821_r8,0.76477_r8,0.79350_r8,0.82265_r8,0.85090_r8,0.87717_r8, & 0.90069_r8,0.92097_r8/ data (bm3i( 1, 2,ibeta ), ibeta=1,10)/ & 0.72172_r8,0.73022_r8,0.74927_r8,0.77324_r8,0.79936_r8,0.82601_r8,0.85199_r8,0.87637_r8, & 0.89843_r8,0.91774_r8/ data (bm3i( 1, 3,ibeta ), ibeta=1,10)/ & 0.78291_r8,0.78896_r8,0.80286_r8,0.82070_r8,0.84022_r8,0.85997_r8,0.87901_r8,0.89669_r8, & 0.91258_r8,0.92647_r8/ data (bm3i( 1, 4,ibeta ), ibeta=1,10)/ & 0.87760_r8,0.88147_r8,0.89025_r8,0.90127_r8,0.91291_r8,0.92420_r8,0.93452_r8,0.94355_r8, & 0.95113_r8,0.95726_r8/ data (bm3i( 1, 5,ibeta ), ibeta=1,10)/ & 0.94988_r8,0.95184_r8,0.95612_r8,0.96122_r8,0.96628_r8,0.97085_r8,0.97467_r8,0.97763_r8, & 0.97971_r8,0.98089_r8/ data (bm3i( 1, 6,ibeta ), ibeta=1,10)/ & 0.98318_r8,0.98393_r8,0.98551_r8,0.98728_r8,0.98889_r8,0.99014_r8,0.99095_r8,0.99124_r8, & 0.99100_r8,0.99020_r8/ data (bm3i( 1, 7,ibeta ), ibeta=1,10)/ & 0.99480_r8,0.99504_r8,0.99551_r8,0.99598_r8,0.99629_r8,0.99635_r8,0.99611_r8,0.99550_r8, & 0.99450_r8,0.99306_r8/ data (bm3i( 1, 8,ibeta ), ibeta=1,10)/ & 0.99842_r8,0.99848_r8,0.99858_r8,0.99861_r8,0.99850_r8,0.99819_r8,0.99762_r8,0.99674_r8, & 0.99550_r8,0.99388_r8/ data (bm3i( 1, 9,ibeta ), ibeta=1,10)/ & 0.99951_r8,0.99951_r8,0.99949_r8,0.99939_r8,0.99915_r8,0.99872_r8,0.99805_r8,0.99709_r8, & 0.99579_r8,0.99411_r8/ data (bm3i( 1,10,ibeta ), ibeta=1,10)/ & 0.99984_r8,0.99982_r8,0.99976_r8,0.99962_r8,0.99934_r8,0.99888_r8,0.99818_r8,0.99719_r8, & 0.99587_r8,0.99417_r8/ data (bm3i( 2, 1,ibeta ), ibeta=1,10)/ & 0.72957_r8,0.73993_r8,0.76303_r8,0.79178_r8,0.82245_r8,0.85270_r8,0.88085_r8,0.90578_r8, & 0.92691_r8,0.94415_r8/ data (bm3i( 2, 2,ibeta ), ibeta=1,10)/ & 0.72319_r8,0.73320_r8,0.75547_r8,0.78323_r8,0.81307_r8,0.84287_r8,0.87107_r8,0.89651_r8, & 0.91852_r8,0.93683_r8/ data (bm3i( 2, 3,ibeta ), ibeta=1,10)/ & 0.74413_r8,0.75205_r8,0.76998_r8,0.79269_r8,0.81746_r8,0.84258_r8,0.86685_r8,0.88938_r8, & 0.90953_r8,0.92695_r8/ data (bm3i( 2, 4,ibeta ), ibeta=1,10)/ & 0.82588_r8,0.83113_r8,0.84309_r8,0.85825_r8,0.87456_r8,0.89072_r8,0.90594_r8,0.91972_r8, & 0.93178_r8,0.94203_r8/ data (bm3i( 2, 5,ibeta ), ibeta=1,10)/ & 0.91886_r8,0.92179_r8,0.92831_r8,0.93624_r8,0.94434_r8,0.95192_r8,0.95856_r8,0.96409_r8, & 0.96845_r8,0.97164_r8/ data (bm3i( 2, 6,ibeta ), ibeta=1,10)/ & 0.97129_r8,0.97252_r8,0.97515_r8,0.97818_r8,0.98108_r8,0.98354_r8,0.98542_r8,0.98665_r8, & 0.98721_r8,0.98709_r8/ data (bm3i( 2, 7,ibeta ), ibeta=1,10)/ & 0.99104_r8,0.99145_r8,0.99230_r8,0.99320_r8,0.99394_r8,0.99439_r8,0.99448_r8,0.99416_r8, & 0.99340_r8,0.99217_r8/ data (bm3i( 2, 8,ibeta ), ibeta=1,10)/ & 0.99730_r8,0.99741_r8,0.99763_r8,0.99779_r8,0.99782_r8,0.99762_r8,0.99715_r8,0.99636_r8, & 0.99519_r8,0.99363_r8/ data (bm3i( 2, 9,ibeta ), ibeta=1,10)/ & 0.99917_r8,0.99919_r8,0.99921_r8,0.99915_r8,0.99895_r8,0.99856_r8,0.99792_r8,0.99698_r8, & 0.99570_r8,0.99404_r8/ data (bm3i( 2,10,ibeta ), ibeta=1,10)/ & 0.99973_r8,0.99973_r8,0.99968_r8,0.99955_r8,0.99928_r8,0.99883_r8,0.99814_r8,0.99716_r8, & 0.99584_r8,0.99415_r8/ data (bm3i( 3, 1,ibeta ), ibeta=1,10)/ & 0.78358_r8,0.79304_r8,0.81445_r8,0.84105_r8,0.86873_r8,0.89491_r8,0.91805_r8,0.93743_r8, & 0.95300_r8,0.96510_r8/ data (bm3i( 3, 2,ibeta ), ibeta=1,10)/ & 0.76412_r8,0.77404_r8,0.79635_r8,0.82404_r8,0.85312_r8,0.88101_r8,0.90610_r8,0.92751_r8, & 0.94500_r8,0.95879_r8/ data (bm3i( 3, 3,ibeta ), ibeta=1,10)/ & 0.74239_r8,0.75182_r8,0.77301_r8,0.79956_r8,0.82809_r8,0.85639_r8,0.88291_r8,0.90658_r8, & 0.92683_r8,0.94350_r8/ data (bm3i( 3, 4,ibeta ), ibeta=1,10)/ & 0.78072_r8,0.78758_r8,0.80317_r8,0.82293_r8,0.84437_r8,0.86589_r8,0.88643_r8,0.90526_r8, & 0.92194_r8,0.93625_r8/ data (bm3i( 3, 5,ibeta ), ibeta=1,10)/ & 0.87627_r8,0.88044_r8,0.88981_r8,0.90142_r8,0.91357_r8,0.92524_r8,0.93585_r8,0.94510_r8, & 0.95285_r8,0.95911_r8/ data (bm3i( 3, 6,ibeta ), ibeta=1,10)/ & 0.95176_r8,0.95371_r8,0.95796_r8,0.96297_r8,0.96792_r8,0.97233_r8,0.97599_r8,0.97880_r8, & 0.98072_r8,0.98178_r8/ data (bm3i( 3, 7,ibeta ), ibeta=1,10)/ & 0.98453_r8,0.98523_r8,0.98670_r8,0.98833_r8,0.98980_r8,0.99092_r8,0.99160_r8,0.99179_r8, & 0.99145_r8,0.99058_r8/ data (bm3i( 3, 8,ibeta ), ibeta=1,10)/ & 0.99534_r8,0.99555_r8,0.99597_r8,0.99637_r8,0.99662_r8,0.99663_r8,0.99633_r8,0.99569_r8, & 0.99465_r8,0.99318_r8/ data (bm3i( 3, 9,ibeta ), ibeta=1,10)/ & 0.99859_r8,0.99864_r8,0.99872_r8,0.99873_r8,0.99860_r8,0.99827_r8,0.99768_r8,0.99679_r8, & 0.99555_r8,0.99391_r8/ data (bm3i( 3,10,ibeta ), ibeta=1,10)/ & 0.99956_r8,0.99956_r8,0.99953_r8,0.99942_r8,0.99918_r8,0.99875_r8,0.99807_r8,0.99711_r8, & 0.99580_r8,0.99412_r8/ data (bm3i( 4, 1,ibeta ), ibeta=1,10)/ & 0.84432_r8,0.85223_r8,0.86990_r8,0.89131_r8,0.91280_r8,0.93223_r8,0.94861_r8,0.96172_r8, & 0.97185_r8,0.97945_r8/ data (bm3i( 4, 2,ibeta ), ibeta=1,10)/ & 0.82299_r8,0.83164_r8,0.85101_r8,0.87463_r8,0.89857_r8,0.92050_r8,0.93923_r8,0.95443_r8, & 0.96629_r8,0.97529_r8/ data (bm3i( 4, 3,ibeta ), ibeta=1,10)/ & 0.77870_r8,0.78840_r8,0.81011_r8,0.83690_r8,0.86477_r8,0.89124_r8,0.91476_r8,0.93460_r8, & 0.95063_r8,0.96316_r8/ data (bm3i( 4, 4,ibeta ), ibeta=1,10)/ & 0.76386_r8,0.77233_r8,0.79147_r8,0.81557_r8,0.84149_r8,0.86719_r8,0.89126_r8,0.91275_r8, & 0.93116_r8,0.94637_r8/ data (bm3i( 4, 5,ibeta ), ibeta=1,10)/ & 0.82927_r8,0.83488_r8,0.84756_r8,0.86346_r8,0.88040_r8,0.89704_r8,0.91257_r8,0.92649_r8, & 0.93857_r8,0.94874_r8/ data (bm3i( 4, 6,ibeta ), ibeta=1,10)/ & 0.92184_r8,0.92481_r8,0.93136_r8,0.93925_r8,0.94724_r8,0.95462_r8,0.96104_r8,0.96634_r8, & 0.97048_r8,0.97348_r8/ data (bm3i( 4, 7,ibeta ), ibeta=1,10)/ & 0.97341_r8,0.97457_r8,0.97706_r8,0.97991_r8,0.98260_r8,0.98485_r8,0.98654_r8,0.98760_r8, & 0.98801_r8,0.98777_r8/ data (bm3i( 4, 8,ibeta ), ibeta=1,10)/ & 0.99192_r8,0.99229_r8,0.99305_r8,0.99385_r8,0.99449_r8,0.99486_r8,0.99487_r8,0.99449_r8, & 0.99367_r8,0.99239_r8/ data (bm3i( 4, 9,ibeta ), ibeta=1,10)/ & 0.99758_r8,0.99768_r8,0.99787_r8,0.99800_r8,0.99799_r8,0.99777_r8,0.99727_r8,0.99645_r8, & 0.99527_r8,0.99369_r8/ data (bm3i( 4,10,ibeta ), ibeta=1,10)/ & 0.99926_r8,0.99928_r8,0.99928_r8,0.99921_r8,0.99900_r8,0.99860_r8,0.99795_r8,0.99701_r8, & 0.99572_r8,0.99405_r8/ data (bm3i( 5, 1,ibeta ), ibeta=1,10)/ & 0.89577_r8,0.90190_r8,0.91522_r8,0.93076_r8,0.94575_r8,0.95876_r8,0.96932_r8,0.97751_r8, & 0.98367_r8,0.98820_r8/ data (bm3i( 5, 2,ibeta ), ibeta=1,10)/ & 0.87860_r8,0.88547_r8,0.90052_r8,0.91828_r8,0.93557_r8,0.95075_r8,0.96319_r8,0.97292_r8, & 0.98028_r8,0.98572_r8/ data (bm3i( 5, 3,ibeta ), ibeta=1,10)/ & 0.83381_r8,0.84240_r8,0.86141_r8,0.88425_r8,0.90707_r8,0.92770_r8,0.94510_r8,0.95906_r8, & 0.96986_r8,0.97798_r8/ data (bm3i( 5, 4,ibeta ), ibeta=1,10)/ & 0.78530_r8,0.79463_r8,0.81550_r8,0.84127_r8,0.86813_r8,0.89367_r8,0.91642_r8,0.93566_r8, & 0.95125_r8,0.96347_r8/ data (bm3i( 5, 5,ibeta ), ibeta=1,10)/ & 0.79614_r8,0.80332_r8,0.81957_r8,0.84001_r8,0.86190_r8,0.88351_r8,0.90368_r8,0.92169_r8, & 0.93718_r8,0.95006_r8/ data (bm3i( 5, 6,ibeta ), ibeta=1,10)/ & 0.88192_r8,0.88617_r8,0.89565_r8,0.90728_r8,0.91931_r8,0.93076_r8,0.94107_r8,0.94997_r8, & 0.95739_r8,0.96333_r8/ data (bm3i( 5, 7,ibeta ), ibeta=1,10)/ & 0.95509_r8,0.95698_r8,0.96105_r8,0.96583_r8,0.97048_r8,0.97460_r8,0.97796_r8,0.98050_r8, & 0.98218_r8,0.98304_r8/ data (bm3i( 5, 8,ibeta ), ibeta=1,10)/ & 0.98596_r8,0.98660_r8,0.98794_r8,0.98943_r8,0.99074_r8,0.99172_r8,0.99227_r8,0.99235_r8, & 0.99192_r8,0.99096_r8/ data (bm3i( 5, 9,ibeta ), ibeta=1,10)/ & 0.99581_r8,0.99600_r8,0.99637_r8,0.99672_r8,0.99691_r8,0.99687_r8,0.99653_r8,0.99585_r8, & 0.99478_r8,0.99329_r8/ data (bm3i( 5,10,ibeta ), ibeta=1,10)/ & 0.99873_r8,0.99878_r8,0.99884_r8,0.99883_r8,0.99869_r8,0.99834_r8,0.99774_r8,0.99684_r8, & 0.99558_r8,0.99394_r8/ data (bm3i( 6, 1,ibeta ), ibeta=1,10)/ & 0.93335_r8,0.93777_r8,0.94711_r8,0.95764_r8,0.96741_r8,0.97562_r8,0.98210_r8,0.98701_r8, & 0.99064_r8,0.99327_r8/ data (bm3i( 6, 2,ibeta ), ibeta=1,10)/ & 0.92142_r8,0.92646_r8,0.93723_r8,0.94947_r8,0.96096_r8,0.97069_r8,0.97842_r8,0.98431_r8, & 0.98868_r8,0.99186_r8/ data (bm3i( 6, 3,ibeta ), ibeta=1,10)/ & 0.88678_r8,0.89351_r8,0.90810_r8,0.92508_r8,0.94138_r8,0.95549_r8,0.96693_r8,0.97578_r8, & 0.98243_r8,0.98731_r8/ data (bm3i( 6, 4,ibeta ), ibeta=1,10)/ & 0.83249_r8,0.84124_r8,0.86051_r8,0.88357_r8,0.90655_r8,0.92728_r8,0.94477_r8,0.95880_r8, & 0.96964_r8,0.97779_r8/ data (bm3i( 6, 5,ibeta ), ibeta=1,10)/ & 0.79593_r8,0.80444_r8,0.82355_r8,0.84725_r8,0.87211_r8,0.89593_r8,0.91735_r8,0.93566_r8, & 0.95066_r8,0.96255_r8/ data (bm3i( 6, 6,ibeta ), ibeta=1,10)/ & 0.84124_r8,0.84695_r8,0.85980_r8,0.87575_r8,0.89256_r8,0.90885_r8,0.92383_r8,0.93704_r8, & 0.94830_r8,0.95761_r8/ data (bm3i( 6, 7,ibeta ), ibeta=1,10)/ & 0.92721_r8,0.93011_r8,0.93647_r8,0.94406_r8,0.95166_r8,0.95862_r8,0.96460_r8,0.96949_r8, & 0.97326_r8,0.97595_r8/ data (bm3i( 6, 8,ibeta ), ibeta=1,10)/ & 0.97573_r8,0.97681_r8,0.97913_r8,0.98175_r8,0.98421_r8,0.98624_r8,0.98772_r8,0.98860_r8, & 0.98885_r8,0.98847_r8/ data (bm3i( 6, 9,ibeta ), ibeta=1,10)/ & 0.99271_r8,0.99304_r8,0.99373_r8,0.99444_r8,0.99499_r8,0.99528_r8,0.99522_r8,0.99477_r8, & 0.99390_r8,0.99258_r8/ data (bm3i( 6,10,ibeta ), ibeta=1,10)/ & 0.99782_r8,0.99791_r8,0.99807_r8,0.99817_r8,0.99813_r8,0.99788_r8,0.99737_r8,0.99653_r8, & 0.99533_r8,0.99374_r8/ data (bm3i( 7, 1,ibeta ), ibeta=1,10)/ & 0.95858_r8,0.96158_r8,0.96780_r8,0.97460_r8,0.98073_r8,0.98575_r8,0.98963_r8,0.99252_r8, & 0.99463_r8,0.99615_r8/ data (bm3i( 7, 2,ibeta ), ibeta=1,10)/ & 0.95091_r8,0.95438_r8,0.96163_r8,0.96962_r8,0.97688_r8,0.98286_r8,0.98751_r8,0.99099_r8, & 0.99353_r8,0.99536_r8/ data (bm3i( 7, 3,ibeta ), ibeta=1,10)/ & 0.92751_r8,0.93233_r8,0.94255_r8,0.95406_r8,0.96473_r8,0.97366_r8,0.98070_r8,0.98602_r8, & 0.98994_r8,0.99278_r8/ data (bm3i( 7, 4,ibeta ), ibeta=1,10)/ & 0.88371_r8,0.89075_r8,0.90595_r8,0.92351_r8,0.94028_r8,0.95474_r8,0.96642_r8,0.97544_r8, & 0.98220_r8,0.98715_r8/ data (bm3i( 7, 5,ibeta ), ibeta=1,10)/ & 0.82880_r8,0.83750_r8,0.85671_r8,0.87980_r8,0.90297_r8,0.92404_r8,0.94195_r8,0.95644_r8, & 0.96772_r8,0.97625_r8/ data (bm3i( 7, 6,ibeta ), ibeta=1,10)/ & 0.81933_r8,0.82655_r8,0.84279_r8,0.86295_r8,0.88412_r8,0.90449_r8,0.92295_r8,0.93890_r8, & 0.95215_r8,0.96281_r8/ data (bm3i( 7, 7,ibeta ), ibeta=1,10)/ & 0.89099_r8,0.89519_r8,0.90448_r8,0.91577_r8,0.92732_r8,0.93820_r8,0.94789_r8,0.95616_r8, & 0.96297_r8,0.96838_r8/ data (bm3i( 7, 8,ibeta ), ibeta=1,10)/ & 0.95886_r8,0.96064_r8,0.96448_r8,0.96894_r8,0.97324_r8,0.97701_r8,0.98004_r8,0.98228_r8, & 0.98371_r8,0.98435_r8/ data (bm3i( 7, 9,ibeta ), ibeta=1,10)/ & 0.98727_r8,0.98786_r8,0.98908_r8,0.99043_r8,0.99160_r8,0.99245_r8,0.99288_r8,0.99285_r8, & 0.99234_r8,0.99131_r8/ data (bm3i( 7,10,ibeta ), ibeta=1,10)/ & 0.99621_r8,0.99638_r8,0.99671_r8,0.99700_r8,0.99715_r8,0.99707_r8,0.99670_r8,0.99599_r8, & 0.99489_r8,0.99338_r8/ data (bm3i( 8, 1,ibeta ), ibeta=1,10)/ & 0.97470_r8,0.97666_r8,0.98064_r8,0.98491_r8,0.98867_r8,0.99169_r8,0.99399_r8,0.99569_r8, & 0.99691_r8,0.99779_r8/ data (bm3i( 8, 2,ibeta ), ibeta=1,10)/ & 0.96996_r8,0.97225_r8,0.97693_r8,0.98196_r8,0.98643_r8,0.99003_r8,0.99279_r8,0.99482_r8, & 0.99630_r8,0.99735_r8/ data (bm3i( 8, 3,ibeta ), ibeta=1,10)/ & 0.95523_r8,0.95848_r8,0.96522_r8,0.97260_r8,0.97925_r8,0.98468_r8,0.98888_r8,0.99200_r8, & 0.99427_r8,0.99590_r8/ data (bm3i( 8, 4,ibeta ), ibeta=1,10)/ & 0.92524_r8,0.93030_r8,0.94098_r8,0.95294_r8,0.96397_r8,0.97317_r8,0.98038_r8,0.98582_r8, & 0.98981_r8,0.99270_r8/ data (bm3i( 8, 5,ibeta ), ibeta=1,10)/ & 0.87576_r8,0.88323_r8,0.89935_r8,0.91799_r8,0.93583_r8,0.95126_r8,0.96377_r8,0.97345_r8, & 0.98072_r8,0.98606_r8/ data (bm3i( 8, 6,ibeta ), ibeta=1,10)/ & 0.83078_r8,0.83894_r8,0.85705_r8,0.87899_r8,0.90126_r8,0.92179_r8,0.93950_r8,0.95404_r8, & 0.96551_r8,0.97430_r8/ data (bm3i( 8, 7,ibeta ), ibeta=1,10)/ & 0.85727_r8,0.86294_r8,0.87558_r8,0.89111_r8,0.90723_r8,0.92260_r8,0.93645_r8,0.94841_r8, & 0.95838_r8,0.96643_r8/ data (bm3i( 8, 8,ibeta ), ibeta=1,10)/ & 0.93337_r8,0.93615_r8,0.94220_r8,0.94937_r8,0.95647_r8,0.96292_r8,0.96840_r8,0.97283_r8, & 0.97619_r8,0.97854_r8/ data (bm3i( 8, 9,ibeta ), ibeta=1,10)/ & 0.97790_r8,0.97891_r8,0.98105_r8,0.98346_r8,0.98569_r8,0.98751_r8,0.98879_r8,0.98950_r8, & 0.98961_r8,0.98912_r8/ data (bm3i( 8,10,ibeta ), ibeta=1,10)/ & 0.99337_r8,0.99367_r8,0.99430_r8,0.99493_r8,0.99541_r8,0.99562_r8,0.99551_r8,0.99501_r8, & 0.99410_r8,0.99274_r8/ data (bm3i( 9, 1,ibeta ), ibeta=1,10)/ & 0.98470_r8,0.98594_r8,0.98844_r8,0.99106_r8,0.99334_r8,0.99514_r8,0.99650_r8,0.99749_r8, & 0.99821_r8,0.99872_r8/ data (bm3i( 9, 2,ibeta ), ibeta=1,10)/ & 0.98184_r8,0.98330_r8,0.98624_r8,0.98934_r8,0.99205_r8,0.99420_r8,0.99582_r8,0.99701_r8, & 0.99787_r8,0.99848_r8/ data (bm3i( 9, 3,ibeta ), ibeta=1,10)/ & 0.97288_r8,0.97498_r8,0.97927_r8,0.98385_r8,0.98789_r8,0.99113_r8,0.99360_r8,0.99541_r8, & 0.99673_r8,0.99766_r8/ data (bm3i( 9, 4,ibeta ), ibeta=1,10)/ & 0.95403_r8,0.95741_r8,0.96440_r8,0.97202_r8,0.97887_r8,0.98444_r8,0.98872_r8,0.99190_r8, & 0.99421_r8,0.99586_r8/ data (bm3i( 9, 5,ibeta ), ibeta=1,10)/ & 0.91845_r8,0.92399_r8,0.93567_r8,0.94873_r8,0.96076_r8,0.97079_r8,0.97865_r8,0.98457_r8, & 0.98892_r8,0.99206_r8/ data (bm3i( 9, 6,ibeta ), ibeta=1,10)/ & 0.86762_r8,0.87533_r8,0.89202_r8,0.91148_r8,0.93027_r8,0.94669_r8,0.96013_r8,0.97062_r8, & 0.97855_r8,0.98441_r8/ data (bm3i( 9, 7,ibeta ), ibeta=1,10)/ & 0.84550_r8,0.85253_r8,0.86816_r8,0.88721_r8,0.90671_r8,0.92490_r8,0.94083_r8,0.95413_r8, & 0.96481_r8,0.97314_r8/ data (bm3i( 9, 8,ibeta ), ibeta=1,10)/ & 0.90138_r8,0.90544_r8,0.91437_r8,0.92513_r8,0.93602_r8,0.94615_r8,0.95506_r8,0.96258_r8, & 0.96868_r8,0.97347_r8/ data (bm3i( 9, 9,ibeta ), ibeta=1,10)/ & 0.96248_r8,0.96415_r8,0.96773_r8,0.97187_r8,0.97583_r8,0.97925_r8,0.98198_r8,0.98394_r8, & 0.98514_r8,0.98559_r8/ data (bm3i( 9,10,ibeta ), ibeta=1,10)/ & 0.98837_r8,0.98892_r8,0.99005_r8,0.99127_r8,0.99232_r8,0.99306_r8,0.99339_r8,0.99328_r8, & 0.99269_r8,0.99161_r8/ data (bm3i(10, 1,ibeta ), ibeta=1,10)/ & 0.99080_r8,0.99158_r8,0.99311_r8,0.99471_r8,0.99607_r8,0.99715_r8,0.99795_r8,0.99853_r8, & 0.99895_r8,0.99925_r8/ data (bm3i(10, 2,ibeta ), ibeta=1,10)/ & 0.98910_r8,0.99001_r8,0.99182_r8,0.99371_r8,0.99533_r8,0.99661_r8,0.99757_r8,0.99826_r8, & 0.99876_r8,0.99912_r8/ data (bm3i(10, 3,ibeta ), ibeta=1,10)/ & 0.98374_r8,0.98506_r8,0.98772_r8,0.99051_r8,0.99294_r8,0.99486_r8,0.99630_r8,0.99736_r8, & 0.99812_r8,0.99866_r8/ data (bm3i(10, 4,ibeta ), ibeta=1,10)/ & 0.97238_r8,0.97453_r8,0.97892_r8,0.98361_r8,0.98773_r8,0.99104_r8,0.99354_r8,0.99538_r8, & 0.99671_r8,0.99765_r8/ data (bm3i(10, 5,ibeta ), ibeta=1,10)/ & 0.94961_r8,0.95333_r8,0.96103_r8,0.96941_r8,0.97693_r8,0.98303_r8,0.98772_r8,0.99119_r8, & 0.99371_r8,0.99551_r8/ data (bm3i(10, 6,ibeta ), ibeta=1,10)/ & 0.90943_r8,0.91550_r8,0.92834_r8,0.94275_r8,0.95608_r8,0.96723_r8,0.97600_r8,0.98263_r8, & 0.98751_r8,0.99103_r8/ data (bm3i(10, 7,ibeta ), ibeta=1,10)/ & 0.86454_r8,0.87200_r8,0.88829_r8,0.90749_r8,0.92630_r8,0.94300_r8,0.95687_r8,0.96785_r8, & 0.97626_r8,0.98254_r8/ data (bm3i(10, 8,ibeta ), ibeta=1,10)/ & 0.87498_r8,0.88048_r8,0.89264_r8,0.90737_r8,0.92240_r8,0.93642_r8,0.94877_r8,0.95917_r8, & 0.96762_r8,0.97429_r8/ data (bm3i(10, 9,ibeta ), ibeta=1,10)/ & 0.93946_r8,0.94209_r8,0.94781_r8,0.95452_r8,0.96111_r8,0.96704_r8,0.97203_r8,0.97602_r8, & 0.97900_r8,0.98106_r8/ data (bm3i(10,10,ibeta ), ibeta=1,10)/ & 0.97977_r8,0.98071_r8,0.98270_r8,0.98492_r8,0.98695_r8,0.98858_r8,0.98970_r8,0.99027_r8, & 0.99026_r8,0.98968_r8/ ! fsb fm correction for intramodal m2 coagulation data bm2ii / & 0.707107_r8, 0.720583_r8, 0.745310_r8, 0.748056_r8, 0.696935_r8, & 0.604164_r8, 0.504622_r8, 0.416559_r8, 0.343394_r8, 0.283641_r8/ ! *** total correction for intramodal m2 coagulation data bm2iitt / & 1.000000_r8, 0.907452_r8, 0.680931_r8, 0.409815_r8, 0.196425_r8, & 0.078814_r8, 0.028473_r8, 0.009800_r8, 0.003322_r8, 0.001129_r8/ ! fsb fm correction for m2 i to j coagulation data (bm2ij ( 1, 1,ibeta), ibeta = 1,10) / & 0.707107_r8, 0.716828_r8, 0.738240_r8, 0.764827_r8, 0.793610_r8, & 0.822843_r8, 0.851217_r8, 0.877670_r8, 0.901404_r8, 0.921944_r8/ data (bm2ij ( 1, 2,ibeta), ibeta = 1,10) / & 0.719180_r8, 0.727975_r8, 0.747638_r8, 0.772334_r8, 0.799234_r8, & 0.826666_r8, 0.853406_r8, 0.878482_r8, 0.901162_r8, 0.920987_r8/ data (bm2ij ( 1, 3,ibeta), ibeta = 1,10) / & 0.760947_r8, 0.767874_r8, 0.783692_r8, 0.803890_r8, 0.826015_r8, & 0.848562_r8, 0.870498_r8, 0.891088_r8, 0.909823_r8, 0.926400_r8/ data (bm2ij ( 1, 4,ibeta), ibeta = 1,10) / & 0.830926_r8, 0.836034_r8, 0.847708_r8, 0.862528_r8, 0.878521_r8, & 0.894467_r8, 0.909615_r8, 0.923520_r8, 0.935959_r8, 0.946858_r8/ data (bm2ij ( 1, 5,ibeta), ibeta = 1,10) / & 0.903643_r8, 0.907035_r8, 0.914641_r8, 0.924017_r8, 0.933795_r8, & 0.943194_r8, 0.951806_r8, 0.959449_r8, 0.966087_r8, 0.971761_r8/ data (bm2ij ( 1, 6,ibeta), ibeta = 1,10) / & 0.954216_r8, 0.956094_r8, 0.960211_r8, 0.965123_r8, 0.970068_r8, & 0.974666_r8, 0.978750_r8, 0.982277_r8, 0.985268_r8, 0.987775_r8/ data (bm2ij ( 1, 7,ibeta), ibeta = 1,10) / & 0.980546_r8, 0.981433_r8, 0.983343_r8, 0.985568_r8, 0.987751_r8, & 0.989735_r8, 0.991461_r8, 0.992926_r8, 0.994150_r8, 0.995164_r8/ data (bm2ij ( 1, 8,ibeta), ibeta = 1,10) / & 0.992142_r8, 0.992524_r8, 0.993338_r8, 0.994272_r8, 0.995174_r8, & 0.995981_r8, 0.996675_r8, 0.997257_r8, 0.997740_r8, 0.998137_r8/ data (bm2ij ( 1, 9,ibeta), ibeta = 1,10) / & 0.996868_r8, 0.997026_r8, 0.997361_r8, 0.997742_r8, 0.998106_r8, & 0.998430_r8, 0.998705_r8, 0.998935_r8, 0.999125_r8, 0.999280_r8/ data (bm2ij ( 1, 10,ibeta), ibeta = 1,10) / & 0.998737_r8, 0.998802_r8, 0.998939_r8, 0.999094_r8, 0.999241_r8, & 0.999371_r8, 0.999481_r8, 0.999573_r8, 0.999648_r8, 0.999709_r8/ data (bm2ij ( 2, 1,ibeta), ibeta = 1,10) / & 0.729600_r8, 0.739948_r8, 0.763059_r8, 0.791817_r8, 0.822510_r8, & 0.852795_r8, 0.881000_r8, 0.905999_r8, 0.927206_r8, 0.944532_r8/ data (bm2ij ( 2, 2,ibeta), ibeta = 1,10) / & 0.727025_r8, 0.737116_r8, 0.759615_r8, 0.787657_r8, 0.817740_r8, & 0.847656_r8, 0.875801_r8, 0.901038_r8, 0.922715_r8, 0.940643_r8/ data (bm2ij ( 2, 3,ibeta), ibeta = 1,10) / & 0.738035_r8, 0.746779_r8, 0.766484_r8, 0.791340_r8, 0.818324_r8, & 0.845546_r8, 0.871629_r8, 0.895554_r8, 0.916649_r8, 0.934597_r8/ data (bm2ij ( 2, 4,ibeta), ibeta = 1,10) / & 0.784185_r8, 0.790883_r8, 0.806132_r8, 0.825501_r8, 0.846545_r8, & 0.867745_r8, 0.888085_r8, 0.906881_r8, 0.923705_r8, 0.938349_r8/ data (bm2ij ( 2, 5,ibeta), ibeta = 1,10) / & 0.857879_r8, 0.862591_r8, 0.873238_r8, 0.886539_r8, 0.900645_r8, & 0.914463_r8, 0.927360_r8, 0.939004_r8, 0.949261_r8, 0.958125_r8/ data (bm2ij ( 2, 6,ibeta), ibeta = 1,10) / & 0.925441_r8, 0.928304_r8, 0.934645_r8, 0.942324_r8, 0.950181_r8, & 0.957600_r8, 0.964285_r8, 0.970133_r8, 0.975147_r8, 0.979388_r8/ data (bm2ij ( 2, 7,ibeta), ibeta = 1,10) / & 0.966728_r8, 0.968176_r8, 0.971323_r8, 0.975027_r8, 0.978705_r8, & 0.982080_r8, 0.985044_r8, 0.987578_r8, 0.989710_r8, 0.991485_r8/ data (bm2ij ( 2, 8,ibeta), ibeta = 1,10) / & 0.986335_r8, 0.986980_r8, 0.988362_r8, 0.989958_r8, 0.991511_r8, & 0.992912_r8, 0.994122_r8, 0.995143_r8, 0.995992_r8, 0.996693_r8/ data (bm2ij ( 2, 9,ibeta), ibeta = 1,10) / & 0.994547_r8, 0.994817_r8, 0.995391_r8, 0.996046_r8, 0.996677_r8, & 0.997238_r8, 0.997719_r8, 0.998122_r8, 0.998454_r8, 0.998727_r8/ data (bm2ij ( 2, 10,ibeta), ibeta = 1,10) / & 0.997817_r8, 0.997928_r8, 0.998163_r8, 0.998429_r8, 0.998683_r8, & 0.998908_r8, 0.999099_r8, 0.999258_r8, 0.999389_r8, 0.999497_r8/ data (bm2ij ( 3, 1,ibeta), ibeta = 1,10) / & 0.783612_r8, 0.793055_r8, 0.814468_r8, 0.841073_r8, 0.868769_r8, & 0.894963_r8, 0.918118_r8, 0.937527_r8, 0.953121_r8, 0.965244_r8/ data (bm2ij ( 3, 2,ibeta), ibeta = 1,10) / & 0.772083_r8, 0.781870_r8, 0.803911_r8, 0.831238_r8, 0.859802_r8, & 0.887036_r8, 0.911349_r8, 0.931941_r8, 0.948649_r8, 0.961751_r8/ data (bm2ij ( 3, 3,ibeta), ibeta = 1,10) / & 0.755766_r8, 0.765509_r8, 0.787380_r8, 0.814630_r8, 0.843526_r8, & 0.871670_r8, 0.897443_r8, 0.919870_r8, 0.938557_r8, 0.953576_r8/ data (bm2ij ( 3, 4,ibeta), ibeta = 1,10) / & 0.763816_r8, 0.772145_r8, 0.790997_r8, 0.814784_r8, 0.840434_r8, & 0.865978_r8, 0.890034_r8, 0.911671_r8, 0.930366_r8, 0.945963_r8/ data (bm2ij ( 3, 5,ibeta), ibeta = 1,10) / & 0.813597_r8, 0.819809_r8, 0.833889_r8, 0.851618_r8, 0.870640_r8, & 0.889514_r8, 0.907326_r8, 0.923510_r8, 0.937768_r8, 0.950003_r8/ data (bm2ij ( 3, 6,ibeta), ibeta = 1,10) / & 0.886317_r8, 0.890437_r8, 0.899643_r8, 0.910955_r8, 0.922730_r8, & 0.934048_r8, 0.944422_r8, 0.953632_r8, 0.961624_r8, 0.968444_r8/ data (bm2ij ( 3, 7,ibeta), ibeta = 1,10) / & 0.944565_r8, 0.946855_r8, 0.951872_r8, 0.957854_r8, 0.963873_r8, & 0.969468_r8, 0.974438_r8, 0.978731_r8, 0.982372_r8, 0.985424_r8/ data (bm2ij ( 3, 8,ibeta), ibeta = 1,10) / & 0.976358_r8, 0.977435_r8, 0.979759_r8, 0.982467_r8, 0.985125_r8, & 0.987540_r8, 0.989642_r8, 0.991425_r8, 0.992916_r8, 0.994150_r8/ data (bm2ij ( 3, 9,ibeta), ibeta = 1,10) / & 0.990471_r8, 0.990932_r8, 0.991917_r8, 0.993048_r8, 0.994142_r8, & 0.995121_r8, 0.995964_r8, 0.996671_r8, 0.997258_r8, 0.997740_r8/ data (bm2ij ( 3, 10,ibeta), ibeta = 1,10) / & 0.996199_r8, 0.996389_r8, 0.996794_r8, 0.997254_r8, 0.997694_r8, & 0.998086_r8, 0.998420_r8, 0.998699_r8, 0.998929_r8, 0.999117_r8/ data (bm2ij ( 4, 1,ibeta), ibeta = 1,10) / & 0.844355_r8, 0.852251_r8, 0.869914_r8, 0.891330_r8, 0.912823_r8, & 0.932259_r8, 0.948642_r8, 0.961767_r8, 0.971897_r8, 0.979510_r8/ data (bm2ij ( 4, 2,ibeta), ibeta = 1,10) / & 0.831550_r8, 0.839954_r8, 0.858754_r8, 0.881583_r8, 0.904592_r8, & 0.925533_r8, 0.943309_r8, 0.957647_r8, 0.968779_r8, 0.977185_r8/ data (bm2ij ( 4, 3,ibeta), ibeta = 1,10) / & 0.803981_r8, 0.813288_r8, 0.834060_r8, 0.859400_r8, 0.885285_r8, & 0.909286_r8, 0.930084_r8, 0.947193_r8, 0.960714_r8, 0.971078_r8/ data (bm2ij ( 4, 4,ibeta), ibeta = 1,10) / & 