| 1 | |
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| 2 | ! FUNCTION FPLAIR Mean free path of air molecules (m) |
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| 3 | ! FUNCTION VISAIR Dynamic viscosity of air |
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| 4 | ! FUNCTION DFWVA Diffusivity of water vapor in air |
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| 5 | ! FUNCTION STSAS Surface tension of H2SO4 solution/vapor |
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| 6 | ! FUNCTION ROSAS Density of liquid sulfuric acid solution |
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| 7 | ! FUNCTION waterps Saturation vapour pressure of pure water |
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| 8 | ! FUNCTION CDTAIR Thermal conduvtivity of air |
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| 9 | |
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| 10 | |
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| 11 | !***************************************************************************** |
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| 12 | FUNCTION FPLAIR(T,P) |
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| 13 | |
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| 14 | ! Molecular mean free path of air molecules |
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| 15 | ! Source: Seinfield's book (2006,p.399) |
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| 16 | |
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| 17 | use free_param |
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| 18 | use donnees |
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| 19 | |
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| 20 | IMPLICIT NONE |
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| 21 | |
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| 22 | REAL :: FPLAIR, T, P, VISAIR |
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| 23 | |
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| 24 | FPLAIR=sqrt((PI*RGAS*T)/(2.0D0*MAIR))*(VISAIR(T)/P) |
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| 25 | |
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| 26 | RETURN |
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| 27 | |
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| 28 | END FUNCTION FPLAIR |
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| 29 | |
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| 30 | |
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| 31 | !***************************************************************************** |
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| 32 | FUNCTION VISAIR(T) |
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| 33 | |
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| 34 | ! Dynamic viscosity of air. |
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| 35 | ! Source: Jones 1942 |
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| 36 | |
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| 37 | ! Input: TAIR: Temperature (K) |
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| 38 | ! Output: VISAIR: Dynamic viscosity of air (kg/(m s))=(Pa s) |
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| 39 | |
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| 40 | use free_param |
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| 41 | use donnees |
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| 42 | |
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| 43 | IMPLICIT NONE |
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| 44 | |
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| 45 | REAL :: T, VISAIR |
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| 46 | REAL :: AA, SS, T0 |
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| 47 | |
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| 48 | AA = (5.27D0-3.0D0)/(5.27D0 -1.0D0) |
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| 49 | SS = -0.435D0 |
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| 50 | T0 = 200.0D0 |
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| 51 | |
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| 52 | VISAIR=1015.0D0*((T/T0)**(0.5D0))*(T0**(AA)+SS)/(T**(AA)+SS) |
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| 53 | VISAIR=VISAIR*1.D-8 |
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| 54 | |
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| 55 | RETURN |
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| 56 | |
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| 57 | END FUNCTION VISAIR |
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| 58 | |
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| 59 | |
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| 60 | !***************************************************************************** |
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| 61 | FUNCTION DFWVA(T,P) |
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| 62 | |
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| 63 | ! Diffusivity of water vapor in air. |
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| 64 | ! Source: Prupacher & Klett:Microphysics of clouds and precipitation, |
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| 65 | ! (1980), 13-3, p. 413 |
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| 66 | ! The relation D = E0 (T/T0)**n (P0/P); n=1.94 has been used. |
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| 67 | |
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| 68 | ! Input: TAIR: Temperature (K); Range: [180,273] |
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| 69 | ! PAIR: Pressure (Pa) |
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| 70 | ! Output: Diffusivity of water vapor in air (m**2/sec) |
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| 71 | |
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| 72 | use free_param |
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| 73 | use donnees |
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| 74 | |
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| 75 | IMPLICIT NONE |
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| 76 | |
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| 77 | REAL :: E0, D1, P0, T0, T, P, DFWVA |
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| 78 | |
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| 79 | PARAMETER(E0=0.211D-4,P0=1.01325D+5,T0=273.15D0,D1=E0*P0) |
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| 80 | |
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| 81 | DFWVA=D1*((T/T0)**1.94D0)/P |
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| 82 | |
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| 83 | RETURN |
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| 84 | |
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| 85 | END FUNCTION DFWVA |
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| 86 | |
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| 87 | |
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| 88 | !***************************************************************************** |
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| 89 | FUNCTION STSAS(T,xmass) |
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| 90 | ! Input: T: Temperature (K) |
