MODULE sbcblk_algo_ncar !!====================================================================== !! *** MODULE sbcblk_algo_ncar *** !! Computes: !! * bulk transfer coefficients C_D, C_E and C_H !! * air temp. and spec. hum. adjusted from zt (2m) to zu (10m) if needed !! * the effective bulk wind speed at 10m Ubzu !! => all these are used in bulk formulas in sbcblk.F90 !! !! Using the bulk formulation/param. of Large & Yeager 2008 !! !! Routine turb_ncar maintained and developed in AeroBulk !! (https://github.com/brodeau/aerobulk/) !! !! L. Brodeau, 2015 !!===================================================================== !! History : 3.6 ! 2016-02 (L.Brodeau) successor of old turb_ncar of former sbcblk_core.F90 !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! turb_ncar : computes the bulk turbulent transfer coefficients !! adjusts t_air and q_air from zt to zu m !! returns the effective bulk wind speed at 10m !!---------------------------------------------------------------------- USE dom_oce ! ocean space and time domain USE sbc_oce, ONLY: ln_cdgw USE sbcwave, ONLY: cdn_wave ! wave module USE phycst ! physical constants USE sbc_phy ! all thermodynamics functions, rho_air, q_sat, etc... !LB IMPLICIT NONE PRIVATE PUBLIC :: TURB_NCAR ! called by sbcblk.F90 !! * Substitutions # include "do_loop_substitute.h90" !!---------------------------------------------------------------------- CONTAINS SUBROUTINE turb_ncar( zt, zu, sst, t_zt, ssq, q_zt, U_zu, & & Cd, Ch, Ce, t_zu, q_zu, Ubzu, & & nb_iter, CdN, ChN, CeN ) !!---------------------------------------------------------------------------------- !! *** ROUTINE turb_ncar *** !! !! ** Purpose : Computes turbulent transfert coefficients of surface !! fluxes according to Large & Yeager (2004) and Large & Yeager (2008) !! 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] !! * sst : bulk SST [K] !! * t_zt : potential air temperature at zt [K] !! * ssq : specific humidity at saturation at SST [kg/kg] !! * q_zt : specific humidity of air at zt [kg/kg] !! * U_zu : scalar wind speed at zu [m/s] !! !! !! OUTPUT : !! -------- !! * Cd : drag coefficient !! * Ch : sensible heat coefficient !! * Ce : evaporation coefficient !! * t_zu : pot. air temperature adjusted at wind height zu [K] !! * q_zu : specific humidity of air // [kg/kg] !! * Ubzu : bulk wind speed at zu [m/s] !! !! OPTIONAL OUTPUT: !! ---------------- !! * CdN : neutral-stability drag coefficient !! * ChN : neutral-stability sensible heat coefficient !! * CeN : neutral-stability evaporation coefficient !! !! ** Author: L. Brodeau, June 2019 / 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) :: sst ! sea surface temperature [Kelvin] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: t_zt ! potential air temperature [Kelvin] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: ssq ! sea surface specific humidity [kg/kg] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: q_zt ! specific 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( out), DIMENSION(jpi,jpj) :: Cd ! transfer coefficient for momentum (tau) REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Ch ! transfer coefficient for sensible heat (Q_sens) REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Ce ! transfert coefficient for evaporation (Q_lat) REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: t_zu ! pot. air temp. adjusted at zu [K] REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: q_zu ! spec. humidity adjusted at zu [kg/kg] REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Ubzu ! bulk wind speed at zu [m/s] ! INTEGER , INTENT(in ), OPTIONAL :: nb_iter ! number of iterations REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: CdN REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: ChN REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: CeN ! INTEGER :: nbit, jit ! iterations... LOGICAL :: l_zt_equal_zu = .FALSE. ! if q and t are given at same height as U ! REAL(wp), DIMENSION(jpi,jpj) :: zCdN, zCeN, zChN ! 10m neutral latent/sensible coefficient REAL(wp), DIMENSION(jpi,jpj) :: zsqrt_Cd, zsqrt_CdN ! root square of Cd and Cd_neutral REAL(wp), DIMENSION(jpi,jpj) :: zeta_u ! stability parameter at height zu REAL(wp), DIMENSION(jpi,jpj) :: ztmp0, ztmp1, ztmp2 !!---------------------------------------------------------------------------------- nbit = nb_iter0 IF( PRESENT(nb_iter) ) nbit = nb_iter l_zt_equal_zu = ( ABS(zu - zt) < 0.01_wp ) ! testing "zu == zt" is risky with double precision Ubzu = MAX( 0.5_wp , U_zu ) ! relative wind speed at zu (normally 10m), we don't want to fall under 0.5 m/s !! First guess of stability: ztmp0 = virt_temp(t_zt, q_zt) - virt_temp(sst, ssq) ! air-sea difference of virtual pot. temp. at zt ztmp1 = 0.5_wp + SIGN(0.5_wp,ztmp0) ! ztmp1 = 1 if dTv > 0 => STABLE, 0 if unstable !! Neutral coefficients at 10m: IF( ln_cdgw ) THEN ! wave drag case cdn_wave(:,:) = cdn_wave(:,:) + rsmall * ( 1._wp - tmask(:,:,1) ) zCdN (:,:) = cdn_wave(:,:) ELSE zCdN = cd_n10_ncar( Ubzu ) ENDIF zsqrt_CdN = SQRT( zCdN ) !! Initializing transf. coeff. with their first guess neutral equivalents : Cd = zCdN Ce = ce_n10_ncar( zsqrt_CdN ) Ch = ch_n10_ncar( zsqrt_CdN , ztmp1 ) ! ztmp1 is stability (1/0) zsqrt_Cd = zsqrt_CdN IF( ln_cdgw ) THEN zCeN = Ce zChN = Ch ENDIF !! Initializing values at z_u with z_t values: t_zu = MAX( t_zt , 180._wp ) ! who knows what's given on masked-continental regions... q_zu = MAX( q_zt , 1.e-6_wp ) ! " !! ITERATION BLOCK DO jit = 1, nbit ! ztmp1 = t_zu - sst ! Updating air/sea differences ztmp2 = q_zu - ssq ! Updating turbulent scales : (L&Y 2004 Eq. (7)) ztmp0 = zsqrt_Cd*Ubzu ! u* ztmp1 = Ch/zsqrt_Cd*ztmp1 ! theta* ztmp2 = Ce/zsqrt_Cd*ztmp2 ! q* ! Estimate the inverse of Obukov length (1/L) at height zu: ztmp0 = One_on_L( t_zu, q_zu, ztmp0, ztmp1, ztmp2 ) !! Stability parameters : zeta_u = zu*ztmp0 zeta_u = sign( min(abs(zeta_u),10._wp), zeta_u ) !! Shifting temperature and humidity at zu (L&Y 2004 Eq. (9b-9c)) IF( .NOT. l_zt_equal_zu ) THEN ztmp0 = zt*ztmp0 ! zeta_t ! ztmp0 = SIGN( MIN(ABS(ztmp0),10._wp), ztmp0 ) ! Temporaty array ztmp0 == zeta_t !!! ztmp0 = LOG(zt/zu) + psi_h_ncar(zeta_u) - psi_h_ncar(ztmp0) ! ztmp0 just used as temp array again! t_zu = t_zt - ztmp1/vkarmn*ztmp0 ! ztmp1 is still theta* L&Y 2004 Eq. (9b) !! q_zu = q_zt - ztmp2/vkarmn*ztmp0 ! ztmp2 is still q* L&Y 2004 Eq. (9c) q_zu = MAX(0._wp, q_zu) END IF ! Update neutral wind