module moldiff_mod implicit none contains subroutine moldiff(ngrid,nlayer,nq, & pplay,pplev,pt,pdt,pq,pdq,ptimestep, & zzlay,pdteuv,pdtconduc,pdqdiff) use tracer_mod, only: igcm_co2, igcm_co, igcm_o, igcm_o1d, & igcm_o2, igcm_o3, igcm_h, igcm_h2, igcm_oh, & igcm_ho2, igcm_h2o2, igcm_n2, igcm_ar, & igcm_h2o_vap, mmol use conc_mod, only: rnew, mmean use comcstfi_h, only: g use moldiffcoeff_mod, only: moldiffcoeff implicit none c c Input/Output c integer,intent(in) :: ngrid ! number of atmospheric columns integer,intent(in) :: nlayer ! number of atmospheric layers integer,intent(in) :: nq ! number of advected tracers real ptimestep real pplay(ngrid,nlayer) real zzlay(ngrid,nlayer) real pplev(ngrid,nlayer+1) real pq(ngrid,nlayer,nq) real pdq(ngrid,nlayer,nq) real pt(ngrid,nlayer) real pdt(ngrid,nlayer) real pdteuv(ngrid,nlayer) real pdtconduc(ngrid,nlayer) real pdqdiff(ngrid,nlayer,nq) c c Local c integer,parameter :: ncompmoldiff = 14 real hco2(ncompmoldiff),ho integer ig,nz,l,n,nn,iq real del1,del2, tmean ,dalfinvdz, d real hh,dcoef,dcoef1,ptfac, ntot, dens, dens2, dens3 real hp(nlayer) real tt(nlayer) real qq(nlayer,ncompmoldiff) real dmmeandz(nlayer) real qnew(nlayer,ncompmoldiff) real zlocal(nlayer) real alf(ncompmoldiff-1,ncompmoldiff-1) real alfinv(nlayer,ncompmoldiff-1,ncompmoldiff-1) real indx(ncompmoldiff-1) real b(nlayer,ncompmoldiff-1) real y(ncompmoldiff-1,ncompmoldiff-1) real aa(nlayer,ncompmoldiff-1,ncompmoldiff-1) real bb(nlayer,ncompmoldiff-1,ncompmoldiff-1) real cc(nlayer,ncompmoldiff-1,ncompmoldiff-1) real atri(nlayer-2) real btri(nlayer-2) real ctri(nlayer-2) real rtri(nlayer-2) real qtri(nlayer-2) real alfdiag(ncompmoldiff-1) real wi(ncompmoldiff), flux(ncompmoldiff), pote cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c tracer numbering in the molecular diffusion cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Atomic oxygen must always be the LAST species of the list as c it is the dominant species at high altitudes.  integer,parameter :: i_co = 1 integer,parameter :: i_n2 = 2 integer,parameter :: i_o2 = 3 integer,parameter :: i_co2 = 4 integer,parameter :: i_h2 = 5 integer,parameter :: i_h = 6 integer,parameter :: i_oh = 7 integer,parameter :: i_ho2 = 8 integer,parameter :: i_h2o = 9 integer,parameter :: i_h2o2 = 10 integer,parameter :: i_o1d = 11 integer,parameter :: i_o3 = 12 integer,parameter :: i_ar = 13 integer,parameter :: i_o = 14 ! Tracer indexes in the GCM: integer,save :: g_co2=0 integer,save :: g_co=0 integer,save :: g_o=0 integer,save :: g_o1d=0 integer,save :: g_o2=0 integer,save :: g_o3=0 integer,save :: g_h=0 integer,save :: g_h2=0 integer,save :: g_oh=0 integer,save :: g_ho2=0 integer,save :: g_h2o2=0 integer,save :: g_n2=0 integer,save :: g_ar=0 integer,save :: g_h2o=0 integer,save :: gcmind(ncompmoldiff) ! array of GCM indexes integer ierr logical,save :: firstcall=.true. real abfac(ncompmoldiff) real,save :: dij(ncompmoldiff,ncompmoldiff) !