| 1 | MODULE sbcblk_algo_ecmwf |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE sbcblk_algo_ecmwf *** |
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| 4 | !! Computes: |
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| 5 | !! * bulk transfer coefficients C_D, C_E and C_H |
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| 6 | !! * air temp. and spec. hum. adjusted from zt (2m) to zu (10m) if needed |
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| 7 | !! * the effective bulk wind speed at 10m U_blk |
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| 8 | !! => all these are used in bulk formulas in sbcblk.F90 |
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| 9 | !! |
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| 10 | !! Using the bulk formulation/param. of IFS of ECMWF (cycle 40r1) |
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| 11 | !! based on IFS doc (avaible online on the ECMWF's website) |
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| 12 | !! |
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| 13 | !! Routine turb_ecmwf maintained and developed in AeroBulk |
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| 14 | !! (https://github.com/brodeau/aerobulk) |
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| 15 | !! |
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| 16 | !! ** Author: L. Brodeau, June 2019 / AeroBulk (https://github.com/brodeau/aerobulk) |
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| 17 | !!---------------------------------------------------------------------- |
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| 18 | !! History : 4.0 ! 2016-02 (L.Brodeau) Original code |
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| 19 | !!---------------------------------------------------------------------- |
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| 20 | |
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| 21 | !!---------------------------------------------------------------------- |
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| 22 | !! turb_ecmwf : computes the bulk turbulent transfer coefficients |
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| 23 | !! adjusts t_air and q_air from zt to zu m |
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| 24 | !! returns the effective bulk wind speed at 10m |
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| 25 | !!---------------------------------------------------------------------- |
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| 26 | USE oce ! ocean dynamics and tracers |
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| 27 | USE dom_oce ! ocean space and time domain |
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| 28 | USE phycst ! physical constants |
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| 29 | USE iom ! I/O manager library |
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| 30 | USE lib_mpp ! distribued memory computing library |
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| 31 | USE in_out_manager ! I/O manager |
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| 32 | USE prtctl ! Print control |
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| 33 | USE sbcwave, ONLY : cdn_wave ! wave module |
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| 34 | #if defined key_si3 || defined key_cice |
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| 35 | USE sbc_ice ! Surface boundary condition: ice fields |
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| 36 | #endif |
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| 37 | USE lib_fortran ! to use key_nosignedzero |
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| 38 | |
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| 39 | USE sbc_oce ! Surface boundary condition: ocean fields |
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| 40 | USE sbcblk_phy ! all thermodynamics functions, rho_air, q_sat, etc... !LB |
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| 41 | USE sbcblk_skin ! cool-skin/warm layer scheme (CSWL_ECMWF) !LB |
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| 42 | |
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| 43 | IMPLICIT NONE |
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| 44 | PRIVATE |
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| 45 | |
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| 46 | PUBLIC :: TURB_ECMWF ! called by sbcblk.F90 |
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| 47 | |
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| 48 | ! !! ECMWF own values for given constants, taken form IFS documentation... |
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| 49 | REAL(wp), PARAMETER :: charn0 = 0.018 ! Charnock constant (pretty high value here !!! |
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| 50 | ! ! => Usually 0.011 for moderate winds) |
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| 51 | REAL(wp), PARAMETER :: zi0 = 1000. ! scale height of the atmospheric boundary layer...1 |
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| 52 | REAL(wp), PARAMETER :: Beta0 = 1. ! gustiness parameter ( = 1.25 in COAREv3) |
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| 53 | REAL(wp), PARAMETER :: alpha_M = 0.11 ! For roughness length (smooth surface term) |
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| 54 | REAL(wp), PARAMETER :: alpha_H = 0.40 ! (Chapter 3, p.34, IFS doc Cy31r1) |
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| 55 | REAL(wp), PARAMETER :: alpha_Q = 0.62 ! |
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| 56 | |
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| 57 | INTEGER , PARAMETER :: nb_itt = 5 ! number of itterations |
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| 58 | |
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| 59 | !!---------------------------------------------------------------------- |
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| 60 | CONTAINS |
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| 61 | |
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| 62 | SUBROUTINE TURB_ECMWF( zt, zu, T_s, t_zt, q_s, q_zt, U_zu, & |
