! SVN:$Id: ice_shortwave.F90 1304 2015-11-12 19:28:14Z afrobert@nps.edu $ !======================================================================= ! ! The albedo and absorbed/transmitted flux parameterizations for ! snow over ice, bare ice and ponded ice. ! ! Presently, two methods are included: ! (1) CCSM3 ! (2) Delta-Eddington ! as two distinct routines. ! Either can be called from the ice driver. ! ! The Delta-Eddington method is described here: ! ! Briegleb, B. P., and B. Light (2007): A Delta-Eddington Multiple ! Scattering Parameterization for Solar Radiation in the Sea Ice ! Component of the Community Climate System Model, NCAR Technical ! Note NCAR/TN-472+STR February 2007 ! ! name: originally ice_albedo ! ! authors: Bruce P. Briegleb, NCAR ! Elizabeth C. Hunke and William H. Lipscomb, LANL ! 2005, WHL: Moved absorbed_solar from ice_therm_vertical to this ! module and changed name from ice_albedo ! 2006, WHL: Added Delta Eddington routines from Bruce Briegleb ! 2006, ECH: Changed data statements in Delta Eddington routines (no ! longer hardwired) ! Converted to free source form (F90) ! 2007, BPB: Completely updated Delta-Eddington code, so that: ! (1) multiple snow layers enabled (i.e. nslyr > 1) ! (2) included SSL for snow surface absorption ! (3) added Sswabs for internal snow layer absorption ! (4) variable sea ice layers allowed (i.e. not hardwired) ! (5) updated all inherent optical properties ! (6) included algae absorption for sea ice lowest layer ! (7) very complete internal documentation included ! 2007, ECH: Improved efficiency ! 2008, BPB: Added aerosols to Delta Eddington code ! 2013, ECH: merged with NCAR version, cleaned up module ice_shortwave use ice_kinds_mod use ice_domain_size, only: nilyr, nslyr, ncat, n_aero, max_blocks, max_aero use ice_constants !use ice_blocks, only: nx_block, ny_block, block, get_block use ice_blocks, only: nx_block, ny_block use ice_diagnostics, only: npnt, print_points, pmloc, piloc, pjloc use ice_fileunits, only: nu_diag use ice_communicate, only: my_task implicit none private public :: init_shortwave, run_dEdd, shortwave_ccsm3 character (len=char_len), public :: & shortwave, & ! shortwave method, 'default' ('ccsm3') or 'dEdd' albedo_type ! albedo parameterization, 'default' ('ccsm3') or 'constant' ! shortwave='dEdd' overrides this parameter ! baseline albedos for ccsm3 shortwave, set in namelist real (kind=dbl_kind), public :: & albicev , & ! visible ice albedo for h > ahmax albicei , & ! near-ir ice albedo for h > ahmax albsnowv, & ! cold snow albedo, visible albsnowi, & ! cold snow albedo, near IR ahmax ! thickness above which ice albedo is constant (m) ! category albedos real (kind=dbl_kind), & dimension (nx_block,ny_block,ncat,max_blocks), public, save :: & alvdrn , & ! visible direct albedo (fraction) alidrn , & ! near-ir direct albedo (fraction) alvdfn , & ! visible diffuse albedo (fraction) alidfn ! near-ir diffuse albedo (fraction) ! albedo components for history real (kind=dbl_kind), & dimension (nx_block,ny_block,ncat,max_blocks), public, save :: & albicen, & ! bare ice albsnon, & ! snow albpndn, & ! pond apeffn ! effective pond area used for radiation calculation ! shortwave components real (kind=dbl_kind), & dimension (nx_block,ny_block,nilyr,ncat,max_blocks), public, save :: & Iswabsn ! SW radiation absorbed in ice layers (W m-2) real (kind=dbl_kind), & dimension (nx_block,ny_block,nslyr,ncat,max_blocks), public, save :: & Sswabsn ! SW radiation absorbed in snow layers (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,ncat,max_blocks), & public, save :: & fswsfcn , & ! SW absorbed at ice/snow surface (W m-2) fswthrun , & ! SW through ice to ocean (W/m^2) fswintn ! SW absorbed in ice interior, below surface (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr+1,ncat,max_blocks), & public, save :: & fswpenln ! visible SW entering ice layers (W m-2) ! dEdd tuning parameters, set in namelist real (kind=dbl_kind), public :: & R_ice , & ! sea ice tuning parameter; +1 > 1sig increase in albedo R_pnd , & ! ponded ice tuning parameter; +1 > 1sig increase in albedo R_snw , & ! snow tuning parameter; +1 > ~.01 change in broadband albedo dT_mlt, & ! change in temp for non-melt to melt snow grain radius change (C) rsnw_mlt, & ! maximum melting snow grain radius (10^-6 m) kalg ! algae absorption coefficient for 0.5 m thick layer real (kind=dbl_kind), parameter, public :: & hi_ssl = 0.050_dbl_kind, & ! ice surface scattering layer thickness (m) hs_ssl = 0.040_dbl_kind ! snow surface scattering layer thickness (m) real (kind=dbl_kind), parameter :: & hpmin = 0.005_dbl_kind, & ! minimum allowed melt pond depth (m) hp0 = 0.200_dbl_kind ! pond depth below which transition to bare ice real (kind=dbl_kind) :: & exp_min ! minimum exponential value !======================================================================= contains !======================================================================= ! ! Initialize shortwave subroutine init_shortwave use ice_calendar, only: nstreams use ice_domain, only: nblocks, blocks_ice use ice_flux, only: alvdf, alidf, alvdr, alidr, & alvdr_ai, alidr_ai, alvdf_ai, alidf_ai, & swvdr, swvdf, swidr, swidf, & albice, albsno, albpnd, apeff_ai, albcnt, coszen, fsnow use ice_orbital, only: init_orbit use ice_state, only: aicen, vicen, vsnon, trcrn, nt_Tsfc use ice_blocks, only: block, get_block use ice_grid, only: tmask, tlat, tlon use ice_meltpond_lvl, only: dhsn, ffracn integer (kind=int_kind) :: & icells ! number of cells with aicen > puny integer (kind=int_kind), dimension(nx_block*ny_block) :: & indxi, indxj ! indirect indices for cells with aicen > puny integer (kind=int_kind) :: & i, j, ij , & ! horizontal indices iblk , & ! block index ilo,ihi,jlo,jhi, & ! beginning and end of physical domain n ! thickness category index real (kind=dbl_kind) :: cszn ! counter for history averaging type (block) :: & this_block ! block information for current block !$OMP PARALLEL DO PRIVATE(iblk,i,j,n) do iblk = 1, nblocks do j = 1, ny_block do i = 1, nx_block alvdf(i,j,iblk) = c0 alidf(i,j,iblk) = c0 alvdr(i,j,iblk) = c0 alidr(i,j,iblk) = c0 alvdr_ai(i,j,iblk) = c0 alidr_ai(i,j,iblk) = c0 alvdf_ai(i,j,iblk) = c0 alidf_ai(i,j,iblk) = c0 enddo enddo ! Initialize do n = 1, ncat do j = 1, ny_block do i = 1, nx_block alvdrn(i,j,n,iblk) = c0 alidrn(i,j,n,iblk) = c0 alvdfn(i,j,n,iblk) = c0 alidfn(i,j,n,iblk) = c0 fswsfcn(i,j,n,iblk) = c0 fswintn(i,j,n,iblk) = c0 fswthrun(i,j,n,iblk) = c0 enddo ! i enddo ! j enddo ! ncat fswpenln(:,:,:,:,iblk) = c0 Iswabsn(:,:,:,:,iblk) = c0 Sswabsn(:,:,:,:,iblk) = c0 enddo ! iblk !$OMP END PARALLEL DO if (trim(shortwave) == 'dEdd') then ! delta Eddington #ifndef CCSMCOUPLED ! These come from the driver in the coupled model. call init_orbit ! initialize orbital parameters #endif !$OMP PARALLEL DO PRIVATE(iblk,ilo,ihi,jlo,jhi,this_block) do iblk = 1, nblocks this_block = get_block(blocks_ice(iblk),iblk) ilo = this_block%ilo ihi = this_block%ihi jlo = this_block%jlo jhi = this_block%jhi ! initialize delta Eddington call run_dEdd(ilo, ihi, jlo, jhi, & aicen(:,:,:,iblk), vicen(:,:,:,iblk), & vsnon(:,:,:,iblk), trcrn(:,:,:,:,iblk), & tlat(:,:,iblk), tlon(:,:,iblk), & tmask(:,:,iblk), & swvdr(:,:,iblk), swvdf(:,:,iblk), & swidr(:,:,iblk), swidf(:,:,iblk), & coszen(:,:,iblk), fsnow(:,:,iblk), & alvdrn(:,:,:,iblk), alvdfn(:,:,:,iblk), & alidrn(:,:,:,iblk), alidfn(:,:,:,iblk), & fswsfcn(:,:,:,iblk), fswintn(:,:,:,iblk), & fswthrun(:,:,:,iblk), fswpenln(:,:,:,:,iblk), & Sswabsn(:,:,:,:,iblk), Iswabsn(:,:,:,:,iblk), & albicen(:,:,:,iblk), albsnon(:,:,:,iblk), & albpndn(:,:,:,iblk), apeffn(:,:,:,iblk), & dhsn(:,:,:,iblk), ffracn(:,:,:,iblk), & initonly = .true. ) enddo !$OMP END PARALLEL DO else ! basic (ccsm3) shortwave !$OMP PARALLEL DO PRIVATE(iblk,ilo,ihi,jlo,jhi,this_block) do iblk = 1, nblocks this_block = get_block(blocks_ice(iblk),iblk) ilo = this_block%ilo ihi = this_block%ihi jlo = this_block%jlo jhi = this_block%jhi call shortwave_ccsm3(nx_block, ny_block, & ilo, ihi, jlo, jhi, & aicen(:,:,:,iblk), vicen(:,:,:,iblk), & vsnon(:,:,:,iblk), & trcrn(:,:,nt_Tsfc,:,iblk), & swvdr(:,:, iblk), swvdf(:,:, iblk), & swidr(:,:, iblk), swidf(:,:, iblk), & alvdrn(:,:,:,iblk), alidrn(:,:,:,iblk), & alvdfn(:,:,:,iblk), alidfn(:,:,:,iblk), & fswsfcn(:,:,:,iblk), fswintn(:,:,:,iblk), & fswthrun(:,:,:,iblk), & fswpenln(:,:,:,:,iblk), & Iswabsn(:,:,:,:,iblk), & Sswabsn(:,:,:,:,iblk), & albicen(:,:,:,iblk), albsnon(:,:,:,iblk), & coszen(:,:,iblk)) enddo ! nblocks !$OMP END PARALLEL DO endif !----------------------------------------------------------------- ! Aggregate albedos !----------------------------------------------------------------- !$OMP PARALLEL DO PRIVATE(iblk,i,j,n,ilo,ihi,jlo,jhi,this_block, & !$OMP ij,icells,cszn,indxi,indxj) do iblk = 1, nblocks this_block = get_block(blocks_ice(iblk),iblk) ilo = this_block%ilo ihi = this_block%ihi jlo = this_block%jlo jhi = this_block%jhi do n = 1, ncat icells = 0 do j = jlo, jhi do i = ilo, ihi if (aicen(i,j,n,iblk) > puny) then icells = icells + 1 indxi(icells) = i indxj(icells) = j endif enddo ! i enddo ! j do ij = 1, icells i = indxi(ij) j = indxj(ij) alvdf(i,j,iblk) = alvdf(i,j,iblk) & + alvdfn(i,j,n,iblk)*aicen(i,j,n,iblk) alidf(i,j,iblk) = alidf(i,j,iblk) & + alidfn(i,j,n,iblk)*aicen(i,j,n,iblk) alvdr(i,j,iblk) = alvdr(i,j,iblk) & + alvdrn(i,j,n,iblk)*aicen(i,j,n,iblk) alidr(i,j,iblk) = alidr(i,j,iblk) & + alidrn(i,j,n,iblk)*aicen(i,j,n,iblk) if (coszen(i,j,iblk) > puny) then ! sun above horizon albice(i,j,iblk) = albice(i,j,iblk) & + albicen(i,j,n,iblk)*aicen(i,j,n,iblk) albsno(i,j,iblk) = albsno(i,j,iblk) & + albsnon(i,j,n,iblk)*aicen(i,j,n,iblk) albpnd(i,j,iblk) = albpnd(i,j,iblk) & + albpndn(i,j,n,iblk)*aicen(i,j,n,iblk) endif apeff_ai(i,j,iblk) = apeff_ai(i,j,iblk) & + apeffn(i,j,n,iblk)*aicen(i,j,n,iblk) enddo enddo ! ncat !---------------------------------------------------------------- ! Store grid box mean albedos and fluxes before scaling by aice !---------------------------------------------------------------- do j = 1, ny_block do i = 1, nx_block alvdf_ai (i,j,iblk) = alvdf (i,j,iblk) alidf_ai (i,j,iblk) = alidf (i,j,iblk) alvdr_ai (i,j,iblk) = alvdr (i,j,iblk) alidr_ai (i,j,iblk) = alidr (i,j,iblk) ! for history averaging cszn = c0 if (coszen(i,j,iblk) > puny) cszn = c1 do n = 1, nstreams albcnt(i,j,iblk,n) = albcnt(i,j,iblk,n) + cszn enddo enddo enddo enddo ! nblocks !$OMP END PARALLEL DO end subroutine init_shortwave !======================================================================= ! ! Driver for basic solar radiation from CCSM3. Albedos and absorbed solar. subroutine shortwave_ccsm3 (nx_block, ny_block, & ilo, ihi, jlo, jhi, & aicen, vicen, & vsnon, Tsfcn, & swvdr, swvdf, & swidr, swidf, & alvdrn, alidrn, & alvdfn, alidfn, & fswsfc, fswint, & fswthru, fswpenl, & Iswabs, SSwabs, & albin, albsn, & coszen) integer (kind=int_kind), intent(in) :: & nx_block, ny_block, & ! block dimensions ilo,ihi,jlo,jhi ! beginning and end of physical domain real (kind=dbl_kind), dimension (nx_block,ny_block,ncat), & intent(in) :: & aicen , & ! concentration of ice per category vicen , & ! volume of ice per category vsnon , & ! volume of ice per category Tsfcn ! surface temperature real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & swvdr , & ! sw down, visible, direct (W/m^2) swvdf , & ! sw down, visible, diffuse (W/m^2) swidr , & ! sw down, near IR, direct (W/m^2) swidf ! sw down, near IR, diffuse (W/m^2) real (kind=dbl_kind), dimension (nx_block,ny_block,ncat), & intent(inout) :: & alvdrn , & ! visible, direct, avg (fraction) alidrn , & ! near-ir, direct, avg (fraction) alvdfn , & ! visible, diffuse, avg (fraction) alidfn , & ! near-ir, diffuse, avg (fraction) fswsfc , & ! SW absorbed at ice/snow surface (W m-2) fswint , & ! SW absorbed in ice interior, below surface (W m-2) fswthru , & ! SW through ice to ocean (W m-2) albin , & ! bare ice albedo albsn ! snow albedo real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr+1,ncat), & intent(inout) :: & fswpenl ! SW entering ice layers (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(out) :: & coszen ! cosine(zenith angle) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr,ncat), & intent(inout) :: & Iswabs ! SW absorbed in particular layer (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nslyr,ncat), & intent(inout) :: & Sswabs ! SW absorbed in particular layer (W m-2) ! local variables integer (kind=int_kind) :: & i, j , & ! horizontal indices icells , & ! number of ice-covered grid cells n ! thickness category index integer (kind=int_kind), dimension (nx_block*ny_block) :: & indxi , & ! indices for ice-covered cells indxj ! ice and snow albedo for each category real (kind=dbl_kind), dimension (nx_block,ny_block):: & alvdrni, & ! visible, direct, ice (fraction) alidrni, & ! near-ir, direct, ice (fraction) alvdfni, & ! visible, diffuse, ice (fraction) alidfni, & ! near-ir, diffuse, ice (fraction) alvdrns, & ! visible, direct, snow (fraction) alidrns, & ! near-ir, direct, snow (fraction) alvdfns, & ! visible, diffuse, snow (fraction) alidfns ! near-ir, diffuse, snow (fraction) !----------------------------------------------------------------- ! Solar radiation: albedo and absorbed shortwave !----------------------------------------------------------------- ! For basic shortwave, set coszen to a constant between 0 and 1. coszen(:,:) = p5 ! sun above the horizon do n = 1, ncat icells = 0 do j = jlo, jhi do i = ilo, ihi if (aicen(i,j,n) > puny) then icells = icells + 1 indxi(icells) = i indxj(icells) = j endif enddo ! i enddo ! j Sswabs(:,:,:,n) = c0 !----------------------------------------------------------------- ! Compute albedos for ice and snow. !----------------------------------------------------------------- if (trim(albedo_type) == 'constant') then call constant_albedos (nx_block, ny_block, & icells, & indxi, indxj, & aicen(:,:,n), & vsnon(:,:,n), & Tsfcn(:,:,n), & alvdrni, alidrni, & alvdfni, alidfni, & alvdrns, alidrns, & alvdfns, alidfns, & alvdrn(:,:,n), & alidrn(:,:,n), & alvdfn(:,:,n), & alidfn(:,:,n), & albin(:,:,n), & albsn(:,:,n)) else ! default call compute_albedos (nx_block, ny_block, & icells, & indxi, indxj, & aicen(:,:,n), & vicen(:,:,n), & vsnon(:,:,n), & Tsfcn(:,:,n), & alvdrni, alidrni, & alvdfni, alidfni, & alvdrns, alidrns, & alvdfns, alidfns, & alvdrn(:,:,n), & alidrn(:,:,n), & alvdfn(:,:,n), & alidfn(:,:,n), & albin(:,:,n), & albsn(:,:,n)) endif !