[12015] | 1 | MODULE sbcblk_phy |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE sbcblk_phy *** |
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| 4 | !! A set of functions to compute air themodynamics parameters |
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| 5 | !! needed by Aerodynamic Bulk Formulas |
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| 6 | !!===================================================================== |
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| 7 | !! 4.0 ! 2019 L. Brodeau from AeroBulk package (https://github.com/brodeau/aerobulk/) |
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| 8 | !!---------------------------------------------------------------------- |
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| 9 | |
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| 10 | !! virt_temp : virtual (aka sensible) temperature (potential or absolute) |
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| 11 | !! rho_air : density of (moist) air (depends on T_air, q_air and SLP |
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| 12 | !! visc_air : kinematic viscosity (aka Nu_air) of air from temperature |
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| 13 | !! L_vap : latent heat of vaporization of water as a function of temperature |
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| 14 | !! cp_air : specific heat of (moist) air (depends spec. hum. q_air) |
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| 15 | !! gamma_moist : adiabatic lapse-rate of moist air |
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| 16 | !! One_on_L : 1. / ( Monin-Obukhov length ) |
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| 17 | !! Ri_bulk : bulk Richardson number aka BRN |
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| 18 | !! q_sat : saturation humidity as a function of SLP and temperature |
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| 19 | !! q_air_rh : specific humidity as a function of RH (fraction, not %), t_air and SLP |
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| 20 | |
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| 21 | USE dom_oce ! ocean space and time domain |
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| 22 | USE phycst ! physical constants |
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| 23 | |
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| 24 | IMPLICIT NONE |
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| 25 | PRIVATE |
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| 26 | |
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| 27 | !! (mainly removed from sbcblk.F90) |
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| 28 | REAL(wp), PARAMETER, PUBLIC :: rCp_dry = 1005.0_wp !: Specic heat of dry air, constant pressure [J/K/kg] |
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| 29 | REAL(wp), PARAMETER, PUBLIC :: rCp_vap = 1860.0_wp !: Specic heat of water vapor, constant pressure [J/K/kg] |
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| 30 | REAL(wp), PARAMETER, PUBLIC :: R_dry = 287.05_wp !: Specific gas constant for dry air [J/K/kg] |
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| 31 | REAL(wp), PARAMETER, PUBLIC :: R_vap = 461.495_wp !: Specific gas constant for water vapor [J/K/kg] |
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| 32 | REAL(wp), PARAMETER, PUBLIC :: reps0 = R_dry/R_vap !: ratio of gas constant for dry air and water vapor => ~ 0.622 |
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| 33 | REAL(wp), PARAMETER, PUBLIC :: rctv0 = R_vap/R_dry !: for virtual temperature (== (1-eps)/eps) => ~ 0.608 |
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| 34 | REAL(wp), PARAMETER, PUBLIC :: rCp_air = 1000.5_wp !: specific heat of air (only used for ice fluxes now...) |
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| 35 | REAL(wp), PARAMETER, PUBLIC :: rCd_ice = 1.4e-3_wp !: transfer coefficient over ice |
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| 36 | REAL(wp), PARAMETER, PUBLIC :: albo = 0.066_wp !: ocean albedo assumed to be constant |
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| 37 | ! |
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| 38 | REAL(wp), PARAMETER, PUBLIC :: rho0_a = 1.2_wp !: Approx. of density of air [kg/m^3] |
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| 39 | REAL(wp), PARAMETER, PUBLIC :: rho0_w = 1025._wp !: Density of sea-water (ECMWF->1025) [kg/m^3] |
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| 40 | REAL(wp), PARAMETER, PUBLIC :: radrw = rho0_a/rho0_w !: Density ratio |
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| 41 | REAL(wp), PARAMETER, PUBLIC :: sq_radrw = SQRT(rho0_a/rho0_w) |
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| 42 | REAL(wp), PARAMETER, PUBLIC :: rCp0_w = 4190._wp !: Specific heat capacity of seawater (ECMWF 4190) [J/K/kg] |
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| 43 | REAL(wp), PARAMETER, PUBLIC :: rnu0_w = 1.e-6_wp !: kinetic viscosity of water [m^2/s] |
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| 44 | REAL(wp), PARAMETER, PUBLIC :: rk0_w = 0.6_wp !: thermal conductivity of water (at 20C) [W/m/K] |
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| 45 | ! |
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| 46 | REAL(wp), PARAMETER, PUBLIC :: emiss_w = 1._wp !: Surface emissivity (black-body long-wave radiation) of sea-water [] |
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| 47 | ! !: Theoretically close to 0.97! Yet, taken equal as 1 to account for |
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| 48 | ! !: the small fraction of downwelling longwave reflected at the |
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| 49 | ! !: surface (Lind & Katsaros, 1986) |
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| 50 | REAL(wp), PARAMETER, PUBLIC :: rdct_qsat_salt = 0.98_wp !: reduction factor on specific humidity at saturation (q_sat(T_s)) due to salt |
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| 51 | REAL(wp), PARAMETER, PUBLIC :: rtt0 = 273.16_wp !: triple point of temperature [K] |
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| 52 | ! |
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| 53 | REAL(wp), PARAMETER, PUBLIC :: rcst_cs = -16._wp*9.80665_wp*rho0_w*rCp0_w*rnu0_w*rnu0_w*rnu0_w/(rk0_w*rk0_w) !: for cool-skin parameterizations... (grav = 9.80665_wp) |
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| 54 | ! => see eq.(14) in Fairall et al. 1996 (eq.(6) of Zeng aand Beljaars is WRONG! (typo?) |
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| 55 | |
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| 56 | |
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| 57 | INTERFACE gamma_moist |
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| 58 | MODULE PROCEDURE gamma_moist_vctr, gamma_moist_sclr |
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| 59 | END INTERFACE gamma_moist |
