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new expression to compute air and surface potential temperatures in bulk formulae (old ticket #2632)
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sbcblk_algo_coare3p0.F90 26.49 KiB
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 Ubzu
!! => 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
!! 4.2 ! 2020-12 (L. Brodeau) Introduction of various air-ice bulk parameterizations + improvements
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! 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 sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer
USE sbcblk_skin_coare ! cool-skin/warm layer scheme (CSWL_ECMWF) !LB
IMPLICIT NONE
PRIVATE
PUBLIC :: SBCBLK_ALGO_COARE3P0_INIT, TURB_COARE3P0
!! * Substitutions
# include "do_loop_substitute.h90"
!! 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
REAL(wp), PARAMETER :: zeta_abs_max = 50._wp
!!----------------------------------------------------------------------
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, Ubzu, &
& nb_iter, Cdn, Chn, Cen, & ! optional output
& 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]
!! * Ubzu : 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) :: Ubzu ! bulk wind speed at zu [m/s]
!
INTEGER , INTENT(in ), OPTIONAL :: nb_iter ! number of iterations
REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: CdN
REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: ChN
REAL(wp), INTENT( out), OPTIONAL, DIMENSION(jpi,jpj) :: CeN
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 :: nbit, jit
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(jpi,jpj) :: zpre, zrhoa, zta ! air pressure [Pa], density [kg/m3] & absolute temperature [k]
!
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)
nbit = nb_iter0
IF( PRESENT(nb_iter) ) nbit = nb_iter
l_zt_equal_zu = ( ABS(zu - zt) < 0.01_wp ) ! 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)
Ubzu = 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*Ubzu*ztmp1/ztmp0 ! (u* = 0.035*Un10)
z0 = charn_coare3p0(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 = MAX( (vkarmn/ztmp0)**2 , Cx_min ) ! first guess of Cd
ztmp0 = vkarmn2/LOG(zt/z0t)/Cd
ztmp2 = Ri_bulk( zu, T_s, t_zu, q_s, q_zu, Ubzu ) ! 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 )
zeta_u = (1._wp - ztmp1) * ztmp0*ztmp2 / (1._wp - ztmp2*zi0*0.004_wp*Beta0**3/zu) & ! BRN < 0
& + ztmp1 * ( ztmp0*ztmp2 + 27._wp/9._wp*ztmp2*ztmp2 ) ! BRN > 0
!! 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 ( Ubzu*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 jit = 1, nbit
!!Inverse of Obukov length (1/L) :
ztmp0 = One_on_L(t_zu, q_zu, u_star, t_star, q_star) ! 1/L == 1/[Obukhov length]
ztmp0 = SIGN( MIN(ABS(ztmp0),200._wp), ztmp0 ) ! 1/L (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
Ubzu = MAX(SQRT(U_zu*U_zu + ztmp2), 0.2_wp) ! include gustiness in bulk wind speed
! => 0.2 prevents Ubzu to be 0 in stable case when U_zu=0.
!! Stability parameters:
zeta_u = zu*ztmp0
zeta_u = SIGN( MIN(ABS(zeta_u),zeta_abs_max), zeta_u )
IF( .NOT. l_zt_equal_zu ) THEN
zeta_t = zt*ztmp0
zeta_t = SIGN( MIN(ABS(zeta_t),zeta_abs_max), 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 = charn_coare3p0(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( Ubzu*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 ).OR.( l_use_wl )) THEN
zpre(:,:) = pres_temp( q_zu(:,:), slp(:,:), zu, ptpot=t_zu(:,:), pta=zta(:,:) )
zrhoa(:,:) = rho_air( zta(:,:), q_zu(:,:), zpre(:,:) )
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, Ubzu, slp, rad_lw, zrhoa, &
& 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, Ubzu, slp, rad_lw, zrhoa, &
& 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(nbit,jit) )
!! 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 jit = 1, nbit
! compute transfer coefficients at zu :
ztmp0 = u_star/Ubzu
Cd = MAX( ztmp0*ztmp0 , Cx_min )
Ch = MAX( ztmp0*t_star/dt_zu , Cx_min )
Ce = MAX( ztmp0*q_star/dq_zu , Cx_min )
IF( .NOT. l_zt_equal_zu ) DEALLOCATE( zeta_t )
IF(PRESENT(Cdn)) Cdn = MAX( vkarmn2 / (LOG(zu/z0 )*LOG(zu/z0 )) , Cx_min )
IF(PRESENT(Chn)) Chn = MAX( vkarmn2 / (LOG(zu/z0t)*LOG(zu/z0t)) , Cx_min )
IF(PRESENT(Cen)) Cen = MAX( vkarmn2 / (LOG(zu/z0t)*LOG(zu/z0t)) , Cx_min )
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 charn_coare3p0( 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) :: charn_coare3p0
REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pwnd ! wind speed
!
INTEGER :: ji, jj ! dummy loop indices
REAL(wp) :: zw, zgt10, zgt18
!!-------------------------------------------------------------------
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
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
!
charn_coare3p0(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_2D
END FUNCTION charn_coare3p0
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_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
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_2D
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_2D( nn_hls, nn_hls, nn_hls, nn_hls )
!
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_2D
END FUNCTION psi_h_coare
!!======================================================================
END MODULE sbcblk_algo_coare3p0