!copyright (C) 2001 MSC-RPN COMM %%%RPNPHY%%%
***S/P FCREST5
*
SUBROUTINE FCREST5(TS,WP,WS,QS,TA,QA,S,NK,PS,FDSS,TPROF,P,FDSI, 1
X D2P,Z0T,BA1,AA1,A1MAX,A1MIN,WKI,WM,A2P,C1,C2,
+ EPSTFN,CTU,RIA,CLAT,C3,C4,WSWK,ALPHA,al,gl,
+ sp,sm,vg,N,TEMPO)
#include "impnone.cdk"
INTEGER N, nk
REAL TS(N),WP(N),WS(N),QS(N),TA(N),QA(N),PS(N),FDSS(N)
REAL TPROF(N),P(N),FDSI(N),D2P(N),BA1(N),AA1(N),A1MAX(N)
REAL A1MIN(N),WKI(N),WM(N),A2P(N),C1(N),C2(N),EPSTFN(N)
REAL CTU(N),RIA(N),CLAT(N),C3(N),C4(N),WSWK(N),ALPHA,TEMPO(N)
real al(n),sp(n),sm(n),vg(n),gl(n)
real s(n,nk),Z0T(N)
*
*Author
* J. Cote (RPN 1983)
*
*Revision
* 001 J. Cote RPN(Nov 1984)SEF version documentation
* 002 M. Lepine - RFE model code revision project (Feb 87)
* - pass work field TEMPO(N) in parameter
* instead of in common block
* 003 J. Mailhot RPN(July 89)-surface infra-red flux from
* *RADIR*
* 004 B. Bilodeau (April 90)
* Put QS to zero if the model is integrated without
* humidity
* 005 N. Brunet (May90)
* Standardization of thermodynamic functions
* 006 N. Brunet (May91)
* New version of thermodynamic functions
* and file of constants
* 007 C.Girard (May91)
* Option WS=CONS for total duration of one integration
* 008 B. Bilodeau (August 1991)- Adaptation to UNIX
*
* 009 C.Girard (Nov92)
* Modification to the definition of the surface humidity
* 010 B. Bilodeau (May 94) - New physics interface
* 011 N. Brunet (May 95) - new surface processes
* 012 B. Bilodeau (June 95) - switch "fonte"
* 013 N. Brunet and C. Girard (Nov 1995) - Bug correction :
* use real temperature ta instead of virtual temperature
* in QSAT calculation
* 014 Y. Delage (Feb 96) Ease passage from stable to unstable
* surface layer in weak wind situations over rough terrain.
* 015 N. Brunet (Oct 97) - get rid of min in FDSI
* 016 N. Brunet (mai 98) - prevent ice sfce temp to go beyond 0 deg C
* 017 N. Brunet (avl 99) - put snow treshold (seuiln) in meter
* 018 M. Lepine (March 2003) - CVMG... Replacements
* 019 W. Yu (March 2004) - TSCONFC
*
*Object
* to do integration of "Force-Restore" equations
*
*Arguments
*
* - Input/Output -
* TS surface temperature
* WP deep soil moisture
* WS surface soil moisture
*
* - Output -
* QS surface specific humidity
*
* - Input -
* TA potential temperature at the last predictive level
* QA specific humidity at the anemometer level
* S local sigma
* NK number of vertical levels
* PS surface pressure in pascals
* FDSS solar flux at the surface * (1-albedo)
* TPROF deep soil temperature
* P rate of precipitation
*
* - Input/Output -
* FDSI infra-red flux at the surface
*
* - Input -
* D2P timestep*(1/RHO(water)*D2)
* Z0T roughness lentgth for heat and moisture fluxes
* BA1 timestep*(1/RHO(water)*D1)*BA/(critical value of which the
* precipitation flows)
* AA1 timestep*(1/RHO(water)*D1)*(A1MAX-BA*WX)
* A1MAX timestep*(1/RHO(water)*D1)*A1MAX
* A1MIN timestep*(1/RHO(water)*D1)*A1MIN
* WKI 1/(critical value in which the surface acts as if it was
* saturated)
* WM critical value of which the precipitation flows
* A2P timestep*A2/(24 hours)
* C1 2*timestep*PI/(24 hours)
* C2 2*timestep*SQRT(PI)/(specific heat of surface*SQRT(surface
* thermal diffusion coefficient*(24 hours)))
* EPSTFN radiation emissivity of the surface (.94 * Stephan-
* Boltzman constant)
* CTU transfer coefficient (CT) * USTAR
* RIA work field
* CLAT work field
* C3 work field
* C4 work field
* WSWK work field
* ALPHA Crank-Nicholson generalized parameter
* AL surface albedo
* SP snow depth
* GL oceanic ice cover
* SM stomatal resistance - computed in stfrst
* VG vegetation types
* N horizontal dimension
* TEMPO work field
*
*Notes
* To predict the temperature and specific humidity at
* the surface by the "Force-Restore" method by Blackadar.
* "STFRST" must be previously called.
