| 1 |
module aaam_bud_m |
| 2 |
|
| 3 |
implicit none |
| 4 |
|
| 5 |
contains |
| 6 |
|
| 7 |
subroutine aaam_bud(rg, ome, phis, dragu, liftu, phyu, dragv, liftv, phyv, & |
| 8 |
p, u, v, aam, torsfc) |
| 9 |
|
| 10 |
! Author: F. Lott (LMD/CNRS). Date: 2003/10/20. Object: Compute |
| 11 |
! different terms of the axial AAAM budget and mountain torque. |
| 12 |
! Only valid for regular rectangular grids. Should be called after |
| 13 |
! "lift_noro". |
| 14 |
|
| 15 |
USE dimensions, ONLY : iim, jjm |
| 16 |
use nr_util, only: assert_eq, assert, pi |
| 17 |
use phyetat0_m, only: rlat, rlon |
| 18 |
USE suphec_m, ONLY: ra |
| 19 |
|
| 20 |
real, intent(in):: rg ! gravity constant |
| 21 |
real, intent(in):: ome ! Earth rotation rate |
| 22 |
real, intent(in):: phis(:) ! (nlon) Geopotential at the ground |
| 23 |
REAL, intent(in):: dragu(:) ! (nlon) orodrag stress (zonal) |
| 24 |
REAL, intent(in):: liftu(:) ! (nlon) orolift stress (zonal) |
| 25 |
REAL, intent(in):: phyu(:) ! (nlon) Stress total de la physique (zonal) |
| 26 |
REAL, intent(in):: dragv(:) ! (nlon) orodrag stress (Meridional) |
| 27 |
REAL, intent(in):: liftv(:) ! (nlon) orolift stress (Meridional) |
| 28 |
REAL, intent(in):: phyv(:) ! (nlon) Stress total de la physique (Meridional) |
| 29 |
|
| 30 |
REAL, intent(in):: p(:, :) |
| 31 |
! (nlon, nlev + 1) pressure (Pa) at model half levels |
| 32 |
|
| 33 |
real, intent(in):: u(:, :), v(:, :) ! (nlon, nlev) horizontal wind (m/s) |
| 34 |
REAL, intent(out):: aam ! axial component of wind AAM |
| 35 |
REAL, intent(out):: torsfc ! axial component of total surface torque |
| 36 |
|
| 37 |
! Local Variables: |
| 38 |
|
| 39 |
INTEGER nlev ! number of vertical levels |
| 40 |
INTEGER i, j, k, l |
| 41 |
REAL dlat, dlon ! latitude and longitude increments (radians) |
| 42 |
|
| 43 |
REAL raam(3) ! wind AAM (components 1 & 2: equatorial; component 3: axial) |
| 44 |
REAL oaam(3) ! mass AAM (components 1 & 2: equatorial; component 3: axial) |
| 45 |
REAL tmou(3) ! resolved mountain torque (3 components) |
| 46 |
REAL tsso(3) ! parameterised moutain drag torque (3 components) |
| 47 |
REAL tbls(3) ! parameterised boundary layer torque (3 components) |
| 48 |
|
| 49 |
REAL ZS(801, 401) ! topographic height |
| 50 |
REAL PS(801, 401) ! surface pressure |
| 51 |
REAL UB(801, 401), VB(801, 401) ! barotropic wind, zonal and meridional |
| 52 |
REAL SSOU(801, 401), SSOV(801, 401) |
| 53 |
REAL BLSU(801, 401), BLSV(801, 401) |
| 54 |
REAL ZLON(801), ZLAT(401) ! longitude and latitude in radians |
| 55 |
|
| 56 |
!------------------------------------------------------------------- |
| 57 |
|
| 58 |