speed at 10m and neutral Cd at 10m (L&Y 2004 Eq. 9a)... ! In very rare low-wind conditions, the old way of estimating the ! neutral wind speed at 10m leads to a negative value that causes the code ! to crash. To prevent this a threshold of 0.25m/s is imposed. ztmp2 = psi_m_ncar(zeta_u) IF( ln_cdgw ) THEN ! surface wave case zsqrt_Cd = vkarmn / ( vkarmn / zsqrt_CdN - ztmp2 ) Cd = zsqrt_Cd * zsqrt_Cd ztmp0 = (LOG(zu/10._wp) - psi_h_ncar(zeta_u)) / vkarmn / zsqrt_CdN ztmp2 = zsqrt_Cd / zsqrt_CdN ztmp1 = 1._wp + zChN * ztmp0 Ch = zChN * ztmp2 / ztmp1 ! L&Y 2004 eq. (10b) ztmp1 = 1._wp + zCeN * ztmp0 Ce = zCeN * ztmp2 / ztmp1 ! L&Y 2004 eq. (10c) ELSE ztmp0 = MAX( 0.25_wp , UN10_from_CD(zu, Ubzu, Cd, ppsi=ztmp2) ) ! U_n10 (ztmp2 == psi_m_ncar(zeta_u)) zCdN = cd_n10_ncar(ztmp0) zsqrt_CdN = sqrt(zCdN) !! Update of transfer coefficients: !! C_D ztmp1 = 1._wp + zsqrt_CdN/vkarmn*(LOG(zu/10._wp) - ztmp2) ! L&Y 2004 Eq. (10a) (ztmp2 == psi_m(zeta_u)) Cd = MAX( zCdN / ( ztmp1*ztmp1 ), Cx_min ) !! C_H and C_E zsqrt_Cd = SQRT( Cd ) ztmp0 = ( LOG(zu/10._wp) - psi_h_ncar(zeta_u) ) / vkarmn / zsqrt_CdN ztmp2 = zsqrt_Cd / zsqrt_CdN ztmp1 = 0.5_wp + SIGN(0.5_wp,zeta_u) ! update stability zChN = 1.e-3_wp * zsqrt_CdN*(18._wp*ztmp1 + 32.7_wp*(1._wp - ztmp1)) ! L&Y 2004 eq. (6c-6d) zCeN = 1.e-3_wp * (34.6_wp * zsqrt_CdN) ! L&Y 2004 eq. (6b) Ch = MAX( zChN*ztmp2 / ( 1._wp + zChN*ztmp0 ) , Cx_min ) ! L&Y 2004 eq. (10b) Ce = MAX( zCeN*ztmp2 / ( 1._wp + zCeN*ztmp0 ) , Cx_min ) ! L&Y 2004 eq. (10c) ENDIF END DO !DO jit = 1, nbit IF(PRESENT(CdN)) CdN(:,:) = zCdN(:,:) IF(PRESENT(CeN)) CeN(:,:) = zCeN(:,:) IF(PRESENT(ChN)) ChN(:,:) = zChN(:,:) END SUBROUTINE turb_ncar FUNCTION cd_n10_ncar( pw10 ) !!---------------------------------------------------------------------------------- !! Estimate of the neutral drag coefficient at 10m as a function !! of neutral wind speed at 10m !! !! Origin: Large & Yeager 2008, Eq. (11) !! !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pw10 ! scalar wind speed at 10m (m/s) REAL(wp), DIMENSION(jpi,jpj) :: cd_n10_ncar ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zgt33, zw, zw6 ! local scalars !!---------------------------------------------------------------------------------- ! DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) ! zw = pw10(ji,jj) zw6 = zw*zw*zw zw6 = zw6*zw6 ! ! When wind speed > 33 m/s => Cyclone conditions => special treatment zgt33 = 0.5_wp + SIGN( 0.5_wp, (zw - 33._wp) ) ! If pw10 < 33. => 0, else => 1 ! cd_n10_ncar(ji,jj) = 1.e-3_wp * ( & & (1._wp - zgt33)*( 2.7_wp/zw + 0.142_wp + zw/13.09_wp - 3.14807E-10_wp*zw6) & ! wind < 33 m/s & + zgt33 * 2.34_wp ) ! wind >= 33 m/s ! cd_n10_ncar(ji,jj) = MAX( cd_n10_ncar(ji,jj), Cx_min ) ! END_2D ! END FUNCTION cd_n10_ncar FUNCTION ch_n10_ncar( psqrtcdn10 , pstab ) !!---------------------------------------------------------------------------------- !! Estimate of the neutral heat transfer coefficient at 10m !! !! Origin: Large & Yeager 2008, Eq. (9) and (12) !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: ch_n10_ncar REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psqrtcdn10 ! sqrt( CdN10 ) REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pstab ! stable ABL => 1 / unstable ABL => 0 !!