MODULE sbcblk_algo_ecmwf !!====================================================================== !! *** MODULE sbcblk_algo_ecmwf *** !! 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 U_blk !! => all these are used in bulk formulas in sbcblk.F90 !! !! Using the bulk formulation/param. of IFS of ECMWF (cycle 40r1) !! based on IFS doc (avaible online on the ECMWF's website) !! !! Routine turb_ecmwf maintained and developed in AeroBulk !! (https://github.com/brodeau/aerobulk) !! !! ** Author: L. Brodeau, June 2019 / AeroBulk (https://github.com/brodeau/aerobulk) !!---------------------------------------------------------------------- !! History : 4.0 ! 2016-02 (L.Brodeau) Original code !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! turb_ecmwf : 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 iom ! I/O manager library USE lib_mpp ! distribued memory computing library USE in_out_manager ! I/O manager USE prtctl ! Print control USE sbcwave, ONLY : cdn_wave ! wave module #if defined key_si3 || defined key_cice USE sbc_ice ! Surface boundary condition: ice fields #endif USE lib_fortran ! to use key_nosignedzero USE sbc_oce ! Surface boundary condition: ocean fields USE sbcblk_phy ! all thermodynamics functions, rho_air, q_sat, etc... !LB USE sbcblk_skin ! cool-skin/warm layer scheme (CSWL_ECMWF) !LB IMPLICIT NONE PRIVATE PUBLIC :: TURB_ECMWF ! called by sbcblk.F90 ! !! ECMWF own values for given constants, taken form IFS documentation... REAL(wp), PARAMETER :: charn0 = 0.018 ! Charnock constant (pretty high value here !!! ! ! => Usually 0.011 for moderate winds) REAL(wp), PARAMETER :: zi0 = 1000. ! scale height of the atmospheric boundary layer...1 REAL(wp), PARAMETER :: Beta0 = 1. ! gustiness parameter ( = 1.25 in COAREv3) REAL(wp), PARAMETER :: alpha_M = 0.11 ! For roughness length (smooth surface term) REAL(wp), PARAMETER :: alpha_H = 0.40 ! (Chapter 3, p.34, IFS doc Cy31r1) REAL(wp), PARAMETER :: alpha_Q = 0.62 ! INTEGER , PARAMETER :: nb_itt = 5 ! number of itterations !!---------------------------------------------------------------------- CONTAINS SUBROUTINE TURB_ECMWF( zt, zu, T_s, t_zt, q_s, q_zt, U_zu, & & Cd, Ch, Ce, t_zu, q_zu, U_blk, & & Cdn, Chn, Cen, & & Qsw, rad_lw, slp, Tsk_b ) !!---------------------------------------------------------------------------------- !! *** ROUTINE turb_ecmwf *** !! !! ** Purpose : Computes turbulent transfert coefficients of surface !! fluxes according to IFS doc. (cycle 40) !! If relevant (zt /= zu), adjust temperature and humidity from height zt to zu !! Returns the effective bulk wind speed at 10m to be used in the bulk formulas !! !! Applies the cool-skin warm-layer correction of the SST to T_s !! if the net shortwave flux at the surface (Qsw), the downwelling longwave !! radiative fluxes at the surface (rad_lw), and the sea-leve pressure (slp) !! are provided as (optional) arguments! !! !! 