!
!################################################################
!################################################################
!##### #####
!##### SUBROUTINE ASSIMVEL #####
!##### #####
!##### Copyright (c) 1993 #####
!##### Center for Analysis and Prediction of Storms ######
!##### University of Oklahoma ######
!##### #####
!################################################################
!################################################################
!
SUBROUTINE assimvel(nx,ny,nz,x,y,z,zp, & 1,21
u,v,w,wcont,ptprt,pprt,qv,qc,qr,qi,qs,qh, &
ubar,vbar,ptbar,pbar,rhostr,qvbar,j1,j2,j3, &
tem1,tem2,tem3,tem4,tem5,tem6,tem7,tem8,tem9, &
tem10,tem11,tem12,tem13)
!
!---------------------------------------------------------------------
!
! PURPOSE:
!
! This subroutine solves a 3-D elliptic equation with
! variable coeficients:
!
! c1*d2q/dx2 + c2*d2q/dy2 + c3*d2q/dz2 - c4*d2q/dxdy - c5*d2q/dxdz
! - c6*d2q/dydz - c7*dq/dx - c8*dq/dy - c9*dq/dz = 'Known Forcing'
!
! subject to the Dirichlet boundary condition:
!
! q = 0 on the x & y boundaries, and
!
! subject to the z-boundary condition:
!
! dq/dz = (z/x**2+y**2)*[2r(vro - vrm) + (xdq/dx + ydq/dy)]
! where: vro - observed radial velocity
! vrm - model derived radial velocity
!
! The solution is obtained by applying a direct SOR technique
! (see Haltiner and Williams "Numerical Prediction and Dynamical
! Weather Prediction", Ch. 5 pg 159.)
!
!---------------------------------------------------------------------
!
!
!-----------------------------------------------------------------------
!
! AUTHOR: Steve Lazarus and Alan Shapiro
! 9/29/93
!
! MODIFICATION HISTORY:
!
! Limin Zhao (10/18/95)
! Modified the code to obtain the 'lamda2' and 'lamda1' simultaneously
! by solving the two related equations interatively. It helps to
! eliminate the sensitivity of the solution to the different
! numerical schemes.
!
! Alan Shapiro and Limin Zhao (10/19/95)
! Put 'lamda1' in new staggered points and modified the related code.
! The above two modifications work together to ensure the divergence
! of the wind field be small enough after the variational adjustment.
!
! Limin Zhao and Alan Shapiro(11/10/95)
! Put a 'patch' on the top boundary to avoid the singularity problem.
! Inside the 'patch', the zero gradient B.C. is used to replace the
! non-zero gradient B.C.
!
! Limin Zhao (11/16/95)
! Set an option for scaling 'lamda1'. When the coefficient 'scoef'
! is set to 1, no scaling is performed.
!
! Limin Zhao (1/11/96)
! Strip out the hole-filling and time interpolation part, and make
! the program mainly to the velocity adjustment, either use Vr or the
! variational adjustment.
!
! Alan Shapiro and Limin Zhao (03/25/96)
! The boundary values in the patch are calculated linearly from
! its latent boundary values.
!
!-----------------------------------------------------------------------
!
! INPUT:
!
! nx Number of grid points in the x-direction (east/west)
! ny Number of grid points in the y-direction (north/south)
! nz Number of grid points in the z-direction (vertical)
!
! x x coordinate of grid points in physical/comp. space (m)
! y y coordinate of grid points in physical/comp. space (m)
! z z coordinate of grid points in computational space (m)
! zp Vertical coordinate of grid points in physical space (m)
!
! u x component of velocity (m/s)
! v y component of velocity (m/s)
! w Vertical component of velocity in Cartesian
! coordinates (m/s)
! wcont Contravariant vertical velocity (m/s)
!
! ptprt Perturbation potential temperature (K)
! pprt Perturbation pressure (Pascal)
! qv Water vapor specific humidity (kg/kg)
! qc Cloud water mixing ratio (kg/kg)
! qr Rainwater mixing ratio (kg/kg)
! qi Cloud ice mixing ratio (kg/kg)
! qs Snow mixing ratio (kg/kg)
! qh Hail mixing ratio (kg/kg)
!
! ubar Base state x velocity component (m/s)
! vbar Base state y velocity component (m/s)
! ptbar Base state potential temperature (K)
! pbar Base state pressure (Pascal)
! rhostr Base state air density (kg/m**3) times j3
! qvbar Base state water vapor specific humidity (kg/kg)
!
! j1 Coordinate transformation Jacobian -d(zp)/dx
! j2 Coordinate transformation Jacobian -d(zp)/dy
! j3 Coordinate transformation Jacobian d(zp)/dz
!
! tem1 Observed radial velocity
! tem5 Model or retrieved radial velocity
!
!---------------------------------------------------------------------
!
! OUTPUT:
!
! tem7 Solution of the Poisson equation (q above).
!
!---------------------------------------------------------------------
!
! WORK ARRAYS:
!
! tem2 Temporary work array.
! tem3 Temporary work array.
! tem4 Temporary work array.
! tem6 Temporary work array.
! tem8 Temporary work array.
! tem9 Temporary work array.
!
! (These arrays are defined and used locally (i.e. inside this
! subroutine), they may also be passed into routines called by
! this one. Exiting the call to this subroutine, these temporary
! work arrays may be used for other purposes, and therefore their
! contents may be overwritten. Please examine the usage of work
! arrays before you alter the code.)
!
!-----------------------------------------------------------------------
!
!
!-----------------------------------------------------------------------
!
! Variable Declarations.
!
!-----------------------------------------------------------------------
!
IMPLICIT NONE ! Force explicit declarations
!
!-----------------------------------------------------------------------
!
!
!-----------------------------------------------------------------------
!
! Include files:
!
!-----------------------------------------------------------------------
!
INCLUDE 'phycst.inc' ! Model physical constants
INCLUDE 'globcst.inc' ! Model control constants
INCLUDE 'assim.inc' ! Assim/Retr control parameters
INCLUDE 'bndry.inc' ! Boundary condition parameters
INCLUDE 'grid.inc'
!
!-----------------------------------------------------------------------
!
INTEGER :: nt ! The no. of t-levels of t-dependent arrays
INTEGER :: tpast ! Index of time level for the past time.
INTEGER :: tpresent ! Index of time level for the present time.
INTEGER :: tfuture ! Index of time level for the future time.
