MODULE icealb !!====================================================================== !! *** MODULE icealb *** !! Ocean forcing: bulk thermohaline forcing of the ice !!===================================================================== !! History : 4.0 ! 2017-07 (C. Rousset) Split ice and ocean albedos !!---------------------------------------------------------------------- #if defined key_lim3 !!---------------------------------------------------------------------- !! 'key_lim3' LIM 3.0 sea-ice model !!---------------------------------------------------------------------- !! ice_alb : albedo for ice (clear and overcast skies) !! alb_init : initialisation of albedo computation !!---------------------------------------------------------------------- USE ice, ONLY: jpl ! sea-ice: number of categories USE phycst ! physical constants ! USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) IMPLICIT NONE PRIVATE PUBLIC ice_alb_init ! called in icestp PUBLIC ice_alb ! called in iceforcing.F90 and iceupdate.F90 REAL(wp), PUBLIC, PARAMETER :: rn_alb_oce = 0.066 !: ocean or lead albedo (Pegau and Paulson, Ann. Glac. 2001) REAL(wp) , PARAMETER :: rc1 = 0.05 ! snow thickness (only for nn_ice_alb=0) REAL(wp) , PARAMETER :: rc2 = 0.10 ! " " REAL(wp) , PARAMETER :: rcloud = 0.06 ! cloud effect on albedo (only-for nn_ice_alb=0) REAL(wp) , PARAMETER :: r1_c1 = 1. / rc1 REAL(wp) , PARAMETER :: r1_c2 = 1. / rc2 ! ! ** albedo namelist (namice_alb) INTEGER :: nn_ice_alb ! type of albedo scheme: 0: Shine & Henderson-Sellers (JGR 1985) ! ! 1: "home made" based on Brandt et al. (JClim 2005) ! ! and Grenfell & Perovich (JGR 2004) ! ! 2: Same as 1 but with melt ponds REAL(wp) :: rn_alb_sdry ! dry snow albedo REAL(wp) :: rn_alb_smlt ! melting snow albedo REAL(wp) :: rn_alb_idry ! dry ice albedo REAL(wp) :: rn_alb_imlt ! bare puddled ice albedo REAL(wp) :: rn_alb_dpnd ! ponded ice albedo !!---------------------------------------------------------------------- !! NEMO/ICE 4.0 , NEMO Consortium (2017) !! $Id: icealb.F90 8268 2017-07-03 15:01:04Z clem $ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE ice_alb( pt_ice, ph_ice, ph_snw, pafrac_pnd, ph_pnd, ld_pnd, pa_ice_cs, pa_ice_os ) !!---------------------------------------------------------------------- !! *** ROUTINE ice_alb *** !! !! ** Purpose : Computation of the albedo of the snow/ice system !! !! ** Method : Two schemes are available (from namelist parameter nn_ice_alb) !! 0: the scheme is that of Shine & Henderson-Sellers (JGR 1985) for clear-skies !! 1: the scheme is "home made" (for cloudy skies) and based on Brandt et al. (J. Climate 2005) !! and Grenfell & Perovich (JGR 2004) !! 2: fractional surface-based formulation of scheme 1 (NEW) !! Description of scheme 1: !! 1) Albedo dependency on ice thickness follows the findings from Brandt et al (2005) !! which are an update of Allison et al. (JGR 1993) ; Brandt et al. 1999 !! 0-5cm : linear function of ice thickness !! 5-150cm: log function of ice thickness !! > 150cm: constant !! 