| 1 | ! (C) Copyright 1988- ECMWF. |
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| 2 | ! |
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| 3 | ! This software is licensed under the terms of the Apache Licence Version 2.0 |
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| 4 | ! which can be obtained at http://www.apache.org/licenses/LICENSE-2.0. |
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| 5 | ! |
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| 6 | ! In applying this licence, ECMWF does not waive the privileges and immunities |
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| 7 | ! granted to it by virtue of its status as an intergovernmental organisation |
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| 8 | ! nor does it submit to any jurisdiction. |
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| 9 | |
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| 10 | !* |
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| 11 | ! ------------------------------------------------------------------ |
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| 12 | |
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| 13 | ! This COMDECK includes the Thermodynamical functions for the cy39 |
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| 14 | ! ECMWF Physics package. |
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| 15 | ! Consistent with YOMCST Basic physics constants, assuming the |
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| 16 | ! partial pressure of water vapour is given by a first order |
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| 17 | ! Taylor expansion of Qs(T) w.r.t. to Temperature, using constants |
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| 18 | ! in YOETHF |
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| 19 | ! Two sets of functions are available. In the first set only the |
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| 20 | ! cases water or ice are distinguished by temperature. This set |
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| 21 | ! consists of the functions FOEDELTA,FOEEW,FOEDE and FOELH. |
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| 22 | ! The second set considers, besides the two cases water and ice |
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| 23 | ! also a mix of both for the temperature range RTICE < T < RTWAT. |
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| 24 | ! This set contains FOEALFA,FOEEWM,FOEDEM,FOELDCPM and FOELHM. |
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| 25 | ! FKOOP modifies the ice saturation mixing ratio for homogeneous |
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| 26 | ! nucleation. FOE_DEWM_DT provides an approximate first derivative |
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| 27 | ! of FOEEWM. |
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| 28 | |
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| 29 | ! Depending on the consideration of mixed phases either the first |
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| 30 | ! set (e.g. surface, post-processing) or the second set |
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| 31 | ! (e.g. clouds, condensation, convection) should be used. |
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| 32 | |
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| 33 | ! ------------------------------------------------------------------ |
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| 34 | ! ***************************************************************** |
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| 35 | |
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| 36 | ! NO CONSIDERATION OF MIXED PHASES |
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| 37 | |
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| 38 | ! ***************************************************************** |
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| 39 | REAL(KIND=JPRB) :: FOEDELTA |
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| 40 | REAL(KIND=JPRB) :: PTARE |
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| 41 | FOEDELTA (PTARE) = MAX (0.0_JPRB,SIGN(1.0_JPRB,PTARE-RTT)) |
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| 42 | |
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| 43 | ! FOEDELTA = 1 water |
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| 44 | ! FOEDELTA = 0 ice |
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| 45 | |
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| 46 | ! THERMODYNAMICAL FUNCTIONS . |
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| 47 | |
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| 48 | ! Pressure of water vapour at saturation |
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| 49 | ! INPUT : PTARE = TEMPERATURE |
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| 50 | REAL(KIND=JPRB) :: FOEEW,FOEDE,FOEDESU,FOELH,FOELDCP |
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| 51 | FOEEW ( PTARE ) = R2ES*EXP (& |
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| 52 | &(R3LES*FOEDELTA(PTARE)+R3IES*(1.0_JPRB-FOEDELTA(PTARE)))*(PTARE-RTT)& |
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| 53 | &/ (PTARE-(R4LES*FOEDELTA(PTARE)+R4IES*(1.0_JPRB-FOEDELTA(PTARE))))) |
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| 54 | |
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| 55 | FOEDE ( PTARE ) = & |
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| 56 | &(FOEDELTA(PTARE)*R5ALVCP+(1.0_JPRB-FOEDELTA(PTARE))*R5ALSCP)& |
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| 57 | &/ (PTARE-(R4LES*FOEDELTA(PTARE)+R4IES*(1.0_JPRB-FOEDELTA(PTARE))))**2 |
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| 58 | |
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| 59 | FOEDESU ( PTARE ) = & |
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| 60 | &(FOEDELTA(PTARE)*R5LES+(1.0_JPRB-FOEDELTA(PTARE))*R5IES)& |
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| 61 | &/ (PTARE-(R4LES*FOEDELTA(PTARE)+R4IES*(1.0_JPRB-FOEDELTA(PTARE))))**2 |