INTEGER :: in,jn,ir0,jr0,ipe,ips,jps,jpe,ipatch
REAL :: acof,bcof
PARAMETER (nt=3, tpast=1, tpresent=2, tfuture=3)
INTEGER :: nx, ny, nz ! Number of grid points in x, y and z directions
INTEGER :: grdbas
REAL :: x (nx) ! The x-coord. of the physical and
! computational grid. Defined at u-point.
REAL :: y (ny) ! The y-coord. of the physical and
! computational grid. Defined at v-point.
REAL :: z (nz) ! The z-coord. of the computational grid.
! Defined at w-point on the staggered grid.
REAL :: zp (nx,ny,nz) ! The physical height coordinate defined at
! w-point of the staggered grid.
REAL :: u (nx,ny,nz,nt) ! Total u-velocity (m/s)
REAL :: v (nx,ny,nz,nt) ! Total v-velocity (m/s)
REAL :: w (nx,ny,nz,nt) ! Total w-velocity (m/s)
REAL :: wcont (nx,ny,nz) ! Contravariant vertical velocity (m/s)
REAL :: ptprt (nx,ny,nz,nt) ! Perturbation potential temperature (K)
REAL :: pprt (nx,ny,nz,nt) ! Perturbation pressure (Pascal)
REAL :: qv (nx,ny,nz,nt) ! Water vapor specific humidity (kg/kg)
REAL :: qc (nx,ny,nz,nt) ! Cloud water mixing ratio (kg/kg)
REAL :: qr (nx,ny,nz,nt) ! Rain water mixing ratio (kg/kg)
REAL :: qi (nx,ny,nz,nt) ! Cloud ice mixing ratio (kg/kg)
REAL :: qs (nx,ny,nz,nt) ! Snow mixing ratio (kg/kg)
REAL :: qh (nx,ny,nz,nt) ! Hail mixing ratio (kg/kg)
REAL :: ubar (nx,ny,nz) ! Base state u-velocity (m/s)
REAL :: vbar (nx,ny,nz) ! Base state v-velocity (m/s)
REAL :: ptbar (nx,ny,nz) ! Base state potential temperature (K)
REAL :: pbar (nx,ny,nz) ! Base state pressure (Pascal).
REAL :: rhostr(nx,ny,nz) ! Base state air density (kg/m**3) times j3
REAL :: qvbar (nx,ny,nz) ! Base state water vapor specific humidity
! (kg/kg)
REAL :: j1 (nx,ny,nz) ! Coordinate transformation Jacobian -d(zp)/d(x)
REAL :: j2 (nx,ny,nz) ! Coordinate transformation Jacobian -d(zp)/d(y)
REAL :: j3 (nx,ny,nz) ! Coordinate transformation Jacobian d(zp)/d(z)
REAL :: tem1(nx,ny,nz)
REAL :: tem2(nx,ny,nz)
REAL :: tem3(nx,ny,nz)
REAL :: tem4(nx,ny,nz)
REAL :: tem5(nx,ny,nz)
REAL :: tem6(nx,ny,nz)
REAL :: tem7(nx,ny,nz)
REAL :: tem8(nx,ny,nz)
REAL :: tem9(nx,ny,nz)
REAL :: tem10(nx,ny,nz)
REAL :: tem11(nx,ny,nz)
REAL :: tem12(nx,ny,nz)
REAL :: tem13(nx,ny,nz)
!
!-----------------------------------------------------------------------
!
! Misc. local variables:
!
!-----------------------------------------------------------------------
!
INTEGER :: icount ! Parameter input flag
SAVE icount
DATA icount /1/
INTEGER :: i, j, k, ir, jr
INTEGER :: istor,jstor,kstor
INTEGER :: nchout ! I/O Channel of unformatted binary restart data
INTEGER :: it,ix
INTEGER :: itmax ! Maximum number of iterations
INTEGER :: istat
INTEGER :: isrc
INTEGER :: tim
INTEGER :: idummy
INTEGER :: itag ! Counter indicating input file date/time
INTEGER :: count
INTEGER :: mdpt
REAL :: t1 ! Time of first data file
REAL :: t2 ! Time of second data file
REAL :: t3 ! Time of third data file
REAL :: assimtim(100)! Time of (all) input data files
REAL :: xs ! Scalar coordinate x-component
REAL :: ys ! Scalar coordinate y-component
REAL :: zs ! Scalar coordinate z-component
REAL :: xs1 ! Scalar coordinate x-component
REAL :: ys1 ! Scalar coordinate y-component
REAL :: zs1 ! Scalar coordinate z-component
REAL :: xmove ! (x,y) position of radar relative to
REAL :: ymove ! moving grid (grid origin at (0,0,0))
REAL :: znz2 ! = z(nz-2) - zshift
REAL :: znz1 ! = z(nz-1) - zshift
REAL :: z2 ! = z(2) - zshift
REAL :: alpha ! Over-relaxation coefficient
REAL :: tol ! An error tolerance, proportional to grid spacing
! and max velocity error
REAL :: veltol ! Maximum tolerable error in velocity
REAL :: newit ! New iterate of q at a point
REAL :: stor ! Stores the new value of q temporarily
REAL :: resid ! the residual of the Poisson equation
REAL :: diff ! Difference between the updated q and old q at a point
REAL :: test ! Value of the maximum difference (qnew-qold) in grid
REAL :: ptol ! Error tolerance for hole-filling
REAL :: anorm
REAL :: anormf
REAL :: test1
REAL :: iterr
REAL :: b1,b2,b3,b4 ! Coefficients of the Poisson equation.
REAL :: b5,b6,b7,b8
REAL :: b9
REAL :: c1,c2,c3,c4 ! Coefficient combinations of b1...b9 in the Poisson
REAL :: c5,c6,c7,c8 ! equation. The coefficients are a function of grid
REAL :: c9,c10 ! spacing and location.
REAL :: tm1,tm2,tm3
REAL :: tm4,tm5,tm6
REAL :: tm7,tm8,tm9
REAL :: scoef
!ccxxx You might need change veltol sometime
! parameter(itmax=100000,veltol=0.01,scoef=1.0) ! original
! parameter(itmax=900000,veltol=0.01,scoef=1.0) ! original
PARAMETER(itmax=900000, veltol=0.5,scoef=1.0)
! parameter(itmax=2, veltol=0.05,scoef=1.0) ! only for test
REAL :: rad ! Radius of sphere in Cartesian coord
REAL :: radh ! Radius of circle in hz. plane
REAL :: radinv ! Inverse radius magnitude
REAL :: rdx2 ! Reciprocal of (dx)**2
REAL :: rdy2 ! Reciprocal of (dy)**2
REAL :: rdz2 ! Reciprocal of (dz)**2
REAL :: term1,term2 ! Analytic terms representing the RHS of the
REAL :: term3,term4 ! Poisson eqn.
