cotwo.F90

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!SFX_LIC Copyright 1994-2014 CNRS, Meteo-France and Universite Paul Sabatier
!SFX_LIC This is part of the SURFEX software governed by the CeCILL-C licence
!SFX_LIC version 1. See LICENSE, CeCILL-C_V1-en.txt and CeCILL-C_V1-fr.txt  
!SFX_LIC for details. version 1.
!     #########
    SUBROUTINE cotwo(PCSP, PF2, PIA, PDS, PGAMMT,               &
                     pfzero, pepso, panmax, pgmest, pgc, pdmax, &
                     pan, pgs, prd, plaitop, plai   )  
!   #########################################################################
!
!!****  *COTWO*  
!!
!!    PURPOSE
!!    -------
!
!     Calculates net assimilation of CO2 and leaf conductance.
!              
!!**  METHOD
!!    ------
!     Calvet et al. 1998 Forr. Agri. Met. [from model of Jacobs(1994)]
!!
!!    EXTERNAL
!!    --------
!!    none
!!
!!    IMPLICIT ARGUMENTS
!!    ------------------
!!      
!!    USE MODD_CO2V_PAR
!!
!!    REFERENCE
!!    ---------
!!
!!    Calvet et al. 1998 Forr. Agri. Met. 
!!      
!!    AUTHOR
!!    ------
!!
!!      A. Boone           * Meteo-France *
!!      (following Belair)
!!
!!    MODIFICATIONS
!!    -------------
!!      Original    27/10/97 
!!      L. Jarlan   27/10/04 : Add of photosynthesis (PPST variable) as output
!!                              of the routine in order to manage the calculation
!!                              of Soil respiration in cotwores and cotworestress
!!      P Le Moigne  09/2005 AGS modifs of L. Jarlan
!!      A.L. Gibelin 07/2009 : Suppress GPP and PPST as outputs
!!                             GPP is calculated in cotwores.f90 and cotworestress.f90
!!      B. Decharme   2012   : optimization
!!      C. Delire     2014   : Assuming a nitrogen profile with an exctinction coefficient 
!!      B. Decharme   07/15  : Bug = Add numerical adjustement for very dry soil 
!!      
!!
!-------------------------------------------------------------------------------
!
USE modd_csts,     ONLY : xmv, xmd, xrholw
USE modd_co2v_par, ONLY : xrdcf, xairtoh2o, xco2toh2o, xcondstmin
USE modd_isba_par, ONLY : xdenom_min
!
!*       0.     DECLARATIONS
!               ------------
!
!
USE yomhook   ,ONLY : lhook,   dr_hook
USE parkind1  ,ONLY : jprb
!
IMPLICIT NONE
!
!*      0.1    declarations of arguments
!
!
!                                      Atmospheric forcing:
REAL, DIMENSION(:),   INTENT(IN):: pcsp, pf2, pia, pds,pgammt
!                                      PCSP  = atmospheric concentration of CO2
!                                      PF2   = normalized soil water stress
!                                      PIA   = incident solar radiation
!                                      PDS   = saturation deficit of atmosphere
!                                              verses the leaf surface (with correction)
!                                      PGAMMT = compensation point
!
!                                      Time constants:
!
REAL, DIMENSION(:), INTENT(IN)  :: pfzero, pepso, panmax, pgmest, pgc, pdmax, plaitop, plai
!                                      PFZERO    = ideal value of F, no photorespiration 
!                                                  or saturation deficit
!                                      PEPSO     = maximum initial quantum use efficiency 
!                                                  (kgCO2 J-1 PAR)
!                                      PGAMM     = CO2 conpensation concentration (kgCO2 kgAir-1)
!                                      PANMAX    = maximum net assimilation
!                                      PGMEST    = temperature response 
!                                                  of mesophyll conductance
!                                      PGC       = cuticular conductance (m s-1)
!                                      PDMAX     = maximum saturation deficit of 
!                                                  atmosphere tolerate by vegetation       
!                                      PLAITOP   = LAI (thickness of canopy) above considered layer 
!                                      PLAI      = canopy LAI 
!
!                                      CO2 model outputs:
REAL, DIMENSION(:),  INTENT(OUT) :: pan, pgs, prd
!                                      PAN   = Net assimilation of CO2
!                                      PGS   = Leaf conductance
!                                      PRD   = Dark Respiration
!
!
!*      0.2    declarations of local variables
!
!
REAL, DIMENSION(SIZE(PAN)) :: zfmin, zdrap, zf, zwork
!                                       ZFMIN = minimum f factor
!                                       ZDRAP = ratio Ds/Dmax
!                                       ZF    = factor related to diffusion
!                                       ZWORK = work array
!
REAL, DIMENSION(SIZE(PAN)) :: zcsp, zci, zcmin, zamin  
!                                       ZCSP    = atmospheric concentration 
!                                                       of CO2
!                                       ZCI     = Leaf Internal concentration 
!                                                       of CO2
!                                       ZCMIN = minimim internal leaf
!                                               CO2 concentration
!                                       ZAMIN   = minimum net 
!                                                       assimilation
!
REAL, DIMENSION(SIZE(PAN)) :: zam, zeps, zlef, zagr, zag
!                                       ZAM     = net assimilation as a 
!                                                 function of CO2 deficit
!                                       ZEPS   = initial quantum 
!                                                use efficiency
!                                       ZLEF    = leaf transpiration 
!                                        ZAGR = assimilation rate ratio
!                                        ZAG  = modified gross assimilation 
!                                               rate
!
REAL, DIMENSION(SIZE(PAN)) :: zgsc, zgs
!                                       ZGSC    = stomatal conductance to CO2
!                                       ZGS     = cuticular conductance (m s-1)
!
INTEGER :: jj, iter
!