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] !! * t_zt : potential air temperature at zt [K] !! * q_zt : specific humidity of air at zt [kg/kg] !! !! INPUT/OUTPUT: !! ------------- !! * T_s : always "bulk SST" as input [K] !! -> unchanged "bulk SST" as output if CSWL not used [K] !! -> skin temperature as output if CSWL used [K] !! !! * q_s : SSQ aka saturation specific humidity at temp. T_s [kg/kg] !! -> doesn't need to be given a value if skin temp computed (in case l_use_skin=True) !! -> MUST be given the correct value if not computing skint temp. (in case l_use_skin=False) !! !! OPTIONAL INPUT (will trigger l_use_skin=TRUE if present!): !! --------------- !! * Qsw : net solar flux (after albedo) at the surface (>0) [W/m^2] !! * rad_lw : downwelling longwave radiation at the surface (>0) [W/m^2] !! * slp : sea-level pressure [Pa] !! * Tsk_b : estimate of skin temperature at previous time-step [K] !! !! 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 speed at 10m [m/s] !! !! !! ** 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(inout), DIMENSION(jpi,jpj) :: T_s ! sea surface temperature [Kelvin] REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: t_zt ! potential air temperature [Kelvin] REAL(wp), INTENT(inout), DIMENSION(jpi,jpj) :: q_s ! 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) :: U_blk ! bulk wind at 10m [m/s] REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Cdn, Chn, Cen ! neutral transfer coefficients ! REAL(wp), INTENT(in ), OPTIONAL, DIMENSION(jpi,jpj) :: Qsw ! [W/m^2] REAL(wp), INTENT(in ), OPTIONAL, DIMENSION(jpi,jpj) :: rad_lw ! [W/m^2] REAL(wp), INTENT(in ), OPTIONAL, DIMENSION(jpi,jpj) :: slp ! [Pa] REAL(wp), INTENT(in ), OPTIONAL, DIMENSION(jpi,jpj) :: Tsk_b ! [Pa] ! INTEGER :: j_itt LOGICAL :: l_zt_equal_zu = .FALSE. ! if q and t are given at same height as U ! REAL(wp), DIMENSION(jpi,jpj) :: & & u_star, t_star, q_star, & & dt_zu, dq_zu, & & znu_a, & !: Nu_air, Viscosity of air & Linv, & !: 1/L (inverse of Monin Obukhov length... & z0, z0t, z0q ! ! Cool skin: LOGICAL :: l_use_skin = .FALSE. REAL(wp), DIMENSION(jpi,jpj) :: zsst ! to back up the initial bulk SST ! REAL(wp), DIMENSION(jpi,jpj) :: func_m, func_h REAL(wp), DIMENSION(jpi,jpj) :: ztmp0, ztmp1, ztmp2 !!---------------------------------------------------------------------------------- ! Cool skin ? IF( PRESENT(Qsw) .AND. PRESENT(rad_lw) .AND. PRESENT(slp) ) THEN l_use_skin = .TRUE. END IF IF (lwp) PRINT *, ' *** LOLO(sbcblk_algo_ecmwf.F90) => l_use_skin =', l_use_skin ! Identical first gess as in COARE, with IFS parameter values though... ! l_zt_equal_zu = .FALSE. IF( ABS(zu - zt) < 0.01_wp ) l_zt_equal_zu = .TRUE. ! testing "zu == zt" is risky with double precision !! Initialization for cool skin: zsst = T_s ! save the bulk SST IF( l_use_skin ) THEN ! First guess for skin temperature: IF( PRESENT(Tsk_b) ) THEN T_s = Tsk_b ELSE T_s = T_s - 0.25 ! sst - 0.25 END IF q_s = rdct_qsat_salt*q_sat(MAX(T_s, 200._wp), slp) ! First guess of q_s END IF !! First guess of temperature and humidity at height zu: 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 ) ! " !! Pot. temp. difference (and we don't want it to be 0!) dt_zu = t_zu - T_s ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) dq_zu = q_zu - q_s ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) znu_a = visc_air(t_zu) ! Air viscosity (m^2/s) at zt given from temperature in (K) ztmp2 = 0.5_wp*0.5_wp ! initial guess for wind gustiness contribution U_blk = SQRT(U_zu*U_zu + ztmp2) ztmp2 = 10000._wp ! optimization: ztmp2 == 1/z0 (with z0 first guess == 0.0001) ztmp0 = LOG(zu*ztmp2) ztmp1 = LOG(10.