2) Albedo dependency on snow thickness follows the findings from Grenfell & Perovich (2004) !! i.e. it increases as -EXP(-snw_thick/0.02) during freezing and -EXP(-snw_thick/0.03) during melting !! 3) Albedo dependency on clouds is speculated from measurements of Grenfell and Perovich (2004) !! i.e. cloudy-clear albedo depend on cloudy albedo following a 2d order polynomial law !! 4) The needed 4 parameters are: dry and melting snow, freezing ice and bare puddled ice !! !! ** Note : The parameterization from Shine & Henderson-Sellers presents several misconstructions: !! 1) ice albedo when ice thick. tends to 0 is different than ocean albedo !! 2) for small ice thick. covered with some snow (<3cm?), albedo is larger !! under melting conditions than under freezing conditions !! 3) the evolution of ice albedo as a function of ice thickness shows !! 3 sharp inflexion points (at 5cm, 100cm and 150cm) that look highly unrealistic !! !! References : Shine & Henderson-Sellers 1985, JGR, 90(D1), 2243-2250. !! Brandt et al. 2005, J. Climate, vol 18 !! Grenfell & Perovich 2004, JGR, vol 109 !!---------------------------------------------------------------------- REAL(wp), INTENT(in ), DIMENSION(:,:,:) :: pt_ice ! ice surface temperature (Kelvin) REAL(wp), INTENT(in ), DIMENSION(:,:,:) :: ph_ice ! sea-ice thickness REAL(wp), INTENT(in ), DIMENSION(:,:,:) :: ph_snw ! snow depth REAL(wp), INTENT(in ), DIMENSION(:,:,:) :: pafrac_pnd ! melt pond relative fraction (per unit ice area) REAL(wp), INTENT(in ), DIMENSION(:,:,:) :: ph_pnd ! melt pond depth LOGICAL , INTENT(in ) :: ld_pnd ! melt ponds radiatively active or not REAL(wp), INTENT( out), DIMENSION(:,:,:) :: pa_ice_cs ! albedo of ice under clear sky REAL(wp), INTENT( out), DIMENSION(:,:,:) :: pa_ice_os ! albedo of ice under overcast sky ! INTEGER :: ji, jj, jl ! dummy loop indices REAL(wp) :: zswitch, z1_c1, z1_c2 ! local scalar REAL(wp) :: z1_href_pnd ! - - REAL(wp) :: zalb_sm, zalb_sf, zalb_st ! albedo of snow melting, freezing, total ! REAL(wp), DIMENSION(jpi,jpj,jpl) :: zalb, zalb_it ! intermediate variable & albedo of ice (snow free) !! MV MP REAL(wp), DIMENSION(jpi,jpj,jpl) :: zalb_pnd ! ponded sea ice albedo REAL(wp), DIMENSION(jpi,jpj,jpl) :: zalb_ice ! bare sea ice albedo REAL(wp), DIMENSION(jpi,jpj,jpl) :: zalb_snw ! snow-covered sea ice albedo REAL(wp), DIMENSION(jpi,jpj,jpl) :: zafrac_snw ! relative snow fraction REAL(wp), DIMENSION(jpi,jpj,jpl) :: zafrac_ice ! relative ice fraction REAL(wp), DIMENSION(jpi,jpj,jpl) :: zafrac_pnd ! relative ice fraction (effective) !!--------------------------------------------------------------------- !----------------------------------------------------- ! Snow-free albedo (no ice thickness dependence yet) !----------------------------------------------------- ! ! Part common to nn_ice_alb = 0, 1, 2 ! IF ( .NOT. ld_pnd ) THEN !--- No melt ponds OR radiatively inactive melt ponds ! Bare ice albedo is prescribed, with implicit assumption on pond fraction and depth WHERE ( ph_snw == 0._wp .AND. pt_ice >= rt0 ) ; zalb(:,:,:) = rn_alb_imlt ELSEWHERE ; zalb(:,:,:) = rn_alb_idry END WHERE ENDIF SELECT CASE ( nn_ice_alb ) ! select a parameterization ! ! !