MODULE sbcisf !!====================================================================== !! *** MODULE sbcisf *** !! Surface module : update surface ocean boundary condition under ice !! shelf !!====================================================================== !! History : 3.2 ! 2011-02 (C.Harris ) Original code isf cav !! X.X ! 2006-02 (C. Wang ) Original code bg03 !! 3.4 ! 2013-03 (P. Mathiot) Merging + parametrization !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! sbc_isf : update sbc under ice shelf !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE eosbn2 ! equation of state USE sbc_oce ! surface boundary condition: ocean fields USE lbclnk ! USE iom ! I/O manager library USE in_out_manager ! I/O manager USE wrk_nemo ! Memory allocation USE timing ! Timing USE lib_fortran ! glob_sum USE zdfbfr USE fldread ! read input field at current time step IMPLICIT NONE PRIVATE PUBLIC sbc_isf, sbc_isf_init, sbc_isf_div, sbc_isf_alloc ! routine called in sbcmod and divcur ! public in order to be able to output then REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: risf_tsc_b, risf_tsc REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: qisf !: net heat flux from ice shelf REAL(wp), PUBLIC :: rn_hisf_tbl !: thickness of top boundary layer [m] LOGICAL , PUBLIC :: ln_divisf !: flag to correct divergence INTEGER , PUBLIC :: nn_isfblk !: INTEGER , PUBLIC :: nn_gammablk !: LOGICAL , PUBLIC :: ln_conserve !: REAL(wp), PUBLIC :: rn_gammat0 !: temperature exchange coeficient REAL(wp), PUBLIC :: rn_gammas0 !: salinity exchange coeficient REAL(wp), PUBLIC :: rdivisf !: flag to test if fwf apply on divergence REAL(wp) , PUBLIC, ALLOCATABLE, SAVE, DIMENSION (:,:) :: rzisf_tbl !:depth of calving front (shallowest point) nn_isf ==2/3 REAL(wp) , PUBLIC, ALLOCATABLE, SAVE, DIMENSION (:,:) :: rhisf_tbl, rhisf_tbl_0 !:thickness of tbl REAL(wp) , PUBLIC, ALLOCATABLE, SAVE, DIMENSION (:,:) :: r1_hisf_tbl !:1/thickness of tbl REAL(wp) , PUBLIC, ALLOCATABLE, SAVE, DIMENSION (:,:) :: ralpha !:proportion of bottom cell influenced by tbl REAL(wp) , PUBLIC, ALLOCATABLE, SAVE, DIMENSION (:,:) :: risfLeff !:effective length (Leff) BG03 nn_isf==2 REAL(wp) , PUBLIC, ALLOCATABLE, SAVE, DIMENSION (:,:) :: ttbl, stbl, utbl, vtbl !:top boundary layer variable at T point INTEGER, PUBLIC, ALLOCATABLE, SAVE, DIMENSION (:,:) :: misfkt, misfkb !:Level of ice shelf base LOGICAL, PUBLIC :: l_isfcpl = .false. ! isf recieved from oasis REAL(wp), PUBLIC, SAVE :: rcpi = 2000.0_wp ! phycst ? REAL(wp), PUBLIC, SAVE :: kappa = 1.54e-6_wp ! phycst ? REAL(wp), PUBLIC, SAVE :: rhoisf = 920.0_wp ! phycst ? REAL(wp), PUBLIC, SAVE :: tsurf = -20.0_wp ! phycst ? REAL(wp), PUBLIC, SAVE :: lfusisf= 0.334e6_wp ! phycst ? !: Variable used in fldread to read the forcing file (nn_isf == 4 .OR. nn_isf == 3) CHARACTER(len=100), PUBLIC :: cn_dirisf = './' !: Root directory for location of ssr files TYPE(FLD_N) , PUBLIC :: sn_qisf, sn_fwfisf !: information about the runoff file to be read TYPE(FLD), ALLOCATABLE, DIMENSION(:) :: sf_qisf, sf_fwfisf TYPE(FLD_N) , PUBLIC :: sn_rnfisf !: information about the runoff file to be read TYPE(FLD), ALLOCATABLE, DIMENSION(:) :: sf_rnfisf TYPE(FLD_N) , PUBLIC :: sn_depmax_isf, sn_depmin_isf, sn_Leff_isf !: information about the runoff file to be read !! * Substitutions # include "domzgr_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.0 , LOCEAN-IPSL (2008) !! $Id: sbcisf.F90 5424 2018-04-27 07:03:10Z ufla $ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE sbc_isf(kt) INTEGER, INTENT(in) :: kt ! ocean time step INTEGER :: ji, jj, jk INTEGER :: ikt, ikb ! top and bottom level of the isf boundary layer REAL(wp) :: zhk REAL(wp) :: zt_frz, zpress REAL(wp), DIMENSION(:,:,:), POINTER :: zfwfisf3d, zqhcisf3d, zqlatisf3d REAL(wp), DIMENSION(:,: ), POINTER :: zqhcisf2d REAL(wp) :: zhisf IF( MOD( kt-1, nn_fsbc) == 0 ) THEN ! compute bottom level of isf tbl and thickness of tbl below the ice shelf DO jj = 1,jpj DO ji = 1,jpi ikt = misfkt(ji,jj) ikb = misfkt(ji,jj) ! thickness of boundary layer at least the top level thickness rhisf_tbl(ji,jj) = MAX(rhisf_tbl_0(ji,jj), fse3t_n(ji,jj,ikt)) ! determine the deepest level influenced by the boundary layer DO jk = ikt, mbkt(ji,jj) IF ( (SUM(fse3t_n(ji,jj,ikt:jk-1)) .LT. rhisf_tbl(ji,jj)) .AND. (tmask(ji,jj,jk) == 