| 1 | module ACAMA_GWD_rando_m |
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| 2 | |
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| 3 | implicit none |
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| 4 | |
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| 5 | contains |
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| 6 | |
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| 7 | SUBROUTINE ACAMA_GWD_rando(DTIME, pp, plat, tt, uu, vv, rot, & |
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| 8 | zustr, zvstr, d_u, d_v,east_gwstress,west_gwstress) |
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| 9 | |
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| 10 | ! Parametrization of the momentum flux deposition due to a discrete |
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| 11 | ! number of gravity waves. |
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| 12 | ! Author: F. Lott, A. de la Camara |
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| 13 | ! July, 24th, 2014 |
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| 14 | ! Gaussian distribution of the source, source is vorticity squared |
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| 15 | ! Reference: de la Camara and Lott (GRL, 2015, vol 42, 2071-2078 ) |
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| 16 | ! Lott et al (JAS, 2010, vol 67, page 157-170) |
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| 17 | ! Lott et al (JAS, 2012, vol 69, page 2134-2151) |
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| 18 | |
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| 19 | ! ONLINE: |
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| 20 | use dimphy, only: klon, klev |
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| 21 | use assert_m, only: assert |
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| 22 | include "YOMCST.h" |
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| 23 | include "clesphys.h" |
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| 24 | ! OFFLINE: |
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| 25 | ! include "dimensions.h" |
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| 26 | ! include "dimphy.h" |
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| 27 | !END DIFFERENCE |
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| 28 | include "YOEGWD.h" |
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| 29 | |
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| 30 | ! 0. DECLARATIONS: |
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| 31 | |
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| 32 | ! 0.1 INPUTS |
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| 33 | REAL, intent(in)::DTIME ! Time step of the Physics |
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| 34 | REAL, intent(in):: PP(:, :) ! (KLON, KLEV) Pressure at full levels |
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| 35 | REAL, intent(in):: ROT(:,:) ! Relative vorticity |
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| 36 | REAL, intent(in):: TT(:, :) ! (KLON, KLEV) Temp at full levels |
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| 37 | REAL, intent(in):: UU(:, :) ! (KLON, KLEV) Zonal wind at full levels |
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| 38 | REAL, intent(in):: VV(:, :) ! (KLON, KLEV) Merid wind at full levels |
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| 39 | REAL, intent(in):: PLAT(:) ! (KLON) LATITUDE |
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| 40 | |
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| 41 | ! 0.2 OUTPUTS |
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| 42 | REAL, intent(out):: zustr(:), zvstr(:) ! (KLON) Surface Stresses |
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| 43 | |
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| 44 | REAL, intent(inout):: d_u(:, :), d_v(:, :) |
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| 45 | REAL, intent(inout):: east_gwstress(:, :) ! Profile of eastward stress |
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| 46 | REAL, intent(inout):: west_gwstress(:, :) ! Profile of westward stress |
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| 47 | ! (KLON, KLEV) tendencies on winds |
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| 48 | |
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| 49 | ! O.3 INTERNAL ARRAYS |
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| 50 | REAL BVLOW(klon) ! LOW LEVEL BV FREQUENCY |
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| 51 | REAL ROTBA(KLON),CORIO(KLON) ! BAROTROPIC REL. VORTICITY AND PLANETARY |
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| 52 | REAL UZ(KLON, KLEV + 1) |
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| 53 | |
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| 54 | INTEGER II, JJ, LL |
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| 55 | |
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| 56 | ! 0.3.0 TIME SCALE OF THE LIFE CYCLE OF THE WAVES PARAMETERIZED |
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| 57 | |
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| 58 | REAL DELTAT |
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| 59 | |
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| 60 | ! 0.3.1 GRAVITY-WAVES SPECIFICATIONS |
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| 61 | |
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| 62 | INTEGER, PARAMETER:: NK = 2, NP = 2, NO = 2, NW = NK * NP * NO |
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| 63 | INTEGER JK, JP, JO, JW |
