SUBROUTINE cv3p_mixing(nloc,ncum,nd,na,ntra,icb,nk,inb : ,ph,t,rr,rs,u,v,tra,h,lv,qnk : ,unk,vnk,hp,tv,tvp,ep,clw,sig : ,ment,qent,hent,uent,vent,nent : ,sij,elij,supmax,ments,qents,traent) *************************************************************** * * * CV3P_MIXING : compute mixed draught properties and, * * within a scaling factor, mixed draught * * mass fluxes. * * written by : VTJ Philips,JY Grandpeix, 21/05/2003, 09.14.15* * modified by : * *************************************************************** * implicit none c #include "cvthermo.h" #include "cv3param.h" #include "YOMCST2.h" c inputs: integer ncum, nd, na, ntra, nloc integer icb(nloc), inb(nloc), nk(nloc) real sig(nloc,nd) real qnk(nloc),unk(nloc),vnk(nloc) real ph(nloc,nd+1) real t(nloc,nd), rr(nloc,nd), rs(nloc,nd) real u(nloc,nd), v(nloc,nd) real tra(nloc,nd,ntra) ! input of convect3 real lv(nloc,na) real h(nloc,na) !liquid water static energy of environment real hp(nloc,na) !liquid water static energy of air shed from adiab. asc. real tv(nloc,na), tvp(nloc,na), ep(nloc,na), clw(nloc,na) c outputs: real ment(nloc,na,na), qent(nloc,na,na) real uent(nloc,na,na), vent(nloc,na,na) real sij(nloc,na,na), elij(nloc,na,na) real supmax(nloc,na) ! Highest mixing fraction of mixed updraughts ! with the sign of (h-hp) real traent(nloc,nd,nd,ntra) real ments(nloc,nd,nd), qents(nloc,nd,nd) real sigij(nloc,nd,nd) real hent(nloc,nd,nd) integer nent(nloc,nd) c local variables: integer i, j, k, il, im, jm integer num1, num2 real rti, bf2, anum, denom, dei, altem, cwat, stemp, qp real alt, delp, delm real Qmixmax(nloc), Rmixmax(nloc), SQmRmax(nloc) real Qmixmin(nloc), Rmixmin(nloc), SQmRmin(nloc) real signhpmh(nloc) real Sx, Scrit2 integer Jx real smid(nloc), sjmin(nloc), sjmax(nloc) real Sbef(nloc), Sup(nloc), Smin(nloc) real asij(nloc), smax(nloc), scrit(nloc) real csum(nloc,nd) real awat logical lwork(nloc) c REAL amxupcrit, df, ff INTEGER nstep C c -- Mixing probability distribution functions c real Qcoef1,Qcoef2,QFF,QFFF,Qmix,Rmix,Qmix1,Rmix1,Qmix2,Rmix2,F Qcoef1(F) = tanh(F/gammas) Qcoef2(F) = ( tanh(F/gammas) + gammas * $ log(cosh((1.- F)/gammas)/cosh(F/gammas))) QFF(F) = Max(Min(F,1.),0.) QFFF(F) = Min(QFF(F),scut) Qmix1(F) = ( tanh((QFF(F) - Fmax)/gammas)+Qcoef1max )/ $ Qcoef2max Rmix1(F) = ( gammas*log(cosh((QFF(F)-Fmax)/gammas)) 1 +QFF(F)*Qcoef1max ) / Qcoef2max Qmix2(F) = -Log(1.-QFFF(F))/scut Rmix2(F) = (QFFF(F)+(1.-QFF(F))*Log(1.