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| 60 | |
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| 61 | INTERFACE e_sat |
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| 62 | MODULE PROCEDURE e_sat_vctr, e_sat_sclr |
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| 63 | END INTERFACE e_sat |
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| 64 | |
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| 65 | INTERFACE L_vap |
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| 66 | MODULE PROCEDURE L_vap_vctr, L_vap_sclr |
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| 67 | END INTERFACE L_vap |
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| 68 | |
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| 69 | INTERFACE rho_air |
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| 70 | MODULE PROCEDURE rho_air_vctr, rho_air_sclr |
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| 71 | END INTERFACE rho_air |
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| 72 | |
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| 73 | INTERFACE cp_air |
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| 74 | MODULE PROCEDURE cp_air_vctr, cp_air_sclr |
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| 75 | END INTERFACE cp_air |
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| 76 | |
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| 77 | INTERFACE alpha_sw |
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| 78 | MODULE PROCEDURE alpha_sw_vctr, alpha_sw_sclr |
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| 79 | END INTERFACE alpha_sw |
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| 80 | |
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| 81 | INTERFACE bulk_formula |
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| 82 | MODULE PROCEDURE bulk_formula_vctr, bulk_formula_sclr |
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| 83 | END INTERFACE bulk_formula |
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| 84 | |
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| 85 | |
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| 86 | |
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| 87 | PUBLIC virt_temp |
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| 88 | PUBLIC rho_air |
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| 89 | PUBLIC visc_air |
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| 90 | PUBLIC L_vap |
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| 91 | PUBLIC cp_air |
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| 92 | PUBLIC gamma_moist |
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| 93 | PUBLIC One_on_L |
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| 94 | PUBLIC Ri_bulk |
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| 95 | PUBLIC q_sat |
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| 96 | PUBLIC q_air_rh |
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| 97 | !: |
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| 98 | PUBLIC update_qnsol_tau |
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| 99 | PUBLIC alpha_sw |
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| 100 | PUBLIC bulk_formula |
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| 101 | |
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| 102 | !!---------------------------------------------------------------------- |
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| 103 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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| 104 | !! $Id: sbcblk.F90 10535 2019-01-16 17:36:47Z clem $ |
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| 105 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 106 | !!---------------------------------------------------------------------- |
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| 107 | CONTAINS |
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| 108 | |
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| 109 | FUNCTION virt_temp( pta, pqa ) |
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| 110 | !!------------------------------------------------------------------------ |
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| 111 | !! |
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| 112 | !! Compute the (absolute/potential) virtual temperature, knowing the |
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| 113 | !! (absolute/potential) temperature and specific humidity |
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| 114 | !! |
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| 115 | !! If input temperature is absolute then output vitual temperature is absolute |
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| 116 | !! If input temperature is potential then output vitual temperature is potential |
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| 117 | !! |
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| 118 | !! Author: L. Brodeau, June 2019 / AeroBulk |
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| 119 | !! (https://github.com/brodeau/aerobulk/) |
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| 120 | !!------------------------------------------------------------------------ |
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| 121 | REAL(wp), DIMENSION(jpi,jpj) :: virt_temp !: 1./(Monin Obukhov length) [m^-1] |
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| 122 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pta, & !: absolute or potetntial air temperature [K] |
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| 123 | & pqa !: specific humidity of air [kg/kg] |
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| 124 | !!------------------------------------------------------------------- |
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| 125 | ! |
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| 126 | virt_temp(:,:) = pta(:,:) * (1._wp + rctv0*pqa(:,:)) |
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| 127 | !! |
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| 128 | !! This is exactly the same sing that: |
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| 129 | !! virt_temp = pta * ( pwa + reps0) / (reps0*(1.+pwa)) |
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| 130 | !! with wpa (mixing ration) defined as : pwa = pqa/(1.-pqa) |
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| 131 | ! |
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| 132 | END FUNCTION virt_temp |
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| 133 | |
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| 134 | FUNCTION rho_air_vctr( ptak, pqa, pslp ) |
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| 135 | !!------------------------------------------------------------------------------- |
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| 136 | !! *** FUNCTION rho_air_vctr *** |
