MODULE sbcblk_algo_ecmwf !!====================================================================== !! *** MODULE sbcblk_algo_ecmwf *** !! Computes turbulent components of surface fluxes !! according to the method in IFS of the ECMWF model !! !! * 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 31r2) !! based on IFS doc (avaible online on the ECMWF's website) !! !! !! Routine turb_ecmwf maintained and developed in AeroBulk !! (http://aerobulk.sourceforge.net/) !! !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/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 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 :: rctv0 = 0.608 ! constant to obtain virtual temperature... REAL(wp), PARAMETER :: Cp_dry = 1005.0 ! Specic heat of dry air, constant pressure [J/K/kg] REAL(wp), PARAMETER :: Cp_vap = 1860.0 ! Specic heat of water vapor, constant pressure [J/K/kg] 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 ! !!---------------------------------------------------------------------- CONTAINS SUBROUTINE TURB_ECMWF( zt, zu, sst, t_zt, ssq , q_zt , U_zu, & & Cd, Ch, Ce , t_zu, q_zu, U_blk, & & Cdn, Chn, Cen ) !!---------------------------------------------------------------------------------- !! *** ROUTINE turb_ecmwf *** !! !! 2015: L. Brodeau (brodeau@gmail.com) !! !! ** Purpose : Computes turbulent transfert coefficients of surface !! fluxes according to IFS doc. (cycle 31) !! If relevant (zt /= zu), adjust temperature and humidity from height zt to zu !! !! ** Method : Monin Obukhov Similarity Theory !! !! 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] !! !! !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/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 [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 & Linv, & !: 1/L (inverse of Monin Obukhov length... & z0, z0t, z0q REAL(wp), DIMENSION(jpi,jpj) :: func_m, func_h REAL(wp), DIMENSION(jpi,jpj) :: ztmp0, ztmp1, ztmp2 !!---------------------------------------------------------------------------------- ! ! Identical first gess as in COARE, with IFS parameter values though ! l_zt_equal_zu = .FALSE. IF( ABS(zu - zt) < 0.01 ) l_zt_equal_zu = .TRUE. ! testing "zu == zt" is risky with double precision !! 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) ! z0 = 0.0001 ztmp2 = 10000. ! optimization: ztmp2 == 1/z0 ztmp0 = LOG(zu*ztmp2) ztmp1 = LOG(10.*ztmp2) u_star = 0.035*U_blk*ztmp1/ztmp0 ! (u* = 0.035*Un10) z0 = charn0*u_star*u_star/grav + 0.11*znu_a/u_star z0t = 0.1*EXP(vkarmn/(0.00115/(vkarmn/ztmp1))) ! WARNING: 1/z0t ! Cd = (vkarmn/ztmp0)**2 ! first guess of Cd ztmp0 = vkarmn*vkarmn/LOG(zt*z0t)/Cd ztmp2 = Ri_bulk( zu, t_zu, dt_zu, q_zu, dq_zu, U_blk ) ! Ribu = Bulk Richardson number !! First estimate of zeta_u, depending on the stability, ie sign of Ribu (ztmp2): ztmp1 = 0.5 + SIGN( 0.5 , ztmp2 ) func_m = ztmp0*ztmp2 ! temporary array !! !! Ribu < 0 Ribu > 0 Beta = 1.25 func_h = (1.-ztmp1)*(func_m/(1.+ztmp2/(-zu/(zi0*0.004*Beta0**3)))) & ! temporary array !!! func_h == zeta_u & + ztmp1*(func_m*(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_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's need 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 + 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 ) ! ENDIF !! => that was same first guess as in COARE... !! First guess of inverse of Monin-Obukov length (1/L) : ztmp0 = (1. + rctv0*q_zu) ! the factor to apply to temp. to get virt. temp... Linv = grav*vkarmn*(t_star*ztmp0 + rctv0*t_zu*q_star) / ( u_star*u_star * t_zu*ztmp0 ) !! Functions such as u* = U_blk*vkarmn/func_m ztmp1 = zu + z0 ztmp0 = ztmp1*Linv func_m = LOG(ztmp1) -LOG(z0) - psi_m_ecmwf(ztmp0) + psi_m_ecmwf(z0*Linv) func_h = LOG(ztmp1*z0t) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(1./z0t*Linv) !! ITERATION BLOCK !! *************** DO j_itt = 1, nb_itt !! Bulk Richardson Number at z=zu (Eq. 3.25) ztmp0 = Ri_bulk(zu, t_zu, dt_zu, q_zu, dq_zu, U_blk) !! 