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| 63 | & Cd, Ch, Ce, t_zu, q_zu, U_blk, & |
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| 64 | & Cdn, Chn, Cen, & |
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| 65 | & Qsw, rad_lw, slp ) |
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| 66 | !!---------------------------------------------------------------------------------- |
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| 67 | !! *** ROUTINE turb_ecmwf *** |
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| 68 | !! |
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| 69 | !! ** Purpose : Computes turbulent transfert coefficients of surface |
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| 70 | !! fluxes according to IFS doc. (cycle 40) |
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| 71 | !! If relevant (zt /= zu), adjust temperature and humidity from height zt to zu |
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| 72 | !! Returns the effective bulk wind speed at 10m to be used in the bulk formulas |
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| 73 | !! |
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| 74 | !! Applies the cool-skin warm-layer correction of the SST to T_s |
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| 75 | !! if the net shortwave flux at the surface (Qsw), the downwelling longwave |
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| 76 | !! radiative fluxes at the surface (rad_lw), and the sea-leve pressure (slp) |
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| 77 | !! are provided as (optional) arguments! |
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| 78 | !! |
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| 79 | !! INPUT : |
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| 80 | !! ------- |
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| 81 | !! * zt : height for temperature and spec. hum. of air [m] |
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| 82 | !! * zu : height for wind speed (generally 10m) [m] |
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| 83 | !! * U_zu : scalar wind speed at 10m [m/s] |
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| 84 | !! * t_zt : potential air temperature at zt [K] |
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| 85 | !! * q_zt : specific humidity of air at zt [kg/kg] |
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| 86 | !! |
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| 87 | !! INPUT/OUTPUT: |
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| 88 | !! ------------- |
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| 89 | !! * T_s : SST or skin temperature [K] |
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| 90 | !! * q_s : SSQ aka saturation specific humidity at temp. T_s [kg/kg] |
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| 91 | !! -> doesn't need to be given a value if skin temp computed (in case l_use_skin=True) |
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| 92 | !! -> MUST be given the correct value if not computing skint temp. (in case l_use_skin=False) |
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| 93 | !! |
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| 94 | !! OPTIONAL INPUT (will trigger l_use_skin=TRUE if present!): |
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| 95 | !! --------------- |
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| 96 | !! * Qsw : net solar flux (after albedo) at the surface (>0) [W/m^2] |
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| 97 | !! * rad_lw : downwelling longwave radiation at the surface (>0) [W/m^2] |
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| 98 | !! * slp : sea-level pressure [Pa] |
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| 99 | !! |
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| 100 | !! OUTPUT : |
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| 101 | !! -------- |
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| 102 | !! * Cd : drag coefficient |
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| 103 | !! * Ch : sensible heat coefficient |
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| 104 | !! * Ce : evaporation coefficient |
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| 105 | !! * t_zu : pot. air temperature adjusted at wind height zu [K] |
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| 106 | !! * q_zu : specific humidity of air // [kg/kg] |
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| 107 | !! * U_blk : bulk wind speed at 10m [m/s] |
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| 108 | !! |
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| 109 | !! |
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| 110 | !! ** Author: L. Brodeau, June 2019 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 111 | !!---------------------------------------------------------------------------------- |
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| 112 | REAL(wp), INTENT(in ) :: zt ! height for t_zt and q_zt [m] |
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| 113 | REAL(wp), INTENT(in ) :: zu ! height for U_zu [m] |
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| 114 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj) :: T_s ! sea surface temperature [Kelvin] |
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| 115 | REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: t_zt ! potential air temperature [Kelvin] |
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| 116 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj) :: q_s ! sea surface specific humidity [kg/kg] |
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| 117 | REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: q_zt ! specific air humidity at zt [kg/kg] |
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| 118 | REAL(wp), INTENT(in ), DIMENSION(jpi,jpj) :: U_zu ! relative wind module at zu [m/s] |
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| 119 | REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Cd ! transfer coefficient for momentum (tau) |