REAL(KIND=JPRB) :: zhook_handle
!
!-------------------------------------------------------------------------------
!
IF (lhook) CALL dr_hook('COTWO',0,zhook_handle)
!
!*       X.     COMPUTE PRELIMINARY QUANITIES NEEDED FOR CO2 MODEL
!               --------------------------------------------------
!
DO jj = 1, SIZE(pan) 
  !
  !*       X.     BEGIN CO2 MODEL:
  !               ----------------
  !
  !                                                          Equation #s in 
  !                                                          Jacob's Thesis:
  !
  zwork(jj) = max(pgc(jj)+pgmest(jj),xdenom_min)
  !  
  ! Eq. 3.21
  zfmin(jj) = pgc(jj)/zwork(jj) ! fmin
  ! fmin <= f0, and so f <= f0
  zfmin(jj) = min(zfmin(jj),pfzero(jj))
  ! fmin > 0, and so PCI > PGAMMT
  zfmin(jj) = max(zfmin(jj),xdenom_min)
  !
  ! f from specific humidity deficit ds (g kg-1)
  !
  IF (pdmax(jj).NE.0.) THEN
    zdrap(jj)=min(1.0,pds(jj)/pdmax(jj))
  ELSE
    zdrap(jj)=1.
  ENDIF
  zf(jj)  = pfzero(jj)*(1.0-zdrap(jj)) + zfmin(jj)*zdrap(jj)
  !
  zcsp(jj)  = max(pcsp(jj),pgammt(jj)+1.e-6)
  !
  ! ci/cs ratio = f+(1.-f)*gammt/cs ; internal leaf CO2 concentration:
  !
  zci(jj) = zcsp(jj)*(zf(jj)+(1.0-zf(jj))*pgammt(jj)/zcsp(jj))
  !
  !
  ! Eq. 3.23
  zcmin(jj) = (pgc(jj)*zcsp(jj) + pgmest(jj)*pgammt(jj))/zwork(jj) 
  !
  ! residual photosynthesis rate (kgCO2 kgAir-1 m s-1)
  !
  zamin(jj) = pgmest(jj)*(zcmin(jj)-pgammt(jj))
  !
  !
  ! Eq. 3.12
  !
  ! light response curve (kgCO2 kgAir-1 m s-1)
  !
  zam(jj) = pgmest(jj)*(zci(jj)-pgammt(jj))
  !
  zam(jj) = -zam(jj)/panmax(jj)
  zam(jj) = panmax(jj)*(1.0 - exp(zam(jj)))
  zam(jj) = max(zam(jj),zamin(jj))
  !
  ! Assuming a nitrogen profile within the canopy with a Kn exctinction coefficient (Bonan et al, 2011) 
  ! that applies to dark respiration. Here Kn=0.2 (Mercado et al, 2009).
  ! Rd is divised by LAI to be consistent with the logic of assimilation (calculated per unit LAI)
  ! if not tropical forest, PLAITOP=0, PRD=ZAM*XRDCF
  !
  prd(jj) = zam(jj)*xrdcf/plai(jj)*exp(-0.2*plaitop(jj))
  !
  ! Initial quantum use efficiency (kgCO2 J-1 PAR m3 kgAir-1):
  !
  zeps(jj)   = pepso(jj)*(zci(jj) - pgammt(jj))/(zci(jj) + 2.0*pgammt(jj))
  !
  IF (zam(jj)/=0.) THEN
    pan(jj) = (zam(jj) + prd(jj))*( 1.0 - exp(-zeps(jj)*pia(jj) &
               /(zam(jj) + prd(jj))) ) - prd(jj)  
  ELSE
    pan(jj) = 0.
  ENDIF
  pan(jj) = max(-prd(jj),pan(jj))
  !
  ! Eq. 3.28
  IF (zam(jj)/=0.) THEN
    zagr(jj) = (pan(jj) + prd(jj))/(zam(jj) + prd(jj))   
  ELSE
    zagr(jj)=0.
  ENDIF
  !
  zag(jj)  = pan(jj) - zamin(jj)*zdrap(jj)*zagr(jj) +     &
                   prd(jj)*(1.0-zagr(jj))  
  !
  zlef(jj)    = 0.0                                  ! initialize leaf transpiration
  !
ENDDO
!
!   Iterate bewteen GSC and LEF:
!
! Iterations are for stomatal conductance and stomatal evaporation only
!
DO iter = 1, 3
  !
  DO jj = 1, SIZE(pan)
    !
    ! stomatal conductance for CO2 (m s-1):
    !
    zgsc(jj) = zag(jj)/(zcsp(jj) - zci(jj))
    zgsc(jj) = max( xcondstmin, zgsc(jj))
    zgsc(jj) = zgsc(jj) + xairtoh2o*zlef(jj)*( (zcsp(jj) +      &
                zci(jj))/(2.0*(zcsp(jj) - zci(jj))) )
    !
    IF (iter<3) THEN
    !
      zgs(jj) = 1.6*zgsc(jj)
    !
    ! compute transpiration (kgH2O kgAir-1 m s-1) from specific
    ! humidity deficit
    !
    ! Eq. 3.5
      zlef(jj) = zgs(jj)*pds(jj)
    !
    ENDIF
    !
  ENDDO
  !
ENDDO
!   
!   End of iterations
!
! Final calculation of leaf conductance (stomatal AND cuticular)
!
! Eq. 3.16
pgs(:) = xco2toh2o*zgsc(:) + pgc(:)
!
! Prevent numerical artefact in plant transpiration when
! soilstress is maximum (F2 = 0.0)
!
pgs(:) = pgs(:) * min(1.0,pf2(:)/xdenom_min)
!
IF (lhook) CALL dr_hook('COTWO',1,zhook_handle)
!       
END SUBROUTINE cotwo