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_ecmwf ! cool-skin/warm layer scheme !LB IMPLICIT NONE PRIVATE PUBLIC :: SBCBLK_ALGO_ECMWF_INIT, TURB_ECMWF !! 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 = 10 ! number of itterations !!---------------------------------------------------------------------- CONTAINS SUBROUTINE sbcblk_algo_ecmwf_init(l_use_cs, l_use_wl) !!--------------------------------------------------------------------- !! *** FUNCTION sbcblk_algo_ecmwf_init *** !! !! INPUT : !! ------- !! * l_use_cs : use the cool-skin parameterization !! * l_use_wl : use the warm-layer parameterization !!--------------------------------------------------------------------- LOGICAL , INTENT(in) :: l_use_cs ! use the cool-skin parameterization LOGICAL , INTENT(in) :: l_use_wl ! use the warm-layer parameterization INTEGER :: ierr !!--------------------------------------------------------------------- IF( l_use_wl ) THEN ierr = 0 ALLOCATE ( dT_wl(jpi,jpj), Hz_wl(jpi,jpj), STAT=ierr ) IF( ierr > 0 ) CALL ctl_stop( ' SBCBLK_ALGO_ECMWF_INIT => allocation of dT_wl & Hz_wl failed!' ) dT_wl(:,:) = 0._wp Hz_wl(:,:) = rd0 ! (rd0, constant, = 3m is default for Zeng & Beljaars) ENDIF IF( l_use_cs ) THEN ierr = 0 ALLOCATE ( dT_cs(jpi,jpj), STAT=ierr ) IF( ierr > 0 ) CALL ctl_stop( ' SBCBLK_ALGO_ECMWF_INIT => allocation of dT_cs failed!' ) dT_cs(:,:) = -0.25_wp ! First guess of skin correction ENDIF END SUBROUTINE sbcblk_algo_ecmwf_init SUBROUTINE turb_ecmwf( kt, zt, zu, T_s, t_zt, q_s, q_zt, U_zu, l_use_cs, l_use_wl, & & Cd, Ch, Ce, t_zu, q_zu, U_blk, & & Cdn, Chn, Cen, & & Qsw, rad_lw, slp, pdT_cs, & ! optionals for cool-skin (and warm-layer) & pdT_wl, pHz_wl ) ! optionals for warm-layer only !!---------------------------------------------------------------------- !! *** ROUTINE turb_ecmwf *** !! !! ** Purpose : Computes turbulent transfert coefficients of surface !! fluxes according to IFS doc. (cycle 45r1) !! 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 !! !! 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 : !! ------- !! * kt : current time step (starts at 1) !! * zt : height for temperature and spec. hum. of air [m] !! * zu : height for wind speed (usually 10m) [m] !! * t_zt : potential air temperature at zt [K] !! * q_zt : specific humidity of air at zt [kg/kg] !! * U_zu : scalar wind speed at zu [m/s] !! * l_use_cs : use the cool-skin parameterization !! * l_use_wl : use the warm-layer parameterization !! !! 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_cs=True or l_use_wl=True) !! -> MUST be given the correct value if not computing skint temp. (in case l_use_cs=False or l_use_wl=False) !! !! OPTIONAL INPUT: !! --------------- !! * 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] !! !! OPTIONAL OUTPUT: !! ---------------- !! * pdT_cs : SST increment "dT" for cool-skin correction [K] !! * pdT_wl : SST increment "dT" for warm-layer correction [K] !! * pHz_wl : thickness of warm-layer [m] !! !! 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 zu [m/s] !! !! !! ** Author: L. Brodeau, June 2019 / AeroBulk (https://github.com/brodeau/aerobulk/) !!---------------------------------------------------------------------------------- INTEGER, INTENT(in ) :: kt ! current time step 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] LOGICAL , INTENT(in ) :: l_use_cs ! use the cool-skin parameterization LOGICAL , INTENT(in ) :: l_use_wl ! use the warm-layer parameterization 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 speed at zu [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( out), OPTIONAL, DIMENSION(jpi,jpj) :: pdT_cs REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: pdT_wl ! [K] REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: pHz_wl ! [m] ! 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 REAL(wp), DIMENSION(jpi,jpj) :: dt_zu, dq_zu REAL(wp), DIMENSION(jpi,jpj) :: znu_a !: Nu_air, Viscosity of air REAL(wp), DIMENSION(jpi,jpj) :: Linv !: 1/L (inverse of Monin Obukhov length... REAL(wp), DIMENSION(jpi,jpj) :: z0, z0t, z0q ! REAL(wp), DIMENSION(:,:), ALLOCATABLE :: 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 CHARACTER(len=40), PARAMETER :: crtnm = 'turb_ecmwf@sbcblk_algo_ecmwf.F90' !!