!
!##################################################################
!##################################################################
!###### ######
!###### SUBROUTINE SMOOTH9P_NOBC ######
!###### ######
!###### Developed by ######
!###### Center for Analysis and Prediction of Storms ######
!###### University of Oklahoma ######
!###### ######
!##################################################################
!##################################################################
!
!
SUBROUTINE smooth9p_nobc( arr, nx,ny,ibgn,iend,jbgn,jend, tem1 ) 4
!
!-----------------------------------------------------------------------
!
! PURPOSE:
!
! 1 2 1
! Smooth a 2-D array by the filter of { 2 4 2 }. This subroutine
! 1 2 1
! does not deal with the boundaries. Users are supposed to deal with
! the boundaries themselves based on how they want the BC to be.
!
!-----------------------------------------------------------------------
!
! AUTHOR: Yuhe Liu
!
! 4/13/99
!
! Modification History
!
!-----------------------------------------------------------------------
!
! INPUT:
!
! nx Number of grid points in the x-direction
! ny Number of grid points in the y-direction
! ibgn First index in x-direction in the soomthing region.
! iend Last index in x-direction in the soomthing region.
! jbgn First index in j-direction in the soomthing region.
! jend Last index in j-direction in the soomthing region.
!
! arr 2-D array
!
! OUTPUT:
!
! arr 2-D array
!
! TEMPORARY:
!
! tem1 Temporary 2-D array
!
!-----------------------------------------------------------------------
!
! Variable Declarations.
!
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
INTEGER :: nx ! Number of grid points in the x-direction
INTEGER :: ny ! Number of grid points in the y-direction
INTEGER :: ibgn
INTEGER :: iend
INTEGER :: jbgn
INTEGER :: jend
!
REAL :: arr (nx,ny) ! 2-D array
!
REAL :: tem1(nx,ny) ! Temporary array
!
!-----------------------------------------------------------------------
!
! Misc. local variables:
!
!-----------------------------------------------------------------------
!
INTEGER :: i,j
REAL :: wtf,wtfb,wtfc
!
!-----------------------------------------------------------------------
!
! Include files:
!
!-----------------------------------------------------------------------
!
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
! Beginning of executable code...
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
wtf = 1.0/16.0
wtfb = 1.0/12.0
wtfc = 1.0/9.0
DO j = jbgn+1, jend-1
DO i = ibgn+1, iend-1
tem1(i,j) = wtf &
* ( arr(i-1,j-1) + 2.*arr(i,j-1) + arr(i+1,j-1) &
+ 2.*arr(i-1,j ) + 4.*arr(i,j ) + 2.*arr(i+1,j ) &
+ arr(i-1,j+1) + 2.*arr(i,j+1) + arr(i+1,j+1) )
END DO
END DO
DO j = 1, ny
DO i = 1, nx
arr(i,j) = tem1(i,j)
END DO
END DO
RETURN
END SUBROUTINE smooth9p_nobc
!
!##################################################################
!##################################################################
!###### ######
!###### SUBROUTINE SMOOTH9P ######
!###### ######
!###### Developed by ######
!###### Center for Analysis and Prediction of Storms ######
!###### University of Oklahoma ######
!###### ######
!##################################################################
!##################################################################
!
!
SUBROUTINE smooth9p( arr, nx,ny,ibgn,iend,jbgn,jend, tem1 ) 26
!
!-----------------------------------------------------------------------
!
! PURPOSE:
!
! 1 2 1
! Smooth a 2-D array by the filter of { 2 4 2 }
! 1 2 1
!
!-----------------------------------------------------------------------
!
! AUTHOR: Yuhe Liu
!
! 5/3/94
!
! Modification History
! 8/20/1995 (M. Xue)
! Fixed errors in the index bound of loops 100 and 200.
!
!-----------------------------------------------------------------------
!
! INPUT:
!
! nx Number of grid points in the x-direction
! ny Number of grid points in the y-direction
! ibgn First index in x-direction in the soomthing region.
! iend Last index in x-direction in the soomthing region.
! jbgn First index in j-direction in the soomthing region.
! jend Last index in j-direction in the soomthing region.
!
! arr 2-D array
!
! OUTPUT:
!
! arr 2-D array
!
! TEMPORARY:
!
! tem1 Temporary 2-D array
!
!-----------------------------------------------------------------------
!
! Variable Declarations.
!
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
INTEGER :: nx ! Number of grid points in the x-direction
INTEGER :: ny ! Number of grid points in the y-direction
INTEGER :: ibgn
INTEGER :: iend
INTEGER :: jbgn
INTEGER :: jend
!
