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module aaam_bud_m |
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implicit none |
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contains |
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subroutine aaam_bud(rea, rg, ome, plat, plon, phis, dragu, liftu, phyu, & |
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dragv, liftv, phyv, p, u, v, aam, torsfc) |
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! Author: F. Lott (LMD/CNRS). Date: 2003/10/20. Object: Compute |
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! different terms of the axial AAAM budget and mountain torque. |
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! Only valid for regular rectangular grids. Should be called after |
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! "lift_noro". |
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USE dimens_m, ONLY : iim, jjm |
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use nr_util, only: assert_eq, assert, pi |
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real, intent(in):: rea ! Earth radius |
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real, intent(in):: rg ! gravity constant |
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real, intent(in):: ome ! Earth rotation rate |
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REAL, intent(in):: plat(:), plon(:) |
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! (nlon) latitude and longitude in degrees |
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real, intent(in):: phis(:) ! (nlon) Geopotential at the ground |
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REAL, intent(in):: dragu(:) ! (nlon) orodrag stress (zonal) |
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REAL, intent(in):: liftu(:) ! (nlon) orolift stress (zonal) |
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REAL, intent(in):: phyu(:) ! (nlon) Stress total de la physique (zonal) |
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REAL, intent(in):: dragv(:) ! (nlon) orodrag stress (Meridional) |
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REAL, intent(in):: liftv(:) ! (nlon) orolift stress (Meridional) |
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REAL, intent(in):: phyv(:) ! (nlon) Stress total de la physique (Meridional) |
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REAL, intent(in):: p(:, :) |
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! (nlon, nlev + 1) pressure (Pa) at model half levels |
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real, intent(in):: u(:, :), v(:, :) ! (nlon, nlev) horizontal wind (m/s) |
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REAL, intent(out):: aam ! axial component of wind AAM |
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REAL, intent(out):: torsfc ! axial component of total surface torque |
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! Local Variables: |
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INTEGER nlev ! number of vertical levels |
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INTEGER i, j, k, l |
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REAL hadley, hadday |
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REAL dlat, dlon ! latitude and longitude increments (radians) |
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REAL raam(3) ! wind AAM (components 1 & 2: equatorial; component 3: axial) |
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REAL oaam(3) ! mass AAM (components 1 & 2: equatorial; component 3: axial) |
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REAL tmou(3) ! resolved mountain torque (3 components) |
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REAL tsso(3) ! parameterised moutain drag torque (3 components) |
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REAL tbls(3) ! parameterised boundary layer torque (3 components) |
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integer iax |
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REAL ZS(801, 401) ! topographic height |
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REAL PS(801, 401) ! surface pressure |
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REAL UB(801, 401), VB(801, 401) ! barotropic wind, zonal and meridional |
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REAL SSOU(801, 401), SSOV(801, 401) |
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REAL BLSU(801, 401), BLSV(801, 401) |
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REAL ZLON(801), ZLAT(401) ! longitude and latitude in radians |
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!------------------------------------------------------------------- |
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call assert(size(plat) == (/size(plon), size(phis), size(dragu), & |
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size(liftu), size(phyu), size(dragv), size(liftv), size(phyv), & |
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size(p, 1), size(u, 1), size(v, 1)/), "aaam_bud nlon") |
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nlev = assert_eq(size(p, 2) - 1, size(u, 2), size(v, 2), "aaam_bud nlev") |
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if (iim + 1 > 801 .or. jjm + 1 > 401) then |
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print *, ' Problème de dimension dans aaam_bud' |
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stop 1 |
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endif |
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hadley = 1e18 |
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hadday = 1e18 * 24. * 3600. |
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dlat = pi / jjm |
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dlon = 2 * pi / real(iim) |
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oaam = 0. |
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raam = 0. |
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tmou = 0. |
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tsso = 0. |
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tbls = 0. |
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! Mountain height, pressure and barotropic wind: |
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! North pole values (j = 1): |
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ub(1, 1) = 0. |
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vb(1, 1) = 0. |
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do k = 1, nlev |
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ub(1, 1) = ub(1, 1) + u(1, k) * (p(1, k) - p(1, k + 1)) / rg |