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| 137 | !! |
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| 138 | !! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere |
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| 139 | !! |
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| 140 | !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 141 | !!------------------------------------------------------------------------------- |
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| 142 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K] |
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| 143 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg] |
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| 144 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! pressure in [Pa] |
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| 145 | REAL(wp), DIMENSION(jpi,jpj) :: rho_air_vctr ! density of moist air [kg/m^3] |
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| 146 | !!------------------------------------------------------------------------------- |
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| 147 | rho_air_vctr = MAX( pslp / (R_dry*ptak * ( 1._wp + rctv0*pqa )) , 0.8_wp ) |
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| 148 | END FUNCTION rho_air_vctr |
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| 149 | |
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| 150 | FUNCTION rho_air_sclr( ptak, pqa, pslp ) |
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| 151 | !!------------------------------------------------------------------------------- |
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| 152 | !! *** FUNCTION rho_air_sclr *** |
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| 153 | !! |
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| 154 | !! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere |
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| 155 | !! |
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| 156 | !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 157 | !!------------------------------------------------------------------------------- |
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| 158 | REAL(wp), INTENT(in) :: ptak ! air temperature [K] |
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| 159 | REAL(wp), INTENT(in) :: pqa ! air specific humidity [kg/kg] |
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| 160 | REAL(wp), INTENT(in) :: pslp ! pressure in [Pa] |
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| 161 | REAL(wp) :: rho_air_sclr ! density of moist air [kg/m^3] |
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| 162 | !!------------------------------------------------------------------------------- |
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| 163 | rho_air_sclr = MAX( pslp / (R_dry*ptak * ( 1._wp + rctv0*pqa )) , 0.8_wp ) |
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| 164 | END FUNCTION rho_air_sclr |
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| 165 | |
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| 166 | |
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| 167 | |
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| 168 | FUNCTION visc_air(ptak) |
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| 169 | !!---------------------------------------------------------------------------------- |
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| 170 | !! Air kinetic viscosity (m^2/s) given from temperature in degrees... |
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| 171 | !! |
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| 172 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 173 | !!---------------------------------------------------------------------------------- |
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| 174 | REAL(wp), DIMENSION(jpi,jpj) :: visc_air ! |
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| 175 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature in (K) |
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| 176 | ! |
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| 177 | INTEGER :: ji, jj ! dummy loop indices |
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| 178 | REAL(wp) :: ztc, ztc2 ! local scalar |
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| 179 | !!---------------------------------------------------------------------------------- |
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| 180 | ! |
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| 181 | DO jj = 1, jpj |
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| 182 | DO ji = 1, jpi |
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| 183 | ztc = ptak(ji,jj) - rt0 ! air temp, in deg. C |
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| 184 | ztc2 = ztc*ztc |
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| 185 | visc_air(ji,jj) = 1.326e-5*(1. + 6.542E-3*ztc + 8.301e-6*ztc2 - 4.84e-9*ztc2*ztc) |
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| 186 | END DO |
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| 187 | END DO |
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| 188 | ! |
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| 189 | END FUNCTION visc_air |
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| 190 | |
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| 191 | FUNCTION L_vap_vctr( psst ) |
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| 192 | !!--------------------------------------------------------------------------------- |
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| 193 | !! *** FUNCTION L_vap_vctr *** |
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| 194 | !! |
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| 195 | !! ** Purpose : Compute the latent heat of vaporization of water from temperature |
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| 196 | !! |
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| 197 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 198 | !!---------------------------------------------------------------------------------- |
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| 199 | REAL(wp), DIMENSION(jpi,jpj) :: L_vap_vctr ! latent heat of vaporization [J/kg] |
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| 200 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K] |
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| 201 | !!---------------------------------------------------------------------------------- |
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| 202 | ! |
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| 203 | L_vap_vctr = ( 2.501_wp - 0.00237_wp * ( psst(:,:) - rt0) ) * 1.e6_wp |
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| 204 | ! |
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| 205 | END FUNCTION L_vap_vctr |