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| 62 | |
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| 63 | FOELH ( PTARE ) =& |
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| 64 | &FOEDELTA(PTARE)*RLVTT + (1.0_JPRB-FOEDELTA(PTARE))*RLSTT |
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| 65 | |
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| 66 | FOELDCP ( PTARE ) = & |
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| 67 | &FOEDELTA(PTARE)*RALVDCP + (1.0_JPRB-FOEDELTA(PTARE))*RALSDCP |
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| 68 | |
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| 69 | ! ***************************************************************** |
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| 70 | |
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| 71 | ! CONSIDERATION OF MIXED PHASES |
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| 72 | |
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| 73 | ! ***************************************************************** |
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| 74 | |
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| 75 | ! FOEALFA is calculated to distinguish the three cases: |
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| 76 | |
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| 77 | ! FOEALFA=1 water phase |
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| 78 | ! FOEALFA=0 ice phase |
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| 79 | ! 0 < FOEALFA < 1 mixed phase |
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| 80 | |
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| 81 | ! INPUT : PTARE = TEMPERATURE |
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| 82 | REAL(KIND=JPRB) :: FOEALFA |
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| 83 | FOEALFA (PTARE) = MIN(1.0_JPRB,((MAX(RTICE,MIN(RTWAT,PTARE))-RTICE)& |
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| 84 | &*RTWAT_RTICE_R)**2) |
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| 85 | |
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| 86 | |
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| 87 | ! Pressure of water vapour at saturation |
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| 88 | ! INPUT : PTARE = TEMPERATURE |
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| 89 | REAL(KIND=JPRB) :: FOEEWM,FOEDEM,FOELDCPM,FOELHM,FOE_DEWM_DT |
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| 90 | FOEEWM ( PTARE ) = R2ES *& |
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| 91 | &(FOEALFA(PTARE)*EXP(R3LES*(PTARE-RTT)/(PTARE-R4LES))+& |
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| 92 | &(1.0_JPRB-FOEALFA(PTARE))*EXP(R3IES*(PTARE-RTT)/(PTARE-R4IES))) |
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| 93 | |
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| 94 | FOE_DEWM_DT( PTARE ) = R2ES * ( & |
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| 95 | & R3LES*FOEALFA(PTARE)*EXP(R3LES*(PTARE-RTT)/(PTARE-R4LES)) & |
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| 96 | & *(RTT-R4LES)/(PTARE-R4LES)**2 + & |
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| 97 | & R3IES*(1.0-FOEALFA(PTARE))*EXP(R3IES*(PTARE-RTT)/(PTARE-R4IES)) & |
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| 98 | & *(RTT-R4IES)/(PTARE-R4IES)**2) |
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| 99 | |
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| 100 | FOEDEM ( PTARE ) = FOEALFA(PTARE)*R5ALVCP*(1.0_JPRB/(PTARE-R4LES)**2)+& |
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| 101 | &(1.0_JPRB-FOEALFA(PTARE))*R5ALSCP*(1.0_JPRB/(PTARE-R4IES)**2) |
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| 102 | |
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| 103 | FOELDCPM ( PTARE ) = FOEALFA(PTARE)*RALVDCP+& |
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| 104 | &(1.0_JPRB-FOEALFA(PTARE))*RALSDCP |
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| 105 | |
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| 106 | FOELHM ( PTARE ) =& |
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| 107 | &FOEALFA(PTARE)*RLVTT+(1.0_JPRB-FOEALFA(PTARE))*RLSTT |
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| 108 | |
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| 109 | |
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| 110 | ! Temperature normalization for humidity background change of variable |
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| 111 | ! INPUT : PTARE = TEMPERATURE |
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| 112 | REAL(KIND=JPRB) :: FOETB |
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| 113 | FOETB ( PTARE )=FOEALFA(PTARE)*R3LES*(RTT-R4LES)*(1.0_JPRB/(PTARE-R4LES)**2)+& |
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| 114 | &(1.0_JPRB-FOEALFA(PTARE))*R3IES*(RTT-R4IES)*(1.0_JPRB/(PTARE-R4IES)**2) |
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| 115 | |
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| 116 | ! ------------------------------------------------------------------ |
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| 117 | ! ***************************************************************** |
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| 118 | |
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| 119 | ! CONSIDERATION OF DIFFERENT MIXED PHASE FOR CONV |
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| 120 | |
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| 121 | ! ***************************************************************** |
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| 122 | |
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| 123 | ! FOEALFCU is calculated to distinguish the three cases: |
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| 124 | |
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| 125 | ! FOEALFCU=1 water phase |
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| 126 | ! FOEALFCU=0 ice phase |