0.781787_r8, 0.791080_r8, 0.811931_r8, 0.837749_r8, 0.864768_r8, & 0.890603_r8, 0.913761_r8, 0.933477_r8, 0.949567_r8, 0.962261_r8/ data (bm2ij ( 4, 5,ibeta), ibeta = 1,10) / & 0.791591_r8, 0.799355_r8, 0.816916_r8, 0.838961_r8, 0.862492_r8, & 0.885595_r8, 0.907003_r8, 0.925942_r8, 0.942052_r8, 0.955310_r8/ data (bm2ij ( 4, 6,ibeta), ibeta = 1,10) / & 0.844933_r8, 0.850499_r8, 0.863022_r8, 0.878593_r8, 0.895038_r8, & 0.911072_r8, 0.925939_r8, 0.939227_r8, 0.950765_r8, 0.960550_r8/ data (bm2ij ( 4, 7,ibeta), ibeta = 1,10) / & 0.912591_r8, 0.916022_r8, 0.923607_r8, 0.932777_r8, 0.942151_r8, & 0.951001_r8, 0.958976_r8, 0.965950_r8, 0.971924_r8, 0.976965_r8/ data (bm2ij ( 4, 8,ibeta), ibeta = 1,10) / & 0.959859_r8, 0.961617_r8, 0.965433_r8, 0.969924_r8, 0.974382_r8, & 0.978472_r8, 0.982063_r8, 0.985134_r8, 0.987716_r8, 0.989865_r8/ data (bm2ij ( 4, 9,ibeta), ibeta = 1,10) / & 0.983377_r8, 0.984162_r8, 0.985844_r8, 0.987788_r8, 0.989681_r8, & 0.991386_r8, 0.992860_r8, 0.994104_r8, 0.995139_r8, 0.995991_r8/ data (bm2ij ( 4, 10,ibeta), ibeta = 1,10) / & 0.993343_r8, 0.993672_r8, 0.994370_r8, 0.995169_r8, 0.995937_r8, & 0.996622_r8, 0.997209_r8, 0.997700_r8, 0.998106_r8, 0.998439_r8/ data (bm2ij ( 5, 1,ibeta), ibeta = 1,10) / & 0.895806_r8, 0.901918_r8, 0.915233_r8, 0.930783_r8, 0.945768_r8, & 0.958781_r8, 0.969347_r8, 0.977540_r8, 0.983697_r8, 0.988225_r8/ data (bm2ij ( 5, 2,ibeta), ibeta = 1,10) / & 0.885634_r8, 0.892221_r8, 0.906629_r8, 0.923540_r8, 0.939918_r8, & 0.954213_r8, 0.965873_r8, 0.974951_r8, 0.981794_r8, 0.986840_r8/ data (bm2ij ( 5, 3,ibeta), ibeta = 1,10) / & 0.860120_r8, 0.867858_r8, 0.884865_r8, 0.904996_r8, 0.924724_r8, & 0.942177_r8, 0.956602_r8, 0.967966_r8, 0.976616_r8, 0.983043_r8/ data (bm2ij ( 5, 4,ibeta), ibeta = 1,10) / & 0.827462_r8, 0.836317_r8, 0.855885_r8, 0.879377_r8, 0.902897_r8, & 0.924232_r8, 0.942318_r8, 0.956900_r8, 0.968222_r8, 0.976774_r8/ data (bm2ij ( 5, 5,ibeta), ibeta = 1,10) / & 0.805527_r8, 0.814279_r8, 0.833853_r8, 0.857892_r8, 0.882726_r8, & 0.906095_r8, 0.926690_r8, 0.943938_r8, 0.957808_r8, 0.968615_r8/ data (bm2ij ( 5, 6,ibeta), ibeta = 1,10) / & 0.820143_r8, 0.827223_r8, 0.843166_r8, 0.863002_r8, 0.883905_r8, & 0.904128_r8, 0.922585_r8, 0.938687_r8, 0.952222_r8, 0.963255_r8/ data (bm2ij ( 5, 7,ibeta), ibeta = 1,10) / & 0.875399_r8, 0.880208_r8, 0.890929_r8, 0.904065_r8, 0.917699_r8, & 0.930756_r8, 0.942656_r8, 0.953131_r8, 0.962113_r8, 0.969657_r8/ data (bm2ij ( 5, 8,ibeta), ibeta = 1,10) / & 0.934782_r8, 0.937520_r8, 0.943515_r8, 0.950656_r8, 0.957840_r8, & 0.964516_r8, 0.970446_r8, 0.975566_r8, 0.979905_r8, 0.983534_r8/ data (bm2ij ( 5, 9,ibeta), ibeta = 1,10) / & 0.971369_r8, 0.972679_r8, 0.975505_r8, 0.978797_r8, 0.982029_r8, & 0.984964_r8, 0.987518_r8, 0.989685_r8, 0.991496_r8, 0.992994_r8/ data (bm2ij ( 5, 10,ibeta), ibeta = 1,10) / & 0.988329_r8, 0.988893_r8, 0.990099_r8, 0.991485_r8, 0.992825_r8, & 0.994025_r8, 0.995058_r8, 0.995925_r8, 0.996643_r8, 0.997234_r8/ data (bm2ij ( 6, 1,ibeta), ibeta = 1,10) / & 0.933384_r8, 0.937784_r8, 0.947130_r8, 0.957655_r8, 0.967430_r8, & 0.975639_r8, 0.982119_r8, 0.987031_r8, 0.990657_r8, 0.993288_r8/ data (bm2ij ( 6, 2,ibeta), ibeta = 1,10) / & 0.926445_r8, 0.931227_r8, 0.941426_r8, 0.952975_r8, 0.963754_r8, & 0.972845_r8, 0.980044_r8, 0.985514_r8, 0.989558_r8, 0.992498_r8/ data (bm2ij ( 6, 3,ibeta), ibeta = 1,10) / & 0.907835_r8, 0.913621_r8, 0.926064_r8, 0.940308_r8, 0.953745_r8, & 0.965189_r8, 0.974327_r8, 0.981316_r8, 0.986510_r8, 0.990297_r8/ data (bm2ij ( 6, 4,ibeta), ibeta = 1,10) / & 0.879088_r8, 0.886306_r8, 0.901945_r8, 0.920079_r8, 0.937460_r8, & 0.952509_r8, 0.964711_r8, 0.974166_r8, 0.981265_r8, 0.986484_r8/ data (bm2ij ( 6, 5,ibeta), ibeta = 1,10) / & 0.846500_r8, 0.854862_r8, 0.873189_r8, 0.894891_r8, 0.916264_r8, & 0.935315_r8, 0.951197_r8, 0.963812_r8, 0.973484_r8, 0.980715_r8/ data (bm2ij ( 6, 6,ibeta), ibeta = 1,10) / & 0.828137_r8, 0.836250_r8, 0.854310_r8, 0.876287_r8, 0.898710_r8, & 0.919518_r8, 0.937603_r8, 0.952560_r8, 0.964461_r8, 0.973656_r8/ data (bm2ij ( 6, 7,ibeta), ibeta = 1,10) / & 0.848595_r8, 0.854886_r8, 0.868957_r8, 0.886262_r8, 0.904241_r8, & 0.921376_r8, 0.936799_r8, 0.950096_r8, 0.961172_r8, 0.970145_r8/ data (bm2ij ( 6, 8,ibeta), ibeta = 1,10) / & 0.902919_r8, 0.906922_r8, 0.915760_r8, 0.926427_r8, 0.937312_r8, & 0.947561_r8, 0.956758_r8, 0.964747_r8, 0.971525_r8, 0.977175_r8/ data (bm2ij ( 6, 9,ibeta), ibeta = 1,10) / & 0.952320_r8, 0.954434_r8, 0.959021_r8, 0.964418_r8, 0.969774_r8, & 0.974688_r8, 0.979003_r8, 0.982690_r8, 0.985789_r8, 0.988364_r8/ data (bm2ij ( 6, 10,ibeta), ibeta = 1,10) / & 0.979689_r8, 0.980650_r8, 0.982712_r8, 0.985093_r8, 0.987413_r8, & 0.989502_r8, 0.991308_r8, 0.992831_r8, 0.994098_r8, 0.995142_r8/ data (bm2ij ( 7, 1,ibeta), ibeta = 1,10) / & 0.958611_r8, 0.961598_r8, 0.967817_r8, 0.974620_r8, 0.980752_r8, & 0.985771_r8, 0.989650_r8, 0.992543_r8, 0.994653_r8, 0.996171_r8/ data (bm2ij ( 7, 2,ibeta), ibeta = 1,10) / & 0.954225_r8, 0.957488_r8, 0.964305_r8, 0.971795_r8, 0.978576_r8, & 0.984144_r8, 0.988458_r8, 0.991681_r8, 0.994034_r8, 0.995728_r8/ data (bm2ij ( 7, 3,ibeta), ibeta = 1,10) / & 0.942147_r8, 0.946158_r8, 0.954599_r8, 0.963967_r8, 0.972529_r8, & 0.979612_r8, 0.985131_r8, 0.989271_r8, 0.992301_r8, 0.994487_r8/ data (bm2ij ( 7, 4,ibeta), ibeta = 1,10) / & 0.921821_r8, 0.927048_r8, 0.938140_r8, 0.950598_r8, 0.962118_r8, & 0.971752_r8, 0.979326_r8, 0.985046_r8, 0.989254_r8, 0.992299_r8/ data (bm2ij ( 7, 5,ibeta), ibeta = 1,10) / & 0.893419_r8, 0.900158_r8, 0.914598_r8, 0.931070_r8, 0.946584_r8, & 0.959795_r8, 0.970350_r8, 0.978427_r8, 0.984432_r8, 0.988811_r8/ data (bm2ij ( 7, 6,ibeta), ibeta = 1,10) / & 0.863302_r8, 0.871111_r8, 0.888103_r8, 0.907990_r8, 0.927305_r8, & 0.944279_r8, 0.958245_r8, 0.969211_r8, 0.977540_r8, 0.983720_r8/ data (bm2ij ( 7, 7,ibeta), ibeta = 1,10) / & 0.850182_r8, 0.857560_r8, 0.873890_r8, 0.893568_r8, 0.913408_r8, & 0.931591_r8, 0.947216_r8, 0.960014_r8, 0.970121_r8, 0.977886_r8/ data (bm2ij ( 7, 8,ibeta), ibeta = 1,10) / & 0.875837_r8, 0.881265_r8, 0.893310_r8, 0.907936_r8, 0.922910_r8, & 0.936977_r8, 0.949480_r8, 0.960154_r8, 0.968985_r8, 0.976111_r8/ data (bm2ij ( 7, 9,ibeta), ibeta = 1,10) / & 0.926228_r8, 0.929445_r8, 0.936486_r8, 0.944868_r8, 0.953293_r8, & 0.961108_r8, 0.968028_r8, 0.973973_r8, 0.978974_r8, 0.983118_r8/ data (bm2ij ( 7, 10,ibeta), ibeta = 1,10) / & 0.965533_r8, 0.967125_r8, 0.970558_r8, 0.974557_r8, 0.978484_r8, & 0.982050_r8, 0.985153_r8, 0.987785_r8, 0.989982_r8, 0.991798_r8/ data (bm2ij ( 8, 1,ibeta), ibeta = 1,10) / & 0.974731_r8, 0.976674_r8, 0.980660_r8, 0.984926_r8, 0.988689_r8, & 0.991710_r8, 0.994009_r8, 0.995703_r8, 0.996929_r8, 0.997805_r8/ data (bm2ij ( 8, 2,ibeta), ibeta = 1,10) / & 0.972062_r8, 0.974192_r8, 0.978571_r8, 0.983273_r8, 0.987432_r8, & 0.990780_r8, 0.993333_r8, 0.995218_r8, 0.996581_r8, 0.997557_r8/ data (bm2ij ( 8, 3,ibeta), ibeta = 1,10) / & 0.964662_r8, 0.967300_r8, 0.972755_r8, 0.978659_r8, 0.983921_r8, & 0.988181_r8, 0.991444_r8, 0.993859_r8, 0.995610_r8, 0.996863_r8/ data (bm2ij ( 8, 4,ibeta), ibeta = 1,10) / & 0.951782_r8, 0.955284_r8, 0.962581_r8, 0.970559_r8, 0.977737_r8, & 0.983593_r8, 0.988103_r8, 0.991454_r8, 0.993889_r8, 0.995635_r8/ data (bm2ij ( 8, 5,ibeta), ibeta = 1,10) / & 0.931947_r8, 0.936723_r8, 0.946751_r8, 0.957843_r8, 0.967942_r8, & 0.976267_r8, 0.982734_r8, 0.987571_r8, 0.991102_r8, 0.993642_r8/ data (bm2ij ( 8, 6,ibeta), ibeta = 1,10) / & 0.905410_r8, 0.911665_r8, 0.924950_r8, 0.939908_r8, 0.953798_r8, & 0.965469_r8, 0.974684_r8, 0.981669_r8, 0.986821_r8, 0.990556_r8/ data (bm2ij ( 8, 7,ibeta), ibeta = 1,10) / & 0.878941_r8, 0.886132_r8, 0.901679_r8, 0.919688_r8, 0.936970_r8, & 0.951980_r8, 0.964199_r8, 0.973709_r8, 0.980881_r8, 0.986174_r8/ data (bm2ij ( 8, 8,ibeta), ibeta = 1,10) / & 0.871653_r8, 0.878218_r8, 0.892652_r8, 0.909871_r8, 0.927034_r8, & 0.942592_r8, 0.955836_r8, 0.966604_r8, 0.975065_r8, 0.981545_r8/ data (bm2ij ( 8, 9,ibeta), ibeta = 1,10) / & 0.900693_r8, 0.905239_r8, 0.915242_r8, 0.927232_r8, 0.939335_r8, & 0.950555_r8, 0.960420_r8, 0.968774_r8, 0.975651_r8, 0.981188_r8/ data (bm2ij ( 8, 10,ibeta), ibeta = 1,10) / & 0.944922_r8, 0.947435_r8, 0.952894_r8, 0.959317_r8, 0.965689_r8, & 0.971529_r8, 0.976645_r8, 0.981001_r8, 0.984641_r8, 0.987642_r8/ data (bm2ij ( 9, 1,ibeta), ibeta = 1,10) / & 0.984736_r8, 0.985963_r8, 0.988453_r8, 0.991078_r8, 0.993357_r8, & 0.995161_r8, 0.996519_r8, 0.997512_r8, 0.998226_r8, 0.998734_r8/ data (bm2ij ( 9, 2,ibeta), ibeta = 1,10) / & 0.983141_r8, 0.984488_r8, 0.987227_r8, 0.990119_r8, 0.992636_r8, & 0.994632_r8, 0.996137_r8, 0.997238_r8, 0.998030_r8, 0.998595_r8/ data (bm2ij ( 9, 3,ibeta), ibeta = 1,10) / & 0.978726_r8, 0.980401_r8, 0.983819_r8, 0.987450_r8, 0.990626_r8, & 0.993157_r8, 0.995071_r8, 0.996475_r8, 0.997486_r8, 0.998206_r8/ data (bm2ij ( 9, 4,ibeta), ibeta = 1,10) / & 0.970986_r8, 0.973224_r8, 0.977818_r8, 0.982737_r8, 0.987072_r8, & 0.990546_r8, 0.993184_r8, 0.995124_r8, 0.996523_r8, 0.997521_r8/ data (bm2ij ( 9, 5,ibeta), ibeta = 1,10) / & 0.958579_r8, 0.961700_r8, 0.968149_r8, 0.975116_r8, 0.981307_r8, & 0.986301_r8, 0.990112_r8, 0.992923_r8, 0.994954_r8, 0.996404_r8/ data (bm2ij ( 9, 6,ibeta), ibeta = 1,10) / & 0.940111_r8, 0.944479_r8, 0.953572_r8, 0.963506_r8, 0.972436_r8, & 0.979714_r8, 0.985313_r8, 0.989468_r8, 0.992483_r8, 0.994641_r8/ data (bm2ij ( 9, 7,ibeta), ibeta = 1,10) / & 0.916127_r8, 0.921878_r8, 0.934003_r8, 0.947506_r8, 0.959899_r8, & 0.970199_r8, 0.978255_r8, 0.984314_r8, 0.988755_r8, 0.991960_r8/ data (bm2ij ( 9, 8,ibeta), ibeta = 1,10) / & 0.893848_r8, 0.900364_r8, 0.914368_r8, 0.930438_r8, 0.945700_r8, & 0.958824_r8, 0.969416_r8, 0.977603_r8, 0.983746_r8, 0.988262_r8/ data (bm2ij ( 9, 9,ibeta), ibeta = 1,10) / & 0.892161_r8, 0.897863_r8, 0.910315_r8, 0.925021_r8, 0.939523_r8, & 0.952544_r8, 0.963544_r8, 0.972442_r8, 0.979411_r8, 0.984742_r8/ data (bm2ij ( 9, 10,ibeta), ibeta = 1,10) / & 0.922260_r8, 0.925966_r8, 0.934047_r8, 0.943616_r8, 0.953152_r8, & 0.961893_r8, 0.969506_r8, 0.975912_r8, 0.981167_r8, 0.985394_r8/ data (bm2ij ( 10, 1,ibeta), ibeta = 1,10) / & 0.990838_r8, 0.991598_r8, 0.993128_r8, 0.994723_r8, 0.996092_r8, & 0.997167_r8, 0.997969_r8, 0.998552_r8, 0.998969_r8, 0.999265_r8/ data (bm2ij ( 10, 2,ibeta), ibeta = 1,10) / & 0.989892_r8, 0.990727_r8, 0.992411_r8, 0.994167_r8, 0.995678_r8, & 0.996864_r8, 0.997751_r8, 0.998396_r8, 0.998858_r8, 0.999186_r8/ data (bm2ij ( 10, 3,ibeta), ibeta = 1,10) / & 0.987287_r8, 0.988327_r8, 0.990428_r8, 0.992629_r8, 0.994529_r8, & 0.996026_r8, 0.997148_r8, 0.997965_r8, 0.998551_r8, 0.998967_r8/ data (bm2ij ( 10, 4,ibeta), ibeta = 1,10) / & 0.982740_r8, 0.984130_r8, 0.986952_r8, 0.989926_r8, 0.992508_r8, & 0.994551_r8, 0.996087_r8, 0.997208_r8, 0.998012_r8, 0.998584_r8/ data (bm2ij ( 10, 5,ibeta), ibeta = 1,10) / & 0.975380_r8, 0.977330_r8, 0.981307_r8, 0.985529_r8, 0.989216_r8, & 0.992147_r8, 0.994358_r8, 0.995975_r8, 0.997136_r8, 0.997961_r8/ data (bm2ij ( 10, 6,ibeta), ibeta = 1,10) / & 0.963911_r8, 0.966714_r8, 0.972465_r8, 0.978614_r8, 0.984022_r8, & 0.988346_r8, 0.991620_r8, 0.994020_r8, 0.995747_r8, 0.996974_r8/ data (bm2ij ( 10, 7,ibeta), ibeta = 1,10) / & 0.947187_r8, 0.951161_r8, 0.959375_r8, 0.968258_r8, 0.976160_r8, & 0.982540_r8, 0.987409_r8, 0.991000_r8, 0.993592_r8, 0.995441_r8/ data (bm2ij ( 10, 8,ibeta), ibeta = 1,10) / & 0.926045_r8, 0.931270_r8, 0.942218_r8, 0.954297_r8, 0.965273_r8, & 0.974311_r8, 0.981326_r8, 0.986569_r8, 0.990394_r8, 0.993143_r8/ data (bm2ij ( 10, 9,ibeta), ibeta = 1,10) / & 0.908092_r8, 0.913891_r8, 0.926288_r8, 0.940393_r8, 0.953667_r8, & 0.964987_r8, 0.974061_r8, 0.981038_r8, 0.986253_r8, 0.990078_r8/ data (bm2ij ( 10, 10,ibeta), ibeta = 1,10) / & 0.911143_r8, 0.915972_r8, 0.926455_r8, 0.938721_r8, 0.950701_r8, & 0.961370_r8, 0.970329_r8, 0.977549_r8, 0.983197_r8, 0.987518_r8/ ! fsb total correction factor for m2 coagulation j from i data (bm2ji( 1, 1,ibeta), ibeta = 1,10) / & 0.753466_r8, 0.756888_r8, 0.761008_r8, 0.759432_r8, 0.748675_r8, & 0.726951_r8, 0.693964_r8, 0.650915_r8, 0.600227_r8, 0.545000_r8/ data (bm2ji( 1, 2,ibeta), ibeta = 1,10) / & 0.824078_r8, 0.828698_r8, 0.835988_r8, 0.838943_r8, 0.833454_r8, & 0.817148_r8, 0.789149_r8, 0.750088_r8, 0.701887_r8, 0.647308_r8/ data (bm2ji( 1, 3,ibeta), ibeta = 1,10) / & 1.007389_r8, 1.014362_r8, 1.028151_r8, 1.041011_r8, 1.047939_r8, & 1.045707_r8, 1.032524_r8, 1.007903_r8, 0.972463_r8, 0.927667_r8/ data (bm2ji( 1, 4,ibeta), ibeta = 1,10) / & 1.246157_r8, 1.255135_r8, 1.274249_r8, 1.295351_r8, 1.313362_r8, & 1.325187_r8, 1.329136_r8, 1.324491_r8, 1.311164_r8, 1.289459_r8/ data (bm2ji( 1, 5,ibeta), ibeta = 1,10) / & 1.450823_r8, 1.459551_r8, 1.478182_r8, 1.499143_r8, 1.518224_r8, & 1.533312_r8, 1.543577_r8, 1.548882_r8, 1.549395_r8, 1.545364_r8/ data (bm2ji( 1, 6,ibeta), ibeta = 1,10) / & 1.575248_r8, 1.581832_r8, 1.595643_r8, 1.610866_r8, 1.624601_r8, & 1.635690_r8, 1.643913_r8, 1.649470_r8, 1.652688_r8, 1.653878_r8/ data (bm2ji( 1, 7,ibeta), ibeta = 1,10) / & 1.638426_r8, 1.642626_r8, 1.651293_r8, 1.660641_r8, 1.668926_r8, & 1.675571_r8, 1.680572_r8, 1.684147_r8, 1.686561_r8, 1.688047_r8/ data (bm2ji( 1, 8,ibeta), ibeta = 1,10) / & 1.669996_r8, 1.672392_r8, 1.677283_r8, 1.682480_r8, 1.687028_r8, & 1.690651_r8, 1.693384_r8, 1.695372_r8, 1.696776_r8, 1.697734_r8/ data (bm2ji( 1, 9,ibeta), ibeta = 1,10) / & 1.686148_r8, 1.687419_r8, 1.689993_r8, 1.692704_r8, 1.695057_r8, & 1.696922_r8, 1.698329_r8, 1.699359_r8, 1.700099_r8, 1.700621_r8/ data (bm2ji( 1,10,ibeta), ibeta = 1,10) / & 1.694364_r8, 1.695010_r8, 1.696313_r8, 1.697676_r8, 1.698853_r8, & 1.699782_r8, 1.700482_r8, 1.700996_r8, 1.701366_r8, 1.701631_r8/ data (bm2ji( 2, 1,ibeta), ibeta = 1,10) / & 0.783166_r8, 0.779369_r8, 0.768044_r8, 0.747572_r8, 0.716709_r8, & 0.675422_r8, 0.624981_r8, 0.567811_r8, 0.507057_r8, 0.445975_r8/ data (bm2ji( 2, 2,ibeta), ibeta = 1,10) / & 0.848390_r8, 0.847100_r8, 0.840874_r8, 0.826065_r8, 0.800296_r8, & 0.762625_r8, 0.713655_r8, 0.655545_r8, 0.591603_r8, 0.525571_r8/ data (bm2ji( 2, 3,ibeta), ibeta = 1,10) / & 1.039894_r8, 1.043786_r8, 1.049445_r8, 1.049664_r8, 1.039407_r8, & 1.015322_r8, 0.975983_r8, 0.922180_r8, 0.856713_r8, 0.783634_r8/ data (bm2ji( 2, 4,ibeta), ibeta = 1,10) / & 1.345995_r8, 1.356064_r8, 1.376947_r8, 1.398304_r8, 1.412685_r8, & 1.414611_r8, 1.400652_r8, 1.369595_r8, 1.322261_r8, 1.260993_r8/ data (bm2ji( 2, 5,ibeta), ibeta = 1,10) / & 1.675575_r8, 1.689859_r8, 1.720957_r8, 1.756659_r8, 1.788976_r8, & 1.812679_r8, 1.824773_r8, 1.824024_r8, 