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| 206 | |
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| 207 | FUNCTION L_vap_sclr( psst ) |
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| 208 | !!--------------------------------------------------------------------------------- |
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| 209 | !! *** FUNCTION L_vap_sclr *** |
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| 210 | !! |
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| 211 | !! ** Purpose : Compute the latent heat of vaporization of water from temperature |
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| 212 | !! |
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| 213 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 214 | !!---------------------------------------------------------------------------------- |
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| 215 | REAL(wp) :: L_vap_sclr ! latent heat of vaporization [J/kg] |
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| 216 | REAL(wp), INTENT(in) :: psst ! water temperature [K] |
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| 217 | !!---------------------------------------------------------------------------------- |
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| 218 | ! |
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| 219 | L_vap_sclr = ( 2.501_wp - 0.00237_wp * ( psst - rt0) ) * 1.e6_wp |
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| 220 | ! |
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| 221 | END FUNCTION L_vap_sclr |
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| 222 | |
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| 223 | |
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| 224 | FUNCTION cp_air_vctr( pqa ) |
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| 225 | !!------------------------------------------------------------------------------- |
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| 226 | !! *** FUNCTION cp_air_vctr *** |
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| 227 | !! |
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| 228 | !! ** Purpose : Compute specific heat (Cp) of moist air |
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| 229 | !! |
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| 230 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 231 | !!------------------------------------------------------------------------------- |
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| 232 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg] |
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| 233 | REAL(wp), DIMENSION(jpi,jpj) :: cp_air_vctr ! specific heat of moist air [J/K/kg] |
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| 234 | !!------------------------------------------------------------------------------- |
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| 235 | cp_air_vctr = rCp_dry + rCp_vap * pqa |
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| 236 | END FUNCTION cp_air_vctr |
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| 237 | |
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| 238 | FUNCTION cp_air_sclr( pqa ) |
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| 239 | !!------------------------------------------------------------------------------- |
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| 240 | !! *** FUNCTION cp_air_sclr *** |
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| 241 | !! |
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| 242 | !! ** Purpose : Compute specific heat (Cp) of moist air |
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| 243 | !! |
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| 244 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 245 | !!------------------------------------------------------------------------------- |
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| 246 | REAL(wp), INTENT(in) :: pqa ! air specific humidity [kg/kg] |
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| 247 | REAL(wp) :: cp_air_sclr ! specific heat of moist air [J/K/kg] |
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| 248 | !!------------------------------------------------------------------------------- |
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| 249 | cp_air_sclr = rCp_dry + rCp_vap * pqa |
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| 250 | END FUNCTION cp_air_sclr |
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| 251 | |
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| 252 | |
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| 253 | |
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| 254 | |
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| 255 | |
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| 256 | FUNCTION gamma_moist_vctr( ptak, pqa ) |
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| 257 | !!---------------------------------------------------------------------------------- |
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| 258 | !! *** FUNCTION gamma_moist_vctr *** |
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| 259 | !! |
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| 260 | !! ** Purpose : Compute the moist adiabatic lapse-rate. |
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| 261 | !! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate |
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| 262 | !! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html |
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| 263 | !! |
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| 264 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 265 | !!---------------------------------------------------------------------------------- |
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| 266 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K] |
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| 267 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity [kg/kg] |
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| 268 | REAL(wp), DIMENSION(jpi,jpj) :: gamma_moist_vctr ! moist adiabatic lapse-rate |
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| 269 | ! |
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| 270 | INTEGER :: ji, jj ! dummy loop indices |
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| 271 | !!---------------------------------------------------------------------------------- |
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| 272 | DO jj = 1, jpj |
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| 273 | DO ji = 1, jpi |
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| 274 | gamma_moist_vctr(ji,jj) = gamma_moist_sclr( ptak(ji,jj), pqa(ji,jj) ) |
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| 275 | END DO |
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| 276 | END DO |