----------------------------------------------------------------- ! Compute solar radiation absorbed in ice and penetrating to ocean. !----------------------------------------------------------------- call absorbed_solar (nx_block, ny_block, & icells, & indxi, indxj, & aicen(:,:,n), & vicen(:,:,n), & vsnon(:,:,n), & swvdr, swvdf, & swidr, swidf, & alvdrni, alvdfni, & alidrni, alidfni, & alvdrns, alvdfns, & alidrns, alidfns, & fswsfc(:,:,n), & fswint(:,:,n), & fswthru(:,:,n), & fswpenl(:,:,:,n), & Iswabs(:,:,:,n)) enddo ! ncat end subroutine shortwave_ccsm3 !======================================================================= ! ! Compute albedos for each thickness category subroutine compute_albedos (nx_block, ny_block, & icells, & indxi, indxj, & aicen, vicen, & vsnon, Tsfcn, & alvdrni, alidrni, & alvdfni, alidfni, & alvdrns, alidrns, & alvdfns, alidfns, & alvdrn, alidrn, & alvdfn, alidfn, & albin, albsn) integer (kind=int_kind), intent(in) :: & nx_block, ny_block, & ! block dimensions icells ! number of ice-covered grid cells integer (kind=int_kind), dimension (nx_block*ny_block), & intent(in) :: & indxi , & ! compressed indices for ice-covered cells indxj real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & aicen , & ! concentration of ice per category vicen , & ! volume of ice per category vsnon , & ! volume of ice per category Tsfcn ! surface temperature real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(out) :: & alvdrni , & ! visible, direct, ice (fraction) alidrni , & ! near-ir, direct, ice (fraction) alvdfni , & ! visible, diffuse, ice (fraction) alidfni , & ! near-ir, diffuse, ice (fraction) alvdrns , & ! visible, direct, snow (fraction) alidrns , & ! near-ir, direct, snow (fraction) alvdfns , & ! visible, diffuse, snow (fraction) alidfns , & ! near-ir, diffuse, snow (fraction) alvdrn , & ! visible, direct, avg (fraction) alidrn , & ! near-ir, direct, avg (fraction) alvdfn , & ! visible, diffuse, avg (fraction) alidfn , & ! near-ir, diffuse, avg (fraction) albin , & ! bare ice albsn ! snow ! local variables real (kind=dbl_kind), parameter :: & dT_melt = c1 , & ! change in temp to give dalb_mlt ! albedo change dalb_mlt = -0.075_dbl_kind, & ! albedo change per dT_melt change ! in temp for ice dalb_mltv = -p1 , & ! albedo vis change per dT_melt change ! in temp for snow dalb_mlti = -p15 ! albedo nir change per dT_melt change ! in temp for snow integer (kind=int_kind) :: & i, j real (kind=dbl_kind) :: & hi , & ! ice thickness (m) hs , & ! snow thickness (m) albo, & ! effective ocean albedo, function of ice thickness fh , & ! piecewise linear function of thickness fT , & ! piecewise linear function of surface temperature dTs , & ! difference of Tsfc and Timelt fhtan,& ! factor used in albedo dependence on ice thickness asnow ! fractional area of snow cover integer (kind=int_kind) :: & ij ! horizontal index, combines i and j loops fhtan = atan(ahmax*c4) do j = 1, ny_block do i = 1, nx_block alvdrni(i,j) = albocn alidrni(i,j) = albocn alvdfni(i,j) = albocn alidfni(i,j) = albocn alvdrns(i,j) = albocn alidrns(i,j) = albocn alvdfns(i,j) = albocn alidfns(i,j) = albocn alvdrn(i,j) = albocn alidrn(i,j) = albocn alvdfn(i,j) = albocn alidfn(i,j) = albocn albin(i,j) = c0 albsn(i,j) = c0 enddo enddo !----------------------------------------------------------------- ! Compute albedo for each thickness category. !----------------------------------------------------------------- !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells i = indxi(ij) j = indxj(ij) hi = vicen(i,j) / aicen(i,j) hs = vsnon(i,j) / aicen(i,j) ! bare ice, thickness dependence fh = min(atan(hi*c4)/fhtan,c1) albo = albocn*(c1-fh) alvdfni(i,j) = albicev*fh + albo alidfni(i,j) = albicei*fh + albo ! bare ice, temperature dependence dTs = Timelt - Tsfcn(i,j) fT = min(dTs/dT_melt-c1,c0) alvdfni(i,j) = alvdfni(i,j) - dalb_mlt*fT alidfni(i,j) = alidfni(i,j) - dalb_mlt*fT ! avoid negative albedos for thin, bare, melting ice alvdfni(i,j) = max (alvdfni(i,j), albocn) alidfni(i,j) = max (alidfni(i,j), albocn) if (hs > puny) then alvdfns(i,j) = albsnowv alidfns(i,j) = albsnowi ! snow on ice, temperature dependence alvdfns(i,j) = alvdfns(i,j) - dalb_mltv*fT alidfns(i,j) = alidfns(i,j) - dalb_mlti*fT endif ! hs > puny ! direct albedos (same as diffuse for now) alvdrni(i,j) = alvdfni(i,j) alidrni(i,j) = alidfni(i,j) alvdrns(i,j) = alvdfns(i,j) alidrns(i,j) = alidfns(i,j) ! fractional area of snow cover if (hs > puny) then asnow = hs / (hs + snowpatch) else asnow = c0 endif ! combine ice and snow albedos (for coupler) alvdfn(i,j) = alvdfni(i,j)*(c1-asnow) + & alvdfns(i,j)*asnow alidfn(i,j) = alidfni(i,j)*(c1-asnow) + & alidfns(i,j)*asnow alvdrn(i,j) = alvdrni(i,j)*(c1-asnow) + & alvdrns(i,j)*asnow alidrn(i,j) = alidrni(i,j)*(c1-asnow) + & alidrns(i,j)*asnow ! save ice and snow albedos (for history) albin(i,j) = awtvdr*alvdrni(i,j) + awtidr*alidrni(i,j) & + awtvdf*alvdfni(i,j) + awtidf*alidfni(i,j) albsn(i,j) = awtvdr*alvdrns(i,j) + awtidr*alidrns(i,j) & + awtvdf*alvdfns(i,j) + awtidf*alidfns(i,j) enddo ! ij end subroutine compute_albedos !======================================================================= ! ! Compute albedos for each thickness category subroutine constant_albedos (nx_block, ny_block, & icells, & indxi, indxj, & aicen, & vsnon, Tsfcn, & alvdrni, alidrni, & alvdfni, alidfni, & alvdrns, alidrns, & alvdfns, alidfns, & alvdrn, alidrn, & alvdfn, alidfn, & albin, albsn) integer (kind=int_kind), intent(in) :: & nx_block, ny_block, & ! block dimensions icells ! number of ice-covered grid cells integer (kind=int_kind), dimension (nx_block*ny_block), & intent(in) :: & indxi , & ! compressed indices for ice-covered cells indxj real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & aicen , & ! concentration of ice per category vsnon , & ! volume of ice per category Tsfcn ! surface temperature real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(out) :: & alvdrni , & ! visible, direct, ice (fraction) alidrni , & ! near-ir, direct, ice (fraction) alvdfni , & ! visible, diffuse, ice (fraction) alidfni , & ! near-ir, diffuse, ice (fraction) alvdrns , & ! visible, direct, snow (fraction) alidrns , & ! near-ir, direct, snow (fraction) alvdfns , & ! visible, diffuse, snow (fraction) alidfns , & ! near-ir, diffuse, snow (fraction) alvdrn , & ! visible, direct, avg (fraction) alidrn , & ! near-ir, direct, avg (fraction) alvdfn , & ! visible, diffuse, avg (fraction) alidfn , & ! near-ir, diffuse, avg (fraction) albin , & ! bare ice albsn ! snow ! local variables real (kind=dbl_kind), parameter :: & warmice = 0.68_dbl_kind, & coldice = 0.70_dbl_kind, & warmsnow = 0.77_dbl_kind, & coldsnow = 0.81_dbl_kind integer (kind=int_kind) :: & i, j real (kind=dbl_kind) :: & hs ! snow thickness (m) integer (kind=int_kind) :: & ij ! horizontal index, combines i and j loops do j = 1, ny_block do i = 1, nx_block alvdrn(i,j) = albocn alidrn(i,j) = albocn alvdfn(i,j) = albocn alidfn(i,j) = albocn albin(i,j) = c0 albsn(i,j) = c0 enddo enddo !----------------------------------------------------------------- ! Compute albedo for each thickness category. !----------------------------------------------------------------- !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells i = indxi(ij) j = indxj(ij) hs = vsnon(i,j) / aicen(i,j) if (hs > puny) then ! snow, temperature dependence if (Tsfcn(i,j) >= -c2*puny) then alvdfn(i,j) = warmsnow alidfn(i,j) = warmsnow else alvdfn(i,j) = coldsnow alidfn(i,j) = coldsnow endif else ! hs < puny ! bare ice, temperature dependence if (Tsfcn(i,j) >= -c2*puny) then alvdfn(i,j) = warmice alidfn(i,j) = warmice else alvdfn(i,j) = coldice alidfn(i,j) = coldice endif endif ! hs > puny ! direct albedos (same as diffuse for now) alvdrn (i,j) = alvdfn(i,j) alidrn (i,j) = alidfn(i,j) alvdrni(i,j) = alvdrn(i,j) alidrni(i,j) = alidrn(i,j) alvdrns(i,j) = alvdrn(i,j) alidrns(i,j) = alidrn(i,j) alvdfni(i,j) = alvdfn(i,j) alidfni(i,j) = alidfn(i,j) alvdfns(i,j) = alvdfn(i,j) alidfns(i,j) = alidfn(i,j) ! save ice and snow albedos (for history) albin(i,j) = awtvdr*alvdrni(i,j) + awtidr*alidrni(i,j) & + awtvdf*alvdfni(i,j) + awtidf*alidfni(i,j) albsn(i,j) = awtvdr*alvdrns(i,j) + awtidr*alidrns(i,j) & + awtvdf*alvdfns(i,j) + awtidf*alidfns(i,j) enddo ! ij end subroutine constant_albedos !======================================================================= ! ! Compute solar radiation absorbed in ice and penetrating to ocean ! ! authors William H. Lipscomb, LANL ! C. M. Bitz, UW subroutine absorbed_solar (nx_block, ny_block, & icells, & indxi, indxj, & aicen, & vicen, vsnon, & swvdr, swvdf, & swidr, swidf, & alvdrni, alvdfni, & alidrni, alidfni, & alvdrns, alvdfns, & alidrns, alidfns, & fswsfc, fswint, & fswthru, fswpenl, & Iswabs) use ice_therm_shared, only: heat_capacity integer (kind=int_kind), intent(in) :: & nx_block, ny_block, & ! block dimensions icells ! number of cells with aicen > puny integer (kind=int_kind), dimension(nx_block*ny_block), & intent(in) :: & indxi, indxj ! compressed indices for cells with aicen > puny real (kind=dbl_kind), dimension (nx_block,ny_block), intent(in) :: & aicen , & ! fractional ice area vicen , & ! ice volume vsnon , & ! snow volume swvdr , & ! sw down, visible, direct (W/m^2) swvdf , & ! sw down, visible, diffuse (W/m^2) swidr , & ! sw down, near IR, direct (W/m^2) swidf , & ! sw down, near IR, diffuse (W/m^2) alvdrni , & ! visible, direct albedo,ice alidrni , & ! near-ir, direct albedo,ice alvdfni , & ! visible, diffuse albedo,ice alidfni , & ! near-ir, diffuse albedo,ice alvdrns , & ! visible, direct albedo, snow alidrns , & ! near-ir, direct albedo, snow alvdfns , & ! visible, diffuse albedo, snow alidfns ! near-ir, diffuse albedo, snow real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(out):: & fswsfc , & ! SW absorbed at ice/snow surface (W m-2) fswint , & ! SW absorbed in ice interior, below surface (W m-2) fswthru ! SW through ice to ocean (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr), & intent(out) :: & Iswabs ! SW absorbed in particular layer (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr+1), & intent(out) :: & fswpenl ! visible SW entering ice layers (W m-2) ! local variables real (kind=dbl_kind), parameter :: & i0vis = 0.70_dbl_kind ! fraction of penetrating solar rad (visible) integer (kind=int_kind) :: & i, j , & ! horizontal indices ij , & ! horizontal index, combines i and j loops k ! ice layer index real (kind=dbl_kind), dimension (nx_block,ny_block) :: & fswpen , & ! SW penetrating beneath surface (W m-2) trantop , & ! transmitted frac of penetrating SW at layer top tranbot ! transmitted frac of penetrating SW at layer bot real (kind=dbl_kind) :: & swabs , & ! net SW down at surface (W m-2) swabsv , & ! swabs in vis (wvlngth < 700nm) (W/m^2) swabsi , & ! swabs in nir (wvlngth > 700nm) (W/m^2) fswpenvdr , & ! penetrating SW, vis direct fswpenvdf , & ! penetrating SW, vis diffuse hi , & ! ice thickness (m) hs , & ! snow thickness (m) hilyr , & ! ice layer thickness asnow ! fractional area of snow cover !----------------------------------------------------------------- ! Initialize !----------------------------------------------------------------- do j = 1, ny_block do i = 1, nx_block fswsfc (i,j) = c0 fswint (i,j) = c0 fswthru(i,j) = c0 fswpen (i,j) = c0 trantop(i,j) = c0 tranbot(i,j) = c0 enddo enddo Iswabs (:,:,:) = c0 do ij = 1, icells i = indxi(ij) j = indxj(ij) hs = vsnon(i,j) / aicen(i,j) !----------------------------------------------------------------- ! Fractional snow cover !----------------------------------------------------------------- if (hs > puny) then asnow = hs / (hs + snowpatch) else asnow = c0 endif !----------------------------------------------------------------- ! Shortwave flux absorbed at surface, absorbed internally, ! and penetrating to mixed layer. ! This parameterization assumes that all IR is absorbed at the ! surface; only visible is absorbed in the ice interior or ! transmitted to the ocean. !----------------------------------------------------------------- swabsv = swvdr(i,j) * ( (c1-alvdrni(i,j))*(c1-asnow) & + (c1-alvdrns(i,j))*asnow ) & + swvdf(i,j) * ( (c1-alvdfni(i,j))*(c1-asnow) & + (c1-alvdfns(i,j))*asnow ) swabsi = swidr(i,j) * ( (c1-alidrni(i,j))*(c1-asnow) & + (c1-alidrns(i,j))*asnow ) & + swidf(i,j) * ( (c1-alidfni(i,j))*(c1-asnow) & + (c1-alidfns(i,j))*asnow ) swabs = swabsv + swabsi fswpenvdr = swvdr(i,j) * (c1-alvdrni(i,j)) * (c1-asnow) * i0vis fswpenvdf = swvdf(i,j) * (c1-alvdfni(i,j)) * (c1-asnow) * i0vis ! no penetrating radiation in near IR ! fswpenidr = swidr(i,j) * (c1-alidrni(i,j)) * (c1-asnow) * i0nir ! fswpenidf = swidf(i,j) * (c1-alidfni(i,j)) * (c1-asnow) * i0nir fswpen(i,j) = fswpenvdr + fswpenvdf fswsfc(i,j) = swabs - fswpen(i,j) trantop(i,j) = c1 ! transmittance at top of ice enddo ! ij !----------------------------------------------------------------- ! penetrating SW absorbed in each ice layer !----------------------------------------------------------------- do k = 1, nilyr !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells i = indxi(ij) j = indxj(ij) hi = vicen(i,j) / aicen(i,j) hilyr = hi / real(nilyr,kind=dbl_kind) tranbot(i,j) = exp (-kappav * hilyr * real(k,kind=dbl_kind)) Iswabs(i,j,k) = fswpen(i,j) * (trantop(i,j)-tranbot(i,j)) ! bottom of layer k = top of layer k+1 trantop(i,j) = tranbot(i,j) ! bgc layer model if (k == 1) then ! surface flux fswpenl(i,j,k) = fswpen(i,j) fswpenl(i,j,k+1) = fswpen(i,j) * tranbot(i,j) else fswpenl(i,j,k+1) = fswpen(i,j) * tranbot(i,j) endif enddo ! ij enddo ! nilyr !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells i = indxi(ij) j = indxj(ij) ! SW penetrating thru ice into ocean fswthru(i,j) = fswpen(i,j) * tranbot(i,j) ! SW absorbed in ice interior fswint(i,j) = fswpen(i,j) - fswthru(i,j) enddo ! ij !---------------------------------------------------------------- ! if zero-layer model (no heat capacity), no SW is absorbed in ice ! interior, so add to surface absorption !---------------------------------------------------------------- if (.not. heat_capacity) then !