1) ) ikb = jk END DO rhisf_tbl(ji,jj) = MIN(rhisf_tbl(ji,jj), SUM(fse3t_n(ji,jj,ikt:ikb))) ! limit the tbl to water thickness. misfkb(ji,jj) = ikb ! last wet level of the tbl r1_hisf_tbl(ji,jj) = 1._wp / rhisf_tbl(ji,jj) zhk = SUM( fse3t(ji, jj, ikt:ikb - 1)) * r1_hisf_tbl(ji,jj) ! proportion of tbl cover by cell from ikt to ikb - 1 ralpha(ji,jj) = rhisf_tbl(ji,jj) * (1._wp - zhk ) / fse3t(ji,jj,ikb) ! proportion of bottom cell influenced by boundary layer END DO END DO ! compute salf and heat flux IF (nn_isf == 1) THEN ! realistic ice shelf formulation ! compute T/S/U/V for the top boundary layer CALL sbc_isf_tbl(tsn(:,:,:,jp_tem),ttbl(:,:),'T') CALL sbc_isf_tbl(tsn(:,:,:,jp_sal),stbl(:,:),'T') CALL sbc_isf_tbl(un(:,:,:),utbl(:,:),'U') CALL sbc_isf_tbl(vn(:,:,:),vtbl(:,:),'V') ! iom print CALL iom_put('ttbl',ttbl(:,:)) CALL iom_put('stbl',stbl(:,:)) CALL iom_put('utbl',utbl(:,:)) CALL iom_put('vtbl',vtbl(:,:)) ! compute fwf and heat flux IF( .NOT.l_isfcpl ) THEN ; CALL sbc_isf_cav (kt) ELSE ; qisf(:,:) = fwfisf(:,:) * lfusisf ! heat flux ENDIF ELSE IF (nn_isf == 2) THEN ! Beckmann and Goosse parametrisation stbl(:,:) = soce CALL sbc_isf_bg03(kt) ELSE IF (nn_isf == 3) THEN ! specified runoff in depth (Mathiot et al., XXXX in preparation) IF( .NOT.l_isfcpl ) THEN CALL fld_read ( kt, nn_fsbc, sf_rnfisf ) fwfisf(:,:) = - sf_rnfisf(1)%fnow(:,:,1) ! fresh water flux from the isf (fwfisf <0 mean melting) ENDIF qisf(:,:) = fwfisf(:,:) * lfusisf ! heat flux stbl(:,:) = soce ELSE IF (nn_isf == 4) THEN ! specified fwf and heat flux forcing beneath the ice shelf IF( .NOT.l_isfcpl ) THEN CALL fld_read ( kt, nn_fsbc, sf_fwfisf ) !CALL fld_read ( kt, nn_fsbc, sf_qisf ) fwfisf(:,:) = sf_fwfisf(1)%fnow(:,:,1) ! fwf ENDIF qisf(:,:) = fwfisf(:,:) * lfusisf ! heat flux !qisf(:,:) = sf_qisf(1)%fnow(:,:,1) ! heat flux stbl(:,:) = soce END IF ! compute tsc due to isf ! WARNING water add at temp = 0C, correction term is added, maybe better here but need a 3D variable). ! zpress = grav*rau0*fsdept(ji,jj,jk)*1.e-04 zt_frz = -1.9 !eos_fzp( tsn(ji,jj,jk,jp_sal), zpress ) risf_tsc(:,:,jp_tem) = qisf(:,:) * r1_rau0_rcp - rdivisf * fwfisf(:,:) * zt_frz * r1_rau0 ! ! salt effect already take into account in vertical advection risf_tsc(:,:,jp_sal) = (1.0_wp-rdivisf) * fwfisf(:,:) * soce * r1_rau0 ! lbclnk CALL lbc_lnk(risf_tsc(:,:,jp_tem),'T',1.) CALL lbc_lnk(risf_tsc(:,:,jp_sal),'T',1.) CALL lbc_lnk(fwfisf(:,:) ,'T',1.) CALL lbc_lnk(qisf(:,:) ,'T',1.) ! output IF( iom_use('iceshelf_cea') ) CALL iom_put( 'iceshelf_cea', -fwfisf(:,:) ) ! isf mass flux IF( iom_use('hflx_isf_cea') ) CALL iom_put( 'hflx_isf_cea', risf_tsc(:,:,jp_tem) * rau0 * rcp ) ! isf sensible+latent heat (W/m2) IF( iom_use('qlatisf' ) ) CALL iom_put( 'qlatisf' , qisf(:,:) ) ! isf latent heat IF( iom_use('fwfisf' ) ) CALL iom_put( 'fwfisf' , fwfisf(:,:) ) ! isf mass flux (opposite sign) ! Diagnostics IF( iom_use('fwfisf3d') .OR. iom_use('qlatisf3d') .OR. iom_use('qhcisf3d') .OR. iom_use('qhcisf')) THEN ! CALL wrk_alloc( jpi,jpj,jpk, zfwfisf3d, zqhcisf3d, zqlatisf3d ) CALL wrk_alloc( jpi,jpj, zqhcisf2d ) ! zfwfisf3d(:,:,:) = 0.0_wp ! 3d ice shelf melting (kg/m2/s) zqhcisf3d(:,:,:) = 0.0_wp ! 3d heat content flux (W/m2) zqlatisf3d(:,:,:)= 0.0_wp ! 3d ice shelf melting latent heat flux (W/m2) zqhcisf2d(:,:) = rdivisf * fwfisf(:,:) * zt_frz * rcp ! 2d heat content flux (W/m2) ! DO jj = 1,jpj DO ji = 1,jpi ikt = misfkt(ji,jj) ikb = misfkb(ji,jj) DO jk = ikt, ikb - 1 zhisf = r1_hisf_tbl(ji,jj) * fse3t(ji,jj,jk) zfwfisf3d (ji,jj,jk) = zfwfisf3d (ji,jj,jk) + fwfisf(ji,jj) * zhisf zqhcisf3d (ji,jj,jk) = zqhcisf3d (ji,jj,jk) + zqhcisf2d(ji,jj) * zhisf zqlatisf3d(ji,jj,jk) = zqlatisf3d(ji,jj,jk) + qisf(ji,jj) * zhisf END DO jk = ikb zhisf = r1_hisf_tbl(ji,jj) * fse3t(ji,jj,jk) zfwfisf3d (ji,jj,jk) = zfwfisf3d (ji,jj,jk) + fwfisf (ji,jj) * zhisf * ralpha(ji,jj) zqhcisf3d (ji,jj,jk) = zqhcisf3d (ji,jj,jk) + zqhcisf2d(ji,jj) * zhisf * ralpha(ji,jj) zqlatisf3d(ji,jj,jk) = zqlatisf3d(ji,jj,jk) + qisf (ji,jj) * zhisf * ralpha(ji,jj) END DO END DO ! CALL iom_put( 'fwfisf3d' , zfwfisf3d (:,:,:) ) CALL iom_put( 'qlatisf3d', zqlatisf3d(:,:,:) ) CALL iom_put( 'qhcisf3d' , zqhcisf3d (:,:,:) ) CALL iom_put( 'qhcisf' , zqhcisf2d (:,: ) ) ! CALL wrk_dealloc( jpi,jpj,jpk, zfwfisf3d, zqhcisf3d, zqlatisf3d ) CALL wrk_dealloc( jpi,jpj, zqhcisf2d ) ! END IF ! if apply only on the trend and not as a volume flux (rdivisf = 0), fwfisf have to be set to 0 now fwfisf(:,:) = rdivisf * fwfisf(:,:) ! END IF ! ! IF( kt == nit000 ) THEN ! set the forcing field at nit000 - 1 ! IF( ln_rstart .AND. & ! Restart: read in restart file & iom_varid( numror, 'fwf_isf_b', ldstop = .FALSE. ) > 0 ) THEN IF(lwp) WRITE(numout,*) ' nit000-1 isf tracer content forcing fields read in the restart file' CALL iom_get( numror, jpdom_autoglo, 'fwf_isf_b', fwfisf_b(:,:) ) ! before salt content isf_tsc trend CALL iom_get( numror, jpdom_autoglo, 'isf_sc_b', risf_tsc_b(:,:,jp_sal) ) ! before salt content isf_tsc trend CALL iom_get( numror, jpdom_autoglo, 'isf_hc_b', risf_tsc_b(:,:,jp_tem) ) ! before salt content isf_tsc trend ELSE fwfisf_b(:,:) = fwfisf(:,:) risf_tsc_b(:,:,:)= risf_tsc(:,:,:) END IF ENDIF ! IF( lrst_oce ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'sbc : isf surface tracer content forcing fields written in ocean restart file ', & & 'at it= ', kt,' date= ', ndastp IF(lwp) WRITE(numout,*) '~~~~' CALL iom_rstput( kt, nitrst, numrow, 'fwf_isf_b', fwfisf(:,:) ) CALL iom_rstput( kt, nitrst, numrow, 'isf_hc_b' , risf_tsc(:,:,jp_tem) ) CALL iom_rstput( kt, nitrst, numrow, 'isf_sc_b' , risf_tsc(:,:,jp_sal) ) ENDIF ! END SUBROUTINE sbc_isf SUBROUTINE sbc_isf_init INTEGER :: ji, jj, jk, ijkmin, inum, ierror INTEGER :: ikt, ikb ! top and bottom level of the isf boundary layer REAL(wp) :: zhk CHARACTER(len=256) :: cfisf , cvarzisf, cvarhisf ! name for isf file CHARACTER(LEN=256) :: cnameis ! name of iceshelf file CHARACTER (LEN=32) :: cvarLeff ! variable name for efficient Length scale INTEGER :: ios ! Local integer output status for namelist read ! !!--------------------------------------------------------------------- NAMELIST/namsbc_isf/ nn_isfblk, rn_hisf_tbl, ln_divisf, ln_conserve, rn_gammat0, rn_gammas0, nn_gammablk, & & sn_fwfisf, sn_qisf, sn_rnfisf, sn_depmax_isf, sn_depmin_isf, sn_Leff_isf ! ! REWIND( numnam_ref ) ! Namelist namsbc_rnf in reference namelist : Runoffs READ ( numnam_ref, namsbc_isf, IOSTAT = ios, ERR = 901) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namsbc_isf in reference namelist', lwp ) REWIND( numnam_cfg ) ! Namelist namsbc_rnf in configuration namelist : Runoffs READ ( numnam_cfg, namsbc_isf, IOSTAT = ios, ERR = 902 ) 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namsbc_isf in configuration namelist', lwp ) IF(lwm) WRITE ( numond, namsbc_isf ) IF ( lwp ) WRITE(numout,*) IF ( lwp ) WRITE(numout,*) 'sbc_isf: heat flux of the ice shelf' IF ( lwp ) WRITE(numout,*) '~~~~~~~~~' IF ( lwp ) WRITE(numout,*) 'sbcisf :' IF ( lwp ) WRITE(numout,*) '~~~~~~~~' IF ( lwp ) WRITE(numout,*) ' nn_isf = ', nn_isf IF ( lwp ) WRITE(numout,*) ' nn_isfblk = ', nn_isfblk IF ( lwp ) WRITE(numout,*) ' rn_hisf_tbl = ', rn_hisf_tbl IF ( lwp ) WRITE(numout,*) ' ln_divisf = ', ln_divisf IF ( lwp ) WRITE(numout,*) ' nn_gammablk = ', nn_gammablk IF ( lwp ) WRITE(numout,*) ' rn_tfri2 = ', rn_tfri2 IF (ln_divisf) THEN ! keep it in the namelist ??? used true anyway as for runoff ? (PM) rdivisf = 1._wp ELSE rdivisf = 0._wp END IF ! ! Allocate public variable IF ( sbc_isf_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'sbc_isf : unable to allocate arrays' ) ! ! initialisation qisf(:,:) = 0._wp ; fwfisf(:,:) = 0._wp risf_tsc(:,:,:) = 0._wp ! ! define isf tbl tickness, top and bottom indice IF (nn_isf == 1) THEN rhisf_tbl(:,:) = rn_hisf_tbl misfkt(:,:) = mikt(:,:) ! same indice for bg03 et cav => used in isfdiv ELSE IF ((nn_isf == 3) .OR. (nn_isf == 2)) THEN IF( .NOT.l_isfcpl ) THEN ALLOCATE( sf_rnfisf(1), STAT=ierror ) ALLOCATE( sf_rnfisf(1)%fnow(jpi,jpj,1), sf_rnfisf(1)%fdta(jpi,jpj,1,2) ) CALL fld_fill(sf_rnfisf, (/ sn_rnfisf /), cn_dirisf, 'sbc_isf_init', 'read fresh water flux isf data', 'namsbc_isf') ENDIF !: read effective lenght (BG03) IF (nn_isf == 2) THEN ! Read Data and save some integral values CALL iom_open( sn_Leff_isf%clname, inum ) cvarLeff = 'soLeff' !: variable name for Efficient Length scale CALL iom_get( inum, jpdom_data, cvarLeff, risfLeff , 1) CALL iom_close(inum) ! risfLeff = risfLeff*1000 !: convertion in m END IF ! read depth of the top and bottom of the isf top boundary layer (in this