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| 277 | END FUNCTION gamma_moist_vctr |
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| 278 | |
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| 279 | FUNCTION gamma_moist_sclr( ptak, pqa ) |
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| 280 | !!---------------------------------------------------------------------------------- |
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| 281 | !! ** Purpose : Compute the moist adiabatic lapse-rate. |
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| 282 | !! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate |
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| 283 | !! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html |
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| 284 | !! |
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| 285 | !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 286 | !!---------------------------------------------------------------------------------- |
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| 287 | REAL(wp) :: gamma_moist_sclr |
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| 288 | REAL(wp), INTENT(in) :: ptak, pqa ! air temperature (K) and specific humidity (kg/kg) |
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| 289 | ! |
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| 290 | REAL(wp) :: zta, zqa, zwa, ziRT ! local scalar |
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| 291 | !!---------------------------------------------------------------------------------- |
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| 292 | zta = MAX( ptak, 180._wp) ! prevents screw-up over masked regions where field == 0. |
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| 293 | zqa = MAX( pqa, 1.E-6_wp) ! " " " |
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| 294 | !! |
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| 295 | zwa = zqa / (1._wp - zqa) ! w is mixing ratio w = q/(1-q) | q = w/(1+w) |
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| 296 | ziRT = 1._wp / (R_dry*zta) ! 1/RT |
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| 297 | gamma_moist_sclr = grav * ( 1._wp + rLevap*zwa*ziRT ) / ( rCp_dry + rLevap*rLevap*zwa*reps0*ziRT/zta ) |
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| 298 | !! |
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| 299 | END FUNCTION gamma_moist_sclr |
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| 300 | |
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| 301 | FUNCTION One_on_L( ptha, pqa, pus, pts, pqs ) |
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| 302 | !!------------------------------------------------------------------------ |
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| 303 | !! |
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| 304 | !! Evaluates the 1./(Monin Obukhov length) from air temperature and |
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| 305 | !! specific humidity, and frictional scales u*, t* and q* |
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| 306 | !! |
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| 307 | !! Author: L. Brodeau, June 2016 / AeroBulk |
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| 308 | !! (https://github.com/brodeau/aerobulk/) |
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| 309 | !!------------------------------------------------------------------------ |
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| 310 | REAL(wp), DIMENSION(jpi,jpj) :: One_on_L !: 1./(Monin Obukhov length) [m^-1] |
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| 311 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptha, & !: average potetntial air temperature [K] |
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| 312 | & pqa, & !: average specific humidity of air [kg/kg] |
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| 313 | & pus, pts, pqs !: frictional velocity, temperature and humidity |
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| 314 | ! |
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| 315 | INTEGER :: ji, jj ! dummy loop indices |
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| 316 | REAL(wp) :: zqa ! local scalar |
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| 317 | !!------------------------------------------------------------------- |
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| 318 | ! |
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| 319 | DO jj = 1, jpj |
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| 320 | DO ji = 1, jpi |
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| 321 | ! |
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| 322 | zqa = (1._wp + rctv0*pqa(ji,jj)) |
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| 323 | ! |
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| 324 | ! The main concern is to know whether, the vertical turbulent flux of virtual temperature, < u' theta_v' > is estimated with: |
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| 325 | ! a/ -u* [ theta* (1 + 0.61 q) + 0.61 theta q* ] => this is the one that seems correct! chose this one! |
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| 326 | ! or |
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| 327 | ! b/ -u* [ theta* + 0.61 theta q* ] |
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| 328 | ! |
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| 329 | One_on_L(ji,jj) = grav*vkarmn*( pts(ji,jj)*zqa + rctv0*ptha(ji,jj)*pqs(ji,jj) ) & |
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| 330 | & / MAX( pus(ji,jj)*pus(ji,jj)*ptha(ji,jj)*zqa , 1.E-9_wp ) |
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| 331 | ! |
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| 332 | END DO |
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| 333 | END DO |
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| 334 | ! |
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| 335 | One_on_L = SIGN( MIN(ABS(One_on_L),200._wp), One_on_L ) ! (prevent FPE from stupid values over masked regions...) |
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| 336 | ! |
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| 337 | END FUNCTION One_on_L |
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| 338 | |
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| 339 | FUNCTION Ri_bulk( pz, psst, ptha, pssq, pqa, pub ) |
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| 340 | !!---------------------------------------------------------------------------------- |
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| 341 | !! Bulk Richardson number according to "wide-spread equation"... |
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| 342 | !! |
