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module_interpolate.F
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module_interpolate.F
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module module_interpolate
! Description:
! Routines for interpolation of data in latitude, longitude and time.
!
! Author: Gathered from a number of places and put into the current format by Jim Edwards
!
! Modules Used:
!
! use shr_kind_mod, only: r8 => shr_kind_r8
! use abortutils, only: endrun
! use scamMod, only: single_column
! use cam_logfile, only: iulog
implicit none
private
integer,parameter :: r8 = selected_real_kind(12) ! 8 byte real
! integer,parameter :: r8 = selected_real_kind(8) ! 8 byte real
!
! Public Methods:
!
public :: interp_type, lininterp, vertinterp, bilin, get_timeinterp_factors
public :: lininterp_init, lininterp_finish
type interp_type
real(r8), pointer :: wgts(:)
real(r8), pointer :: wgtn(:)
integer, pointer :: jjm(:)
integer, pointer :: jjp(:)
end type interp_type
interface lininterp
module procedure lininterp_original
module procedure lininterp_full1d
module procedure lininterp1d
module procedure lininterp2d2d
module procedure lininterp2d1d
module procedure lininterp3d2d
end interface
contains
subroutine lininterp_full1d (arrin, yin, nin, arrout, yout, nout)
integer, intent(in) :: nin, nout
real(r8), intent(in) :: arrin(nin), yin(nin), yout(nout)
real(r8), intent(out) :: arrout(nout)
type (interp_type) :: interp_wgts
call lininterp_init(yin, nin, yout, nout, 1, interp_wgts)
call lininterp1d(arrin, nin, arrout, nout, interp_wgts)
call lininterp_finish(interp_wgts)
end subroutine lininterp_full1d
subroutine lininterp_init(yin, nin, yout, nout, extrap_method, interp_wgts, &
cyclicmin, cyclicmax)
!
! Description:
! Initialize a variable of type(interp_type) with weights for linear interpolation.
! this variable can then be used in calls to lininterp1d and lininterp2d.
! yin is a 1d array of length nin of locations to interpolate from - this array must
! be monotonic but can be increasing or decreasing
! yout is a 1d array of length nout of locations to interpolate to, this array need
! not be ordered
! extrap_method determines how to handle yout points beyond the bounds of yin
! if 0 set values outside output grid to 0
! if 1 set to boundary value
! if 2 set to cyclic boundaries
! optional values cyclicmin and cyclicmax can be used to set the bounds of the
! cyclic mapping - these default to 0 and 360.
!
integer, intent(in) :: nin
integer, intent(in) :: nout
real(r8), intent(in) :: yin(:) ! input mesh
real(r8), intent(in) :: yout(:) ! output mesh
integer, intent(in) :: extrap_method ! if 0 set values outside output grid to 0
! if 1 set to boundary value
! if 2 set to cyclic boundaries
real(r8), intent(in), optional :: cyclicmin, cyclicmax
type (interp_type), intent(out) :: interp_wgts
real(r8) :: cmin, cmax
real(r8) :: extrap
real(r8) :: dyinwrap
real(r8) :: ratio
real(r8) :: avgdyin
integer :: i, j, icount
integer :: jj
real(r8), pointer :: wgts(:)
real(r8), pointer :: wgtn(:)
integer, pointer :: jjm(:)
integer, pointer :: jjp(:)
logical :: increasing
character(len=132) :: message
!
! Check validity of input coordinate arrays: must be monotonically increasing,
! and have a total of at least 2 elements
!
if (nin.lt.2) then
call wrf_abort !('LININTERP: Must have at least 2 input points for interpolation')
end if
if(present(cyclicmin)) then
cmin=cyclicmin
else
cmin=0_r8
end if
if(present(cyclicmax)) then
cmax=cyclicmax
else
cmax=360_r8
end if
if(cmax<=cmin) then
call wrf_abort !('LININTERP: cyclic min value must be < max value')
end if
increasing=.true.
icount = 0
do j=1,nin-1
if (yin(j).gt.yin(j+1)) icount = icount + 1
end do
if(icount.eq.nin-1) then
increasing = .false.
icount=0
endif
if (icount.gt.0) then
call wrf_abort !('LININTERP: Non-monotonic input coordinate array found')
end if
allocate(interp_wgts%jjm(nout), &
interp_wgts%jjp(nout), &
interp_wgts%wgts(nout), &
interp_wgts%wgtn(nout))
jjm => interp_wgts%jjm
jjp => interp_wgts%jjp
wgts => interp_wgts%wgts
wgtn => interp_wgts%wgtn
!