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| 64 | INTEGER, PARAMETER:: NA = 5 !number of realizations to get the phase speed |
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| 65 | REAL KMIN, KMAX ! Min and Max horizontal wavenumbers |
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| 66 | REAL CMIN, CMAX ! Min and Max absolute ph. vel. |
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| 67 | REAL CPHA ! absolute PHASE VELOCITY frequency |
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| 68 | REAL ZK(NW, KLON) ! Horizontal wavenumber amplitude |
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| 69 | REAL ZP(NW, KLON) ! Horizontal wavenumber angle |
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| 70 | REAL ZO(NW, KLON) ! Absolute frequency ! |
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| 71 | |
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| 72 | ! Waves Intr. freq. at the 1/2 lev surrounding the full level |
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| 73 | REAL ZOM(NW, KLON), ZOP(NW, KLON) |
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| 74 | |
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| 75 | ! Wave EP-fluxes at the 2 semi levels surrounding the full level |
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| 76 | REAL WWM(NW, KLON), WWP(NW, KLON) |
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| 77 | |
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| 78 | REAL RUW0(NW, KLON) ! Fluxes at launching level |
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| 79 | |
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| 80 | REAL RUWP(NW, KLON), RVWP(NW, KLON) |
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| 81 | ! Fluxes X and Y for each waves at 1/2 Levels |
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| 82 | |
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| 83 | INTEGER LAUNCH, LTROP ! Launching altitude and tropo altitude |
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| 84 | |
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| 85 | REAL XLAUNCH ! Controle the launching altitude |
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| 86 | REAL XTROP ! SORT of Tropopause altitude |
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| 87 | REAL RUW(KLON, KLEV + 1) ! Flux x at semi levels |
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| 88 | REAL RVW(KLON, KLEV + 1) ! Flux y at semi levels |
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| 89 | |
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| 90 | REAL PRMAX ! Maximum value of PREC, and for which our linear formula |
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| 91 | ! for GWs parameterisation apply |
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| 92 | |
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| 93 | ! 0.3.2 PARAMETERS OF WAVES DISSIPATIONS |
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| 94 | |
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| 95 | REAL RDISS, ZOISEC ! COEFF DE DISSIPATION, SECURITY FOR INTRINSIC FREQ |
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| 96 | REAL CORSEC ! SECURITY FOR INTRINSIC CORIOLIS |
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| 97 | REAL RUWFRT,SATFRT |
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| 98 | |
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| 99 | ! 0.3.3 BACKGROUND FLOW AT 1/2 LEVELS AND VERTICAL COORDINATE |
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| 100 | |
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| 101 | REAL H0 ! Characteristic Height of the atmosphere |
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| 102 | REAL DZ ! Characteristic depth of the source! |
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| 103 | REAL PR, TR ! Reference Pressure and Temperature |
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| 104 | |
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| 105 | REAL ZH(KLON, KLEV + 1) ! Log-pressure altitude |
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| 106 | |
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| 107 | REAL UH(KLON, KLEV + 1), VH(KLON, KLEV + 1) ! Winds at 1/2 levels |
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| 108 | REAL PH(KLON, KLEV + 1) ! Pressure at 1/2 levels |
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| 109 | REAL PSEC ! Security to avoid division by 0 pressure |
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| 110 | REAL PHM1(KLON, KLEV + 1) ! 1/Press at 1/2 levels |
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| 111 | REAL BV(KLON, KLEV + 1) ! Brunt Vaisala freq. (BVF) at 1/2 levels |
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| 112 | REAL BVSEC ! Security to avoid negative BVF |
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| 113 | |
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| 114 | !----------------------------------------------------------------- |
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| 115 | |
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| 116 | ! 1. INITIALISATIONS |
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| 117 | |
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| 118 | ! 1.1 Basic parameter |
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| 119 | |
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| 120 | ! Are provided from elsewhere (latent heat of vaporization, dry |
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| 121 | ! gaz constant for air, gravity constant, heat capacity of dry air |
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| 122 | ! at constant pressure, earth rotation rate, pi). |