-QFFF(F)))/scut Qmix(F) = qqa1*Qmix1(F) + qqa2*Qmix2(F) Rmix(F) = qqa1*Rmix1(F) + qqa2*Rmix2(F) C INTEGER ifrst DATA ifrst/0/ C c===================================================================== c --- INITIALIZE VARIOUS ARRAYS USED IN THE COMPUTATIONS c===================================================================== c c -- Initialize mixing PDF coefficients IF (ifrst .EQ. 0) THEN ifrst = 1 Qcoef1max = Qcoef1(Fmax) Qcoef2max = Qcoef2(Fmax) c ENDIF c c ori do 360 i=1,ncum*nlp do 361 j=1,nl do 360 i=1,ncum nent(i,j)=0 c in convect3, m is computed in cv3_closure c ori m(i,1)=0.0 360 continue 361 continue c ori do 400 k=1,nlp c ori do 390 j=1,nlp do 400 j=1,nl do 390 k=1,nl do 385 i=1,ncum qent(i,k,j)=rr(i,j) uent(i,k,j)=u(i,j) vent(i,k,j)=v(i,j) elij(i,k,j)=0.0 hent(i,k,j)=0.0 ment(i,k,j)=0.0 sij(i,k,j)=0.0 385 continue 390 continue 400 continue do k=1,ntra do j=1,nd ! instead nlp do i=1,nd ! instead nlp do il=1,ncum traent(il,i,j,k)=tra(il,j,k) enddo enddo enddo enddo c===================================================================== c --- CALCULATE ENTRAINED AIR MASS FLUX (ment), TOTAL WATER MIXING c --- RATIO (QENT), TOTAL CONDENSED WATER (elij), AND MIXING c --- FRACTION (sij) c===================================================================== do 750 i=minorig+1, nl do 710 j=minorig,nl do 700 il=1,ncum if( (i.ge.icb(il)).and.(i.le.inb(il)).and. : (j.ge.(icb(il)-1)).and.(j.le.inb(il)))then rti=qnk(il)-ep(il,i)*clw(il,i) bf2=1.+lv(il,j)*lv(il,j)*rs(il,j)/(rrv*t(il,j)*t(il,j)*cpd) anum=h(il,j)-hp(il,i)+(cpv-cpd)*t(il,j)*(rti-rr(il,j)) denom=h(il,i)-hp(il,i)+(cpd-cpv)*(rr(il,i)-rti)*t(il,j) dei=denom if(abs(dei).lt.0.01)dei=0.01 sij(il,i,j)=anum/dei sij(il,i,i)=1.0 altem=sij(il,i,j)*rr(il,i)+(1.-sij(il,i,j))*rti-rs(il,j) altem=altem/bf2 cwat=clw(il,j)*(1.-ep(il,j)) stemp=sij(il,i,j) if((stemp.lt.0.0.or.stemp.gt.1.0.or.altem.gt.cwat) : .and.j.gt.i)then anum=anum-lv(il,j)*(rti-rs(il,j)-cwat*bf2) denom=denom+lv(il,j)*(rr(il,i)-rti) if(abs(denom).lt.0.01)denom=0.01 sij(il,i,j)=anum/denom altem=sij(il,i,j)*rr(il,i)+(1.-sij(il,i,j))*rti-rs(il,j) altem=altem-(bf2-1.)*cwat end if if(sij(il,i,j).gt.0.0)then ccc ment(il,i,j)=m(il,i) ment(il,i,j)=1. elij(il,i,j)=altem elij(il,i,j)=amax1(0.0,elij(il,i,j)) nent(il,i)=nent(il,i)+1 endif sij(il,i,j)=amax1(0.0,sij(il,i,j)) sij(il,i,j)=amin1(1.0,sij(il,i,j)) endif ! new 700 continue 710 continue c c *** if no air can entrain at level i assume that updraft detrains *** c *** at that level and calculate detrained air flux and properties *** c c@ do 170 i=icb(il),inb(il) do 740 il=1,ncum if ((i.ge.icb(il)).and.(i.le.inb(il)) : .and.(nent(il,i).eq.0)) then c@ if(nent(il,i).eq.0)then ccc ment(il,i,i)=m(il,i) ment(il,i,i)=1. qent(il,i,i)=qnk(il)-ep(il,i)*clw(il,i) uent(il,i,i)=unk(il) vent(il,i,i)=vnk(il) elij(il,i,i)=clw(il,i)*(1.-ep(il,i)) sij(il,i,i)=0.0 end if 740 continue 750 continue do j=1,ntra do i=minorig+1,nl do il=1,ncum if (i.ge.icb(il) .and. i.le.inb(il) : .and. nent(il,i).eq.0) then traent(il,i,i,j)=tra(il,nk(il),j) endif enddo enddo enddo do 100 j=minorig,nl do 101 i=minorig,nl do 102 il=1,ncum if ((j.ge.