MODULE sbcblk_algo_coare3p5 !!====================================================================== !! *** MODULE sbcblk_algo_coare3p5 *** !! Computes turbulent components of surface fluxes !! according to Edson et al. 2013 (COARE v3.5) /JPO !! !! * 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 U_blk !! => all these are used in bulk formulas in sbcblk.F90 !! !! Using the bulk formulation/param. of COARE v3.5, Edson et al. 2013 !! !! !! Routine turb_coare3p5 maintained and developed in AeroBulk !! (http://aerobulk.sourceforge.net/) !! !! Author: Laurent Brodeau, 2016, brodeau@gmail.com !! !!====================================================================== !! History : 3.6 ! 2016-02 (L.Brodeau) Original code !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! turb_coare3p5 : 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 oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE sbc_oce ! Surface boundary condition: ocean fields USE sbcwave, ONLY : cdn_wave ! wave module #if defined key_si3 || defined key_cice USE sbc_ice ! Surface boundary condition: ice fields #endif ! USE iom ! I/O manager library USE lib_mpp ! distribued memory computing library USE in_out_manager ! I/O manager USE prtctl ! Print control USE lib_fortran ! to use key_nosignedzero IMPLICIT NONE PRIVATE PUBLIC :: TURB_COARE3P5 ! called by sbcblk.F90 ! ! COARE own values for given constants: REAL(wp), PARAMETER :: charn0_max = 0.028 ! value above which the Charnock paramter levels off for winds > 18 REAL(wp), PARAMETER :: zi0 = 600. ! scale height of the atmospheric boundary layer...1 REAL(wp), PARAMETER :: Beta0 = 1.25 ! gustiness parameter REAL(wp), PARAMETER :: rctv0 = 0.608 ! constant to obtain virtual temperature... !!---------------------------------------------------------------------- CONTAINS SUBROUTINE turb_coare3p5( zt, zu, sst, t_zt, ssq, q_zt, U_zu, & & Cd, Ch, Ce, t_zu, q_zu, U_blk, & & Cdn, Chn, Cen ) !!---------------------------------------------------------------------------------- !! *** ROUTINE turb_coare3p5 *** !! !! ** Purpose : Computes turbulent transfert coefficients of surface !! fluxes according to Fairall et al. (2003) !! If relevant (zt /= zu), adjust temperature and humidity from height zt to zu !! !! ** Method : Monin Obukhov Similarity Theory !! !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk) !! !! INPUT : !! ------- !! * zt : height for temperature and spec. hum. of air [m] !! * zu : height for wind speed (generally 10m) [m] !! * U_zu : scalar wind speed at 10m [m/s] !! * sst : 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] !! !! !! 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] !! * U_blk : bulk wind at 10m [m/s] !! !!---------------------------------------------------------------------------------- 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 [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) :: U_blk ! bulk wind at 10m [m/s] REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Cdn, Chn, Cen ! neutral transfer coefficients ! INTEGER :: j_itt LOGICAL :: l_zt_equal_zu = .FALSE. ! if q and t are given at same height as U INTEGER , PARAMETER :: nb_itt = 4 ! number of itterations ! REAL(wp), DIMENSION(jpi,jpj) :: & & u_star, t_star, q_star, & & dt_zu, dq_zu, & & znu_a, & !: Nu_air, Viscosity of air & z0, z0t REAL(wp), DIMENSION(jpi,jpj) :: zeta_u ! stability parameter at height zu REAL(wp), DIMENSION(jpi,jpj) :: ztmp0, ztmp1, ztmp2 REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zeta_t ! stability parameter at height zt !!