case, isf front depth and grounding line depth) CALL iom_open( sn_depmax_isf%clname, inum ) cvarhisf = TRIM(sn_depmax_isf%clvar) CALL iom_get( inum, jpdom_data, cvarhisf, rhisf_tbl, 1) !: depth of deepest point of the ice shelf base CALL iom_close(inum) ! CALL iom_open( sn_depmin_isf%clname, inum ) cvarzisf = TRIM(sn_depmin_isf%clvar) CALL iom_get( inum, jpdom_data, cvarzisf, rzisf_tbl, 1) !: depth of shallowest point of the ice shelves base CALL iom_close(inum) ! rhisf_tbl(:,:) = rhisf_tbl(:,:) - rzisf_tbl(:,:) !: tickness isf boundary layer !! compute first level of the top boundary layer DO ji = 1, jpi DO jj = 1, jpj jk = 2 DO WHILE ( jk .LE. mbkt(ji,jj) .AND. gdepw_0(ji,jj,jk) < rzisf_tbl(ji,jj) ) ; jk = jk + 1 ; END DO misfkt(ji,jj) = jk-1 END DO END DO ELSE IF ( nn_isf == 4 ) THEN ! as in nn_isf == 1 rhisf_tbl(:,:) = rn_hisf_tbl misfkt(:,:) = mikt(:,:) ! same indice for bg03 et cav => used in isfdiv ! load variable used in fldread (use for temporal interpolation of isf fwf forcing) IF( .NOT.l_isfcpl ) THEN ALLOCATE( sf_fwfisf(1), sf_qisf(1), STAT=ierror ) ALLOCATE( sf_fwfisf(1)%fnow(jpi,jpj,1), sf_fwfisf(1)%fdta(jpi,jpj,1,2) ) ALLOCATE( sf_qisf(1)%fnow(jpi,jpj,1), sf_qisf(1)%fdta(jpi,jpj,1,2) ) CALL fld_fill(sf_fwfisf, (/ sn_fwfisf /), cn_dirisf, 'sbc_isf_init', 'read fresh water flux isf data', 'namsbc_isf') !CALL fld_fill( sf_qisf , (/ sn_qisf /), cn_dirisf, 'sbc_isf_init', 'read heat flux isf data' , 'namsbc_isf' ) ENDIF END IF ! save initial top boundary layer thickness rhisf_tbl_0(:,:) = rhisf_tbl(:,:) ! END SUBROUTINE sbc_isf_init INTEGER FUNCTION sbc_isf_alloc() !!---------------------------------------------------------------------- !! *** FUNCTION sbc_isf_rnf_alloc *** !!---------------------------------------------------------------------- sbc_isf_alloc = 0 ! set to zero if no array to be allocated IF( .NOT. ALLOCATED( qisf ) ) THEN ALLOCATE( risf_tsc(jpi,jpj,jpts), risf_tsc_b(jpi,jpj,jpts), qisf(jpi,jpj) , & & rhisf_tbl(jpi,jpj) , r1_hisf_tbl(jpi,jpj), rzisf_tbl(jpi,jpj) , & & ttbl(jpi,jpj) , stbl(jpi,jpj) , utbl(jpi,jpj) , & & vtbl(jpi, jpj) , risfLeff(jpi,jpj) , rhisf_tbl_0(jpi,jpj), & & ralpha(jpi,jpj) , misfkt(jpi,jpj) , misfkb(jpi,jpj) , & & STAT= sbc_isf_alloc ) ! IF( lk_mpp ) CALL mpp_sum ( sbc_isf_alloc ) IF( sbc_isf_alloc /= 0 ) CALL ctl_warn('sbc_isf_alloc: failed to allocate arrays.') ! ENDIF END FUNCTION SUBROUTINE sbc_isf_bg03(kt) !!========================================================================== !! *** SUBROUTINE sbcisf_bg03 *** !! add net heat and fresh water flux from ice shelf melting !! into the adjacent ocean using the parameterisation by !! Beckmann and Goosse (2003), "A parameterization of ice shelf-ocean !! interaction for climate models", Ocean Modelling 5(2003) 157-170. !! (hereafter BG) !!========================================================================== !!---------------------------------------------------------------------- !! sbc_isf_bg03 : routine called from sbcmod !!---------------------------------------------------------------------- !! !! ** Purpose : Add heat and fresh water fluxes due to ice shelf melting !! ** Reference : Beckmann et Goosse, 2003, Ocean Modelling !! !! History : !! ! 06-02 (C. Wang) Original code !!---------------------------------------------------------------------- INTEGER, INTENT ( in ) :: kt INTEGER :: ji, jj, jk, jish !temporary integer INTEGER :: ijkmin INTEGER :: ii, ij, ik INTEGER :: inum REAL(wp) :: zt_sum ! sum of the temperature between 200m and 600m REAL(wp) :: zt_ave ! averaged temperature between 200m and 600m REAL(wp) :: zt_frz ! freezing point temperature at depth z REAL(wp) :: zpress ! pressure to compute the freezing point in depth !!---------------------------------------------------------------------- IF ( nn_timing == 1 ) CALL timing_start('sbc_isf_bg03') ! ! This test is false only in the very first time step of a run (JMM ???- Initialy build to skip 1rst year of run ) DO ji = 1, jpi DO jj = 1, jpj ik = misfkt(ji,jj) !! Initialize arrays to 0 (each step) zt_sum = 0.e0_wp IF ( ik .GT. 1 ) THEN ! 