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, p.33, IFS doc - Cy31r1 !! Update func_m with new Linv: ztmp1 = zu + z0 func_m = LOG(ztmp1) -LOG(z0) - psi_m_ecmwf(ztmp1*Linv) + psi_m_ecmwf(z0*Linv) !! Need to update roughness lengthes: u_star = U_blk*vkarmn/func_m ztmp2 = u_star*u_star ztmp1 = znu_a/u_star z0 = alpha_M*ztmp1 + charn0*ztmp2/grav z0t = alpha_H*ztmp1 ! eq.3.26, Chap.3, p.34, IFS doc - Cy31r1 z0q = alpha_Q*ztmp1 !! Update wind at 10m taking into acount convection-related wind gustiness: ! Only true when unstable (L<0) => when ztmp0 < 0 => - !!! ztmp2 = ztmp2 * (MAX(-zi0*Linv/vkarmn,0.))**(2./3.) ! => 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) ! 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+z0)*Linv) ! temporary array !!! func_m = psi_h_ecmwf((zt+z0)*Linv) ! temporary array !!! ztmp2 = psi_h_ecmwf(z0t*Linv) ztmp0 = func_h - ztmp2 ztmp1 = vkarmn/(LOG(zu+z0) - 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+z0) - 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 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 !! Updating because of updated z0 and z0t and new Linv... ztmp1 = zu + z0 ztmp0 = ztmp1*Linv func_m = log(ztmp1) - LOG(z0 ) - psi_m_ecmwf(ztmp0) + psi_m_ecmwf(z0 *Linv) func_h = log(ztmp1) - LOG(z0t) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(z0t*Linv) END DO Cd = vkarmn*vkarmn/(func_m*func_m) Ch = vkarmn*vkarmn/(func_m*func_h) ztmp1 = log((zu + z0)/z0q) - psi_h_ecmwf((zu + z0)*Linv) + psi_h_ecmwf(z0q*Linv) ! func_q Ce = vkarmn*vkarmn/(func_m*ztmp1) ztmp1 = zu + z0 Cdn = vkarmn*vkarmn / (log(ztmp1/z0 )*log(ztmp1/z0 )) Chn = vkarmn*vkarmn / (log(ztmp1/z0t)*log(ztmp1/z0t)) Cen = vkarmn*vkarmn / (log(ztmp1/z0q)*log(ztmp1/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://sourceforge.net/p/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. ) !! Very stable conditions (L positif and big!): ! ! Unstable (Paulson 1970): ! eq.3.20, Chap.3, p.33, IFS doc - Cy31r1 zx = SQRT(ABS(1. - 16.*zzeta)) ztmp = 1. + SQRT(zx) ztmp = ztmp*ztmp psi_unst = LOG( 0.125*ztmp*(1. + zx) ) & & -2.*ATAN( SQRT(zx) ) + 0.5*rpi ! ! Unstable: ! eq.3.22, Chap.3, p.33, IFS doc - Cy31r1 psi_stab = -2./3.*(zzeta - 5./0.35)*EXP(-0.35*zzeta) & & - zzeta - 2./3.*5./0.35 ! ! Combining: stab = 0.5 + SIGN(0.5, zzeta) ! zzeta > 0 => stab = 1 ! psi_m_ecmwf(ji,jj) = (1. - 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://sourceforge.net/p/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.) ! Very stable conditions (L positif and big!): ! zx = ABS(1. - 16.*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.*LOG(0.5*(1. + zx*zx)) ! eq.3.20, Chap.3, p.33, IFS doc - Cy31r1 ! ! Stable: psi_stab = -2./3.*(zzeta - 5./0.35)*EXP(-0.35*zzeta) & ! eq.3.22, Chap.3, p.33, IFS doc - Cy31r1 & - ABS(1. + 2./3.*zzeta)**1.5 - 2./3.*5./0.35 + 1. ! LB: added ABS() to avoid NaN values when unstable, which contaminates the unstable solution... ! stab = 0.5 + SIGN(0.5, zzeta) ! zzeta > 0 => stab = 1 ! ! psi_h_ecmwf(ji,jj) = (1. - stab) * psi_unst & ! (zzeta < 0) Unstable & + stab * psi_stab ! (zzeta > 0) Stable ! END DO END DO ! END FUNCTION psi_h_ecmwf FUNCTION Ri_bulk( pz, ptz, pdt, pqz, pdq, pub ) !!---------------------------------------------------------------------------------- !! Bulk Richardson number (Eq. 3.25 IFS doc) !! !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://sourceforge.net/p/aerobulk) !!---------------------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: Ri_bulk ! ! REAL(wp) , INTENT(in) :: pz ! height above the sea [m] REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptz ! air temperature at pz m [K] REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pdt ! ptz - sst [K] REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqz ! air temperature at pz m [kg/kg] REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pdq ! pqz - ssq [kg/kg] REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pub ! bulk wind speed [m/s] !!---------------------------------------------------------------------------------- ! Ri_bulk = grav*pz/(pub*pub) & & * ( pdt/(ptz - 0.5_wp*(pdt + grav*pz/(Cp_dry+Cp_vap*pqz))) & & + rctv0*pdq ) ! END FUNCTION Ri_bulk 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 in (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_ecmwf