! Initialize index arrays for later checking
!
jjm = 0
jjp = 0
extrap = 0.
if(extrap_method.eq.0) then
!
! For values which extend beyond boundaries, set weights
! such that values will be 0.
!
do j=1,nout
if(increasing) then
if (yout(j).lt.yin(1)) then
jjm(j) = 1
jjp(j) = 1
wgts(j) = 0.
wgtn(j) = 0.
extrap = extrap + 1.
else if (yout(j).gt.yin(nin)) then
jjm(j) = nin
jjp(j) = nin
wgts(j) = 0.
wgtn(j) = 0.
extrap = extrap + 1.
end if
else
if (yout(j).gt.yin(1)) then
jjm(j) = 1
jjp(j) = 1
wgts(j) = 0.
wgtn(j) = 0.
extrap = extrap + 1.
else if (yout(j).lt.yin(nin)) then
jjm(j) = nin
jjp(j) = nin
wgts(j) = 0.
wgtn(j) = 0.
extrap = extrap + 1.
end if
end if
end do
else if(extrap_method.eq.1) then
!
! For values which extend beyond boundaries, set weights
! such that values will just be copied.
!
do j=1,nout
if(increasing) then
if (yout(j).le.yin(1)) then
jjm(j) = 1
jjp(j) = 1
wgts(j) = 1.
wgtn(j) = 0.
extrap = extrap + 1.
else if (yout(j).gt.yin(nin)) then
jjm(j) = nin
jjp(j) = nin
wgts(j) = 1.
wgtn(j) = 0.
extrap = extrap + 1.
end if
else
if (yout(j).gt.yin(1)) then
jjm(j) = 1
jjp(j) = 1
wgts(j) = 1.
wgtn(j) = 0.
extrap = extrap + 1.
else if (yout(j).le.yin(nin)) then
jjm(j) = nin
jjp(j) = nin
wgts(j) = 1.
wgtn(j) = 0.
extrap = extrap + 1.
end if
end if
end do
else if(extrap_method.eq.2) then
!
! For values which extend beyond boundaries, set weights
! for circular boundaries
!
dyinwrap = yin(1) + (cmax-cmin) - yin(nin)
avgdyin = abs(yin(nin)-yin(1))/(nin-1.)
ratio = dyinwrap/avgdyin
if (ratio < 0.9 .or. ratio > 1.1) then
write(message,*) 'Lininterp: Bad dyinwrap value =',dyinwrap,&
' avg=', avgdyin, yin(1),yin(nin)
call wrf_message( trim(message) )
call wrf_abort !('interpolate_data')
end if
do j=1,nout
if(increasing) then
if (yout(j) <= yin(1)) then
jjm(j) = nin
jjp(j) = 1
wgts(j) = (yin(1)-yout(j))/dyinwrap
wgtn(j) = (yout(j)+(cmax-cmin) - yin(nin))/dyinwrap
else if (yout(j) > yin(nin)) then
jjm(j) = nin
jjp(j) = 1
wgts(j) = (yin(1)+(cmax-cmin)-yout(j))/dyinwrap
wgtn(j) = (yout(j)-yin(nin))/dyinwrap
end if
else
if (yout(j) > yin(1)) then
jjm(j) = nin
jjp(j) = 1
wgts(j) = (yin(1)-yout(j))/dyinwrap
wgtn(j) = (yout(j)+(cmax-cmin) - yin(nin))/dyinwrap
else if (yout(j) <= yin(nin)) then
jjm(j) = nin
jjp(j) = 1
wgts(j) = (yin(1)+(cmax-cmin)-yout(j))/dyinwrap
wgtn(j) = (yout(j)+(cmax-cmin)-yin(nin))/dyinwrap
end if
endif
end do
end if
!