1.810412_r8, 1.784630_r8/ data (bm2ji( 2, 6,ibeta), ibeta = 1,10) / & 1.919835_r8, 1.933483_r8, 1.962973_r8, 1.996810_r8, 2.028377_r8, & 2.054172_r8, 2.072763_r8, 2.083963_r8, 2.088190_r8, 2.086052_r8/ data (bm2ji( 2, 7,ibeta), ibeta = 1,10) / & 2.064139_r8, 2.074105_r8, 2.095233_r8, 2.118909_r8, 2.140688_r8, & 2.158661_r8, 2.172373_r8, 2.182087_r8, 2.188330_r8, 2.191650_r8/ data (bm2ji( 2, 8,ibeta), ibeta = 1,10) / & 2.144871_r8, 2.150990_r8, 2.163748_r8, 2.177731_r8, 2.190364_r8, & 2.200712_r8, 2.208687_r8, 2.214563_r8, 2.218716_r8, 2.221502_r8/ data (bm2ji( 2, 9,ibeta), ibeta = 1,10) / & 2.189223_r8, 2.192595_r8, 2.199540_r8, 2.207033_r8, 2.213706_r8, & 2.219125_r8, 2.223297_r8, 2.226403_r8, 2.228660_r8, 2.230265_r8/ data (bm2ji( 2,10,ibeta), ibeta = 1,10) / & 2.212595_r8, 2.214342_r8, 2.217912_r8, 2.221723_r8, 2.225082_r8, & 2.227791_r8, 2.229869_r8, 2.231417_r8, 2.232551_r8, 2.233372_r8/ data (bm2ji( 3, 1,ibeta), ibeta = 1,10) / & 0.837870_r8, 0.824476_r8, 0.793119_r8, 0.750739_r8, 0.700950_r8, & 0.646691_r8, 0.590508_r8, 0.534354_r8, 0.479532_r8, 0.426856_r8/ data (bm2ji( 3, 2,ibeta), ibeta = 1,10) / & 0.896771_r8, 0.885847_r8, 0.859327_r8, 0.821694_r8, 0.775312_r8, & 0.722402_r8, 0.665196_r8, 0.605731_r8, 0.545742_r8, 0.486687_r8/ data (bm2ji( 3, 3,ibeta), ibeta = 1,10) / & 1.076089_r8, 1.071727_r8, 1.058845_r8, 1.036171_r8, 1.002539_r8, & 0.957521_r8, 0.901640_r8, 0.836481_r8, 0.764597_r8, 0.689151_r8/ data (bm2ji( 3, 4,ibeta), ibeta = 1,10) / & 1.409571_r8, 1.415168_r8, 1.425346_r8, 1.432021_r8, 1.428632_r8, & 1.409696_r8, 1.371485_r8, 1.312958_r8, 1.236092_r8, 1.145293_r8/ data (bm2ji( 3, 5,ibeta), ibeta = 1,10) / & 1.862757_r8, 1.880031_r8, 1.918394_r8, 1.963456_r8, 2.004070_r8, & 2.030730_r8, 2.036144_r8, 2.016159_r8, 1.970059_r8, 1.900079_r8/ data (bm2ji( 3, 6,ibeta), ibeta = 1,10) / & 2.289741_r8, 2.313465_r8, 2.366789_r8, 2.431612_r8, 2.495597_r8, & 2.549838_r8, 2.588523_r8, 2.608665_r8, 2.609488_r8, 2.591662_r8/ data (bm2ji( 3, 7,ibeta), ibeta = 1,10) / & 2.597157_r8, 2.618731_r8, 2.666255_r8, 2.722597_r8, 2.777531_r8, & 2.825187_r8, 2.862794_r8, 2.889648_r8, 2.906199_r8, 2.913380_r8/ data (bm2ji( 3, 8,ibeta), ibeta = 1,10) / & 2.797975_r8, 2.813116_r8, 2.845666_r8, 2.882976_r8, 2.918289_r8, & 2.948461_r8, 2.972524_r8, 2.990687_r8, 3.003664_r8, 3.012284_r8/ data (bm2ji( 3, 9,ibeta), ibeta = 1,10) / & 2.920832_r8, 2.929843_r8, 2.948848_r8, 2.970057_r8, 2.989632_r8, & 3.006057_r8, 3.019067_r8, 3.028979_r8, 3.036307_r8, 3.041574_r8/ data (bm2ji( 3,10,ibeta), ibeta = 1,10) / & 2.989627_r8, 2.994491_r8, 3.004620_r8, 3.015720_r8, 3.025789_r8, & 3.034121_r8, 3.040664_r8, 3.045641_r8, 3.049347_r8, 3.052066_r8/ data (bm2ji( 4, 1,ibeta), ibeta = 1,10) / & 0.893179_r8, 0.870897_r8, 0.820996_r8, 0.759486_r8, 0.695488_r8, & 0.634582_r8, 0.579818_r8, 0.532143_r8, 0.490927_r8, 0.454618_r8/ data (bm2ji( 4, 2,ibeta), ibeta = 1,10) / & 0.948355_r8, 0.927427_r8, 0.880215_r8, 0.821146_r8, 0.758524_r8, & 0.697680_r8, 0.641689_r8, 0.591605_r8, 0.546919_r8, 0.506208_r8/ data (bm2ji( 4, 3,ibeta), ibeta = 1,10) / & 1.109562_r8, 1.093648_r8, 1.056438_r8, 1.007310_r8, 0.951960_r8, & 0.894453_r8, 0.837364_r8, 0.781742_r8, 0.727415_r8, 0.673614_r8/ data (bm2ji( 4, 4,ibeta), ibeta = 1,10) / & 1.423321_r8, 1.417557_r8, 1.402442_r8, 1.379079_r8, 1.347687_r8, & 1.308075_r8, 1.259703_r8, 1.201983_r8, 1.134778_r8, 1.058878_r8/ data (bm2ji( 4, 5,ibeta), ibeta = 1,10) / & 1.933434_r8, 1.944347_r8, 1.968765_r8, 1.997653_r8, 2.023054_r8, & 2.036554_r8, 2.029949_r8, 1.996982_r8, 1.934982_r8, 1.845473_r8/ data (bm2ji( 4, 6,ibeta), ibeta = 1,10) / & 2.547772_r8, 2.577105_r8, 2.645918_r8, 2.735407_r8, 2.830691_r8, & 2.917268_r8, 2.981724_r8, 3.013684_r8, 3.007302_r8, 2.961560_r8/ data (bm2ji( 4, 7,ibeta), ibeta = 1,10) / & 3.101817_r8, 3.139271_r8, 3.225851_r8, 3.336402_r8, 3.453409_r8, & 3.563116_r8, 3.655406_r8, 3.724014_r8, 3.766113_r8, 3.781394_r8/ data (bm2ji( 4, 8,ibeta), ibeta = 1,10) / & 3.540920_r8, 3.573780_r8, 3.647439_r8, 3.737365_r8, 3.828468_r8, & 3.911436_r8, 3.981317_r8, 4.036345_r8, 4.076749_r8, 4.103751_r8/ data (bm2ji( 4, 9,ibeta), ibeta = 1,10) / & 3.856771_r8, 3.879363_r8, 3.928579_r8, 3.986207_r8, 4.042173_r8, & 4.091411_r8, 4.132041_r8, 4.164052_r8, 4.188343_r8, 4.206118_r8/ data (bm2ji( 4,10,ibeta), ibeta = 1,10) / & 4.053923_r8, 4.067191_r8, 4.095509_r8, 4.127698_r8, 4.158037_r8, & 4.184055_r8, 4.205135_r8, 4.221592_r8, 4.234115_r8, 4.243463_r8/ data (bm2ji( 5, 1,ibeta), ibeta = 1,10) / & 0.935846_r8, 0.906814_r8, 0.843358_r8, 0.768710_r8, 0.695885_r8, & 0.631742_r8, 0.579166_r8, 0.538471_r8, 0.508410_r8, 0.486863_r8/ data (bm2ji( 5, 2,ibeta), ibeta = 1,10) / & 0.988308_r8, 0.959524_r8, 0.896482_r8, 0.821986_r8, 0.748887_r8, & 0.684168_r8, 0.630908_r8, 0.589516_r8, 0.558676_r8, 0.536056_r8/ data (bm2ji( 5, 3,ibeta), ibeta = 1,10) / & 1.133795_r8, 1.107139_r8, 1.048168_r8, 0.977258_r8, 0.906341_r8, & 0.842477_r8, 0.789093_r8, 0.746731_r8, 0.713822_r8, 0.687495_r8/ data (bm2ji( 5, 4,ibeta), ibeta = 1,10) / & 1.405692_r8, 1.385781_r8, 1.340706_r8, 1.284776_r8, 1.227085_r8, & 1.173532_r8, 1.127008_r8, 1.087509_r8, 1.052712_r8, 1.018960_r8/ data (bm2ji( 5, 5,ibeta), ibeta = 1,10) / & 1.884992_r8, 1.879859_r8, 1.868463_r8, 1.854995_r8, 1.841946_r8, & 1.829867_r8, 1.816972_r8, 1.799319_r8, 1.771754_r8, 1.729406_r8/ data (bm2ji( 5, 6,ibeta), ibeta = 1,10) / & 2.592275_r8, 2.612268_r8, 2.661698_r8, 2.731803_r8, 2.815139_r8, & 2.901659_r8, 2.978389_r8, 3.031259_r8, 3.048045_r8, 3.021122_r8/ data (bm2ji( 5, 7,ibeta), ibeta = 1,10) / & 3.390321_r8, 3.435519_r8, 3.545615_r8, 3.698419_r8, 3.876958_r8, & 4.062790_r8, 4.236125_r8, 4.378488_r8, 4.475619_r8, 4.519170_r8/ data (bm2ji( 5, 8,ibeta), ibeta = 1,10) / & 4.161376_r8, 4.216558_r8, 4.346896_r8, 4.519451_r8, 4.711107_r8, & 4.902416_r8, 5.077701_r8, 5.226048_r8, 5.341423_r8, 5.421764_r8/ data (bm2ji( 5, 9,ibeta), ibeta = 1,10) / & 4.843961_r8, 4.892035_r8, 5.001492_r8, 5.138515_r8, 5.281684_r8, & 5.416805_r8, 5.535493_r8, 5.634050_r8, 5.712063_r8, 5.770996_r8/ data (bm2ji( 5,10,ibeta), ibeta = 1,10) / & 5.352093_r8, 5.385119_r8, 5.458056_r8, 5.545311_r8, 5.632162_r8, & 5.710566_r8, 5.777005_r8, 5.830863_r8, 5.873123_r8, 5.905442_r8/ data (bm2ji( 6, 1,ibeta), ibeta = 1,10) / & 0.964038_r8, 0.930794_r8, 0.859433_r8, 0.777776_r8, 0.700566_r8, & 0.634671_r8, 0.582396_r8, 0.543656_r8, 0.517284_r8, 0.501694_r8/ data (bm2ji( 6, 2,ibeta), ibeta = 1,10) / & 1.013416_r8, 0.979685_r8, 0.907197_r8, 0.824135_r8, 0.745552_r8, & 0.678616_r8, 0.625870_r8, 0.587348_r8, 0.561864_r8, 0.547674_r8/ data (bm2ji( 6, 3,ibeta), ibeta = 1,10) / & 1.145452_r8, 1.111457_r8, 1.038152_r8, 0.953750_r8, 0.873724_r8, & 0.805955_r8, 0.753621_r8, 0.717052_r8, 0.694920_r8, 0.684910_r8/ data (bm2ji( 6, 4,ibeta), ibeta = 1,10) / & 1.376547_r8, 1.345004_r8, 1.276415_r8, 1.196704_r8, 1.121091_r8, & 1.058249_r8, 1.012197_r8, 0.983522_r8, 0.970323_r8, 0.968933_r8/ data (bm2ji( 6, 5,ibeta), ibeta = 1,10) / & 1.778801_r8, 1.755897_r8, 1.706074_r8, 1.649008_r8, 1.597602_r8, & 1.560087_r8, 1.540365_r8, 1.538205_r8, 1.549738_r8, 1.568333_r8/ data (bm2ji( 6, 6,ibeta), ibeta = 1,10) / & 2.447603_r8, 2.445172_r8, 2.443762_r8, 2.451842_r8, 2.475877_r8, & 2.519039_r8, 2.580118_r8, 2.653004_r8, 2.727234_r8, 2.789738_r8/ data (bm2ji( 