REAL :: term5
REAL :: vphi,vtheta ! Model tangential and polar velocities
REAL :: rcos ! Squareroot of x**2+y**2
INTEGER :: newebc ! East boundary condition parameter.
INTEGER :: newwbc ! West boundary condition parameter.
INTEGER :: newnbc ! North boundary condition parameter.
INTEGER :: newsbc ! South boundary condition parameter.
REAL :: vro,vrm ! Used for diagnostics/testing
REAL :: vradj
REAL :: fpat ! temp variable for forcing "patch"
REAL :: maxdiv ! Maximum divergence (diagnostic calculation)
INTEGER :: imx,jmx ! Gridpoint location of max divp
INTEGER :: kmx
INTEGER :: imx1,jmx1,kmx1
REAL :: maxw
REAL :: rrr ! used for (x**2+y**2+z**2)**0.5
!
!-----------------------------------------------------------------------
!
! Routines called:
!
!-----------------------------------------------------------------------
!
EXTERNAL aamult
EXTERNAL assimrd
EXTERNAL retrint
EXTERNAL avgx
EXTERNAL avgy
EXTERNAL avgz
EXTERNAL dtadump
EXTERNAL gtdmpfn
EXTERNAL bcu
EXTERNAL bcv
EXTERNAL rhouvw
EXTERNAL lbcw
EXTERNAL vbcw
EXTERNAL smth
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
! Beginning of executable code ...
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
!
!-----------------------------------------------------------------------
!
!
! The following is a brief summary of the assimilation flags
! available within this routine. For a more detailed review
! of the options see ASSIMCON.F.
!
! ivar Variational adjustment flag:
!
! = 0, NO variational adjustment this model time step
! = 1, Perform variational adjustment this model time step
!
! insrt Insertion flag:
!
! = 0, Do NOT insert velocities this time step
! = 1, Insert velocities this time step
!
! A matrix describing the assimilation options herein:
!
! ivar insrt Comments
! --------------------------------------------------------
! 0 0 Nothing - Exit assimilation mode
! 0 1 Direct insertion only
! 1 0 Variational adjustment only
! 1 1 Variational adjustment + direct insertion
!
! NOTE: If irecov=1, then the ingest and time interpolation of
! 3 input data files occurs herein.
!
!-----------------------------------------------------------------------
!
WRITE(6,*)'code in assimvel'
IF ( insrt == 0.AND.ivar == 0.) RETURN
!
!-----------------------------------------------------------------------
!
! Has switch been set for a direct insertion only? If yes, ingest
! data.
!
! NOTE: Insertion of data is done here ONLY if there is no
! variational adjustment (ivopt=0). If ivopt=1, then the
! adjusted data is inserted at the end of this routine.
!
!-----------------------------------------------------------------------
!
tim = tpresent
umove=0.0
vmove=0.0
xmove= xshift - umove*(curtim-assimtim(1))
ymove= yshift - vmove*(curtim-assimtim(1))
!
!-------------------------------------------------------------------------
!
! Interpolate input 'model' velocity components to scalar grid point.
! Where:
! tem2 = scalar u component
! tem3 = scalar v component
! tem4 = scalar w component
!
!-------------------------------------------------------------------------
!
DO k = 1,nz
DO j = 1,ny
DO i = 1,nx
tem7(i,j,k) = u(i,j,k,tim)
tem8(i,j,k) = v(i,j,k,tim)
tem9(i,j,k) = w(i,j,k,tim)
END DO
END DO
END DO
!
CALL avgx
(tem7, 0, nx,ny,nz, &
1,nx-1,1,ny-1,1,nz-1,tem2)
CALL avgy(tem8, 0, nx,ny,nz, &
1,nx-1,1,ny-1,1,nz-1,tem3)
CALL avgz(tem9, 0, nx,ny,nz, &
1,nx-1,1,ny-1,1,nz-1,tem4)
!
!----------------------------------------------------------------------
!
! Calculate the first guess radial velocity component using
! the hole-filled and blended velocity data.
!
!----------------------------------------------------------------------
!
DO k = 1, nz-1
DO j = 1, ny-1
DO i = 1, nx-1
xs = 0.5*(x(i)+x(i+1)) - xmove
ys = 0.5*(y(j)+y(j+1)) - ymove
zs = 0.5*(z(k)+z(k+1)) - zshift
rad = SQRT(xs**2+ys**2+zs**2)
tem5(i,j,k) = (tem2(i,j,k)*xs+tem3(i,j,k)*ys+ &
tem4(i,j,k)*zs)/rad
END DO
END DO
END DO
!
!----------------------------------------------------------------------
!
! Save rhobar in tem9
!
!----------------------------------------------------------------------
!
DO k=1,nz
DO j=1,ny
DO i=1,nx
tem9(i,j,k) = rhostr(i,j,k)/j3(i,j,k)
END DO
END DO
END DO
!
!----------------------------------------------------------------------
!
! Check whether the variational adjusment is needed.
!
!----------------------------------------------------------------------
!
IF ( insrt == 1.AND.ivar == 0) THEN
WRITE(6,'(/5x,a)') 'Performing a direct insertion only'
!
!-----------------------------------------------------------------------
!
! Calculate the model tangential velocity, vphi, and model polar
! velocity, vtheta, at a scalar point. The adjusted winds ua,va,
! and wa, are constructed (at a scalar point) as follows:
!
! tem6 = ua = Vr*x/rad + vphi*y/rcos - vtheta*x*z/rad*rcos
! tem7 = va = Vr*y/rad - vphi*x/rcos - vtheta*y*z/rad*rcos
! tem8 = wa = Vr*z/rad + vtheta*rcos/rad
!
! Where,
! rcos = sqrt(x**2+y**2)
! rad = sqrt(x**2+y**2+z**2)
! tem1 = Vr (model (OSSE) or observed radial velocity)
!
! For more details on this insertion technique, see the write-up
! "Direct insertion of single-Doppler radial winds into a numerical
! model" by Alan Shapiro.
!
!-----------------------------------------------------------------------
!