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells i = indxi(ij) j = indxj(ij) ! SW absorbed at snow/ice surface fswsfc(i,j) = fswsfc(i,j) + fswint(i,j) ! SW absorbed in ice interior (nilyr = 1) fswint(i,j) = c0 Iswabs(i,j,1) = c0 enddo ! ij endif ! heat_capacity end subroutine absorbed_solar ! End ccsm3 shortwave method !======================================================================= ! Begin Delta-Eddington shortwave method ! Compute initial data for Delta-Eddington method, specifically, ! the approximate exponential look-up table. ! ! author: Bruce P. Briegleb, NCAR ! 2011 ECH modified for melt pond tracers ! 2013 ECH merged with NCAR version subroutine run_dEdd(ilo,ihi,jlo,jhi, & aicen, vicen, & vsnon, trcrn, & tlat, tlon, & tmask, & swvdr, swvdf, & swidr, swidf, & coszen, fsnow, & alvdrn, alvdfn, & alidrn, alidfn, & fswsfcn, fswintn, & fswthrun, fswpenln, & Sswabsn, Iswabsn, & albicen, albsnon, & albpndn, apeffn, & dhsn, ffracn, & initonly ) use ice_calendar, only: dt use ice_meltpond_cesm, only: hs0 use ice_meltpond_topo, only: hp1 use ice_meltpond_lvl, only: hs1, pndaspect use ice_orbital, only: compute_coszen use ice_state, only: ntrcr, nt_Tsfc, nt_alvl, nt_apnd, nt_hpnd, nt_ipnd, & tr_pond_cesm, tr_pond_lvl, tr_pond_topo use ice_domain_size, only: max_ntrcr integer (kind=int_kind), intent(in) :: & ilo,ihi,jlo,jhi logical(kind=log_kind), dimension(nx_block,ny_block), intent(in) :: & tmask ! land/boundary mask, thickness (T-cell) real(kind=dbl_kind), dimension(nx_block,ny_block), intent(in) :: & tlat, & ! latitude of temp pts (radians) tlon, & ! longitude of temp pts (radians) swvdr, & ! sw down, visible, direct (W/m^2) swvdf, & ! sw down, visible, diffuse (W/m^2) swidr, & ! sw down, near IR, direct (W/m^2) swidf, & ! sw down, near IR, diffuse (W/m^2) fsnow ! snowfall rate (kg/m^2 s) real(kind=dbl_kind), dimension(nx_block,ny_block,ncat), intent(in) :: & aicen, & ! concentration of ice vicen, & ! volume per unit area of ice (m) vsnon, & ! volume per unit area of snow (m) ffracn ! fraction of fsurfn used to melt ipond real(kind=dbl_kind), dimension(nx_block,ny_block,max_ntrcr,ncat), intent(in) :: & trcrn ! tracers real(kind=dbl_kind), dimension(nx_block,ny_block,ncat), intent(inout) :: & dhsn ! depth difference for snow on sea ice and pond ice real(kind=dbl_kind), dimension(nx_block,ny_block), intent(out) :: & coszen ! cosine solar zenith angle, < 0 for sun below horizon real(kind=dbl_kind), dimension(nx_block,ny_block,ncat), intent(inout) :: & alvdrn, & ! visible direct albedo (fraction) alvdfn, & ! near-ir direct albedo (fraction) alidrn, & ! visible diffuse albedo (fraction) alidfn, & ! near-ir diffuse albedo (fraction) fswsfcn, & ! SW absorbed at ice/snow surface (W m-2) fswintn, & ! SW absorbed in ice interior, below surface (W m-2) fswthrun, & ! SW through ice to ocean (W/m^2) albicen, & ! albedo bare ice albsnon, & ! albedo snow albpndn, & ! albedo pond apeffn ! effective pond area used for radiation calculation real(kind=dbl_kind), dimension(nx_block,ny_block,nslyr,ncat), intent(inout) :: & Sswabsn ! SW radiation absorbed in snow layers (W m-2) real(kind=dbl_kind), dimension(nx_block,ny_block,nilyr,ncat), intent(inout) :: & Iswabsn ! SW radiation absorbed in ice layers (W m-2) real(kind=dbl_kind), dimension(nx_block,ny_block,nilyr+1,ncat), intent(inout) :: & fswpenln ! visible SW entering ice layers (W m-2) logical (kind=log_kind), optional :: & initonly ! flag to indicate init only, default is false ! local temporary variables integer (kind=int_kind) :: & icells ! number of cells with aicen > puny integer (kind=int_kind), dimension(nx_block*ny_block) :: & indxi, indxj ! indirect indices for cells with aicen > puny ! other local variables ! snow variables for Delta-Eddington shortwave real (kind=dbl_kind), dimension (nx_block,ny_block) :: & fsn , & ! snow horizontal fraction hsn ! snow depth (m) real (kind=dbl_kind), dimension (nx_block,ny_block,nslyr) :: & rhosnwn , & ! snow density (kg/m3) rsnwn ! snow grain radius (micrometers) ! pond variables for Delta-Eddington shortwave real (kind=dbl_kind), dimension (nx_block,ny_block) :: & fpn , & ! pond fraction of ice cover hpn ! actual pond depth (m) integer (kind=int_kind) :: & i, j, ij , & ! horizontal indices n ! thickness category index real (kind=dbl_kind) :: & ipn , & ! refrozen pond ice thickness (m), mean over ice fraction hp , & ! pond depth hs , & ! snow depth asnow , & ! fractional area of snow cover rp , & ! volume fraction of retained melt water to total liquid content hmx , & ! maximum available snow infiltration equivalent depth dhs , & ! local difference in snow depth on sea ice and pond ice spn , & ! snow depth on refrozen pond (m) tmp ! 0 or 1 logical (kind=log_kind) :: & linitonly ! local initonly value real (kind=dbl_kind), parameter :: & argmax = c10 ! maximum argument of exponential linitonly = .false. if (present(initonly)) then linitonly = initonly endif exp_min = exp(-argmax) ! identify ice-ocean cells icells = 0 do j = 1, ny_block do i = 1, nx_block if (tmask(i,j)) then icells = icells + 1 indxi(icells) = i indxj(icells) = j endif enddo ! i enddo ! j ! cosine of the zenith angle call compute_coszen (nx_block, ny_block, & icells, & indxi, indxj, & tlat (:,:), tlon(:,:), & coszen(:,:), dt) do n = 1, ncat icells = 0 do j = jlo, jhi do i = ilo, ihi if (aicen(i,j,n) > puny) then icells = icells + 1 indxi(icells) = i indxj(icells) = j endif enddo ! i enddo ! j ! note that rhoswn, rsnw, fp, hp and Sswabs ARE NOT dimensioned with ncat ! BPB 19 Dec 2006 ! set snow properties call shortwave_dEdd_set_snow(nx_block, ny_block, & icells, & indxi, indxj, & aicen(:,:,n), vsnon(:,:,n), & trcrn(:,:,nt_Tsfc,n), fsn, hsn, & rhosnwn, rsnwn) ! set pond properties if (tr_pond_cesm) then apeffn(:,:,n) = c0 ! for history do ij = 1, icells i = indxi(ij) j = indxj(ij) ! fraction of ice area fpn(i,j) = trcrn(i,j,nt_apnd,n) ! pond depth over fraction fpn hpn(i,j) = trcrn(i,j,nt_hpnd,n) ! snow infiltration if (hsn(i,j) >= hs_min .and. hs0 > puny) then asnow = min(hsn(i,j)/hs0, c1) ! delta-Eddington formulation fpn(i,j) = (c1 - asnow) * fpn(i,j) hpn(i,j) = pndaspect * fpn(i,j) endif apeffn(i,j,n) = fpn(i,j) ! for history enddo elseif (tr_pond_lvl) then apeffn(:,:,n) = c0 ! for history do ij = 1, icells i = indxi(ij) j = indxj(ij) fpn(i,j) = c0 ! fraction of ice covered in pond hpn(i,j) = c0 ! pond depth over fpn ! refrozen pond lid thickness avg over ice ! allow snow to cover pond ice ipn = trcrn(i,j,nt_alvl,n) * trcrn(i,j,nt_apnd,n) & * trcrn(i,j,nt_ipnd,n) dhs = dhsn(i,j,n) ! snow depth difference, sea ice - pond if (.not. linitonly .and. ipn > puny .and. & dhs < puny .and. fsnow(i,j)*dt > hs_min) & dhs = hsn(i,j) - fsnow(i,j)*dt ! initialize dhs>0 spn = hsn(i,j) - dhs ! snow depth on pond ice if (.not. linitonly .and. ipn*spn < puny) dhs = c0 dhsn(i,j,n) = dhs ! save: constant until reset to 0 ! not using ipn assumes that lid ice is perfectly clear ! if (ipn <= 0.3_dbl_kind) then ! fraction of ice area fpn(i,j) = trcrn(i,j,nt_apnd,n) * trcrn(i,j,nt_alvl,n) ! pond depth over fraction fpn hpn(i,j) = trcrn(i,j,nt_hpnd,n) ! reduce effective pond area absorbing surface heat flux ! due to flux already having been used to melt pond ice fpn(i,j) = (c1 - ffracn(i,j,n)) * fpn(i,j) ! taper pond area with snow on pond ice if (dhs > puny .and. spn >= puny .and. hs1 > puny) then asnow = min(spn/hs1, c1) fpn(i,j) = (c1 - asnow) * fpn(i,j) endif ! infiltrate snow hp = hpn(i,j) if (hp > puny) then hs = hsn(i,j) rp = rhofresh*hp/(rhofresh*hp + rhos*hs) if (rp < p15) then fpn(i,j) = c0 hpn(i,j) = c0 else hmx = hs*(rhofresh - rhos)/rhofresh tmp = max(c0, sign(c1, hp-hmx)) ! 1 if hp>=hmx, else 0 hp = (rhofresh*hp + rhos*hs*tmp) & / (rhofresh - rhos*(c1-tmp)) hsn(i,j) = hs - hp*fpn(i,j)*(c1-tmp) hpn(i,j) = hp * tmp fpn(i,j) = fpn(i,j) * tmp endif fsn(i,j) = min(fsn(i,j), c1-fpn(i,j)) endif ! hp > puny ! endif ! masking by lid ice apeffn(i,j,n) = fpn(i,j) ! for history enddo ! ij elseif (tr_pond_topo) then apeffn(:,:,n) = c0 ! for history do ij = 1, icells i = indxi(ij) j = indxj(ij) ! Lid effective if thicker than hp1 if (trcrn(i,j,nt_apnd,n)*aicen(i,j,n) > puny .and. & trcrn(i,j,nt_ipnd,n) < hp1) then fpn(i,j) = trcrn(i,j,nt_apnd,n) else fpn(i,j) = c0 endif if (trcrn(i,j,nt_apnd,n) > puny) then hpn(i,j) = trcrn(i,j,nt_hpnd,n) else fpn(i,j) = c0 hpn(i,j) = c0 endif ! If ponds are present snow fraction reduced to ! non-ponded part dEdd scheme fsn(i,j) = min(fsn(i,j), c1-fpn(i,j)) apeffn(i,j,n) = fpn(i,j) enddo else call shortwave_dEdd_set_pond(nx_block, ny_block, & icells, & indxi, indxj, & trcrn(:,:,nt_Tsfc,n), & fsn, fpn, & hpn) apeffn(:,:,n) = fpn(:,:) ! for history fpn = c0 hpn = c0 endif call shortwave_dEdd(nx_block, ny_block, & ntrcr, icells, & indxi, indxj, & coszen(:,:), & aicen(:,:,n), vicen(:,:,n), & hsn, fsn, & rhosnwn, rsnwn, & fpn, hpn, & trcrn(:,:,1:ntrcr,n), & swvdr(:,:), swvdf(:,:), & swidr(:,:), swidf(:,:), & alvdrn(:,:,n), alvdfn(:,:,n), & alidrn(:,:,n), alidfn(:,:,n), & fswsfcn(:,:,n), fswintn(:,:,n), & fswthrun(:,:,n), & Sswabsn(:,:,:,n), & Iswabsn(:,:,:,n), & albicen(:,:,n), & albsnon(:,:,n), albpndn(:,:,n), & fswpenln(:,:,:,n)) enddo ! ncat end subroutine run_dEdd !======================================================================= ! ! Compute snow/bare ice/ponded ice shortwave albedos, absorbed and transmitted ! flux using the Delta-Eddington solar radiation method as described in: ! ! "A Delta-Eddington Multiple Scattering Parameterization for Solar Radiation ! in the Sea Ice Component of the Community Climate System Model" ! B.P.Briegleb and B.Light NCAR/TN-472+STR February 2007 ! ! Compute shortwave albedos and fluxes for three surface types: ! snow over ice, bare ice and ponded ice. ! ! Albedos and fluxes are output for later use by thermodynamic routines. ! Invokes three calls to compute_dEdd, which sets inherent optical properties ! appropriate for the surface type. Within compute_dEdd, a call to solution_dEdd ! evaluates the Delta-Eddington solution. The final albedos and fluxes are then ! evaluated in compute_dEdd. Albedos and fluxes are transferred to output in ! this routine. ! ! NOTE regarding albedo diagnostics: This method yields zero albedo values ! if there is no incoming solar and thus the albedo diagnostics are masked ! out when the sun is below the horizon. To estimate albedo from the history ! output (post-processing), compute ice albedo using ! (1 - albedo)*swdn = swabs. -ECH ! ! author: Bruce P. Briegleb, NCAR ! 2013: E Hunke merged with NCAR version ! subroutine shortwave_dEdd (nx_block, ny_block, & ntrcr, icells, & indxi, indxj, & coszen, & aice, vice, & hs, fs, & rhosnw, rsnw, & fp, hp, & trcr, & swvdr, swvdf, & swidr, swidf, & alvdr, alvdf, & alidr, alidf, & fswsfc, fswint, & fswthru, Sswabs, & Iswabs, albice, & albsno, albpnd, & fswpenl) use ice_state, only: nt_aero, tr_aero integer (kind=int_kind), & intent(in) :: & nx_block, ny_block, & ! block dimensions ntrcr , & ! number of tracers in use icells ! number of ice-covered grid cells integer (kind=int_kind), dimension (nx_block*ny_block), & intent(in) :: & indxi , & ! compressed indices for ice-covered cells indxj real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & coszen , & ! cosine of solar zenith angle aice , & ! concentration of ice vice , & ! volume of ice hs , & ! snow depth fs ! horizontal coverage of snow real (kind=dbl_kind), dimension (nx_block,ny_block,nslyr), & intent(in) :: & rhosnw , & ! density in snow layer (kg/m3) rsnw ! grain radius in snow layer (m) real (kind=dbl_kind), dimension (nx_block,ny_block,ntrcr), & intent(in) :: & trcr ! aerosol tracers real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & fp , & ! pond fractional coverage (0 to 1) hp , & ! pond depth (m) swvdr , & ! sw down, visible, direct (W/m^2) swvdf , & ! sw down, visible, diffuse (W/m^2) swidr , & ! sw down, near IR, direct (W/m^2) swidf ! sw down, near IR, diffuse (W/m^2) real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(inout) :: & alvdr , & ! visible, direct, albedo (fraction) alvdf , & ! visible, diffuse, albedo (fraction) alidr , & ! near-ir, direct, albedo (fraction) alidf , & ! near-ir, diffuse, albedo (fraction) fswsfc , & ! SW absorbed at snow/bare ice/pondedi ice surface (W m-2) fswint , & ! SW interior absorption (below surface, above ocean,W m-2) fswthru ! SW through snow/bare ice/ponded ice into ocean (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr+1), & intent(inout) :: & fswpenl ! visible SW entering ice layers (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nslyr), & intent(inout) :: & Sswabs ! SW absorbed in snow layer (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr), & intent(inout) :: & Iswabs ! SW absorbed in ice layer (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(out) :: & albice , & ! bare ice albedo, for history albsno , & ! snow albedo, for history albpnd ! pond albedo, for history ! local variables real (kind=dbl_kind),dimension (nx_block,ny_block) :: & fnidr ! fraction of direct to total down surface flux in nir real (kind=dbl_kind), dimension(nx_block,ny_block) :: & hstmp , & ! snow thickness (set to 0 for bare ice case) hi , & ! ice thickness (all sea ice layers, m) fi ! snow/bare ice fractional coverage (0 to 1) real (kind=dbl_kind), dimension (nx_block,ny_block,4*n_aero) :: & aero_mp ! aerosol mass path in kg/m2 integer (kind=int_kind) :: & srftyp ! surface type over ice: (0=air, 1=snow, 2=pond) integer (kind=int_kind) :: & i , & ! longitude index j , & ! latitude index ij , & ! horizontal index, combines i and j loops k , & ! level index na , & ! aerosol index icells_DE ! number of cells in Delta-Eddington calculation integer (kind=int_kind), dimension (nx_block*ny_block) :: & indxi_DE , & ! compressed indices for Delta-Eddington cells indxj_DE real (kind=dbl_kind) :: & vsno ! volume of snow ! for printing points integer (kind=int_kind) :: & n ! point number for prints logical (kind=log_kind) :: & dbug ! true/false flag real (kind=dbl_kind) :: & swdn , & ! swvdr(i,j)+swvdf(i,j)+swidr(i,j)+swidf(i,j) swab , & ! fswsfc(i,j)+fswint(i,j)+fswthru(i,j) swalb ! (1.-swab/(swdn+.0001)) ! for history real (kind=dbl_kind), dimension (nx_block,ny_block) :: & avdrl , & ! visible, direct, albedo (fraction) avdfl , & ! visible, diffuse, albedo (fraction) aidrl , & ! near-ir, direct, albedo (fraction) aidfl ! near-ir, diffuse, albedo (fraction) !