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| 120 | REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Ch ! transfer coefficient for sensible heat (Q_sens) |
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| 121 | REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Ce ! transfert coefficient for evaporation (Q_lat) |
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| 122 | REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: t_zu ! pot. air temp. adjusted at zu [K] |
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| 123 | REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: q_zu ! spec. humidity adjusted at zu [kg/kg] |
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| 124 | REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: U_blk ! bulk wind at 10m [m/s] |
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| 125 | REAL(wp), INTENT( out), DIMENSION(jpi,jpj) :: Cdn, Chn, Cen ! neutral transfer coefficients |
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| 126 | ! |
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| 127 | REAL(wp), INTENT(in ), OPTIONAL, DIMENSION(jpi,jpj) :: Qsw ! [W/m^2] |
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| 128 | REAL(wp), INTENT(in ), OPTIONAL, DIMENSION(jpi,jpj) :: rad_lw ! [W/m^2] |
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| 129 | REAL(wp), INTENT(in ), OPTIONAL, DIMENSION(jpi,jpj) :: slp ! [Pa] |
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| 130 | ! |
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| 131 | INTEGER :: j_itt |
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| 132 | LOGICAL :: l_zt_equal_zu = .FALSE. ! if q and t are given at same height as U |
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| 133 | ! |
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| 134 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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| 135 | & u_star, t_star, q_star, & |
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| 136 | & dt_zu, dq_zu, & |
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| 137 | & znu_a, & !: Nu_air, Viscosity of air |
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| 138 | & Linv, & !: 1/L (inverse of Monin Obukhov length... |
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| 139 | & z0, z0t, z0q |
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| 140 | ! |
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| 141 | ! Cool skin: |
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| 142 | LOGICAL :: l_use_skin = .FALSE. |
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| 143 | REAL(wp), DIMENSION(jpi,jpj) :: zsst ! to back up the initial bulk SST |
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| 144 | ! |
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| 145 | REAL(wp), DIMENSION(jpi,jpj) :: func_m, func_h |
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| 146 | REAL(wp), DIMENSION(jpi,jpj) :: ztmp0, ztmp1, ztmp2 |
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| 147 | !!---------------------------------------------------------------------------------- |
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| 148 | |
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| 149 | ! Cool skin ? |
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| 150 | IF( PRESENT(Qsw) .AND. PRESENT(rad_lw) .AND. PRESENT(slp) ) THEN |
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| 151 | l_use_skin = .TRUE. |
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| 152 | END IF |
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| 153 | IF (lwp) PRINT *, ' *** LOLO(sbcblk_algo_ecmwf.F90) => l_use_skin =', l_use_skin |
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| 154 | |
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| 155 | ! Identical first gess as in COARE, with IFS parameter values though... |
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| 156 | ! |
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| 157 | l_zt_equal_zu = .FALSE. |
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| 158 | IF( ABS(zu - zt) < 0.01 ) l_zt_equal_zu = .TRUE. ! testing "zu == zt" is risky with double precision |
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| 159 | |
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| 160 | !! Initialization for cool skin: |
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| 161 | IF( l_use_skin ) THEN |
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| 162 | zsst = T_s ! save the bulk SST |
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| 163 | T_s = T_s - 0.25 ! First guess of correction |
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| 164 | q_s = rdct_qsat_salt*q_sat(MAX(T_s, 200._wp), slp) ! First guess of q_s |
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| 165 | END IF |
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| 166 | |
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| 167 | !! First guess of temperature and humidity at height zu: |
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| 168 | t_zu = MAX( t_zt , 180._wp ) ! who knows what's given on masked-continental regions... |
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| 169 | q_zu = MAX( q_zt , 1.e-6_wp ) ! " |
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| 170 | |
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| 171 | !! Pot. temp. difference (and we don't want it to be 0!) |
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| 172 | dt_zu = t_zu - T_s ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) |
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| 173 | dq_zu = q_zu - q_s ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) |
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| 174 | |
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| 175 | znu_a = visc_air(t_zu) ! Air viscosity (m^2/s) at zt given from temperature in (K) |
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| 176 | |
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| 177 | ztmp2 = 0.5_wp*0.5_wp ! initial guess for wind gustiness contribution |