DO k = 1, nz-1
DO j = 1, ny-1
DO i = 1, nx-1
xs = 0.5*(x(i)+x(i+1)) - xmove
ys = 0.5*(y(j)+y(j+1)) - ymove
zs = 0.5*(z(k)+z(k+1)) - zshift
rad = SQRT(xs**2+ys**2+zs**2)
rcos = SQRT(xs**2+ys**2)
vphi = (1./rcos)*(tem2(i,j,k)*ys - tem3(i,j,k)*xs)
vtheta= (1./(rad*rcos))*(-tem2(i,j,k)*xs*zs &
-tem3(i,j,k)*ys*zs &
+tem4(i,j,k)*(rcos**2))
!-----------------------------------------------------
! Comment out overwrite of obs radial component
! 01-03-99 SSW for AMS99
!
! tem6(i,j,k) = tem1(i,j,k)*xs/rad + vphi*ys/rcos
! : - vtheta*xs*zs/(rad*rcos)
! tem7(i,j,k) = tem1(i,j,k)*ys/rad - vphi*xs/rcos
! : - vtheta*ys*zs/(rad*rcos)
! tem8(i,j,k) = tem1(i,j,k)*zs/rad + vtheta*rcos/rad
!
tem6(i,j,k) = tem2(i,j,k)
tem7(i,j,k) = tem3(i,j,k)
tem8(i,j,k) = tem4(i,j,k)
!-----------------------------------------------------
!
END DO
END DO
END DO
!
!-----------------------------------------------------------------------
!
! Reconstruct the model velocity field on the Arakawa C-grid. u,v,
! and w are stored in tem2,tem3, and tem4 respectively until the
! boundary conditions are applied at the end of this routine.
!
!-----------------------------------------------------------------------
!
DO k = 2, nz-1
DO j = 2, ny-1
DO i = 2, nx-1
tem2(i,j,k) = .5*(tem6(i-1,j,k)+tem6(i,j,k))
tem3(i,j,k) = .5*(tem7(i,j-1,k)+tem7(i,j,k))
tem4(i,j,k) = .5*(tem8(i,j,k-1)+tem8(i,j,k))
END DO
END DO
END DO
GO TO 270 ! Apply boundary conditions
!
!----------------------------------------------------------------------
!
! Perform a variational adjustment
!
!----------------------------------------------------------------------
!
ELSE
PRINT *,'Performing a variational adjustment'
!
!----------------------------------------------------------------------
!
! Redefine the following arrays such that:
!
! tem1 = tem1*rhostr tem4 = tem4*rhostr
! tem2 = tem2*rhostr tem5 = tem5*rhostr
! tem3 = tem3*rhostr
!
!----------------------------------------------------------------------
!
CALL aamult(tem1,tem9,nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem1)
CALL avgsu(tem9,nx,ny,nz, 1,ny-1, 1,nz-1, tem6, tem10)
CALL aamult(u(1,1,1,tim),tem6,nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem2)
CALL avgsv(tem9,nx,ny,nz, 1,nx-1, 1,nz-1, tem6, tem10)
CALL aamult(v(1,1,1,tim),tem6,nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem3)
CALL avgsw(tem9,nx,ny,nz, 1,nx-1, 1,ny-1, tem6)
CALL aamult(w(1,1,1,tim),tem6,nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem4)
CALL aamult(tem5,tem9,nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem5)
CALL avgsw(tem9,nx,ny,nz, 1,nx-1, 1,ny-1, tem12) ! store rhobar at
! w points.
WRITE(6,*) 'after redefine'
!
!----------------------------------------------------------------------
!
! Set the optimum over-relaxation coefficient, alpha.
! WARNING: In order to avoid solution 'blow-up', alpha should be
! near 1.
!
!----------------------------------------------------------------------
!
! alpha=0.25 ! original value; under relaxation, slow convergence
! alpha=1.00 ! under relaxation, slow convergence
alpha=0.75 ! under relaxation, slow convergence
! alpha=0.15 ! under relaxation, slow convergence
! alpha=1.5 ! SOR; optimum -> 2 for large dimensions.
DO k = 1,nz
DO j = 1,ny
DO i = 1,nx
tem6(i,j,k) = 0.0
tem7(i,j,k) = 0.0
tem8(i,j,k) = 0.0
tem10(i,j,k) = 0.0
tem11(i,j,k) = 0.0
END DO
END DO
END DO
dxinv = 1./dx
dyinv = 1./dy
dzinv = 1./dz
rdx2 = dxinv*dxinv ! reciprocal of (dx)**2
rdy2 = dyinv*dyinv ! reciprocal of (dy)**2
rdz2 = dzinv*dzinv ! reciprocal of (dz)**2
!
!----------------------------------------------------------------------
!
! Start the interation loop.
!
!----------------------------------------------------------------------
!
WRITE(6,*) 'start iteration'
DO it = 1,itmax
!
!----------------------------------------------------------------------
!
! Compute the right hand side of the Poisson equation and store it
! in tem6. This will be handled externally once the code is
! completed and tested.
!
!----------------------------------------------------------------------
!
DO k = 2, nz-2
DO j = 2, ny-2
DO i = 2, nx-2
!
!
! xs1 = x(i+1) - xmove
! ys1 = y(j+1) - ymove
! zs1 = z(k+1) - zshift
!
! xs = x(i) - xmove
! ys = y(j) - ymove
! zs = z(k) - zshift
!
! term1 = dxinv*(tem2(i+1,j,k)-tem2(i,j,k))
! : + dyinv*(tem3(i,j+1,k)-tem3(i,j,k))
! : + dzinv*(tem4(i,j,k+1)-tem4(i,j,k))
!
!
! term2 = dxinv*(xs1*(tem8(i+1,j,k)+tem8(i+1,j+1,k)
! : + tem8(i+1,j,k+1)+tem8(i+1,j+1,k+1))
! : - xs*(tem8(i,j,k)+tem8(i,j+1,k)
! : + tem8(i,j,k+1)+tem8(i,j+1,k+1)))
! : + dyinv*(ys1*(tem8(i,j+1,k)+tem8(i+1,j+1,k)
! : + tem8(i,j+1,k+1)+tem8(i+1,j+1,k+1))
! : - ys*(tem8(i,j,k)+tem8(i+1,j,k)
! : + tem8(i,j,k+1)+tem8(i+1,j,k+1)))
! : + dzinv*(zs1*(tem8(i,j,k+1)+tem8(i+1,j,k+1)
! : + tem8(i,j+1,k+1)+tem8(i+1,j+1,k+1))
! : - zs*(tem8(i,j,k)+tem8(i+1,j,k)
! : + tem8(i,j+1,k)+tem8(i+1,j+1,k)))
!
! term2 = term2/scoef
!
! tem6(i,j,k) = -2.0*term1 + 0.25*term2
!
