C&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& SUBROUTINE MIXLEN(LMHK,LPBL,HPBL,U,V,T,Q,Q2,APE,Z,GM,GH,EL) C ****************************************************************** C * * C * LEVEL 2.5 MIXING LENGTH * C * * C ****************************************************************** c c July 1997: Modified to restore averaging of layer values of l, c ELL, a la Mesinger 1993, Res. Act. Atmos. Ocean. Mod., No. 18, c 4.36-4.38; c c A problem removed which may have led to the Òabove PBLÓ scheme c for preliminary EL to be used inadvertently at times and places c where the PBL scheme was supposed to have been used c C----------------------------------------------------------------------- INCLUDE "parmeta" INCLUDE "mpp.h" #include "sp.h" C----------------------------------------------------------------------- P A R A M E T E R &(LP1=LM+1,LM1=LM-1) C----------------------------------------------------------------------- P A R A M E T E R &(EPSQ2=0.2,EPSL=0.32,EPSRU=1.E-12,EPSRS=1.E-12 &,FH=1.01,ALPH=.20,VKRM=.40,ELFC=0.23 ,EL0MAX=1000.) C----------------------------------------------------------------------- P A R A M E T E R C----------------------------------------------------------------------- &(G=9.8,BETA=1./270.,BTG=BETA*G &,PRT=1.0,GAM1=0.2222222222222222222 &,A1=0.659888514560862645,A2=0.6574209922667784586 &,B1=11.87799326209552761,B2=7.226971804046074028 &,C1=0.000830955950095854396) C----------------------------------------------------------------------- CUN &(G=9.8,BETA=1./270.,BTG=BETA*G CUN &,PRT=1.0,GAM1=0.2222222222222222222 CUN &,A1=0.3310949523016403346,A2=0.8273378704055731278 CUN &,B1=5.959709141429526024,B2=3.626088092074591135 CUN &,C1=-0.3330651924968952113) C----------------------------------------------------------------------- CMY &(G=9.8,BETA=1./270.,BTG=BETA*G CMY &,PRT=0.8,GAM1=0.2222222222222222222 CMY &,A1=0.9222222350809054114,A2=0.7350190142719400952 CMY &,B1=16.60000023145629741,B2=10.10000014082581951 CMY &,C1=0.0805318118080613468) C--------------COEFFICIENTS OF THE TERMS IN THE DENOMINATOR------------- P A R A M E T E R &(ADNM=18.*A1*A1*A2*(B2-3.*A2)*BTG &,ADNH= 9.*A1*A2*A2*(12.*A1+3.*B2)*BTG*BTG &,BDNM= 6.*A1*A1 &,BDNH= 3.*A2*(7.*A1+B2)*BTG C--------------FREE TERM IN THE EQUILIBRIUM EQUATION FOR (L/Q)**2------- &,AEQM= 3.*A1*A2*B1*(3.*A2+3.*B2*C1+18.*A1*C1-B2)*BTG & +18.*A1*A1*A2*(B2-3.*A2)*BTG &,AEQH= 9.*A1*A2*A2*B1*BTG*BTG+9.*A1*A2*A2*(12.*A1+3.*B2)*BTG*BTG C--------------FORBIDDEN TURBULENCE AREA-------------------------------- &,REQU=-AEQH/AEQM*1.02,EPSGH=1.E-9,EPSGM=REQU*EPSGH C--------------NEAR ISOTROPY FOR SHEAR TURBULENCE, WW/Q2 LOWER LIMIT---- &,UBRYL=(18.*REQU*A1*A1*A2*B2*C1*BTG+9.*A1*A2*A2*B2*BTG*BTG) & /(REQU*ADNM+ADNH) &,UBRY=(1.+EPSRS)*UBRYL &,UBRY3=3.*UBRY &,AUBM=54.*A1*A1*A2*B2*C1*BTG -ADNM*UBRY3 &,AUBH=27.*A1*A2*A2*B2*BTG*BTG-ADNH*UBRY3 &,BUBM=18.*A1*A1*C1 -BDNM*UBRY3 &,BUBH=(9.*A1*A2+3.