REAL :: arr (nx,ny) ! 2-D array
!
REAL :: tem1(nx,ny) ! Temporary array
!
!-----------------------------------------------------------------------
!
! Misc. local variables:
!
!-----------------------------------------------------------------------
!
INTEGER :: i,j
REAL :: wtf,wtfb,wtfc
!
!-----------------------------------------------------------------------
!
! Include files:
!
!-----------------------------------------------------------------------
!
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
! Beginning of executable code...
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
wtf = 1.0/16.0
wtfb = 1.0/12.0
wtfc = 1.0/9.0
DO j = jbgn+1, jend-1
DO i = ibgn+1, iend-1
tem1(i,j) = wtf &
* ( arr(i-1,j-1) + 2.*arr(i,j-1) + arr(i+1,j-1) &
+ 2.*arr(i-1,j ) + 4.*arr(i,j ) + 2.*arr(i+1,j ) &
+ arr(i-1,j+1) + 2.*arr(i,j+1) + arr(i+1,j+1) )
END DO
END DO
DO j = jbgn+1, jend-1
tem1(ibgn,j) = wtfb &
* ( 2.*arr(ibgn,j-1) + arr(ibgn+1,j-1) &
+ 4.*arr(ibgn,j ) + 2.*arr(ibgn+1,j ) &
+ 2.*arr(ibgn,j+1) + arr(ibgn+1,j+1) )
tem1(iend,j) = wtfb &
* ( arr(iend-1,j-1) + 2.*arr(iend,j-1) &
+ 2.*arr(iend-1,j ) + 4.*arr(iend,j ) &
+ arr(iend-1,j+1) + 2.*arr(iend,j+1) )
END DO
DO i = ibgn+1, iend-1
tem1(i,jbgn) = wtfb &
* ( 2.*arr(i-1,jbgn ) + 4.*arr(i,jbgn ) + 2.*arr(i+1,jbgn ) &
+ arr(i-1,jbgn+1) + 2.*arr(i,jbgn+1) + arr(i+1,jbgn+1) )
tem1(i,jend) = wtfb &
* ( arr(i-1,jend-1) + 2.*arr(i,jend-1) + arr(i+1,jend-1) &
+ 2.*arr(i-1,jend ) + 4.*arr(i,jend ) + 2.*arr(i+1,jend ) )
END DO
tem1(ibgn,jbgn) = wtfc &
* ( 2.*arr(ibgn,jbgn+1) + arr(ibgn+1,jbgn+1) &
+ 4.*arr(ibgn,jbgn ) + 2.*arr(ibgn+1,jbgn ) )
tem1(ibgn,jend) = wtfc &
* ( 4.*arr(ibgn,jend ) + 2.*arr(ibgn+1,jend ) &
+ 2.*arr(ibgn,jend-1) + arr(ibgn+1,jend-1) )
tem1(iend,jbgn) = wtfc &
* ( arr(iend-1,jbgn+1) + 2.*arr(iend,jbgn+1) &
+ 2.*arr(iend-1,jbgn ) + 4.*arr(iend,jbgn ) )
tem1(iend,jend) = wtfc &
* ( 2.*arr(iend-1,jend ) + 4.*arr(iend, jend) &
+ arr(iend-1,jend-1) + 2.*arr(iend-1,jend) )
DO j = 1, ny
DO i = 1, nx
arr(i,j) = tem1(i,j)
END DO
END DO
RETURN
END SUBROUTINE smooth9p
!
!##################################################################
!##################################################################
!###### ######
!###### SUBROUTINE SMOOTH25P ######
!###### ######
!###### Developed by ######
!###### Center for Analysis and Prediction of Storms ######
!###### University of Oklahoma ######
!###### ######
!##################################################################
!##################################################################
!
!
SUBROUTINE smooth25p( arr, nx,ny,ibgn,iend,jbgn,jend, tem1 ) 4
!
!-----------------------------------------------------------------------
!
! PURPOSE:
!
! To perform a 25 point smoothing on a 2-D array.
!
!
! 1 4 6 4 1
! 4 16 24 16 4
! Smooth a 2-D array by the filter of { 6 24 36 24 6 }
! 4 16 24 16 4
! 1 4 6 4 1
!
!
! 1 2 1
! At the inner boundary 9-point filter will be used: { 2 4 2 }
! 1 2 1
!
! 2 1
! At the outer boundary 6-point filter will be used: { 4 2 }
! 2 1
!
