MODULE albedo !!====================================================================== !! *** MODULE albedo *** !! Ocean forcing: bulk thermohaline forcing of the ocean (or ice) !!===================================================================== !! History : 8.0 ! 2001-04 (LIM 1.0) !! NEMO 1.0 ! 2003-07 (C. Ethe, G. Madec) Optimization (old name:shine) !! - ! 2004-11 (C. Talandier) add albedo_init !! - ! 2006-06 (M. Vancoppenolle) LIM 3.0 !! - ! 2006-08 (G. Madec) cleaning for surface module !! 3.6 ! 2016-01 (C. Rousset) new parameterization for sea ice albedo !! x.x ! 2017-05 (M. Vancoppenolle, O. Lecomte) Melt ponds !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! albedo_ice : albedo for ice (clear and overcast skies) !! albedo_oce : albedo for ocean (clear and overcast skies) !! albedo_init : initialisation of albedo computation !!---------------------------------------------------------------------- USE phycst ! physical constants USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE wrk_nemo ! work arrays USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) IMPLICIT NONE PRIVATE PUBLIC albedo_ice ! routine called sbcice_lim.F90 PUBLIC albedo_oce ! routine called by ??? INTEGER :: albd_init = 0 !: control flag for initialization REAL(wp) :: rmue = 0.40 ! cosine of local solar altitude REAL(wp) :: ralb_oce = 0.066 ! ocean or lead albedo (Pegau and Paulson, Ann. Glac. 2001) REAL(wp) :: c1 = 0.05 ! snow thickness (only for nn_ice_alb=0) REAL(wp) :: c2 = 0.10 ! " " REAL(wp) :: rcloud = 0.06 ! cloud effect on albedo (only-for nn_ice_alb=0) ! !!* namelist namsbc_alb INTEGER :: nn_ice_alb REAL(wp) :: rn_alb_sdry, rn_alb_smlt, rn_alb_idry, rn_alb_imlt, rn_alb_dpnd !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE albedo_ice( pt_ice, ph_ice, ph_snw, pafrac_pnd, ph_pnd, ld_pnd, pa_ice_cs, pa_ice_os ) !!---------------------------------------------------------------------- !! *** ROUTINE albedo_ice *** !! !! ** 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 INTEGER :: ijpl ! number of ice categories (3rd dim of ice input arrays) REAL(wp) :: ralb_im, ralb_sf, ralb_sm, ralb_if, ralb_dp REAL(wp) :: zswitch, z1_c1, z1_c2 REAL(wp) :: zhref_pnd REAL(wp) :: zalb_sm, zalb_sf, zalb_st ! albedo of snow melting, freezing, total REAL(wp), POINTER, DIMENSION(:,:,:) :: zalb, zalb_it ! intermediate variable & albedo of ice (snow free) REAL(wp), POINTER, DIMENSION(:,:,:) :: zalb_pnd ! ponded sea ice albedo REAL(wp), POINTER, DIMENSION(:,:,:) :: zalb_ice ! bare sea ice albedo REAL(wp), POINTER, DIMENSION(:,:,:) :: zalb_snw ! snow-covered sea ice albedo REAL(wp), POINTER, DIMENSION(:,:,:) :: zafrac_snw ! relative snow fraction REAL(wp), POINTER, DIMENSION(:,:,:) :: zafrac_ice ! relative ice fraction REAL(wp), POINTER, DIMENSION(:,:,:) :: zafrac_pnd ! relative ice fraction (effective) !! !!--------------------------------------------------------------------- WRITE(numout,*) ' albedo_ice ' WRITE(numout,*) ' ld_pnd : ', ld_pnd WRITE(numout,*) ' nn_ice_alb : ', nn_ice_alb ijpl = SIZE( pt_ice, 3 ) ! number of ice categories CALL wrk_alloc( jpi,jpj,ijpl, zalb, zalb_it ) CALL wrk_alloc( jpi,jpj,ijpl, zalb_pnd, zalb_ice, zalb_snw ) CALL wrk_alloc( jpi,jpj,ijpl, zalb_pnd, zafrac_snw, zafrac_ice, zafrac_pnd ) IF( albd_init == 0 ) CALL albedo_init ! initialization ralb_sf = rn_alb_sdry ! dry snow ralb_sm = rn_alb_smlt ! melting snow ralb_if = rn_alb_idry ! bare frozen ice ralb_im = rn_alb_imlt ! bare puddled ice (assumes implicit contribution of melt ponds) ralb_dp = rn_alb_dpnd ! deep pond albedo !----------------------------------------------------- ! Snow-free albedo (no ice thickness dependence yet) !