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| 123 | |
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| 124 | ! 1.2 Tuning parameters of V14 |
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| 125 | |
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| 126 | ! Values for linear in rot (recommended): |
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| 127 | ! RUWFRT=0.005 ! As RUWMAX but for frontal waves |
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| 128 | ! SATFRT=1.00 ! As SAT but for frontal waves |
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| 129 | ! Values when rot^2 is used |
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| 130 | ! RUWFRT=0.02 ! As RUWMAX but for frontal waves |
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| 131 | ! SATFRT=1.00 ! As SAT but for frontal waves |
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| 132 | ! CMAX = 30. ! Characteristic phase speed |
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| 133 | ! Values when rot^2*EXP(-pi*sqrt(J)) is used |
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| 134 | ! RUWFRT=2.5 ! As RUWMAX but for frontal waves ~ N0*F0/4*DZ |
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| 135 | ! SATFRT=0.60 ! As SAT but for frontal waves |
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| 136 | RUWFRT=gwd_front_ruwmax |
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| 137 | SATFRT=gwd_front_sat |
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| 138 | CMAX = 50. ! Characteristic phase speed |
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| 139 | ! Phase speed test |
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| 140 | ! RUWFRT=0.01 |
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| 141 | ! CMAX = 50. ! Characteristic phase speed (TEST) |
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| 142 | ! Values when rot^2 and exp(-m^2*dz^2) are used |
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| 143 | ! RUWFRT=0.03 ! As RUWMAX but for frontal waves |
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| 144 | ! SATFRT=1.00 ! As SAT but for frontal waves |
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| 145 | ! CRUCIAL PARAMETERS FOR THE WIND FILTERING |
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| 146 | XLAUNCH=0.95 ! Parameter that control launching altitude |
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| 147 | RDISS = 0.5 ! Diffusion parameter |
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| 148 | |
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| 149 | ! maximum of rain for which our theory applies (in kg/m^2/s) |
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| 150 | |
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| 151 | DZ = 1000. ! Characteristic depth of the source |
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| 152 | XTROP=0.2 ! Parameter that control tropopause altitude |
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| 153 | DELTAT=24.*3600. ! Time scale of the waves (first introduced in 9b) |
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| 154 | ! DELTAT=DTIME ! No AR-1 Accumulation, OR OFFLINE |
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| 155 | |
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| 156 | KMIN = 2.E-5 |
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| 157 | ! minimum horizontal wavenumber (inverse of the subgrid scale resolution) |
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| 158 | |
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| 159 | KMAX = 1.E-3 ! Max horizontal wavenumber |
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| 160 | CMIN = 1. ! Min phase velocity |
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| 161 | |
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| 162 | TR = 240. ! Reference Temperature |
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| 163 | PR = 101300. ! Reference pressure |
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| 164 | H0 = RD * TR / RG ! Characteristic vertical scale height |
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| 165 | |
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| 166 | BVSEC = 5.E-3 ! Security to avoid negative BVF |
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| 167 | PSEC = 1.E-6 ! Security to avoid division by 0 pressure |
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| 168 | ZOISEC = 1.E-6 ! Security FOR 0 INTRINSIC FREQ |
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| 169 | CORSEC = ROMEGA*2.*SIN(2.*RPI/180.)! Security for CORIO |
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| 170 | |
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| 171 | ! ONLINE |
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| 172 | call assert(klon == (/size(pp, 1), size(tt, 1), size(uu, 1), & |
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| 173 | size(vv, 1), size(rot,1), size(zustr), size(zvstr), size(d_u, 1), & |
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| 174 | size(d_v, 1), & |
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| 175 | size(east_gwstress,1), size(west_gwstress,1) /), & |
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| 176 | "ACAMA_GWD_RANDO klon") |
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| 177 | call assert(klev == (/size(pp, 2), size(tt, 2), size(uu, 2), & |
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| 178 | size(vv, 2), size(d_u, 2), size(d_v, 2), & |
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| 179 | size(east_gwstress,2), size(west_gwstress,2) /), & |