! Loop though output indices finding input indices and weights
!
if(increasing) then
do j=1,nout
do jj=1,nin-1
if (yout(j).gt.yin(jj) .and. yout(j).le.yin(jj+1)) then
jjm(j) = jj
jjp(j) = jj + 1
wgts(j) = (yin(jj+1)-yout(j))/(yin(jj+1)-yin(jj))
wgtn(j) = (yout(j)-yin(jj))/(yin(jj+1)-yin(jj))
exit
end if
end do
end do
else
do j=1,nout
do jj=1,nin-1
if (yout(j).le.yin(jj) .and. yout(j).gt.yin(jj+1)) then
jjm(j) = jj
jjp(j) = jj + 1
wgts(j) = (yin(jj+1)-yout(j))/(yin(jj+1)-yin(jj))
wgtn(j) = (yout(j)-yin(jj))/(yin(jj+1)-yin(jj))
exit
end if
end do
end do
end if
#ifndef SPMD
!
! Check grid overlap
!
extrap = 100.*extrap/real(nout,r8)
if (extrap.gt.50. ) then
write(message,*) 'interpolate_data:','yout=',minval(yout),maxval(yout),increasing,nout
call wrf_message( trim(message) )
write(message,*) 'interpolate_data:','yin=',yin(1),yin(nin)
call wrf_message( trim(message) )
write(message,*) 'interpolate_data:',extrap,' % of output grid will have to be extrapolated'
call wrf_message( trim(message) )
call wrf_abort !('interpolate_data: ')
end if
#endif
!
! Check that interp/extrap points have been found for all outputs
!
icount = 0
do j=1,nout
if (jjm(j).eq.0 .or. jjp(j).eq.0) icount = icount + 1
ratio=wgts(j)+wgtn(j)
if((ratio<0.9.or.ratio>1.1).and.extrap_method.ne.0) then
write(message,*) j, wgts(j),wgtn(j),jjm(j),jjp(j), increasing,extrap_method
call wrf_message( trim(message) )
call wrf_abort !('Bad weight computed in LININTERP_init')
end if
end do
if (icount.gt.0) then
call wrf_abort !('LININTERP: Point found without interp indices')
end if
end subroutine lininterp_init
subroutine lininterp1d (arrin, n1, arrout, m1, interp_wgts)
!-----------------------------------------------------------------------
!
! Purpose: Do a linear interpolation from input mesh to output
! mesh with weights as set in lininterp_init.
!
!
! Author: Jim Edwards
!
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
implicit none
!-----------------------------------------------------------------------
!
! Arguments
!
integer, intent(in) :: n1 ! number of input latitudes
integer, intent(in) :: m1 ! number of output latitudes
real(r8), intent(in) :: arrin(n1) ! input array of values to interpolate
type(interp_type), intent(in) :: interp_wgts
real(r8), intent(out) :: arrout(m1) ! interpolated array
!
! Local workspace
!
integer j ! latitude indices
integer, pointer :: jjm(:)
integer, pointer :: jjp(:)
real(r8), pointer :: wgts(:)
real(r8), pointer :: wgtn(:)
jjm => interp_wgts%jjm
jjp => interp_wgts%jjp
wgts => interp_wgts%wgts
wgtn => interp_wgts%wgtn
!
! Do the interpolation
!
do j=1,m1
arrout(j) = arrin(jjm(j))*wgts(j) + arrin(jjp(j))*wgtn(j)
end do
return
end subroutine lininterp1d
subroutine lininterp2d2d(arrin, n1, n2, arrout, m1, m2, wgt1, wgt2)
implicit none
!-----------------------------------------------------------------------
!
! Arguments
!
integer, intent(in) :: n1, n2, m1, m2
real(r8), intent(in) :: arrin(n1,n2) ! input array of values to interpolate
type(interp_type), intent(in) :: wgt1, wgt2
real(r8), intent(out) :: arrout(m1,m2) ! interpolated array
!
