MODULE sbcblk_algo_ice_lg15 !!====================================================================== !! *** MODULE sbcblk_algo_ice_lg15 *** !! Computes turbulent components of surface fluxes over sea-ice !! !! !! Lüpkes, C., and Gryanik, V. M. ( 2015), A stability‐dependent parametrization !! of transfer coefficients for momentum and heat over polar sea ice to be used in climate models, !! J. Geophys. Res. Atmos., 120, 552– 581, doi:10.1002/2014JD022418. !! !! => Despite the fact that the sea-ice concentration (frice) must be provided, !! only transfer coefficients, and air temp. + hum. height adjustement !! over ice are returned/performed. !! ==> 'frice' is only here to estimate the form drag caused by sea-ice... !! !! Routine turb_ice_lg15 maintained and developed in AeroBulk !! (https://github.com/brodeau/aerobulk/) !! !! Author: Laurent Brodeau, Summer 2020 !! !!---------------------------------------------------------------------- USE par_kind, ONLY: wp USE par_oce, ONLY: jpi, jpj USE phycst ! physical constants USE sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer USE sbcblk_algo_ice_cdn IMPLICIT NONE PRIVATE PUBLIC :: turb_ice_lg15 REAL(wp), PARAMETER :: ralpha_0 = 0.2_wp ! (Eq.12) (ECHAM6 value) !! To be namelist parameters in NEMO: REAL(wp), PARAMETER :: rz0_i_s_0 = 0.69e-3_wp ! Eq. 43 [m] REAL(wp), PARAMETER :: rz0_i_f_0 = 4.54e-4_wp ! bottom p.562 MIZ [m] LOGICAL, PARAMETER :: l_add_form_drag = .TRUE. LOGICAL, PARAMETER :: l_use_pond_info = .FALSE. LOGICAL, PARAMETER :: l_dbg_print = .FALSE. INTEGER , PARAMETER :: nbit = 8 ! number of itterations !!---------------------------------------------------------------------- CONTAINS SUBROUTINE turb_ice_lg15( zt, zu, Ts_i, t_zt, qs_i, q_zt, U_zu, frice, & & Cd_i, Ch_i, Ce_i, t_zu_i, q_zu_i, & & CdN, ChN, CeN, xz0, xu_star, xL, xUN10 ) !!---------------------------------------------------------------------- !! *** ROUTINE turb_ice_lg15 *** !! !! ** Purpose : Computes turbulent transfert coefficients of surface !! fluxes according to: !! Lüpkes, C., and Gryanik, V. M. ( 2015), A stability‐dependent !! parametrization of transfer coefficients for momentum and heat !! over polar sea ice to be used in climate models, !! J. Geophys. Res. Atmos., 120, 552– 581, doi:10.1002/2014JD022418. !! !! If relevant (zt /= zu), adjust temperature and humidity from height zt to zu !! Returns the effective bulk wind speed at zu to be used in the bulk formulas !! !! INPUT : !! ------- !! * zt : height for temperature and spec. hum. of air [m] !! * zu : height for wind speed (usually 10m) [m] !! * Ts_i : surface temperature of sea-ice [K] !! * t_zt : potential air temperature at zt [K] !! * qs_i : saturation specific humidity at temp. Ts_i over ice [kg/kg] !! * q_zt : specific humidity of air at zt [kg/kg] !! * U_zu : scalar wind speed at zu [m/s] !! * frice : sea-ice concentration (fraction) !! !! OUTPUT : !! -------- !! * Cd_i : drag coefficient over sea-ice !! * Ch_i : sensible heat coefficient over sea-ice !! * Ce_i : sublimation coefficient over sea-ice !! * t_zu_i : pot. air temp. adjusted at zu over sea-ice [K] !! * q_zu_i : spec. hum. of air adjusted at zu over sea-ice [kg/kg] !! !! OPTIONAL OUTPUT: !! ---------------- !! * CdN : neutral-stability drag coefficient !! * ChN : neutral-stability sensible heat coefficient !! * CeN : neutral-stability evaporation coefficient !! * xz0 : return the aerodynamic roughness length (integration constant for wind stress) [m] !! * xu_star : return u* the friction velocity [m/s] !! * xL : return the Obukhov length [m] !! * xUN10 : neutral wind speed at 10m [m/s] !! !! ** Author: L. Brodeau, January 2020 / AeroBulk (https://github.com/brodeau/aerobulk/) !!---------------------------------------------------------------------------------- REAL(wp), INTENT(in ) :: zt ! height for t_zt and q_zt [m] REAL(wp), INTENT(in ) :: zu ! height for U_zu [m] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: Ts_i ! ice surface temperature [Kelvin] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: t_zt ! potential air temperature [Kelvin] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: qs_i ! sat. spec. hum. at ice/air interface [kg/kg] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: q_zt ! spec. air humidity at zt [kg/kg] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: U_zu ! relative wind module at zu [m/s] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: frice ! sea-ice concentration (fraction) REAL(wp), INTENT(out), DIMENSION(jpi,jpj) :: Cd_i ! drag coefficient over sea-ice REAL(wp), INTENT(out), DIMENSION(jpi,jpj) :: Ch_i ! transfert coefficient for heat over ice REAL(wp), INTENT(out), DIMENSION(jpi,jpj) :: Ce_i ! transfert coefficient for sublimation over ice REAL(wp), INTENT(out), DIMENSION(jpi,jpj) :: t_zu_i ! pot. air temp. adjusted at zu [K] REAL(wp), INTENT(out), DIMENSION(jpi,jpj) :: q_zu_i ! spec. humidity adjusted at zu [kg/kg] !!---------------------------------------------------------------------------------- REAL(wp), INTENT(out), DIMENSION(jpi,jpj), OPTIONAL :: CdN REAL(wp), INTENT(out), DIMENSION(jpi,jpj), OPTIONAL :: ChN REAL(wp), INTENT(out), DIMENSION(jpi,jpj), OPTIONAL :: CeN REAL(wp), INTENT(out), DIMENSION(jpi,jpj), OPTIONAL :: xz0 ! Aerodynamic roughness length [m] REAL(wp), INTENT(out), DIMENSION(jpi,jpj), OPTIONAL :: xu_star ! u*, friction velocity REAL(wp), INTENT(out), DIMENSION(jpi,jpj), OPTIONAL :: xL ! zeta (zu/L) REAL(wp), INTENT(out), DIMENSION(jpi,jpj), OPTIONAL :: xUN10 ! Neutral wind at zu !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(:,:), ALLOCATABLE :: Ubzu REAL(wp), DIMENSION(:,:), ALLOCATABLE :: xtmp1, xtmp2 ! temporary stuff REAL(wp), DIMENSION(:,:), ALLOCATABLE :: dt_zu, dq_zu REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zz0_s, zz0_f, RiB ! third dimensions (size=2): REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zCdN_s, zChN_s, zCdN_f, zChN_f !! INTEGER :: jit LOGICAL :: l_zt_equal_zu = .FALSE. ! if q and t are given at same height as U !! LOGICAL :: lreturn_cdn=.FALSE., lreturn_chn=.FALSE., lreturn_cen=.FALSE. LOGICAL :: lreturn_z0=.FALSE., lreturn_ustar=.FALSE., lreturn_L=.FALSE., lreturn_UN10=.FALSE. !! CHARACTER(len=40), PARAMETER :: crtnm = 'turb_ice_lg15@sbcblk_algo_ice_lg15.f90' !!