(icb(il)-1)).and.(j.le.inb(il)) : .and.(i.ge.icb(il)).and.(i.le.inb(il)))then sigij(il,i,j)=sij(il,i,j) endif 102 continue 101 continue 100 continue c@ enddo c@170 continue c===================================================================== c --- NORMALIZE ENTRAINED AIR MASS FLUXES c --- TO REPRESENT EQUAL PROBABILITIES OF MIXING c===================================================================== call zilch(csum,nloc*nd) do il=1,ncum lwork(il) = .FALSE. enddo DO 789 i=minorig+1,nl num1=0 do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) ) num1=num1+1 enddo if (num1.le.0) goto 789 do 781 il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) ) then lwork(il)=(nent(il,i).ne.0) Signhpmh(il) = sign(1.,hp(il,i)-h(il,i)) qp=qnk(il)-ep(il,i)*clw(il,i) anum=h(il,i)-hp(il,i)-lv(il,i)*(qp-rs(il,i)) : +(cpv-cpd)*t(il,i)*(qp-rr(il,i)) denom=h(il,i)-hp(il,i)+lv(il,i)*(rr(il,i)-qp) : +(cpd-cpv)*t(il,i)*(rr(il,i)-qp) if(abs(denom).lt.0.01)denom=0.01 scrit(il)=min(anum/denom,1.) alt=qp-rs(il,i)+scrit(il)*(rr(il,i)-qp) c cjyg1 Find maximum of SIJ for J>I, if any, and new critical value Scrit2 c such that : Sij > Scrit2 => mixed draught will detrain at J mixed draught will detrain at J>I c Sx = 0. Jx = 0. Sbef(il) = max(0.,signhpmh(il)) DO j = i+1,inb(il) IF (Sbef(il) .LT. Sij(il,i,j)) THEN Sx = max(Sij(il,i,j),Sx) Jx = J ENDIF Sbef(il) = Sij(il,i,j) ENDDO c Scrit2 = min(Scrit(il),Sx)*max(0.,-signhpmh(il)) : +Scrit(il)*max(0.,signhpmh(il)) c Scrit(il) = Scrit2 c cjyg Correction pour la nouvelle logique; la correction pour ALT c est un peu au hazard if(scrit(il).le.0.0)scrit(il)=0.0 if(alt.le.0.0) scrit(il)=1.0 C smax(il)=0.0 asij(il)=0.0 Sup(il)=0. ! upper S-value reached by descending draughts endif 781 continue do 175 j=minorig,nl num2=0 do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. : j.ge.(icb(il)-1) .and. j.le.inb(il) : .and. lwork(il) ) num2=num2+1 enddo if (num2.le.0) goto 175 c ----------------------------------------------- IF (j .GT. i) THEN c ----------------------------------------------- do 782 il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. : j.ge.(icb(il)-1) .and. j.le.inb(il) : .and. lwork(il) ) then if(sij(il,i,j).gt.0.0)then Smid(il)=min(Sij(il,i,j),Scrit(il)) Sjmax(il)=Smid(il) Sjmin(il)=Smid(il) IF (Smid(il) .LT. Smin(il) .AND. 1 Sij(il,i,j+1) .LT. Smid(il)) THEN Smin(il)=Smid(il) Sjmax(il)=min( (Sij(il,i,j+1)+Sij(il,i,j))/2. , 1 Sij(il,i,j) , 1 Scrit(il) ) Sjmin(il)=max( (Sbef(il)+Sij(il,i,j))/2. , 1 Sij(il,i,j) ) Sjmin(il)=min(Sjmin(il),Scrit(il)) Sbef(il) = Sij(il,i,j) ENDIF endif endif 782 continue c ----------------------------------------------- ELSE IF (j .EQ. i) THEN c ----------------------------------------------- do 783 il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. : j.ge.