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vb(1, 1) = vb(1, 1) + v(1, k) * (p(1, k) - p(1, k + 1)) / rg |
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enddo |
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zlat(1) = plat(1) * pi / 180. |
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do i = 1, iim + 1 |
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zs(i, 1) = phis(1) / rg |
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ps(i, 1) = p(1, 1) |
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ub(i, 1) = ub(1, 1) |
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vb(i, 1) = vb(1, 1) |
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ssou(i, 1) = dragu(1) + liftu(1) |
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ssov(i, 1) = dragv(1) + liftv(1) |
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blsu(i, 1) = phyu(1) - dragu(1) - liftu(1) |
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blsv(i, 1) = phyv(1) - dragv(1) - liftv(1) |
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enddo |
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l = 1 |
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do j = 2, jjm |
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! Values at Greenwich (Periodicity) |
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zs(iim + 1, j) = phis(l + 1) / rg |
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ps(iim + 1, j) = p(l + 1, 1) |
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ssou(iim + 1, j) = dragu(l + 1) + liftu(l + 1) |
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ssov(iim + 1, j) = dragv(l + 1) + liftv(l + 1) |
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blsu(iim + 1, j) = phyu(l + 1) - dragu(l + 1) - liftu(l + 1) |
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blsv(iim + 1, j) = phyv(l + 1) - dragv(l + 1) - liftv(l + 1) |
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zlon(iim + 1) = - plon(l + 1) * pi / 180. |
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zlat(j) = plat(l + 1) * pi / 180. |
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ub(iim + 1, j) = 0. |
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vb(iim + 1, j) = 0. |
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do k = 1, nlev |
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ub(iim + 1, j) = ub(iim + 1, j) & |
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+ u(l + 1, k) * (p(l + 1, k) - p(l + 1, k + 1)) / rg |
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vb(iim + 1, j) = vb(iim + 1, j) & |
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+ v(l + 1, k) * (p(l + 1, k) - p(l + 1, k + 1)) / rg |
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enddo |
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do i = 1, iim |
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l = l + 1 |
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zs(i, j) = phis(l) / rg |
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ps(i, j) = p(l, 1) |
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ssou(i, j) = dragu(l) + liftu(l) |
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ssov(i, j) = dragv(l) + liftv(l) |
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blsu(i, j) = phyu(l) - dragu(l) - liftu(l) |
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blsv(i, j) = phyv(l) - dragv(l) - liftv(l) |
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zlon(i) = plon(l) * pi / 180. |
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ub(i, j) = 0. |
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vb(i, j) = 0. |
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do k = 1, nlev |
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ub(i, j) = ub(i, j) + u(l, k) * (p(l, k) - p(l, k + 1)) / rg |
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vb(i, j) = vb(i, j) + v(l, k) * (p(l, k) - p(l, k + 1)) / rg |
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enddo |
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enddo |
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enddo |
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! South Pole |
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l = l + 1 |
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ub(1, jjm + 1) = 0. |
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vb(1, jjm + 1) = 0. |
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do k = 1, nlev |
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ub(1, jjm + 1) = ub(1, jjm + 1) + u(l, k) * (p(l, k) - p(l, k + 1)) / rg |
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vb(1, jjm + 1) = vb(1, jjm + 1) + v(l, k) * (p(l, k) - p(l, k + 1)) / rg |
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enddo |
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zlat(jjm + 1) = plat(l) * pi / 180. |
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do i = 1, iim + 1 |
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zs(i, jjm + 1) = phis(l) / rg |
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ps(i, jjm + 1) = p(l, 1) |
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ssou(i, jjm + 1) = dragu(l) + liftu(l) |
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ssov(i, jjm + 1) = dragv(l) + liftv(l) |
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blsu(i, jjm + 1) = phyu(l) - dragu(l) - liftu(l) |
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blsv(i, jjm + 1) = phyv(l) - dragv(l) - liftv(l) |
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ub(i, jjm + 1) = ub(1, jjm + 1) |
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vb(i, jjm + 1) = vb(1, jjm + 1) |
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enddo |
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! Moment angulaire |
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DO j = 1, jjm |
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DO i = 1, iim |
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raam(1) = raam(1) - rea**3 * dlon * dlat * 0.5 * (cos(zlon(i )) & |
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* sin(zlat(j )) * cos(zlat(j )) * ub(i , j ) + cos(zlon(i )) & |
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* sin(zlat(j + 1)) * cos(zlat(j + 1)) * ub(i , j + 1)) & |
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+ rea**3 * dlon * dlat * 0.5 * (sin(zlon(i )) * cos(zlat(j )) & |
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* vb(i , j ) + sin(zlon(i )) * cos(zlat(j + 1)) * vb(i , j + 1)) |
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oaam(1) = oaam(1) - ome * rea**4 * dlon * dlat / rg * 0.5 & |
