MODULE sbcblk_algo_coare3p0 !!====================================================================== !! *** MODULE sbcblk_algo_coare3p0 *** !! !! After Fairall et al, 2003 !! 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 !! !! Routine turb_coare3p0 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_coare3p0 : 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_coare ! cool-skin/warm layer scheme (CSWL_ECMWF) !LB IMPLICIT NONE PRIVATE PUBLIC :: SBCBLK_ALGO_COARE3P0_INIT, TURB_COARE3P0 !! COARE own values for given constants: REAL(wp), PARAMETER :: zi0 = 600._wp ! scale height of the atmospheric boundary layer... REAL(wp), PARAMETER :: Beta0 = 1.25_wp ! gustiness parameter INTEGER , PARAMETER :: nb_itt = 10 ! number of itterations !!---------------------------------------------------------------------- CONTAINS SUBROUTINE sbcblk_algo_coare3p0_init(l_use_cs, l_use_wl) !!--------------------------------------------------------------------- !! *** FUNCTION sbcblk_algo_coare3p0_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 ( Tau_ac(jpi,jpj) , Qnt_ac(jpi,jpj), dT_wl(jpi,jpj), Hz_wl(jpi,jpj), STAT=ierr ) IF( ierr > 0 ) CALL ctl_stop( ' SBCBLK_ALGO_COARE3P0_INIT => allocation of Tau_ac, Qnt_ac, dT_wl & Hz_wl failed!' ) Tau_ac(:,:) = 0._wp Qnt_ac(:,:) = 0._wp dT_wl(:,:) = 0._wp Hz_wl(:,:) = Hwl_max ENDIF IF( l_use_cs ) THEN ierr = 0 ALLOCATE ( dT_cs(jpi,jpj), STAT=ierr ) IF( ierr > 0 ) CALL ctl_stop( ' SBCBLK_ALGO_COARE3P0_INIT => allocation of dT_cs failed!' ) dT_cs(:,:) = -0.25_wp ! First guess of skin correction ENDIF END SUBROUTINE sbcblk_algo_coare3p0_init SUBROUTINE turb_coare3p0( 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_coare3p0 *** !! !! ** 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 !! 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) :: 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 REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zsst ! to back up the initial bulk SST ! CHARACTER(len=40), PARAMETER :: crtnm = 'turb_coare3p0@sbcblk_algo_coare3p0' !!---------------------------------------------------------------------------------- IF( kt == nit000 ) CALL SBCBLK_ALGO_COARE3P0_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 IF( .NOT. l_zt_equal_zu ) ALLOCATE( zeta_t(jpi,jpj) ) !! 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 !! 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 = alfa_charn_3p0(U_zu)*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 ) ztmp0 = ztmp0*ztmp2 zeta_u = (1._wp-ztmp1) * (ztmp0/(1._wp+ztmp2/(-zu/(zi0*0.004_wp*Beta0**3)))) & ! BRN < 0 & + ztmp1 * (ztmp0*(1._wp + 27._wp/9._wp*ztmp2/ztmp0)) ! BRN > 0 !#LB: should make sure that the "ztmp0" of "27./9.*ztmp2/ztmp0" 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_coare(zeta_u)) u_star = MAX ( U_blk*vkarmn/(LOG(zu) - LOG(z0) - psi_m_coare(zeta_u)) , 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) zeta_t = zt*zeta_u/zu 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_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 !! 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] ztmp0 = SIGN( MIN(ABS(ztmp0),200._wp), ztmp0 ) ! (prevents FPE from stupid values from masked region later on...) ztmp1 = u_star*u_star ! u*^2 !! Update wind at zu with convection-related wind gustiness in unstable conditions (Fairall et al. 2003, Eq.8): ztmp2 = Beta0*Beta0*ztmp1*(MAX(-zi0*ztmp0/vkarmn,0._wp))**(2._wp/3._wp) ! square of wind gustiness contribution, ztmp2 == Ug^2 !! ! 