call assert(size(phis) == (/size(dragu), size(liftu), size(phyu), & |
| 59 |
size(dragv), size(liftv), size(phyv), size(p, 1), size(u, 1), & |
| 60 |
size(v, 1)/), "aaam_bud nlon") |
| 61 |
nlev = assert_eq(size(p, 2) - 1, size(u, 2), size(v, 2), "aaam_bud nlev") |
| 62 |
|
| 63 |
if (iim + 1 > 801 .or. jjm + 1 > 401) then |
| 64 |
print *, ' Problème de dimension dans aaam_bud' |
| 65 |
stop 1 |
| 66 |
endif |
| 67 |
|
| 68 |
dlat = pi / jjm |
| 69 |
dlon = 2 * pi / real(iim) |
| 70 |
|
| 71 |
oaam = 0. |
| 72 |
raam = 0. |
| 73 |
tmou = 0. |
| 74 |
tsso = 0. |
| 75 |
tbls = 0. |
| 76 |
|
| 77 |
! Mountain height, pressure and barotropic wind: |
| 78 |
|
| 79 |
! North pole values (j = 1): |
| 80 |
|
| 81 |
ub(1, 1) = 0. |
| 82 |
vb(1, 1) = 0. |
| 83 |
do k = 1, nlev |
| 84 |
ub(1, 1) = ub(1, 1) + u(1, k) * (p(1, k) - p(1, k + 1)) / rg |
| 85 |
vb(1, 1) = vb(1, 1) + v(1, k) * (p(1, k) - p(1, k + 1)) / rg |
| 86 |
enddo |
| 87 |
|
| 88 |
zlat(1) = rlat(1) * pi / 180. |
| 89 |
|
| 90 |
do i = 1, iim + 1 |
| 91 |
zs(i, 1) = phis(1) / rg |
| 92 |
ps(i, 1) = p(1, 1) |
| 93 |
ub(i, 1) = ub(1, 1) |
| 94 |
vb(i, 1) = vb(1, 1) |
| 95 |
ssou(i, 1) = dragu(1) + liftu(1) |
| 96 |
ssov(i, 1) = dragv(1) + liftv(1) |
| 97 |
blsu(i, 1) = phyu(1) - dragu(1) - liftu(1) |
| 98 |
blsv(i, 1) = phyv(1) - dragv(1) - liftv(1) |
| 99 |
enddo |
| 100 |
|
| 101 |
l = 1 |
| 102 |
do j = 2, jjm |
| 103 |
! Values at Greenwich (Periodicity) |
| 104 |
|
| 105 |
zs(iim + 1, j) = phis(l + 1) / rg |
| 106 |
ps(iim + 1, j) = p(l + 1, 1) |
| 107 |
ssou(iim + 1, j) = dragu(l + 1) + liftu(l + 1) |
| 108 |
ssov(iim + 1, j) = dragv(l + 1) + liftv(l + 1) |
| 109 |
blsu(iim + 1, j) = phyu(l + 1) - dragu(l + 1) - liftu(l + 1) |
| 110 |
blsv(iim + 1, j) = phyv(l + 1) - dragv(l + 1) - liftv(l + 1) |
| 111 |
zlon(iim + 1) = - rlon(l + 1) * pi / 180. |
| 112 |
zlat(j) = rlat(l + 1) * pi / 180. |
| 113 |
|
| 114 |
ub(iim + 1, j) = 0. |
| 115 |
vb(iim + 1, j) = 0. |
| 116 |
do k = 1, nlev |
| 117 |
ub(iim + 1, j) = ub(iim + 1, j) & |
| 118 |
+ u(l + 1, k) * (p(l + 1, k) - p(l + 1, k + 1)) / rg |
| 119 |
vb(iim + 1, j) = vb(iim + 1, j) & |
| 120 |
+ v(l + 1, k) * (p(l + 1, k) - p(l + 1, k + 1)) / rg |
| 121 |
enddo |
| 122 |
|
| 123 |
do i = 1, iim |
| 124 |
l = l + 1 |
| 125 |
zs(i, j) = phis(l) / rg |
| 126 |
ps(i, j) = p(l, 1) |
| 127 |
ssou(i, j) = dragu(l) + liftu(l) |
| 128 |
ssov(i, j) = dragv(l) + liftv(l) |
| 129 |
blsu(i, j) = phyu(l) - dragu(l) - liftu(l) |
| 130 |
blsv(i, j) = phyv(l) - dragv(l) - liftv(l) |
| 131 |
zlon(i) = rlon(l) * pi / 180. |
| 132 |
|
| 133 |
ub(i, j) = 0. |
| 134 |
vb(i, j) = 0. |
| 135 |
do k = 1, nlev |
| 136 |