! **** new formulation
!
xs = 0.5 * ( x(i) + x(i+1) ) - xmove
ys = 0.5 * ( y(j) + y(j+1) ) - ymove
zs = 0.5 * ( z(k) + z(k+1) ) - zshift
rrr = SQRT(xs*xs + ys*ys + zs*zs)
term1 = dxinv*(tem2(i+1,j,k)-tem2(i,j,k)) &
+ dyinv*(tem3(i,j+1,k)-tem3(i,j,k)) &
+ dzinv*(tem4(i,j,k+1)-tem4(i,j,k))
term2 = xs*dxinv*( (tem8(i+1,j,k)+tem8(i+1,j+1,k) &
+ tem8(i+1,j,k+1)+tem8(i+1,j+1,k+1)) &
- (tem8(i,j,k)+tem8(i,j+1,k) &
+ tem8(i,j,k+1)+tem8(i,j+1,k+1)) ) &
+ ys*dyinv*( (tem8(i,j+1,k)+tem8(i+1,j+1,k) &
+ tem8(i,j+1,k+1)+tem8(i+1,j+1,k+1)) &
- (tem8(i,j,k)+tem8(i+1,j,k) &
+ tem8(i,j,k+1)+tem8(i+1,j,k+1)) ) &
+ zs*dzinv*( (tem8(i,j,k+1)+tem8(i+1,j,k+1) &
+ tem8(i,j+1,k+1)+tem8(i+1,j+1,k+1)) &
- (tem8(i,j,k)+tem8(i+1,j,k) &
+ tem8(i,j+1,k)+tem8(i+1,j+1,k)) )
term2 = 0.25 * term2 + 2.0 * 0.125 * &
( tem8(i, j, k )+tem8(i+1,j, k ) + &
tem8(i, j+1,k )+tem8(i+1,j+1,k ) + &
tem8(i, j, k+1)+tem8(i+1,j, k+1) + &
tem8(i, j+1,k+1)+tem8(i+1,j+1,k+1) )
term2 = term2/rrr
tem6(i,j,k) = - 2.0 * term1 + term2
END DO
END DO
END DO
!
!----------------------------------------------------------------------
!
! Solve the elliptic equation via the successive overrelaxation
! method. Check for convergence. The following coefficients
! are defined as:
!
! b1 = rdx2
! b2 = rdy2
! b3 = rdz2
!
!----------------------------------------------------------------------
!
b1 = rdx2
b2 = rdy2
b3 = rdz2
c1 = -2.*(b1 + b2 + b3)
c2 = b1
c3 = b1
c4 = b2
c5 = b2
c6 = b3
c7 = b3
test = 0.0
DO k = 2, nz-2
DO j = 2, ny-2
DO i = 2, nx-2
tm1 = c2*tem7(i+1,j,k)
tm2 = c3*tem7(i-1,j,k)
tm3 = c4*tem7(i,j+1,k)
tm4 = c5*tem7(i,j-1,k)
tm5 = c6*tem7(i,j,k+1)
tm6 = c7*tem7(i,j,k-1)
resid = c1*tem7(i,j,k) + tm1 + tm2 + tm3 + tm4 &
+ tm5 + tm6 - tem6(i,j,k)
newit = tem7(i,j,k) - alpha*resid/c1 ! SOR method
! diff = abs(newit - tem7(i,j,k))
! diff = abs(newit - tem7(i,j,k)) / tem9(i,j,k)
diff = ABS(resid/c1) / tem9(i,j,k) ! alpha excluded;
! normakized residual
IF(diff > test) THEN
test = diff
imx = i
jmx = j
kmx = k
END IF
!
! tem7(i,j,k) = newit
tem11(i,j,k) = newit
tem10(i,j,k) = resid !outputs for test
END DO
END DO
END DO
! write(6,*) 'after relaxation'
!ccxxx
!ccxxx Test simutenous relaxation
!ccxxx
DO k = 2, nz-2
DO j = 2, ny-2
DO i = 2, nx-2
tem7(i,j,k) = tem11(i,j,k)
END DO
END DO
END DO
!
!----------------------------------------------------------------------
!
! Set the boundary conditions on Xl, Xr, Yl, & Yr
!
!----------------------------------------------------------------------
!
DO k = 2, nz-2 !XL,XR B.C.
DO j = 2, ny-2
tem7(1,j,k) = - tem7(2,j,k)
tem7(nx-1,j,k) = - tem7(nx-2,j,k)
END DO
END DO
DO k = 2,nz-2 !YL,YR B.C
DO i = 2,nx-2
tem7(i,1,k) = - tem7(i,2,k)
tem7(i,ny-1,k) = - tem7(i,ny-2,k)
END DO
END DO
!
!----------------------------------------------------------------------
!
! Set the top and bottom boundary conditions.
!
!----------------------------------------------------------------------
!
z2 = z(2) - zshift
znz1 = z(nz-1) - zshift
DO i=2,nx-2
DO j=2,ny-2
! xs = x(i) - xmove
! ys = y(j) - ymove
!
! radh = sqrt(xs*xs + ys*ys)
!
! tem7(i,j,1) = tem7(i,j,2) !'lamda2' grad B.C.
! : - 0.25*dz*z2*(tem8(i,j,2)+tem8(i,j+1,2)
! : + tem8(i+1,j,2)+tem8(i+1,j+1,2))/scoef
!
! tem7(i,j,nz-1) = tem7(i,j,nz-2)
! : + 0.25*dz*znz1*(tem8(i,j,nz-1)+tem8(i,j+1,nz-1)
! : + tem8(i+1,j,nz-1)+tem8(i+1,j+1,nz-1))/scoef
!
xs = 0.5 * ( x(i) + x(i+1) ) - xmove
ys = 0.5 * ( y(j) + y(j+1) ) - ymove
rrr = SQRT(xs*xs + ys*ys + z2*z2)
tem7(i,j,1) = tem7(i,j,2) & !'lamda2' grad B.C.
- 0.25*dz*z2*(tem8(i,j,2)+tem8(i,j+1,2) &
+ tem8(i+1,j,2)+tem8(i+1,j+1,2)) / rrr &
+ 2.0 * dz * tem4(i,j,2)
rrr = SQRT(xs*xs + ys*ys + znz1*znz1)
tem7(i,j,nz-1) = tem7(i,j,nz-2) &
+ 0.25*dz*znz1*(tem8(i,j,nz-1)+tem8(i,j+1,nz-1) &
+ tem8(i+1,j,nz-1)+tem8(i+1,j+1,nz-1)) / rrr &
- 2.0 * dz * tem4(i,j,nz-1)
END DO
END DO
!ccxxx
!ccxxx Patch: you might like to change it.