*
* Algorithm for the solution of DY/DT = F
*
* Y(T+TAU)-Y(T) = TAU*( ALPHA*F(T+TAU))+(1-ALPHA)*F(T) )
* F(T+TAU) = F(T)+DF/DY*(Y(T+TAU)-Y(T))
* Y(T+TAU) = Y(T) + TAU*F(T)/(1-ALPHA*TAU*DF/DY)
*
* The equation for WP is solved with ALPHA=0
* See the Master's thesis by J.Mailhot for more details.
* All the arguments are dimensions of N except ALPHA
* and N
*
*IMPLICITES
*
#include "clefcon.cdk"
#include "surfcon.cdk"
*
#include "scfrst.cdk"
*
#include "options.cdk"
*
*
*
**
*
*
INTEGER J
REAL QSAT,STS3,C3TEM
real chls
real t1, tfon, vta
real radiat, fcha, fvap, ha
real rest, msn
real tsms, tend
real y1, y2, rej
real dtcs, t1rej, frac, tftmp, betadt
real dthv,tva,tvs,ctucl,aa,bb,cc
real seuiln
real tsinit
LOGICAL WSCONS
*
#include "consphy.cdk"
#include "dintern.cdk"
#include "fintern.cdk"
CDIR$ IVDEP
DATA WSCONS/.TRUE./
*
*
chls = chlc + chlf
y1=0.8
y2=0.3
seuiln = 0.05
* ----------------------------------------------------------------------
* PLANT STOMATAL RESISTANCE (MINIMAL UNDER NO WATER STRESS - UNITS: S/M)
*
* RSTOMAT=60.0
* *** voir variable sm
* ----------------------------------------------------------------------
*
*VDIR NODEP
DO 1 J=1,N
*
* pour l'option TSCONFC (TS constant)
tsinit = ts(j)
*
* note: la variable TA, valide au niveau NK, est definie comme suit:
* ta = s(-,nk)**(-cappa)*t(-,nk)
* or, dans certains calculs ci-dessous, nous avons besoin de
* la vraie temperature;
* c'est pourquoi on definit la variable suivante: VTA
*
vta = ta(j)*s(j,nk)**cappa
*
RIA(J)=EPSTFN(J)*FDSI(J)/STEFAN
*
* ADDITION DES FLUX IR ET VIS
RIA(J)=RIA(J)+FDSS(J)
*
if (ts(j)-tcdk .gt. 0.) then
clat(j) = chlc
else
clat(j) = chls
endif
WSWK(J)= MIN ( WS(J)*WKI(J) , 1.0 )
* WSWK(J) = MAX ( 0.5*(1.-COS(PI*WSWK(J))) , .05 )
*
IF(SATUCO)THEN
QSAT = FOQST(vta,PS(J)*s(j,nk))
C4(J) = FODQS(QSAT,vta)
ELSE
QSAT = FOQSA(vta,PS(J)*s(j,nk))
C4(J) = FODQA(QSAT,vta)
ENDIF
C4(J)=CLAT(J)*C4(J)/CPD
C3(J)=(4.0*EPSTFN(J)*vta**3)
X /(CPD*RIMB*PS(J)*CTU(J)/vta)
C3(J)=(1.0+C3(J))/(C4(J)*(1.0-WSWK(J))
X +(1.0+C3(J))*(1.0+CTU(J)*sm(j)))
WSWK(J)=WSWK(J)*C3(J)
*
CLAT(J)=CLAT(J)*WSWK(J)
*
* POUR SERFLX
*
TEMPO(J)=TS(J)
TEMPO(N+J)=CLAT(J)
*
IF(SATUCO)THEN
QSAT = FOQST(TS(J),PS(J))
C4(J) = FODQS(QSAT,TS(J))
ELSE
QSAT = FOQSA(TS(J),PS(J))
C4(J) = FODQA(QSAT,TS(J))
ENDIF
C4(J)=CPD+CLAT(J)*C4(J)
CLAT(J)=CLAT(J)*(QSAT-QA(J))
C3TEM=RIMB*PS(J)*CTU(J)/TS(J)
STS3=EPSTFN(J)*TS(J)**3
*
tsms = ts(j)
*
* --- on fait une solution analytique de fcrest - c'est la raison
* du terme "betadt" - selon note de C. Girard
* --- la raison du if suivant: betadt peut etre egal a zero
* si au-dessus de l'eau, ce qui genere division par zero.
*
C if(mg(j) .ge. 0.5)then
tva=(1+DELTA*QA(J))*TA(J)
tvs=(1+DELTA*QS(J))*TS(J)
betadt = C2(J)*(C3TEM*C4(J)+4.0*STS3)+C1(J)
aa=STS3*TS(J)-RIA(J)
bb=CLAT(J)+CPD*(TS(J)-TA(J))
cc=C1(J)*(TS(J)-TPROF(J))
TS(J)=TS(J)-(C2(J)*(aa+C3TEM*bb)+cc)
1 *(1.- exp(-betadt))/betadt
dthv=tva-tvs-TS(J)+tsms
* in weak wind situations with large Z0T the transfer coefficient changes
* from near zero in stable conditions to a medium/large value in unstable
* conditions. The linearization is not valid in this case and the following
* prevents large oscillation. For the free convection formula, see BLM 58, p 29.
if(tva-tvs.gt.-0.1 .and. dthv.lt.0.) then
ctucl=KARMAN**2*sqrt(-dthv*CI*GRAV*Z0T(J)/(tva*27.))