ub(i, j) = ub(i, j) + u(l, k) * (p(l, k) - p(l, k + 1)) / rg |
| 137 |
vb(i, j) = vb(i, j) + v(l, k) * (p(l, k) - p(l, k + 1)) / rg |
| 138 |
enddo |
| 139 |
enddo |
| 140 |
enddo |
| 141 |
|
| 142 |
! South Pole |
| 143 |
|
| 144 |
l = l + 1 |
| 145 |
ub(1, jjm + 1) = 0. |
| 146 |
vb(1, jjm + 1) = 0. |
| 147 |
do k = 1, nlev |
| 148 |
ub(1, jjm + 1) = ub(1, jjm + 1) + u(l, k) * (p(l, k) - p(l, k + 1)) / rg |
| 149 |
vb(1, jjm + 1) = vb(1, jjm + 1) + v(l, k) * (p(l, k) - p(l, k + 1)) / rg |
| 150 |
enddo |
| 151 |
zlat(jjm + 1) = rlat(l) * pi / 180. |
| 152 |
|
| 153 |
do i = 1, iim + 1 |
| 154 |
zs(i, jjm + 1) = phis(l) / rg |
| 155 |
ps(i, jjm + 1) = p(l, 1) |
| 156 |
ssou(i, jjm + 1) = dragu(l) + liftu(l) |
| 157 |
ssov(i, jjm + 1) = dragv(l) + liftv(l) |
| 158 |
blsu(i, jjm + 1) = phyu(l) - dragu(l) - liftu(l) |
| 159 |
blsv(i, jjm + 1) = phyv(l) - dragv(l) - liftv(l) |
| 160 |
ub(i, jjm + 1) = ub(1, jjm + 1) |
| 161 |
vb(i, jjm + 1) = vb(1, jjm + 1) |
| 162 |
enddo |
| 163 |
|
| 164 |
! Moment angulaire |
| 165 |
|
| 166 |
DO j = 1, jjm |
| 167 |
DO i = 1, iim |
| 168 |
raam(1) = raam(1) - ra**3 * dlon * dlat * 0.5 * (cos(zlon(i )) & |
| 169 |
* sin(zlat(j )) * cos(zlat(j )) * ub(i , j ) + cos(zlon(i )) & |
| 170 |
* sin(zlat(j + 1)) * cos(zlat(j + 1)) * ub(i , j + 1)) & |
| 171 |
+ ra**3 * dlon * dlat * 0.5 * (sin(zlon(i )) * cos(zlat(j )) & |
| 172 |
* vb(i , j ) + sin(zlon(i )) * cos(zlat(j + 1)) * vb(i , j + 1)) |
| 173 |
|
| 174 |
oaam(1) = oaam(1) - ome * ra**4 * dlon * dlat / rg * 0.5 & |
| 175 |
* (cos(zlon(i )) * cos(zlat(j ))**2 * sin(zlat(j )) & |
| 176 |
* ps(i , j ) + cos(zlon(i )) * cos(zlat(j + 1))**2 & |
| 177 |
* sin(zlat(j + 1)) * ps(i , j + 1)) |
| 178 |
|
| 179 |
raam(2) = raam(2) - ra**3 * dlon * dlat * 0.5 * (sin(zlon(i )) & |
| 180 |
* sin(zlat(j )) * cos(zlat(j )) * ub(i , j ) + sin(zlon(i )) & |
| 181 |
* sin(zlat(j + 1)) * cos(zlat(j + 1)) * ub(i , j + 1)) & |
| 182 |
- ra**3 * dlon * dlat * 0.5 * (cos(zlon(i )) * cos(zlat(j )) & |
| 183 |
* vb(i , j ) + cos(zlon(i )) * cos(zlat(j + 1)) * vb(i , j + 1)) |
| 184 |
|
| 185 |
oaam(2) = oaam(2) - ome * ra**4 * dlon * dlat / rg * 0.5 & |
| 186 |
* (sin(zlon(i )) * cos(zlat(j ))**2 * sin(zlat(j )) & |
| 187 |
* ps(i , j ) + sin(zlon(i )) * cos(zlat(j + 1))**2 & |
| 188 |
* sin(zlat(j + 1)) * ps(i , j + 1)) |
| 189 |
|
| 190 |
raam(3) = raam(3) + ra**3 * dlon * dlat * 0.5 * (cos(zlat(j))**2 & |
| 191 |
* ub(i, j) + cos(zlat(j + 1))**2 * ub(i, j + 1)) |
| 192 |
|
| 193 |
oaam(3) = oaam(3) + ome * ra**4 * dlon * dlat / rg * 0.5 & |
| 194 |
* (cos(zlat(j))**3 * ps(i, j) + cos(zlat(j + 1))**3 & |
| 195 |
* ps(i, j + 1)) |
