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, 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 | INTERFACE gamma_moist |
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28 | MODULE PROCEDURE gamma_moist_vctr, gamma_moist_sclr |
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29 | END INTERFACE gamma_moist |
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30 | |
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31 | PUBLIC virt_temp |
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32 | PUBLIC rho_air |
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33 | PUBLIC visc_air |
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34 | PUBLIC L_vap |
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35 | PUBLIC cp_air |
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36 | PUBLIC gamma_moist |
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37 | PUBLIC One_on_L |
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38 | PUBLIC Ri_bulk |
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39 | PUBLIC q_sat |
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40 | PUBLIC q_air_rh |
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41 | |
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42 | !!---------------------------------------------------------------------- |
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43 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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44 | !! $Id: sbcblk.F90 10535 2019-01-16 17:36:47Z clem $ |
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45 | !! Software governed by the CeCILL license (see ./LICENSE) |
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46 | !!---------------------------------------------------------------------- |
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47 | CONTAINS |
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48 | |
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49 | FUNCTION virt_temp( pta, pqa ) |
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50 | !!------------------------------------------------------------------------ |
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51 | !! |
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52 | !! Compute the (absolute/potential) virtual temperature, knowing the |
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53 | !! (absolute/potential) temperature and specific humidity |
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54 | !! |
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55 | !! If input temperature is absolute then output vitual temperature is absolute |
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56 | !! If input temperature is potential then output vitual temperature is potential |
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57 | !! |
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58 | !! Author: L. Brodeau, June 2019 / AeroBulk |
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59 | !! (https://github.com/brodeau/aerobulk/) |
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60 | !!------------------------------------------------------------------------ |
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61 | REAL(wp), DIMENSION(jpi,jpj) :: virt_temp !: 1./(Monin Obukhov length) [m^-1] |
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62 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pta, & !: absolute or potetntial air temperature [K] |
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63 | & pqa !: specific humidity of air [kg/kg] |
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64 | !!------------------------------------------------------------------- |
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65 | ! |
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66 | virt_temp(:,:) = pta(:,:) * (1._wp + rctv0*pqa(:,:)) |
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67 | !! |
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68 | !! This is exactly the same sing that: |
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69 | !! virt_temp = pta * ( pwa + reps0) / (reps0*(1.+pwa)) |
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70 | !! with wpa (mixing ration) defined as : pwa = pqa/(1.-pqa) |
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71 | ! |
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72 | END FUNCTION virt_temp |
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73 | |
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74 | FUNCTION rho_air( ptak, pqa, pslp ) |
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75 | !!------------------------------------------------------------------------------- |
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76 | !! *** FUNCTION rho_air *** |
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77 | !! |
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78 | !! ** Purpose : compute density of (moist) air using the eq. of state of the atmosphere |
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79 | !! |
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80 | !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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81 | !!------------------------------------------------------------------------------- |
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82 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K] |
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83 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg] |
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84 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! pressure in [Pa] |
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85 | REAL(wp), DIMENSION(jpi,jpj) :: rho_air ! density of moist air [kg/m^3] |
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86 | !!------------------------------------------------------------------------------- |
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87 | ! |
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88 | rho_air = pslp / ( R_dry*ptak * ( 1._wp + rctv0*pqa ) ) |
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89 | ! |
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90 | END FUNCTION rho_air |
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91 | |
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92 | FUNCTION visc_air(ptak) |
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93 | !!---------------------------------------------------------------------------------- |
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94 | !! Air kinetic viscosity (m^2/s) given from temperature in degrees... |
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95 | !! |
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96 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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97 | !!---------------------------------------------------------------------------------- |
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98 | REAL(wp), DIMENSION(jpi,jpj) :: visc_air ! |
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99 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature in (K) |
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100 | ! |
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101 | INTEGER :: ji, jj ! dummy loop indices |
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102 | REAL(wp) :: ztc, ztc2 ! local scalar |
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103 | !!---------------------------------------------------------------------------------- |
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104 | ! |
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105 | DO jj = 1, jpj |
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106 | DO ji = 1, jpi |
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107 | ztc = ptak(ji,jj) - rt0 ! air temp, in deg. C |
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108 | ztc2 = ztc*ztc |
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109 | 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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110 | END DO |
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111 | END DO |
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112 | ! |
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113 | END FUNCTION visc_air |