------------------------------------------ CASE( 0 ) ! Shine and Henderson-Sellers (1985) ! (based on clear sky values) ! !------------------------------------------ ! ! ! Thickness-dependent bare ice albedo WHERE ( 1.5 < ph_ice ) ; zalb_it = zalb ELSEWHERE( 1.0 < ph_ice .AND. ph_ice <= 1.5 ) ; zalb_it = 0.472 + 2.0 * ( zalb - 0.472 ) * ( ph_ice - 1.0 ) ELSEWHERE( 0.05 < ph_ice .AND. ph_ice <= 1.0 ) ; zalb_it = 0.2467 + 0.7049 * ph_ice & & - 0.8608 * ph_ice * ph_ice & & + 0.3812 * ph_ice * ph_ice * ph_ice ELSEWHERE ; zalb_it = 0.1 + 3.6 * ph_ice END WHERE ! IF ( ld_pnd ) THEN ! Depth-dependent ponded ice albedo z1_href_pnd = 1. / 0.05 ! inverse of the characteristic length scale (Lecomte et al. 2015) zalb_pnd = rn_alb_dpnd - ( rn_alb_dpnd - zalb_it ) * EXP( - ph_pnd * z1_href_pnd ) ! ! Snow-free ice albedo is a function of pond fraction WHERE ( ph_snw == 0._wp .AND. pt_ice >= rt0 ) zalb_it = zalb_it * ( 1. - pafrac_pnd ) + zalb_pnd * pafrac_pnd END WHERE ENDIF ! !!gm: optimization ( rn_alb_smlt - rn_alb_imlt ) * r1_c2 can be computed one for all !!gm before the DO-loop below DO jl = 1, jpl DO jj = 1, jpj DO ji = 1, jpi ! ! Freezing snow ! no effect of underlying ice layer IF snow thickness > c1. Albedo does not depend on snow thick if > rc2 zswitch = 1._wp - MAX( 0._wp , SIGN( 1._wp , - ( ph_snw(ji,jj,jl) - rc1 ) ) ) zalb_sf = ( 1._wp - zswitch ) * ( zalb_it(ji,jj,jl) & & + ph_snw(ji,jj,jl) * ( rn_alb_sdry - zalb_it(ji,jj,jl) ) * r1_c1 ) & & + zswitch * rn_alb_sdry ! ! ! Melting snow ! no effect of underlying ice layer. Albedo does not depend on snow thick IF > rc2 zswitch = MAX( 0._wp , SIGN( 1._wp , ph_snw(ji,jj,jl) - rc2 ) ) zalb_sm = ( 1._wp - zswitch ) * ( rn_alb_imlt + ph_snw(ji,jj,jl) * ( rn_alb_smlt - rn_alb_imlt ) * r1_c2 ) & & + zswitch * rn_alb_smlt ! ! ! Snow albedo zswitch = MAX( 0._wp , SIGN( 1._wp , pt_ice(ji,jj,jl) - rt0_snow ) ) zalb_st = zswitch * zalb_sm + ( 1._wp - zswitch ) * zalb_sf ! ! ! Surface albedo zswitch = 1._wp - MAX( 0._wp , SIGN( 1._wp , - ph_snw(ji,jj,jl) ) ) pa_ice_cs(ji,jj,jl) = zswitch * zalb_st + ( 1._wp - zswitch ) * zalb_it(ji,jj,jl) ! END DO END DO END DO ! pa_ice_os(:,:,:) = pa_ice_cs(:,:,:) + rcloud ! Oberhuber correction for overcast sky ! ! ! !------------------------------------------ CASE( 1 ) ! New parameterization (2016) ! (based on overcast sky values) ! !------------------------------------------ ! ! compilation of values from literature (reference overcast sky values) ! rn_alb_sdry = 0.85 ! dry snow ! rn_alb_smlt = 0.75 ! melting snow ! rn_alb_idry = 0.60 ! bare frozen ice ! rn_alb_dpnd = 0.36 ! ponded-ice overcast albedo (Lecomte et al, 2015) ! ! early melt pnds 0.27, late melt ponds 0.14 Grenfell & Perovich ! Perovich et al 2002 (Sheba) => the only dataset for which all types of ice/snow were retrieved ! rn_alb_sdry = 0.85 ! dry snow ! rn_alb_smlt = 0.72 ! melting snow ! rn_alb_idry = 0.65 ! bare frozen ice ! Brandt et al 2005 (East Antarctica) ! rn_alb_sdry = 0.87 ! dry snow ! rn_alb_smlt = 0.82 ! melting snow ! rn_alb_idry = 0.54 ! bare frozen ice ! ! !