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| 127 | ! 0 < FOEALFCU < 1 mixed phase |
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| 128 | |
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| 129 | ! INPUT : PTARE = TEMPERATURE |
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| 130 | REAL(KIND=JPRB) :: FOEALFCU |
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| 131 | FOEALFCU (PTARE) = MIN(1.0_JPRB,((MAX(RTICECU,MIN(RTWAT,PTARE))& |
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| 132 | &-RTICECU)*RTWAT_RTICECU_R)**2) |
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| 133 | |
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| 134 | |
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| 135 | ! Pressure of water vapour at saturation |
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| 136 | ! INPUT : PTARE = TEMPERATURE |
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| 137 | REAL(KIND=JPRB) :: FOEEWMCU,FOEDEMCU,FOELDCPMCU,FOELHMCU |
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| 138 | FOEEWMCU ( PTARE ) = R2ES *& |
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| 139 | &(FOEALFCU(PTARE)*EXP(R3LES*(PTARE-RTT)/(PTARE-R4LES))+& |
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| 140 | &(1.0_JPRB-FOEALFCU(PTARE))*EXP(R3IES*(PTARE-RTT)/(PTARE-R4IES))) |
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| 141 | |
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| 142 | FOEDEMCU ( PTARE )=FOEALFCU(PTARE)*R5ALVCP*(1.0_JPRB/(PTARE-R4LES)**2)+& |
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| 143 | &(1.0_JPRB-FOEALFCU(PTARE))*R5ALSCP*(1.0_JPRB/(PTARE-R4IES)**2) |
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| 144 | |
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| 145 | FOELDCPMCU ( PTARE ) = FOEALFCU(PTARE)*RALVDCP+& |
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| 146 | &(1.0_JPRB-FOEALFCU(PTARE))*RALSDCP |
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| 147 | |
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| 148 | FOELHMCU ( PTARE ) =& |
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| 149 | &FOEALFCU(PTARE)*RLVTT+(1.0_JPRB-FOEALFCU(PTARE))*RLSTT |
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| 150 | ! ------------------------------------------------------------------ |
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| 151 | |
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| 152 | ! Pressure of water vapour at saturation |
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| 153 | ! This one is for the WMO definition of saturation, i.e. always |
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| 154 | ! with respect to water. |
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| 155 | ! |
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| 156 | ! Duplicate to FOEELIQ and FOEEICE for separate ice variable |
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| 157 | ! FOEELIQ always respect to water |
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| 158 | ! FOEEICE always respect to ice |
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| 159 | ! FOEELIQ2ICE is the ratio of vapour pressures over water and ice |
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| 160 | ! (analytically simplified to avoid a suspected Cray compiler bug and using a single call to exp) |
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| 161 | ! (could use FOEEW and FOEEWMO, but naming convention unclear) |
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| 162 | ! FOELSON returns e wrt liquid water using D Sonntag (1994, Met. Zeit.) |
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| 163 | ! - now recommended for use with radiosonde data (WMO CIMO guide, 2014) |
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| 164 | ! unlike the FOEE functions does not include 1/(RETV+1.0_JPRB) factor |
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| 165 | |
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| 166 | REAL(KIND=JPRB) :: FOEEWMO, FOEELIQ, FOEEICE, FOEELIQ2ICE, FOELSON |
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| 167 | FOEEWMO( PTARE ) = R2ES*EXP(R3LES*(PTARE-RTT)/(PTARE-R4LES)) |
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| 168 | FOEELIQ( PTARE ) = R2ES*EXP(R3LES*(PTARE-RTT)/(PTARE-R4LES)) |
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| 169 | FOEEICE( PTARE ) = R2ES*EXP(R3IES*(PTARE-RTT)/(PTARE-R4IES)) |
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| 170 | FOEELIQ2ICE( PTARE ) = EXP( (PTARE-RTT)*(R3LES/(PTARE-R4LES) - R3IES/(PTARE-R4IES))) |
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| 171 | FOELSON( PTARE ) = EXP( -6096.9385_JPRB/PTARE + 21.2409642_JPRB & |
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| 172 | - 2.711193E-2_JPRB * PTARE & |
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| 173 | + 1.673952E-5_JPRB * PTARE**2 & |
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| 174 | + 2.433502_JPRB * LOG(PTARE)) |
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| 175 | |
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| 176 | REAL(KIND=JPRB) :: FOEEWM_V,FOEEWMCU_V,FOELES_V,FOEIES_V |
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| 177 | REAL(KIND=JPRB) :: EXP1,EXP2 |
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| 178 | FOELES_V(PTARE)=R3LES*(PTARE-RTT)/(PTARE-R4LES) |
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| 179 | FOEIES_V(PTARE)=R3IES*(PTARE-RTT)/(PTARE-R4IES) |
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| 180 | FOEEWM_V( PTARE,EXP1,EXP2 )=R2ES*(FOEALFA(PTARE)*EXP1+ & |
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| 181 | & (1.0_JPRB-FOEALFA(PTARE))*EXP2) |
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| 182 | FOEEWMCU_V ( PTARE,EXP1,EXP2 ) = R2ES*(FOEALFCU(PTARE)*EXP1+& |
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| 183 | &(1.0_JPRB-FOEALFCU(PTARE))*EXP2) |
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| 184 | |
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