! locals
!
integer i,j ! indices
integer, pointer :: iim(:), jjm(:)
integer, pointer :: iip(:), jjp(:)
real(r8), pointer :: wgts1(:), wgts2(:)
real(r8), pointer :: wgtn1(:), wgtn2(:)
real(r8) :: arrtmp(n1,m2)
jjm => wgt2%jjm
jjp => wgt2%jjp
wgts2 => wgt2%wgts
wgtn2 => wgt2%wgtn
iim => wgt1%jjm
iip => wgt1%jjp
wgts1 => wgt1%wgts
wgtn1 => wgt1%wgtn
do j=1,m2
do i=1,n1
arrtmp(i,j) = arrin(i,jjm(j))*wgts2(j) + arrin(i,jjp(j))*wgtn2(j)
end do
end do
do j=1,m2
do i=1,m1
arrout(i,j) = arrtmp(iim(i),j)*wgts1(i) + arrtmp(iip(i),j)*wgtn1(i)
end do
end do
end subroutine lininterp2d2d
subroutine lininterp2d1d(arrin, n1, n2, arrout, m1, wgt1, wgt2, fldname)
implicit none
!-----------------------------------------------------------------------
!
! Arguments
!
integer, intent(in) :: n1, n2, m1
real(r8), intent(in) :: arrin(n1,n2) ! input array of values to interpolate
type(interp_type), intent(in) :: wgt1, wgt2
real(r8), intent(out) :: arrout(m1) ! interpolated array
character(len=*), intent(in), optional :: fldname(:)
!
! locals
!
integer i ! indices
integer, pointer :: iim(:), jjm(:)
integer, pointer :: iip(:), jjp(:)
real(r8), pointer :: wgts(:), wgte(:)
real(r8), pointer :: wgtn(:), wgtw(:)
jjm => wgt2%jjm
jjp => wgt2%jjp
wgts => wgt2%wgts
wgtn => wgt2%wgtn
iim => wgt1%jjm
iip => wgt1%jjp
wgtw => wgt1%wgts
wgte => wgt1%wgtn
do i=1,m1
arrout(i) = arrin(iim(i),jjm(i))*wgtw(i)*wgts(i)+arrin(iip(i),jjm(i))*wgte(i)*wgts(i) + &
arrin(iim(i),jjp(i))*wgtw(i)*wgtn(i)+arrin(iip(i),jjp(i))*wgte(i)*wgtn(i)
end do
end subroutine lininterp2d1d
subroutine lininterp3d2d(arrin, n1, n2, n3, arrout, m1, len1, wgt1, wgt2)
implicit none
!-----------------------------------------------------------------------
!
! Arguments
!
integer, intent(in) :: n1, n2, n3, m1, len1 ! m1 is to len1 as ncols is to pcols
real(r8), intent(in) :: arrin(n1,n2,n3) ! input array of values to interpolate
type(interp_type), intent(in) :: wgt1, wgt2
real(r8), intent(out) :: arrout(len1, n3) ! interpolated array
!
! locals
!
integer i, k ! indices
integer, pointer :: iim(:), jjm(:)
integer, pointer :: iip(:), jjp(:)
real(r8), pointer :: wgts(:), wgte(:)
real(r8), pointer :: wgtn(:), wgtw(:)
jjm => wgt2%jjm
jjp => wgt2%jjp
wgts => wgt2%wgts
wgtn => wgt2%wgtn
iim => wgt1%jjm
iip => wgt1%jjp
wgtw => wgt1%wgts
wgte => wgt1%wgtn
do k=1,n3
do i=1,m1
arrout(i,k) = arrin(iim(i),jjm(i),k)*wgtw(i)*wgts(i)+arrin(iip(i),jjm(i),k)*wgte(i)*wgts(i) + &
arrin(iim(i),jjp(i),k)*wgtw(i)*wgtn(i)+arrin(iip(i),jjp(i),k)*wgte(i)*wgtn(i)
end do
end do
end subroutine lininterp3d2d
subroutine lininterp_finish(interp_wgts)
type(interp_type) :: interp_wgts
deallocate(interp_wgts%jjm, &
interp_wgts%jjp, &
interp_wgts%wgts, &
interp_wgts%wgtn)
nullify(interp_wgts%jjm, &
interp_wgts%jjp, &
interp_wgts%wgts, &
interp_wgts%wgtn)
end subroutine lininterp_finish
subroutine lininterp_original (arrin, yin, nlev, nlatin, arrout, &
yout, nlatout)
!-----------------------------------------------------------------------
!