*ztmp2) u_star = 0.035_wp*U_blk*ztmp1/ztmp0 ! (u* = 0.035*Un10) z0 = charn0*u_star*u_star/grav + 0.11_wp*znu_a/u_star z0 = MIN(ABS(z0), 0.001_wp) ! (prevent FPE from stupid values from masked region later on...) !#LOLO z0t = 1._wp / ( 0.1_wp*EXP(vkarmn/(0.00115/(vkarmn/ztmp1))) ) z0t = MIN(ABS(z0t), 0.001_wp) ! (prevent FPE from stupid values from masked region later on...) !#LOLO ztmp2 = vkarmn/ztmp0 Cd = ztmp2*ztmp2 ! first guess of Cd ztmp0 = vkarmn*vkarmn/LOG(zt/z0t)/Cd ztmp2 = Ri_bulk( zu, T_s, t_zu, q_s, q_zu, U_blk ) ! Bulk Richardson Number (BRN) !! First estimate of zeta_u, depending on the stability, ie sign of BRN (ztmp2): ztmp1 = 0.5 + SIGN( 0.5_wp , ztmp2 ) func_m = ztmp0*ztmp2 ! temporary array !! func_h = (1._wp-ztmp1) * (func_m/(1._wp+ztmp2/(-zu/(zi0*0.004_wp*Beta0**3)))) & ! BRN < 0 ! temporary array !!! func_h == zeta_u & + ztmp1 * (func_m*(1._wp + 27._wp/9._wp*ztmp2/func_m)) ! BRN > 0 !#LB: should make sure that the "func_m" of "27./9.*ztmp2/func_m" is "ztmp0*ztmp2" and not "ztmp0==vkarmn*vkarmn/LOG(zt/z0t)/Cd" ! !! First guess M-O stability dependent scaling params.(u*,t*,q*) to estimate z0 and z/L ztmp0 = vkarmn/(LOG(zu/z0t) - psi_h_ecmwf(func_h)) u_star = U_blk*vkarmn/(LOG(zu) - LOG(z0) - psi_m_ecmwf(func_h)) t_star = dt_zu*ztmp0 q_star = dq_zu*ztmp0 ! What needs to be done if zt /= zu: IF( .NOT. l_zt_equal_zu ) THEN !! First update of values at zu (or zt for wind) ztmp0 = psi_h_ecmwf(func_h) - psi_h_ecmwf(zt*func_h/zu) ! zt*func_h/zu == 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_wp + SIGN(0.5_wp,q_zu))*q_zu !Makes it impossible to have negative humidity : ! dt_zu = t_zu - T_s ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) dq_zu = q_zu - q_s ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) END IF !! => that was same first guess as in COARE... !! First guess of inverse of Monin-Obukov length (1/L) : Linv = One_on_L( t_zu, q_zu, u_star, t_star, q_star ) !! Functions such as u* = U_blk*vkarmn/func_m ztmp0 = zu*Linv func_m = LOG(zu) - LOG(z0) - psi_m_ecmwf(ztmp0) + psi_m_ecmwf( z0*Linv) func_h = LOG(zu) - LOG(z0t) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(z0t*Linv) !! ITERATION BLOCK DO j_itt = 1, nb_itt !! Bulk Richardson Number at z=zu (Eq. 3.25) ztmp0 = Ri_bulk( zu, T_s, t_zu, q_s, q_zu, U_blk ) ! Bulk Richardson Number (BRN) !! New estimate of the inverse of the Monin-Obukhon length (Linv == zeta/zu) : Linv = ztmp0*func_m*func_m/func_h / zu ! From Eq. 3.23, Chap.3.2.3, IFS doc - Cy40r1 !! Note: it is slightly different that the L we would get with the usual Linv = SIGN( MIN(ABS(Linv),200._wp), Linv ) ! (prevent FPE from stupid values from masked region later on...) !