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| 178 | U_blk = SQRT(U_zu*U_zu + ztmp2) |
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| 179 | |
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| 180 | ztmp2 = 10000._wp ! optimization: ztmp2 == 1/z0 (with z0 first guess == 0.0001) |
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| 181 | ztmp0 = LOG(zu*ztmp2) |
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| 182 | ztmp1 = LOG(10.*ztmp2) |
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| 183 | u_star = 0.035_wp*U_blk*ztmp1/ztmp0 ! (u* = 0.035*Un10) |
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| 184 | |
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| 185 | z0 = charn0*u_star*u_star/grav + 0.11_wp*znu_a/u_star |
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| 186 | z0 = MIN(ABS(z0), 0.001_wp) ! (prevent FPE from stupid values from masked region later on...) !#LOLO |
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| 187 | z0t = 1._wp / ( 0.1_wp*EXP(vkarmn/(0.00115/(vkarmn/ztmp1))) ) |
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| 188 | z0t = MIN(ABS(z0t), 0.001_wp) ! (prevent FPE from stupid values from masked region later on...) !#LOLO |
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| 189 | |
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| 190 | ztmp2 = vkarmn/ztmp0 |
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| 191 | Cd = ztmp2*ztmp2 ! first guess of Cd |
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| 192 | |
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| 193 | ztmp0 = vkarmn*vkarmn/LOG(zt/z0t)/Cd |
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| 194 | |
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| 195 | ztmp2 = Ri_bulk( zu, T_s, t_zu, q_s, q_zu, U_blk ) ! Bulk Richardson Number (BRN) |
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| 196 | |
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| 197 | !! First estimate of zeta_u, depending on the stability, ie sign of BRN (ztmp2): |
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| 198 | ztmp1 = 0.5 + SIGN( 0.5_wp , ztmp2 ) |
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| 199 | func_m = ztmp0*ztmp2 ! temporary array !! |
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| 200 | 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 |
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| 201 | & + ztmp1 * (func_m*(1._wp + 27._wp/9._wp*ztmp2/func_m)) ! BRN > 0 |
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| 202 | !#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" ! |
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| 203 | |
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| 204 | !! First guess M-O stability dependent scaling params.(u*,t*,q*) to estimate z0 and z/L |
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| 205 | ztmp0 = vkarmn/(LOG(zu/z0t) - psi_h_ecmwf(func_h)) |
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| 206 | |
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| 207 | u_star = U_blk*vkarmn/(LOG(zu) - LOG(z0) - psi_m_ecmwf(func_h)) |
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| 208 | t_star = dt_zu*ztmp0 |
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| 209 | q_star = dq_zu*ztmp0 |
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| 210 | |
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| 211 | ! What's need to be done if zt /= zu: |
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| 212 | IF( .NOT. l_zt_equal_zu ) THEN |
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| 213 | !! First update of values at zu (or zt for wind) |
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| 214 | ztmp0 = psi_h_ecmwf(func_h) - psi_h_ecmwf(zt*func_h/zu) ! zt*func_h/zu == zeta_t |
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| 215 | ztmp1 = LOG(zt/zu) + ztmp0 |
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| 216 | t_zu = t_zt - t_star/vkarmn*ztmp1 |
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| 217 | q_zu = q_zt - q_star/vkarmn*ztmp1 |
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| 218 | q_zu = (0.5_wp + SIGN(0.5_wp,q_zu))*q_zu !Makes it impossible to have negative humidity : |
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| 219 | ! |
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| 220 | dt_zu = t_zu - T_s ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) |
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| 221 | dq_zu = q_zu - q_s ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) |
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| 222 | END IF |
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| 223 | |
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| 224 | |
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| 225 | !! => that was same first guess as in COARE... |
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| 226 | |
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| 227 | |
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| 228 | !! First guess of inverse of Monin-Obukov length (1/L) : |
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| 229 | Linv = One_on_L( t_zu, q_zu, u_star, t_star, q_star ) |
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| 230 | |
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| 231 | !! Functions such as u* = U_blk*vkarmn/func_m |
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| 232 | ztmp0 = zu*Linv |
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| 233 | func_m = LOG(zu) - LOG(z0) - psi_m_ecmwf(ztmp0) + psi_m_ecmwf( z0*Linv) |
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| 234 | func_h = LOG(zu) - LOG(z0t) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(z0t*Linv) |
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| 235 | |
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| 236 | !! ITERATION BLOCK |
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| 237 | DO j_itt = 1, nb_itt |
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| 238 | |
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| 239 | !! Bulk Richardson Number at z=zu (Eq. 3.25) |