---------------------------------------------------------------------------------- ! l_zt_equal_zu = .FALSE. IF( ABS(zu - zt) < 0.01 ) l_zt_equal_zu = .TRUE. ! testing "zu == zt" is risky with double precision IF( .NOT. l_zt_equal_zu ) ALLOCATE( zeta_t(jpi,jpj) ) !! First guess of temperature and humidity at height zu: t_zu = MAX(t_zt , 0.0) ! who knows what's given on masked-continental regions... q_zu = MAX(q_zt , 1.E-6) ! " !! Pot. temp. difference (and we don't want it to be 0!) dt_zu = t_zu - sst ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6), dt_zu ) dq_zu = q_zu - ssq ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9), dq_zu ) znu_a = visc_air(t_zt) ! Air viscosity (m^2/s) at zt given from temperature in (K) ztmp2 = 0.5*0.5 ! initial guess for wind gustiness contribution U_blk = SQRT(U_zu*U_zu + ztmp2) ztmp2 = 10000. ! optimization: ztmp2 == 1/z0 (with z0 first guess == 0.0001) ztmp0 = LOG(zu*ztmp2) ztmp1 = LOG(10.*ztmp2) u_star = 0.035*U_blk*ztmp1/ztmp0 ! (u* = 0.035*Un10) !! COARE 3.5 first guess of UN10 is U_zu ztmp2 = MIN( 0.0017*U_zu - 0.005 , charn0_max) ! alpha Charnock parameter (Eq. 13 Edson al. 2013) ztmp2 = MAX( ztmp2 , 0. ) ! alpha Charnock parameter (Eq. 13 Edson al. 2013) z0 = ztmp2*u_star*u_star/grav + 0.11*znu_a/u_star z0t = 0.1*EXP(vkarmn/(0.00115/(vkarmn/ztmp1))) ! WARNING: 1/z0t ! ztmp2 = vkarmn/ztmp0 Cd = ztmp2*ztmp2 ! first guess of Cd ztmp0 = vkarmn*vkarmn/LOG(zt*z0t)/Cd !Ribcu = -zu/(zi0*0.004*Beta0**3) !! Saturation Rib, zi0 = tropicalbound. layer depth ztmp2 = grav*zu*(dt_zu + rctv0*t_zu*dq_zu)/(t_zu*U_blk*U_blk) !! Ribu Bulk Richardson number ztmp1 = 0.5 + sign(0.5 , ztmp2) ztmp0 = ztmp0*ztmp2 !! Ribu < 0 Ribu > 0 Beta = 1.25 zeta_u = (1.-ztmp1) * (ztmp0/(1.+ztmp2/(-zu/(zi0*0.004*Beta0**3)))) & & + ztmp1 * (ztmp0*(1. + 27./9.*ztmp2/ztmp0)) !! First guess M-O stability dependent scaling params.(u*,t*,q*) to estimate z0 and z/L ztmp0 = vkarmn/(LOG(zu*z0t) - psi_h_coare(zeta_u)) u_star = U_blk*vkarmn/(LOG(zu) - LOG(z0) - psi_m_coare(zeta_u)) t_star = dt_zu*ztmp0 q_star = dq_zu*ztmp0 ! What's need to be done if zt /= zu: IF( .NOT. l_zt_equal_zu ) THEN zeta_t = zt*zeta_u/zu !! First update of values at zu (or zt for wind) ztmp0 = psi_h_coare(zeta_u) - psi_h_coare(zeta_t) ztmp1 = log(zt/zu) + ztmp0 t_zu = t_zt - t_star/vkarmn*ztmp1 q_zu = q_zt - q_star/vkarmn*ztmp1 q_zu = (0.5 + sign(0.5,q_zu))*q_zu !Makes it impossible to have negative humidity : dt_zu = t_zu - sst ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6), dt_zu ) dq_zu = q_zu - ssq ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9), dq_zu ) END IF !! ITERATION BLOCK DO j_itt = 1, nb_itt !!Inverse of Monin-Obukov length (1/L) : ztmp0 = One_on_L(t_zu, q_zu, u_star, t_star, q_star) ! 1/L == 1/[Monin-Obukhov length] ztmp1 = u_star*u_star ! u*^2 !! Update wind at 10m taking into acount convection-related wind gustiness: ! Ug = Beta*w* (Beta = 1.25, Fairall et al. 2003, Eq.8): ztmp2 = Beta0*Beta0*ztmp1*(MAX(-zi0*ztmp0/vkarmn,0.))