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* (cos(zlon(i )) * cos(zlat(j ))**2 * sin(zlat(j )) & |
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* ps(i , j ) + cos(zlon(i )) * cos(zlat(j + 1))**2 & |
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* sin(zlat(j + 1)) * ps(i , j + 1)) |
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raam(2) = raam(2) - rea**3 * dlon * dlat * 0.5 * (sin(zlon(i )) & |
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* sin(zlat(j )) * cos(zlat(j )) * ub(i , j ) + sin(zlon(i )) & |
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* sin(zlat(j + 1)) * cos(zlat(j + 1)) * ub(i , j + 1)) & |
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- rea**3 * dlon * dlat * 0.5 * (cos(zlon(i )) * cos(zlat(j )) & |
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* vb(i , j ) + cos(zlon(i )) * cos(zlat(j + 1)) * vb(i , j + 1)) |
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oaam(2) = oaam(2) - ome * rea**4 * dlon * dlat / rg * 0.5 & |
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* (sin(zlon(i )) * cos(zlat(j ))**2 * sin(zlat(j )) & |
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* ps(i , j ) + sin(zlon(i )) * cos(zlat(j + 1))**2 & |
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* sin(zlat(j + 1)) * ps(i , j + 1)) |
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raam(3) = raam(3) + rea**3 * dlon * dlat * 0.5 * (cos(zlat(j))**2 & |
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* ub(i, j) + cos(zlat(j + 1))**2 * ub(i, j + 1)) |
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oaam(3) = oaam(3) + ome * rea**4 * dlon * dlat / rg * 0.5 & |
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* (cos(zlat(j))**3 * ps(i, j) + cos(zlat(j + 1))**3 & |
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* ps(i, j + 1)) |
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ENDDO |
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ENDDO |
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! Couple des montagnes : |
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DO j = 1, jjm |
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DO i = 1, iim |
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tmou(1) = tmou(1) - rea**2 * dlon * 0.5 * sin(zlon(i)) & |
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* (zs(i, j) - zs(i, j + 1)) & |
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* (cos(zlat(j + 1)) * ps(i, j + 1) + cos(zlat(j)) * ps(i, j)) |
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tmou(2) = tmou(2) + rea**2 * dlon * 0.5 * cos(zlon(i)) & |
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* (zs(i, j) - zs(i, j + 1)) & |
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* (cos(zlat(j + 1)) * ps(i, j + 1) + cos(zlat(j)) * ps(i, j)) |
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ENDDO |
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ENDDO |
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DO j = 2, jjm |
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DO i = 1, iim |
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tmou(1) = tmou(1) + rea**2 * dlat * 0.5 * sin(zlat(j)) & |
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* (zs(i + 1, j) - zs(i, j)) & |
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* (cos(zlon(i + 1)) * ps(i + 1, j) + cos(zlon(i)) * ps(i, j)) |
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tmou(2) = tmou(2) + rea**2 * dlat * 0.5 * sin(zlat(j)) & |
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* (zs(i + 1, j) - zs(i, j)) & |
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* (sin(zlon(i + 1)) * ps(i + 1, j) + sin(zlon(i)) * ps(i, j)) |
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tmou(3) = tmou(3) - rea**2 * dlat * 0.5* cos(zlat(j)) & |
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* (zs(i + 1, j) - zs(i, j)) * (ps(i + 1, j) + ps(i, j)) |
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ENDDO |
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ENDDO |
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! Couples des differentes friction au sol : |
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DO j = 2, jjm |
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DO i = 1, iim |
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tsso(1) = tsso(1) - rea**3 * cos(zlat(j)) * dlon * dlat* & |
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ssou(i, j) * sin(zlat(j)) * cos(zlon(i)) & |
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+ rea**3 * cos(zlat(j)) * dlon * dlat* & |
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ssov(i, j) * sin(zlon(i)) |
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tsso(2) = tsso(2) - rea**3 * cos(zlat(j)) * dlon * dlat* & |
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ssou(i, j) * sin(zlat(j)) * sin(zlon(i)) & |
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- rea**3 * cos(zlat(j)) * dlon * dlat* & |
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ssov(i, j) * cos(zlon(i)) |
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tsso(3) = tsso(3) + rea**3 * cos(zlat(j)) * dlon * dlat* & |
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ssou(i, j) * cos(zlat(j)) |
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tbls(1) = tbls(1) - rea**3 * cos(zlat(j)) * dlon * dlat* & |
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blsu(i, j) * sin(zlat(j)) * cos(zlon(i)) & |
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+ rea**3 * cos(zlat(j)) * dlon * dlat* & |
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blsv(i, j) * sin(zlon(i)) |
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tbls(2) = tbls(2) - rea**3 * cos(zlat(j)) * dlon * dlat* & |
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blsu(i, j) * sin(zlat(j)) * sin(zlon(i)) & |
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- rea**3 * cos(zlat(j)) * dlon * dlat* & |
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blsv(i, j) * cos(zlon(i)) |
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tbls(3) = tbls(3) + rea**3 * cos(zlat(j)) * dlon * dlat* & |
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blsu(i, j) * cos(zlat(j)) |
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ENDDO |
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ENDDO |
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aam = raam(3) |
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torsfc = tmou(3) + tsso(3) + tbls(3) |
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END subroutine aaam_bud |
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end module aaam_bud_m |
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