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| 343 | !! ** Author: L. Brodeau, June 2019 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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| 344 | !!---------------------------------------------------------------------------------- |
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| 345 | REAL(wp), DIMENSION(jpi,jpj) :: Ri_bulk |
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| 346 | REAL(wp) , INTENT(in) :: pz ! height above the sea (aka "delta z") [m] |
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| 347 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! SST [K] |
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| 348 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptha ! pot. air temp. at height "pz" [K] |
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| 349 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pssq ! 0.98*q_sat(SST) [kg/kg] |
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| 350 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air spec. hum. at height "pz" [kg/kg] |
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| 351 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pub ! bulk wind speed [m/s] |
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| 352 | ! |
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| 353 | INTEGER :: ji, jj ! dummy loop indices |
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| 354 | REAL(wp) :: zqa, zta, zgamma, zdth_v, ztv, zsstv ! local scalars |
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| 355 | !!------------------------------------------------------------------- |
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| 356 | ! |
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| 357 | DO jj = 1, jpj |
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| 358 | DO ji = 1, jpi |
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| 359 | ! |
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| 360 | zqa = 0.5_wp*(pqa(ji,jj)+pssq(ji,jj)) ! ~ mean q within the layer... |
---|
| 361 | zta = 0.5_wp*( psst(ji,jj) + ptha(ji,jj) - gamma_moist(ptha(ji,jj),zqa)*pz ) ! ~ mean absolute temperature of air within the layer |
---|
| 362 | zta = 0.5_wp*( psst(ji,jj) + ptha(ji,jj) - gamma_moist(zta, zqa)*pz ) ! ~ mean absolute temperature of air within the layer |
---|
| 363 | zgamma = gamma_moist(zta, zqa) ! Adiabatic lapse-rate for moist air within the layer |
---|
| 364 | ! |
---|
| 365 | zsstv = psst(ji,jj)*(1._wp + rctv0*pssq(ji,jj)) ! absolute==potential virtual SST (absolute==potential because z=0!) |
---|
| 366 | ! |
---|
| 367 | zdth_v = ptha(ji,jj)*(1._wp + rctv0*pqa(ji,jj)) - zsstv ! air-sea delta of "virtual potential temperature" |
---|
| 368 | ! |
---|
| 369 | ztv = 0.5_wp*( zsstv + (ptha(ji,jj) - zgamma*pz)*(1._wp + rctv0*pqa(ji,jj)) ) ! ~ mean absolute virtual temp. within the layer |
---|
| 370 | ! |
---|
| 371 | Ri_bulk(ji,jj) = grav*zdth_v*pz / ( ztv*pub(ji,jj)*pub(ji,jj) ) ! the usual definition of Ri_bulk |
---|
| 372 | ! |
---|
| 373 | END DO |
---|
| 374 | END DO |
---|
| 375 | END FUNCTION Ri_bulk |
---|
| 376 | |
---|
| 377 | |
---|
| 378 | FUNCTION e_sat_vctr(ptak) |
---|
| 379 | !!************************************************** |
---|
| 380 | !! ptak: air temperature [K] |
---|
| 381 | !! e_sat: water vapor at saturation [Pa] |
---|
| 382 | !! |
---|
| 383 | !! Recommended by WMO |
---|
| 384 | !! |
---|
| 385 | !! Goff, J. A., 1957: Saturation pressure of water on the new kelvin |
---|
| 386 | !! temperature scale. Transactions of the American society of heating |
---|
| 387 | !! and ventilating engineers, 347–354. |
---|
| 388 | !! |
---|
| 389 | !! rt0 should be 273.16 (triple point of water) and not 273.15 like here |
---|
| 390 | !!************************************************** |
---|
| 391 | |
---|
| 392 | REAL(wp), DIMENSION(jpi,jpj) :: e_sat_vctr !: vapour pressure at saturation [Pa] |
---|
| 393 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak !: temperature (K) |
---|
| 394 | |
---|
| 395 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ztmp |
---|
| 396 | |
---|
| 397 | ALLOCATE ( ztmp(jpi,jpj) ) |
---|
| 398 | |
---|
| 399 | ztmp(:,:) = rtt0/ptak(:,:) |
---|
| 400 | |
---|
| 401 | e_sat_vctr = 100.*( 10.**(10.79574*(1. - ztmp) - 5.028*LOG10(ptak/rtt0) & |
---|
| 402 | & + 1.50475*10.**(-4)*(1. - 10.**(-8.2969*(ptak/rtt0 - 1.)) ) & |
---|
| 403 | & + 0.42873*10.**(-3)*(10.**(4.76955*(1. - ztmp)) - 1.) + 0.78614) ) |
---|
| 404 | |
---|
| 405 | DEALLOCATE ( ztmp ) |
---|
| 406 | |
---|
| 407 | END FUNCTION e_sat_vctr |
---|
| 408 | |
---|
| 409 | |
---|
| 410 | FUNCTION e_sat_sclr( ptak ) |
---|
| 411 | !!---------------------------------------------------------------------------------- |
---|
| 412 | !! *** FUNCTION e_sat_sclr *** |
---|
| 413 | !! < SCALAR argument version > |
---|
| 414 | !! ** Purpose : water vapor at saturation in [Pa] |
---|
| 415 | !! Based on accurate estimate by Goff, 1957 |
---|
| 416 | !! |
---|
| 417 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
---|
| 418 | !! |
---|
| 419 | !! Note: what rt0 should be here, is 273.16 (triple point of water) and not 273.15 like here |
---|
| 420 | !!---------------------------------------------------------------------------------- |
---|
| 421 | REAL(wp), INTENT(in) :: ptak ! air temperature [K] |
---|
| 422 | REAL(wp) :: e_sat_sclr ! water vapor at saturation [kg/kg] |
---|
| 423 | ! |
---|
| 424 | REAL(wp) :: zta, ztmp ! local scalar |
---|
| 425 | !!---------------------------------------------------------------------------------- |
---|
| 426 | ! |
---|
| 427 | zta = MAX( ptak , 180._wp ) ! air temp., prevents fpe0 errors dute to unrealistically low values over masked regions... |
---|
| 428 | ztmp = rt0 / zta |
---|
| 429 | ! |
---|
| 430 | ! Vapour pressure at saturation [Pa] : WMO, (Goff, 1957) |
---|
| 431 | e_sat_sclr = 100.*( 10.**( 10.79574*(1. - ztmp) - 5.028*LOG10(zta/rt0) & |
---|
| 432 | & + 1.50475*10.**(-4)*(1. - 10.**(-8.2969*(zta/rt0 - 1.)) ) & |
---|
| 433 | & + 0.42873*10.**(-3)*(10.**(4.76955*(1. - ztmp)) - 1.) + 0.78614) ) |
---|
| 434 | ! |
---|
| 435 | END FUNCTION e_sat_sclr |
---|
| 436 | |
---|
| 437 | |
---|
| 438 | FUNCTION q_sat( ptak, pslp ) |
---|
| 439 | !!---------------------------------------------------------------------------------- |
---|
| 440 | !! *** FUNCTION q_sat *** |
---|
| 441 | !! |
---|
| 442 | !! ** Purpose : Specific humidity at saturation in [kg/kg] |
---|
| 443 | !! Based on accurate estimate of "e_sat" |
---|
| 444 | !! aka saturation water vapor (Goff, 1957) |
---|
| 445 | !! |
---|
| 446 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
---|
| 447 | !!---------------------------------------------------------------------------------- |
---|
| 448 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K] |
---|
| 449 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa] |
---|
| 450 | REAL(wp), DIMENSION(jpi,jpj) :: q_sat ! Specific humidity at saturation [kg/kg] |
---|
| 451 | ! |
---|
| 452 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 453 | REAL(wp) :: ze_sat ! local scalar |