--- Computation of snow-free ice albedo z1_c1 = 1. / ( LOG(1.5) - LOG(0.05) ) z1_c2 = 1. / 0.05 ! !--- Accounting for the ice-thickness dependency WHERE ( 1.5 < ph_ice ) ; zalb_it = zalb ELSE WHERE( 0.05 < ph_ice .AND. ph_ice <= 1.5 ) ; zalb_it = zalb + ( 0.18 - zalb ) * z1_c1 * ( LOG(1.5) - LOG(ph_ice) ) ELSE WHERE ; zalb_it = rn_alb_oce + ( 0.18 - rn_alb_oce ) * z1_c2 * ph_ice END WHERE ! IF ( ld_pnd ) THEN ! Depth-dependent ponded ice albedo z1_href_pnd = 0.05 ! inverse of the characteristic length scale (Lecomte et al. 2015) zalb_pnd = rn_alb_dpnd - ( rn_alb_dpnd - zalb_it ) * EXP( - ph_pnd * z1_href_pnd ) ! ! ! Snow-free ice albedo is weighted mean of ponded ice and bare ice contributions WHERE ( ph_snw == 0._wp .AND. pt_ice >= rt0 ) zalb_it = zalb_it * ( 1. - pafrac_pnd ) + zalb_pnd * pafrac_pnd END WHERE ENDIF ! ! !--- Overcast sky surface albedo (accounting for snow, ice melt ponds) z1_c1 = 1. / 0.02 z1_c2 = 1. / 0.03 DO jl = 1, jpl DO jj = 1, jpj DO ji = 1, jpi ! Snow depth dependence of snow albedo zalb_sf = rn_alb_sdry - ( rn_alb_sdry - zalb_it(ji,jj,jl)) * EXP( - ph_snw(ji,jj,jl) * z1_c1 ); zalb_sm = rn_alb_smlt - ( rn_alb_smlt - zalb_it(ji,jj,jl)) * EXP( - ph_snw(ji,jj,jl) * z1_c2 ); ! Snow albedo (MV I guess we could use rt0 instead of rt0_snow) zswitch = MAX( 0._wp , SIGN( 1._wp , pt_ice(ji,jj,jl) - rt0_snow ) ) zalb_st = zswitch * zalb_sm + ( 1._wp - zswitch ) * zalb_sf ! Surface albedo zswitch = MAX( 0._wp , SIGN( 1._wp , - ph_snw(ji,jj,jl) ) ) pa_ice_os(ji,jj,jl) = ( 1._wp - zswitch ) * zalb_st + zswitch * zalb_it(ji,jj,jl) END DO END DO END DO ! ! !--- Clear sky surface albedo pa_ice_cs = pa_ice_os - ( - 0.1010 * pa_ice_os * pa_ice_os + 0.1933 * pa_ice_os - 0.0148 ); ! ! ! !------------------------------------------ CASE( 2 ) ! Fractional surface-based parameterization (2017) ! !------------------------------------------ ! MV: I propose this formulation that is more elegant, and more easy to expand towards ! varying pond and snow fraction. ! Formulation 1 has issues to handle ponds and snow together that can't easily be fixed. ! This one handles it better, I believe. ! ! !== Snow, bare ice and ponded ice fractions ==! ! ! ! Specific fractions (zafrac) refer to relative area covered by snow within each ice category ! ! !--- Effective pond fraction (for now, we prevent melt ponds and snow at the same time) zafrac_pnd = 0._wp IF ( ld_pnd ) THEN WHERE( ph_snw == 0._wp ) zafrac_pnd = pafrac_pnd ! Snow fully "shades" melt ponds ENDIF ! ! !--- Specific snow fraction (for now, prescribed) WHERE( ph_snw > 0._wp ) ; zafrac_snw = 1. ELSEWHERE ; zafrac_snw = 0. END WHERE ! ! !--- Specific ice fraction zafrac_ice = 1. - zafrac_snw - zafrac_pnd ! ! !== Snow-covered, pond-covered, and bare ice albedos ==! ! ! !