! Purpose: Do a linear interpolation from input mesh defined by yin to output
! mesh defined by yout. Where extrapolation is necessary, values will
! be copied from the extreme edge of the input grid. Vectorization is over
! the vertical (nlev) dimension.
!
! Method: Check validity of input, then determine weights, then do the N-S interpolation.
!
! Author: Jim Rosinski
! Modified: Jim Edwards so that there is no requirement of monotonacity on the yout array
!
!-----------------------------------------------------------------------
implicit none
!-----------------------------------------------------------------------
!
! Arguments
!
integer, intent(in) :: nlev ! number of vertical levels
integer, intent(in) :: nlatin ! number of input latitudes
integer, intent(in) :: nlatout ! number of output latitudes
real(r8), intent(in) :: arrin(nlev,nlatin) ! input array of values to interpolate
real(r8), intent(in) :: yin(nlatin) ! input mesh
real(r8), intent(in) :: yout(nlatout) ! output mesh
real(r8), intent(out) :: arrout(nlev,nlatout) ! interpolated array
!
! Local workspace
!
integer j, jj ! latitude indices
integer jjprev ! latitude indices
integer k ! level index
integer icount ! number of values
real(r8) extrap ! percent grid non-overlap
!
! Dynamic
!
integer :: jjm(nlatout)
integer :: jjp(nlatout)
real(r8) :: wgts(nlatout)
real(r8) :: wgtn(nlatout)
!
! Check validity of input coordinate arrays: must be monotonically increasing,
! and have a total of at least 2 elements
!
if (nlatin.lt.2) then
call wrf_abort !('LININTERP: Must have at least 2 input points for interpolation')
end if
icount = 0
do j=1,nlatin-1
if (yin(j).gt.yin(j+1)) icount = icount + 1
end do
if (icount.gt.0) then
call wrf_abort !('LININTERP: Non-monotonic coordinate array(s) found')
end if
!
! Initialize index arrays for later checking
!
do j=1,nlatout
jjm(j) = 0
jjp(j) = 0
end do
!
! For values which extend beyond N and S boundaries, set weights
! such that values will just be copied.
!
extrap = 0.
do j=1,nlatout
if (yout(j).le.yin(1)) then
jjm(j) = 1
jjp(j) = 1
wgts(j) = 1.
wgtn(j) = 0.
extrap=extrap+1.
else if (yout(j).gt.yin(nlatin)) then
jjm(j) = nlatin
jjp(j) = nlatin
wgts(j) = 1.
wgtn(j) = 0.
extrap=extrap+1.
endif
end do
!
! Loop though output indices finding input indices and weights
!
do j=1,nlatout
do jj=1,nlatin-1
if (yout(j).gt.yin(jj) .and. yout(j).le.yin(jj+1)) then
jjm(j) = jj
jjp(j) = jj + 1
wgts(j) = (yin(jj+1)-yout(j))/(yin(jj+1)-yin(jj))
wgtn(j) = (yout(j)-yin(jj))/(yin(jj+1)-yin(jj))
exit
end if
end do
end do
!
! Check that interp/extrap points have been found for all outputs
!
icount = 0
do j=1,nlatout
if (jjm(j).eq.0 .or. jjp(j).eq.0) then
icount = icount + 1
end if
end do
if (icount.gt.0) then
call wrf_abort !('LININTERP: Point found without interp indices')
end if
!
! Do the interpolation
!
do j=1,nlatout
do k=1,nlev
arrout(k,j) = arrin(k,jjm(j))*wgts(j) + arrin(k,jjp(j))*wgtn(j)
end do
end do
return
end subroutine lininterp_original
subroutine bilin (arrin, xin, yin, nlondin, nlonin, &
nlevdin, nlev, nlatin, arrout, xout, &
yout, nlondout, nlonout, nlevdout, nlatout)
!-----------------------------------------------------------------------
!
! Purpose:
!