$OMP THREADPRIVATE(g_co2,g_co,g_o,g_o1d,g_o2,g_o3,g_h,g_h2) !$OMP THREADPRIVATE(g_oh,g_ho2,g_h2o2,g_n2,g_ar,g_h2o,gcmind) !$OMP THREADPRIVATE(firstcall,dij) ! Initializations at first call if (firstcall) then call moldiffcoeff(dij) print*,'MOLDIFF EXO' ! identify the indexes of the tracers we'll need g_co2=igcm_co2 if (g_co2.eq.0) then write(*,*) "moldiff: Error; no CO2 tracer !!!" stop endif g_co=igcm_co if (g_co.eq.0) then write(*,*) "moldiff: Error; no CO tracer !!!" stop endif g_o=igcm_o if (g_o.eq.0) then write(*,*) "moldiff: Error; no O tracer !!!" stop endif g_o1d=igcm_o1d if (g_o1d.eq.0) then write(*,*) "moldiff: Error; no O1D tracer !!!" stop endif g_o2=igcm_o2 if (g_o2.eq.0) then write(*,*) "moldiff: Error; no O2 tracer !!!" stop endif g_o3=igcm_o3 if (g_o3.eq.0) then write(*,*) "moldiff: Error; no O3 tracer !!!" stop endif g_h=igcm_h if (g_h.eq.0) then write(*,*) "moldiff: Error; no H tracer !!!" stop endif g_h2=igcm_h2 if (g_h2.eq.0) then write(*,*) "moldiff: Error; no H2 tracer !!!" stop endif g_oh=igcm_oh if (g_oh.eq.0) then write(*,*) "moldiff: Error; no OH tracer !!!" stop endif g_ho2=igcm_ho2 if (g_ho2.eq.0) then write(*,*) "moldiff: Error; no HO2 tracer !!!" stop endif g_h2o2=igcm_h2o2 if (g_h2o2.eq.0) then write(*,*) "moldiff: Error; no H2O2 tracer !!!" stop endif g_n2=igcm_n2 if (g_n2.eq.0) then write(*,*) "moldiff: Error; no N2 tracer !!!" stop endif g_ar=igcm_ar if (g_ar.eq.0) then write(*,*) "moldiff: Error; no AR tracer !!!" stop endif g_h2o=igcm_h2o_vap if (g_h2o.eq.0) then write(*,*) "moldiff: Error; no water vapor tracer !!!" stop endif cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c fill array to relate local indexes to gcm indexes cccccccccccccccccccccccccccccccccccccccccccccccccccccccc gcmind(i_co) = g_co gcmind(i_n2) = g_n2 gcmind(i_o2) = g_o2 gcmind(i_co2) = g_co2 gcmind(i_h2) = g_h2 gcmind(i_h) = g_h gcmind(i_oh) = g_oh gcmind(i_ho2) = g_ho2 gcmind(i_h2o) = g_h2o gcmind(i_h2o2) = g_h2o2 gcmind(i_o1d) = g_o1d gcmind(i_o3) = g_o3 gcmind(i_o) = g_o gcmind(i_ar) = g_ar firstcall= .false. endif ! of if (firstcall) c cccccccccccccccccccccccccccccccccccccccccccccccccccccccc nz=nlayer do ig=1,ngrid do l=2,nz-1 tt(l)=pt(ig,l)+pdt(ig,l)*ptimestep & +pdteuv(ig,l)*ptimestep & +pdtconduc(ig,l)*ptimestep do nn=1,ncompmoldiff qq(l,nn)=pq(ig,l,gcmind(nn))+pdq(ig,l,gcmind(nn))*ptimestep qq(l,nn)=max(qq(l,nn),1.e-30) enddo hp(l)=-log(pplay(ig,l+1)/pplay(ig,l-1)) dmmeandz(l)=(mmean(ig,l+1)-mmean(ig,l-1))/hp(l) enddo tt(1)=pt(ig,1) +pdt(ig,1)*ptimestep & +pdteuv(ig,1)*ptimestep & +pdtconduc(ig,1)*ptimestep tt(nz)=pt(ig,nz)+pdt(ig,nz)*ptimestep & +pdteuv(ig,nz)*ptimestep & +pdtconduc(ig,nz)*ptimestep do nn=1,ncompmoldiff qq(1,nn)=pq(ig,1,gcmind(nn))+pdq(ig,1,gcmind(nn))*ptimestep qq(nz,nn)=pq(ig,nz,gcmind(nn))+pdq(ig,nz,gcmind(nn))*ptimestep qq(1,nn)=max(qq(1,nn),1.e-30) qq(nz,nn)=max(qq(nz,nn),1.e-30) enddo hp(1)=-log(pplay(ig,2)/pplay(ig,1)) dmmeandz(1)=(-3.