!ccxxx
ir0 = xmove/dx + 1
jr0 = ymove/dy + 1
ipatch =5
ips=ir0-ipatch
ipe=ir0+ipatch
jps=jr0-ipatch
jpe=jr0+ipatch
IF((ir0-ipatch) < 2) ips=2
IF((jr0-ipatch) < 2) jps=2
IF((ir0+ipatch) > (nx-2)) ipe=nx-2
IF((jr0+ipatch) > (ny-2)) jpe=ny-2
DO in = ips,ipe
DO jn = jps,jpe
acof = (jn-jps)/(jpe-jps)
tem7(in,jn,nz-1) = (tem7(in,jpe,nz-1)-tem7(in,jps,nz-1))*acof &
+ tem7(in,jps,nz-1)
acof = (in-ips)/(ipe-ips)
tem7(in,jn,nz-1) = 0.5*(tem7(in,jn,nz-1) + ((tem7(ipe,jn,nz-1) &
- tem7(ips,jn,nz-1))*acof) + tem7(ips,jn,nz-1))
! acof = (in-ips)/(ipe-ips)
! bcof = (jn-jps)/(jpe-jps)
! tem7(in,jn,nz-1) = (1.0-acof)*(1.0-bcof)*tem7(ips,jps,nz-1)
! : + (1.0-acof)* bcof *tem7(ips,jpe,nz-1)
! : + acof * bcof *tem7(ipe,jpe,nz-1)
! : + acof *(1.0-bcof)*tem7(ipe,jps,nz-1)
!
! tem7(in,jn,nz-1) = 0.5 * (tem7(in,jn,nz-1) + tem7(in,jn,nz-2))
!
! tem7(in,jn,nz-1) = tem7(in,jn,nz-2) ! zeor gradient
END DO
END DO
! ir0 = xmove/dx + 1
! jr0 = ymove/dy + 1
! ipatch = 10 ! within a radius of 20 km
! ips=ir0-ipatch
! ipe=ir0+ipatch
! jps=jr0-ipatch
! jpe=jr0+ipatch
! if((ir0-ipatch).lt.2) ips=2
! if((jr0-ipatch).lt.2) jps=2
! if((ir0+ipatch).gt.(nx-2)) ipe=nx-2
! if((jr0+ipatch).gt.(ny-2)) jpe=ny-2
!
! DO in = ips,ipe
! DO jn = jps,jpe
! tem7(in,jn,1) = 0.5 * ( tem7(in,jn,1) +
! : 0.25*(tem7(in-1,jn,1)+tem7(in+1,jn,1)+
! : tem7(in,jn-1,1)+tem7(in,jn+1,1)) )
! tem7(in,jn,nz-1) = 0.5 * ( tem7(in,jn,nz-1) +
! : 0.25*(tem7(in-1,jn,nz-1)+tem7(in+1,jn,nz-1)+
! : tem7(in,jn-1,nz-1)+tem7(in,jn+1,nz-1)) )
! END DO
! END DO
! DO k = 2, nz-2
! DO in = ips,ipe
! DO jn = jps,jpe
! tem7(in,jn,k) = 0.5 * ( tem7(in,jn,k) +
! : (tem7(in-1,jn,k)+tem7(in+1,jn,k)+
! : tem7(in,jn-1,k)+tem7(in,jn+1,k)+
! : tem7(in,jn,k-1)+tem7(in,jn,k+1))/6.0 )
! END DO
! END DO
! END DO
DO i=2,nx-2
tem7(i,1,1) = - tem7(i,2,1)
tem7(i,1,nz-1) = - tem7(i,2,nz-1)
tem7(i,ny-1,1) = - tem7(i,ny-2,1)
tem7(i,ny-1,nz-1) = - tem7(i,ny-2,nz-1)
END DO
DO j=2,ny-2
tem7(1,j,1) = - tem7(2,j,1)
tem7(1,j,nz-1) = - tem7(2,j,nz-1)
tem7(nx-1,j,1) = - tem7(nx-2,j,1)
tem7(nx-1,j,nz-1) = - tem7(nx-2,j,nz-1)
END DO
!
!----------------------------------------------------------------------
!
! Set the corner points.
!
!----------------------------------------------------------------------
!
DO k = 1,nz-1
tem7(1,1,k) = - tem7(2,2,k)
tem7(1,ny-1,k) = - tem7(2,ny-2,k)
tem7(nx-1,1,k) = - tem7(nx-2,2,k)
tem7(nx-1,ny-1,k) = - tem7(nx-2,ny-2,k)
END DO
!
!----------------------------------------------------------------------
!
! Determine the first Lagrange Multiplier, Lamda1. Lamda1 is
! assumed valid at integer points(i,j,k). The result is
! stored in tem8.
!
!----------------------------------------------------------------------
!
test1=0.0
DO k = 2, nz-1
DO j = 2, ny-1
DO i = 2, nx-1
xs = x(i) - xmove
ys = y(j) - ymove
zs = z(k) - zshift
rad = SQRT(xs**2+ys**2+zs**2)
radinv = 1./(rad**2)
IF( rad < 1.0 ) THEN
rad = 1.0
radinv = 1./(rad**2)
END IF
term1 = dxinv*xs*((tem7(i,j-1,k-1)-tem7(i-1,j-1,k-1)) &
+ (tem7(i,j-1,k)-tem7(i-1,j-1,k)) &
+ (tem7(i,j,k-1)-tem7(i-1,j,k-1)) &
+ (tem7(i,j,k)-tem7(i-1,j,k)))
term2 = dyinv*ys*((tem7(i-1,j,k-1)-tem7(i-1,j-1,k-1)) &
+ (tem7(i,j,k-1)-tem7(i,j-1,k-1)) &
+ (tem7(i-1,j,k)-tem7(i-1,j-1,k)) &
+ (tem7(i,j,k)-tem7(i,j-1,k)))
term3 = dzinv*zs*((tem7(i,j-1,k)-tem7(i,j-1,k-1)) &
+ (tem7(i-1,j-1,k)-tem7(i-1,j-1,k-1)) &
+ (tem7(i-1,j,k)-tem7(i-1,j,k-1)) &
+ (tem7(i,j,k)-tem7(i,j,k-1)))
term4 = 0.125*((tem5(i,j,k)+tem5(i-1,j,k) &
+ tem5(i-1,j-1,k)+tem5(i,j-1,k) &
+ tem5(i,j,k-1)+tem5(i-1,j,k-1) &
+ tem5(i-1,j-1,k-1)+tem5(i,j-1,k-1)) &
- (tem1(i,j,k)+tem1(i-1,j,k) &
+ tem1(i-1,j-1,k)+tem1(i,j-1,k) &
+ tem1(i,j,k-1)+tem1(i-1,j,k-1) &
+ tem1(i-1,j-1,k-1)+tem1(i,j-1,k-1)))
! term5 = 2.0*term4/rad + 0.25*radinv*(term1+term2+term3)
term5 = 2.0*term4 + 0.25*(term1+term2+term3)/rad
diff = ABS(term5-tem8(i,j,k)) / tem12(i,j,k)
IF(diff > test1) THEN
test1 = diff
imx1 = i
jmx1 = j
kmx1 = k
END IF
tem8(i,j,k) = scoef*term5
END DO
END DO
END DO
DO k = 2, nz-1
DO j = 2, ny-1
DO i = 2, nx-1
xs = x(i) - xmove
ys = y(j) - ymove
zs = z(k) - zshift
rad = SQRT(xs**2+ys**2+zs**2)
IF( rad < 1.0 ) THEN
tem8(i,j,k) = 0.0
radinv = 0.0
IF(i > 2) THEN
tem8(i,j,k) = tem8(i,j,k) + tem8(i-1,j,k)
radinv = radinv + 1.