(icb(il)-1) .and. j.le.inb(il) : .and. lwork(il) ) then if(sij(il,i,j).gt.0.0)then Smid(il) = 1. Sjmin(il) = max((Sij(il,i,j-1)+Smid(il))/2.,Scrit(il)) 1 *max(0.,-signhpmh(il)) 1 +min((Sij(il,i,j+1)+Smid(il))/2.,Scrit(il)) 1 *max(0., signhpmh(il)) Sjmin(il) = max(Sjmin(il),Sup(il)) Sjmax(il) = 1. c c- preparation des variables Scrit, Smin et Sbef pour la partie j>i Scrit(il) = min(Sjmin(il),Sjmax(il),Scrit(il)) Smin(il) = 1. Sbef(il) = max(0.,signhpmh(il)) Supmax(il,i) = sign(Scrit(il),-signhpmh(il)) endif endif 783 continue c ----------------------------------------------- ELSE IF ( j .LT. i) THEN c ----------------------------------------------- do 784 il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. : j.ge.(icb(il)-1) .and. j.le.inb(il) : .and. lwork(il) ) then if(sij(il,i,j).gt.0.0)then Smid(il)=max(Sij(il,i,j),Scrit(il)) Sjmax(il) = Smid(il) Sjmin(il) = Smid(il) IF (Smid(il) .GT. Smax(il) .AND. 1 Sij(il,i,j+1) .GT. Smid(il)) THEN Smax(il) = Smid(il) Sjmax(il) = max( (Sij(il,i,j+1)+Sij(il,i,j))/2. , 1 Sij(il,i,j) ) Sjmax(il) = max(Sjmax(il),Scrit(il)) Sjmin(il) = min( (Sbef(il)+Sij(il,i,j))/2. , 1 Sij(il,i,j) ) Sjmin(il) = max(Sjmin(il),Scrit(il)) Sbef(il) = Sij(il,i,j) ENDIF IF (abs(Sjmin(il)-Sjmax(il)) .GT. 1.e-10) Sup(il)= 1 max(Sjmin(il),Sjmax(il),Sup(il)) endif endif 784 continue c ----------------------------------------------- END IF c ----------------------------------------------- c c do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. : j.ge.(icb(il)-1) .and. j.le.inb(il) : .and. lwork(il) ) then if(sij(il,i,j).gt.0.0)then rti=rr(il,1)-ep(il,i)*clw(il,i) Qmixmax(il)=Qmix(Sjmax(il)) Qmixmin(il)=Qmix(Sjmin(il)) Rmixmax(il)=Rmix(Sjmax(il)) Rmixmin(il)=Rmix(Sjmin(il)) SQmRmax(il)= Sjmax(il)*Qmix(Sjmax(il))-Rmix(Sjmax(il)) SQmRmin(il)= Sjmin(il)*Qmix(Sjmin(il))-Rmix(Sjmin(il)) c Ment(il,i,j) = abs(Qmixmax(il)-Qmixmin(il))*Ment(il,i,j) c c Sigij(i,j) is the 'true' mixing fraction of mixture Ment(i,j) IF (abs(Qmixmax(il)-Qmixmin(il)) .GT. 1.e-10) THEN Sigij(il,i,j) = : (SQmRmax(il)-SQmRmin(il))/(Qmixmax(il)-Qmixmin(il)) ELSE Sigij(il,i,j) = 0. ENDIF c c -- Compute Qent, uent, vent according to the true mixing fraction Qent(il,i,j) = (1.-Sigij(il,i,j))*rti : + Sigij(il,i,j)*rr(il,i) uent(il,i,j) = (1.-Sigij(il,i,j))*unk(il) : + Sigij(il,i,j)*u(il,i) vent(il,i,j) = (1.-Sigij(il,i,j))*vnk(il) : + Sigij(il,i,j)*v(il,i) c c-- Compute liquid water static energy of mixed draughts IF (j .GT. i) THEN awat=elij(il,i,j)-(1.