*mmean(ig,1)+4.*mmean(ig,2) & -mmean(ig,3))/(2.*hp(1)) hp(nz)=-log(pplay(ig,nz)/pplay(ig,nz-1)) dmmeandz(nz)=(3.*mmean(ig,nz)-4.*mmean(ig,nz-1) & +mmean(ig,nz-2))/(2.*hp(nz)) c c Setting-up matrix of alfa coefficients from Dickinson and Ridley 1972 c do l=1,nz if(abs(dmmeandz(l)) .lt. 1.e-5) dmmeandz(l)=0.0 hh=rnew(ig,l)*tt(l)/g ptfac=(1.e5/pplay(ig,l))*(tt(l)/273)**1.75 ntot=pplay(ig,l)/(1.381e-23*tt(l)) ! in #/m3 do nn=1,ncompmoldiff-1 ! rows alfdiag(nn)=0. dcoef1=dij(nn,i_o)*ptfac do n=1,ncompmoldiff-1 ! columns y(nn,n)=0. dcoef=dij(nn,n)*ptfac alf(nn,n)=qq(l,nn)/ntot/1.66e-27 & *(1./(mmol(gcmind(n))*dcoef)-1./(mmol(g_o)*dcoef1)) alfdiag(nn)=alfdiag(nn) & +(1./(mmol(gcmind(n))*dcoef)-1./(mmol(g_o)*dcoef1)) & *qq(l,n) enddo dcoef=dij(nn,nn)*ptfac alfdiag(nn)=alfdiag(nn) & -(1./(mmol(gcmind(nn))*dcoef)-1./(mmol(g_o)*dcoef1)) & *qq(l,nn) alf(nn,nn)=-(alfdiag(nn) & +1./(mmol(g_o)*dcoef1))/ntot/1.66e-27 y(nn,nn)=1. b(l,nn)=-(dmmeandz(l)/mmean(ig,l) & +mmol(gcmind(nn))/mmean(ig,l)-1.) enddo c c Inverting the alfa matrix c call ludcmp_sp(alf,ncompmoldiff-1,ncompmoldiff-1,indx,d,ierr) c TEMPORAIRE ***************************** if (ierr.ne.0) then write(*,*)'In moldiff: Problem in LUDCMP_SP with matrix alf' write(*,*) 'Singular matrix ?' c write(*,*) 'Matrix alf = ', alf write(*,*) 'ig, l=',ig, l write(*,*) 'No molecular diffusion this time !' pdqdiff(1:ngrid,1:nlayer,1:nq)=0 return c stop end if c ******************************************* do n=1,ncompmoldiff-1 call lubksb_sp(alf,ncompmoldiff-1,ncompmoldiff-1,indx,y(1,n)) do nn=1,ncompmoldiff-1 alfinv(l,nn,n)=y(nn,n)/hh enddo enddo enddo c c Calculating coefficients of the system c zlocal(1)=zzlay(ig,1) do l=2,nz-1 del1=hp(l)*pplay(ig,l)/(g*ptimestep) del2=(hp(l)/2)**2*pplay(ig,l)/(g*ptimestep) do nn=1,ncompmoldiff-1 do n=1,ncompmoldiff-1 dalfinvdz=(alfinv(l+1,nn,n)-alfinv(l-1,nn,n))/hp(l) aa(l,nn,n)=-dalfinvdz/del1+alfinv(l,nn,n)/del2 & +alfinv(l-1,nn,n)*b(l-1,n)/del1 bb(l,nn,n)=-2.*alfinv(l,nn,n)/del2 cc(l,nn,n)=dalfinvdz/del1+alfinv(l,nn,n)/del2 & -alfinv(l+1,nn,n)*b(l+1,n)/del1 enddo enddo zlocal(l)=zzlay(ig,l) enddo zlocal(nz)=zzlay(ig,nz) ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c Escape velocity from Jeans equation for the flux of H and H2 c (Hunten 1973, eq. 5) do n=1,ncompmoldiff wi(n)=1. flux(n)=0. abfac(n)=1. enddo dens=pplay(ig,nz)/(rnew(ig,nz)*tt(nz)) c c For H: c pote=(3398000.