! Do a bilinear interpolation from input mesh defined by xin, yin to output
! mesh defined by xout, yout. Circularity is assumed in the x-direction so
! input x-grid must be in degrees east and must start from Greenwich. When
! extrapolation is necessary in the N-S direction, values will be copied
! from the extreme edge of the input grid. Vectorization is over the
! longitude dimension. Input grid is assumed rectangular. Output grid
! is assumed ragged, i.e. xout is a 2-d mesh.
!
! Method: Interpolate first in longitude, then in latitude.
!
! Author: Jim Rosinski
!
!-----------------------------------------------------------------------
! use shr_kind_mod, only: r8 => shr_kind_r8
! use abortutils, only: endrun
!-----------------------------------------------------------------------
implicit none
!-----------------------------------------------------------------------
integer,parameter :: r8 = selected_real_kind(12) ! 8 byte real
!
! Input arguments
!
integer, intent(in) :: nlondin ! longitude dimension of input grid
integer, intent(in) :: nlonin ! number of real longitudes (input)
integer, intent(in) :: nlevdin ! vertical dimension of input grid
integer, intent(in) :: nlev ! number of vertical levels
integer, intent(in) :: nlatin ! number of input latitudes
integer, intent(in) :: nlatout ! number of output latitudes
integer, intent(in) :: nlondout ! longitude dimension of output grid
integer, intent(in) :: nlonout(nlatout) ! number of output longitudes per lat
integer, intent(in) :: nlevdout ! vertical dimension of output grid
real(r8), intent(in) :: arrin(nlondin,nlevdin,nlatin) ! input array of values to interpolate
real(r8), intent(in) :: xin(nlondin) ! input x mesh
real(r8), intent(in) :: yin(nlatin) ! input y mesh
real(r8), intent(in) :: xout(nlondout,nlatout) ! output x mesh
real(r8), intent(in) :: yout(nlatout) ! output y mesh
!
! Output arguments
!
real(r8), intent(out) :: arrout(nlondout,nlevdout,nlatout) ! interpolated array
!
! Local workspace
!
integer :: i, ii, iw, ie, iiprev ! longitude indices
integer :: j, jj, js, jn, jjprev ! latitude indices
integer :: k ! level index
integer :: icount ! number of bad values
real(r8) :: extrap ! percent grid non-overlap
real(r8) :: dxinwrap ! delta-x on input grid for 2-pi
real(r8) :: avgdxin ! avg input delta-x
real(r8) :: ratio ! compare dxinwrap to avgdxin
real(r8) :: sum ! sum of weights (used for testing)
!
! Dynamic
!
integer :: iim(nlondout) ! interpolation index to the left
integer :: iip(nlondout) ! interpolation index to the right
integer :: jjm(nlatout) ! interpolation index to the south
integer :: jjp(nlatout) ! interpolation index to the north
real(r8) :: wgts(nlatout) ! interpolation weight to the north
real(r8) :: wgtn(nlatout) ! interpolation weight to the north
real(r8) :: wgte(nlondout) ! interpolation weight to the north
real(r8) :: wgtw(nlondout) ! interpolation weight to the north
real(r8) :: igrid(nlonin) ! interpolation weight to the north
character(len=132) :: message
!
! Check validity of input coordinate arrays: must be monotonically increasing,
! and have a total of at least 2 elements
!
if (nlonin < 2 .or. nlatin < 2) then
call wrf_abort ! ('BILIN: Must have at least 2 input points for interpolation')
end if
if (xin(1) < 0._r8 .or. xin(nlonin) > 360._r8) then
call wrf_abort ! ('BILIN: Input x-grid must be between 0 and 360')
end if
icount = 0
do i=1,nlonin-1
if (xin(i) >= xin(i+1)) icount = icount + 1
end do
do j=1,nlatin-1
if (yin(j) >= yin(j+1)) icount = icount + 1
end do
do j=1,nlatout-1
if (yout(j) >= yout(j+1)) icount = icount + 1
end do
do j=1,nlatout
do i=1,nlonout(j)-1
if (xout(i,j) >= xout(i+1,j)) icount = icount + 1
end do
end do
if (icount > 0) then
call wrf_abort ! ('BILIN: Non-monotonic coordinate array(s) found')
end if
if (yout(nlatout) <= yin(1) .or. yout(1) >= yin(nlatin)) then
call wrf_abort ! ('BILIN: No overlap in y-coordinates')
end if
do j=1,nlatout
if (xout(1,j) < 0._r8 .or. xout(nlonout(j),j) > 360._r8) then
call wrf_abort ! ('BILIN: Output x-grid must be between 0 and 360')
end if
if (xout(nlonout(j),j) <= xin(1) .or. &
xout(1,j) >= xin(nlonin)) then
call wrf_abort ! ('BILIN: No overlap in x-coordinates')
end if
end do
!