3. -----------the average temperature between 200m and 600m --------------------- DO jk = misfkt(ji,jj),misfkb(ji,jj) ! freezing point temperature at ice shelf base BG eq. 2 (JMM sign pb ??? +7.64e-4 !!!) ! after verif with UNESCO, wrong sign in BG eq. 2 ! Calculate freezing temperature zpress = grav*rau0*fsdept(ji,jj,ik)*1.e-04 CALL eos_fzp(tsb(ji,jj,ik,jp_sal), zt_frz, zpress) zt_sum = zt_sum + (tsn(ji,jj,ik,jp_tem)-zt_frz) * fse3t(ji,jj,ik) * tmask(ji,jj,ik) ! sum temp ENDDO zt_ave = zt_sum/rhisf_tbl(ji,jj) ! calcul mean value ! 4. ------------Net heat flux and fresh water flux due to the ice shelf ! For those corresponding to zonal boundary qisf(ji,jj) = - rau0 * rcp * rn_gammat0 * risfLeff(ji,jj) * e1t(ji,jj) * zt_ave & & / (e1t(ji,jj) * e2t(ji,jj)) * tmask(ji,jj,ik) fwfisf(ji,jj) = qisf(ji,jj) / lfusisf !fresh water flux kg/(m2s) ELSE qisf(ji,jj) = 0._wp ; fwfisf(ji,jj) = 0._wp END IF ENDDO ENDDO ! IF( nn_timing == 1 ) CALL timing_stop('sbc_isf_bg03') END SUBROUTINE sbc_isf_bg03 SUBROUTINE sbc_isf_cav( kt ) !!--------------------------------------------------------------------- !! *** ROUTINE sbc_isf_cav *** !! !! ** Purpose : handle surface boundary condition under ice shelf !! !! ** Method : - !! !! ** Action : utau, vtau : remain unchanged !! taum, wndm : remain unchanged !! qns : update heat flux below ice shelf !! emp, emps : update freshwater flux below ice shelf !!--------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! ocean time step ! LOGICAL :: ln_isomip = .true. REAL(wp), DIMENSION(:,:), POINTER :: zfrz,zpress,zti REAL(wp), DIMENSION(:,:), POINTER :: zgammat2d, zgammas2d !REAL(wp), DIMENSION(:,:), POINTER :: zqisf, zfwfisf REAL(wp) :: zlamb1, zlamb2, zlamb3 REAL(wp) :: zeps1,zeps2,zeps3,zeps4,zeps6,zeps7 REAL(wp) :: zaqe,zbqe,zcqe,zaqer,zdis,zsfrz,zcfac REAL(wp) :: zfwflx, zhtflx, zhtflx_b REAL(wp) :: zgammat, zgammas REAL(wp) :: zeps = -1.e-20_wp !== Local constant initialization ==! INTEGER :: ji, jj ! dummy loop indices INTEGER :: ii0, ii1, ij0, ij1 ! temporary integers INTEGER :: ierror ! return error code LOGICAL :: lit=.TRUE. INTEGER :: nit !!--------------------------------------------------------------------- ! ! coeficient for linearisation of tfreez zlamb1=-0.0575 zlamb2=0.0901 zlamb3=-7.61e-04 IF( nn_timing == 1 ) CALL timing_start('sbc_isf_cav') ! CALL wrk_alloc( jpi,jpj, zfrz,zpress,zti, zgammat2d, zgammas2d ) zcfac=0.0_wp IF (ln_conserve) zcfac=1.0_wp zpress(:,:)=0.0_wp zgammat2d(:,:)=0.0_wp zgammas2d(:,:)=0.0_wp ! ! !CDIR COLLAPSE DO jj = 1, jpj DO ji = 1, jpi ! Crude approximation for pressure (but commonly used) ! 1e-04 to convert from Pa to dBar zpress(ji,jj)=grav*rau0*fsdepw(ji,jj,mikt(ji,jj))*1.e-04 ! END DO END DO ! convert CT to Tpot IF (ln_useCT) ttbl=eos_pt_from_ct(ttbl,stbl) ! Calculate in-situ temperature (ref to surface) zti(:,:)=tinsitu( ttbl, stbl, zpress ) ! Calculate freezing temperature CALL eos_fzp( sss_m(:,:), zfrz(:,:), zpress ) zhtflx=0._wp ; zfwflx=0._wp IF (nn_isfblk == 1) THEN DO jj = 1, jpj DO ji = 1, jpi IF (mikt(ji,jj) > 1 ) THEN nit = 1; lit = .TRUE.; zgammat=rn_gammat0; zgammas=rn_gammas0; zhtflx_b=0._wp DO WHILE ( lit ) ! compute gamma CALL sbc_isf_gammats(zgammat, zgammas, zhtflx, zfwflx, ji, jj, lit) ! zhtflx is upward heat flux (out of ocean) zhtflx = zgammat*rcp*rau0*(zti(ji,jj)-zfrz(ji,jj)) ! zwflx is upward water flux zfwflx = - zhtflx/lfusisf ! test convergence and compute gammat IF ( (zhtflx - zhtflx_b) .LE. 0.01 ) lit = .FALSE. nit = nit + 1 IF (nit .GE. 100) CALL ctl_stop( 'STOP', 'sbc_isf_hol99 : too many iteration ...' ) ! save gammat and compute zhtflx_b zgammat2d(ji,jj)=zgammat zhtflx_b = zhtflx END DO qisf(ji,jj) = - zhtflx ! For genuine ISOMIP protocol this should probably be something like fwfisf(ji,jj) = zfwflx ELSE fwfisf(ji,jj) = 0._wp qisf(ji,jj) = 0._wp END IF ! END DO END DO ELSE IF (nn_isfblk == 2 ) THEN ! More complicated 3 equation thermodynamics as in MITgcm !CDIR COLLAPSE DO jj = 2, jpj DO ji = 2, jpi IF (mikt(ji,jj) > 1 ) THEN nit=1; lit=.TRUE.; zgammat=rn_gammat0; zgammas=rn_gammas0; zhtflx_b=0._wp; zhtflx=0._wp DO WHILE ( lit ) CALL sbc_isf_gammats(zgammat, zgammas, zhtflx, zfwflx, ji, jj, lit) zeps1=rcp*rau0*zgammat zeps2=lfusisf*rau0*zgammas zeps3=rhoisf*rcpi*kappa/risfdep(ji,jj) zeps4=zlamb2+zlamb3*risfdep(ji,jj) zeps6=zeps4-zti(ji,jj) zeps7=zeps4-tsurf zaqe=zlamb1 * (zeps1 + zeps3) zaqer=0.5/zaqe zbqe=zeps1*zeps6+zeps3*zeps7-zeps2 zcqe=zeps2*stbl(ji,jj) zdis=zbqe*zbqe-4.0*zaqe*zcqe ! Presumably zdis can never be negative because gammas