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| 240 | ztmp0 = Ri_bulk( zu, T_s, t_zu, q_s, q_zu, U_blk ) ! Bulk Richardson Number (BRN) |
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| 241 | |
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| 242 | !! New estimate of the inverse of the Monin-Obukhon length (Linv == zeta/zu) : |
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| 243 | Linv = ztmp0*func_m*func_m/func_h / zu ! From Eq. 3.23, Chap.3.2.3, IFS doc - Cy40r1 |
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| 244 | !! Note: it is slightly different that the L we would get with the usual |
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| 245 | Linv = SIGN( MIN(ABS(Linv),200._wp), Linv ) ! (prevent FPE from stupid values from masked region later on...) !#LOLO |
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| 246 | |
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| 247 | !! Update func_m with new Linv: |
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| 248 | 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! |
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| 249 | |
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| 250 | !! Need to update roughness lengthes: |
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| 251 | u_star = U_blk*vkarmn/func_m |
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| 252 | ztmp2 = u_star*u_star |
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| 253 | ztmp1 = znu_a/u_star |
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| 254 | z0 = MIN( ABS( alpha_M*ztmp1 + charn0*ztmp2/grav ) , 0.001_wp) |
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| 255 | z0t = MIN( ABS( alpha_H*ztmp1 ) , 0.001_wp) ! eq.3.26, Chap.3, p.34, IFS doc - Cy31r1 |
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| 256 | z0q = MIN( ABS( alpha_Q*ztmp1 ) , 0.001_wp) |
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| 257 | |
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| 258 | !! Update wind at 10m taking into acount convection-related wind gustiness: |
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| 259 | !! => Chap. 3.2, IFS doc - Cy40r1, Eq.3.17 and Eq.3.18 + Eq.3.8 |
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| 260 | ! Only true when unstable (L<0) => when ztmp0 < 0 => - !!! |
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| 261 | 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) |
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| 262 | !! => equivalent using Beta=1 (gustiness parameter, 1.25 for COARE, also zi0=600 in COARE..) |
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| 263 | U_blk = MAX( SQRT(U_zu*U_zu + ztmp2) , 0.2_wp ) ! eq.3.17, Chap.3, p.32, IFS doc - Cy31r1 |
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| 264 | ! => 0.2 prevents U_blk to be 0 in stable case when U_zu=0. |
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| 265 | |
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| 266 | |
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| 267 | !! Need to update "theta" and "q" at zu in case they are given at different heights |
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| 268 | !! as well the air-sea differences: |
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| 269 | IF( .NOT. l_zt_equal_zu ) THEN |
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| 270 | !! Arrays func_m and func_h are free for a while so using them as temporary arrays... |
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| 271 | func_h = psi_h_ecmwf(zu*Linv) ! temporary array !!! |
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| 272 | func_m = psi_h_ecmwf(zt*Linv) ! temporary array !!! |
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| 273 | |
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| 274 | ztmp2 = psi_h_ecmwf(z0t*Linv) |
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| 275 | ztmp0 = func_h - ztmp2 |
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| 276 | ztmp1 = vkarmn/(LOG(zu) - LOG(z0t) - ztmp0) |
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| 277 | t_star = dt_zu*ztmp1 |
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| 278 | ztmp2 = ztmp0 - func_m + ztmp2 |
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| 279 | ztmp1 = LOG(zt/zu) + ztmp2 |
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| 280 | t_zu = t_zt - t_star/vkarmn*ztmp1 |
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| 281 | |
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| 282 | ztmp2 = psi_h_ecmwf(z0q*Linv) |
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| 283 | ztmp0 = func_h - ztmp2 |
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| 284 | ztmp1 = vkarmn/(LOG(zu) - LOG(z0q) - ztmp0) |
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| 285 | q_star = dq_zu*ztmp1 |
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| 286 | ztmp2 = ztmp0 - func_m + ztmp2 |
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| 287 | ztmp1 = LOG(zt/zu) + ztmp2 |
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| 288 | q_zu = q_zt - q_star/vkarmn*ztmp1 |
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| 289 | END IF |
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| 290 | |
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| 291 | !! Updating because of updated z0 and z0t and new Linv... |
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| 292 | ztmp0 = zu*Linv |
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| 293 | func_m = log(zu) - LOG(z0 ) - psi_m_ecmwf(ztmp0) + psi_m_ecmwf(z0 *Linv) |
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| 294 | func_h = log(zu) - LOG(z0t) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(z0t*Linv) |
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| 295 | |
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| 296 | !! SKIN related part |
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| 297 | !! ----------------- |
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| 298 | IF( l_use_skin ) THEN |
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| 299 | !! compute transfer coefficients at zu : lolo: verifier... |