---------------------------------------------------------------------------------- IF( kt == nit000 ) CALL SBCBLK_ALGO_ECMWF_INIT(l_use_cs, l_use_wl) 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 !! Initializations for cool skin and warm layer: IF( l_use_cs .AND. (.NOT.(PRESENT(Qsw) .AND. PRESENT(rad_lw) .AND. PRESENT(slp))) ) & & CALL ctl_stop( '['//TRIM(crtnm)//'] => ' , 'you need to provide Qsw, rad_lw & slp to use cool-skin param!' ) IF( l_use_wl .AND. (.NOT.(PRESENT(Qsw) .AND. PRESENT(rad_lw) .AND. PRESENT(slp))) ) & & CALL ctl_stop( '['//TRIM(crtnm)//'] => ' , 'you need to provide Qsw, rad_lw & slp to use warm-layer param!' ) IF( l_use_cs .OR. l_use_wl ) THEN ALLOCATE ( zsst(jpi,jpj) ) zsst = T_s ! backing up the bulk SST IF( l_use_cs ) T_s = T_s - 0.25_wp ! First guess of correction q_s = rdct_qsat_salt*q_sat(MAX(T_s, 200._wp), slp) ! First guess of q_s ENDIF ! Identical first gess as in COARE, with IFS parameter values though... ! !! 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) U_blk = SQRT(U_zu*U_zu + 0.5_wp*0.5_wp) ! initial guess for wind gustiness contribution ztmp0 = LOG( zu*10000._wp) ! optimization: 10000. == 1/z0 (with z0 first guess == 0.0001) ztmp1 = LOG(10._wp*10000._wp) ! " " " 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( MAX(ABS(z0), 1.E-9) , 1._wp ) ! (prevents FPE from stupid values from masked region later on) z0t = 1._wp / ( 0.1_wp*EXP(vkarmn/(0.00115/(vkarmn/ztmp1))) ) z0t = MIN( MAX(ABS(z0t), 1.E-9) , 1._wp ) ! (prevents FPE from stupid values from masked region later on) Cd = (vkarmn/ztmp0)**2 ! 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 = MAX ( U_blk*vkarmn/(LOG(zu) - LOG(z0) - psi_m_ecmwf(func_h)) , 1.E-9 ) ! (MAX => prevents FPE from stupid values from masked region later on) 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 ) ENDIF !! => 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...) !! 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 zu with convection-related wind gustiness in unstable conditions (Chap. 3.2, IFS doc - Cy40r1, Eq.3.17 and Eq.3.18 + Eq.3.8) ztmp2 = Beta0*Beta0*ztmp2*(MAX(-zi0*Linv/vkarmn,0._wp))**(2._wp/3._wp) ! square of wind gustiness contribution (combining Eq. 3.8 and 3.18, hap.3, IFS doc - Cy31r1) !! ! Only true when unstable (L<0) => when ztmp0 < 0 => explains "-" before zi0 U_blk = MAX(SQRT(U_zu*U_zu + ztmp2), 0.2_wp) ! include gustiness in bulk wind speed ! => 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 ENDIF !! 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) IF( l_use_cs ) THEN !! Cool-skin contribution CALL UPDATE_QNSOL_TAU( zu, T_s, q_s, t_zu, q_zu, u_star, t_star, q_star, U_zu, U_blk, slp, rad_lw, & & ztmp1, ztmp0, Qlat=ztmp2) ! Qnsol -> ztmp1 / Tau -> ztmp0 CALL CS_ECMWF( Qsw, ztmp1, u_star, zsst ) ! Qnsol -> ztmp1 T_s(:,:) = zsst(:,:) + dT_cs(:,:)*tmask(:,:,1) IF( l_use_wl ) T_s(:,:) = T_s(:,:) + dT_wl(:,:)*tmask(:,:,1) q_s(:,:) = rdct_qsat_salt*q_sat(MAX(T_s(:,:), 200._wp), slp(:,:)) ENDIF IF( l_use_wl ) THEN !! Warm-layer contribution CALL UPDATE_QNSOL_TAU( zu, T_s, q_s, t_zu, q_zu, u_star, t_star, q_star, U_zu, U_blk, slp, rad_lw, & & ztmp1, ztmp2) ! Qnsol -> ztmp1 / Tau -> ztmp2 CALL WL_ECMWF( Qsw, ztmp1, u_star, zsst ) !! Updating T_s and q_s !!! T_s(:,:) = zsst(:,:) + dT_wl(:,:)*tmask(:,:,1) ! IF( l_use_cs ) T_s(:,:) = T_s(:,:) + dT_cs(:,:)*tmask(:,:,1) q_s(:,:) = rdct_qsat_salt*q_sat(MAX(T_s(:,:), 200._wp), slp(:,:)) ENDIF IF( l_use_cs .OR. l_use_wl .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 ) ENDIF 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)) IF( l_use_cs .AND. PRESENT(pdT_cs) ) pdT_cs = dT_cs IF( l_use_wl .AND. PRESENT(pdT_wl) ) pdT_wl = dT_wl IF( l_use_wl .AND. PRESENT(pHz_wl) ) pHz_wl = Hz_wl IF( l_use_cs .OR. l_use_wl ) DEALLOCATE ( zsst ) 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