is very small compared to gammat zsfrz=(-zbqe-SQRT(zdis))*zaqer IF (zsfrz .lt. 0.0) zsfrz=(-zbqe+SQRT(zdis))*zaqer zfrz(ji,jj)=zeps4+zlamb1*zsfrz ! zfwflx is upward water flux zfwflx= rau0 * zgammas * ( (zsfrz-stbl(ji,jj)) / zsfrz ) IF ( rdivisf==0 ) THEN ! zhtflx is upward heat flux (out of ocean) ! If non conservative we have zcfac=0.0 so zhtflx is as ISOMIP but with different zfrz value zhtflx = ( zgammat*rau0 - zcfac*zfwflx ) * rcp * (zti(ji,jj) - zfrz(ji,jj) ) ! zwflx is upward water flux ! If non conservative we have zcfac=0.0 so what follows is then zfwflx*sss_m/zsfrz zfwflx = ( zgammas*rau0 - zcfac*zfwflx ) * (zsfrz - stbl(ji,jj)) / stbl(ji,jj) ELSE zhtflx = zgammat*rau0 * rcp * (zti(ji,jj) - zfrz(ji,jj) ) ! nothing to do for fwf END IF ! test convergence and compute gammat IF (( zhtflx - zhtflx_b) .LE. 0.01 ) lit = .FALSE. nit = nit + 1 IF (nit .GE. 51) THEN WRITE(numout,*) "sbcisf : too many iteration ... ", & & zhtflx, zhtflx_b, zgammat, zgammas, nn_gammablk, ji, jj, mikt(ji,jj), narea CALL ctl_stop( 'STOP', 'sbc_isf_hol99 : too many iteration ...' ) END IF ! save gammat and compute zhtflx_b zgammat2d(ji,jj)=zgammat zgammas2d(ji,jj)=zgammas zhtflx_b = zhtflx END DO ! If non conservative we have zcfac=0.0 so zhtflx is as ISOMIP but with different zfrz value qisf(ji,jj) = - zhtflx ! If non conservative we have zcfac=0.0 so what follows is then zfwflx*sss_m/zsfrz fwfisf(ji,jj) = zfwflx ELSE fwfisf(ji,jj) = 0._wp qisf(ji,jj) = 0._wp ENDIF ! END DO END DO ENDIF ! lbclnk CALL lbc_lnk(zgammas2d(:,:),'T',1.) CALL lbc_lnk(zgammat2d(:,:),'T',1.) ! output CALL iom_put('isfgammat', zgammat2d) CALL iom_put('isfgammas', zgammas2d) ! CALL wrk_dealloc( jpi,jpj, zfrz,zpress,zti, zgammat2d, zgammas2d ) ! IF( nn_timing == 1 ) CALL timing_stop('sbc_isf_cav') END SUBROUTINE sbc_isf_cav SUBROUTINE sbc_isf_gammats(gt, gs, zqhisf, zqwisf, ji, jj, lit ) !!---------------------------------------------------------------------- !! ** Purpose : compute the coefficient echange for heat flux !! !! ** Method : gamma assume constant or depends of u* and stability !! !! ** References : Holland and Jenkins, 1999, JPO, p1787-1800, eq 14 !! Jenkins et al., 2010, JPO, p2298-2312 !!--------------------------------------------------------------------- REAL(wp), INTENT(inout) :: gt, gs, zqhisf, zqwisf INTEGER , INTENT(in) :: ji,jj LOGICAL , INTENT(inout) :: lit INTEGER :: ikt ! loop index REAL(wp) :: zut, zvt, zustar ! U, V at T point and friction velocity REAL(wp) :: zdku, zdkv ! U, V shear REAL(wp) :: zPr, zSc, zRc ! Prandtl, Scmidth and Richardson number REAL(wp) :: zmob, zmols ! Monin Obukov length, coriolis factor at T point REAL(wp) :: zbuofdep, zhnu ! Bouyancy length scale, sublayer tickness REAL(wp) :: zhmax ! limitation of mol REAL(wp) :: zetastar ! stability parameter REAL(wp) :: zgmolet, zgmoles, zgturb ! contribution of modelecular sublayer and turbulence REAL(wp) :: zcoef ! temporary coef REAL(wp) :: zdep REAL(wp), PARAMETER :: zxsiN = 0.052 ! dimensionless constant REAL(wp), PARAMETER :: epsln = 1.0e-20 ! a small positive number REAL(wp), PARAMETER :: znu = 1.95e-6 ! kinamatic viscosity of sea water (m2.s-1) REAL(wp) :: rcs = 1.0e-3_wp ! conversion: mm/s ==> m/s REAL(wp), DIMENSION(2) :: zts, zab !!--------------------------------------------------------------------- ! IF( nn_gammablk == 0 ) THEN !! gamma is constant (specified in namelist) gt = rn_gammat0 gs = rn_gammas0 lit = .FALSE. ELSE IF ( nn_gammablk == 1 ) THEN !! gamma is assume to be proportional to u* !! WARNING in case of Losh 2008 tbl parametrization, !! you have to used the mean value of u in the boundary layer) !! not yet coded !! Jenkins et al., 2010, JPO, p2298-2312 ikt = mikt(ji,jj) !! Compute U and V at T points ! zut = 0.5 * ( utbl(ji-1,jj ) + utbl(ji,jj) ) ! zvt = 0.5 * ( vtbl(ji ,jj-1) + vtbl(ji,jj) ) zut = utbl(ji,jj) zvt = vtbl(ji,jj) !! compute ustar zustar = SQRT( rn_tfri2 * (zut * zut + zvt * zvt) ) !! Compute mean value over the TBL !! Compute gammats gt = zustar * rn_gammat0 gs = zustar * rn_gammas0 lit = .FALSE. ELSE IF ( nn_gammablk == 2 ) THEN !! gamma depends of stability of boundary layer !! WARNING in case of Losh 2008 tbl parametrization, !! you have to used the mean value of u in the boundary layer) !! not yet coded !! Holland and Jenkins, 