#LOLO !! Update func_m with new Linv: func_m = LOG(zu) -LOG(z0) - psi_m_ecmwf(zu*Linv) + psi_m_ecmwf(z0*Linv) ! LB: should be "zu+z0" rather than "zu" alone, but z0 is tiny wrt zu! !! Need to update roughness lengthes: u_star = U_blk*vkarmn/func_m ztmp2 = u_star*u_star ztmp1 = znu_a/u_star z0 = MIN( ABS( alpha_M*ztmp1 + charn0*ztmp2/grav ) , 0.001_wp) z0t = MIN( ABS( alpha_H*ztmp1 ) , 0.001_wp) ! eq.3.26, Chap.3, p.34, IFS doc - Cy31r1 z0q = MIN( ABS( alpha_Q*ztmp1 ) , 0.001_wp) !! Update wind at 10m taking into acount convection-related wind gustiness: !! => Chap. 3.2, IFS doc - Cy40r1, Eq.3.17 and Eq.3.18 + Eq.3.8 ! Only true when unstable (L<0) => when ztmp0 < 0 => - !!! ztmp2 = ztmp2 * ( MAX(-zi0*Linv/vkarmn , 0._wp))**(2._wp/3._wp) ! => w*^2 (combining Eq. 3.8 and 3.18, hap.3, IFS doc - Cy31r1) !! => equivalent using Beta=1 (gustiness parameter, 1.25 for COARE, also zi0=600 in COARE..) U_blk = MAX( SQRT(U_zu*U_zu + ztmp2) , 0.2_wp ) ! eq.3.17, Chap.3, p.32, IFS doc - Cy31r1 ! => 0.2 prevents U_blk to be 0 in stable case when U_zu=0. !! Need to update "theta" and "q" at zu in case they are given at different heights !! as well the air-sea differences: IF( .NOT. l_zt_equal_zu ) THEN !! Arrays func_m and func_h are free for a while so using them as temporary arrays... func_h = psi_h_ecmwf(zu*Linv) ! temporary array !!! func_m = psi_h_ecmwf(zt*Linv) ! temporary array !!! ztmp2 = psi_h_ecmwf(z0t*Linv) ztmp0 = func_h - ztmp2 ztmp1 = vkarmn/(LOG(zu) - LOG(z0t) - ztmp0) t_star = dt_zu*ztmp1 ztmp2 = ztmp0 - func_m + ztmp2 ztmp1 = LOG(zt/zu) + ztmp2 t_zu = t_zt - t_star/vkarmn*ztmp1 ztmp2 = psi_h_ecmwf(z0q*Linv) ztmp0 = func_h - ztmp2 ztmp1 = vkarmn/(LOG(zu) - LOG(z0q) - ztmp0) q_star = dq_zu*ztmp1 ztmp2 = ztmp0 - func_m + ztmp2 ztmp1 = LOG(zt/zu) + ztmp2 q_zu = q_zt - q_star/vkarmn*ztmp1 END IF !! Updating because of updated z0 and z0t and new Linv... ztmp0 = zu*Linv func_m = log(zu) - LOG(z0 ) - psi_m_ecmwf(ztmp0) + psi_m_ecmwf(z0 *Linv) func_h = log(zu) - LOG(z0t) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(z0t*Linv) !! SKIN related part !! ----------------- IF( l_use_skin ) THEN !! compute transfer coefficients at zu : lolo: verifier... Ch = vkarmn*vkarmn/(func_m*func_h) ztmp1 = LOG(zu) - LOG(z0q) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(z0q*Linv) ! func_q Ce = vkarmn*vkarmn/(func_m*ztmp1) ! Non-Solar heat flux to the ocean: ztmp1 = U_blk*MAX(rho_air(t_zu, q_zu, slp), 1._wp) ! rho*U10 ztmp2 = T_s*T_s ztmp1 = ztmp1 * ( Ce*L_vap(T_s)*(q_zu - q_s) + Ch*cp_air(q_zu)*(t_zu - T_s) ) & ! Total turb. heat flux & + rad_lw - emiss_w*stefan*ztmp2*ztmp2 ! Net longwave flux !! => "ztmp1" is the net non-solar surface heat flux ! !! Updating the values of the skin temperature T_s and q_s : CALL CSWL_ECMWF( Qsw, ztmp1, u_star, zsst, T_s ) q_s = rdct_qsat_salt*q_sat(MAX(T_s, 200._wp), slp) ! 200 -> just to avoid numerics problem on masked regions if silly values are given END IF IF( (l_use_skin).OR.