! 2 1
! At the corners 4-point filter is used: { }
! 4 2
!
!-----------------------------------------------------------------------
!
! AUTHOR: Yuhe Liu
! 5/3/94
!
!-----------------------------------------------------------------------
!
! INPUT:
!
! nx Number of grid points in the x-direction
! ny Number of grid points in the y-direction
! ibgn First index in x-direction in the soomthing region.
! iend Last index in x-direction in the soomthing region.
! jbgn First index in j-direction in the soomthing region.
! jend Last index in j-direction in the soomthing region.
!
! arr 2-D array
!
! OUTPUT:
!
! arr 2-D array smoothed
!
! TEMPORARY:
!
! tem1 Temporary 2-D array
!
!-----------------------------------------------------------------------
!
! Variable Declarations.
!
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
INTEGER :: nx ! Number of grid points in the x-direction
INTEGER :: ny ! Number of grid points in the y-direction
INTEGER :: ibgn,iend,jbgn,jend
!
REAL :: arr(nx,ny) ! 2-D array
!
REAL :: tem1(nx,ny) ! Temporary array
!
!-----------------------------------------------------------------------
!
! Misc. local variables:
!
!-----------------------------------------------------------------------
!
INTEGER :: i,j
REAL :: wtf
REAL :: wtfb1
REAL :: wtfb2
REAL :: wtfc
REAL :: wt(5,5)
DATA wt/ 1., 4., 6., 4., 1., &
4., 16., 24., 16., 4., &
6., 24., 36., 24., 6., &
4., 16., 24., 16., 4., &
1., 4., 6., 4., 1./
REAL :: wtb(3,3)
DATA wtb/ 1., 2., 1., &
2., 4., 2., &
1., 2., 1./
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
! Beginning of executable code...
!
!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
!
wtf = 1./256.
DO j = jbgn+2, jend-2
DO i = ibgn+2, iend-2
tem1(i,j) = wtf &
* ( wt(1,1)*arr(i-2,j-2) + wt(2,1)*arr(i-1,j-2) &
+ wt(3,1)*arr(i, j-2) + wt(4,1)*arr(i+1,j-2) &
+ wt(5,1)*arr(i+2,j-2) &
+ wt(1,2)*arr(i-2,j-1) + wt(2,2)*arr(i-1,j-1) &
+ wt(3,2)*arr(i, j-1) + wt(4,2)*arr(i+1,j-1) &
+ wt(5,2)*arr(i+2,j-1) &
+ wt(1,3)*arr(i-2,j ) + wt(2,3)*arr(i-1,j ) &
+ wt(3,3)*arr(i, j ) + wt(4,3)*arr(i+1,j ) &
+ wt(5,3)*arr(i+2,j ) &
+ wt(1,4)*arr(i-2,j+1) + wt(2,4)*arr(i-1,j+1) &
+ wt(3,4)*arr(i, j+1) + wt(4,4)*arr(i+1,j+1) &
+ wt(5,4)*arr(i+2,j+1) &
+ wt(1,5)*arr(i-2,j+2) + wt(2,5)*arr(i-1,j+2) &
+ wt(3,5)*arr(i, j+2) + wt(4,5)*arr(i+1,j+2) &
+ wt(5,5)*arr(i+2,j+2) )
END DO
END DO
wtfb1 = 1./16.
wtfb2 = 1./12.