1999, JPO, p1787-1800, eq 14 !! as MOL depends of flux and flux depends of MOL, best will be iteration (TO DO) ikt = mikt(ji,jj) !! Compute U and V at T points zut = 0.5 * ( utbl(ji-1,jj ) + utbl(ji,jj) ) zvt = 0.5 * ( vtbl(ji ,jj-1) + vtbl(ji,jj) ) !! compute ustar zustar = SQRT( rn_tfri2 * (zut * zut + zvt * zvt) ) IF (zustar == 0._wp) THEN ! only for kt = 1 I think gt = rn_gammat0 gs = rn_gammas0 ELSE !! compute Rc number (as done in zdfric.F90) zcoef = 0.5 / fse3w(ji,jj,ikt) ! ! shear of horizontal velocity zdku = zcoef * ( un(ji-1,jj ,ikt ) + un(ji,jj,ikt ) & & -un(ji-1,jj ,ikt+1) - un(ji,jj,ikt+1) ) zdkv = zcoef * ( vn(ji ,jj-1,ikt ) + vn(ji,jj,ikt ) & & -vn(ji ,jj-1,ikt+1) - vn(ji,jj,ikt+1) ) ! ! richardson number (minimum value set to zero) zRc = rn2(ji,jj,ikt+1) / ( zdku*zdku + zdkv*zdkv + 1.e-20 ) !! compute Pr and Sc number (can be improved) zPr = 13.8 zSc = 2432.0 !! compute gamma mole zgmolet = 12.5 * zPr ** (2.0/3.0) - 6.0 zgmoles = 12.5 * zSc ** (2.0/3.0) -6.0 !! compute bouyancy zts(jp_tem) = ttbl(ji,jj) zts(jp_sal) = stbl(ji,jj) zdep = fsdepw(ji,jj,ikt) ! CALL eos_rab( zts, zdep, zab ) ! !! compute length scale zbuofdep = grav * ( zab(jp_tem) * zqhisf - zab(jp_sal) * zqwisf ) !!!!!!!!!!!!!!!!!!!!!!!!!!!! !! compute Monin Obukov Length ! Maximum boundary layer depth zhmax = fsdept(ji,jj,mbkt(ji,jj)) - fsdepw(ji,jj,mikt(ji,jj)) -0.001 ! Compute Monin obukhov length scale at the surface and Ekman depth: zmob = zustar ** 3 / (vkarmn * (zbuofdep + epsln)) zmols = SIGN(1._wp, zmob) * MIN(ABS(zmob), zhmax) * tmask(ji,jj,ikt) !! compute eta* (stability parameter) zetastar = 1 / ( SQRT(1 + MAX(zxsiN * zustar / ( ABS(ff(ji,jj)) * zmols * zRc ), 0.0))) !! compute the sublayer thickness zhnu = 5 * znu / zustar !! compute gamma turb zgturb = 1/vkarmn * LOG(zustar * zxsiN * zetastar * zetastar / ( ABS(ff(ji,jj)) * zhnu )) & & + 1 / ( 2 * zxsiN * zetastar ) - 1/vkarmn !! compute gammats gt = zustar / (zgturb + zgmolet) gs = zustar / (zgturb + zgmoles) END IF END IF END SUBROUTINE SUBROUTINE sbc_isf_tbl( varin, varout, cptin ) !!---------------------------------------------------------------------- !! *** SUBROUTINE sbc_isf_tbl *** !! !! ** Purpose : compute mean T/S/U/V in the boundary layer !! !!---------------------------------------------------------------------- REAL(wp), DIMENSION(:,:,:), INTENT(in) :: varin REAL(wp), DIMENSION(:,:) , INTENT(out):: varout CHARACTER(len=1), INTENT(in) :: cptin ! point of variable in/out REAL(wp) :: ze3, zhk REAL(wp), DIMENSION(:,:), POINTER :: zikt INTEGER :: ji,jj,jk INTEGER :: ikt,ikb INTEGER, DIMENSION(:,:), POINTER :: mkt, mkb CALL wrk_alloc( jpi,jpj, mkt, mkb ) CALL wrk_alloc( jpi,jpj, zikt ) ! get first and last level of tbl mkt(:,:) = misfkt(:,:) mkb(:,:) = misfkb(:,:) varout(:,:)=0._wp DO jj = 2,jpj DO ji = 2,jpi IF (ssmask(ji,jj) == 1) THEN ikt = mkt(ji,jj) ikb = mkb(ji,jj) ! level fully include in the ice shelf boundary layer DO jk = ikt, ikb - 1 ze3 = fse3t_n(ji,jj,jk) IF (cptin == 'T' ) varout(ji,jj) = varout(ji,jj) + varin(ji,jj,jk) * r1_hisf_tbl(ji,jj) * ze3 IF (cptin == 'U' ) varout(ji,jj) = varout(ji,jj) + 0.5_wp * (varin(ji,jj,jk) + varin(ji-1,jj,jk)) & & * r1_hisf_tbl(ji,jj) * ze3 IF (cptin == 'V' ) varout(ji,jj) = varout(ji,jj) + 0.5_wp * (varin(ji,jj,jk) + varin(ji,jj-1,jk)) & & * r1_hisf_tbl(ji,jj) * ze3 END DO ! level partially include in ice shelf boundary layer zhk = SUM( fse3t_n(ji, jj, ikt:ikb - 1)) * r1_hisf_tbl(ji,jj) IF (cptin == 'T') & & varout(ji,jj) = varout(ji,jj) + varin(ji,jj,ikb) * (1._wp - zhk) IF (cptin == 'U') & & varout(ji,jj) = varout(ji,jj) + 0.5_wp * (varin(ji,jj,ikb) + varin(ji-1,jj,ikb)) * (1._wp - zhk) IF (cptin == 'V') & & varout(ji,jj) = varout(ji,jj) + 0.5_wp * (varin(ji,jj,ikb) + varin(ji,jj-1,ikb)) * (1._wp - zhk) END IF END DO END DO CALL wrk_dealloc( jpi,jpj, mkt, mkb ) CALL wrk_dealloc( jpi,jpj, zikt ) IF (cptin == 'T') CALL lbc_lnk(varout,'T',1.) IF (cptin == 'U' .OR. cptin == 'V') CALL lbc_lnk(varout,'T',-1.) END SUBROUTINE sbc_isf_tbl SUBROUTINE sbc_isf_div( phdivn ) !!---------------------------------------------------------------------- !! *** SUBROUTINE sbc_isf_div *** !! !! ** Purpose : update the horizontal divergence with the runoff inflow !! !! ** Method : !! CAUTION : risf_tsc(:,:,jp_sal) is negative (outflow) increase the !! divergence and expressed in m/s !! !! ** Action : phdivn decreased by the runoff inflow !!