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| 180 | "ACAMA_GWD_RANDO klev") |
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| 181 | ! END ONLINE |
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| 182 | |
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| 183 | IF(DELTAT < DTIME)THEN |
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| 184 | PRINT *, 'flott_gwd_rando: deltat < dtime!' |
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| 185 | STOP 1 |
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| 186 | ENDIF |
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| 187 | |
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| 188 | IF (KLEV < NW) THEN |
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| 189 | PRINT *, 'flott_gwd_rando: you will have problem with random numbers' |
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| 190 | STOP 1 |
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| 191 | ENDIF |
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| 192 | |
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| 193 | ! 2. EVALUATION OF THE BACKGROUND FLOW AT SEMI-LEVELS |
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| 194 | |
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| 195 | ! Pressure and Inv of pressure |
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| 196 | DO LL = 2, KLEV |
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| 197 | PH(:, LL) = EXP((LOG(PP(:, LL)) + LOG(PP(:, LL - 1))) / 2.) |
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| 198 | PHM1(:, LL) = 1. / PH(:, LL) |
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| 199 | end DO |
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| 200 | |
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| 201 | PH(:, KLEV + 1) = 0. |
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| 202 | PHM1(:, KLEV + 1) = 1. / PSEC |
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| 203 | PH(:, 1) = 2. * PP(:, 1) - PH(:, 2) |
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| 204 | |
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| 205 | ! Launching altitude |
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| 206 | |
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| 207 | LAUNCH=0 |
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| 208 | LTROP =0 |
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| 209 | DO LL = 1, KLEV |
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| 210 | IF (PH(KLON / 2, LL) / PH(KLON / 2, 1) > XLAUNCH) LAUNCH = LL |
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| 211 | ENDDO |
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| 212 | DO LL = 1, KLEV |
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| 213 | IF (PH(KLON / 2, LL) / PH(KLON / 2, 1) > XTROP) LTROP = LL |
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| 214 | ENDDO |
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| 215 | |
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| 216 | ! PRINT *,'LAUNCH IN ACAMARA:',LAUNCH |
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| 217 | |
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| 218 | ! Log pressure vert. coordinate |
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| 219 | DO LL = 1, KLEV + 1 |
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| 220 | ZH(:, LL) = H0 * LOG(PR / (PH(:, LL) + PSEC)) |
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| 221 | end DO |
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| 222 | |
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| 223 | ! BV frequency |
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| 224 | DO LL = 2, KLEV |
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| 225 | ! BVSEC: BV Frequency (UH USED IS AS A TEMPORARY ARRAY DOWN TO WINDS) |
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| 226 | UH(:, LL) = 0.5 * (TT(:, LL) + TT(:, LL - 1)) & |
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| 227 | * RD**2 / RCPD / H0**2 + (TT(:, LL) & |
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| 228 | - TT(:, LL - 1)) / (ZH(:, LL) - ZH(:, LL - 1)) * RD / H0 |
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| 229 | end DO |
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| 230 | BVLOW = 0.5 * (TT(:, LTROP )+ TT(:, LAUNCH)) & |
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| 231 | * RD**2 / RCPD / H0**2 + (TT(:, LTROP ) & |
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| 232 | - TT(:, LAUNCH))/(ZH(:, LTROP )- ZH(:, LAUNCH)) * RD / H0 |
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| 233 | |
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| 234 | UH(:, 1) = UH(:, 2) |
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| 235 | UH(:, KLEV + 1) = UH(:, KLEV) |
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| 236 | BV(:, 1) = UH(:, 2) |
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| 237 | BV(:, KLEV + 1) = UH(:, KLEV) |
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| 238 | ! SMOOTHING THE BV HELPS |
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| 239 | DO LL = 2, KLEV |
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| 240 | BV(:, LL)=(UH(:, LL+1)+2.*UH(:, LL)+UH(:, LL-1))/4. |
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| 241 | end DO |
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| 242 | |
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| 243 | BV=MAX(SQRT(MAX(BV, 0.)), BVSEC) |
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| 244 | BVLOW=MAX(SQRT(MAX(BVLOW, 0.)), BVSEC) |
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| 245 | |
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| 246 | ! WINDS |