(.NOT. l_zt_equal_zu) ) THEN dt_zu = t_zu - T_s ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) dq_zu = q_zu - q_s ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) END IF END DO !DO j_itt = 1, nb_itt Cd = vkarmn*vkarmn/(func_m*func_m) Ch = vkarmn*vkarmn/(func_m*func_h) ztmp2 = log(zu/z0q) - psi_h_ecmwf(zu*Linv) + psi_h_ecmwf(z0q*Linv) ! func_q Ce = vkarmn*vkarmn/(func_m*ztmp2) Cdn = vkarmn*vkarmn / (log(zu/z0 )*log(zu/z0 )) Chn = vkarmn*vkarmn / (log(zu/z0t)*log(zu/z0t)) Cen = vkarmn*vkarmn / (log(zu/z0q)*log(zu/z0q)) END SUBROUTINE TURB_ECMWF FUNCTION psi_m_ecmwf( pzeta ) !!---------------------------------------------------------------------------------- !! Universal profile stability function for momentum !! ECMWF / as in IFS cy31r1 documentation, available online !! at ecmwf.int !! !! 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_ecmwf REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zzeta, zx, ztmp, psi_unst, psi_stab, stab !!---------------------------------------------------------------------------------- ! DO jj = 1, jpj DO ji = 1, jpi ! zzeta = MIN( pzeta(ji,jj) , 5._wp ) !! Very stable conditions (L positif and big!): ! ! Unstable (Paulson 1970): ! eq.3.20, Chap.3, p.33, IFS doc - Cy31r1 zx = SQRT(ABS(1._wp - 16._wp*zzeta)) ztmp = 1._wp + SQRT(zx) ztmp = ztmp*ztmp psi_unst = LOG( 0.125_wp*ztmp*(1._wp + zx) ) & & -2._wp*ATAN( SQRT(zx) ) + 0.5_wp*rpi ! ! Unstable: ! eq.3.22, Chap.3, p.33, IFS doc - Cy31r1 psi_stab = -2._wp/3._wp*(zzeta - 5._wp/0.35_wp)*EXP(-0.35_wp*zzeta) & & - zzeta - 2._wp/3._wp*5._wp/0.35_wp ! ! Combining: stab = 0.5_wp + SIGN(0.5_wp, zzeta) ! zzeta > 0 => stab = 1 ! psi_m_ecmwf(ji,jj) = (1._wp - stab) * psi_unst & ! (zzeta < 0) Unstable & + stab * psi_stab ! (zzeta > 0) Stable ! END DO END DO ! END FUNCTION psi_m_ecmwf FUNCTION psi_h_ecmwf( pzeta ) !!---------------------------------------------------------------------------------- !! Universal profile stability function for temperature and humidity !! ECMWF / as in IFS cy31r1 documentation, available online !! at ecmwf.int !! !! 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_ecmwf REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zzeta, zx, psi_unst, psi_stab, stab !!---------------------------------------------------------------------------------- ! DO jj = 1, jpj DO ji = 1, jpi ! zzeta = MIN(pzeta(ji,jj) , 5._wp) ! Very stable conditions (L positif and big!): ! zx = ABS(1._wp - 16._wp*zzeta)**.25 ! this is actually (1/phi_m)**2 !!! ! ! eq.3.19, Chap.3, p.33, IFS doc - Cy31r1 ! Unstable (Paulson 1970) : psi_unst = 2._wp*LOG(0.5_wp*(1._wp + zx*zx)) ! eq.3.20, Chap.3, p.33, IFS doc - Cy31r1 ! ! Stable: psi_stab = -2._wp/3._wp*(zzeta - 5._wp/0.35_wp)*EXP(-0.35_wp*zzeta) & ! eq.3.22, Chap.3, p.33, IFS doc - Cy31r1 & - ABS(1._wp + 2._wp/3._wp*zzeta)**1.5_wp - 2._wp/3._wp*5._wp/0.35_wp + 1._wp ! LB: added ABS() to avoid NaN values when unstable, which contaminates the unstable solution... ! stab = 0.5_wp + SIGN(0.5_wp, zzeta) ! zzeta > 0 => stab = 1 ! ! psi_h_ecmwf(ji,jj) = (1._wp - stab) * psi_unst & ! (zzeta < 0) Unstable & + stab * psi_stab ! (zzeta > 0) Stable ! END DO END DO ! END FUNCTION psi_h_ecmwf !!====================================================================== END MODULE sbcblk_algo_ecmwf