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. !! Stability parameters: zeta_u = zu*ztmp0 zeta_u = SIGN( MIN(ABS(zeta_u),50.0_wp), zeta_u ) IF( .NOT. l_zt_equal_zu ) THEN zeta_t = zt*ztmp0 zeta_t = SIGN( MIN(ABS(zeta_t),50.0_wp), zeta_t ) ENDIF !! Adjustment the wind at 10m (not needed in the current algo form): !IF( zu \= 10._wp ) U10 = U_zu + u_star/vkarmn*(LOG(10._wp/zu) - psi_m_coare(10._wp*ztmp0) + psi_m_coare(zeta_u)) !! Roughness lengthes z0, z0t (z0q = z0t) : ztmp2 = u_star/vkarmn*LOG(10./z0) ! Neutral wind speed at 10m z0 = alfa_charn_3p0(ztmp2)*ztmp1/grav + 0.11_wp*znu_a/u_star ! Roughness length (eq.6) [ ztmp1==u*^2 ] z0 = MIN( MAX(ABS(z0), 1.E-9) , 1._wp ) ! (prevents FPE from stupid values from masked region later on) ztmp1 = ( znu_a / (z0*u_star) )**0.6_wp ! (1./Re_r)^0.72 (Re_r: roughness Reynolds number) COARE3.6-specific! z0t = MIN( 1.1E-4_wp , 5.5E-5_wp*ztmp1 ) ! Scalar roughness for both theta and q (eq.28) #LB: some use 1.15 not 1.1 !!! z0t = MIN( MAX(ABS(z0t), 1.E-9) , 1._wp ) ! (prevents FPE from stupid values from masked region later on) !! Turbulent scales at zu : ztmp0 = psi_h_coare(zeta_u) ztmp1 = vkarmn/(LOG(zu) - LOG(z0t) - ztmp0) ! #LB: in ztmp0, some use psi_h_coare(zeta_t) rather than psi_h_coare(zeta_t) ??? t_star = dt_zu*ztmp1 q_star = dq_zu*ztmp1 u_star = MAX( U_blk*vkarmn/(LOG(zu) - LOG(z0) - psi_m_coare(zeta_u)) , 1.E-9 ) ! (MAX => prevents FPE from stupid values from masked region later on) IF( .NOT. l_zt_equal_zu ) THEN !! Re-updating temperature and humidity at zu if zt /= zu : ztmp1 = LOG(zt/zu) + ztmp0 - psi_h_coare(zeta_t) t_zu = t_zt - t_star/vkarmn*ztmp1 q_zu = q_zt - q_star/vkarmn*ztmp1 ENDIF 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, zeta_u, Qlat=ztmp2) ! Qnsol -> ztmp1 / Tau -> zeta_u CALL CS_COARE( Qsw, ztmp1, u_star, zsst, ztmp2 ) ! ! Qnsol -> ztmp1 / Qlat -> ztmp2 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, zeta_u) ! Qnsol -> ztmp1 / Tau -> zeta_u !! In WL_COARE or , Tau_ac and Qnt_ac must be updated at the final itteration step => add a flag to do this! CALL WL_COARE( Qsw, ztmp1, zeta_u, zsst, MOD(nb_itt,j_itt) ) !! 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 ! 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 ) 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_coare3p0 FUNCTION alfa_charn_3p0( pwnd ) !!------------------------------------------------------------------- !! Compute the Charnock parameter as a function of the wind speed !! !! (Fairall et al., 2003 p.577-578) !! !! Wind below 10 m/s : alfa = 0.011 !! Wind between 10 and 18 m/s : linear increase from 0.011 to 0.018 !! Wind greater than 18 m/s : alfa = 0.018 !! !! Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) !!------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj) :: alfa_charn_3p0 REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pwnd ! wind speed ! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zw, zgt10, zgt18 !!------------------------------------------------------------------- ! DO jj = 1, jpj DO ji = 1, jpi ! zw = pwnd(ji,jj) ! wind speed ! ! Charnock's constant, increases with the wind : zgt10 = 0.5 + SIGN(0.5_wp,(zw - 10)) ! If zw<10. --> 0, else --> 1 zgt18 = 0.5 + SIGN(0.5_wp,(zw - 18.)) ! If zw<18. --> 0, else --> 1 ! alfa_charn_3p0(ji,jj) = (1. - zgt10)*0.011 & ! wind is lower than 10 m/s & + zgt10*((1. - zgt18)*(0.011 + (0.018 - 0.011) & & *(zw - 10.)/(18. - 10.)) + zgt18*( 0.018 ) ) ! Hare et al. (1999) ! END DO END DO ! END FUNCTION alfa_charn_3p0 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://github.com/brodeau/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._wp, 0.35_wp*zta) zstab = 0.5 + SIGN(0.5_wp, 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://github.com/brodeau/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._wp,0.35_wp*zta) zstab = 0.5 + SIGN(0.5_wp, 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 !!====================================================================== END MODULE sbcblk_algo_coare3p0