*A2*B2)*BTG-BDNH*UBRY3 &,CUBR=1. - UBRY3,RCUBR=1./CUBR) C----------------------------------------------------------------------- D I M E N S I O N & U (LM),V (LM) &,T (LM),Q (LM),Q2 (LM) D I M E N S I O N & GM (LM1),GH (LM1),EL (LM1) &,APE (LM ) &,Z (LP1) C----------------------------------------------------------------------- D I M E N S I O N & ELM (LM1),ELL (LM ) &,Q1 (LM ),THV (LM ) C----------------------------------------------------------------------- C*********************************************************************** LMHM=LMHK-1 LMHP=LMHK+1 C--------------FIND THE HEIGHT OF THE PBL------------------------------- LPBL=LMHK DO 100 IVI=1,LMHK L=LMHK-IVI IF(Q2(L).LE.EPSQ2*FH)THEN CVVVVVVVVVVVVVV NOT NECESSARY IF DRIVEN BY TURBL VVVVVVVVVVVVVVVVVVVVVVV C Q2(L)=EPSQ2 CAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA LPBL=L GO TO 110 ENDIF 100 CONTINUE LPBL=1 C--------------THE HEIGHT OF THE PBL------------------------------------ 110 HPBL=Z(LPBL)-Z(LMHP) C----------------------------------------------------------------------- DO 120 L=1,LMHK Q1(L)=0. THV(L)=(0.608*Q(L)+1.)*T(L)*APE(L) 120 CONTINUE C----------------------------------------------------------------------- DO 130 L=LPBL,LMHK Q1(L)=SQRT(Q2(L)) 130 CONTINUE C----------------------------------------------------------------------- SZQ=0. SQ =0. DO 140 L=1,LMHM QDZL=(Q1(L)+Q1(L+1))*(Z(L+1)-Z(L+2)) SZQ=(Z(L+1)+Z(L+2)-Z(LMHP)-Z(LMHP))*QDZL+SZQ SQ=QDZL+SQ RDZ=2./(Z(L)-Z(L+2)) GML=((U(L)-U(L+1))**2+(V(L)-V(L+1))**2)*RDZ*RDZ GM(L)=AMAX1(GML,EPSGM) GHL=(THV(L)-THV(L+1))*RDZ IF(ABS(GHL).LE.EPSGH) GHL=EPSGH GH(L)=GHL 140 CONTINUE C--------------COMPUTATION OF ASYMPTOTIC L IN BLACKADAR FORMULA--------- EL0=AMIN1(ALPH*SZQ*0.5/SQ,EL0MAX) C----------------------------------------------------------------------- DO 150 L=1,LMHM GML=GM(L) GHL=GH(L) IF(GHL.GE.EPSGH)THEN IF(GML/GHL.LE.REQU)THEN ELM(L)=EPSL ELSE AUBR=(AUBM*GML+AUBH*GHL)*GHL BUBR= BUBM*GML+BUBH*GHL QOL2ST=(-0.5*BUBR+SQRT(BUBR*BUBR*0.25-AUBR*CUBR))*RCUBR QOL2ST=AMAX1(QOL2ST,1.E-8) ELOQ2X=1./QOL2ST ELM(L)=AMAX1(SQRT(ELOQ2X*Q2(L)),EPSL) ENDIF ELSE ADEN=(ADNM*GML+ADNH*GHL)*GHL BDEN= BDNM*GML+BDNH*GHL QOL2UN= -0.5*BDEN+SQRT(BDEN*BDEN*0.25-ADEN) ELOQ2X=1./((1.+EPSRU)*QOL2UN) ELM(L)=AMAX1(SQRT(ELOQ2X*Q2(L)),EPSL) ENDIF 150 CONTINUE C----------------------------------------------------------------------- c LPBLM=LPBL-1 c DO 160 L=1,LPBLM c EL(L)=AMIN1((Z(L)-Z(L+2))*ELFC,ELM(L)) c160 CONTINUE c DO 165 L=LPBL,LMHM c VKRMZ=(Z(L+1)-Z(LMHP))*VKRM c165 EL(L)=AMIN1(VKRMZ/(VKRMZ/EL0+1.),ELM(L)) C----------------------------------------------------------------------- c Note: LPBL is the EL value of L of the interface starting with the c lowest interface and going up for the first time having Q2 .le. c a specified value c DO 160 L=1,LPBL ELL(L)= (Z(L)-Z(L+1))*ELFC 160 CONTINUE IF(LPBL.LT.LMHK)THEN LPBLP=LPBL+1 DO 165 L=LPBLP,LMHK VKRMZ=(0.5*(Z(L)+Z(L+1))-Z(LMHP))*VKRM ELL(L)= VKRMZ/(VKRMZ/EL0+1.) 165 CONTINUE ENDIF C----------------------------------------------------------------------- DO 260 L=1,LMHM EL(L)=AMIN1(0.5*(ELL(L)+ELL(L+1)),ELM(L)) 260 CONTINUE C----------------------------------------------------------------------- RETURN END