---------------------------------------------------------------------------------- ALLOCATE ( Ubzu(jpi,jpj) ) ALLOCATE ( xtmp1(jpi,jpj), xtmp2(jpi,jpj) ) ALLOCATE ( dt_zu(jpi,jpj), dq_zu(jpi,jpj) ) ALLOCATE ( zz0_s(jpi,jpj), zz0_f(jpi,jpj), RiB(jpi,jpj), & & zCdN_s(jpi,jpj), zChN_s(jpi,jpj), zCdN_f(jpi,jpj), zChN_f(jpi,jpj) ) lreturn_cdn = PRESENT(CdN) lreturn_chn = PRESENT(ChN) lreturn_cen = PRESENT(CeN) lreturn_z0 = PRESENT(xz0) lreturn_ustar = PRESENT(xu_star) lreturn_L = PRESENT(xL) lreturn_UN10 = PRESENT(xUN10) l_zt_equal_zu = ( ABS(zu - zt) < 0.01_wp ) !! Scalar wind speed cannot be below 0.2 m/s Ubzu = MAX( U_zu, wspd_thrshld_ice ) !! First guess of temperature and humidity at height zu: t_zu_i = MAX( t_zt , 100._wp ) ! who knows what's given on masked-continental regions... q_zu_i = MAX( q_zt , 0.1e-6_wp ) ! " !! Air-Ice & Air-Sea differences (and we don't want them to be 0!) dt_zu = t_zu_i - Ts_i ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) dq_zu = q_zu_i - qs_i ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) !! Very crude first guess: Cd_i(:,:) = 1.4e-3_wp Ch_i(:,:) = 1.4e-3_wp Ce_i(:,:) = 1.4e-3_wp !! For skin drag : zz0_s(:,:) = rz0_i_s_0 !#LB/RFI! ! Room for improvement. We use the same z0_skin everywhere (= rz0_i_s_0)... zCdN_s(:,:) = Cd_from_z0( zu, zz0_s(:,:) ) zChN_s(:,:) = vkarmn2 / ( LOG( zu / zz0_s(:,:) ) * LOG( zu / (ralpha_0*zz0_s(:,:)) ) ) ! (Eq.11,12) [ "" ] !! For form drag in MIZ: zz0_f(:,:) = 0._wp zCdN_f(:,:) = 0._wp zChN_f(:,:) = 0._wp IF ( l_add_form_drag ) THEN zz0_f(:,:) = rz0_i_f_0 !#LB/RFI! ! Room for improvement. We use the same z0_form everywhere !!! zCdN_f(:,:) = CdN_f_LG15_light( zu, frice(:,:), zz0_f(:,:) ) zChN_f(:,:) = zCdN_f(:,:)/( 1._wp + LOG(1._wp/ralpha_0)/vkarmn*SQRT(zCdN_f(:,:)) ) ! (Eq.60,61) [ "" ] END IF !! Some other first guess values, needed to compute wind at zt: Cd_i(:,:) = zCdN_s(:,:) + zCdN_f(:,:) Ch_i(:,:) = zChN_s(:,:) + zChN_f(:,:) RiB(:,:) = Ri_bulk( zt, Ts_i(:,:), t_zt(:,:), qs_i(:,:), q_zt(:,:), Ubzu(:,:) ) ! over ice (index=1) !! ITERATION BLOCK DO jit = 1, nbit IF(l_dbg_print) PRINT *, 'LOLO: LOOP #', INT(jit,1) IF(l_dbg_print) PRINT *, 'LOLO: theta_zu, Ts_i, Ubzu =', REAL(t_zu_i(:,:),4), REAL(Ts_i(:,:),4), REAL(Ubzu(:,:),4) IF(l_dbg_print) PRINT *, 'LOLO: q_zu =', REAL(q_zu_i(:,:),4) IF(l_dbg_print) PRINT *, 'LOLO: CdN_s, zCdN_f =', REAL(zCdN_s(:,:),4), REAL(zCdN_f(:,:),4) !! Bulk Richardson Number !! ====================== !! PROBLEM: when computed at z=zu, with adjusted theta and q, it is numerically unstable in some rare events (unstable) !! => fix: compute RiB at zt, with ajusted wind at zt... => seems to be more stable IF( .NOT. l_zt_equal_zu ) THEN ! U_zt = U_zu + u_star/vkarmn*(LOG(zt/zu) + psi_m_coare(zu/L) - psi_m_coare(zt/L)) xtmp1(:,:) = zCdN_s(:,:) + zCdN_f(:,:) ! total neutral drag coeff! xtmp2(:,:) = zz0_s(:,:) + zz0_f(:,:) ! total roughness length z0 xtmp1 = LOG(zt/zu) + f_h_louis( zu, RiB(:,:), xtmp1(:,:), xtmp2(:,:) ) & & - f_h_louis( zt, RiB(:,:), xtmp1(:,:), xtmp2(:,:) ) xtmp2(:,:) = MAX( Ubzu(:,:) + (SQRT(Cd_i(:,:))*Ubzu)*xtmp1 , wspd_thrshld_ice ) ! wind at zt ( SQRT(Cd_i(:,:))*Ubzu == u* !) xtmp2(:,:) = MIN( xtmp2(:,:) , Ubzu(:,:) ) IF(l_dbg_print) PRINT *, 'LOLO: ADJUSTED WIND AT ZT =', xtmp2 ELSE