6, 7,ibeta), ibeta = 1,10) / & 3.368490_r8, 3.399821_r8, 3.481357_r8, 3.606716_r8, 3.772101_r8, & 3.969416_r8, 4.184167_r8, 4.396163_r8, 4.582502_r8, 4.721838_r8/ data (bm2ji( 6, 8,ibeta), ibeta = 1,10) / & 4.426458_r8, 4.489861_r8, 4.648250_r8, 4.877510_r8, 5.160698_r8, & 5.477495_r8, 5.803123_r8, 6.111250_r8, 6.378153_r8, 6.586050_r8/ data (bm2ji( 6, 9,ibeta), ibeta = 1,10) / & 5.568061_r8, 5.644988_r8, 5.829837_r8, 6.081532_r8, 6.371214_r8, & 6.672902_r8, 6.963737_r8, 7.226172_r8, 7.449199_r8, 7.627886_r8/ data (bm2ji( 6,10,ibeta), ibeta = 1,10) / & 6.639152_r8, 6.707020_r8, 6.863974_r8, 7.065285_r8, 7.281744_r8, & 7.492437_r8, 7.683587_r8, 7.847917_r8, 7.983296_r8, 8.090977_r8/ data (bm2ji( 7, 1,ibeta), ibeta = 1,10) / & 0.980853_r8, 0.945724_r8, 0.871244_r8, 0.787311_r8, 0.708818_r8, & 0.641987_r8, 0.588462_r8, 0.547823_r8, 0.518976_r8, 0.500801_r8/ data (bm2ji( 7, 2,ibeta), ibeta = 1,10) / & 1.026738_r8, 0.990726_r8, 0.914306_r8, 0.828140_r8, 0.747637_r8, & 0.679351_r8, 0.625127_r8, 0.584662_r8, 0.556910_r8, 0.540749_r8/ data (bm2ji( 7, 3,ibeta), ibeta = 1,10) / & 1.146496_r8, 1.108808_r8, 1.028695_r8, 0.938291_r8, 0.854101_r8, & 0.783521_r8, 0.728985_r8, 0.690539_r8, 0.667272_r8, 0.657977_r8/ data (bm2ji( 7, 4,ibeta), ibeta = 1,10) / & 1.344846_r8, 1.306434_r8, 1.224543_r8, 1.132031_r8, 1.046571_r8, & 0.976882_r8, 0.926488_r8, 0.896067_r8, 0.884808_r8, 0.891027_r8/ data (bm2ji( 7, 5,ibeta), ibeta = 1,10) / & 1.670227_r8, 1.634583_r8, 1.558421_r8, 1.472939_r8, 1.396496_r8, & 1.339523_r8, 1.307151_r8, 1.300882_r8, 1.319622_r8, 1.360166_r8/ data (bm2ji( 7, 6,ibeta), ibeta = 1,10) / & 2.224548_r8, 2.199698_r8, 2.148284_r8, 2.095736_r8, 2.059319_r8, & 2.050496_r8, 2.075654_r8, 2.136382_r8, 2.229641_r8, 2.347958_r8/ data (bm2ji( 7, 7,ibeta), ibeta = 1,10) / & 3.104483_r8, 3.105947_r8, 3.118398_r8, 3.155809_r8, 3.230427_r8, & 3.350585_r8, 3.519071_r8, 3.731744_r8, 3.976847_r8, 4.235616_r8/ data (bm2ji( 7, 8,ibeta), ibeta = 1,10) / & 4.288426_r8, 4.331456_r8, 4.447024_r8, 4.633023_r8, 4.891991_r8, & 5.221458_r8, 5.610060_r8, 6.036467_r8, 6.471113_r8, 6.880462_r8/ data (bm2ji( 7, 9,ibeta), ibeta = 1,10) / & 5.753934_r8, 5.837061_r8, 6.048530_r8, 6.363800_r8, 6.768061_r8, & 7.241280_r8, 7.755346_r8, 8.276666_r8, 8.771411_r8, 9.210826_r8/ data (bm2ji( 7,10,ibeta), ibeta = 1,10) / & 7.466219_r8, 7.568810_r8, 7.819032_r8, 8.168340_r8, 8.582973_r8, & 9.030174_r8, 9.478159_r8, 9.899834_r8, 10.275940_r8, 10.595910_r8/ data (bm2ji( 8, 1,ibeta), ibeta = 1,10) / & 0.990036_r8, 0.954782_r8, 0.880531_r8, 0.797334_r8, 0.719410_r8, & 0.652220_r8, 0.596923_r8, 0.552910_r8, 0.519101_r8, 0.494529_r8/ data (bm2ji( 8, 2,ibeta), ibeta = 1,10) / & 1.032428_r8, 0.996125_r8, 0.919613_r8, 0.833853_r8, 0.753611_r8, & 0.684644_r8, 0.628260_r8, 0.583924_r8, 0.550611_r8, 0.527407_r8/ data (bm2ji( 8, 3,ibeta), ibeta = 1,10) / & 1.141145_r8, 1.102521_r8, 1.021017_r8, 0.929667_r8, 0.844515_r8, & 0.772075_r8, 0.714086_r8, 0.670280_r8, 0.639824_r8, 0.621970_r8/ data (bm2ji( 8, 4,ibeta), ibeta = 1,10) / & 1.314164_r8, 1.273087_r8, 1.186318_r8, 1.089208_r8, 0.999476_r8, & 0.924856_r8, 0.867948_r8, 0.829085_r8, 0.807854_r8, 0.803759_r8/ data (bm2ji( 8, 5,ibeta), ibeta = 1,10) / & 1.580611_r8, 1.538518_r8, 1.449529_r8, 1.350459_r8, 1.260910_r8, & 1.190526_r8, 1.143502_r8, 1.121328_r8, 1.124274_r8, 1.151974_r8/ data (bm2ji( 8, 6,ibeta), ibeta = 1,10) / & 2.016773_r8, 1.977721_r8, 1.895727_r8, 1.806974_r8, 1.732891_r8, & 1.685937_r8, 1.673026_r8, 1.697656_r8, 1.761039_r8, 1.862391_r8/ data (bm2ji( 8, 7,ibeta), ibeta = 1,10) / & 2.750093_r8, 2.723940_r8, 2.672854_r8, 2.628264_r8, 2.612250_r8, & 2.640406_r8, 2.723211_r8, 2.866599_r8, 3.071893_r8, 3.335217_r8/ data (bm2ji( 8, 8,ibeta), ibeta = 1,10) / & 3.881905_r8, 3.887143_r8, 3.913667_r8, 3.981912_r8, 4.111099_r8, & 4.316575_r8, 4.608146_r8, 4.988157_r8, 5.449592_r8, 5.974848_r8/ data (bm2ji( 8, 9,ibeta), ibeta = 1,10) / & 5.438870_r8, 5.492742_r8, 5.640910_r8, 5.886999_r8, 6.241641_r8, & 6.710609_r8, 7.289480_r8, 7.960725_r8, 8.693495_r8, 9.446644_r8/ data (bm2ji( 8,10,ibeta), ibeta = 1,10) / & 7.521152_r8, 7.624621_r8, 7.892039_r8, 8.300444_r8, 8.839787_r8, & 9.493227_r8, 10.231770_r8, 11.015642_r8, 11.799990_r8, 12.542260_r8/ data (bm2ji( 9, 1,ibeta), ibeta = 1,10) / & 0.994285_r8, 0.960012_r8, 0.887939_r8, 0.807040_r8, 0.730578_r8, & 0.663410_r8, 0.606466_r8, 0.559137_r8, 0.520426_r8, 0.489429_r8/ data (bm2ji( 9, 2,ibeta), ibeta = 1,10) / & 1.033505_r8, 0.998153_r8, 0.923772_r8, 0.840261_r8, 0.761383_r8, & 0.692242_r8, 0.633873_r8, 0.585709_r8, 0.546777_r8, 0.516215_r8/ data (bm2ji( 9, 3,ibeta), ibeta = 1,10) / & 1.132774_r8, 1.094907_r8, 1.015161_r8, 0.925627_r8, 0.841293_r8, & 0.767888_r8, 0.706741_r8, 0.657439_r8, 0.619135_r8, 0.591119_r8/ data (bm2ji( 9, 4,ibeta), ibeta = 1,10) / & 1.286308_r8, 1.245273_r8, 1.158809_r8, 1.061889_r8, 0.971208_r8, & 0.893476_r8, 0.830599_r8, 0.782561_r8, 0.748870_r8, 0.729198_r8/ data (bm2ji( 9, 5,ibeta), ibeta = 1,10) / & 1.511105_r8, 1.467141_r8, 1.374520_r8, 1.271162_r8, 1.175871_r8, & 1.096887_r8, 1.037243_r8, 0.997820_r8, 0.978924_r8, 0.980962_r8/ data (bm2ji( 9, 6,ibeta), ibeta = 1,10) / & 1.857468_r8, 1.812177_r8, 1.717002_r8, 1.612197_r8, 1.519171_r8, & 1.448660_r8, 1.405871_r8, 1.393541_r8, 1.413549_r8, 1.467532_r8/ data (bm2ji( 9, 7,ibeta), ibeta = 1,10) / & 2.430619_r8, 2.388452_r8, 2.301326_r8, 2.210241_r8, 2.139724_r8, & 2.104571_r8, 2.114085_r8, 2.174696_r8, 2.291294_r8, 2.467500_r8/ data (bm2ji( 9, 8,ibeta), ibeta = 1,10) / & 3.385332_r8, 3.357690_r8, 3.306611_r8, 3.269804_r8, 3.274462_r8, & 3.340862_r8, 3.484609_r8, 3.717740_r8, 4.048748_r8, 4.481588_r8/ data (bm2ji( 9, 9,ibeta), ibeta = 1,10) / & 4.850497_r8, 4.858280_r8, 4.896008_r8, 4.991467_r8, 5.171511_r8, & 5.459421_r8, 5.873700_r8, 6.426128_r8, 7.119061_r8, 7.942603_r8/ data (bm2ji( 9,10,ibeta), ibeta = 1,10) / & 6.957098_r8, 7.020164_r8, 7.197272_r8, 7.499331_r8, 7.946554_r8, & 8.555048_r8, 9.330503_r8, 10.263610_r8, 11.327454_r8, 12.478332_r8/ data (bm2ji(10, 1,ibeta), ibeta = 1,10) / & 0.994567_r8, 0.961842_r8, 0.892854_r8, 0.814874_r8, 0.740198_r8, & 0.673303_r8, 0.615105_r8, 0.565139_r8, 0.522558_r8, 0.486556_r8/ data (bm2ji(10, 2,ibeta), ibeta = 1,10) / & 1.031058_r8, 0.997292_r8, 0.926082_r8, 0.845571_r8, 0.768501_r8, & 0.699549_r8, 0.639710_r8, 0.588538_r8, 0.545197_r8, 0.508894_r8/ data (bm2ji(10, 3,ibeta), ibeta = 1,10) / & 1.122535_r8, 1.086287_r8, 1.009790_r8, 0.923292_r8, 0.840626_r8, & 0.766982_r8, 0.703562_r8, 0.650004_r8, 0.605525_r8, 0.569411_r8/ data (bm2ji(10, 4,ibeta), ibeta = 1,10) / & 1.261142_r8, 1.221555_r8, 1.137979_r8, 1.043576_r8, 0.953745_r8, & 0.874456_r8, 0.807292_r8, 0.752109_r8, 0.708326_r8, 0.675477_r8/ data (bm2ji(10, 5,ibeta), ibeta = 1,10) / & 1.456711_r8, 1.413432_r8, 1.322096_r8, 1.219264_r8, 1.122319_r8, & 1.038381_r8, 0.969743_r8, 0.916811_r8, 0.879544_r8, 0.858099_r8/ data (bm2ji(10, 6,ibeta), ibeta = 1,10) / & 1.741792_r8, 1.695157_r8, 1.596897_r8, 1.487124_r8, 1.385734_r8, & 1.301670_r8, 1.238638_r8, 1.198284_r8, 1.181809_r8, 1.190689_r8/ data (bm2ji(10, 7,ibeta), ibeta = 1,10) / & 2.190197_r8, 2.141721_r8, 2.040226_r8, 1.929245_r8, 1.832051_r8, & 1.760702_r8, 1.721723_r8, 1.719436_r8, 1.757705_r8, 1.840677_r8/ data (bm2ji(10, 8,ibeta), ibeta = 1,10) / & 