END IF
IF(i < nx-1) THEN
tem8(i,j,k) = tem8(i,j,k) + tem8(i+1,j,k)
radinv = radinv + 1.
END IF
IF(j > 2) THEN
tem8(i,j,k) = tem8(i,j,k) + tem8(i,j-1,k)
radinv = radinv + 1.
END IF
IF(j < ny-1) THEN
tem8(i,j,k) = tem8(i,j,k) + tem8(i,j+1,k)
radinv = radinv + 1.
END IF
IF(k > 2) THEN
tem8(i,j,k) = tem8(i,j,k) + tem8(i,j,k-1)
radinv = radinv + 1.
END IF
IF(k < nz-1) THEN
tem8(i,j,k) = tem8(i,j,k) + tem8(i,j,k+1)
radinv = radinv + 1.
END IF
tem8(i,j,k) = tem8(i,j,k) / radinv
WRITE(6,*) 'Do patching for lamda1 at i,j,k=',i,j,k
END IF
END DO
END DO
END DO
!
!----------------------------------------------------------------------
!
! Test for solution convergence.
!
!----------------------------------------------------------------------
!
! tol = sqrt(dx**2+dy**2+dz**2)*veltol
tol = MIN( MIN(dx, dy), dz) * veltol
! ix = mod(it,1)
ix = MOD(it,50)
IF(it == 50) THEN
WRITE(6,*) ' Max diff at iteration: imx,jmx,kmx,test,test1'
END IF
IF(ix == 0) THEN
WRITE(6,'(i9,2x,2i4,i3,e16.6,2x,2i4,i3,e16.6)') &
it,imx,jmx,kmx,test, imx1,jmx1,kmx1,test1
END IF
! IF(test.le.tol.and.it.gt.2) THEN
IF(test <= tol .AND. test1 <= veltol .AND. it > 2) THEN
WRITE(6,'(/5x,a,i6,/5x,a,2f12.6)') &
'The SOR technique converged. The # of iterations was ', &
it,' The tolerance level was set at: ',veltol,tol
WRITE(6,'(i9,2x,2i4,i3,e16.6,2x,2i4,i3,e16.6)') &
it,imx,jmx,kmx,test, imx1,jmx1,kmx1,test1
GO TO 258
END IF
END DO
STOP
258 CONTINUE
WRITE(6,*) 'patch: xmove,ymove,ir0,jr0,ipatch=', &
xmove,ymove,ir0,jr0,ipatch
WRITE(6,*) 'patch: ips,ipe,jps,jpe=',ips,ipe,jps,jpe
2201 CONTINUE
!
!----------------------------------------------------------------------
!
! Determine the adjusted velocity, ua, store results in tem2:
!
! 2*rhobar*(Ua-Um) + lamda1*x - dlamda2/dx = 0
!
! NOTE: rhobar (tem9) is assumed horizontally homogenous.
!
!----------------------------------------------------------------------
!
DO k = 1,nz-1
DO j = 1,ny-1
DO i = 1,nx-1
tem9(i,j,k)= rhostr(i,j,k)/j3(i,j,k)
END DO
END DO
END DO
CALL avgsu(tem9,nx,ny,nz, 1,ny-1, 1,nz-1, tem6, tem10)
DO k = 2, nz-2
DO j = 2, ny-2
DO i = 2, nx-1
! xs = x(i) - xmove
!
! tem2(i,j,k) = u(i,j,k,tim) + (.5/tem6(i,j,k))
! : *(dxinv*(tem7(i,j,k)-tem7(i-1,j,k))
! : - 0.25*xs*(tem8(i,j,k)+tem8(i,j+1,k)
! : + tem8(i,j,k+1)+tem8(i,j+1,k+1)))
!
xs = x(i) - xmove
ys = 0.5 * ( y(j) + y(j+1) ) - ymove
zs = 0.5 * ( z(k) + z(k+1) ) - zshift
rrr = SQRT(xs*xs + ys*ys + zs*zs)
tem2(i,j,k) = u(i,j,k,tim) + (.5/tem6(i,j,k)) &
* ( dxinv*(tem7(i,j,k)-tem7(i-1,j,k)) &
- 0.25*(xs/rrr)*(tem8(i,j,k)+tem8(i,j+1,k) &
+tem8(i,j,k+1)+tem8(i,j+1,k+1)) )
END DO
END DO
END DO
!
!----------------------------------------------------------------------
!
! Determine the adjusted velocity, va, store results in tem3:
!
! 2*rhobar*(Va-Vm) + lamda1*y - dlamda2/dy = 0
!
! NOTE: rhobar (tem9) is assumed horizontally homogenous.
!
!----------------------------------------------------------------------
!
CALL avgsv(tem9,nx,ny,nz, 1,nx-1, 1,nz-1, tem6, tem10)
DO k = 2, nz-2
DO j = 2, ny-1
DO i = 2, nx-2
! ys = y(j) - ymove
!