---------------------------------------------------------------------------------- IF( ANY(pstab < -0.00001) .OR. ANY(pstab > 1.00001) ) THEN PRINT *, 'ERROR: ch_n10_ncar@mod_blk_ncar.f90: pstab =' PRINT *, pstab STOP END IF ! ch_n10_ncar = MAX( 1.e-3_wp * psqrtcdn10*( 18._wp*pstab + 32.7_wp*(1._wp - pstab) ) , Cx_min ) ! Eq. (9) & (12) Large & Yeager, 2008 ! END FUNCTION ch_n10_ncar FUNCTION ce_n10_ncar( psqrtcdn10 ) !!---------------------------------------------------------------------------------- !! Estimate of the neutral heat transfer coefficient at 10m !! !! Origin: Large & Yeager 2008, Eq. (9) and (13) !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: ce_n10_ncar REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psqrtcdn10 ! sqrt( CdN10 ) !!---------------------------------------------------------------------------------- ce_n10_ncar = MAX( 1.e-3_wp * ( 34.6_wp * psqrtcdn10 ) , Cx_min ) ! END FUNCTION ce_n10_ncar FUNCTION psi_m_ncar( pzeta ) !!---------------------------------------------------------------------------------- !! Universal profile stability function for momentum !! !! Psis, L&Y 2004, Eq. (8c), (8d), (8e) !! !! pzeta : stability paramenter, z/L where z is altitude measurement !! and L is M-O length !! !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: psi_m_ncar REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zta, zx2, zx, zpsi_unst, zpsi_stab, zstab ! local scalars !!---------------------------------------------------------------------------------- DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) zta = pzeta(ji,jj) ! zx2 = SQRT( ABS(1._wp - 16._wp*zta) ) ! (1 - 16z)^0.5 zx2 = MAX( zx2 , 1._wp ) zx = SQRT(zx2) ! (1 - 16z)^0.25 zpsi_unst = 2._wp*LOG( (1._wp + zx )*0.5_wp ) & & + LOG( (1._wp + zx2)*0.5_wp ) & & - 2._wp*ATAN(zx) + rpi*0.5_wp ! zpsi_stab = -5._wp*zta ! zstab = 0.5_wp + SIGN(0.5_wp, zta) ! zta > 0 => zstab = 1 ! psi_m_ncar(ji,jj) = zstab * zpsi_stab & ! (zta > 0) Stable & + (1._wp - zstab) * zpsi_unst ! (zta < 0) Unstable ! ! END_2D END FUNCTION psi_m_ncar FUNCTION psi_h_ncar( pzeta ) !!---------------------------------------------------------------------------------- !! Universal profile stability function for temperature and humidity !! !! Psis, L&Y 2004, Eq. (8c), (8d), (8e) !! !! pzeta : stability paramenter, z/L where z is altitude measurement !! and L is M-O length !! !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: psi_h_ncar REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zta, zx2, zpsi_unst, zpsi_stab, zstab ! local scalars !!---------------------------------------------------------------------------------- ! DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) ! zta = pzeta(ji,jj) ! zx2 = SQRT( ABS(1._wp - 16._wp*zta) ) ! (1 -16z)^0.5 zx2 = MAX( zx2 , 1._wp ) zpsi_unst = 2._wp*LOG( 0.5_wp*(1._wp + zx2) ) ! zpsi_stab = -5._wp*zta ! zstab = 0.5_wp + SIGN(0.5_wp, zta) ! zta > 0 => zstab = 1 ! psi_h_ncar(ji,jj) = zstab * zpsi_stab & ! (zta > 0) Stable & + (1._wp - zstab) * zpsi_unst ! (zta < 0) Unstable ! END_2D END FUNCTION psi_h_ncar !!====================================================================== END MODULE sbcblk_algo_ncar