+zlocal(nz))/ & (1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h)*g)) wi(i_h)=sqrt(2.*1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h))) & /(2.*sqrt(3.1415))*(1.+pote)*exp(-pote) flux(i_h)=qq(nz,i_h)*dens/(1.6605e-27*mmol(g_h))*wi(i_h) flux(i_h)=flux(i_h)*1.6606e-27 abfac(i_h)=0. c c For H2: c pote=(3398000.+zlocal(nz))/ & (1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h2)*g)) wi(i_h2)=sqrt(2.*1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h2))) & /(2.*sqrt(3.1415))*(1.+pote)*exp(-pote) flux(i_h2)=qq(nz,i_h2)*dens/(1.6605e-27*mmol(g_h2))*wi(i_h2) flux(i_h2)=flux(i_h2)*1.6606e-27 abfac(i_h2)=0. c ********* TEMPORAIRE : no escape for h and h2 c do n=1,ncomptot c wi(n)=1. c flux(n)=0. c abfac(n)=1. c enddo c ******************************************** ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc c c Setting coefficients for tridiagonal matrix and solving the system c do nn=1,ncompmoldiff-1 do l=2,nz-1 atri(l-1)=aa(l,nn,nn) btri(l-1)=bb(l,nn,nn)+1. ctri(l-1)=cc(l,nn,nn) rtri(l-1)=qq(l,nn) do n=1,ncompmoldiff-1 rtri(l-1)=rtri(l-1)-(aa(l,nn,n)*qq(l-1,n) & +bb(l,nn,n)*qq(l,n) & +cc(l,nn,n)*qq(l+1,n)) enddo rtri(l-1)=rtri(l-1)+(aa(l,nn,nn)*qq(l-1,nn) & +bb(l,nn,nn)*qq(l,nn) & +cc(l,nn,nn)*qq(l+1,nn)) enddo c c Boundary conditions: c Escape flux for H and H2 at top c Diffusive equilibrium for the other species at top c Perfect mixing for all at bottom c rtri(nz-2)=rtri(nz-2) & -ctri(nz-2)*flux(nn)*mmol(gcmind(nn))/(dens*wi(nn)) atri(nz-2)=atri(nz-2) & -abfac(nn)*ctri(nz-2)/(3.-2.*hp(nz)*b(nz,nn)) btri(nz-2)=btri(nz-2) & +abfac(nn)*4.*ctri(nz-2)/(3.-2.*hp(nz)*b(nz,nn)) c rtri(1)=rtri(1)-atri(1)*qq(1,nn) btri(1)=btri(1)+atri(1) call tridag_sp(atri,btri,ctri,rtri,qtri,nz-2) do l=2,nz-1 c qnew(l,nn)=qtri(l-1) qnew(l,nn)=max(qtri(l-1),1.e-30) enddo qnew(nz,nn)=flux(nn)*mmol(gcmind(nn))/(dens*wi(nn)) & +abfac(nn)*(4.*qnew(nz-1,nn)-qnew(nz-2,nn)) & /(3.-2.*hp(nz)*b(nz,nn)) c qnew(1,nn)=qq(1,nn) qnew(1,nn)=qnew(2,nn) qnew(nz,nn)=max(qnew(nz,nn),1.e-30) qnew(1,nn)=max(qnew(1,nn),1.e-30) enddo ! loop on species DO l=1,nz if(zlocal(l).gt.65000.)then pdqdiff(ig,l,g_o)=0. do n=1,ncompmoldiff-1 pdqdiff(ig,l,gcmind(n))=(qnew(l,n)-qq(l,n)) pdqdiff(ig,l,g_o)=pdqdiff(ig,l,g_o)-(qnew(l,n)-qq(l,n)) pdqdiff(ig,l,gcmind(n))=pdqdiff(ig,l,gcmind(n))/ptimestep enddo pdqdiff(ig,l,g_o)=pdqdiff(ig,l,g_o)/ptimestep endif ENDDO c do l=2,nz c do n=1,ncomptot-1 c hco2(n)=qnew(l,n)*pplay(ig,l)/(rnew(ig,l)*tt(l)) / c & (qnew(l-1,n)*pplay(ig,l-1)/(rnew(ig,l-1)*tt(l-1))) c hco2(n)=-(zlocal(l)-zlocal(l-1))/log(hco2(n))/1000. c enddo c write(225,*),l,pt(1,l),(hco2(n),n=1,6) c write(226,*),l,pt(1,l),(hco2(n),n=7,12) c enddo enddo ! ig loop end subroutine moldiff c ******************************************************************** c ******************************************************************** c ******************************************************************** subroutine tridag_sp(a,b,c,r,u,n) c parameter (nmax=100) c dimension gam(nmax),a(n),b(n),c(n),r(n),u(n) integer,intent(in) :: n real,intent(in) :: a(n),b(n),c(n),r(n) real,intent(out) :: u(n) real :: gam(n),bet integer :: j if(b(1).eq.0.)then stop 'tridag_sp: error: b(1)=0 !!! ' endif bet=b(1) u(1)=r(1)/bet do j=2,n gam(j)=c(j-1)/bet bet=b(j)-a(j)*gam(j) if(bet.eq.0.) then stop 'tridag_sp: error: bet=0 !!! ' endif u(j)=(r(j)-a(j)*u(j-1))/bet enddo do j=n-1,1,-1 u(j)=u(j)-gam(j+1)*u(j+1) enddo end subroutine tridag_sp c ******************************************************************** c ******************************************************************** c ******************************************************************** SUBROUTINE LUBKSB_SP(A,N,NP,INDX,B) implicit none integer i,j,n,np,ii,ll real sum real a(np,np),indx(np),b(np) c DIMENSION A(NP,NP),INDX(N),B(N) II=0 DO 12 I=1,N LL=INDX(I) SUM=B(LL) B(LL)=B(I) IF (II.NE.0)THEN DO 11 J=II,I-1 SUM=SUM-A(I,J)*B(J) 11 CONTINUE ELSE IF (SUM.NE.0.) THEN II=I ENDIF B(I)=SUM 12 CONTINUE DO 14 I=N,1,-1 SUM=B(I) IF(I.LT.N)THEN DO 13 J=I+1,N SUM=SUM-A(I,J)*B(J) 13 CONTINUE ENDIF B(I)=SUM/A(I,I) 14 CONTINUE END SUBROUTINE LUBKSB_SP c ******************************************************************** c ******************************************************************** c ******************************************************************** SUBROUTINE LUDCMP_SP(A,N,NP,INDX,D,ierr) implicit none integer n,np,nmax,i,j,k,imax real d,tiny,aamax real a(np,np),indx(np) integer ierr ! error =0 if OK, =1 if problem PARAMETER (NMAX=100,TINY=1.0E-20) c DIMENSION A(NP,NP),INDX(N),VV(NMAX) real sum,vv(nmax),dum D=1. DO 12 I=1,N AAMAX=0. DO 11 J=1,N IF (ABS(A(I,J)).GT.AAMAX) AAMAX=ABS(A(I,J)) 11 CONTINUE IF (AAMAX.EQ.0.) then write(*,*) 'In moldiff: Problem in LUDCMP_SP with matrix A' write(*,*) 'Singular matrix ?' c write(*,*) 'Matrix A = ', A c TO DEBUG : ierr =1 return c stop END IF VV(I)=1./AAMAX 12 CONTINUE DO 19 J=1,N IF (J.GT.1) THEN DO 14 I=1,J-1 SUM=A(I,J) IF (I.GT.1)THEN DO 13 K=1,I-1 SUM=SUM-A(I,K)*A(K,J) 13 CONTINUE A(I,J)=SUM ENDIF 14 CONTINUE ENDIF AAMAX=0. DO 16 I=J,N SUM=A(I,J) IF (J.GT.1)THEN DO 15 K=1,J-1 SUM=SUM-A(I,K)*A(K,J) 15 CONTINUE A(I,J)=SUM ENDIF DUM=VV(I)*ABS(SUM) IF (DUM.GE.AAMAX) THEN IMAX=I AAMAX=DUM ENDIF 16 CONTINUE IF (J.NE.IMAX)THEN DO 17 K=1,N DUM=A(IMAX,K) A(IMAX,K)=A(J,K) A(J,K)=DUM 17 CONTINUE D=-D VV(IMAX)=VV(J) ENDIF INDX(J)=IMAX IF(J.NE.N)THEN IF(A(J,J).EQ.0.)A(J,J)=TINY DUM=1./A(J,J) DO 18 I=J+1,N A(I,J)=A(I,J)*DUM 18 CONTINUE ENDIF 19 CONTINUE IF(A(N,N).EQ.0.)A(N,N)=TINY ierr =0 END SUBROUTINE LUDCMP_SP end module moldiff_mod