! tem3(i,j,k) = v(i,j,k,tim) + (.5/tem6(i,j,k))
! : *(dyinv*(tem7(i,j,k)-tem7(i,j-1,k))
! : - 0.25*ys*(tem8(i,j,k)+tem8(i+1,j,k)
! : + tem8(i,j,k+1)+tem8(i+1,j,k+1)))
xs = 0.5 * ( x(i) + x(i+1) ) - xmove
ys = y(j) - ymove
zs = 0.5 * ( z(k) + z(k+1) ) - zshift
rrr = SQRT(xs*xs + ys*ys + zs*zs)
tem3(i,j,k) = v(i,j,k,tim) + (.5/tem6(i,j,k)) &
* ( dyinv*(tem7(i,j,k)-tem7(i,j-1,k)) &
- 0.25*(ys/rrr)*(tem8(i,j,k)+tem8(i+1,j,k) &
+tem8(i,j,k+1)+tem8(i+1,j,k+1)) )
END DO
END DO
END DO
!
!----------------------------------------------------------------------
!
! Determine the adjusted velocity, wa, store results in tem4:
!
! 2*rhobar*(Wa-Wm) + lamda1*z - dlamda2/dz = 0
!
!----------------------------------------------------------------------
!
CALL avgsw(tem9,nx,ny,nz, 1,nx-1, 1,ny-1, tem6)
WRITE(6,*) 'Maximum vertical velocity after adjustment'
DO k = 2, nz-1
maxw=0
DO j = 2, ny-2
DO i = 2, nx-2
! zs = z(k) - zshift
!
! tem4(i,j,k) = w(i,j,k,tim) + (0.5/tem6(i,j,k))
! : *(dzinv*(tem7(i,j,k)-tem7(i,j,k-1))
! : - 0.25*zs*(tem8(i,j,k)+tem8(i+1,j,k)
! : + tem8(i,j+1,k)+tem8(i+1,j+1,k)))
xs = 0.5 * ( x(i) + x(i+1) ) - xmove
ys = 0.5 * ( y(j) + y(j+1) ) - ymove
zs = z(k) - zshift
rrr = SQRT(xs*xs + ys*ys + zs*zs)
tem4(i,j,k) = w(i,j,k,tim) + (0.5/tem6(i,j,k)) &
* ( dzinv*(tem7(i,j,k)-tem7(i,j,k-1)) &
- 0.25*(zs/rrr)*(tem8(i,j,k)+tem8(i+1,j,k) &
+tem8(i,j+1,k)+tem8(i+1,j+1,k)) )
IF (ABS(tem4(i,j,k)) > maxw) THEN
maxw = ABS(tem4(i,j,k))
imx=i
jmx=j
END IF
END DO
END DO
WRITE(6,*) ' imx,jmx,k,maxw: ',imx,jmx,k,maxw
END DO
END IF
!
!-----------------------------------------------------------------------
!
! Exit adjustment/or direct insertion
!
!-----------------------------------------------------------------------
!
270 CONTINUE
!
!-----------------------------------------------------------------------
!
! Compare the model radial velocity and observed radial velocity
!
!-----------------------------------------------------------------------
!
CALL avgx(tem2, 0, nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem6)
CALL avgy(tem3, 0, nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem7)
CALL avgz(tem4, 0, nx,ny,nz,1,nx-1,1,ny-1,1,nz-1,tem8)
WRITE(6,*) 'Check vr & print out if abs(vradj-vro) > 1.5 m/s'
DO k=2,nz-2
DO j=2,ny-2
DO i=2,nx-2
xs = 0.5*(x(i)+x(i+1)) - xmove
ys = 0.5*(y(j)+y(j+1)) - ymove
zs = 0.5*(z(k)+z(k+1)) - zshift
rad = SQRT(xs**2+ys**2+zs**2)
vradj = (tem6(i,j,k)*xs + tem7(i,j,k)*ys &
+ tem8(i,j,k)*zs)/rad
vro = tem1(i,j,k)/tem9(i,j,k)
vrm = tem5(i,j,k)/tem9(i,j,k)
! IF(abs(vradj-vro).gt.1.5) THEN
! write(6,*) ' i,j,k,vradj,vro,vrm: ',i,j,k,vradj,vro,vrm
! ENDIF
END DO
END DO
END DO
!
!-----------------------------------------------------------------------
!
! NOTE: This next section is designed to determine whether or not
! mass conservation has been satisfied. It is not an essential
! part of the assimilation package.
!
! Stagger rhostar(stored in tem9).
!
!-----------------------------------------------------------------------
!
CALL avgsu(tem9,nx,ny,nz, 1,ny-1, 1,nz-1, tem6, tem10)
CALL avgsv(tem9,nx,ny,nz, 1,nx-1, 1,nz-1, tem7, tem10)
CALL avgsw(tem9,nx,ny,nz, 1,nx-1, 1,ny-1, tem8)
!
!-----------------------------------------------------------------------
!
! Calculate del dot rho V using the adjusted velocities.
!
!-----------------------------------------------------------------------
!
WRITE(6,*) 'background divergence'
DO k=2,nz-2
maxdiv = 0.0
DO j=4,ny-4
DO i=4,nx-4
tem1(i,j,k)= &
(u(i+1,j,k,tim)*tem6(i+1,j,k)-u(i,j,k,tim)*tem6(i,j,k))*dxinv &
+(v(i,j+1,k,tim)*tem7(i,j+1,k)-v(i,j,k,tim)*tem7(i,j,k))*dyinv &
+(w(i,j,k+1,tim)*tem8(i,j,k+1)-w(i,j,k,tim)*tem8(i,j,k))*dzinv
IF (ABS(tem1(i,j,k)) > maxdiv) THEN
maxdiv = ABS(tem1(i,j,k))
imx = i
jmx = j
END IF
END DO
END DO
maxdiv=tem1(imx,jmx,k)
PRINT *,' maxdiv,imx,jmx,k = ',maxdiv,imx,jmx,k
END DO
WRITE(6,*) 'adjusted divergence'
DO k=2,nz-2
maxdiv = 0.0
DO j=4,ny-4
DO i=4,nx-4
tem1(i,j,k)= &
(tem2(i+1,j,k)*tem6(i+1,j,k)-tem2(i,j,k)*tem6(i,j,k))*dxinv &
+(tem3(i,j+1,k)*tem7(i,j+1,k)-tem3(i,j,k)*tem7(i,j,k))*dyinv &
+(tem4(i,j,k+1)*tem8(i,j,k+1)-tem4(i,j,k)*tem8(i,j,k))*dzinv
IF (ABS(tem1(i,j,k)) > maxdiv) THEN
maxdiv = ABS(tem1(i,j,k))
imx = i
jmx = j
END IF
END DO
END DO
maxdiv=tem1(imx,jmx,k)
PRINT *,' maxdiv,imx,jmx,k = ',maxdiv,imx,jmx,k
END DO
RETURN
END SUBROUTINE assimvel