---------------------------------------------------------------------- REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: phdivn ! horizontal divergence !! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ikt, ikb INTEGER :: nk_isf REAL(wp) :: zhk, z1_hisf_tbl, zhisf_tbl REAL(wp) :: zfact ! local scalar !!---------------------------------------------------------------------- ! zfact = 0.5_wp ! IF (lk_vvl) THEN ! need to re compute level distribution of isf fresh water DO jj = 1,jpj DO ji = 1,jpi ikt = misfkt(ji,jj) ikb = misfkt(ji,jj) ! thickness of boundary layer at least the top level thickness rhisf_tbl(ji,jj) = MAX(rhisf_tbl_0(ji,jj), fse3t(ji,jj,ikt)) ! determine the deepest level influenced by the boundary layer ! test on tmask useless ????? DO jk = ikt, mbkt(ji,jj) IF ( (SUM(fse3t(ji,jj,ikt:jk-1)) .LT. rhisf_tbl(ji,jj)) .AND. (tmask(ji,jj,jk) == 1) ) ikb = jk END DO rhisf_tbl(ji,jj) = MIN(rhisf_tbl(ji,jj), SUM(fse3t(ji,jj,ikt:ikb))) ! limit the tbl to water thickness. misfkb(ji,jj) = ikb ! last wet level of the tbl r1_hisf_tbl(ji,jj) = 1._wp / rhisf_tbl(ji,jj) zhk = SUM( fse3t(ji, jj, ikt:ikb - 1)) * r1_hisf_tbl(ji,jj) ! proportion of tbl cover by cell from ikt to ikb - 1 ralpha(ji,jj) = rhisf_tbl(ji,jj) * (1._wp - zhk ) / fse3t(ji,jj,ikb) ! proportion of bottom cell influenced by boundary layer END DO END DO END IF ! vvl case ! DO jj = 1,jpj DO ji = 1,jpi ikt = misfkt(ji,jj) ikb = misfkb(ji,jj) ! level fully include in the ice shelf boundary layer DO jk = ikt, ikb - 1 phdivn(ji,jj,jk) = phdivn(ji,jj,jk) + ( fwfisf(ji,jj) + fwfisf_b(ji,jj) ) & & * r1_hisf_tbl(ji,jj) * r1_rau0 * zfact END DO ! level partially include in ice shelf boundary layer phdivn(ji,jj,ikb) = phdivn(ji,jj,ikb) + ( fwfisf(ji,jj) & & + fwfisf_b(ji,jj) ) * r1_hisf_tbl(ji,jj) * r1_rau0 * zfact * ralpha(ji,jj) !== ice shelf melting mass distributed over several levels ==! END DO END DO ! END SUBROUTINE sbc_isf_div FUNCTION tinsitu( ptem, psal, ppress ) RESULT( pti ) !!---------------------------------------------------------------------- !! *** ROUTINE eos_init *** !! !! ** Purpose : Compute the in-situ temperature [Celcius] !! !! ** Method : !! !! Reference : Bryden,h.,1973,deep-sea res.,20,401-408 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptem ! potential temperature [Celcius] REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu] REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ppress ! pressure [dBar] REAL(wp), DIMENSION(:,:), POINTER :: pti ! in-situ temperature [Celcius] ! REAL(wp) :: fsatg ! REAL(wp) :: pfps, pfpt, pfphp REAL(wp) :: zt, zs, zp, zh, zq, zxk INTEGER :: ji, jj ! dummy loop indices ! CALL wrk_alloc( jpi,jpj, pti ) ! DO jj=1,jpj DO ji=1,jpi zh = ppress(ji,jj) ! Theta1 zt = ptem(ji,jj) zs = psal(ji,jj) zp = 0.0 zxk= zh * fsatg( zs, zt, zp ) zt = zt + 0.5 * zxk zq = zxk ! Theta2 zp = zp + 0.5 * zh zxk= zh*fsatg( zs, zt, zp ) zt = zt + 0.29289322 * ( zxk - zq ) zq = 0.58578644 * zxk + 0.121320344 * zq ! Theta3 zxk= zh * fsatg( zs, zt, zp ) zt = zt + 1.707106781 * ( zxk - zq ) zq = 3.414213562 * zxk - 4.121320344 * zq ! Theta4 zp = zp + 0.5 * zh zxk= zh * fsatg( zs, zt, zp ) pti(ji,jj) = zt + ( zxk - 2.0 * zq ) / 6.0 END DO END DO ! CALL wrk_dealloc( jpi,jpj, pti ) ! END FUNCTION tinsitu ! FUNCTION fsatg( pfps, pfpt, pfphp ) !!---------------------------------------------------------------------- !! *** FUNCTION fsatg *** !! !! ** Purpose : Compute the Adiabatic laspse rate [Celcius].[decibar]^-1 !! !! ** Reference : Bryden,h.,1973,deep-sea res.,20,401-408 !! !! ** units : pressure pfphp decibars !! temperature pfpt deg celsius (ipts-68) !! salinity pfps (ipss-78) !! adiabatic fsatg deg. c/decibar !!---------------------------------------------------------------------- REAL(wp) :: pfps, pfpt, pfphp REAL(wp) :: fsatg ! fsatg = (((-2.1687e-16*pfpt+1.8676e-14)*pfpt-4.6206e-13)*pfphp & & +((2.7759e-12*pfpt-1.1351e-10)*(pfps-35.)+((-5.4481e-14*pfpt & & +8.733e-12)*pfpt-6.7795e-10)*pfpt+1.8741e-8))*pfphp & & +(-4.2393e-8*pfpt+1.8932e-6)*(pfps-35.) & & +((6.6228e-10*pfpt-6.836e-8)*pfpt+8.5258e-6)*pfpt+3.5803e-5 ! END FUNCTION fsatg !!====================================================================== END MODULE sbcisf