2.940764_r8, 2.895085_r8, 2.801873_r8, 2.707112_r8, 2.638603_r8, & 2.613764_r8, 2.644686_r8, 2.741255_r8, 2.912790_r8, 3.168519_r8/ data (bm2ji(10, 9,ibeta), ibeta = 1,10) / & 4.186191_r8, 4.155844_r8, 4.101953_r8, 4.069102_r8, 4.089886_r8, & 4.189530_r8, 4.389145_r8, 4.707528_r8, 5.161567_r8, 5.765283_r8/ data (bm2ji(10,10,ibeta), ibeta = 1,10) / & 6.119526_r8, 6.127611_r8, 6.171174_r8, 6.286528_r8, 6.508738_r8, & 6.869521_r8, 7.396912_r8, 8.113749_r8, 9.034683_r8, 10.162190_r8/ ! *** end of data statements. ! *** start calculations: constii = abs( half * ( two ) ** two3rds - one ) sqrttwo = sqrt(two) dlgsqt2 = one / log( sqrttwo ) esat01 = exp( 0.125_r8 * xxlsgat * xxlsgat ) esac01 = exp( 0.125_r8 * xxlsgac * xxlsgac ) esat04 = esat01 ** 4 esac04 = esac01 ** 4 esat05 = esat04 * esat01 esac05 = esac04 * esac01 esat08 = esat04 * esat04 esac08 = esac04 * esac04 esat09 = esat08 * esat01 esac09 = esac08 * esac01 esat16 = esat08 * esat08 esac16 = esac08 * esac08 esat20 = esat16 * esat04 esac20 = esac16 * esac04 esat24 = esat20 * esat04 esac24 = esac20 * esac04 esat25 = esat20 * esat05 esac25 = esac20 * esac05 esat36 = esat20 * esat16 esac36 = esac20 * esac16 esat49 = esat24 * esat25 esat64 = esat20 * esat20 * esat24 esac64 = esac20 * esac20 * esac24 esat100 = esat64 * esat36 dgat2 = dgatk * dgatk dgat3 = dgatk * dgatk * dgatk dgac2 = dgacc * dgacc dgac3 = dgacc * dgacc * dgacc sqdgat = sqrt( dgatk ) sqdgac = sqrt( dgacc ) sqdgat5 = dgat2 * sqdgat sqdgac5 = dgac2 * sqdgac sqdgat7 = dgat3 * sqdgat xm2at = dgat2 * esat16 xm3at = dgat3 * esat36 xm2ac = dgac2 * esac16 xm3ac = dgac3 * esac36 ! *** for the free molecular regime: page h.3 of whitby et al. (1991) r = sqdgac / sqdgat r2 = r * r r3 = r2 * r rx4 = r2 * r2 r5 = r3 * r2 r6 = r3 * r3 rx8 = rx4 * rx4 ri1 = one / r ri2 = one / r2 ri3 = one / r3 ri4 = ri2 * ri2 kngat = two * lamda / dgatk kngac = two * lamda / dgacc ! *** calculate ratio of geometric mean diameters rat = dgacc / dgatk ! *** trap subscripts for bm0 and bm0i, between 1 and 10 ! see page h.5 of whitby et al. (1991) n2n = max( 1, min( 10, & nint( 4.0_r8 * ( sgatk - 0.75_r8 ) ) ) ) n2a = max( 1, min( 10, & nint( 4.0_r8 * ( sgacc - 0.75_r8 ) ) ) ) n1 = max( 1, min( 10, & 1 + nint( dlgsqt2 * log( rat ) ) ) ) ! *** intermodal coagulation ! *** set up for zeroeth moment ! *** near-continuum form: equation h.10a of whitby et al. (1991) coagnc0 = knc * ( & two + a * ( kngat * ( esat04 + r2 * esat16 * esac04 ) & + kngac * ( esac04 + ri2 * esac16 * esat04 ) ) & + ( r2 + ri2 ) * esat04 * esac04 ) ! *** free-molecular form: equation h.7a of whitby et al. (1991) coagfm0 = kfmatac * sqdgat * bm0ij(n1,n2n,n2a) * ( & esat01 + r * esac01 + two * r2 * esat01 * esac04 & + rx4 * esat09 * esac16 + ri3 * esat16 * esac09 & + two * ri1 * esat04 + esac01 ) ! *** loss to accumulation mode ! *** harmonic mean coagatac0 = coagnc0 * coagfm0 / ( coagnc0 + coagfm0 ) qn12 = coagatac0 ! *** set up for second moment ! the second moment equations are new and begin with equations a1 ! through a4 of binkowski and shankar (1995). after some algebraic ! rearrangement and application of the extended mean value theorem ! of integral calculus, equations are obtained that can be solved ! analytically with correction factors as has been done by ! whitby et al. (1991) ! *** the term ( dp1 + dp2 ) ** (2/3) in equations a3 and a4 of ! binkowski and shankar (1995) is approximated by ! (dgat ** 3 + dgac **3 ) ** 2/3 ! *** near-continuum form i1nc = knc * dgat2 * ( & two * esat16 & + r2 * esat04 * esac04 & + ri2 * esat36 * esac04 & + a * kngat * ( & esat04 & + ri2 * esat16 * esac04 & + ri4 * esat36 * esac16 & + r2 * esac04 ) ) ! *** free-molecular form i1fm = kfmatac * sqdgat5 * bm2ij(n1,n2n,n2a) * ( & esat25 & + two * r2 * esat09 * esac04 & + rx4 * esat01 * esac16 & + ri3 * esat64 * esac09 & + two * ri1 * esat36 * esac01 & + r * esat16 * esac01 ) ! *** loss to accumulation mode ! *** harmonic mean i1 = ( i1fm * i1nc ) / ( i1fm + i1nc ) coagatac2 = i1 qs12 = coagatac2 ! *** gain by accumulation mode coagacat2 = ( ( one + r6 ) ** two3rds - rx4 ) * i1 qs21 = coagacat2 * bm2ji(n1,n2n,n2a) ! *** set up for third moment ! *** near-continuum form: equation h.10b of whitby et al. (1991) coagnc3 = knc * dgat3 * ( & two * esat36 & + a * kngat * ( esat16 + r2 * esat04 * esac04 ) & + a * kngac * ( esat36 * esac04 + ri2 * esat64 * esac16 ) & + r2 * esat16 * esac04 + ri2 * esat64 * esac04 ) ! *** free_molecular form: equation h.7b of whitby et al. (1991) coagfm3 = kfmatac * sqdgat7 * bm3i( n1, n2n, n2a ) * ( & esat49 & + r * esat36 * esac01 & + two * r2 * esat25 * esac04 & + rx4 * esat09 * esac16 & + ri3 * esat100 * esac09 & + two * ri1 * esat64 * esac01 ) ! *** gain by accumulation mode = loss from aitken mode ! *** harmonic mean coagatac3 = coagnc3 * coagfm3 / ( coagnc3 + coagfm3 ) qv12 = coagatac3 ! *** intramodal coagulation ! *** zeroeth moment ! *** aitken mode ! *** near-continuum form: equation h.12a of whitby et al. (1991) coagnc_at = knc * (one + esat08 + a * kngat * (esat20 + esat04)) ! *** free-molecular form: equation h.11a of whitby et al. (1991) coagfm_at = kfmat * sqdgat * bm0(n2n) * & ( esat01 + esat25 + two * esat05 ) ! *** harmonic mean coagatat0 = coagfm_at * coagnc_at / ( coagfm_at + coagnc_at ) qn11 = coagatat0 ! *** accumulation mode ! *** near-continuum form: equation h.12a of whitby et al. (1991) coagnc_ac = knc * (one + esac08 + a * kngac * (esac20 + esac04)) ! *** free-molecular form: equation h.11a of whitby et al. (1991) coagfm_ac = kfmac * sqdgac * bm0(n2a) * & ( esac01 + esac25 + two * esac05 ) ! *** harmonic mean coagacac0 = coagfm_ac * coagnc_ac / ( coagfm_ac + coagnc_ac ) qn22 = coagacac0 ! *** set up for second moment ! the second moment equations are new and begin with 3.11a on page ! 45 of whitby et al. (1991). after some algebraic rearrangement and ! application of the extended mean value theorem of integral calculus ! equations are obtained that can be solved analytically with ! correction factors as has been done by whitby et al. (1991) ! *** aitken mode ! *** near-continuum i1nc_at = knc * dgat2 * ( & two * esat16 & + esat04 * esat04 & + esat36 * esat04 & + a * kngat * ( & two * esat04 & + esat16 * esat04 & + esat36 * esat16 ) ) ! *** free- molecular form i1fm_at = kfmat * sqdgat5 * bm2ii(n2n) * ( & esat25 & + two * esat09 * esat04 & + esat01 * esat16 & + esat64 * esat09 & + two * esat36 * esat01 & + esat16 * esat01 ) i1_at = ( i1nc_at * i1fm_at ) / ( i1nc_at + i1fm_at ) coagatat2 = constii * i1_at qs11 = coagatat2 * bm2iitt(n2n) ! *** accumulation mode ! *** near-continuum i1nc_ac = knc * dgac2 * ( & two * esac16 & + esac04 * esac04 & + esac36 * esac04 & + a * kngac * ( & two * esac04 & + esac16 * esac04 & + esac36 * esac16 ) ) ! *** free- molecular form i1fm_ac = kfmac * sqdgac5 * bm2ii(n2a) * ( & esac25 & + two * esac09 * esac04 & + esac01 * esac16 & + esac64 * esac09 & + two * esac36 * esac01 & + esac16 * esac01 ) i1_ac = ( i1nc_ac * i1fm_ac ) / ( i1nc_ac + i1fm_ac ) coagacac2 = constii * i1_ac qs22 = coagacac2 * bm2iitt(n2a) return end subroutine getcoags !---------------------------------------------------------------------- !---------------------------------------------------------------------- end module modal_aero_coag