----------------------------------------------------------------------- do j = 1, ny_block do i = 1, nx_block ! zero storage albedos and fluxes for accumulation over surface types: hstmp(i,j) = c0 hi(i,j) = c0 fi(i,j) = c0 alvdr(i,j) = c0 alvdf(i,j) = c0 alidr(i,j) = c0 alidf(i,j) = c0 avdrl(i,j) = c0 avdfl(i,j) = c0 aidrl(i,j) = c0 aidfl(i,j) = c0 fswsfc(i,j) = c0 fswint(i,j) = c0 fswthru(i,j) = c0 ! compute fraction of nir down direct to total over all points: fnidr(i,j) = c0 if( swidr(i,j) + swidf(i,j) > puny ) then fnidr(i,j) = swidr(i,j)/(swidr(i,j)+swidf(i,j)) endif albice(i,j) = c0 albsno(i,j) = c0 albpnd(i,j) = c0 enddo enddo fswpenl(:,:,:) = c0 Sswabs(:,:,:) = c0 Iswabs(:,:,:) = c0 ! compute aerosol mass path aero_mp(:,:,:) = c0 if( tr_aero ) then !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu ! assume 4 layers for each aerosol, a snow SSL, snow below SSL, ! sea ice SSL, and sea ice below SSL, in that order. do na = 1, 4*n_aero, 4 do ij = 1, icells i = indxi(ij) j = indxj(ij) vsno = hs(i,j) * aice(i,j) if (coszen(i,j) > puny) then ! sun above horizon aero_mp(i,j,na ) = trcr(i,j,nt_aero-1+na )*vsno aero_mp(i,j,na+1) = trcr(i,j,nt_aero-1+na+1)*vsno aero_mp(i,j,na+2) = trcr(i,j,nt_aero-1+na+2)*vice(i,j) aero_mp(i,j,na+3) = trcr(i,j,nt_aero-1+na+3)*vice(i,j) endif ! aice > 0 and coszen > 0 enddo ! ij enddo ! na endif ! if aerosols ! compute shortwave radiation accounting for snow/ice (both snow over ! ice and bare ice) and ponded ice (if any): !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu ! find bare ice points icells_DE = 0 do ij = 1, icells i = indxi(ij) j = indxj(ij) ! sea ice points with sun above horizon if (coszen(i,j) > puny) then ! evaluate sea ice thickness and fraction hi(i,j) = vice(i,j) / aice(i,j) fi(i,j) = c1 - fs(i,j) - fp(i,j) ! bare sea ice points if(fi(i,j) > c0) then icells_DE = icells_DE + 1 indxi_DE(icells_DE) = i indxj_DE(icells_DE) = j ! bare ice endif ! fi > 0 endif ! coszen > 0 enddo ! ij ! calculate bare sea ice srftyp = 0 if (icells_DE > 0) & call compute_dEdd & (nx_block,ny_block, & icells_DE, indxi_DE, indxj_DE, fnidr, coszen, & swvdr, swvdf, swidr, swidf, srftyp, & hstmp, rhosnw, rsnw, hi, hp, & fi, aero_mp, avdrl, avdfl, & aidrl, aidfl, & fswsfc, fswint, & fswthru, Sswabs, & Iswabs, fswpenl) !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) alvdr(i,j) = alvdr(i,j) + avdrl(i,j) *fi(i,j) alvdf(i,j) = alvdf(i,j) + avdfl(i,j) *fi(i,j) alidr(i,j) = alidr(i,j) + aidrl(i,j) *fi(i,j) alidf(i,j) = alidf(i,j) + aidfl(i,j) *fi(i,j) ! for history albice(i,j) = albice(i,j) & + awtvdr*avdrl(i,j) + awtidr*aidrl(i,j) & + awtvdf*avdfl(i,j) + awtidf*aidfl(i,j) enddo !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu ! find snow-covered ice points icells_DE = 0 do ij = 1, icells i = indxi(ij) j = indxj(ij) ! sea ice points with sun above horizon if (coszen(i,j) > puny) then ! snow-covered sea ice points if(fs(i,j) > c0) then icells_DE = icells_DE + 1 indxi_DE(icells_DE) = i indxj_DE(icells_DE) = j ! snow-covered ice endif ! fs > 0 endif ! coszen > 0 enddo ! ij ! calculate snow covered sea ice srftyp = 1 if (icells_DE > 0) & call compute_dEdd & (nx_block,ny_block, & icells_DE, indxi_DE, indxj_DE, fnidr, coszen, & swvdr, swvdf, swidr, swidf, srftyp, & hs, rhosnw, rsnw, hi, hp, & fs, aero_mp, avdrl, avdfl, & aidrl, aidfl, & fswsfc, fswint, & fswthru, Sswabs, & Iswabs, fswpenl) !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) alvdr(i,j) = alvdr(i,j) + avdrl(i,j) *fs(i,j) alvdf(i,j) = alvdf(i,j) + avdfl(i,j) *fs(i,j) alidr(i,j) = alidr(i,j) + aidrl(i,j) *fs(i,j) alidf(i,j) = alidf(i,j) + aidfl(i,j) *fs(i,j) ! for history albsno(i,j) = albsno(i,j) & + awtvdr*avdrl(i,j) + awtidr*aidrl(i,j) & + awtvdf*avdfl(i,j) + awtidf*aidfl(i,j) enddo !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu ! find ponded points icells_DE = 0 do ij = 1, icells i = indxi(ij) j = indxj(ij) hi(i,j) = c0 ! sea ice points with sun above horizon if (coszen(i,j) > puny) then hi(i,j) = vice(i,j) / aice(i,j) ! if non-zero pond fraction and sufficient pond depth if( fp(i,j) > puny .and. hp(i,j) > hpmin ) then icells_DE = icells_DE + 1 indxi_DE(icells_DE) = i indxj_DE(icells_DE) = j ! ponded ice endif endif ! coszen > puny enddo ! ij ! calculate ponded ice srftyp = 2 if (icells_DE > 0) & call compute_dEdd & (nx_block,ny_block, & icells_DE, indxi_DE, indxj_DE, fnidr, coszen, & swvdr, swvdf, swidr, swidf, srftyp, & hs, rhosnw, rsnw, hi, hp, & fp, aero_mp, avdrl, avdfl, & aidrl, aidfl, & fswsfc, fswint, & fswthru, Sswabs, & Iswabs, fswpenl) !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) alvdr(i,j) = alvdr(i,j) + avdrl(i,j) *fp(i,j) alvdf(i,j) = alvdf(i,j) + avdfl(i,j) *fp(i,j) alidr(i,j) = alidr(i,j) + aidrl(i,j) *fp(i,j) alidf(i,j) = alidf(i,j) + aidfl(i,j) *fp(i,j) ! for history albpnd(i,j) = albpnd(i,j) & + awtvdr*avdrl(i,j) + awtidr*aidrl(i,j) & + awtvdf*avdfl(i,j) + awtidf*aidfl(i,j) enddo dbug = .false. if (dbug .and. print_points) then do n = 1, npnt if (my_task == pmloc(n)) then i = piloc(n) j = pjloc(n) if( coszen(i,j) > .01_dbl_kind ) then write(nu_diag,*) ' my_task = ',my_task & ,' printing point = ',n & ,' i and j = ',i,j write(nu_diag,*) ' coszen = ', & coszen(i,j) write(nu_diag,*) ' swvdr swvdf = ', & swvdr(i,j),swvdf(i,j) write(nu_diag,*) ' swidr swidf = ', & swidr(i,j),swidf(i,j) write(nu_diag,*) ' aice = ', & aice(i,j) write(nu_diag,*) ' hs = ', & hs(i,j) write(nu_diag,*) ' hp = ', & hp(i,j) write(nu_diag,*) ' fs = ', & fs(i,j) write(nu_diag,*) ' fi = ', & fi(i,j) write(nu_diag,*) ' fp = ', & fp(i,j) write(nu_diag,*) ' hi = ', & hi(i,j) write(nu_diag,*) ' alvdr alvdf = ', & alvdr(i,j),alvdf(i,j) write(nu_diag,*) ' alidr alidf = ', & alidr(i,j),alidf(i,j) write(nu_diag,*) ' fswsfc fswint fswthru = ', & fswsfc(i,j),fswint(i,j),fswthru(i,j) swdn = swvdr(i,j)+swvdf(i,j)+swidr(i,j)+swidf(i,j) swab = fswsfc(i,j)+fswint(i,j)+fswthru(i,j) swalb = (1.-swab/(swdn+.0001)) write(nu_diag,*) ' swdn swab swalb = ',swdn,swab,swalb do k = 1, nslyr write(nu_diag,*) ' snow layer k = ', k, & ' rhosnw = ', & rhosnw(i,j,k), & ' rsnw = ', & rsnw(i,j,k) enddo do k = 1, nslyr write(nu_diag,*) ' snow layer k = ', k, & ' Sswabs(k) = ', Sswabs(i,j,k) enddo do k = 1, nilyr write(nu_diag,*) ' sea ice layer k = ', k, & ' Iswabs(k) = ', Iswabs(i,j,k) enddo endif ! coszen(i,j) > .01 endif ! my_task enddo ! n for printing points endif ! if print_points end subroutine shortwave_dEdd !======================================================================= ! ! Evaluate snow/ice/ponded ice inherent optical properties (IOPs), and ! then calculate the multiple scattering solution by calling solution_dEdd. ! ! author: Bruce P. Briegleb, NCAR ! 2013: E Hunke merged with NCAR version subroutine compute_dEdd & (nx_block,ny_block, & icells_DE, indxi_DE, indxj_DE, fnidr, coszen, & swvdr, swvdf, swidr, swidf, srftyp, & hs, rhosnw, rsnw, hi, hp, & fi, aero_mp, alvdr, alvdf, & alidr, alidf, & fswsfc, fswint, & fswthru, Sswabs, & Iswabs, fswpenl) use ice_therm_shared, only: heat_capacity use ice_state, only: tr_aero integer (kind=int_kind), & intent(in) :: & nx_block, ny_block, & ! block dimensions icells_DE ! number of sea ice grid cells for surface type integer (kind=int_kind), dimension(nx_block*ny_block), & intent(in) :: & indxi_DE, & ! compressed indices for sea ice cells for surface type indxj_DE real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & fnidr , & ! fraction of direct to total down flux in nir coszen , & ! cosine solar zenith angle swvdr , & ! shortwave down at surface, visible, direct (W/m^2) swvdf , & ! shortwave down at surface, visible, diffuse (W/m^2) swidr , & ! shortwave down at surface, near IR, direct (W/m^2) swidf ! shortwave down at surface, near IR, diffuse (W/m^2) integer (kind=int_kind), intent(in) :: & srftyp ! surface type over ice: (0=air, 1=snow, 2=pond) real (kind=dbl_kind), dimension(nx_block,ny_block), & intent(in) :: & hs ! snow thickness (m) real (kind=dbl_kind), dimension (nx_block,ny_block,nslyr), & intent(in) :: & rhosnw , & ! snow density in snow layer (kg/m3) rsnw ! snow grain radius in snow layer (m) real (kind=dbl_kind), dimension(nx_block,ny_block), & intent(in) :: & hi , & ! ice thickness (m) hp , & ! pond depth (m) fi ! snow/bare ice fractional coverage (0 to 1) real (kind=dbl_kind), dimension (nx_block,ny_block,4*n_aero), & intent(in) :: & aero_mp ! aerosol mass path in kg/m2 real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(inout) :: & alvdr , & ! visible, direct, albedo (fraction) alvdf , & ! visible, diffuse, albedo (fraction) alidr , & ! near-ir, direct, albedo (fraction) alidf , & ! near-ir, diffuse, albedo (fraction) fswsfc , & ! SW absorbed at snow/bare ice/pondedi ice surface (W m-2) fswint , & ! SW interior absorption (below surface, above ocean,W m-2) fswthru ! SW through snow/bare ice/ponded ice into ocean (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr+1), & intent(inout) :: & fswpenl ! visible SW entering ice layers (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nslyr), & intent(inout) :: & Sswabs ! SW absorbed in snow layer (W m-2) real (kind=dbl_kind), dimension (nx_block,ny_block,nilyr), & intent(inout) :: & Iswabs ! SW absorbed in ice layer (W m-2) !----------------------------------------------------------------------- ! ! Set up optical property profiles, based on snow, sea ice and ponded ! ice IOPs from: ! ! Briegleb, B. P., and B. Light (2007): A Delta-Eddington Multiple ! Scattering Parameterization for Solar Radiation in the Sea Ice ! Component of the Community Climate System Model, NCAR Technical ! Note NCAR/TN-472+STR February 2007 ! ! Computes column Delta-Eddington radiation solution for specific ! surface type: either snow over sea ice, bare sea ice, or ponded sea ice. ! ! Divides solar spectrum into 3 intervals: 0.2-0.7, 0.7-1.19, and ! 1.19-5.0 micro-meters. The latter two are added (using an assumed ! partition of incident shortwave in the 0.7-5.0 micro-meter band between ! the 0.7-1.19 and 1.19-5.0 micro-meter band) to give the final output ! of 0.2-0.7 visible and 0.7-5.0 near-infrared albedos and fluxes. ! ! Specifies vertical layer optical properties based on input snow depth, ! density and grain radius, along with ice and pond depths, then computes ! layer by layer Delta-Eddington reflectivity, transmissivity and combines ! layers (done by calling routine solution_dEdd). Finally, surface albedos ! and internal fluxes/flux divergences are evaluated. ! ! Description of the level and layer index conventions. This is ! for the standard case of one snow layer and four sea ice layers. ! ! Please read the following; otherwise, there is 99.9% chance you ! will be confused about indices at some point in time........ :) ! ! CICE4.0 snow treatment has one snow layer above the sea ice. This ! snow layer has finite heat capacity, so that surface absorption must ! be distinguished from internal. The Delta-Eddington solar radiation ! thus adds extra surface scattering layers to both snow and sea ice. ! Note that in the following, we assume a fixed vertical layer structure ! for the radiation calculation. In other words, we always have the ! structure shown below for one snow and four sea ice layers, but for ! ponded ice the pond fills "snow" layer 1 over the sea ice, and for ! bare sea ice the top layers over sea ice are treated as transparent air. ! ! SSL = surface scattering layer for either snow or sea ice ! DL = drained layer for sea ice immediately under sea ice SSL ! INT = interior layers for sea ice below the drained layer. ! ! Notice that the radiation level starts with 0 at the top. Thus, ! the total number radiation layers is klev+1, where klev is the ! sum of nslyr, the number of CCSM snow layers, and nilyr, the ! number of CCSM sea ice layers, plus the sea ice SSL: ! klev = 1 + nslyr + nilyr ! ! For the standard case illustrated below, nslyr=1, nilyr=4, ! and klev=6, with the number of layer interfaces klevp=klev+1. ! Layer interfaces are the surfaces on which reflectivities, ! transmissivities and fluxes are evaluated. ! ! CCSM3 Sea Ice Model Delta-Eddington Solar Radiation ! Layers and Interfaces ! Layer Index Interface Index ! --------------------- --------------------- 0 ! 0 \\\ snow SSL \\\ ! snow layer 1 --------------------- 1 ! 1 rest of snow layer ! +++++++++++++++++++++ +++++++++++++++++++++ 2 ! 2 \\\ sea ice SSL \\\ ! sea ice layer 1 --------------------- 3 ! 3 sea ice DL ! --------------------- --------------------- 4 ! ! sea ice layer 2 4 sea ice INT ! ! --------------------- --------------------- 5 ! ! sea ice layer 3 5 sea ice INT ! ! --------------------- --------------------- 6 ! ! sea ice layer 4 6 sea ice INT ! ! --------------------- --------------------- 7 ! ! When snow lies over sea ice, the radiation absorbed in the ! snow SSL is used for surface heating, and that in the rest ! of the snow layer for its internal heating. For sea ice in ! this case, all of the radiant heat absorbed in both the ! sea ice SSL and the DL are used for sea ice layer 1 heating. ! ! When pond lies over sea ice, and for bare sea ice, all of the ! radiant heat absorbed within and above the sea ice SSL is used ! for surface heating, and that absorbed in the sea ice DL is ! used for sea ice layer 1 heating. ! ! Basically, vertical profiles of the layer extinction optical depth (tau), ! single scattering albedo (w0) and asymmetry parameter (g) are required over ! the klev+1 layers, where klev+1 = 2 + nslyr + nilyr. All of the surface type ! information and snow/ice iop properties are evaulated in this routine, so ! the tau,w0,g profiles can be passed to solution_dEdd for multiple scattering ! evaluation. Snow, bare ice and ponded ice iops are contained in data arrays ! in this routine. ! !