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114 | |
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115 | FUNCTION L_vap( psst ) |
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116 | !!--------------------------------------------------------------------------------- |
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117 | !! *** FUNCTION L_vap *** |
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118 | !! |
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119 | !! ** Purpose : Compute the latent heat of vaporization of water out of temperature |
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120 | !! |
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121 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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122 | !!---------------------------------------------------------------------------------- |
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123 | REAL(wp), DIMENSION(jpi,jpj) :: L_vap ! latent heat of vaporization [J/kg] |
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124 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! water temperature [K] |
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125 | !!---------------------------------------------------------------------------------- |
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126 | ! |
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127 | L_vap = ( 2.501 - 0.00237 * ( psst(:,:) - rt0) ) * 1.e6 |
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128 | ! |
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129 | END FUNCTION L_vap |
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130 | |
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131 | FUNCTION cp_air( pqa ) |
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132 | !!------------------------------------------------------------------------------- |
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133 | !! *** FUNCTION cp_air *** |
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134 | !! |
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135 | !! ** Purpose : Compute specific heat (Cp) of moist air |
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136 | !! |
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137 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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138 | !!------------------------------------------------------------------------------- |
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139 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air specific humidity [kg/kg] |
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140 | REAL(wp), DIMENSION(jpi,jpj) :: cp_air ! specific heat of moist air [J/K/kg] |
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141 | !!------------------------------------------------------------------------------- |
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142 | ! |
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143 | cp_air = rCp_dry + rCp_vap * pqa |
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144 | ! |
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145 | END FUNCTION cp_air |
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146 | |
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147 | FUNCTION gamma_moist_vctr( ptak, pqa ) |
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148 | !!---------------------------------------------------------------------------------- |
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149 | !! *** FUNCTION gamma_moist_vctr *** |
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150 | !! |
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151 | !! ** Purpose : Compute the moist adiabatic lapse-rate. |
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152 | !! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate |
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153 | !! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html |
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154 | !! |
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155 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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156 | !!---------------------------------------------------------------------------------- |
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157 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K] |
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158 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! specific humidity [kg/kg] |
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159 | REAL(wp), DIMENSION(jpi,jpj) :: gamma_moist_vctr ! moist adiabatic lapse-rate |
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160 | ! |
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161 | INTEGER :: ji, jj ! dummy loop indices |
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162 | REAL(wp) :: zta, zqa, zwa, ziRT ! local scalar |
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163 | !!---------------------------------------------------------------------------------- |
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164 | ! |
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165 | DO jj = 1, jpj |
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166 | DO ji = 1, jpi |
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167 | zta = MAX( ptak(ji,jj), 180._wp) ! prevents screw-up over masked regions where field == 0. |
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168 | zqa = MAX( pqa(ji,jj), 1.E-6_wp) ! " " " |
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169 | ! |
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170 | zwa = zqa / (1. - zqa) ! w is mixing ratio w = q/(1-q) | q = w/(1+w) |
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171 | ziRT = 1._wp/(R_dry*zta) ! 1/RT |
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172 | gamma_moist_vctr(ji,jj) = grav * ( 1._wp + rLevap*zwa*ziRT ) / ( rCp_dry + rLevap*rLevap*zwa*reps0*ziRT/zta ) |
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173 | END DO |
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174 | END DO |
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175 | ! |
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176 | END FUNCTION gamma_moist_vctr |
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177 | |
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178 | FUNCTION gamma_moist_sclr( ptak, pqa ) |
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179 | !!---------------------------------------------------------------------------------- |
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180 | !! ** Purpose : Compute the moist adiabatic lapse-rate. |
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181 | !! => http://glossary.ametsoc.org/wiki/Moist-adiabatic_lapse_rate |
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182 | !! => http://www.geog.ucsb.edu/~joel/g266_s10/lecture_notes/chapt03/oh10_3_01/oh10_3_01.html |
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183 | !! |
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184 | !! ** Author: L. Brodeau, June 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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185 | !!---------------------------------------------------------------------------------- |
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186 | REAL(wp) :: gamma_moist_sclr |
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187 | REAL(wp), INTENT(in) :: ptak, pqa ! air temperature (K) and specific humidity (kg/kg) |
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188 | ! |
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189 | REAL(wp) :: zta, zqa, zwa, ziRT ! local scalar |
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190 | !!---------------------------------------------------------------------------------- |
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191 | zta = MAX( ptak, 180._wp) ! prevents screw-up over masked regions where field == 0. |
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192 | zqa = MAX( pqa, 1.E-6_wp) ! " " " |
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193 | !! |
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194 | zwa = zqa / (1._wp - zqa) ! w is mixing ratio w = q/(1-q) | q = w/(1+w) |