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| 300 | Ch = vkarmn*vkarmn/(func_m*func_h) |
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| 301 | ztmp1 = LOG(zu) - LOG(z0q) - psi_h_ecmwf(ztmp0) + psi_h_ecmwf(z0q*Linv) ! func_q |
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| 302 | Ce = vkarmn*vkarmn/(func_m*ztmp1) |
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| 303 | ! Non-Solar heat flux to the ocean: |
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| 304 | ztmp1 = U_blk*MAX(rho_air(t_zu, q_zu, slp), 1._wp) ! rho*U10 |
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| 305 | ztmp2 = T_s*T_s |
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| 306 | ztmp1 = ztmp1 * ( Ce*rLevap*(q_zu - q_s) + Ch*rCp_dry*(t_zu - T_s) ) & ! Total turb. heat flux |
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| 307 | & + (rad_lw - emiss_w*stefan*ztmp2*ztmp2) ! Net longwave flux |
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| 308 | !! Updating the values of the skin temperature T_s and q_s : |
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| 309 | CALL CSWL_ECMWF( Qsw, ztmp1, u_star, zsst, T_s ) |
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| 310 | 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 |
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| 311 | END IF |
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| 312 | |
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| 313 | IF( (l_use_skin).OR.(.NOT. l_zt_equal_zu) ) THEN |
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| 314 | dt_zu = t_zu - T_s ; dt_zu = SIGN( MAX(ABS(dt_zu),1.E-6_wp), dt_zu ) |
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| 315 | dq_zu = q_zu - q_s ; dq_zu = SIGN( MAX(ABS(dq_zu),1.E-9_wp), dq_zu ) |
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| 316 | END IF |
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| 317 | |
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| 318 | END DO !DO j_itt = 1, nb_itt |
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| 319 | |
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| 320 | Cd = vkarmn*vkarmn/(func_m*func_m) |
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| 321 | Ch = vkarmn*vkarmn/(func_m*func_h) |
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| 322 | ztmp2 = log(zu/z0q) - psi_h_ecmwf(zu*Linv) + psi_h_ecmwf(z0q*Linv) ! func_q |
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| 323 | Ce = vkarmn*vkarmn/(func_m*ztmp2) |
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| 324 | |
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| 325 | Cdn = vkarmn*vkarmn / (log(zu/z0 )*log(zu/z0 )) |
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| 326 | Chn = vkarmn*vkarmn / (log(zu/z0t)*log(zu/z0t)) |
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| 327 | Cen = vkarmn*vkarmn / (log(zu/z0q)*log(zu/z0q)) |
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| 328 | |
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| 329 | END SUBROUTINE TURB_ECMWF |
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| 330 | |
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| 331 | |
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| 332 | FUNCTION psi_m_ecmwf( pzeta ) |
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| 333 | !!---------------------------------------------------------------------------------- |
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| 334 | !! Universal profile stability function for momentum |
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| 335 | !! ECMWF / as in IFS cy31r1 documentation, available online |
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| 336 | !! at ecmwf.int |
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| 337 | !! |
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| 338 | !! pzeta : stability paramenter, z/L where z is altitude measurement |
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| 339 | !! and L is M-O length |
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| 340 | !! |
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| 341 | !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 342 | !!---------------------------------------------------------------------------------- |
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| 343 | REAL(wp), DIMENSION(jpi,jpj) :: psi_m_ecmwf |
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| 344 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta |
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| 345 | ! |
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| 346 | INTEGER :: ji, jj ! dummy loop indices |
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| 347 | REAL(wp) :: zzeta, zx, ztmp, psi_unst, psi_stab, stab |
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| 348 | !!---------------------------------------------------------------------------------- |
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| 349 | ! |
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| 350 | DO jj = 1, jpj |
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| 351 | DO ji = 1, jpi |
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| 352 | ! |
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| 353 | zzeta = MIN( pzeta(ji,jj) , 5._wp ) !! Very stable conditions (L positif and big!): |
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| 354 | ! |
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| 355 | ! Unstable (Paulson 1970): |
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| 356 | ! eq.3.20, Chap.3, p.33, IFS doc - Cy31r1 |
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| 357 | zx = SQRT(ABS(1._wp - 16._wp*zzeta)) |
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| 358 | ztmp = 1._wp + SQRT(zx) |
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| 359 | ztmp = ztmp*ztmp |
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| 360 | psi_unst = LOG( 0.125_wp*ztmp*(1._wp + zx) ) & |
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| 361 | & -2._wp*ATAN( SQRT(zx) ) + 0.5_wp*rpi |
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| 362 | ! |
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| 363 | ! Unstable: |