----------------------------------------------------------------------- ! local variables integer (kind=int_kind) :: & i , & ! longitude index j , & ! latitude index k , & ! level index ij , & ! horizontal index, combines i and j loops ns , & ! spectral index nr , & ! index for grain radius tables ki , & ! index for internal absorption km , & ! k starting index for snow, sea ice internal absorption kp , & ! k+1 or k+2 index for snow, sea ice internal absorption ksrf , & ! level index for surface absorption ksnow , & ! level index for snow density and grain size kii ! level starting index for sea ice (nslyr+1) integer (kind=int_kind), parameter :: & klev = nslyr + nilyr + 1 , & ! number of radiation layers - 1 klevp = klev + 1 ! number of radiation interfaces - 1 ! (0 layer is included also) integer (kind=int_kind), parameter :: & nspint = 3 , & ! number of solar spectral intervals nmbrad = 32 ! number of snow grain radii in tables real (kind=dbl_kind), dimension(icells_DE) :: & avdr , & ! visible albedo, direct (fraction) avdf , & ! visible albedo, diffuse (fraction) aidr , & ! near-ir albedo, direct (fraction) aidf ! near-ir albedo, diffuse (fraction) real (kind=dbl_kind), dimension(icells_DE) :: & fsfc , & ! shortwave absorbed at snow/bare ice/ponded ice surface (W m-2) fint , & ! shortwave absorbed in interior (W m-2) fthru ! shortwave through snow/bare ice/ponded ice to ocean (W/m^2) real (kind=dbl_kind), dimension(icells_DE,nslyr) :: & Sabs ! shortwave absorbed in snow layer (W m-2) real (kind=dbl_kind), dimension(icells_DE,nilyr) :: & Iabs ! shortwave absorbed in ice layer (W m-2) real (kind=dbl_kind), dimension(icells_DE,nilyr+1) :: & fthrul ! shortwave through to ice layers (W m-2) real (kind=dbl_kind), dimension (icells_DE,nspint) :: & wghtns ! spectral weights real (kind=dbl_kind), parameter :: & cp67 = 0.67_dbl_kind , & ! nir band weight parameter cp33 = 0.33_dbl_kind , & ! nir band weight parameter cp78 = 0.78_dbl_kind , & ! nir band weight parameter cp22 = 0.22_dbl_kind , & ! nir band weight parameter cp01 = 0.01_dbl_kind ! for ocean visible albedo real (kind=dbl_kind), dimension (0:klev,icells_DE) :: & tau , & ! layer extinction optical depth w0 , & ! layer single scattering albedo g ! layer asymmetry parameter ! following arrays are defined at model interfaces; 0 is the top of the ! layer above the sea ice; klevp is the sea ice/ocean interface. real (kind=dbl_kind), dimension (0:klevp,icells_DE) :: & trndir , & ! solar beam down transmission from top trntdr , & ! total transmission to direct beam for layers above trndif , & ! diffuse transmission to diffuse beam for layers above rupdir , & ! reflectivity to direct radiation for layers below rupdif , & ! reflectivity to diffuse radiation for layers below rdndif ! reflectivity to diffuse radiation for layers above real (kind=dbl_kind), dimension (0:klevp,icells_DE) :: & dfdir , & ! down-up flux at interface due to direct beam at top surface dfdif ! down-up flux at interface due to diffuse beam at top surface real (kind=dbl_kind) :: & refk , & ! interface k multiple scattering term delr , & ! snow grain radius interpolation parameter ! inherent optical properties (iop) for snow Qs , & ! Snow extinction efficiency ks , & ! Snow extinction coefficient (/m) ws , & ! Snow single scattering albedo gs ! Snow asymmetry parameter real (kind=dbl_kind), dimension(nslyr,icells_DE) :: & frsnw ! snow grain radius in snow layer * adjustment factor (m) ! actual used ice and ponded ice IOPs, allowing for tuning ! modifications of the above "_mn" value real (kind=dbl_kind), dimension (nspint) :: & ki_ssl , & ! Surface-scattering-layer ice extinction coefficient (/m) wi_ssl , & ! Surface-scattering-layer ice single scattering albedo gi_ssl , & ! Surface-scattering-layer ice asymmetry parameter ki_dl , & ! Drained-layer ice extinction coefficient (/m) wi_dl , & ! Drained-layer ice single scattering albedo gi_dl , & ! Drained-layer ice asymmetry parameter ki_int , & ! Interior-layer ice extinction coefficient (/m) wi_int , & ! Interior-layer ice single scattering albedo gi_int , & ! Interior-layer ice asymmetry parameter ki_p_ssl , & ! Ice under pond srf scat layer extinction coefficient (/m) wi_p_ssl , & ! Ice under pond srf scat layer single scattering albedo gi_p_ssl , & ! Ice under pond srf scat layer asymmetry parameter ki_p_int , & ! Ice under pond extinction coefficient (/m) wi_p_int , & ! Ice under pond single scattering albedo gi_p_int ! Ice under pond asymmetry parameter real (kind=dbl_kind), dimension(0:klev,icells_DE) :: & dzk ! layer thickness real (kind=dbl_kind) :: & dz , & ! snow, sea ice or pond water layer thickness dz_ssl , & ! snow or sea ice surface scattering layer thickness fs ! scaling factor to reduce (nilyr<4) or increase (nilyr>4) DL ! extinction coefficient to maintain DL optical depth constant ! with changing number of sea ice layers, to approximately ! conserve computed albedo for constant physical depth of sea ! ice when the number of sea ice layers vary real (kind=dbl_kind) :: & sig , & ! scattering coefficient for tuning kabs , & ! absorption coefficient for tuning sigp ! modified scattering coefficient for tuning real (kind=dbl_kind), dimension (icells_DE) :: & albodr , & ! spectral ocean albedo to direct rad albodf ! spectral ocean albedo to diffuse rad ! for melt pond transition to bare sea ice for small pond depths real (kind=dbl_kind) :: & sig_i , & ! ice scattering coefficient (/m) sig_p , & ! pond scattering coefficient (/m) kext ! weighted extinction coefficient (/m) ! aerosol optical properties from Mark Flanner, 26 June 2008 ! order assumed: hydrophobic black carbon, hydrophilic black carbon, ! four dust aerosols by particle size range: ! dust1(.05-0.5 micron), dust2(0.5-1.25 micron), ! dust3(1.25-2.5 micron), dust4(2.5-5.0 micron) ! spectral bands same as snow/sea ice: (0.3-0.7 micron, 0.7-1.19 micron ! and 1.19-5.0 micron in wavelength) integer (kind=int_kind) :: & na ! aerosol index real (kind=dbl_kind) :: & taer , & ! total aerosol extinction optical depth waer , & ! total aerosol single scatter albedo gaer , & ! total aerosol asymmetry parameter swdr , & ! shortwave down at surface, direct (W/m^2) swdf , & ! shortwave down at surface, diffuse (W/m^2) rnilyr , & ! real(nilyr) rnslyr , & ! real(nslyr) rns , & ! real(ns) tmp_0, tmp_ks, tmp_kl ! temp variables ! snow grain radii (micro-meters) for table real (kind=dbl_kind), dimension(nmbrad), parameter :: & rsnw_tab = (/ & ! snow grain radius for each table entry (micro-meters) 5._dbl_kind, 7._dbl_kind, 10._dbl_kind, 15._dbl_kind, & 20._dbl_kind, 30._dbl_kind, 40._dbl_kind, 50._dbl_kind, & 65._dbl_kind, 80._dbl_kind, 100._dbl_kind, 120._dbl_kind, & 140._dbl_kind, 170._dbl_kind, 200._dbl_kind, 240._dbl_kind, & 290._dbl_kind, 350._dbl_kind, 420._dbl_kind, 500._dbl_kind, & 570._dbl_kind, 660._dbl_kind, 760._dbl_kind, 870._dbl_kind, & 1000._dbl_kind, 1100._dbl_kind, 1250._dbl_kind, 1400._dbl_kind, & 1600._dbl_kind, 1800._dbl_kind, 2000._dbl_kind, 2500._dbl_kind/) ! snow extinction efficiency (unitless) real (kind=dbl_kind), dimension (nspint,nmbrad), parameter :: & Qs_tab = reshape((/ & 2.131798_dbl_kind, 2.187756_dbl_kind, 2.267358_dbl_kind, & 2.104499_dbl_kind, 2.148345_dbl_kind, 2.236078_dbl_kind, & 2.081580_dbl_kind, 2.116885_dbl_kind, 2.175067_dbl_kind, & 2.062595_dbl_kind, 2.088937_dbl_kind, 2.130242_dbl_kind, & 2.051403_dbl_kind, 2.072422_dbl_kind, 2.106610_dbl_kind, & 2.039223_dbl_kind, 2.055389_dbl_kind, 2.080586_dbl_kind, & 2.032383_dbl_kind, 2.045751_dbl_kind, 2.066394_dbl_kind, & 2.027920_dbl_kind, 2.039388_dbl_kind, 2.057224_dbl_kind, & 2.023444_dbl_kind, 2.033137_dbl_kind, 2.048055_dbl_kind, & 2.020412_dbl_kind, 2.028840_dbl_kind, 2.041874_dbl_kind, & 2.017608_dbl_kind, 2.024863_dbl_kind, 2.036046_dbl_kind, & 2.015592_dbl_kind, 2.022021_dbl_kind, 2.031954_dbl_kind, & 2.014083_dbl_kind, 2.019887_dbl_kind, 2.028853_dbl_kind, & 2.012368_dbl_kind, 2.017471_dbl_kind, 2.025353_dbl_kind, & 2.011092_dbl_kind, 2.015675_dbl_kind, 2.022759_dbl_kind, & 2.009837_dbl_kind, 2.013897_dbl_kind, 2.020168_dbl_kind, & 2.008668_dbl_kind, 2.012252_dbl_kind, 2.017781_dbl_kind, & 2.007627_dbl_kind, 2.010813_dbl_kind, 2.015678_dbl_kind, & 2.006764_dbl_kind, 2.009577_dbl_kind, 2.013880_dbl_kind, & 2.006037_dbl_kind, 2.008520_dbl_kind, 2.012382_dbl_kind, & 2.005528_dbl_kind, 2.007807_dbl_kind, 2.011307_dbl_kind, & 2.005025_dbl_kind, 2.007079_dbl_kind, 2.010280_dbl_kind, & 2.004562_dbl_kind, 2.006440_dbl_kind, 2.009333_dbl_kind, & 2.004155_dbl_kind, 2.005898_dbl_kind, 2.008523_dbl_kind, & 2.003794_dbl_kind, 2.005379_dbl_kind, 2.007795_dbl_kind, & 2.003555_dbl_kind, 2.005041_dbl_kind, 2.007329_dbl_kind, & 2.003264_dbl_kind, 2.004624_dbl_kind, 2.006729_dbl_kind, & 2.003037_dbl_kind, 2.004291_dbl_kind, 2.006230_dbl_kind, & 2.002776_dbl_kind, 2.003929_dbl_kind, 2.005700_dbl_kind, & 2.002590_dbl_kind, 2.003627_dbl_kind, 2.005276_dbl_kind, & 2.002395_dbl_kind, 2.003391_dbl_kind, 2.004904_dbl_kind, & 2.002071_dbl_kind, 2.002922_dbl_kind, 2.004241_dbl_kind/), & (/nspint,nmbrad/)) ! snow single scattering albedo (unitless) real (kind=dbl_kind), dimension (nspint,nmbrad), parameter :: & ws_tab = reshape((/ & 0.9999994_dbl_kind, 0.9999673_dbl_kind, 0.9954589_dbl_kind, & 0.9999992_dbl_kind, 0.9999547_dbl_kind, 0.9938576_dbl_kind, & 0.9999990_dbl_kind, 0.9999382_dbl_kind, 0.9917989_dbl_kind, & 0.9999985_dbl_kind, 0.9999123_dbl_kind, 0.9889724_dbl_kind, & 0.9999979_dbl_kind, 0.9998844_dbl_kind, 0.9866190_dbl_kind, & 0.9999970_dbl_kind, 0.9998317_dbl_kind, 0.9823021_dbl_kind, & 0.9999960_dbl_kind, 0.9997800_dbl_kind, 0.9785269_dbl_kind, & 0.9999951_dbl_kind, 0.9997288_dbl_kind, 0.9751601_dbl_kind, & 0.9999936_dbl_kind, 0.9996531_dbl_kind, 0.9706974_dbl_kind, & 0.9999922_dbl_kind, 0.9995783_dbl_kind, 0.9667577_dbl_kind, & 0.9999903_dbl_kind, 0.9994798_dbl_kind, 0.9621007_dbl_kind, & 0.9999885_dbl_kind, 0.9993825_dbl_kind, 0.9579541_dbl_kind, & 0.9999866_dbl_kind, 0.9992862_dbl_kind, 0.9541924_dbl_kind, & 0.9999838_dbl_kind, 0.9991434_dbl_kind, 0.9490959_dbl_kind, & 0.9999810_dbl_kind, 0.9990025_dbl_kind, 0.9444940_dbl_kind, & 0.9999772_dbl_kind, 0.9988171_dbl_kind, 0.9389141_dbl_kind, & 0.9999726_dbl_kind, 0.9985890_dbl_kind, 0.9325819_dbl_kind, & 0.9999670_dbl_kind, 0.9983199_dbl_kind, 0.9256405_dbl_kind, & 0.9999605_dbl_kind, 0.9980117_dbl_kind, 0.9181533_dbl_kind, & 0.9999530_dbl_kind, 0.9976663_dbl_kind, 0.9101540_dbl_kind, & 0.9999465_dbl_kind, 0.9973693_dbl_kind, 0.9035031_dbl_kind, & 0.9999382_dbl_kind, 0.9969939_dbl_kind, 0.8953134_dbl_kind, & 0.9999289_dbl_kind, 0.9965848_dbl_kind, 0.8865789_dbl_kind, & 0.9999188_dbl_kind, 0.9961434_dbl_kind, 0.8773350_dbl_kind, & 0.9999068_dbl_kind, 0.9956323_dbl_kind, 0.8668233_dbl_kind, & 0.9998975_dbl_kind, 0.9952464_dbl_kind, 0.8589990_dbl_kind, & 0.9998837_dbl_kind, 0.9946782_dbl_kind, 0.8476493_dbl_kind, & 0.9998699_dbl_kind, 0.9941218_dbl_kind, 0.8367318_dbl_kind, & 0.9998515_dbl_kind, 0.9933966_dbl_kind, 0.8227881_dbl_kind, & 0.9998332_dbl_kind, 0.9926888_dbl_kind, 0.8095131_dbl_kind, & 0.9998148_dbl_kind, 0.9919968_dbl_kind, 0.7968620_dbl_kind, & 0.9997691_dbl_kind, 0.9903277_dbl_kind, 0.7677887_dbl_kind/), & (/nspint,nmbrad/)) ! snow asymmetry parameter (unitless) real (kind=dbl_kind), dimension (nspint,nmbrad), parameter :: & gs_tab = reshape((/ & 0.859913_dbl_kind, 0.848003_dbl_kind, 0.824415_dbl_kind, & 0.867130_dbl_kind, 0.858150_dbl_kind, 0.848445_dbl_kind, & 0.873381_dbl_kind, 0.867221_dbl_kind, 0.861714_dbl_kind, & 0.878368_dbl_kind, 0.874879_dbl_kind, 0.874036_dbl_kind, & 0.881462_dbl_kind, 0.879661_dbl_kind, 0.881299_dbl_kind, & 0.884361_dbl_kind, 0.883903_dbl_kind, 0.890184_dbl_kind, & 0.885937_dbl_kind, 0.886256_dbl_kind, 0.895393_dbl_kind, & 0.886931_dbl_kind, 0.887769_dbl_kind, 0.899072_dbl_kind, & 0.887894_dbl_kind, 0.889255_dbl_kind, 0.903285_dbl_kind, & 0.888515_dbl_kind, 0.890236_dbl_kind, 0.906588_dbl_kind, & 0.889073_dbl_kind, 0.891127_dbl_kind, 0.910152_dbl_kind, & 0.889452_dbl_kind, 0.891750_dbl_kind, 0.913100_dbl_kind, & 0.889730_dbl_kind, 0.892213_dbl_kind, 0.915621_dbl_kind, & 0.890026_dbl_kind, 0.892723_dbl_kind, 0.918831_dbl_kind, & 0.890238_dbl_kind, 0.893099_dbl_kind, 0.921540_dbl_kind, & 0.890441_dbl_kind, 0.893474_dbl_kind, 0.924581_dbl_kind, & 0.890618_dbl_kind, 0.893816_dbl_kind, 0.927701_dbl_kind, & 0.890762_dbl_kind, 0.894123_dbl_kind, 0.930737_dbl_kind, & 0.890881_dbl_kind, 0.894397_dbl_kind, 0.933568_dbl_kind, & 0.890975_dbl_kind, 0.894645_dbl_kind, 0.936148_dbl_kind, & 0.891035_dbl_kind, 0.894822_dbl_kind, 0.937989_dbl_kind, & 0.891097_dbl_kind, 0.895020_dbl_kind, 0.939949_dbl_kind, & 0.891147_dbl_kind, 0.895212_dbl_kind, 0.941727_dbl_kind, & 0.891189_dbl_kind, 0.895399_dbl_kind, 0.943339_dbl_kind, & 0.891225_dbl_kind, 0.895601_dbl_kind, 0.944915_dbl_kind, & 0.891248_dbl_kind, 0.895745_dbl_kind, 0.945950_dbl_kind, & 0.891277_dbl_kind, 0.895951_dbl_kind, 0.947288_dbl_kind, & 0.891299_dbl_kind, 0.896142_dbl_kind, 0.948438_dbl_kind, & 0.891323_dbl_kind, 0.896388_dbl_kind, 0.949762_dbl_kind, & 0.891340_dbl_kind, 0.896623_dbl_kind, 0.950916_dbl_kind, & 0.891356_dbl_kind, 0.896851_dbl_kind, 0.951945_dbl_kind, & 0.891386_dbl_kind, 0.897399_dbl_kind, 0.954156_dbl_kind/), & (/nspint,nmbrad/)) ! inherent optical property (iop) arrays for ice and ponded ice ! mn = specified mean (or base) value ! ki = extinction coefficient (/m) ! wi = single scattering albedo ! gi = asymmetry parameter ! ice surface scattering layer (ssl) iops real (kind=dbl_kind), dimension (nspint), parameter :: & ki_ssl_mn = (/ 1000.1_dbl_kind, 1003.7_dbl_kind, 7042._dbl_kind/), & wi_ssl_mn = (/ .9999_dbl_kind, .9963_dbl_kind, .9088_dbl_kind/), & gi_ssl_mn = (/ .94_dbl_kind, .94_dbl_kind, .94_dbl_kind/) ! ice drained layer (dl) iops real (kind=dbl_kind), dimension (nspint), parameter :: & ki_dl_mn = (/ 100.2_dbl_kind, 107.7_dbl_kind, 1309._dbl_kind /), & wi_dl_mn = (/ .9980_dbl_kind, .9287_dbl_kind, .0305_dbl_kind /), & gi_dl_mn = (/ .94_dbl_kind, .94_dbl_kind, .94_dbl_kind /) ! ice interior layer (int) iops real (kind=dbl_kind), dimension (nspint), parameter :: & ki_int_mn = (/ 20.2_dbl_kind, 27.7_dbl_kind, 1445._dbl_kind /), & wi_int_mn = (/ .9901_dbl_kind, .7223_dbl_kind, .0277_dbl_kind /), & gi_int_mn = (/ .94_dbl_kind, .94_dbl_kind, .94_dbl_kind /) ! ponded ice surface scattering layer (ssl) iops real (kind=dbl_kind), dimension (nspint), parameter :: & ki_p_ssl_mn = (/ 70.2_dbl_kind, 77.7_dbl_kind, 1309._dbl_kind/), & wi_p_ssl_mn = (/ .9972_dbl_kind, .9009_dbl_kind, .0305_dbl_kind/), & gi_p_ssl_mn = (/ .94_dbl_kind, .94_dbl_kind, .94_dbl_kind /) ! ponded ice interior layer (int) iops real (kind=dbl_kind), dimension (nspint), parameter :: & ki_p_int_mn = (/ 20.2_dbl_kind, 27.7_dbl_kind, 1445._dbl_kind/), & wi_p_int_mn = (/ .9901_dbl_kind, .7223_dbl_kind, .0277_dbl_kind/), & gi_p_int_mn = (/ .94_dbl_kind, .94_dbl_kind, .94_dbl_kind /) ! inherent optical property (iop) arrays for pond water and underlying ocean ! kw = Pond water extinction coefficient (/m) ! ww = Pond water single scattering albedo ! gw = Pond water asymmetry parameter real (kind=dbl_kind), dimension (nspint), parameter :: & kw = (/ 0.20_dbl_kind, 12.0_dbl_kind, 729._dbl_kind /), & ww = (/ 0.00_dbl_kind, 0.00_dbl_kind, 0.00_dbl_kind /), & gw = (/ 0.00_dbl_kind, 0.00_dbl_kind, 0.00_dbl_kind /) real (kind=dbl_kind), parameter :: & rhoi = 917.0_dbl_kind,& ! pure ice mass density (kg/m3) fr_max = 1.00_dbl_kind, & ! snow grain adjustment factor max fr_min = 0.80_dbl_kind, & ! snow grain adjustment factor min ! tuning parameters ! ice and pond scat coeff fractional change for +- one-sigma in albedo fp_ice = 0.15_dbl_kind, & ! ice fraction of scat coeff for + stn dev in alb fm_ice = 0.15_dbl_kind, & ! ice fraction of scat coeff for - stn dev in alb fp_pnd = 2.00_dbl_kind, & ! ponded ice fraction of scat coeff for + stn dev in alb fm_pnd = 0.50_dbl_kind ! ponded ice fraction of scat coeff for - stn dev in alb ! aerosol optical properties -> band | ! v aerosol ! for combined dust category, use category 4 properties real (kind=dbl_kind), dimension(nspint,max_aero), parameter :: & kaer_tab = reshape((/ & ! aerosol mass extinction cross section (m2/kg) 11580.61872, 5535.41835, 2793.79690, & 25798.96479, 11536.03871, 4688.24207, & 196.49772, 204.14078, 214.42287, & 2665.85867, 2256.71027, 820.36024, & 840.78295, 1028.24656, 1163.03298, & 387.51211, 414.68808, 450.29814/), & (/nspint,max_aero/)), & waer_tab = reshape((/ & ! aerosol single scatter albedo (fraction) 0.29003, 0.17349, 0.06613, & 0.51731, 0.41609, 0.21324, & 0.84467, 0.94216, 0.95666, & 0.97764, 0.99402, 0.98552, & 0.94146, 0.98527, 0.99093, & 0.90034, 0.96543, 0.97678/), & (/nspint,max_aero/)), & gaer_tab = reshape((/ & ! aerosol asymmetry parameter (cos(theta)) 0.35445, 0.19838, 0.08857, & 0.52581, 0.32384, 0.14970, & 0.83162, 0.78306, 0.74375, & 0.68861, 0.70836, 0.54171, & 0.70239, 0.66115, 0.71983, & 0.78734, 0.73580, 0.64411/), & (/nspint,max_aero/)) !