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195 | ziRT = 1._wp / (R_dry*zta) ! 1/RT |
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196 | gamma_moist_sclr = grav * ( 1._wp + rLevap*zwa*ziRT ) / ( rCp_dry + rLevap*rLevap*zwa*reps0*ziRT/zta ) |
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197 | !! |
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198 | END FUNCTION gamma_moist_sclr |
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199 | |
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200 | FUNCTION One_on_L( ptha, pqa, pus, pts, pqs ) |
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201 | !!------------------------------------------------------------------------ |
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202 | !! |
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203 | !! Evaluates the 1./(Monin Obukhov length) from air temperature and |
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204 | !! specific humidity, and frictional scales u*, t* and q* |
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205 | !! |
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206 | !! Author: L. Brodeau, June 2016 / AeroBulk |
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207 | !! (https://github.com/brodeau/aerobulk/) |
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208 | !!------------------------------------------------------------------------ |
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209 | REAL(wp), DIMENSION(jpi,jpj) :: One_on_L !: 1./(Monin Obukhov length) [m^-1] |
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210 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptha, & !: average potetntial air temperature [K] |
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211 | & pqa, & !: average specific humidity of air [kg/kg] |
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212 | & pus, pts, pqs !: frictional velocity, temperature and humidity |
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213 | ! |
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214 | INTEGER :: ji, jj ! dummy loop indices |
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215 | REAL(wp) :: zqa ! local scalar |
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216 | !!------------------------------------------------------------------- |
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217 | ! |
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218 | DO jj = 1, jpj |
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219 | DO ji = 1, jpi |
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220 | ! |
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221 | zqa = (1._wp + rctv0*pqa(ji,jj)) |
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222 | ! |
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223 | ! The main concern is to know whether, the vertical turbulent flux of virtual temperature, < u' theta_v' > is estimated with: |
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224 | ! 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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225 | ! or |
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226 | ! b/ -u* [ theta* + 0.61 theta q* ] |
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227 | ! |
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228 | One_on_L(ji,jj) = grav*vkarmn*( pts(ji,jj)*zqa + rctv0*ptha(ji,jj)*pqs(ji,jj) ) & |
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229 | & / MAX( pus(ji,jj)*pus(ji,jj)*ptha(ji,jj)*zqa , 1.E-9_wp ) |
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230 | ! |
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231 | END DO |
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232 | END DO |
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233 | ! |
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234 | 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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235 | ! |
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236 | END FUNCTION One_on_L |
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237 | |
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238 | FUNCTION Ri_bulk( pz, psst, ptha, pssq, pqa, pub ) |
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239 | !!---------------------------------------------------------------------------------- |
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240 | !! Bulk Richardson number according to "wide-spread equation"... |
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241 | !! |
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242 | !! ** Author: L. Brodeau, June 2019 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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243 | !!---------------------------------------------------------------------------------- |
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244 | REAL(wp), DIMENSION(jpi,jpj) :: Ri_bulk |
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245 | REAL(wp) , INTENT(in) :: pz ! height above the sea (aka "delta z") [m] |
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246 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: psst ! SST [K] |
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247 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptha ! pot. air temp. at height "pz" [K] |
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248 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pssq ! 0.98*q_sat(SST) [kg/kg] |
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249 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pqa ! air spec. hum. at height "pz" [kg/kg] |
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250 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pub ! bulk wind speed [m/s] |
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251 | ! |
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252 | INTEGER :: ji, jj ! dummy loop indices |
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253 | REAL(wp) :: zqa, zta, zgamma, zdth_v, ztv, zsstv ! local scalars |
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254 | !!------------------------------------------------------------------- |
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255 | ! |
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256 | DO jj = 1, jpj |
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257 | DO ji = 1, jpi |
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258 | ! |
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259 | zqa = 0.5_wp*(pqa(ji,jj)+pssq(ji,jj)) ! ~ mean q within the layer... |
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260 | 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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261 | 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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262 | zgamma = gamma_moist(zta, zqa) ! Adiabatic lapse-rate for moist air within the layer |
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263 | ! |
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264 | zsstv = psst(ji,jj)*(1._wp + rctv0*pssq(ji,jj)) ! absolute==potential virtual SST (absolute==potential because z=0!) |
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265 | ! |
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266 | zdth_v = ptha(ji,jj)*(1._wp + rctv0*pqa(ji,jj)) - zsstv ! air-sea delta of "virtual potential temperature" |
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267 | ! |
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268 | 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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269 | ! |
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270 | Ri_bulk(ji,jj) = grav*zdth_v*pz / ( ztv*pub(ji,jj)*pub(ji,jj) ) ! the usual definition of Ri_bulk |
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271 | ! |
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272 | END DO |
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273 | END DO |
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274 | END FUNCTION Ri_bulk |
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275 | |
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276 | |
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277 | FUNCTION e_sat_sclr( ptak, pslp ) |