**(2./3.) ! => ztmp2 == Ug^2 !! ! Only true when unstable (L<0) => when ztmp0 < 0 => explains "-" before 600. U_blk = MAX(sqrt(U_zu*U_zu + ztmp2), 0.2) ! include gustiness in bulk wind speed ! => 0.2 prevents U_blk to be 0 in stable case when U_zu=0. !! COARE 3.5: Charnock parameter is computed from the neutral wind speed at 10m: Eq. 13 (Edson al. 2013) ztmp2 = u_star/vkarmn*LOG(10./z0) ! UN10 Neutral wind at 10m! ztmp2 = MIN( 0.0017*ztmp2 - 0.005 , charn0_max) ! alpha Charnock parameter (Eq. 13 Edson al. 2013) ztmp2 = MAX( ztmp2 , 0. ) !! Roughness lengthes z0, z0t (z0q = z0t) : z0 = ztmp2*ztmp1/grav + 0.11*znu_a/u_star ! Roughness length (eq.6) ztmp1 = z0*u_star/znu_a ! Re_r: roughness Reynolds number !z0t = MIN( 1.1E-4 , 5.5E-5*ztmp1**(-0.6) ) ! COARE 3.0 !! Chris Fairall and Jim Edsson, private communication, March 2016 / COARE 3.5 : z0t = MIN( 1.6e-4 , 5.8E-5*ztmp1**(-0.72)) ! These thermal roughness lengths give Stanton and !z0q = z0t ! Dalton numbers that closely approximate COARE3.0 !! Stability parameters: zeta_u = zu*ztmp0 ; zeta_u = sign( min(abs(zeta_u),50.0), zeta_u ) IF( .NOT. l_zt_equal_zu ) THEN zeta_t = zt*ztmp0 ; zeta_t = sign( min(abs(zeta_t),50.0), zeta_t ) END IF !! Turbulent scales at zu=10m : ztmp0 = psi_h_coare(zeta_u) ztmp1 = vkarmn/(LOG(zu) -LOG(z0t) - ztmp0) t_star = dt_zu*ztmp1 q_star = dq_zu*ztmp1 u_star = U_blk*vkarmn/(LOG(zu) -LOG(z0) - psi_m_coare(zeta_u)) IF( .NOT. l_zt_equal_zu ) THEN ! What's need to be done if zt /= zu !! Re-updating temperature and humidity at zu : ztmp2 = ztmp0 - psi_h_coare(zeta_t) ztmp1 = log(zt/zu) + ztmp2 t_zu = t_zt - t_star/vkarmn*ztmp1 q_zu = q_zt - q_star/vkarmn*ztmp1 dt_zu = t_zu - sst ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6), dt_zu ) dq_zu = q_zu - ssq ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9), dq_zu ) END IF END DO ! ! compute transfer coefficients at zu : ztmp0 = u_star/U_blk Cd = ztmp0*ztmp0 Ch = ztmp0*t_star/dt_zu Ce = ztmp0*q_star/dq_zu ! ztmp1 = zu + z0 Cdn = vkarmn*vkarmn / (log(ztmp1/z0 )*log(ztmp1/z0 )) Chn = vkarmn*vkarmn / (log(ztmp1/z0t)*log(ztmp1/z0t)) Cen = Chn ! IF( .NOT. l_zt_equal_zu ) DEALLOCATE( zeta_t ) ! END SUBROUTINE turb_coare3p5 FUNCTION One_on_L( ptha, pqa, pus, pts, pqs ) !!------------------------------------------------------------------------ !! !! Evaluates the 1./(Monin Obukhov length) from air temperature and !! specific humidity, and frictional scales u*, t* and q* !! !! Author: L. Brodeau, june 2016 / AeroBulk !! (https://sourceforge.net/p/aerobulk) !!------------------------------------------------------------------------ REAL(wp), DIMENSION(jpi,jpj) :: One_on_L !: 1./(Monin Obukhov length) [m^-1] REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptha, & !: average potetntial air temperature [K] & pqa, & !: average specific humidity of air [kg/kg] & pus, pts, pqs !: frictional velocity, temperature and humidity ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zqa ! local scalar ! DO jj = 1, jpj DO ji = 1, jpi ! zqa = (1. + rctv0*pqa(ji,jj)) ! One_on_L(ji,jj) = grav*vkarmn*(pts(ji,jj)*zqa + rctv0*ptha(ji,jj)*pqs(ji,jj)) & & / ( pus(ji,jj)*pus(ji,jj) * ptha(ji,jj)*zqa ) ! END DO END DO ! END FUNCTION One_on_L FUNCTION psi_m_coare( pzeta ) !!---------------------------------------------------------------------------------- !! ** Purpose: compute the universal profile stability function for momentum !! COARE 3.0, Fairall et al. 2003 !! pzeta : stability paramenter, z/L where z is altitude !! measurement and L is M-O length !! Stability function for wind speed and scalars matching Kansas and free !! convection forms with weighting f convective form, follows Fairall et !! al (1996) with profile constants from Grachev et al (2000) BLM stable !! form from Beljaars and Holtslag (1991) !! !