----------------------------------------------------------------------- ! Initialize and tune bare ice/ponded ice iops rnilyr = c1/real(nilyr,kind=dbl_kind) rnslyr = c1/real(nslyr,kind=dbl_kind) kii = nslyr + 1 ! initialize albedos and fluxes to 0 fthrul(:,:) = c0 Iabs(:,:) = c0 do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) avdr(ij) = c0 avdf(ij) = c0 aidr(ij) = c0 aidf(ij) = c0 fsfc(ij) = c0 fint(ij) = c0 fthru(ij) = c0 ! spectral weights ! weights 2 (0.7-1.19 micro-meters) and 3 (1.19-5.0 micro-meters) ! are chosen based on 1D calculations using ratio of direct to total ! near-infrared solar (0.7-5.0 micro-meter) which indicates clear/cloudy ! conditions: more cloud, the less 1.19-5.0 relative to the ! 0.7-1.19 micro-meter due to cloud absorption. wghtns(ij,1) = c1 wghtns(ij,2) = cp67 + (cp78-cp67)*(c1-fnidr(i,j)) ! wghtns(ij,3) = cp33 + (cp22-cp33)*(c1-fnidr(i,j)) wghtns(ij,3) = c1 - wghtns(ij,2) ! find snow grain adjustment factor, dependent upon clear/overcast sky ! estimate. comparisons with SNICAR show better agreement with DE when ! this factor is included (clear sky near 1 and overcast near 0.8 give ! best agreement). Multiply by rnsw here for efficiency. do k = 1, nslyr frsnw(k,ij) = (fr_max*fnidr(i,j) + fr_min*(c1-fnidr(i,j)))*rsnw(i,j,k) Sabs(ij,k) = c0 enddo ! layer thicknesses ! snow dz = hs(i,j)*rnslyr ! for small enough snow thickness, ssl thickness half of top snow layer !ech: note this is highly resolution dependent! dzk(0,ij) = min(hs_ssl, dz/c2) dzk(1,ij) = dz - dzk(0,ij) if (nslyr > 1) then do k = 2, nslyr dzk(k,ij) = dz enddo endif ! ice dz = hi(i,j)*rnilyr ! empirical reduction in sea ice ssl thickness for ice thinner than 1.5m; ! factor of 30 gives best albedo comparison with limited observations dz_ssl = hi_ssl !ech: note hardwired parameters ! if( hi(i,j) < 1.5_dbl_kind ) dz_ssl = hi(i,j)/30._dbl_kind dz_ssl = min(hi_ssl, hi(i,j)/30._dbl_kind) ! set sea ice ssl thickness to half top layer if sea ice thin enough !ech: note this is highly resolution dependent! dz_ssl = min(dz_ssl, dz/c2) dzk(kii,ij) = dz_ssl dzk(kii+1,ij) = dz - dz_ssl if (kii+2 <= klev) then do k = kii+2, klev dzk(k,ij) = dz enddo endif enddo ! ij ! adjust sea ice iops with tuning parameters; tune only the ! scattering coefficient by factors of R_ice, R_pnd, where ! R values of +1 correspond approximately to +1 sigma changes in albedo, and ! R values of -1 correspond approximately to -1 sigma changes in albedo ! Note: the albedo change becomes non-linear for R values > +1 or < -1 if( R_ice >= c0 ) then do ns = 1, nspint sigp = ki_ssl_mn(ns)*wi_ssl_mn(ns)*(c1+fp_ice*R_ice) ki_ssl(ns) = sigp+ki_ssl_mn(ns)*(c1-wi_ssl_mn(ns)) wi_ssl(ns) = sigp/ki_ssl(ns) gi_ssl(ns) = gi_ssl_mn(ns) sigp = ki_dl_mn(ns)*wi_dl_mn(ns)*(c1+fp_ice*R_ice) ki_dl(ns) = sigp+ki_dl_mn(ns)*(c1-wi_dl_mn(ns)) wi_dl(ns) = sigp/ki_dl(ns) gi_dl(ns) = gi_dl_mn(ns) sigp = ki_int_mn(ns)*wi_int_mn(ns)*(c1+fp_ice*R_ice) ki_int(ns) = sigp+ki_int_mn(ns)*(c1-wi_int_mn(ns)) wi_int(ns) = sigp/ki_int(ns) gi_int(ns) = gi_int_mn(ns) enddo else !if( R_ice < c0 ) then do ns = 1, nspint sigp = ki_ssl_mn(ns)*wi_ssl_mn(ns)*(c1+fm_ice*R_ice) sigp = max(sigp, c0) ki_ssl(ns) = sigp+ki_ssl_mn(ns)*(c1-wi_ssl_mn(ns)) wi_ssl(ns) = sigp/ki_ssl(ns) gi_ssl(ns) = gi_ssl_mn(ns) sigp = ki_dl_mn(ns)*wi_dl_mn(ns)*(c1+fm_ice*R_ice) sigp = max(sigp, c0) ki_dl(ns) = sigp+ki_dl_mn(ns)*(c1-wi_dl_mn(ns)) wi_dl(ns) = sigp/ki_dl(ns) gi_dl(ns) = gi_dl_mn(ns) sigp = ki_int_mn(ns)*wi_int_mn(ns)*(c1+fm_ice*R_ice) sigp = max(sigp, c0) ki_int(ns) = sigp+ki_int_mn(ns)*(c1-wi_int_mn(ns)) wi_int(ns) = sigp/ki_int(ns) gi_int(ns) = gi_int_mn(ns) enddo endif ! adjust ice iops ! adjust ponded ice iops with tuning parameters if( R_pnd >= c0 ) then do ns = 1, nspint sigp = ki_p_ssl_mn(ns)*wi_p_ssl_mn(ns)*(c1+fp_pnd*R_pnd) ki_p_ssl(ns) = sigp+ki_p_ssl_mn(ns)*(c1-wi_p_ssl_mn(ns)) wi_p_ssl(ns) = sigp/ki_p_ssl(ns) gi_p_ssl(ns) = gi_p_ssl_mn(ns) sigp = ki_p_int_mn(ns)*wi_p_int_mn(ns)*(c1+fp_pnd*R_pnd) ki_p_int(ns) = sigp+ki_p_int_mn(ns)*(c1-wi_p_int_mn(ns)) wi_p_int(ns) = sigp/ki_p_int(ns) gi_p_int(ns) = gi_p_int_mn(ns) enddo else !if( R_pnd < c0 ) then do ns = 1, nspint sigp = ki_p_ssl_mn(ns)*wi_p_ssl_mn(ns)*(c1+fm_pnd*R_pnd) sigp = max(sigp, c0) ki_p_ssl(ns) = sigp+ki_p_ssl_mn(ns)*(c1-wi_p_ssl_mn(ns)) wi_p_ssl(ns) = sigp/ki_p_ssl(ns) gi_p_ssl(ns) = gi_p_ssl_mn(ns) sigp = ki_p_int_mn(ns)*wi_p_int_mn(ns)*(c1+fm_pnd*R_pnd) sigp = max(sigp, c0) ki_p_int(ns) = sigp+ki_p_int_mn(ns)*(c1-wi_p_int_mn(ns)) wi_p_int(ns) = sigp/ki_p_int(ns) gi_p_int(ns) = gi_p_int_mn(ns) enddo endif ! adjust ponded ice iops ! use srftyp to determine interface index of surface absorption if (srftyp == 1) then ! snow covered sea ice ksrf = 1 else ! bare sea ice or ponded ice ksrf = nslyr + 2 endif !----------------------------------------------------------------------- ! begin spectral loop do ns = 1, nspint ! set optical properties of air/snow/pond overlying sea ice ! air if( srftyp == 0 ) then do ij = 1, icells_DE do k=0,nslyr tau(k,ij) = c0 w0(k,ij) = c0 g(k,ij) = c0 enddo enddo ! snow else if( srftyp == 1 ) then do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) ! interpolate snow iops using input snow grain radius, ! snow density and tabular data do k=0,nslyr ! use top rsnw, rhosnw for snow ssl and rest of top layer ksnow = k - min(k-1,0) ! find snow iops using input snow density and snow grain radius: if( frsnw(ksnow,ij) < rsnw_tab(1) ) then Qs = Qs_tab(ns,1) ws = ws_tab(ns,1) gs = gs_tab(ns,1) else if( frsnw(ksnow,ij) >= rsnw_tab(nmbrad) ) then Qs = Qs_tab(ns,nmbrad) ws = ws_tab(ns,nmbrad) gs = gs_tab(ns,nmbrad) else ! linear interpolation in rsnw do nr=2,nmbrad if( rsnw_tab(nr-1) <= frsnw(ksnow,ij) .and. & frsnw(ksnow,ij) < rsnw_tab(nr)) then delr = (frsnw(ksnow,ij) - rsnw_tab(nr-1)) / & (rsnw_tab(nr) - rsnw_tab(nr-1)) Qs = Qs_tab(ns,nr-1)*(c1-delr) + & Qs_tab(ns,nr)*delr ws = ws_tab(ns,nr-1)*(c1-delr) + & ws_tab(ns,nr)*delr gs = gs_tab(ns,nr-1)*(c1-delr) + & gs_tab(ns,nr)*delr endif enddo ! nr endif ks = Qs*((rhosnw(i,j,ksnow)/rhoi)*3._dbl_kind / & (4._dbl_kind*frsnw(ksnow,ij)*1.0e-6_dbl_kind)) tau(k,ij) = ks*dzk(k,ij) w0(k,ij) = ws g(k,ij) = gs enddo ! k ! aerosol in snow if (tr_aero) then taer = c0 waer = c0 gaer = c0 do na=1,4*n_aero,4 taer = taer + & aero_mp(i,j,na)*kaer_tab(ns,(1+(na-1)/4)) waer = waer + & aero_mp(i,j,na)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4)) gaer = gaer + & aero_mp(i,j,na)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4))*gaer_tab(ns,(1+(na-1)/4)) enddo ! na gaer = gaer/(waer+puny) waer = waer/(taer+puny) do k=1,nslyr taer = c0 waer = c0 gaer = c0 do na=1,4*n_aero,4 taer = taer + & (aero_mp(i,j,na+1)*rnslyr)*kaer_tab(ns,(1+(na-1)/4)) waer = waer + & (aero_mp(i,j,na+1)*rnslyr)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4)) gaer = gaer + & (aero_mp(i,j,na+1)*rnslyr)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4))*gaer_tab(ns,(1+(na-1)/4)) enddo ! na gaer = gaer/(waer+puny) waer = waer/(taer+puny) g(k,ij) = (g(k,ij)*w0(k,ij)*tau(k,ij) + gaer*waer*taer) / & (w0(k,ij)*tau(k,ij) + waer*taer) w0(k,ij) = (w0(k,ij)*tau(k,ij) + waer*taer) / & (tau(k,ij) + taer) tau(k,ij) = tau(k,ij) + taer enddo ! k endif ! tr_aero enddo ! ij ! pond else !if( srftyp == 2 ) then do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) ! pond water layers evenly spaced dz = hp(i,j)/(c1/rnslyr+c1) do k=0,nslyr tau(k,ij) = kw(ns)*dz w0(k,ij) = ww(ns) g(k,ij) = gw(ns) ! no aerosol in pond enddo ! k enddo ! ij ... optical properties above sea ice set endif ! srftyp ! set optical properties of sea ice ! bare or snow-covered sea ice layers if( srftyp <= 1 ) then do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) ! ssl k = kii tau(k,ij) = ki_ssl(ns)*dzk(k,ij) w0(k,ij) = wi_ssl(ns) g(k,ij) = gi_ssl(ns) ! dl k = kii + 1 ! scale dz for dl relative to 4 even-layer-thickness 1.5m case fs = p25/rnilyr tau(k,ij) = ki_dl(ns)*dzk(k,ij)*fs w0(k,ij) = wi_dl(ns) g(k,ij) = gi_dl(ns) ! int above lowest layer if (kii+2 <= klev-1) then do k = kii+2, klev-1 tau(k,ij) = ki_int(ns)*dzk(k,ij) w0(k,ij) = wi_int(ns) g(k,ij) = gi_int(ns) enddo endif ! lowest layer k = klev ! add algae to lowest sea ice layer, visible only: kabs = ki_int(ns)*(c1-wi_int(ns)) if( ns == 1 ) then ! total layer absorption optical depth fixed at value ! of kalg*0.50m, independent of actual layer thickness kabs = kabs + kalg*(0.50_dbl_kind/dzk(k,ij)) endif sig = ki_int(ns)*wi_int(ns) tau(k,ij) = (kabs+sig)*dzk(k,ij) w0(k,ij) = (sig/(sig+kabs)) g(k,ij) = gi_int(ns) ! aerosol in sea ice if (tr_aero) then k = kii ! sea ice SSL taer = c0 waer = c0 gaer = c0 do na=1,4*n_aero,4 taer = taer + & aero_mp(i,j,na+2)*kaer_tab(ns,(1+(na-1)/4)) waer = waer + & aero_mp(i,j,na+2)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4)) gaer = gaer + & aero_mp(i,j,na+2)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4))*gaer_tab(ns,(1+(na-1)/4)) enddo ! na gaer = gaer/(waer+puny) waer = waer/(taer+puny) g(k,ij) = (g(k,ij)*w0(k,ij)*tau(k,ij) + gaer*waer*taer) / & (w0(k,ij)*tau(k,ij) + waer*taer) w0(k,ij) = (w0(k,ij)*tau(k,ij) + waer*taer) / & (tau(k,ij) + taer) tau(k,ij) = tau(k,ij) + taer do k = kii+1, klev taer = c0 waer = c0 gaer = c0 do na=1,4*n_aero,4 taer = taer + & (aero_mp(i,j,na+3)*rnilyr)*kaer_tab(ns,(1+(na-1)/4)) waer = waer + & (aero_mp(i,j,na+3)*rnilyr)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4)) gaer = gaer + & (aero_mp(i,j,na+3)*rnilyr)*kaer_tab(ns,(1+(na-1)/4))* & waer_tab(ns,(1+(na-1)/4))*gaer_tab(ns,(1+(na-1)/4)) enddo ! na gaer = gaer/(waer+puny) waer = waer/(taer+puny) g(k,ij) = (g(k,ij)*w0(k,ij)*tau(k,ij) + gaer*waer*taer) / & (w0(k,ij)*tau(k,ij) + waer*taer) w0(k,ij) = (w0(k,ij)*tau(k,ij) + waer*taer) / & (tau(k,ij) + taer) tau(k,ij) = tau(k,ij) + taer enddo ! k endif ! tr_aero enddo ! ij ! sea ice layers under ponds else !if( srftyp == 2 ) then do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) k = kii tau(k,ij) = ki_p_ssl(ns)*dzk(k,ij) w0(k,ij) = wi_p_ssl(ns) g(k,ij) = gi_p_ssl(ns) k = kii + 1 tau(k,ij) = ki_p_int(ns)*dzk(k,ij) w0(k,ij) = wi_p_int(ns) g(k,ij) = gi_p_int(ns) if (kii+2 <= klev) then do k = kii+2, klev tau(k,ij) = ki_p_int(ns)*dzk(k,ij) w0(k,ij) = wi_p_int(ns) g(k,ij) = gi_p_int(ns) enddo ! k endif ! adjust pond iops if pond depth within specified range if( hpmin <= hp(i,j) .and. hp(i,j) <= hp0 ) then k = kii sig_i = ki_ssl(ns)*wi_ssl(ns) sig_p = ki_p_ssl(ns)*wi_p_ssl(ns) sig = sig_i + (sig_p-sig_i)*(hp(i,j)/hp0) kext = sig + ki_p_ssl(ns)*(c1-wi_p_ssl(ns)) tau(k,ij) = kext*dzk(k,ij) w0(k,ij) = sig/kext g(k,ij) = gi_p_int(ns) k = kii + 1 ! scale dz for dl relative to 4 even-layer-thickness 1.5m case fs = p25/rnilyr sig_i = ki_dl(ns)*wi_dl(ns)*fs sig_p = ki_p_int(ns)*wi_p_int(ns) sig = sig_i + (sig_p-sig_i)*(hp(i,j)/hp0) kext = sig + ki_p_int(ns)*(c1-wi_p_int(ns)) tau(k,ij) = kext*dzk(k,ij) w0(k,ij) = sig/kext g(k,ij) = gi_p_int(ns) if (kii+2 <= klev) then do k = kii+2, klev sig_i = ki_int(ns)*wi_int(ns) sig_p = ki_p_int(ns)*wi_p_int(ns) sig = sig_i + (sig_p-sig_i)*(hp(i,j)/hp0) kext = sig + ki_p_int(ns)*(c1-wi_p_int(ns)) tau(k,ij) = kext*dzk(k,ij) w0(k,ij) = sig/kext g(k,ij) = gi_p_int(ns) enddo ! k endif endif ! small pond depth transition to bare sea ice enddo ! ij ... optical properties of sea ice set endif ! srftyp ! set reflectivities for ocean underlying sea ice do ij = 1, icells_DE rns = real(ns-1, kind=dbl_kind) albodr(ij) = cp01 * (c1 - min(rns, c1)) albodf(ij) = cp01 * (c1 - min(rns, c1)) enddo ! ij ! layer input properties now completely specified: tau, w0, g, ! albodr, albodf; now compute the Delta-Eddington solution ! reflectivities and transmissivities for each layer; then, ! combine the layers going downwards accounting for multiple ! scattering between layers, and finally start from the ! underlying ocean and combine successive layers upwards to ! the surface; see comments in solution_dEdd for more details. call solution_dEdd & (nx_block, ny_block, & icells_DE, indxi_DE, indxj_DE, coszen, srftyp, & tau, w0, g, albodr, albodf, & trndir, trntdr, trndif, rupdir, rupdif, & rdndif) ! the interface reflectivities and transmissivities required ! to evaluate interface fluxes are returned from solution_dEdd; ! now