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278 | !!---------------------------------------------------------------------------------- |
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279 | !! *** FUNCTION e_sat_sclr *** |
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280 | !! < SCALAR argument version > |
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281 | !! ** Purpose : water vapor at saturation in [Pa] |
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282 | !! Based on accurate estimate by Goff, 1957 |
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283 | !! |
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284 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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285 | !! |
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286 | !! Note: what rt0 should be here, is 273.16 (triple point of water) and not 273.15 like here |
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287 | !!---------------------------------------------------------------------------------- |
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288 | REAL(wp), INTENT(in) :: ptak ! air temperature [K] |
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289 | REAL(wp), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa] |
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290 | REAL(wp) :: e_sat_sclr ! water vapor at saturation [kg/kg] |
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291 | ! |
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292 | REAL(wp) :: zta, ztmp ! local scalar |
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293 | !!---------------------------------------------------------------------------------- |
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294 | ! |
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295 | zta = MAX( ptak , 180._wp ) ! air temp., prevents fpe0 errors dute to unrealistically low values over masked regions... |
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296 | ztmp = rt0 / zta |
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297 | ! |
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298 | ! Vapour pressure at saturation [Pa] : WMO, (Goff, 1957) |
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299 | e_sat_sclr = 100.*( 10.**( 10.79574*(1. - ztmp) - 5.028*LOG10(zta/rt0) & |
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300 | & + 1.50475*10.**(-4)*(1. - 10.**(-8.2969*(zta/rt0 - 1.)) ) & |
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301 | & + 0.42873*10.**(-3)*(10.**(4.76955*(1. - ztmp)) - 1.) + 0.78614) ) |
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302 | ! |
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303 | END FUNCTION e_sat_sclr |
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304 | |
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305 | |
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306 | FUNCTION q_sat( ptak, pslp ) |
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307 | !!---------------------------------------------------------------------------------- |
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308 | !! *** FUNCTION q_sat *** |
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309 | !! |
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310 | !! ** Purpose : Specific humidity at saturation in [kg/kg] |
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311 | !! Based on accurate estimate of "e_sat" |
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312 | !! aka saturation water vapor (Goff, 1957) |
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313 | !! |
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314 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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315 | !!---------------------------------------------------------------------------------- |
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316 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak ! air temperature [K] |
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317 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp ! sea level atmospheric pressure [Pa] |
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318 | REAL(wp), DIMENSION(jpi,jpj) :: q_sat ! Specific humidity at saturation [kg/kg] |
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319 | ! |
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320 | INTEGER :: ji, jj ! dummy loop indices |
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321 | REAL(wp) :: ze_sat ! local scalar |
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322 | !!---------------------------------------------------------------------------------- |
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323 | ! |
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324 | DO jj = 1, jpj |
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325 | DO ji = 1, jpi |
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326 | ! |
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327 | ze_sat = e_sat_sclr( ptak(ji,jj), pslp(ji,jj) ) |
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328 | ! |
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329 | q_sat(ji,jj) = reps0 * ze_sat/( pslp(ji,jj) - (1._wp - reps0)*ze_sat ) |
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330 | ! |
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331 | END DO |
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332 | END DO |
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333 | ! |
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334 | END FUNCTION q_sat |
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335 | |
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336 | FUNCTION q_air_rh(prha, ptak, pslp) |
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337 | !!---------------------------------------------------------------------------------- |
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338 | !! Specific humidity of air out of Relative Humidity |
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339 | !! |
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340 | !! ** Author: L. Brodeau, june 2016 / AeroBulk (https://github.com/brodeau/aerobulk/) |
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341 | !!---------------------------------------------------------------------------------- |
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342 | REAL(wp), DIMENSION(jpi,jpj) :: q_air_rh |
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343 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: prha !: relative humidity [fraction, not %!!!] |
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344 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: ptak !: air temperature [K] |
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345 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pslp !: atmospheric pressure [Pa] |
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346 | ! |
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347 | INTEGER :: ji, jj ! dummy loop indices |
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348 | REAL(wp) :: ze ! local scalar |
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349 | !!---------------------------------------------------------------------------------- |
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350 | ! |
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351 | DO jj = 1, jpj |
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352 | DO ji = 1, jpi |
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353 | ze = prha(ji,jj)*e_sat_sclr(ptak(ji,jj), pslp(ji,jj)) |
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354 | q_air_rh(ji,jj) = ze*reps0/(pslp(ji,jj) - (1. - reps0)*ze) |
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355 | END DO |
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356 | END DO |
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357 | ! |
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358 | END FUNCTION q_air_rh |
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359 | |
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360 | |
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361 | !!====================================================================== |
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362 | END MODULE sbcblk_phy |
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