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| 364 | ! eq.3.22, Chap.3, p.33, IFS doc - Cy31r1 |
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| 365 | psi_stab = -2._wp/3._wp*(zzeta - 5._wp/0.35_wp)*EXP(-0.35_wp*zzeta) & |
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| 366 | & - zzeta - 2._wp/3._wp*5._wp/0.35_wp |
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| 367 | ! |
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| 368 | ! Combining: |
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| 369 | stab = 0.5_wp + SIGN(0.5_wp, zzeta) ! zzeta > 0 => stab = 1 |
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| 370 | ! |
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| 371 | psi_m_ecmwf(ji,jj) = (1._wp - stab) * psi_unst & ! (zzeta < 0) Unstable |
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| 372 | & + stab * psi_stab ! (zzeta > 0) Stable |
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| 373 | ! |
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| 374 | END DO |
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| 375 | END DO |
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| 376 | ! |
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| 377 | END FUNCTION psi_m_ecmwf |
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| 378 | |
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| 379 | |
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| 380 | FUNCTION psi_h_ecmwf( pzeta ) |
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| 381 | !!---------------------------------------------------------------------------------- |
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| 382 | !! Universal profile stability function for temperature and humidity |
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| 383 | !! ECMWF / as in IFS cy31r1 documentation, available online |
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| 384 | !! at ecmwf.int |
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| 385 | !! |
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| 386 | !! pzeta : stability paramenter, z/L where z is altitude measurement |
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| 387 | !! and L is M-O length |
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| 388 | !! |
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| 389 | !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 390 | !!---------------------------------------------------------------------------------- |
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| 391 | REAL(wp), DIMENSION(jpi,jpj) :: psi_h_ecmwf |
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| 392 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pzeta |
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| 393 | ! |
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| 394 | INTEGER :: ji, jj ! dummy loop indices |
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| 395 | REAL(wp) :: zzeta, zx, psi_unst, psi_stab, stab |
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| 396 | !!---------------------------------------------------------------------------------- |
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| 397 | ! |
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| 398 | DO jj = 1, jpj |
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| 399 | DO ji = 1, jpi |
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| 400 | ! |
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| 401 | zzeta = MIN(pzeta(ji,jj) , 5._wp) ! Very stable conditions (L positif and big!): |
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| 402 | ! |
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| 403 | zx = ABS(1._wp - 16._wp*zzeta)**.25 ! this is actually (1/phi_m)**2 !!! |
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| 404 | ! ! eq.3.19, Chap.3, p.33, IFS doc - Cy31r1 |
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| 405 | ! Unstable (Paulson 1970) : |
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| 406 | psi_unst = 2._wp*LOG(0.5_wp*(1._wp + zx*zx)) ! eq.3.20, Chap.3, p.33, IFS doc - Cy31r1 |
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| 407 | ! |
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| 408 | ! Stable: |
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| 409 | 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 |
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| 410 | & - ABS(1._wp + 2._wp/3._wp*zzeta)**1.5_wp - 2._wp/3._wp*5._wp/0.35_wp + 1._wp |
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| 411 | ! LB: added ABS() to avoid NaN values when unstable, which contaminates the unstable solution... |
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| 412 | ! |
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| 413 | stab = 0.5_wp + SIGN(0.5_wp, zzeta) ! zzeta > 0 => stab = 1 |
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| 414 | ! |
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| 415 | ! |
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| 416 | psi_h_ecmwf(ji,jj) = (1._wp - stab) * psi_unst & ! (zzeta < 0) Unstable |
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| 417 | & + stab * psi_stab ! (zzeta > 0) Stable |
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| 418 | ! |
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| 419 | END DO |
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| 420 | END DO |
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| 421 | ! |
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| 422 | END FUNCTION psi_h_ecmwf |
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| 423 | |
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| 424 | |
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| 425 | |
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| 426 | |
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| 427 | |
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| 428 | !!====================================================================== |
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| 429 | END MODULE sbcblk_algo_ecmwf |
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