compute up and down fluxes for each interface, using the ! combined layer properties at each interface: ! ! layers interface ! ! --------------------- k ! k ! --------------------- do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) do k=0,klevp ! interface scattering refk = c1/(c1 - rdndif(k,ij)*rupdif(k,ij)) ! dir tran ref from below times interface scattering, plus diff ! tran and ref from below times interface scattering ! fdirup(k,ij) = (trndir(k,ij)*rupdir(k,ij) + & ! (trntdr(k,ij)-trndir(k,ij)) & ! *rupdif(k,ij))*refk ! dir tran plus total diff trans times interface scattering plus ! dir tran with up dir ref and down dif ref times interface scattering ! fdirdn(k,ij) = trndir(k,ij) + (trntdr(k,ij) & ! - trndir(k,ij) + trndir(k,ij) & ! *rupdir(k,ij)*rdndif(k,ij))*refk ! diffuse tran ref from below times interface scattering ! fdifup(k,ij) = trndif(k,ij)*rupdif(k,ij)*refk ! diffuse tran times interface scattering ! fdifdn(k,ij) = trndif(k,ij)*refk ! dfdir = fdirdn - fdirup dfdir(k,ij) = trndir(k,ij) & + (trntdr(k,ij)-trndir(k,ij)) * (c1 - rupdif(k,ij)) * refk & - trndir(k,ij)*rupdir(k,ij) * (c1 - rdndif(k,ij)) * refk if (dfdir(k,ij) < puny) dfdir(k,ij) = c0 !echmod necessary? ! dfdif = fdifdn - fdifup dfdif(k,ij) = trndif(k,ij) * (c1 - rupdif(k,ij)) * refk if (dfdif(k,ij) < puny) dfdif(k,ij) = c0 !echmod necessary? enddo ! k enddo ! ij ! calculate final surface albedos and fluxes- ! all absorbed flux above ksrf is included in surface absorption if( ns == 1) then ! visible do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) swdr = swvdr(i,j) swdf = swvdf(i,j) avdr(ij) = rupdir(0,ij) avdf(ij) = rupdif(0,ij) tmp_0 = dfdir(0 ,ij)*swdr + dfdif(0 ,ij)*swdf tmp_ks = dfdir(ksrf ,ij)*swdr + dfdif(ksrf ,ij)*swdf tmp_kl = dfdir(klevp,ij)*swdr + dfdif(klevp,ij)*swdf ! for layer biology: save visible only do k = nslyr+2, klevp ! Start at DL layer of ice after SSL scattering fthrul(ij,k-nslyr-1) = dfdir(k,ij)*swdr + dfdif(k,ij)*swdf enddo fsfc(ij) = fsfc(ij) + tmp_0 - tmp_ks fint(ij) = fint(ij) + tmp_ks - tmp_kl fthru(ij) = fthru(ij) + tmp_kl ! if snow covered ice, set snow internal absorption; else, Sabs=0 if( srftyp == 1 ) then ki = 0 do k=1,nslyr ! skip snow SSL, since SSL absorption included in the surface ! absorption fsfc above km = k kp = km + 1 ki = ki + 1 Sabs(ij,ki) = Sabs(ij,ki) & + dfdir(km,ij)*swdr + dfdif(km,ij)*swdf & - (dfdir(kp,ij)*swdr + dfdif(kp,ij)*swdf) enddo ! k endif ! complex indexing to insure proper absorptions for sea ice ki = 0 do k=nslyr+2,nslyr+1+nilyr ! for bare ice, DL absorption for sea ice layer 1 km = k kp = km + 1 ! modify for top sea ice layer for snow over sea ice if( srftyp == 1 ) then ! must add SSL and DL absorption for sea ice layer 1 if( k == nslyr+2 ) then km = k - 1 kp = km + 2 endif endif ki = ki + 1 Iabs(ij,ki) = Iabs(ij,ki) & + dfdir(km,ij)*swdr + dfdif(km,ij)*swdf & - (dfdir(kp,ij)*swdr + dfdif(kp,ij)*swdf) enddo ! k enddo ! ij else !if(ns > 1) then ! near IR do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) swdr = swidr(i,j) swdf = swidf(i,j) ! let fr1 = alb_1*swd*wght1 and fr2 = alb_2*swd*wght2 be the ns=2,3 ! reflected fluxes respectively, where alb_1, alb_2 are the band ! albedos, swd = nir incident shortwave flux, and wght1, wght2 are ! the 2,3 band weights. thus, the total reflected flux is: ! fr = fr1 + fr2 = alb_1*swd*wght1 + alb_2*swd*wght2 hence, the ! 2,3 nir band albedo is alb = fr/swd = alb_1*wght1 + alb_2*wght2 aidr(ij) = aidr(ij) + rupdir(0,ij)*wghtns(ij,ns) aidf(ij) = aidf(ij) + rupdif(0,ij)*wghtns(ij,ns) tmp_0 = dfdir(0 ,ij)*swdr + dfdif(0 ,ij)*swdf tmp_ks = dfdir(ksrf ,ij)*swdr + dfdif(ksrf ,ij)*swdf tmp_kl = dfdir(klevp,ij)*swdr + dfdif(klevp,ij)*swdf tmp_0 = tmp_0 * wghtns(ij,ns) tmp_ks = tmp_ks * wghtns(ij,ns) tmp_kl = tmp_kl * wghtns(ij,ns) fsfc(ij) = fsfc(ij) + tmp_0 - tmp_ks fint(ij) = fint(ij) + tmp_ks - tmp_kl fthru(ij) = fthru(ij) + tmp_kl ! if snow covered ice, set snow internal absorption; else, Sabs=0 if( srftyp == 1 ) then ki = 0 do k=1,nslyr ! skip snow SSL, since SSL absorption included in the surface ! absorption fsfc above km = k kp = km + 1 ki = ki + 1 Sabs(ij,ki) = Sabs(ij,ki) & + (dfdir(km,ij)*swdr + dfdif(km,ij)*swdf & - (dfdir(kp,ij)*swdr + dfdif(kp,ij)*swdf)) & * wghtns(ij,ns) enddo ! k endif ! complex indexing to insure proper absorptions for sea ice ki = 0 do k=nslyr+2,nslyr+1+nilyr ! for bare ice, DL absorption for sea ice layer 1 km = k kp = km + 1 ! modify for top sea ice layer for snow over sea ice if( srftyp == 1 ) then ! must add SSL and DL absorption for sea ice layer 1 if( k == nslyr+2 ) then km = k - 1 kp = km + 2 endif endif ki = ki + 1 Iabs(ij,ki) = Iabs(ij,ki) & + (dfdir(km,ij)*swdr + dfdif(km,ij)*swdf & - (dfdir(kp,ij)*swdr + dfdif(kp,ij)*swdf)) & * wghtns(ij,ns) enddo ! k enddo ! ij endif ! ns = 1, ns > 1 enddo ! end spectral loop ns ! accumulate fluxes over bare sea ice !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) alvdr(i,j) = avdr(ij) alvdf(i,j) = avdf(ij) alidr(i,j) = aidr(ij) alidf(i,j) = aidf(ij) fswsfc(i,j) = fswsfc(i,j) + fsfc(ij) *fi(i,j) fswint(i,j) = fswint(i,j) + fint(ij) *fi(i,j) fswthru(i,j) = fswthru(i,j) + fthru(ij)*fi(i,j) enddo ! ij do k = 1, nslyr !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) Sswabs(i,j,k) = Sswabs(i,j,k) + Sabs(ij,k)*fi(i,j) enddo ! ij enddo ! k do k = 1, nilyr !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) Iswabs(i,j,k) = Iswabs(i,j,k) + Iabs(ij,k)*fi(i,j) ! bgc layer fswpenl(i,j,k) = fswpenl(i,j,k) + fthrul(ij,k)* fi(i,j) if (k == nilyr) then fswpenl(i,j,k+1) = fswpenl(i,j,k+1) + fthrul(ij,k+1)*fi(i,j) endif enddo ! ij enddo ! k !---------------------------------------------------------------- ! if ice has zero heat capacity, no SW can be absorbed ! in the ice/snow interior, so add to surface absorption. ! Note: nilyr = nslyr = 1 for this case !---------------------------------------------------------------- if (.not. heat_capacity) then !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) ! SW absorbed at snow/ice surface fswsfc(i,j) = fswsfc(i,j) + Iswabs(i,j,1) + Sswabs(i,j,1) ! SW absorbed in ice interior fswint(i,j) = c0 Iswabs(i,j,1) = c0 Sswabs(i,j,1) = c0 enddo ! ij endif ! heat_capacity end subroutine compute_dEdd !======================================================================= ! ! Given input vertical profiles of optical properties, evaluate the ! monochromatic Delta-Eddington solution. ! ! author: Bruce P. Briegleb, NCAR ! 2013: E Hunke merged with NCAR version subroutine solution_dEdd & (nx_block, ny_block, & icells_DE, indxi_DE, indxj_DE, coszen, srftyp, & tau, w0, g, albodr, albodf, & trndir, trntdr, trndif, rupdir, rupdif, & rdndif) integer (kind=int_kind), & intent(in) :: & nx_block, ny_block, & ! block dimensions icells_DE ! number of sea ice grid cells for surface type integer (kind=int_kind), dimension(nx_block*ny_block), & intent(in) :: & indxi_DE, & ! compressed indices for sea ice cells for surface type indxj_DE real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & coszen ! cosine solar zenith angle integer (kind=int_kind), intent(in) :: & srftyp ! surface type over ice: (0=air, 1=snow, 2=pond) integer (kind=int_kind), parameter :: & klev = nslyr + nilyr + 1 , & ! number of radiation layers - 1 klevp = klev + 1 ! number of radiation interfaces - 1 real (kind=dbl_kind), dimension(0:klev,icells_DE), & intent(in) :: & tau , & ! layer extinction optical depth w0 , & ! layer single scattering albedo g ! layer asymmetry parameter real (kind=dbl_kind), dimension(icells_DE), & intent(in) :: & albodr , & ! ocean albedo to direct rad albodf ! ocean albedo to diffuse rad ! following arrays are defined at model interfaces; 0 is the top of the ! layer above the sea ice; klevp is the sea ice/ocean interface. real (kind=dbl_kind), dimension (0:klevp,icells_DE), & intent(out) :: & trndir , & ! solar beam down transmission from top trntdr , & ! total transmission to direct beam for layers above trndif , & ! diffuse transmission to diffuse beam for layers above rupdir , & ! reflectivity to direct radiation for layers below rupdif , & ! reflectivity to diffuse radiation for layers below rdndif ! reflectivity to diffuse radiation for layers above !----------------------------------------------------------------------- ! ! Delta-Eddington solution for snow/air/pond over sea ice ! ! Generic solution for a snow/air/pond input column of klev+1 layers, ! with srftyp determining at what interface fresnel refraction occurs. ! ! Computes layer reflectivities and transmissivities, from the top down ! to the lowest interface using the Delta-Eddington solutions for each ! layer; combines layers from top down to lowest interface, and from the ! lowest interface (underlying ocean) up to the top of the column. ! ! Note that layer diffuse reflectivity and transmissivity are computed ! by integrating the direct over several gaussian angles. This is ! because the diffuse reflectivity expression sometimes is negative, ! but the direct reflectivity is always well-behaved. We assume isotropic ! radiation in the upward and downward hemispheres for this integration. ! ! Assumes monochromatic (spectrally uniform) properties across a band ! for the input optical parameters. ! ! If total transmission of the direct beam to the interface above a particular ! layer is less than trmin, then no further Delta-Eddington solutions are ! evaluated for layers below. ! ! The following describes how refraction is handled in the calculation. ! ! First, we assume that radiation is refracted when entering either ! sea ice at the base of the surface scattering layer, or water (i.e. melt ! pond); we assume that radiation does not refract when entering snow, nor ! upon entering sea ice from a melt pond, nor upon entering the underlying ! ocean from sea ice. ! ! To handle refraction, we define a "fresnel" layer, which physically ! is of neglible thickness and is non-absorbing, which can be combined to ! any sea ice layer or top of melt pond. The fresnel layer accounts for ! refraction of direct beam and associated reflection and transmission for ! solar radiation. A fresnel layer is combined with the top of a melt pond ! or to the surface scattering layer of sea ice if no melt pond lies over it. ! ! Some caution must be exercised for the fresnel layer, because any layer ! to which it is combined is no longer a homogeneous layer, as are all other ! individual layers. For all other layers for example, the direct and diffuse ! reflectivities/transmissivities (R/T) are the same for radiation above or ! below the layer. This is the meaning of homogeneous! But for the fresnel ! layer this is not so. Thus, the R/T for this layer must be distinguished ! for radiation above from that from radiation below. For generality, we ! treat all layers to be combined as inhomogeneous. ! !----------------------------------------------------------------------- ! local variables integer (kind=int_kind) :: & kfrsnl ! radiation interface index for fresnel layer ! following variables are defined for each layer; 0 refers to the top ! layer. In general we must distinguish directions above and below in ! the diffuse reflectivity and transmissivity, as layers are not assumed ! to be homogeneous (apart from the single layer Delta-Edd solutions); ! the direct is always from above. real (kind=dbl_kind), dimension (0:klev) :: & rdir , & ! layer reflectivity to direct radiation rdif_a , & ! layer reflectivity to diffuse radiation from above rdif_b , & ! layer reflectivity to diffuse radiation from below tdir , & ! layer transmission to direct radiation (solar beam + diffuse) tdif_a , & ! layer transmission to diffuse radiation from above tdif_b , & ! layer transmission to diffuse radiation from below trnlay ! solar beam transm for layer (direct beam only) integer (kind=int_kind) :: & i , & ! longitude index j , & ! latitude index ij , & ! longitude/latitude index k ! level index real (kind=dbl_kind), parameter :: & trmin = 0.001_dbl_kind ! minimum total transmission allowed ! total transmission is that due to the direct beam; i.e. it includes ! both the directly transmitted solar beam and the diffuse downwards ! transmitted radiation resulting from scattering out of the direct beam real (kind=dbl_kind) :: & tautot , & ! layer optical depth wtot , & ! layer single scattering albedo gtot , & ! layer asymmetry parameter ftot , & ! layer forward scattering fraction ts , & ! layer scaled extinction optical depth ws , & ! layer scaled single scattering albedo gs , & ! layer scaled asymmetry parameter rintfc , & ! reflection (multiple) at an interface refkp1 , & ! interface multiple scattering for k+1 refkm1 , & ! interface multiple scattering for k-1 tdrrdir , & ! direct tran times layer direct ref tdndif ! total down diffuse = tot tran - direct tran ! perpendicular and parallel relative to plane of incidence and scattering real (kind=dbl_kind) :: & R1 , & ! perpendicular polarization reflection amplitude R2 , & ! parallel polarization reflection amplitude T1 , & ! perpendicular polarization transmission amplitude T2 , & ! parallel polarization transmission amplitude Rf_dir_a , & ! fresnel reflection to direct radiation Tf_dir_a , & ! fresnel transmission to direct radiation Rf_dif_a , & ! fresnel reflection to diff radiation from above Rf_dif_b , & ! fresnel reflection to diff radiation from below Tf_dif_a , & ! fresnel transmission to diff radiation from above Tf_dif_b ! fresnel transmission to diff radiation from below ! refractive index for sea ice, water; pre-computed, band-independent, ! diffuse fresnel reflectivities real (kind=dbl_kind), parameter :: & refindx = 1.310_dbl_kind , & ! refractive index of sea ice (water also) cp063 = 0.063_dbl_kind , & ! diffuse fresnel reflectivity from above cp455 = 0.455_dbl_kind ! diffuse fresnel reflectivity from below real (kind=dbl_kind), dimension(icells_DE) :: & mu0 , & ! cosine solar zenith angle incident mu0nij ! cosine solar zenith angle in medium below fresnel level real (kind=dbl_kind) :: & mu0n ! cosine solar zenith angle in medium real (kind=dbl_kind) :: & alpha , & ! term in direct reflectivity and transmissivity gamma , & ! term in direct reflectivity and transmissivity el , & ! term in alpha,gamma,n,u taus , & ! scaled extinction optical depth omgs , & ! scaled single particle scattering albedo asys , & ! scaled asymmetry parameter u , & ! term in diffuse reflectivity and transmissivity n , & ! term in diffuse reflectivity and transmissivity lm , & ! temporary for el mu , & ! cosine solar zenith for either snow or water ne ! temporary for n real (kind=dbl_kind) :: & w , & ! dummy argument for statement function uu , & ! dummy argument for statement function gg , & ! dummy argument for statement function e , & ! dummy argument for statement function f , & ! dummy argument for statement function t , & ! dummy argument for statement function et ! dummy argument for statement function real (kind=dbl_kind) :: & alp , & ! temporary for alpha gam , & ! temporary for gamma ue , & ! temporary for u extins , & ! extinction amg , & ! alp - gam apg ! alp + gam integer (kind=int_kind), parameter :: & ngmax = 8 ! number of gaussian angles in hemisphere real (kind=dbl_kind), dimension (ngmax), parameter :: & gauspt & ! gaussian angles (radians) = (/ .9894009_dbl_kind, .9445750_dbl_kind, & .8656312_dbl_kind, .7554044_dbl_kind, & .6178762_dbl_kind, .4580168_dbl_kind, & .2816036_dbl_kind, .0950125_dbl_kind/), & gauswt & ! gaussian weights = (/ .0271525_dbl_kind, .0622535_dbl_kind, & .0951585_dbl_kind, .1246290_dbl_kind, & .1495960_dbl_kind, .1691565_dbl_kind, & .1826034_dbl_kind, .1894506_dbl_kind/) integer (kind=int_kind) :: & ng ! gaussian integration index real (kind=dbl_kind) :: & gwt , & ! gaussian weight swt , & ! sum of weights trn , & ! layer transmission rdr , & ! rdir for gaussian integration tdr , & ! tdir for gaussian integration smr , & ! accumulator for rdif gaussian integration smt ! accumulator for tdif gaussian integration ! Delta-Eddington solution expressions alpha(w,uu,gg,e) = p75*w*uu*((c1 + gg*(c1-w))/(c1 - e*e*uu*uu)) gamma(w,uu,gg,e) = p5*w*((c1 + c3*gg*(c1-w)*uu*uu) & / (c1-e*e*uu*uu)) n(uu,et) = ((uu+c1)*(uu+c1)/et ) - ((uu-c1)*(uu-c1)*et) u(w,gg,e) = c1p5*(c1 - w*gg)/e el(w,gg) = sqrt(c3*(c1-w)*(c1 - w*gg)) taus(w,f,t) = (c1 - w*f)*t omgs(w,f) = (c1 - f)*w/(c1 - w*f) asys(gg,f) = (gg - f)/(c1 - f) !