| 196 |
ENDDO |
| 197 |
ENDDO |
| 198 |
|
| 199 |
! Couple des montagnes : |
| 200 |
|
| 201 |
DO j = 1, jjm |
| 202 |
DO i = 1, iim |
| 203 |
tmou(1) = tmou(1) - ra**2 * dlon * 0.5 * sin(zlon(i)) & |
| 204 |
* (zs(i, j) - zs(i, j + 1)) & |
| 205 |
* (cos(zlat(j + 1)) * ps(i, j + 1) + cos(zlat(j)) * ps(i, j)) |
| 206 |
tmou(2) = tmou(2) + ra**2 * dlon * 0.5 * cos(zlon(i)) & |
| 207 |
* (zs(i, j) - zs(i, j + 1)) & |
| 208 |
* (cos(zlat(j + 1)) * ps(i, j + 1) + cos(zlat(j)) * ps(i, j)) |
| 209 |
ENDDO |
| 210 |
ENDDO |
| 211 |
|
| 212 |
DO j = 2, jjm |
| 213 |
DO i = 1, iim |
| 214 |
tmou(1) = tmou(1) + ra**2 * dlat * 0.5 * sin(zlat(j)) & |
| 215 |
* (zs(i + 1, j) - zs(i, j)) & |
| 216 |
* (cos(zlon(i + 1)) * ps(i + 1, j) + cos(zlon(i)) * ps(i, j)) |
| 217 |
tmou(2) = tmou(2) + ra**2 * dlat * 0.5 * sin(zlat(j)) & |
| 218 |
* (zs(i + 1, j) - zs(i, j)) & |
| 219 |
* (sin(zlon(i + 1)) * ps(i + 1, j) + sin(zlon(i)) * ps(i, j)) |
| 220 |
tmou(3) = tmou(3) - ra**2 * dlat * 0.5* cos(zlat(j)) & |
| 221 |
* (zs(i + 1, j) - zs(i, j)) * (ps(i + 1, j) + ps(i, j)) |
| 222 |
ENDDO |
| 223 |
ENDDO |
| 224 |
|
| 225 |
! Couples des differentes friction au sol : |
| 226 |
|
| 227 |
DO j = 2, jjm |
| 228 |
DO i = 1, iim |
| 229 |
tsso(1) = tsso(1) - ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 230 |
ssou(i, j) * sin(zlat(j)) * cos(zlon(i)) & |
| 231 |
+ ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 232 |
ssov(i, j) * sin(zlon(i)) |
| 233 |
|
| 234 |
tsso(2) = tsso(2) - ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 235 |
ssou(i, j) * sin(zlat(j)) * sin(zlon(i)) & |
| 236 |
- ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 237 |
ssov(i, j) * cos(zlon(i)) |
| 238 |
|
| 239 |
tsso(3) = tsso(3) + ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 240 |
ssou(i, j) * cos(zlat(j)) |
| 241 |
|
| 242 |
tbls(1) = tbls(1) - ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 243 |
blsu(i, j) * sin(zlat(j)) * cos(zlon(i)) & |
| 244 |
+ ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 245 |
blsv(i, j) * sin(zlon(i)) |
| 246 |
|
| 247 |
tbls(2) = tbls(2) - ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 248 |
blsu(i, j) * sin(zlat(j)) * sin(zlon(i)) & |
| 249 |
- ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 250 |
blsv(i, j) * cos(zlon(i)) |
| 251 |
|
| 252 |
tbls(3) = tbls(3) + ra**3 * cos(zlat(j)) * dlon * dlat* & |
| 253 |
blsu(i, j) * cos(zlat(j)) |
| 254 |
ENDDO |
| 255 |
ENDDO |
| 256 |
|
| 257 |
aam = raam(3) |
| 258 |
torsfc = tmou(3) + tsso(3) + tbls(3) |
| 259 |
|
| 260 |
END subroutine aaam_bud |
| 261 |
|
| 262 |
end module aaam_bud_m |
Parent Directory
| 
Revision Log