-ep(il,j))*clw(il,j) awat=amax1(awat,0.0) ELSE awat = 0. ENDIF Hent(il,i,j) = (1.-Sigij(il,i,j))*HP(il,i) : + Sigij(il,i,j)*H(il,i) : + (LV(il,j)+(cpd-cpv)*t(il,j))*awat c c print *,'mix : i,j,hent(il,i,j),sigij(il,i,j) ', c : i,j,hent(il,i,j),sigij(il,i,j) c c -- ASij is the integral of P(F) over the relevant F interval ASij(il) = ASij(il) 1 + abs(Qmixmax(il)*(1.-Sjmax(il))+Rmixmax(il) 1 -Qmixmin(il)*(1.-Sjmin(il))-Rmixmin(il)) c endif endif enddo do k=1,ntra do il=1,ncum if( (i.ge.icb(il)).and.(i.le.inb(il)).and. : (j.ge.(icb(il)-1)).and.(j.le.inb(il)) : .and. lwork(il) ) then if(sij(il,i,j).gt.0.0)then traent(il,i,j,k)=sigij(il,i,j)*tra(il,i,k) : +(1.-sigij(il,i,j))*tra(il,nk(il),k) endif endif enddo enddo c c -- If I=J (detrainement and entrainement at the same level), then only the c -- adiabatic ascent part of the mixture is considered IF (I .EQ. J) THEN do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. : j.ge.(icb(il)-1) .and. j.le.inb(il) : .and. lwork(il) ) then if(sij(il,i,j).gt.0.0)then rti=qnk(il)-ep(il,i)*clw(il,i) ccc Ment(il,i,i) = m(il,i)*abs(Qmixmax(il)*(1.-Sjmax(il)) Ment(il,i,i) = abs(Qmixmax(il)*(1.-Sjmax(il)) 1 +Rmixmax(il) 1 -Qmixmin(il)*(1.-Sjmin(il))-Rmixmin(il)) Qent(il,i,i) = rti uent(il,i,i) = unk(il) vent(il,i,i) = vnk(il) Hent(il,i,i) = hp(il,i) Elij(il,i,i) = clw(il,i)*(1.-ep(il,i)) Sigij(il,i,i) = 0. endif endif enddo do k=1,ntra do il=1,ncum if( (i.ge.icb(il)).and.(i.le.inb(il)).and. : (j.ge.(icb(il)-1)).and.(j.le.inb(il)) : .and. lwork(il) ) then if(sij(il,i,j).gt.0.0)then traent(il,i,i,k)=tra(il,nk(il),k) endif endif enddo enddo c ENDIF c 175 continue do il=1,ncum if (i.ge.icb(il).and.i.le.inb(il).and.lwork(il)) then asij(il)=amax1(1.0e-16,asij(il)) asij(il)=1.0/asij(il) csum(il,i)=0.0 endif enddo do 180 j=minorig,nl do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. lwork(il) : .and. j.ge.(icb(il)-1) .and. j.le.inb(il) ) then ment(il,i,j)=ment(il,i,j)*asij(il) endif enddo 180 continue do 197 j=minorig,nl do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. lwork(il) : .and. j.ge.(icb(il)-1) .and. j.le.inb(il) ) then csum(il,i)=csum(il,i)+ment(il,i,j) endif enddo 197 continue do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. lwork(il) : .and. csum(il,i).lt.1. ) then ccc : .and. csum(il,i).lt.m(il,i) ) then nent(il,i)=0 ccc ment(il,i,i)=m(il,i) ment(il,i,i)=1. qent(il,i,i)=qnk(il)-ep(il,i)*clw(il,i) uent(il,i,i)=unk(il) vent(il,i,i)=vnk(il) elij(il,i,i)=clw(il,i)*(1.-ep(il,i)) sij(il,i,i)=0.0 endif enddo ! il do j=1,ntra do il=1,ncum if ( i.ge.icb(il) .and. i.le.inb(il) .and. lwork(il) : .and. csum(il,i).lt.1. ) then ccc : .and. csum(il,i).lt.m(il,i) ) then traent(il,i,i,j)=tra(il,nk(il),j) endif enddo enddo c 789 continue c return end