DO j = jbgn+1, jend-1
tem1(ibgn+1,j) = wtfb1 &
* ( wtb(1,1)*arr(ibgn, j-1) + wtb(2,1)*arr(ibgn+1,j-1) &
+ wtb(3,1)*arr(ibgn+2,j-1) &
+ wtb(1,2)*arr(ibgn, j ) + wtb(2,2)*arr(ibgn+1,j ) &
+ wtb(3,2)*arr(ibgn+2,j ) &
+ wtb(1,3)*arr(ibgn ,j+1) + wtb(2,3)*arr(ibgn+1,j+1) &
+ wtb(3,3)*arr(ibgn+2,j+1) )
tem1(ibgn,j) = wtfb2 &
* ( wtb(2,1)*arr(ibgn,j-1) + wtb(3,1)*arr(ibgn+1,j-1) &
+ wtb(2,2)*arr(ibgn,j ) + wtb(3,2)*arr(ibgn+1,j ) &
+ wtb(2,3)*arr(ibgn,j+1) + wtb(3,3)*arr(ibgn+1,j+1) )
tem1(iend-1,j) = wtfb1 &
* ( wtb(1,1)*arr(iend-2,j-1) + wtb(2,1)*arr(iend-1,j-1) &
+ wtb(3,1)*arr(iend, j-1) &
+ wtb(1,2)*arr(iend-2,j ) + wtb(2,2)*arr(iend-1,j ) &
+ wtb(3,2)*arr(iend, j ) &
+ wtb(1,3)*arr(iend-2,j+1) + wtb(2,3)*arr(iend-1,j+1) &
+ wtb(3,3)*arr(iend, j+1) )
tem1(iend,j) = wtfb2 &
* ( wtb(1,1)*arr(iend-1,j-1) + wtb(2,1)*arr(iend,j-1) &
+ wtb(1,2)*arr(iend-1,j ) + wtb(2,2)*arr(iend,j ) &
+ wtb(1,3)*arr(iend-1,j+1) + wtb(2,3)*arr(iend,j+1) )
END DO
DO i = ibgn+1, iend-1
tem1(i,jbgn+1) = wtfb1 &
* ( wtb(1,1)*arr(i-1,jbgn) + wtb(2,1)*arr(i,jbgn ) &
+ wtb(3,1)*arr(i+1,jbgn) &
+ wtb(1,2)*arr(i-1,jbgn+1) + wtb(2,2)*arr(i,jbgn+1) &
+ wtb(3,2)*arr(i+1,jbgn+1) &
+ wtb(1,3)*arr(i-1,jbgn+2) + wtb(2,3)*arr(i,jbgn+2) &
+ wtb(3,3)*arr(i+1,jbgn+2) )
tem1(i,jbgn) = wtfb2 &
* ( wtb(1,2)*arr(i-1,jbgn) + wtb(2,2)*arr(i,jbgn ) &
+ wtb(3,2)*arr(i+1,jbgn) &
+ wtb(1,3)*arr(i-1,jbgn+1) + wtb(2,3)*arr(i,jbgn+1) &
+ wtb(3,3)*arr(i+1,jbgn+1) )
tem1(i,jend-1) = wtfb1 &
* ( wtb(1,1)*arr(i-1,jend-2) + wtb(2,1)*arr(i,jend-2) &
+ wtb(3,1)*arr(i+1,jend-2) &
+ wtb(1,2)*arr(i-1,jend-1) + wtb(2,2)*arr(i,jend-1) &
+ wtb(3,2)*arr(i+1,jend-1) &
+ wtb(1,3)*arr(i-1,jend ) + wtb(2,3)*arr(i,jend ) &
+ wtb(3,3)*arr(i+1,jend ) )
tem1(i,jend) = wtfb2 &
* ( wtb(1,1)*arr(i-1,jend-1) + wtb(2,1)*arr(i,jend-1) &
+ wtb(3,1)*arr(i+1,jend-1) &
+ wtb(1,2)*arr(i-1,jend ) + wtb(2,2)*arr(i,jend ) &
+ wtb(3,2)*arr(i+1,jend ) )
END DO
wtfc = 1./9.
tem1(ibgn,jbgn) = wtfc &
* ( wtb(1,2)*arr(ibgn,jbgn+1) + wtb(1,3)*arr(ibgn+1,jbgn+1) &
+ wtb(2,2)*arr(ibgn,jbgn ) + wtb(2,3)*arr(ibgn+1,jbgn ) )
tem1(iend,jbgn) = wtfc &
* ( wtb(1,1)*arr(iend-1,jbgn+1) + wtb(1,2)*arr(iend,jbgn+1) &
+ wtb(2,1)*arr(iend-1,jbgn ) + wtb(2,2)*arr(iend,jbgn ) )
tem1(ibgn,jend) = wtfc &
* ( wtb(2,2)*arr(ibgn,jend ) + wtb(3,2)*arr(ibgn+1,jend ) &
+ wtb(2,3)*arr(ibgn,jend-1) + wtb(3,3)*arr(ibgn+1,jend-1) )
tem1(iend,jend) = wtfc &
* ( wtb(2,1)*arr(iend-1,jend ) + wtb(2,2)*arr(iend,jend ) &
+ wtb(3,1)*arr(iend-1,jend-1) + wtb(3,2)*arr(iend,jend-1) )
DO j = jbgn, jend
DO i = ibgn, iend
arr(i,j) = tem1(i,j)
END DO
END DO
RETURN
END SUBROUTINE smooth25p
!
!##################################################################
!##################################################################
!###### ######
!###### SUBROUTINE SMOOTH3D ######
!###### ######
!###### Developed by ######
!###### Center for Analysis and Prediction of Storms ######
!###### University of Oklahoma ######
!###### ######
!##################################################################
!##################################################################
!