----------------------------------------------------- ! ! Part common to nn_ice_alb = 0, 1, 2 ! zalb = ralb_if 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_ice ) ; zalb = ralb_im ; END WHERE ! !!! MV I think we could replace rt0_ice by rt0 and get rid of rt0 ENDIF SELECT CASE ( nn_ice_alb ) !------------------------------------------ ! Shine and Henderson-Sellers (1985) !------------------------------------------ ! NB: This parameterization is based on clear sky values CASE( 0 ) ! Thickness-dependent bare ice albedo WHERE ( 1.5 < ph_ice ) ; zalb_it = zalb ELSE WHERE( 1.0 < ph_ice .AND. ph_ice <= 1.5 ) ; zalb_it = 0.472 + 2.0 * ( zalb - 0.472 ) * ( ph_ice - 1.0 ) ELSE WHERE( 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 ELSE WHERE ; zalb_it = 0.1 + 3.6 * ph_ice END WHERE IF ( ld_pnd ) THEN ! Depth-dependent ponded ice albedo zhref_pnd = 0.05 ! Characteristic length scale for thickness dependence of ponded ice albedo, Lecomte et al (2015) zalb_pnd = ralb_dp - ( ralb_dp - zalb_it ) * EXP( - ph_pnd / zhref_pnd ) ! Snow-free ice albedo is a function of pond fraction WHERE ( ph_snw == 0._wp .AND. pt_ice >= rt0_ice ) ; zalb_it = zalb_it * ( 1. - pafrac_pnd ) + zalb_pnd * pafrac_pnd ; END WHERE ENDIF ! Note that this way of coding things means that the thickness ! dependence of bare ice albedo is also altering the ponded ice albedo ! I'm not sure that this is valid, but at least, this maintains ! consistency with previous formulation (see below) DO jl = 1, ijpl 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 > c2 ! ! freezing snow zswitch = 1._wp - MAX( 0._wp , SIGN( 1._wp , - ( ph_snw(ji,jj,jl) - c1 ) ) ) zalb_sf = ( 1._wp - zswitch ) * ( zalb_it(ji,jj,jl) & & + ph_snw(ji,jj,jl) * ( ralb_sf - zalb_it(ji,jj,jl) ) / c1 ) & & + zswitch * ralb_sf ! Melting snow ! no effect of underlying ice layer. Albedo does not depend on snow thick IF > c2 zswitch = MAX( 0._wp , SIGN( 1._wp , ph_snw(ji,jj,jl) - c2 ) ) zalb_sm = ( 1._wp - zswitch ) * ( ralb_im + ph_snw(ji,jj,jl) * ( ralb_sm - ralb_im ) / c2 ) & & + zswitch * ralb_sm ! 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 !------------------------------------------ ! New parameterization (2016) !------------------------------------------ ! NB: This parameterization is based on overcast skies values CASE( 1 ) ! ! Reference (overcast sky) values ! ralb_sf = 0.85 ! dry snow ! ralb_sm = 0.75 ! melting snow ! ralb_if = 0.60 ! bare frozen ice ! ralb_dp = 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 ! ralb_sf = 0.85 ! dry snow ! ralb_sm = 0.72 ! melting snow ! ralb_if = 0.65 ! bare frozen ice ! Brandt et al 2005 (East Antarctica) ! ralb_sf = 0.87 ! dry snow ! ralb_sm = 0.82 ! melting snow ! ralb_if = 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 = ralb_oce + ( 0.18 - ralb_oce ) * z1_c2 * ph_ice END WHERE IF ( ld_pnd ) THEN ! Depth-dependent ponded ice albedo zhref_pnd = 0.05 ! Characteristic length scale for thickness dependence of ponded ice albedo, Lecomte et al (2015) zalb_pnd = ralb_dp - ( ralb_dp - zalb_it ) * EXP( - ph_pnd / zhref_pnd ) ! Snow-free ice albedo is weighted mean of ponded ice and bare ice contributions WHERE ( ph_snw == 0._wp .AND. pt_ice >= rt0_ice ) ; zalb_it = zalb_it * ( 1. - pafrac_pnd ) + zalb_pnd * pafrac_pnd ; END WHERE ENDIF z1_c1 = 1. / 0.02 z1_c2 = 1. / 0.03 ! Overcast sky surface albedo (accounting for snow, ice melt ponds) DO jl = 1, ijpl DO jj = 1, jpj DO ji = 1, jpi ! Snow depth dependence of snow albedo zalb_sf = ralb_sf - ( ralb_sf - zalb_it(ji,jj,jl)) * EXP( - ph_snw(ji,jj,jl) * z1_c1 ); zalb_sm = ralb_sm - ( ralb_sm - 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 ); !--------------------------------------------------- ! Fractional surface-based parameterization (2017) !