---|
| 454 | !!---------------------------------------------------------------------------------- |
---|
| 455 | ! |
---|
| 456 | DO jj = 1, jpj |
---|
| 457 | DO ji = 1, jpi |
---|
| 458 | ! |
---|
| 459 | ze_sat = e_sat_sclr( ptak(ji,jj) ) |
---|
| 460 | ! |
---|
| 461 | q_sat(ji,jj) = reps0 * ze_sat/( pslp(ji,jj) - (1._wp - reps0)*ze_sat ) |
---|
| 462 | ! |
---|
| 463 | END DO |
---|
| 464 | END DO |
---|
| 465 | ! |
---|
| 466 | END FUNCTION q_sat |
---|
| 467 | |
---|
| 468 | FUNCTION q_air_rh(prha, ptak, pslp) |
---|
| 469 | !!---------------------------------------------------------------------------------- |
---|
| 470 | !! Specific humidity of air out of Relative Humidity |
---|
| 471 | !! |
---|
| 472 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
---|
| 473 | !!---------------------------------------------------------------------------------- |
---|
| 474 | REAL(wp), DIMENSION(jpi,jpj) :: q_air_rh |
---|
| 475 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: prha !: relative humidity [fraction, not %!!!] |
---|
| 476 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak !: air temperature [K] |
---|
| 477 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp !: atmospheric pressure [Pa] |
---|
| 478 | ! |
---|
| 479 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 480 | REAL(wp) :: ze ! local scalar |
---|
| 481 | !!---------------------------------------------------------------------------------- |
---|
| 482 | ! |
---|
| 483 | DO jj = 1, jpj |
---|
| 484 | DO ji = 1, jpi |
---|
| 485 | ze = prha(ji,jj)*e_sat_sclr(ptak(ji,jj)) |
---|
| 486 | q_air_rh(ji,jj) = ze*reps0/(pslp(ji,jj) - (1. - reps0)*ze) |
---|
| 487 | END DO |
---|
| 488 | END DO |
---|
| 489 | ! |
---|
| 490 | END FUNCTION q_air_rh |
---|
| 491 | |
---|
| 492 | |
---|
| 493 | SUBROUTINE UPDATE_QNSOL_TAU( pzu, pTs, pqs, pTa, pqa, pust, ptst, pqst, pwnd, pUb, pslp, prlw, & |
---|
| 494 | & pQns, pTau, & |
---|
| 495 | & Qlat) |
---|
| 496 | !!---------------------------------------------------------------------------------- |
---|
| 497 | !! Purpose: returns the non-solar heat flux to the ocean aka "Qlat + Qsen + Qlw" |
---|
| 498 | !! and the module of the wind stress => pTau = Tau |
---|
| 499 | !! ** Author: L. Brodeau, Sept. 2019 / AeroBulk (https://github.com/brodeau/aerobulk/) |
---|
| 500 | !!---------------------------------------------------------------------------------- |
---|
| 501 | REAL(wp), INTENT(in) :: pzu ! height above the sea-level where all this takes place (normally 10m) |
---|
| 502 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTs ! water temperature at the air-sea interface [K] |
---|
| 503 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqs ! satur. spec. hum. at T=pTs [kg/kg] |
---|
| 504 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTa ! potential air temperature at z=pzu [K] |
---|
| 505 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity at z=pzu [kg/kg] |
---|
| 506 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pust ! u* |
---|
| 507 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptst ! t* |
---|
| 508 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqst ! q* |
---|
| 509 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pwnd ! wind speed module at z=pzu [m/s] |
---|
| 510 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUb ! bulk wind speed at z=pzu (inc. pot. effect of gustiness etc) [m/s] |
---|
| 511 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea-level atmospheric pressure [Pa] |
---|
| 512 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: prlw ! downwelling longwave radiative flux [W/m^2] |
---|
| 513 | ! |
---|
| 514 | REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pQns ! non-solar heat flux to the ocean aka "Qlat + Qsen + Qlw" [W/m^2]] |
---|
| 515 | REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pTau ! module of the wind stress [N/m^2] |
---|
| 516 | ! |
---|
| 517 | REAL(wp), DIMENSION(jpi,jpj), OPTIONAL, INTENT(out) :: Qlat |
---|
| 518 | ! |
---|
| 519 | REAL(wp) :: zdt, zdq, zCd, zCh, zCe, zTs2, zz0, & |
---|
| 520 | & zQlat, zQsen, zQlw |
---|
| 521 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 522 | !!---------------------------------------------------------------------------------- |
---|
| 523 | DO jj = 1, jpj |
---|
| 524 | DO ji = 1, jpi |
---|
| 525 | |
---|
| 526 | zdt = pTa(ji,jj) - pTs(ji,jj) ; zdt = SIGN( MAX(ABS(zdt),1.E-6_wp), zdt ) |
---|
| 527 | zdq = pqa(ji,jj) - pqs(ji,jj) ; zdq = SIGN( MAX(ABS(zdq),1.E-9_wp), zdq ) |
---|
| 528 | zz0 = pust(ji,jj)/pUb(ji,jj) |
---|
| 529 | zCd = zz0*zz0 |
---|
| 530 | zCh = zz0*ptst(ji,jj)/zdt |
---|
| 531 | zCe = zz0*pqst(ji,jj)/zdq |
---|
| 532 | |
---|
| 533 | CALL BULK_FORMULA( pzu, pTs(ji,jj), pqs(ji,jj), pTa(ji,jj), pqa(ji,jj), & |
---|
| 534 | & zCd, zCh, zCe, & |
---|
[12081] | 535 | & pwnd(ji,jj), pUb(ji,jj), pslp(ji,jj), & |
---|
[12015] | 536 | & pTau(ji,jj), zQsen, zQlat ) |
---|
| 537 | |
---|
| 538 | zTs2 = pTs(ji,jj)*pTs(ji,jj) |
---|
| 539 | zQlw = emiss_w*(prlw(ji,jj) - stefan*zTs2*zTs2) ! Net longwave flux |
---|
| 540 | |
---|
| 541 | pQns(ji,jj) = zQlat + zQsen + zQlw |
---|
| 542 | |
---|
| 543 | IF( PRESENT(Qlat) ) Qlat(ji,jj) = zQlat |
---|
| 544 | END DO |
---|
| 545 | END DO |
---|
| 546 | END SUBROUTINE UPDATE_QNSOL_TAU |
---|
| 547 | |
---|
| 548 | |
---|
| 549 | SUBROUTINE BULK_FORMULA_VCTR( pzu, pTs, pqs, pTa, pqa, & |
---|
| 550 | & pCd, pCh, pCe, & |
---|
| 551 | & pwnd, pUb, pslp, & |
---|
| 552 | & pTau, pQsen, pQlat, pEvap, prhoa ) |
---|
| 553 | !!---------------------------------------------------------------------------------- |
---|
| 554 | REAL(wp), INTENT(in) :: pzu ! height above the sea-level where all this takes place (normally 10m) |
---|
| 555 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTs ! water temperature at the air-sea interface [K] |
---|
| 556 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqs ! satur. spec. hum. at T=pTs [kg/kg] |
---|
| 557 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pTa ! potential air temperature at z=pzu [K] |
---|
| 558 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity at z=pzu [kg/kg] |
---|
| 559 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCd |
---|
| 560 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCh |
---|
| 561 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pCe |
---|
| 562 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pwnd ! wind speed module at z=pzu [m/s] |
---|
| 563 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pUb ! bulk wind speed at z=pzu (inc. pot. effect of gustiness etc) [m/s] |
---|
| 564 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea-level atmospheric pressure [Pa] |
---|
| 565 | !! |
---|
| 566 | REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pTau ! module of the wind stress [N/m^2] |
---|
| 567 | REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pQsen ! [W/m^2] |
---|
| 568 | REAL(wp), DIMENSION(jpi,jpj), INTENT(out) :: pQlat ! [W/m^2] |
---|
| 569 | !! |