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk) !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: psi_m_coare REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zta, zphi_m, zphi_c, zpsi_k, zpsi_c, zf, zc, zstab !!---------------------------------------------------------------------------------- ! DO jj = 1, jpj DO ji = 1, jpi ! zta = pzeta(ji,jj) ! zphi_m = ABS(1. - 15.*zta)**.25 !!Kansas unstable ! zpsi_k = 2.*LOG((1. + zphi_m)/2.) + LOG((1. + zphi_m*zphi_m)/2.) & & - 2.*ATAN(zphi_m) + 0.5*rpi ! zphi_c = ABS(1. - 10.15*zta)**.3333 !!Convective ! zpsi_c = 1.5*LOG((1. + zphi_c + zphi_c*zphi_c)/3.) & & - 1.7320508*ATAN((1. + 2.*zphi_c)/1.7320508) + 1.813799447 ! zf = zta*zta zf = zf/(1. + zf) zc = MIN(50., 0.35*zta) zstab = 0.5 + SIGN(0.5, zta) ! psi_m_coare(ji,jj) = (1. - zstab) * ( (1. - zf)*zpsi_k + zf*zpsi_c ) & ! (zta < 0) & - zstab * ( 1. + 1.*zta & ! (zta > 0) & + 0.6667*(zta - 14.28)/EXP(zc) + 8.525 ) ! " ! END DO END DO ! END FUNCTION psi_m_coare FUNCTION psi_h_coare( pzeta ) !!--------------------------------------------------------------------- !! Universal profile stability function for temperature and humidity !! COARE 3.0, Fairall et al. 2003 !! !! pzeta : stability paramenter, z/L where z is altitude measurement !! and L is M-O length !! !! Stability function for wind speed and scalars matching Kansas and free !! convection forms with weighting f convective form, follows Fairall et !! al (1996) with profile constants from Grachev et al (2000) BLM stable !! form from Beljaars and Holtslag (1991) !! !! Author: L. Brodeau, june 2016 / AeroBulk !! (https://sourceforge.net/p/aerobulk) !!---------------------------------------------------------------- !! REAL(wp), DIMENSION(jpi,jpj) :: psi_h_coare REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zta, zphi_h, zphi_c, zpsi_k, zpsi_c, zf, zc, zstab ! DO jj = 1, jpj DO ji = 1, jpi ! zta = pzeta(ji,jj) ! zphi_h = (ABS(1. - 15.*zta))**.5 !! Kansas unstable (zphi_h = zphi_m**2 when unstable, zphi_m when stable) ! zpsi_k = 2.*LOG((1. + zphi_h)/2.) ! zphi_c = (ABS(1. - 34.15*zta))**.3333 !! Convective ! zpsi_c = 1.5*LOG((1. + zphi_c + zphi_c*zphi_c)/3.) & & -1.7320508*ATAN((1. + 2.*zphi_c)/1.7320508) + 1.813799447 ! zf = zta*zta zf = zf/(1. + zf) zc = MIN(50.,0.35*zta) zstab = 0.5 + SIGN(0.5, zta) ! psi_h_coare(ji,jj) = (1. - zstab) * ( (1. - zf)*zpsi_k + zf*zpsi_c ) & & - zstab * ( (ABS(1. + 2.*zta/3.))**1.5 & & + .6667*(zta - 14.28)/EXP(zc) + 8.525 ) ! END DO END DO ! END FUNCTION psi_h_coare FUNCTION visc_air( ptak ) !!--------------------------------------------------------------------- !! Air kinetic viscosity (m^2/s) given from temperature in degrees... !! !! Author: L. Brodeau, june 2016 / AeroBulk !! (https://sourceforge.net/p/aerobulk) !!--------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: visc_air REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K] ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: ztc, ztc2 ! local scalar ! DO jj = 1, jpj DO ji = 1, jpi ztc = ptak(ji,jj) - rt0 ! air temp, in deg. C ztc2 = ztc*ztc visc_air(ji,jj) = 1.326E-5*(1. + 6.542E-3*ztc + 8.301E-6*ztc2 - 4.84E-9*ztc2*ztc) END DO END DO ! END FUNCTION visc_air !!====================================================================== END MODULE sbcblk_algo_coare3p5