xtmp2(:,:) = Ubzu(:,:) END IF RiB(:,:) = Ri_bulk( zt, Ts_i(:,:), t_zt(:,:), qs_i(:,:), q_zt(:,:), xtmp2(:,:) ) ! over ice (index=1) IF(l_dbg_print) PRINT *, 'LOLO: RiB_zt =', RiB(:,:) ! Momentum and Heat transfer coefficients WITHOUT FORM DRAG / (Eq.6) and (Eq.10): Cd_i(:,:) = zCdN_s(:,:) * f_m_louis( zu, RiB(:,:), zCdN_s(:,:), zz0_s(:,:) ) ! (Eq.6) Ch_i(:,:) = zChN_s(:,:) * f_h_louis( zu, RiB(:,:), zCdN_s(:,:), zz0_s(:,:) ) ! (Eq.10) / LOLO: why "zCdN_s" (xtmp1) and not "zChn" ??? IF(l_dbg_print) PRINT *, 'LOLO: f_m_louis_s =', f_m_louis( zu, RiB(:,:), zCdN_s(:,:), zz0_s(:,:) ) IF(l_dbg_print) PRINT *, 'LOLO: f_h_louis_s =', f_h_louis( zu, RiB(:,:), zCdN_s(:,:), zz0_s(:,:) ) IF(l_dbg_print) PRINT *, 'LOLO: Cd / skin only / ice =', REAL(Cd_i(:,:),4) IF ( l_add_form_drag ) THEN !! Form-drag-related NEUTRAL momentum and Heat transfer coefficients: !! MIZ: Cd_i(:,:) = Cd_i(:,:) + zCdN_f(:,:) * f_m_louis( zu, RiB(:,:), zCdN_f(:,:), zz0_f(:,:) ) ! (Eq.6) Ch_i(:,:) = Ch_i(:,:) + zChN_f(:,:) * f_h_louis( zu, RiB(:,:), zCdN_f(:,:), zz0_f(:,:) ) ! (Eq.10) / LOLO: why "zCdN_f" and not "zChn" ??? IF(l_dbg_print) PRINT *, 'LOLO: f_m_louis_f =', f_m_louis( zu, RiB(:,:), zCdN_f(:,:), zz0_f(:,:) ) IF(l_dbg_print) PRINT *, 'LOLO: f_h_louis_f =', f_h_louis( zu, RiB(:,:), zCdN_f(:,:), zz0_f(:,:) ) IF(l_dbg_print) PRINT *, 'LOLO: Cd / form only / ice =', REAL(zCdN_f(:,:) * f_m_louis( zu, RiB(:,:), zCdN_f(:,:), zz0_f(:,:) ),4) END IF IF(l_dbg_print) PRINT *, 'LOLO: Cd, Ch / TOTAL / ice =', REAL(Cd_i(:,:),4), REAL(Ch_i(:,:),4) !! Adjusting temperature and humidity from zt to zu: IF( .NOT. l_zt_equal_zu ) THEN !! Over ice: xtmp1(:,:) = zCdN_s(:,:) + zCdN_f(:,:) ! total neutral drag coeff! xtmp2(:,:) = zz0_s(:,:) + zz0_f(:,:) ! total roughness length z0 xtmp1 = LOG(zt/zu) + f_h_louis( zu, RiB(:,:), xtmp1(:,:), xtmp2(:,:) ) & & - f_h_louis( zt, RiB(:,:), xtmp1(:,:), xtmp2(:,:) ) xtmp2 = 1._wp/SQRT(Cd_i(:,:)) t_zu_i(:,:) = t_zt - (Ch_i(:,:) * dt_zu(:,:) * xtmp2) / vkarmn * xtmp1 ! t_star = Ch * dt_zu / SQRT(Cd) q_zu_i(:,:) = q_zt - (Ch_i(:,:) * dq_zu(:,:) * xtmp2) / vkarmn * xtmp1 ! q_star = Ce * dq_zu / SQRT(Cd) q_zu_i(:,:) = MAX(0._wp, q_zu_i(:,:)) dt_zu(:,:) = t_zu_i(:,:) - Ts_i dq_zu(:,:) = q_zu_i(:,:) - qs_i dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) END IF IF(l_dbg_print) PRINT *, ''!LOLO END DO !DO jit = 1, nbit Ce_i(:,:) = Ch_i(:,:) IF( lreturn_cdn ) CdN = zCdN_s(:,:)+zCdN_f(:,:) IF( lreturn_chn ) ChN = zChN_s(:,:)+zChN_f(:,:) IF( lreturn_cen ) CeN = zChN_s(:,:)+zChN_f(:,:) IF( lreturn_z0 ) xz0 = z0_from_Cd( zu, zCdN_s(:,:)+zCdN_f(:,:) ) IF( lreturn_ustar ) xu_star = SQRT(Cd_i) * Ubzu IF( lreturn_L ) THEN xtmp1 = SQRT(Cd_i) xL = 1./One_on_L( t_zu_i, q_zu_i, xtmp1*Ubzu, Ch_i*dt_zu(:,:)/xtmp1, Ce_i*dq_zu(:,:)/xtmp1 ) END IF IF( lreturn_UN10 ) THEN xtmp1 = zCdN_s(:,:) + zCdN_f(:,:) ! => CdN xUN10 = SQRT(Cd_i) * Ubzu/vkarmn * LOG( 10._wp / z0_from_Cd(zu, xtmp1) ) END IF DEALLOCATE ( Ubzu ) DEALLOCATE ( xtmp1, xtmp2 ) DEALLOCATE ( dt_zu, dq_zu ) DEALLOCATE ( zz0_s, zz0_f, RiB, zCdN_s, zChN_s, zCdN_f, zChN_f ) END SUBROUTINE turb_ice_lg15 !!====================================================================== END MODULE sbcblk_algo_ice_lg15