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| 91 | ! xmass: Mass fraction of H2SO4 [0;1] |
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| 92 | ! Output: Surface tension of sulfuric acid solution (N/m) |
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| 93 | |
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| 94 | ! about 230-323 K , x=0,...,1 |
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| 95 | !(valid down to the solid phase limit temp, which depends on molefraction) |
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| 96 | |
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| 97 | use donnees |
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| 98 | IMPLICIT NONE |
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| 99 | REAL :: STSAS |
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| 100 | REAL, INTENT(IN):: xmass, T |
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| 101 | REAL :: a, b, T1, Tc, xmole |
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| 102 | |
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| 103 | IF (T .LT. 305.15) THEN |
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| 104 | |
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| 105 | !low temperature surface tension |
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| 106 | ! Hanna Vehkam‰ki and Markku Kulmala and Ismo Napari |
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| 107 | ! and Kari E. J. Lehtinen and Claudia Timmreck and Madis Noppel and Ari Laaksonen, 2002, |
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| 108 | ! An improved parameterization for sulfuric acid/water nucleation rates for tropospheric |
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| 109 | !and stratospheric conditions, () J. Geophys. Res., 107, pp. 4622-4631 |
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| 110 | |
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| 111 | a= 0.11864 + xmass* (-0.11651 & |
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| 112 | + xmass* ( 0.76852 & |
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| 113 | + xmass* (-2.40909 & |
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| 114 | + xmass* (2.95434 & |
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| 115 | + xmass* (-1.25852))))) |
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| 116 | |
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| 117 | b= -0.00015709 + xmass* (0.00040102 & |
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| 118 | + xmass*(-0.00239950 & |
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| 119 | + xmass* (0.007611235 & |
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| 120 | + xmass*(-0.00937386 & |
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| 121 | + xmass*0.00389722)))) |
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| 122 | STSAS=a+T*b |
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| 123 | |
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| 124 | ELSE |
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| 125 | |
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| 126 | xmole = (xmass/MSA)*(1./((xmass/MSA)+(1.-xmass)/MWV)) |
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| 127 | |
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| 128 | ! high temperature surface tension |
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| 129 | !H. Vehkam‰ki and M. Kulmala and K.E. J. lehtinen, 2003, |
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| 130 | !Modelling binary homogeneous nucleation of water-sulfuric acid vapours: |
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| 131 | ! parameterisation for high temperature emissions, () Environ. Sci. Technol., 37, 3392-3398 |
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| 132 | |
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| 133 | Tc= 647.15*(1.0-xmole)*(1.0-xmole) & |
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| 134 | + 900.0 * xmole * xmole & |
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| 135 | + 3156.186* xmole *(1-xmole) !critical temperature |
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| 136 | T1=1.0-T/Tc |
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| 137 | |
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| 138 | a= 0.2358 + xmole*(-0.529 & |
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| 139 | + xmole* (4.073 & |
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| 140 | + xmole*(-12.6707 & |
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| 141 | + xmole* (15.3552 & |
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| 142 | + xmole*(-6.3138))))) |
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| 143 | |
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| 144 | b= -0.14738 + xmole* (0.6253 & |
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| 145 | + xmole*(-5.4808 & |
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| 146 | + xmole*(17.2366 & |
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| 147 | + xmole*(-21.0487 & |
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| 148 | + xmole*(8.719))))) |
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| 149 | STSAS=(a+b*T1)*T1**(1.256) |
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| 150 | |
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| 151 | END IF |
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| 152 | RETURN |
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| 153 | |
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| 154 | END FUNCTION STSAS |
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| 155 | |
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| 156 | |
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| 157 | !***************************************************************************** |
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| 158 | FUNCTION ROSAS(T,xmass) |
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| 159 | |
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| 160 | ! |
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| 161 | ! calculates the density of the liquid in kg/m^3 |
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| 162 | ! xmass=mass fraction of h2so4, T in kelvins |
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| 163 | ! Hanna Vehkam‰ki and Markku Kulmala and Ismo Napari |
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| 164 | ! and Kari E. J. Lehtinen and Claudia Timmreck and Madis Noppel and Ari Laaksonen, 2002, |
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| 165 | ! An improved parameterization for sulfuric acid/water nucleation rates for tropospheric |
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| 166 | !and stratospheric conditions, () J. Geophys. Res., 107, pp. 4622-4631 |
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| 167 | |
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| 168 | ! about 220-373 K , x=0,...,1 |
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| 169 | !(valid down to the solid phase limit temp, which depends on molefraction) |
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| 170 | |
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| 171 | IMPLICIT NONE |
