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pcmin.f
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SUBROUTINE PCMIN(SST,PSL,P,T,R,NA,N,PMIN,VMAX,IFL)
C
C Revised on 9/24/2005 to fix convergence problems at high pressure
C
C *** This subroutine calculates the maximum wind speed ***
C *** and mimimum central pressure ***
C *** achievable in tropical cyclones, given a sounding ***
C *** and a sea surface temperature. ***
C
C INPUT: SST: Sea surface temperature in C
C
C PSL: Sea level pressure (mb)
C
C P,T,R: One-dimensional arrays of dimension NA
C containing pressure (mb), temperature (C),
C and mixing ratio (g/kg). The arrays MUST be
C arranged so that the lowest index corresponds
C to the lowest model level, with increasing index
C corresponding to decreasing pressure. The temperature
C sounding should extend to at least the tropopause and
C preferably to the lower stratosphere, however the
C mixing ratios are not important above the boundary
C layer. Missing mixing ratios can be replaced by zeros.
C
C NA: The dimension of P,T and R
C
C N: The actual number of points in the sounding
C (N is less than or equal to NA)
C
C OUTPUT: PMIN is the minimum central pressure, in mb
C
C VMAX is the maximum surface wind speed, in m/s
C (reduced to reflect surface drag)
C
C IFL is a flag: A value of 1 means OK; a value of 0
C indicates no convergence (hypercane); a value of 2
C means that the CAPE routine failed.
C
C-----------------------------------------------------------------------------
REAL T(NA), P(NA), R(NA)
C
C *** Adjustable constant: Ratio of C_k to C_D ***
C
CKCD=0.9
C
C *** Adjustable constant for buoyancy of displaced parcels: ***
C *** 0=Reversible ascent; 1=Pseudo-adiabatic ascent ***
C
SIG=0.0
C
C *** Adjustable switch: if IDISS = 0, no dissipative heating is ***
C *** allowed; otherwise, it is ***
C
IDISS=1
C
C *** Exponent, b, in assumed profile of azimuthal velocity in eye, ***
C *** V=V_m(r/r_m)^b. Used only in calculation of central pressure ***
C
b=2.0
C
C *** Set level from which parcels lifted ***
C
NK=1
C
C *** Factor to reduce gradient wind to 10 m wind
C
VREDUC=0.8
C
C *** Normalize certain quantities ***
C
SSTK=SST+273.15
ES0=6.112*EXP(17.67*SST/(243.5+SST))
DO 40 I=1,N
R(I)=R(I)*0.001
T(I)=T(I)+273.15
40 CONTINUE
C
C *** Default values ***
C
VMAX=0.0
PMIN=PSL
IFL=1
C
NP=0
PM=950.0
C
C *** Find environmental CAPE ***
C
TP=T(NK)
RP=R(NK)
PP=P(NK)
CALL CAPE(TP,RP,PP,T,R,P,NA,N,SIG,CAPEA,TOA,IFLAG)
IF(IFLAG.NE.1)IFL=2
C
C *** Begin iteration to find mimimum pressure ***
C
100 CONTINUE
C