C3TEM=RIMB*PS(J)*MAX(CTU(J),0.5*(CTU(J)+ctucl))/TS(J)
betadt = C2(J)*(C3TEM*C4(J)+4.0*STS3)+C1(J)
TS(J)=tsms-(C2(J)*(aa+C3TEM*bb)+cc)
1 *(1.- exp(-betadt))/betadt
endif
*
*
IF (SNOWMELT) THEN
*
* --------------------------------------------------------------
* ------- fonte de la neige ------
* si ts, calcule ci-dessus, est superieur a 0 deg C, on devrait
* normalement utiliser cette energie a faire fondre la neige s'il
* y en a. Or, dans notre modele, la surface n'est pas seulement
* compose de neige, mais aussi de vegetation; par exemple, AL
* au-dessus des forets de coniferes a un albedo de l'ordre de 25%
* meme s'il y a beaucoup de neige au sol. Donc, seulement une partie
* de l'energie disponible ira dans la fonte de neige. La temperature
* de fonte (TFON) sera fonction de l'energie disponible (T1) et
* de l'albedo.
* cette relation est empirico-intuitive.
*
if(sp(j) .gt. seuiln .and. ts(j) .gt. tcdk)then
*
rej=((y1-y2)/0.7)*(al(j)-0.8) + y1
t1 = ts(j) - tcdk
t1rej = t1 * rej
*
tftmp = ts(j) - t1rej
dtcs = ta(j) - tftmp
* -- t1rej est la temperature qu'on soustrait a ts pour avoir
* 'tfon'. Comme le modele a de la difficulte a avoir une
* une forte inversion entre la surface et 1.5 m, on refroidit
* moins ts dans ces cas.
if(dtcs .gt. 0.0)then
frac = exp(-4.0*dtcs)
t1rej = t1rej * frac
end if
*
tfon = ts(j) - t1rej
*
* -- nouveau ts est egal a tfon
* -- on recalcule le terme c3tem pour s/r diagsf (via serflx)
ts(j) = tfon
c3tem = rimb*ps(j)*ctu(j)/ts(j)
* -- on calcule la quantite de neige fondue en m/s (MSN)
radiat = epstfn(j)*ts(j)**4 - ria(j)
fcha = c3tem*cpd*(ts(j)-ta(j))
if(satuco)then
qsat = foqst(ts(j),ps(j))
else
qsat = foqsa(ts(j),ps(j))
end if
fvap = c3tem*wswk(j)*chls*(qsat-qa(j))
ha = radiat + fcha + fvap
rest = (c1(j)/c2(j))*(ts(j) - tprof(j))
tend = (ts(j)-tsms)/c2(j)
msn = -(ha + rest + tend)/(rauw*chlf)
end if
*
* on empeche une surface de glace de depasser 0 deg C
*
if(gl(j) .ge. 0.5 .and. ts(j) .gt. tcdk) ts(j) = tcdk
*
ENDIF
*
* -----------------------------------------------------------------
*
*
* POUR SERFLX
*
c4(j) = c3tem
RIA(J)=(1.0-ALPHA)*TEMPO(J)+ALPHA*TS(J)
*
IF(SATUCO)THEN
QSAT = FOQST(TS(J),PS(J))
ELSE
QSAT = FOQSA(TS(J),PS(J))
ENDIF
*
* --- solution de l'equation force-restore pour
* humidite du sol
*
IF(.NOT.WSCONS) THEN
*
C3TEM=C3TEM*(QSAT-QA(J))
*
WP(J)=MAX( MIN( WP(J)-D2P(J)*(WSWK(J)*C3TEM-P(J)) , WM(J) ) ,
+ 0.0)
*
CLAT(J)=MIN ( MAX ( AA1(J)+BA1(J)*WS(J) , A1MIN(J) ) ,
+ A1MAX(J) )
*
C3TEM=WKI(J)*C3TEM*C3(J)
*
WS(J)=MAX( MIN ( WS(J)-
+ (CLAT(J)*(C3TEM*WS(J)-P(J))+A2P(J)*(WS(J)-WP(J)))
+ /(1.0+ALPHA*(CLAT(J)*C3TEM+A2P(J))) , WM(J) ), 0.0 )
*
WSWK(J)= MIN ( WS(J)*WKI(J) , 1.0 )
* WSWK(J) = MAX ( 0.5*(1.-COS(PI*WSWK(J))) , .05 )
WSWK(J)=WSWK(J)*C3(J)
*
ENDIF
*
QS(J)= MIN( WSWK(J)*(QSAT-QA(J)) + QA(J) , QSAT )
*
if (tsconfc) ts(j) = tsinit
*
*
1 CONTINUE
*
*
* METTRE QS A ZERO SI LE MODELE EST SEC.
IF (.NOT. (WET.AND.EVAP) ) THEN
*
DO 2 J=1,N
QS(J) = 0.0
2 CONTINUE
*
ENDIF
*
RETURN
END