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| 247 | DO LL = 2, KLEV |
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| 248 | UH(:, LL) = 0.5 * (UU(:, LL) + UU(:, LL - 1)) ! Zonal wind |
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| 249 | VH(:, LL) = 0.5 * (VV(:, LL) + VV(:, LL - 1)) ! Meridional wind |
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| 250 | UZ(:, LL) = ABS((SQRT(UU(:, LL)**2+VV(:, LL)**2) & |
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| 251 | - SQRT(UU(:,LL-1)**2+VV(:, LL-1)**2)) & |
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| 252 | /(ZH(:, LL)-ZH(:, LL-1)) ) |
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| 253 | end DO |
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| 254 | UH(:, 1) = 0. |
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| 255 | VH(:, 1) = 0. |
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| 256 | UH(:, KLEV + 1) = UU(:, KLEV) |
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| 257 | VH(:, KLEV + 1) = VV(:, KLEV) |
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| 258 | |
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| 259 | UZ(:, 1) = UZ(:, 2) |
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| 260 | UZ(:, KLEV + 1) = UZ(:, KLEV) |
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| 261 | UZ(:, :) = MAX(UZ(:,:), PSEC) |
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| 262 | |
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| 263 | ! BAROTROPIC VORTICITY AND INTEGRATED CORIOLIS PARAMETER |
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| 264 | |
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| 265 | CORIO(:) = MAX(ROMEGA*2.*ABS(SIN(PLAT(:)*RPI/180.)),CORSEC) |
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| 266 | ROTBA(:)=0. |
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| 267 | DO LL = 1,KLEV-1 |
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| 268 | !ROTBA(:) = ROTBA(:) + (ROT(:,LL)+ROT(:,LL+1))/2./RG*(PP(:,LL)-PP(:,LL+1)) |
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| 269 | ! Introducing the complete formula (exp of Richardson number): |
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| 270 | ROTBA(:) = ROTBA(:) + & |
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| 271 | !((ROT(:,LL)+ROT(:,LL+1))/2.)**2 & |
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| 272 | (CORIO(:)*TANH(ABS(ROT(:,LL)+ROT(:,LL+1))/2./CORIO(:)))**2 & |
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| 273 | /RG*(PP(:,LL)-PP(:,LL+1)) & |
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| 274 | * EXP(-RPI*BV(:,LL+1)/UZ(:,LL+1)) & |
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| 275 | ! * DZ*BV(:,LL+1)/4./ABS(CORIO(:)) |
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| 276 | * DZ*BV(:,LL+1)/4./1.E-4 ! Changes after 1991 |
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| 277 | !ARRET |
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| 278 | ENDDO |
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| 279 | ! PRINT *,'MAX ROTBA:',MAXVAL(ROTBA) |
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| 280 | ! ROTBA(:)=(1.*ROTBA(:) & ! Testing zone |
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| 281 | ! +0.15*CORIO(:)**2 & |
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| 282 | ! /(COS(PLAT(:)*RPI/180.)+0.02) & |
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| 283 | ! )*DZ*0.01/0.0001/4. ! & ! Testing zone |
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| 284 | ! MODIF GWD4 AFTER 1985 |
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| 285 | ! *(1.25+SIN(PLAT(:)*RPI/180.))/(1.05+SIN(PLAT(:)*RPI/180.))/1.25 |
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| 286 | ! *1./(COS(PLAT(:)*RPI/180.)+0.02) |
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| 287 | ! CORIO(:) = MAX(ROMEGA*2.*ABS(SIN(PLAT(:)*RPI/180.)),ZOISEC)/RG*PP(:,1) |
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| 288 | |
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| 289 | ! 3 WAVES CHARACTERISTICS CHOSEN RANDOMLY AT THE LAUNCH ALTITUDE |
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| 290 | |
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| 291 | ! The mod functions of weird arguments are used to produce the |
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| 292 | ! waves characteristics in an almost stochastic way |
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| 293 | |
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| 294 | JW = 0 |
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| 295 | DO JP = 1, NP |
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| 296 | DO JK = 1, NK |
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| 297 | DO JO = 1, NO |
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| 298 | JW = JW + 1 |
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| 299 | ! Angle |
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| 300 | DO II = 1, KLON |
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| 301 | ! Angle (0 or PI so far) |
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| 302 | ! ZP(JW, II) = (SIGN(1., 0.5 - MOD(TT(II, JW) * 10., 1.)) + 1.) & |
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| 303 | ! * RPI / 2. |
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| 304 | ! Angle between 0 and pi |
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| 305 | ZP(JW, II) = MOD(TT(II, JW) * 10., 1.) * RPI |
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| 306 | ! TEST WITH POSITIVE WAVES ONLY (Part I/II) |
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| 307 | ! ZP(JW, II) = 0. |