--- Bare ice albedo z1_c1 = 1. / ( LOG(1.5) - LOG(0.05) ) z1_c2 = 1. / 0.05 WHERE ( 1.5 < ph_ice ) ; zalb_ice = zalb ELSEWHERE( 0.05 < ph_ice .AND. ph_ice <= 1.5 ) ; zalb_ice = zalb + ( 0.18 - zalb ) * z1_c1 * & & ( LOG(1.5) - LOG(ph_ice) ) ELSEWHERE ; zalb_ice = rn_alb_oce + ( 0.18 - rn_alb_oce ) * z1_c2 * ph_ice END WHERE ! z1_c1 = 1. / 0.02 !--- Snow-covered ice albedo (freezing, melting cases) z1_c2 = 1. / 0.03 ! WHERE( pt_ice < rt0_snow ) ; zalb_snw = rn_alb_sdry - ( rn_alb_sdry - zalb_ice ) * EXP( - ph_snw * z1_c1 ) ELSEWHERE ; zalb_snw = rn_alb_smlt - ( rn_alb_smlt - zalb_ice ) * EXP( - ph_snw * z1_c2 ) END WHERE ! IF ( ld_pnd ) THEN !--- Depth-dependent ponded ice albedo z1_href_pnd = 0.05 ! inverse of the characteristic length scale (Lecomte et al. 2015) zalb_pnd = rn_alb_dpnd - ( rn_alb_dpnd - zalb_ice ) * EXP( - ph_pnd * z1_href_pnd ) ELSE zalb_pnd = rn_alb_dpnd ENDIF ! !--- Surface albedo is weighted mean of snow, ponds and bare ice contributions pa_ice_os = zafrac_snw * zalb_snw + zafrac_pnd * zalb_pnd + zafrac_ice * zalb_ice pa_ice_cs = pa_ice_os - ( - 0.1010 * pa_ice_os * pa_ice_os + 0.1933 * pa_ice_os - 0.0148 ) END SELECT ! END SUBROUTINE ice_alb SUBROUTINE ice_alb_init !!---------------------------------------------------------------------- !! *** ROUTINE alb_init *** !! !! ** Purpose : initializations for the albedo parameters !! !! ** Method : Read the namelist namice_alb !!---------------------------------------------------------------------- INTEGER :: ios ! Local integer output status for namelist read !! NAMELIST/namice_alb/ nn_ice_alb, rn_alb_sdry, rn_alb_smlt, rn_alb_idry, rn_alb_imlt, rn_alb_dpnd !!---------------------------------------------------------------------- ! REWIND( numnam_ice_ref ) ! Namelist namice_alb in reference namelist : Albedo parameters READ ( numnam_ice_ref, namice_alb, IOSTAT = ios, ERR = 901) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namice_alb in reference namelist', lwp ) REWIND( numnam_ice_cfg ) ! Namelist namsbc_alb in configuration namelist : Albedo parameters READ ( numnam_ice_cfg, namice_alb, IOSTAT = ios, ERR = 902 ) 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namice_alb in configuration namelist', lwp ) IF(lwm) WRITE ( numoni, namice_alb ) ! IF(lwp) THEN ! Control print WRITE(numout,*) WRITE(numout,*) 'albedo : set albedo parameters' WRITE(numout,*) '~~~~~~~' WRITE(numout,*) ' Namelist namice_alb : albedo ' WRITE(numout,*) ' choose the albedo parameterization nn_ice_alb = ', nn_ice_alb WRITE(numout,*) ' albedo of dry snow rn_alb_sdry = ', rn_alb_sdry WRITE(numout,*) ' albedo of melting snow rn_alb_smlt = ', rn_alb_smlt WRITE(numout,*) ' albedo of dry ice rn_alb_idry = ', rn_alb_idry WRITE(numout,*) ' albedo of bare puddled ice rn_alb_imlt = ', rn_alb_imlt WRITE(numout,*) ' albedo of ponded ice rn_alb_dpnd = ', rn_alb_dpnd ENDIF ! END SUBROUTINE ice_alb_init #else !!---------------------------------------------------------------------- !! Default option Dummy module NO LIM 3.0 sea-ice model !!---------------------------------------------------------------------- #endif !!====================================================================== END MODULE icealb