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... |
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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 |
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362 | zta = 0.5_wp*( psst(ji,jj) + ptha(ji,jj) - gamma_moist(zta, zqa)*pz ) ! ~ mean absolute temperature of air within the layer |
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363 | zgamma = gamma_moist(zta, zqa) ! Adiabatic lapse-rate for moist air within the layer |
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364 | ! |
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365 | zsstv = psst(ji,jj)*(1._wp + rctv0*pssq(ji,jj)) ! absolute==potential virtual SST (absolute==potential because z=0!) |
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366 | ! |
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367 | zdth_v = ptha(ji,jj)*(1._wp + rctv0*pqa(ji,jj)) - zsstv ! air-sea delta of "virtual potential temperature" |
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368 | ! |
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369 | ztv = 0.5_wp*( zsstv + (ptha(ji,jj) - zgamma*pz)*(1._wp + rctv0*pqa(ji,jj)) ) ! ~ mean absolute virtual temp. within the layer |
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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 |
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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, & |
---|
535 | & pwnd(ji,jj), pUb(ji,jj), pslp(ji,jj), & |
---|
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 | !! |
---|
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] |
---|
572 | !! |
---|
573 | REAL(wp) :: ztaa, zgamma, zrho, zUrho, zevap |
---|
574 | INTEGER :: ji, jj, jq ! dummy loop indices |
---|
575 | !!---------------------------------------------------------------------------------- |
---|
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 | |
---|
596 | IF( PRESENT(pEvap) ) pEvap(ji,jj) = - zevap |
---|
597 | IF( PRESENT(prhoa) ) prhoa(ji,jj) = zrho |
---|
598 | |
---|
599 | END DO |
---|
600 | END DO |
---|
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 | |
---|
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! |
---|
640 | |
---|
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 | |
---|
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 | |
---|
686 | |
---|
687 | !!====================================================================== |
---|
688 | END MODULE sbcblk_phy |
---|