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| 308 | ! Horizontal wavenumber amplitude |
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| 309 | ZK(JW, II) = KMIN + (KMAX - KMIN) * MOD(TT(II, JW) * 100., 1.) |
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| 310 | ! Horizontal phase speed |
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| 311 | CPHA = 0. |
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| 312 | DO JJ = 1, NA |
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| 313 | CPHA = CPHA + & |
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| 314 | CMAX*2.*(MOD(TT(II, JW+4*(JJ-1)+JJ)**2, 1.)-0.5)*SQRT(3.)/SQRT(NA*1.) |
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| 315 | END DO |
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| 316 | IF (CPHA.LT.0.) THEN |
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| 317 | CPHA = -1.*CPHA |
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| 318 | ZP(JW,II) = ZP(JW,II) + RPI |
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| 319 | ! TEST WITH POSITIVE WAVES ONLY (Part II/II) |
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| 320 | ! ZP(JW, II) = 0. |
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| 321 | ENDIF |
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| 322 | CPHA = CPHA + CMIN !we dont allow |c|<1m/s |
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| 323 | ! Absolute frequency is imposed |
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| 324 | ZO(JW, II) = CPHA * ZK(JW, II) |
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| 325 | ! Intrinsic frequency is imposed |
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| 326 | ZO(JW, II) = ZO(JW, II) & |
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| 327 | + ZK(JW, II) * COS(ZP(JW, II)) * UH(II, LAUNCH) & |
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| 328 | + ZK(JW, II) * SIN(ZP(JW, II)) * VH(II, LAUNCH) |
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| 329 | ! Momentum flux at launch lev |
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| 330 | ! LAUNCHED RANDOM WAVES WITH LOG-NORMAL AMPLITUDE |
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| 331 | ! RIGHT IN THE SH (GWD4 after 1990) |
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| 332 | RUW0(JW, II) = 0. |
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| 333 | DO JJ = 1, NA |
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| 334 | RUW0(JW, II) = RUW0(JW,II) + & |
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| 335 | 2.*(MOD(TT(II, JW+4*(JJ-1)+JJ)**2, 1.)-0.5)*SQRT(3.)/SQRT(NA*1.) |
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| 336 | END DO |
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| 337 | RUW0(JW, II) = RUWFRT & |
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| 338 | * EXP(RUW0(JW,II))/1250. & ! 2 mpa at south pole |
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| 339 | *((1.05+SIN(PLAT(II)*RPI/180.))/(1.01+SIN(PLAT(II)*RPI/180.))-2.05/2.01) |
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| 340 | ! RUW0(JW, II) = RUWFRT |
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| 341 | ENDDO |
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| 342 | end DO |
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| 343 | end DO |
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| 344 | end DO |
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| 345 | |
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| 346 | ! 4. COMPUTE THE FLUXES |
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| 347 | |
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| 348 | ! 4.0 |
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| 349 | |
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| 350 | ! 4.1 Vertical velocity at launching altitude to ensure |
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| 351 | ! the correct value to the imposed fluxes. |
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| 352 | |
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| 353 | DO JW = 1, NW |
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| 354 | |
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| 355 | ! Evaluate intrinsic frequency at launching altitude: |
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| 356 | ZOP(JW, :) = ZO(JW, :) & |
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| 357 | - ZK(JW, :) * COS(ZP(JW, :)) * UH(:, LAUNCH) & |
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| 358 | - ZK(JW, :) * SIN(ZP(JW, :)) * VH(:, LAUNCH) |
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| 359 | |
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| 360 | ! VERSION WITH FRONTAL SOURCES |
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| 361 | |
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| 362 | ! Momentum flux at launch level imposed by vorticity sources |
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| 363 | |
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| 364 | ! tanh limitation for values above CORIO (inertial instability). |
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| 365 | ! WWP(JW, :) = RUW0(JW, :) & |
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| 366 | WWP(JW, :) = RUWFRT & |
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| 367 | ! * (CORIO(:)*TANH(ROTBA(:)/CORIO(:)))**2 & |
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| 368 | ! * ABS((CORIO(:)*TANH(ROTBA(:)/CORIO(:)))*CORIO(:)) & |
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| 369 | ! CONSTANT FLUX |
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| 370 | ! * (CORIO(:)*CORIO(:)) & |