----------------------------------------------------------------------- ! initialize all output to 0 do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) do k = 0, klevp trndir(k,ij) = c0 trntdr(k,ij) = c0 trndif(k,ij) = c0 rupdir(k,ij) = c0 rupdif(k,ij) = c0 rdndif(k,ij) = c0 enddo ! initialize top interface of top layer trndir(0,ij) = c1 trntdr(0,ij) = c1 trndif(0,ij) = c1 rdndif(0,ij) = c0 ! mu0 is cosine solar zenith angle above the fresnel level; make ! sure mu0 is large enough for stable and meaningful radiation ! solution: .01 is like sun just touching horizon with its lower edge mu0(ij) = max(coszen(i,j),p01) ! mu0n is cosine solar zenith angle used to compute the layer ! Delta-Eddington solution; it is initially computed to be the ! value below the fresnel level, i.e. the cosine solar zenith ! angle below the fresnel level for the refracted solar beam: mu0nij(ij) = sqrt(c1-((c1-mu0(ij)**2)/(refindx*refindx))) enddo ! ij ! compute level of fresnel refraction ! if ponded sea ice, fresnel level is the top of the pond. kfrsnl = 0 ! if snow over sea ice or bare sea ice, fresnel level is ! at base of sea ice SSL (and top of the sea ice DL); the ! snow SSL counts for one, then the number of snow layers, ! then the sea ice SSL which also counts for one: if( srftyp < 2 ) kfrsnl = nslyr + 2 ! proceed down one layer at a time; if the total transmission to ! the interface just above a given layer is less than trmin, then no ! Delta-Eddington computation for that layer is done. do ij = 1, icells_DE i = indxi_DE(ij) j = indxj_DE(ij) ! begin main level loop do k = 0, klev ! initialize all layer apparent optical properties to 0 rdir (k) = c0 rdif_a(k) = c0 rdif_b(k) = c0 tdir (k) = c0 tdif_a(k) = c0 tdif_b(k) = c0 trnlay(k) = c0 ! compute next layer Delta-eddington solution only if total transmission ! of radiation to the interface just above the layer exceeds trmin. if (trntdr(k,ij) > trmin ) then ! calculation over layers with penetrating radiation tautot = tau(k,ij) wtot = w0(k,ij) gtot = g(k,ij) ftot = gtot*gtot ts = taus(wtot,ftot,tautot) ws = omgs(wtot,ftot) gs = asys(gtot,ftot) lm = el(ws,gs) ue = u(ws,gs,lm) mu0n = mu0nij(ij) ! if level k is above fresnel level and the cell is non-pond, use the ! non-refracted beam instead if( srftyp < 2 .and. k < kfrsnl ) mu0n = mu0(ij) extins = max(exp_min, exp(-lm*ts)) ne = n(ue,extins) ! first calculation of rdif, tdif using Delta-Eddington formulas ! rdif_a(k) = (ue+c1)*(ue-c1)*(c1/extins - extins)/ne rdif_a(k) = (ue**2-c1)*(c1/extins - extins)/ne tdif_a(k) = c4*ue/ne ! evaluate rdir,tdir for direct beam trnlay(k) = max(exp_min, exp(-ts/mu0n)) alp = alpha(ws,mu0n,gs,lm) gam = gamma(ws,mu0n,gs,lm) apg = alp + gam amg = alp - gam rdir(k) = apg*rdif_a(k) + amg*(tdif_a(k)*trnlay(k) - c1) tdir(k) = apg*tdif_a(k) + (amg* rdif_a(k)-apg+c1)*trnlay(k) ! recalculate rdif,tdif using direct angular integration over rdir,tdir, ! since Delta-Eddington rdif formula is not well-behaved (it is usually ! biased low and can even be negative); use ngmax angles and gaussian ! integration for most accuracy: R1 = rdif_a(k) ! use R1 as temporary T1 = tdif_a(k) ! use T1 as temporary swt = c0 smr = c0 smt = c0 do ng=1,ngmax mu = gauspt(ng) gwt = gauswt(ng) swt = swt + mu*gwt trn = max(exp_min, exp(-ts/mu)) alp = alpha(ws,mu,gs,lm) gam = gamma(ws,mu,gs,lm) apg = alp + gam amg = alp - gam rdr = apg*R1 + amg*T1*trn - amg tdr = apg*T1 + amg*R1*trn - apg*trn + trn smr = smr + mu*rdr*gwt smt = smt + mu*tdr*gwt enddo ! ng rdif_a(k) = smr/swt tdif_a(k) = smt/swt ! homogeneous layer rdif_b(k) = rdif_a(k) tdif_b(k) = tdif_a(k) ! add fresnel layer to top of desired layer if either ! air or snow overlies ice; we ignore refraction in ice ! if a melt pond overlies it: if( k == kfrsnl ) then ! compute fresnel reflection and transmission amplitudes ! for two polarizations: 1=perpendicular and 2=parallel to ! the plane containing incident, reflected and refracted rays. R1 = (mu0(ij) - refindx*mu0n) / & (mu0(ij) + refindx*mu0n) R2 = (refindx*mu0(ij) - mu0n) / & (refindx*mu0(ij) + mu0n) T1 = c2*mu0(ij) / & (mu0(ij) + refindx*mu0n) T2 = c2*mu0(ij) / & (refindx*mu0(ij) + mu0n) ! unpolarized light for direct beam Rf_dir_a = p5 * (R1*R1 + R2*R2) Tf_dir_a = p5 * (T1*T1 + T2*T2)*refindx*mu0n/mu0(ij) ! precalculated diffuse reflectivities and transmissivities ! for incident radiation above and below fresnel layer, using ! the direct albedos and accounting for complete internal ! reflection from below; precalculated because high order ! number of gaussian points (~256) is required for convergence: ! above Rf_dif_a = cp063 Tf_dif_a = c1 - Rf_dif_a ! below Rf_dif_b = cp455 Tf_dif_b = c1 - Rf_dif_b ! the k = kfrsnl layer properties are updated to combined ! the fresnel (refractive) layer, always taken to be above ! the present layer k (i.e. be the top interface): rintfc = c1 / (c1-Rf_dif_b*rdif_a(k)) tdir(k) = Tf_dir_a*tdir(k) + & Tf_dir_a*rdir(k) * & Rf_dif_b*rintfc*tdif_a(k) rdir(k) = Rf_dir_a + & Tf_dir_a*rdir(k) * & rintfc*Tf_dif_b rdif_a(k) = Rf_dif_a + & Tf_dif_a*rdif_a(k) * & rintfc*Tf_dif_b rdif_b(k) = rdif_b(k) + & tdif_b(k)*Rf_dif_b * & rintfc*tdif_a(k) tdif_a(k) = tdif_a(k)*rintfc*Tf_dif_a tdif_b(k) = tdif_b(k)*rintfc*Tf_dif_b ! update trnlay to include fresnel transmission trnlay(k) = Tf_dir_a*trnlay(k) endif ! k = kfrsnl endif ! trntdr(k,ij) > trmin ! initialize current layer properties to zero; only if total ! transmission to the top interface of the current layer exceeds the ! minimum, will these values be computed below: ! Calculate the solar beam transmission, total transmission, and ! reflectivity for diffuse radiation from below at interface k, ! the top of the current layer k: ! ! layers interface ! ! --------------------- k-1 ! k-1 ! --------------------- k ! k ! --------------------- ! For k = klevp ! note that we ignore refraction between sea ice and underlying ocean: ! ! layers interface ! ! --------------------- k-1 ! k-1 ! --------------------- k ! \\\\\\\ ocean \\\\\\\ trndir(k+1,ij) = trndir(k,ij)*trnlay(k) refkm1 = c1/(c1 - rdndif(k,ij)*rdif_a(k)) tdrrdir = trndir(k,ij)*rdir(k) tdndif = trntdr(k,ij) - trndir(k,ij) trntdr(k+1,ij) = trndir(k,ij)*tdir(k) + & (tdndif + tdrrdir*rdndif(k,ij))*refkm1*tdif_a(k) rdndif(k+1,ij) = rdif_b(k) + & (tdif_b(k)*rdndif(k,ij)*refkm1*tdif_a(k)) trndif(k+1,ij) = trndif(k,ij)*refkm1*tdif_a(k) enddo ! k end main level loop ! compute reflectivity to direct and diffuse radiation for layers ! below by adding succesive layers starting from the underlying ! ocean and working upwards: ! ! layers interface ! ! --------------------- k ! k ! --------------------- k+1 ! k+1 ! --------------------- rupdir(klevp,ij) = albodr(ij) rupdif(klevp,ij) = albodf(ij) do k=klev,0,-1 ! interface scattering refkp1 = c1/( c1 - rdif_b(k)*rupdif(k+1,ij)) ! dir from top layer plus exp tran ref from lower layer, interface ! scattered and tran thru top layer from below, plus diff tran ref ! from lower layer with interface scattering tran thru top from below rupdir(k,ij) = rdir(k) & + ( trnlay(k) *rupdir(k+1,ij) & + (tdir(k)-trnlay(k))*rupdif(k+1,ij))*refkp1*tdif_b(k) ! dif from top layer from above, plus dif tran upwards reflected and ! interface scattered which tran top from below rupdif(k,ij) = rdif_a(k) + tdif_a(k)*rupdif(k+1,ij)*refkp1*tdif_b(k) enddo ! k enddo ! ij end subroutine solution_dEdd !======================================================================= ! ! Set snow horizontal coverage, density and grain radius diagnostically ! for the Delta-Eddington solar radiation method. ! ! author: Bruce P. Briegleb, NCAR ! 2013: E Hunke merged with NCAR version subroutine shortwave_dEdd_set_snow(nx_block, ny_block, & icells, & indxi, indxj, & aice, vsno, & Tsfc, fs, hs, & rhosnw, rsnw) use ice_meltpond_cesm, only: hs0 integer (kind=int_kind), & intent(in) :: & nx_block, ny_block, & ! block dimensions icells ! number of ice-covered grid cells integer (kind=int_kind), dimension (nx_block*ny_block), & intent(in) :: & indxi , & ! compressed indices for ice-covered cells indxj real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & aice , & ! concentration of ice vsno , & ! volume of snow Tsfc ! surface temperature real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(out) :: & fs , & ! horizontal coverage of snow hs ! snow depth real (kind=dbl_kind), dimension (nx_block,ny_block,nslyr), & intent(out) :: & rhosnw , & ! density in snow layer (kg/m3) rsnw ! grain radius in snow layer (micro-meters) ! local variables integer (kind=int_kind) :: & i , & ! longitude index j , & ! latitude index ij , & ! horizontal index, combines i and j loops ks ! snow vertical index real (kind=dbl_kind) :: & fT , & ! piecewise linear function of surface temperature dTs , & ! difference of Tsfc and Timelt rsnw_nm ! actual used nonmelt snow grain radius (micro-meters) real (kind=dbl_kind), parameter :: & ! units for the following are 1.e-6 m (micro-meters) rsnw_fresh = 100._dbl_kind, & ! freshly-fallen snow grain radius rsnw_nonmelt = 500._dbl_kind, & ! nonmelt snow grain radius rsnw_sig = 250._dbl_kind ! assumed sigma for snow grain radius !----------------------------------------------------------------------- fs(:,:) = c0 hs(:,:) = c0 do ks = 1, nslyr do j = 1, ny_block do i = 1, nx_block rhosnw(i,j,ks) = c0 rsnw(i,j,ks) = c0 enddo enddo enddo !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells i = indxi(ij) j = indxj(ij) ! set snow horizontal fraction hs(i,j) = vsno(i,j) / aice(i,j) if (hs(i,j) >= hs_min) then fs(i,j) = c1 if (hs0 > puny) fs(i,j) = min(hs(i,j)/hs0, c1) endif ! bare ice, temperature dependence dTs = Timelt - Tsfc(i,j) fT = -min(dTs/dT_mlt-c1,c0) ! tune nonmelt snow grain radius if desired: note that ! the sign is negative so that if R_snw is 1, then the ! snow grain radius is reduced and thus albedo increased. rsnw_nm = rsnw_nonmelt - R_snw*rsnw_sig rsnw_nm = max(rsnw_nm, rsnw_fresh) rsnw_nm = min(rsnw_nm, rsnw_mlt) do ks = 1, nslyr ! snow density ccsm3 constant value rhosnw(i,j,ks) = rhos ! snow grain radius between rsnw_nonmelt and rsnw_mlt rsnw(i,j,ks) = rsnw_nm + (rsnw_mlt-rsnw_nm)*fT rsnw(i,j,ks) = max(rsnw(i,j,ks), rsnw_fresh) rsnw(i,j,ks) = min(rsnw(i,j,ks), rsnw_mlt) enddo ! ks enddo ! ij end subroutine shortwave_dEdd_set_snow !======================================================================= ! ! Set pond fraction and depth diagnostically for ! the Delta-Eddington solar radiation method. ! ! author: Bruce P. Briegleb, NCAR ! 2013: E Hunke merged with NCAR version subroutine shortwave_dEdd_set_pond(nx_block, ny_block, & icells, & indxi, indxj, & Tsfc, & fs, fp, & hp) integer (kind=int_kind), & intent(in) :: & nx_block, ny_block, & ! block dimensions icells ! number of ice-covered grid cells integer (kind=int_kind), dimension (nx_block*ny_block), & intent(in) :: & indxi , & ! compressed indices for ice-covered cells indxj real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(in) :: & Tsfc , & ! surface temperature fs ! horizontal coverage of snow real (kind=dbl_kind), dimension (nx_block,ny_block), & intent(out) :: & fp , & ! pond fractional coverage (0 to 1) hp ! pond depth (m) ! local variables integer (kind=int_kind) :: & i , & ! longitude index j , & ! latitude index ij ! horizontal index, combines i and j loops real (kind=dbl_kind) :: & fT , & ! piecewise linear function of surface temperature dTs ! difference of Tsfc and Timelt real (kind=dbl_kind), parameter :: & dT_pnd = c1 ! change in temp for pond fraction and depth !----------------------------------------------------------------------- do j = 1, ny_block do i = 1, nx_block fp(i,j) = c0 hp(i,j) = c0 enddo enddo ! find pond fraction and depth for ice points !DIR$ CONCURRENT !Cray !cdir nodep !NEC !ocl novrec !Fujitsu do ij = 1, icells i = indxi(ij) j = indxj(ij) ! bare ice, temperature dependence dTs = Timelt - Tsfc(i,j) fT = -min(dTs/dT_pnd-c1,c0) ! pond fp(i,j) = 0.3_dbl_kind*fT*(c1-fs(i,j)) hp(i,j) = 0.3_dbl_kind*fT*(c1-fs(i,j)) enddo ! ij end subroutine shortwave_dEdd_set_pond ! End Delta-Eddington shortwave method !======================================================================= end module ice_shortwave !=======================================================================