--------------------------------------------------- CASE( 2 ) ! 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 ; END WHERE ! Snow fully "shades" melt ponds ENDIF !--- Specific snow fraction (for now, prescribed) WHERE ( ph_snw > 0._wp ) ; zafrac_snw = 1. ELSE WHERE ; 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 ELSE WHERE( 0.05 < ph_ice .AND. ph_ice <= 1.5 ) ; zalb_ice = zalb + ( 0.18 - zalb ) * z1_c1 * & & ( LOG(1.5) - LOG(ph_ice) ) ELSE WHERE ; zalb_ice = ralb_oce + ( 0.18 - ralb_oce ) * z1_c2 * ph_ice END WHERE ! Snow-covered ice albedo (freezing, melting cases) z1_c1 = 1. / 0.02 z1_c2 = 1. / 0.03 WHERE( pt_ice < rt0_snow ) ; zalb_snw = ralb_sf - ( ralb_sf - zalb_ice ) * EXP( - ph_snw * z1_c1 ); ELSE WHERE ; zalb_snw = ralb_sm - ( ralb_sm - zalb_ice ) * EXP( - ph_snw * z1_c2 ); END WHERE ! Depth-dependent ponded ice albedo zhref_pnd = 0.05 ! Characteristic length scale for thickness dependence of ponded ice albedo, Lecomte et al (2015) zalb_pnd = ralb_dp - ( ralb_dp - zalb_ice ) * EXP( - ph_pnd / zhref_pnd ) ! 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 CALL wrk_dealloc( jpi,jpj,ijpl, zalb, zalb_it ) CALL wrk_dealloc( jpi,jpj,ijpl, zalb_pnd, zalb_ice, zalb_snw ) CALL wrk_dealloc( jpi,jpj,ijpl, zalb_pnd, zafrac_snw, zafrac_ice, zafrac_pnd ) ! END SUBROUTINE albedo_ice SUBROUTINE albedo_oce( pa_oce_os , pa_oce_cs ) !!---------------------------------------------------------------------- !! *** ROUTINE albedo_oce *** !! !! ** Purpose : Computation of the albedo of the ocean !!---------------------------------------------------------------------- REAL(wp), DIMENSION(:,:), INTENT(out) :: pa_oce_os ! albedo of ocean under overcast sky REAL(wp), DIMENSION(:,:), INTENT(out) :: pa_oce_cs ! albedo of ocean under clear sky !! REAL(wp) :: zcoef !!---------------------------------------------------------------------- ! zcoef = 0.05 / ( 1.1 * rmue**1.4 + 0.15 ) ! Parameterization of Briegled and Ramanathan, 1982 pa_oce_cs(:,:) = zcoef pa_oce_os(:,:) = 0.06 ! Parameterization of Kondratyev, 1969 and Payne, 1972 ! END SUBROUTINE albedo_oce SUBROUTINE albedo_init !!---------------------------------------------------------------------- !! *** ROUTINE albedo_init *** !! !! ** Purpose : initializations for the albedo parameters !! !! ** Method : Read the namelist namsbc_alb !!---------------------------------------------------------------------- INTEGER :: ios ! Local integer output status for namelist read NAMELIST/namsbc_alb/ nn_ice_alb, rn_alb_sdry, rn_alb_smlt, rn_alb_idry , rn_alb_imlt, rn_alb_dpnd !!---------------------------------------------------------------------- ! albd_init = 1 ! indicate that the initialization has been done ! REWIND( numnam_ref ) ! Namelist namsbc_alb in reference namelist : Albedo parameters READ ( numnam_ref, namsbc_alb, IOSTAT = ios, ERR = 901) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namsbc_alb in reference namelist', lwp ) REWIND( numnam_cfg ) ! Namelist namsbc_alb in configuration namelist : Albedo parameters READ ( numnam_cfg, namsbc_alb, IOSTAT = ios, ERR = 902 ) 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namsbc_alb in configuration namelist', lwp ) IF(lwm) WRITE ( numond, namsbc_alb ) ! IF(lwp) THEN ! Control print WRITE(numout,*) WRITE(numout,*) 'albedo : set albedo parameters' WRITE(numout,*) '~~~~~~~' WRITE(numout,*) ' Namelist namsbc_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 ice rn_alb_imlt = ', rn_alb_imlt WRITE(numout,*) ' albedo of ponded ice rn_alb_dpnd = ', rn_alb_dpnd ENDIF ! END SUBROUTINE albedo_init !!====================================================================== END MODULE albedo