! $Id $

SUBROUTINE sw_case_williamson91_6(vcov, ucov, teta, masse, ps)

  !=======================================================================
  !
  !   Author:    Thomas Dubos      original: 26/01/2010
  !   -------
  !
  !   Subject:
  !   ------
  !   Realise le cas-test 6 de Williamson et al. (1991) : onde de Rossby-Haurwitz
  !
  !   Method:
  !   --------
  !
  !   Interface:
  !   ----------
  !
  !  Input:
  !  ------
  !
  !  Output:
  !  -------
  !
  !=======================================================================
  USE comconst_mod, ONLY: cpp, omeg, rad
  USE comvert_mod, ONLY: ap, bp, preff

  IMPLICIT NONE
  !-----------------------------------------------------------------------
  !   Declararations:
  !   ---------------

  include "dimensions.h"
  include "paramet.h"
  include "comgeom.h"
  include "iniprint.h"

  !   Arguments:
  !   ----------

  !   variables dynamiques
  REAL :: vcov(ip1jm, llm), ucov(ip1jmp1, llm) ! vents covariants
  REAL :: teta(ip1jmp1, llm)                 ! temperature potentielle
  REAL :: ps(ip1jmp1)                       ! pression  au sol
  REAL :: masse(ip1jmp1, llm)                ! masse d'air
  REAL :: phis(ip1jmp1)                     ! geopotentiel au sol

  !   Local:
  !   ------

  REAL :: p (ip1jmp1, llmp1)               ! pression aux interfac.des couches
  REAL :: pks(ip1jmp1)                      ! exner au  sol
  REAL :: pk(ip1jmp1, llm)                   ! exner au milieu des couches
  REAL :: pkf(ip1jmp1, llm)                  ! exner filt.au milieu des couches
  REAL :: alpha(ip1jmp1, llm), beta(ip1jmp1, llm)

  REAL :: sinth, costh, costh2, Ath, Bth, Cth, lon, dps
  INTEGER :: i, j, ij

  REAL, PARAMETER :: rho = 1 ! masse volumique de l'air (arbitraire)
  REAL, PARAMETER :: K = 7.848e-6  ! K = \omega
  REAL, PARAMETER :: gh0 = 9.80616 * 8e3
  INTEGER, PARAMETER :: R0 = 4, R1 = R0 + 1, R2 = R0 + 2         ! mode 4
  ! NB : rad = 6371220 dans W91 (6371229 dans LMDZ)
  ! omeg = 7.292e-5 dans W91 (7.2722e-5 dans LMDZ)

  IF(0==0) THEN
    ! Williamson et al. (1991) : onde de Rossby-Haurwitz
    teta = preff / rho / cpp
    ! geopotentiel (pression de surface)
    do j = 1, jjp1
      costh2 = cos(rlatu(j))**2
      Ath = (R0 + 1) * (costh2**2) + (2 * R0 * R0 - R0 - 2) * costh2 - 2 * R0 * R0
      Ath = .25 * (K**2) * (costh2**(R0 - 1)) * Ath
      Ath = .5 * K * (2 * omeg + K) * costh2 + Ath
      Bth = (R1 * R1 + 1) - R1 * R1 * costh2
      Bth = 2 * (omeg + K) * K / (R1 * R2) * (costh2**(R0 / 2)) * Bth
      Cth = R1 * costh2 - R2
      Cth = .25 * K * K * (costh2**R0) * Cth
      do i = 1, iip1
        ij = (j - 1) * iip1 + i
        lon = rlonv(i)
        dps = Ath + Bth * cos(R0 * lon) + Cth * cos(2 * R0 * lon)
        ps(ij) = rho * (gh0 + (rad**2) * dps)
      enddo
    enddo
    write(lunout, *) 'W91 ps', MAXVAL(ps), MINVAL(ps)
    ! vitesse zonale ucov
    do j = 1, jjp1
      costh = cos(rlatu(j))
      costh2 = costh**2
      Ath = rad * K * costh
      Bth = R0 * (1 - costh2) - costh2
      Bth = rad * K * Bth * (costh**(R0 - 1))
      do i = 1, iip1
        ij = (j - 1) * iip1 + i
        lon = rlonu(i)
        ucov(ij, 1) = (Ath + Bth * cos(R0 * lon))
      enddo
    enddo
    write(lunout, *) 'W91 u', MAXVAL(ucov(:, 1)), MINVAL(ucov(:, 1))
    ucov(:, 1) = ucov(:, 1) * cu
    ! vitesse meridienne vcov
    do j = 1, jjm
      sinth = sin(rlatv(j))
      costh = cos(rlatv(j))
      Ath = -rad * K * R0 * sinth * (costh**(R0 - 1))
      do i = 1, iip1
        ij = (j - 1) * iip1 + i
        lon = rlonv(i)
        vcov(ij, 1) = Ath * sin(R0 * lon)
      enddo
    enddo
    write(lunout, *) 'W91 v', MAXVAL(vcov(:, 1)), MINVAL(vcov(:, 1))
    vcov(:, 1) = vcov(:, 1) * cv

    ! ucov=0
    ! vcov=0
  ELSE
    ! test non-tournant, onde se propageant en latitude
    do j = 1, jjp1
      do i = 1, iip1
        ij = (j - 1) * iip1 + i
        ps(ij) = 1e5 * (1 + .1 * exp(-100 * (1 + sin(rlatu(j)))**2))
      enddo
    enddo

    ! rho = preff/(cpp*teta)
    teta = .01 * preff / cpp   ! rho = 100 ; phi = ps/rho = 1e3 ; c=30 m/s = 2600 km/j = 23 degres / j
    ucov = 0.
    vcov = 0.
  END IF

  CALL pression (ip1jmp1, ap, bp, ps, p)
  CALL massdair(p, masse)

END SUBROUTINE sw_case_williamson91_6
!-----------------------------------------------------------------------