C *** Find CAPE at radius of maximum winds ***
C
TP=T(NK)
PP=MIN(PM,1000.0)
RP=0.622*R(NK)*PSL/(PP*(0.622+R(NK))-R(NK)*PSL)
CALL CAPE(TP,RP,PP,T,R,P,NA,N,SIG,CAPEM,TOM,IFLAG)
IF(IFLAG.NE.1)IFL=2
C
C *** Find saturation CAPE at radius of maximum winds ***
C
TP=SSTK
PP=MIN(PM,1000.0)
RP=0.622*ES0/(PP-ES0)
CALL CAPE(TP,RP,PP,T,R,P,NA,N,SIG,CAPEMS,TOMS,IFLAG)
IF(IFLAG.NE.1)IFL=2
RAT=SSTK/TOMS
IF(IDISS.EQ.0)RAT=1.0
C
C *** Initial estimate of minimum pressure ***
C
RS0=RP
TV1=T(1)*(1.+R(1)/0.622)/(1.+R(1))
TVAV=0.5*(TV1+SSTK*(1.+RS0/0.622)/(1.+RS0))
C CAT=0.5*CKCD*RAT*(CAPEMS-CAPEM)
CAT=CAPEM-CAPEA+0.5*CKCD*RAT*(CAPEMS-CAPEM)
CAT=MAX(CAT,0.0)
PNEW=PSL*EXP(-CAT/(287.04*TVAV))
C
C *** Test for convergence ***
C
IF(ABS(PNEW-PM).GT.0.2)THEN
PM=PNEW
NP=NP+1
IF(NP.GT.1000.OR.PM.LT.400.0)THEN
PMIN=PSL
IFL=0
GOTO 900
END IF
GOTO 100
ELSE
CATFAC=0.5*(1.+1./b)
C CAT=CKCD*RAT*CATFAC*(CAPEMS-CAPEM)
CAT=CAPEM-CAPEA+CKCD*RAT*CATFAC*(CAPEMS-CAPEM)
CAT=MAX(CAT,0.0)
PMIN=PSL*EXP(-CAT/(287.04*TVAV))
END IF
900 CONTINUE
FAC=MAX(0.0,(CAPEMS-CAPEM))
VMAX=VREDUC*SQRT(CKCD*RAT*FAC)
C
C *** Renormalize sounding arrays ***
C
DO 910 I=1,N
R(I)=R(I)*1000.0
T(I)=T(I)-273.15
910 CONTINUE
C
RETURN
END
C
SUBROUTINE CAPE(TP,RP,PP,T,R,P,ND,N,SIG,CAPED,TOB,IFLAG)
C
C This subroutine calculates the CAPE of a parcel with pressure PP (mb),
C temperature TP (K) and mixing ratio RP (gm/gm) given a sounding
C of temperature (T in K) and mixing ratio (R in gm/gm) as a function
C of pressure (P in mb). ND is the dimension of the arrays T,R and P,
C while N is the actual number of points in the sounding. CAPED is
C the calculated value of CAPE and TOB is the temperature at the
C level of neutral buoyancy. IFLAG is a flag
C integer. If IFLAG = 1, routine is successful; if it is 0, routine did
C not run owing to improper sounding (e.g.no water vapor at parcel level).
C IFLAG=2 indicates that routine did not converge.
C
REAL T(ND),R(ND),P(ND),TVRDIF(100)
REAL NA
C
C *** Default values ***
C
CAPED=0.0
TOB=T(1)
IFLAG=1
C
C *** Check that sounding is suitable ***
C
IF(RP.LT.1.0E-6.OR.TP.LT.200.0)THEN
IFLAG=0
RETURN
END IF
C
C *** Assign values of thermodynamic constants ***
C
CPD=1005.7
CPV=1870.0
C CL=4190.0
CL=2500.0
CPVMCL=CPV-CL
RV=461.5
RD=287.04
EPS=RD/RV
ALV0=2.501E6
C
C *** Define various parcel quantities, including reversible ***
C *** entropy, S. ***
C
TPC=TP-273.15
ESP=6.112*EXP(17.67*TPC/(243.5+TPC))
EVP=RP*PP/(EPS+RP)
RH=EVP/ESP
RH=MIN(RH,1.0)
ALV=ALV0+CPVMCL*TPC
S=(CPD+RP*CL)*LOG(TP)-RD*LOG(PP-EVP)+
1 ALV*RP/TP-RP*RV*LOG(RH)
C
C *** Find lifted condensation pressure, PLCL ***
C