---|
[12081] | 570 | REAL(wp), DIMENSION(jpi,jpj), INTENT(out), OPTIONAL :: pEvap ! Evaporation [kg/m^2/s] |
---|
| 571 | REAL(wp), DIMENSION(jpi,jpj), INTENT(out), OPTIONAL :: prhoa ! Air density at z=pzu [kg/m^3] |
---|
[12015] | 572 | !! |
---|
| 573 | REAL(wp) :: ztaa, zgamma, zrho, zUrho, zevap |
---|
| 574 | INTEGER :: ji, jj, jq ! dummy loop indices |
---|
| 575 | !!---------------------------------------------------------------------------------- |
---|
[12081] | 576 | DO jj = 1, jpj |
---|
| 577 | DO ji = 1, jpi |
---|
| 578 | |
---|
| 579 | !! Need ztaa, absolute temperature at pzu (formula to estimate rho_air needs absolute temperature, not the potential temperature "pTa") |
---|
| 580 | ztaa = pTa(ji,jj) ! first guess... |
---|
| 581 | DO jq = 1, 4 |
---|
| 582 | zgamma = gamma_moist( 0.5*(ztaa+pTs(ji,jj)) , pqa(ji,jj) ) |
---|
| 583 | ztaa = pTa(ji,jj) - zgamma*pzu ! Absolute temp. is slightly colder... |
---|
| 584 | END DO |
---|
| 585 | zrho = rho_air(ztaa, pqa(ji,jj), pslp(ji,jj)) |
---|
| 586 | zrho = rho_air(ztaa, pqa(ji,jj), pslp(ji,jj)-zrho*grav*pzu) ! taking into account that we are pzu m above the sea level where SLP is given! |
---|
| 587 | |
---|
| 588 | zUrho = pUb(ji,jj)*MAX(zrho, 1._wp) ! rho*U10 |
---|
| 589 | |
---|
| 590 | pTau(ji,jj) = zUrho * pCd(ji,jj) * pwnd(ji,jj) ! Wind stress module |
---|
| 591 | |
---|
| 592 | zevap = zUrho * pCe(ji,jj) * (pqa(ji,jj) - pqs(ji,jj)) |
---|
| 593 | pQsen(ji,jj) = zUrho * pCh(ji,jj) * (pTa(ji,jj) - pTs(ji,jj)) * cp_air(pqa(ji,jj)) |
---|
| 594 | pQlat(ji,jj) = L_vap(pTs(ji,jj)) * zevap |
---|
| 595 | |
---|
[12015] | 596 | IF( PRESENT(pEvap) ) pEvap(ji,jj) = - zevap |
---|
| 597 | IF( PRESENT(prhoa) ) prhoa(ji,jj) = zrho |
---|
[12081] | 598 | |
---|
[12015] | 599 | END DO |
---|
[12081] | 600 | END DO |
---|
[12015] | 601 | END SUBROUTINE BULK_FORMULA_VCTR |
---|
| 602 | |
---|
| 603 | |
---|
| 604 | SUBROUTINE BULK_FORMULA_SCLR( pzu, pTs, pqs, pTa, pqa, & |
---|
| 605 | & pCd, pCh, pCe, & |
---|
| 606 | & pwnd, pUb, pslp, & |
---|
| 607 | & pTau, pQsen, pQlat, pEvap, prhoa ) |
---|
| 608 | !!---------------------------------------------------------------------------------- |
---|
| 609 | REAL(wp), INTENT(in) :: pzu ! height above the sea-level where all this takes place (normally 10m) |
---|
| 610 | REAL(wp), INTENT(in) :: pTs ! water temperature at the air-sea interface [K] |
---|
| 611 | REAL(wp), INTENT(in) :: pqs ! satur. spec. hum. at T=pTs [kg/kg] |
---|
| 612 | REAL(wp), INTENT(in) :: pTa ! potential air temperature at z=pzu [K] |
---|
| 613 | REAL(wp), INTENT(in) :: pqa ! specific humidity at z=pzu [kg/kg] |
---|
| 614 | REAL(wp), INTENT(in) :: pCd |
---|
| 615 | REAL(wp), INTENT(in) :: pCh |
---|
| 616 | REAL(wp), INTENT(in) :: pCe |
---|
| 617 | REAL(wp), INTENT(in) :: pwnd ! wind speed module at z=pzu [m/s] |
---|
| 618 | REAL(wp), INTENT(in) :: pUb ! bulk wind speed at z=pzu (inc. pot. effect of gustiness etc) [m/s] |
---|
| 619 | REAL(wp), INTENT(in) :: pslp ! sea-level atmospheric pressure [Pa] |
---|
| 620 | !! |
---|
| 621 | REAL(wp), INTENT(out) :: pTau ! module of the wind stress [N/m^2] |
---|
| 622 | REAL(wp), INTENT(out) :: pQsen ! [W/m^2] |
---|
| 623 | REAL(wp), INTENT(out) :: pQlat ! [W/m^2] |
---|
| 624 | !! |
---|
| 625 | REAL(wp), INTENT(out), OPTIONAL :: pEvap ! Evaporation [kg/m^2/s] |
---|
| 626 | REAL(wp), INTENT(out), OPTIONAL :: prhoa ! Air density at z=pzu [kg/m^3] |
---|
| 627 | !! |
---|
| 628 | REAL(wp) :: ztaa, zgamma, zrho, zUrho, zevap |
---|
| 629 | INTEGER :: jq |
---|
| 630 | !!---------------------------------------------------------------------------------- |
---|
| 631 | |
---|
[12081] | 632 | !! Need ztaa, absolute temperature at pzu (formula to estimate rho_air needs absolute temperature, not the potential temperature "pTa") |
---|
| 633 | ztaa = pTa ! first guess... |
---|
| 634 | DO jq = 1, 4 |
---|
| 635 | zgamma = gamma_moist( 0.5*(ztaa+pTs) , pqa ) |
---|
| 636 | ztaa = pTa - zgamma*pzu ! Absolute temp. is slightly colder... |
---|
| 637 | END DO |
---|
| 638 | zrho = rho_air(ztaa, pqa, pslp) |
---|
| 639 | zrho = rho_air(ztaa, pqa, pslp-zrho*grav*pzu) ! taking into account that we are pzu m above the sea level where SLP is given! |
---|
[12015] | 640 | |
---|
[12081] | 641 | zUrho = pUb*MAX(zrho, 1._wp) ! rho*U10 |
---|
| 642 | |
---|
| 643 | pTau = zUrho * pCd * pwnd ! Wind stress module |
---|
| 644 | |
---|
| 645 | zevap = zUrho * pCe * (pqa - pqs) |
---|
| 646 | pQsen = zUrho * pCh * (pTa - pTs) * cp_air(pqa) |
---|
| 647 | pQlat = L_vap(pTs) * zevap |
---|
| 648 | |
---|
| 649 | IF( PRESENT(pEvap) ) pEvap = - zevap |
---|
| 650 | IF( PRESENT(prhoa) ) prhoa = zrho |
---|
| 651 | |
---|
[12015] | 652 | END SUBROUTINE BULK_FORMULA_SCLR |
---|
| 653 | |
---|
| 654 | |
---|
| 655 | |
---|
| 656 | |
---|
| 657 | FUNCTION alpha_sw_vctr( psst ) |
---|
| 658 | !!--------------------------------------------------------------------------------- |
---|
| 659 | !! *** FUNCTION alpha_sw_vctr *** |
---|
| 660 | !! |
---|
| 661 | !! ** Purpose : ROUGH estimate of the thermal expansion coefficient of sea-water at the surface (P =~ 1010 hpa) |
---|
| 662 | !! |
---|
| 663 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
---|
| 664 | !!---------------------------------------------------------------------------------- |
---|
| 665 | REAL(wp), DIMENSION(jpi,jpj) :: alpha_sw_vctr ! thermal expansion coefficient of sea-water [1/K] |
---|
| 666 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K] |
---|
| 667 | !!---------------------------------------------------------------------------------- |
---|
| 668 | alpha_sw_vctr = 2.1e-5_wp * MAX(psst(:,:)-rt0 + 3.2_wp, 0._wp)**0.79 |
---|
| 669 | END FUNCTION alpha_sw_vctr |
---|
| 670 | |
---|
| 671 | FUNCTION alpha_sw_sclr( psst ) |
---|
| 672 | !!--------------------------------------------------------------------------------- |
---|
| 673 | !! *** FUNCTION alpha_sw_sclr *** |
---|
| 674 | !! |
---|
| 675 | !! ** Purpose : ROUGH estimate of the thermal expansion coefficient of sea-water at the surface (P =~ 1010 hpa) |
---|
| 676 | !! |
---|
| 677 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
---|
| 678 | !!---------------------------------------------------------------------------------- |
---|
| 679 | REAL(wp) :: alpha_sw_sclr ! thermal expansion coefficient of sea-water [1/K] |
---|
| 680 | REAL(wp), INTENT(in) :: psst ! sea-water temperature [K] |
---|
| 681 | !!---------------------------------------------------------------------------------- |
---|
| 682 | alpha_sw_sclr = 2.1e-5_wp * MAX(psst-rt0 + 3.2_wp, 0._wp)**0.79 |
---|
| 683 | END FUNCTION alpha_sw_sclr |
---|
| 684 | |
---|
| 685 | |
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| 686 | |
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| 687 | !!====================================================================== |
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| 688 | END MODULE sbcblk_phy |
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