!
SUBROUTINE smooth3d(nx,ny,nz,ibgn,iend,jbgn,jend,kbgn,kend, & 18
s,ht,zin,zwork,zout)
!
!-----------------------------------------------------------------------
!
! PURPOSE:
!
! Performs symmetrical 3-dimensional smoothing of input field
! zin which is output as zout, the smoothed field. A work array
! zwork, dimension (nx,ny) is required.
!
!-----------------------------------------------------------------------
!
! AUTHOR: K. Brewster
! 3/1989
!
!-----------------------------------------------------------------------
!
! INPUT:
!
! nx Number of grid points in the x-direction
! ny Number of grid points in the y-direction
! nz Number of grid points in the z-direction
! ibgn First index in i-direction in the soomthing region.
! iend Last index in i-direction in the soomthing region.
! jbgn First index in j-direction in the soomthing region.
! jend Last index in j-direction in the soomthing region.
! kbgn First index in k-direction in the soomthing region.
! kend Last index in k-direction in the soomthing region.
!
! s
! ht
!
! zin 3-d array to be smoothed.
!
! OUTPUT:
!
! zout 3-D smoothed array
!
! WORK ARRAY:
!
! zwork Temporary work array
!
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
INTEGER :: nx,ny,nz
INTEGER :: ibgn,iend
INTEGER :: jbgn,jend
INTEGER :: kbgn,kend
REAL :: s
REAL :: ht(nx,ny,nz)
REAL :: zin(nx,ny,nz),zwork(nx,ny,nz),zout(nx,ny,nz)
!
! Misc internal variables
!
INTEGER :: i,j,k
REAL :: wcen,wsid,whigh
!
! write (6,'(a/a,7x,a,12x,a,12x,a,12x,a,12x,a)')
! :'zin(i,j,k), k=5', ' j\\i', '39', '40', '41', '42', '43'
! write (6,'(i3,5e14.6)') (j,(zin(i,j,5),i=nx-4,nx),j=ny-4,ny)
wcen=1.-s
wsid=s*0.5
!
!-----------------------------------------------------------------------
!
! I direction 3pt smoothing
!
!-----------------------------------------------------------------------
!
DO k=kbgn, kend
DO j=jbgn, jend
DO i=ibgn+1, iend-1
zwork(i,j,k)=zin(i ,j,k)*wcen + &
zin(i+1,j,k)*wsid + &
zin(i-1,j,k)*wsid
END DO
END DO
DO j=jbgn,jend
zwork(ibgn,j,k)=zin(ibgn,j,k)
zwork(iend,j,k)=zin(iend,j,k)
END DO
!
!-----------------------------------------------------------------------
!
! J direction 3 point smoothing.
!
!-----------------------------------------------------------------------
!
DO j=jbgn+1, jend-1
DO i=ibgn, iend
zout(i,j,k)=zwork(i ,j,k)*wcen + &
zwork(i,j+1,k)*wsid + &
zwork(i,j-1,k)*wsid
END DO
END DO
DO i=ibgn, iend
zout(i,jbgn,k)=zwork(i,jbgn,k)
zout(i,jend,k)=zwork(i,jend,k)
END DO
END DO
!
! Transfer output back to work array.
!
DO k=kbgn,kend
DO j=jbgn,jend
DO i=ibgn,iend
zwork(i,j,k)=zout(i,j,k)
END DO
END DO
END DO
!
!-----------------------------------------------------------------------
!
! Smooth in vertical
!
!-----------------------------------------------------------------------
!
DO j=jbgn,jend
DO i=ibgn,iend
DO k=kbgn+1,kend-1
whigh=(ht(i,j, k)-ht(i,j,k-1))/ &
(ht(i,j,k+1)-ht(i,j,k-1))
zout(i,j,k)=zwork(i,j,k)*wcen + &
s*( whigh*zwork(i,j,k+1) + &
(1.-whigh)*zwork(i,j,k-1) )
END DO
zout(i,j,kbgn)=zwork(i,j,kbgn)
zout(i,j,kend)=zwork(i,j,kend)
END DO
END DO
!
! write (6,'(a/a,7x,a,12x,a,12x,a,12x,a,12x,a)')
! :'zout(i,j,k), k=5', ' j\\i', '39', '40', '41', '42', '43'
! write (6,'(i3,5e14.6)') (j,(zout(i,j,5),i=nx-4,nx),j=ny-4,ny)
!
RETURN
END SUBROUTINE smooth3d