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| 172 | REAL :: ROSAS |
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| 173 | REAL, INTENT(IN) :: T, xmass |
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| 174 | REAL :: a,b,c |
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| 175 | |
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| 176 | |
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| 177 | a= 0.7681724 + xmass* (2.1847140 & |
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| 178 | + xmass* (7.1630022 & |
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| 179 | + xmass* (-44.31447 & |
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| 180 | + xmass* (88.75606 & |
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| 181 | + xmass*(-75.73729 & |
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| 182 | + xmass* 23.43228 ))))) |
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| 183 | |
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| 184 | b= 1.808225e-3 + xmass* (-9.294656e-3 & |
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| 185 | + xmass* (-0.03742148 & |
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| 186 | + xmass* (0.2565321 & |
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| 187 | + xmass* (-0.5362872 & |
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| 188 | + xmass* (0.4857736 & |
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| 189 | + xmass* (-0.1629592)))))) |
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| 190 | |
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| 191 | c= -3.478524e-6 + xmass* (1.335867e-5 & |
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| 192 | + xmass* (5.195706e-5 & |
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| 193 | + xmass*(-3.717636e-4 & |
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| 194 | + xmass* (7.990811e-4 & |
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| 195 | + xmass*(-7.458060e-4 & |
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| 196 | + xmass* 2.58139e-4))))) |
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| 197 | |
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| 198 | ROSAS= a+T*(b+c*T) ! g/cm^3 |
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| 199 | ROSAS= ROSAS*1.0e3 !kg/m^3 |
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| 200 | |
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| 201 | RETURN |
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| 202 | END FUNCTION ROSAS |
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| 203 | |
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| 204 | |
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| 205 | !**************************************************************** |
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| 206 | FUNCTION waterps(t) |
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| 207 | |
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| 208 | ! Saturation vapour pressure of pure water in Pa |
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| 209 | ! temperature t in K |
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| 210 | |
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| 211 | ! for 0 to 100C: Wexler 1976 |
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| 212 | ! for <0C (validity range 123-332K): Murphy and Koop 2005 |
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| 213 | |
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| 214 | use free_param |
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| 215 | use donnees |
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| 216 | |
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| 217 | IMPLICIT NONE |
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| 218 | |
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| 219 | REAL:: waterps, t,w |
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| 220 | |
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| 221 | if(t .ge. 273.15D0) then |
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| 222 | waterps=exp(-2991.2729D0*(t**(-2.))-6017.0128D0/t+18.87643854D0 & |
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| 223 | & -0.028354721D0*t+0.17838301D-4*t**2.-0.84150417D-9*t**3. & |
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| 224 | & +0.44412543D-12*t**4.+2.858487D0*LOG(t)) |
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| 225 | else if(t .lt. 273.15D0) then |
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| 226 | waterps=exp(54.842763D0-6763.22D0/t-4.210D0*LOG(t)+0.000367D0*t & |
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| 227 | & + tanh(0.0415D0*(t- 218.8D0))*(53.878D0- 1331.22D0/t & |
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| 228 | & - 9.44523D0*LOG(t) + 0.014025D0*t)) |
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| 229 | else |
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| 230 | stop 'no good temperatures in waterps!' |
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| 231 | endif |
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| 232 | |
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| 233 | END FUNCTION waterps |
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| 234 | |
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| 235 | |
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| 236 | !**************************************************************** |
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| 237 | FUNCTION CDTAIR(T) |
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| 238 | |
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| 239 | ! Thermal conduvtivity of air |
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| 240 | ! Source: Prupacher & Klett:Microphysics of clouds and precipitation, |
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| 241 | ! (1980), p 418, 13-16 |
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| 242 | ! Formula used: CDTAIR=4.381276E-3+7.117560E-5*TAIR |
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| 243 | |
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| 244 | ! Input: TAIR: Air temperature (K) |
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| 245 | ! Output: Thermal conductivity of air (J/(m sec K)) |
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| 246 | |
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| 247 | use free_param |
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| 248 | use donnees |
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| 249 | |
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| 250 | IMPLICIT NONE |
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| 251 | |
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| 252 | REAL :: CDTAIR, T |
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| 253 | |
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| 254 | CDTAIR=4.381276D-3+7.117560D-5*T |
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| 255 | |
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| 256 | RETURN |
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| 257 | |
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| 258 | END FUNCTION CDTAIR |
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| 259 | |
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