CHI=TP/(1669.0-122.0*RH-TP)
PLCL=PP*(RH**CHI)
C
C *** Begin updraft loop ***
C
NCMAX=0
DO J=1,N
TVRDIF(J)=0.0
END DO
C
JMIN=1E6
DO 200 J=1,N
C
C *** Don't bother lifting parcel above 60 mb and skip sections of sounding below parcel level ***
C
IF(P(J).LT.59.0.OR.P(J).GE.PP)GOTO 200
C
JMIN=MIN(JMIN,J)
C
C *** Parcel quantities below lifted condensation level ***
C
IF(P(J).GE.PLCL)THEN
TG=TP*(P(J)/PP)**(RD/CPD)
RG=RP
C
C *** Calculate buoyancy ***
C
TLVR=TG*(1.+RG/EPS)/(1.+RG)
TVRDIF(J)=TLVR-T(J)*(1.+R(J)/EPS)/(1.+R(J))
ELSE
C
C *** Parcel quantities above lifted condensation level ***
C
TG=T(J)
TJC=T(J)-273.15
ES=6.112*EXP(17.67*TJC/(243.5+TJC))
RG=EPS*ES/(P(J)-ES)
C
C *** Iteratively calculate lifted parcel temperature and mixing ***
C *** ratio for reversible ascent ***
C
NC=0
120 CONTINUE
NC=NC+1
C
C *** Calculate estimates of the rates of change of the entropy ***
C *** with temperature at constant pressure ***
C
ALV=ALV0+CPVMCL*(TG-273.15)
SL=(CPD+RP*CL+ALV*ALV*RG/(RV*TG*TG))/TG
EM=RG*P(J)/(EPS+RG)
SG=(CPD+RP*CL)*LOG(TG)-RD*LOG(P(J)-EM)+
1 ALV*RG/TG
IF(NC.LT.3)THEN
AP=0.3
ELSE
AP=1.0
END IF
TGNEW=TG+AP*(S-SG)/SL
C
C *** Test for convergence ***
C
IF(ABS(TGNEW-TG).GT.0.001)THEN
TG=TGNEW
TC=TG-273.15
ENEW=6.112*EXP(17.67*TC/(243.5+TC))
C
C *** Bail out if things get out of hand ***
C
IF(NC.GT.500.OR.ENEW.GT.(P(J)-1.0))THEN
IFLAG=2
RETURN
END IF
RG=EPS*ENEW/(P(J)-ENEW)
GOTO 120
END IF
NCMAX=MAX(NC,NCMAX)
C
C *** Calculate buoyancy ***
C
RMEAN=SIG*RG+(1.-SIG)*RP
TLVR=TG*(1.+RG/EPS)/(1.+RMEAN)
TVRDIF(J)=TLVR-T(J)*(1.+R(J)/EPS)/(1.+R(J))
END IF
200 CONTINUE
C
C *** Begin loop to find NA, PA, and CAPE from reversible ascent ***
C
NA=0.0
PA=0.0
C
C *** Find maximum level of positive buoyancy, INB ***
C
INB=1
DO 550 J=N,JMIN,-1
IF(TVRDIF(J).GT.0.0)INB=MAX(INB,J)
550 CONTINUE
IF(INB.EQ.1)RETURN
C
C *** Find positive and negative areas and CAPE ***
C
IF(INB.GT.1)THEN
DO 600 J=JMIN+1,INB
PFAC=RD*(TVRDIF(J)+TVRDIF(J-1))*(P(J-1)-P(J))/(P(J)+P(J-1))
PA=PA+MAX(PFAC,0.0)
NA=NA-MIN(PFAC,0.0)
600 CONTINUE
C
C *** Find area between parcel pressure and first level above it ***
C
PMA=(PP+P(JMIN))
PFAC=RD*(PP-P(JMIN))/PMA
PA=PA+PFAC*MAX(TVRDIF(JMIN),0.0)
NA=NA-PFAC*MIN(TVRDIF(JMIN),0.0)
C
C *** Find residual positive area above INB and TO ***
C
PAT=0.0
TOB=T(INB)
IF(INB.LT.N)THEN
PINB=(P(INB+1)*TVRDIF(INB)-P(INB)*TVRDIF(INB+1))/
1 (TVRDIF(INB)-TVRDIF(INB+1))
PAT=RD*TVRDIF(INB)*(P(INB)-PINB)/(P(INB)+PINB)
TOB=(T(INB)*(PINB-P(INB+1))+T(INB+1)*(P(INB)-PINB))/
1 (P(INB)-P(INB+1))
END IF
C
C *** Find CAPE ***
C
CAPED=PA+PAT-NA
CAPED=MAX(CAPED,0.0)
END IF
C
RETURN
END