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| 371 | ! MODERATION BY THE DEPTH OF THE SOURCE (DZ HERE) |
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| 372 | ! *EXP(-BVLOW(:)**2/MAX(ABS(ZOP(JW, :)),ZOISEC)**2 & |
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| 373 | ! *ZK(JW, :)**2*DZ**2) & |
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| 374 | ! COMPLETE FORMULA: |
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| 375 | !* CORIO(:)**2*TANH(ROTBA(:)/CORIO(:)**2) & |
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| 376 | * ROTBA(:) & |
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| 377 | ! RESTORE DIMENSION OF A FLUX |
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| 378 | ! *RD*TR/PR |
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| 379 | ! *1. + RUW0(JW, :) |
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| 380 | *1. |
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| 381 | |
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| 382 | ! Factor related to the characteristics of the waves: NONE |
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| 383 | |
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| 384 | ! Moderation by the depth of the source (dz here): NONE |
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| 385 | |
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| 386 | ! Put the stress in the right direction: |
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| 387 | |
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| 388 | RUWP(JW, :) = SIGN(1., ZOP(JW, :))*COS(ZP(JW, :)) * WWP(JW, :) |
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| 389 | RVWP(JW, :) = SIGN(1., ZOP(JW, :))*SIN(ZP(JW, :)) * WWP(JW, :) |
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| 390 | |
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| 391 | end DO |
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| 392 | |
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| 393 | ! 4.2 Uniform values below the launching altitude |
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| 394 | |
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| 395 | DO LL = 1, LAUNCH |
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| 396 | RUW(:, LL) = 0 |
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| 397 | RVW(:, LL) = 0 |
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| 398 | DO JW = 1, NW |
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| 399 | RUW(:, LL) = RUW(:, LL) + RUWP(JW, :) |
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| 400 | RVW(:, LL) = RVW(:, LL) + RVWP(JW, :) |
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| 401 | end DO |
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| 402 | end DO |
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| 403 | |
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| 404 | ! 4.3 Loop over altitudes, with passage from one level to the next |
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| 405 | ! done by i) conserving the EP flux, ii) dissipating a little, |
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| 406 | ! iii) testing critical levels, and vi) testing the breaking. |
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| 407 | |
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| 408 | DO LL = LAUNCH, KLEV - 1 |
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| 409 | ! Warning: all the physics is here (passage from one level |
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| 410 | ! to the next) |
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| 411 | DO JW = 1, NW |
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| 412 | ZOM(JW, :) = ZOP(JW, :) |
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| 413 | WWM(JW, :) = WWP(JW, :) |
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| 414 | ! Intrinsic Frequency |
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| 415 | ZOP(JW, :) = ZO(JW, :) - ZK(JW, :) * COS(ZP(JW, :)) * UH(:, LL + 1) & |
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| 416 | - ZK(JW, :) * SIN(ZP(JW, :)) * VH(:, LL + 1) |
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| 417 | |
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| 418 | ! No breaking (Eq.6) |
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| 419 | ! Dissipation (Eq. 8) |
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| 420 | WWP(JW, :) = WWM(JW, :) * EXP(- 4. * RDISS * PR / (PH(:, LL + 1) & |
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| 421 | + PH(:, LL)) * ((BV(:, LL + 1) + BV(:, LL)) / 2.)**3 & |
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| 422 | / MAX(ABS(ZOP(JW, :) + ZOM(JW, :)) / 2., ZOISEC)**4 & |
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| 423 | * ZK(JW, :)**3 * (ZH(:, LL + 1) - ZH(:, LL))) |
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| 424 | |
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| 425 | ! Critical levels (forced to zero if intrinsic frequency changes sign) |
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| 426 | ! Saturation (Eq. 12) |
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| 427 | WWP(JW, :) = min(WWP(JW, :), MAX(0., & |
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| 428 | SIGN(1., ZOP(JW, :) * ZOM(JW, :))) * ABS(ZOP(JW, :))**3 & |
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| 429 | ! / BV(:, LL + 1) * EXP(- ZH(:, LL + 1) / H0) * SATFRT**2 * KMIN**2 & |
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| 430 | / BV(:, LL + 1) * EXP(- ZH(:, LL + 1) / H0) * KMIN**2 & |
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| 431 | ! *(SATFRT*(2.5+1.5*TANH((ZH(:,LL+1)/H0-8.)/2.)))**2 & |
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| 432 | *SATFRT**2 & |
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| 433 | / ZK(JW, :)**4) |
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| 434 | end DO |
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| 435 | |
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| 436 | ! Evaluate EP-flux from Eq. 7 and give the right orientation to |
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| 437 | ! the stress |
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| 438 | |
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| 439 | DO JW = 1, NW |
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| 440 | RUWP(JW, :) = SIGN(1., ZOP(JW, :))*COS(ZP(JW, :)) * WWP(JW, :) |
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| 441 | RVWP(JW, :) = SIGN(1., ZOP(JW, :))*SIN(ZP(JW, :)) * WWP(JW, :) |
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| 442 | end DO |
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| 443 | |
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| 444 | RUW(:, LL + 1) = 0. |
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| 445 | RVW(:, LL + 1) = 0. |
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| 446 | |
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| 447 | DO JW = 1, NW |
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| 448 | RUW(:, LL + 1) = RUW(:, LL + 1) + RUWP(JW, :) |
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| 449 | RVW(:, LL + 1) = RVW(:, LL + 1) + RVWP(JW, :) |
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| 450 | EAST_GWSTRESS(:, LL)=EAST_GWSTRESS(:, LL)+MAX(0.,RUWP(JW,:))/FLOAT(NW) |
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| 451 | WEST_GWSTRESS(:, LL)=WEST_GWSTRESS(:, LL)+MIN(0.,RUWP(JW,:))/FLOAT(NW) |
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| 452 | end DO |
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| 453 | end DO |
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| 454 | |
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| 455 | ! 5 CALCUL DES TENDANCES: |
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| 456 | |
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| 457 | ! 5.1 Rectification des flux au sommet et dans les basses couches |
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| 458 | |
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| 459 | RUW(:, KLEV + 1) = 0. |
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| 460 | RVW(:, KLEV + 1) = 0. |
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| 461 | RUW(:, 1) = RUW(:, LAUNCH) |
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| 462 | RVW(:, 1) = RVW(:, LAUNCH) |
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| 463 | DO LL = 1, LAUNCH |
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| 464 | RUW(:, LL) = RUW(:, LAUNCH+1) |
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| 465 | RVW(:, LL) = RVW(:, LAUNCH+1) |
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| 466 | EAST_GWSTRESS(:, LL)=EAST_GWSTRESS(:, LAUNCH) |
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| 467 | WEST_GWSTRESS(:, LL)=WEST_GWSTRESS(:, LAUNCH) |
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| 468 | end DO |
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| 469 | |
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| 470 | ! AR-1 RECURSIVE FORMULA (13) IN VERSION 4 |
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| 471 | DO LL = 1, KLEV |
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| 472 | D_U(:, LL) = (1.-DTIME/DELTAT) * D_U(:, LL) + DTIME/DELTAT/REAL(NW) * & |
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| 473 | RG * (RUW(:, LL + 1) - RUW(:, LL)) & |
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| 474 | / (PH(:, LL + 1) - PH(:, LL)) * DTIME |
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| 475 | ! NO AR1 FOR MERIDIONAL TENDENCIES |
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| 476 | ! D_V(:, LL) = (1.-DTIME/DELTAT) * D_V(:, LL) + DTIME/DELTAT/REAL(NW) * & |
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| 477 | D_V(:, LL) = 1./REAL(NW) * & |
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| 478 | RG * (RVW(:, LL + 1) - RVW(:, LL)) & |
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| 479 | / (PH(:, LL + 1) - PH(:, LL)) * DTIME |
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| 480 | ENDDO |
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| 481 | |
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| 482 | ! Cosmetic: evaluation of the cumulated stress |
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| 483 | ZUSTR = 0. |
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| 484 | ZVSTR = 0. |
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| 485 | DO LL = 1, KLEV |
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| 486 | ZUSTR = ZUSTR + D_U(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL))/DTIME |
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| 487 | ! ZVSTR = ZVSTR + D_V(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL))/DTIME |
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| 488 | ENDDO |
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| 489 | ! COSMETICS TO VISUALIZE ROTBA |
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| 490 | ZVSTR = ROTBA |
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| 491 | |
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| 492 | END SUBROUTINE ACAMA_GWD_RANDO |
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| 493 | |
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| 494 | end module ACAMA_GWD_rando_m |
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