! Initialize index arrays for later checking
!
do j=1,nlatout
jjm(j) = 0
jjp(j) = 0
end do
!
! For values which extend beyond N and S boundaries, set weights
! such that values will just be copied.
!
do js=1,nlatout
if (yout(js) > yin(1)) exit
jjm(js) = 1
jjp(js) = 1
wgts(js) = 1._r8
wgtn(js) = 0._r8
end do
do jn=nlatout,1,-1
if (yout(jn) <= yin(nlatin)) exit
jjm(jn) = nlatin
jjp(jn) = nlatin
wgts(jn) = 1._r8
wgtn(jn) = 0._r8
end do
!
! Loop though output indices finding input indices and weights
!
jjprev = 1
do j=js,jn
do jj=jjprev,nlatin-1
if (yout(j) > yin(jj) .and. yout(j) <= yin(jj+1)) then
jjm(j) = jj
jjp(j) = jj + 1
wgts(j) = (yin(jj+1) - yout(j)) / (yin(jj+1) - yin(jj))
wgtn(j) = (yout(j) - yin(jj)) / (yin(jj+1) - yin(jj))
goto 30
end if
end do
call wrf_abort ! ('BILIN: Failed to find interp values')
30 jjprev = jj
end do
dxinwrap = xin(1) + 360._r8 - xin(nlonin)
!
! Check for sane dxinwrap values. Allow to differ no more than 10% from avg
!
avgdxin = (xin(nlonin)-xin(1))/(nlonin-1._r8)
ratio = dxinwrap/avgdxin
if (ratio < 0.9_r8 .or. ratio > 1.1_r8) then
write(message,*)'BILIN: Insane dxinwrap value =',dxinwrap,' avg=', avgdxin
call wrf_message( trim(message) )
call wrf_abort !
end if
!
! Check grid overlap
! Do not do on spmd since distributed output grid may be expected to fail this test
#ifndef SPMD
extrap = 100._r8*((js - 1._r8) + real(nlatout - jn,r8))/nlatout
if (extrap > 20._r8) then
write(message,*)'BILIN:',extrap,' % of N/S output grid will have to be extrapolated'
call wrf_message( trim(message) )
end if
#endif
!
! Check that interp/extrap points have been found for all outputs, and that
! they are reasonable (i.e. within 32-bit roundoff)
!
icount = 0
do j=1,nlatout
if (jjm(j) == 0 .or. jjp(j) == 0) icount = icount + 1
sum = wgts(j) + wgtn(j)
if (sum < 0.99999_r8 .or. sum > 1.00001_r8) icount = icount + 1
if (wgts(j) < 0._r8 .or. wgts(j) > 1._r8) icount = icount + 1
if (wgtn(j) < 0._r8 .or. wgtn(j) > 1._r8) icount = icount + 1
end do
if (icount > 0) then
call wrf_abort ! ('BILIN: something bad in latitude indices or weights')
end if
!
! Do the bilinear interpolation
!
do j=1,nlatout
!
! Initialize index arrays for later checking
!
do i=1,nlondout
iim(i) = 0
iip(i) = 0
end do
!
! For values which extend beyond E and W boundaries, set weights such that
! values will be interpolated between E and W edges of input grid.
!
do iw=1,nlonout(j)
if (xout(iw,j) > xin(1)) exit
iim(iw) = nlonin
iip(iw) = 1
wgtw(iw) = (xin(1) - xout(iw,j)) /dxinwrap
wgte(iw) = (xout(iw,j)+360._r8 - xin(nlonin))/dxinwrap
end do
do ie=nlonout(j),1,-1
if (xout(ie,j) <= xin(nlonin)) exit
iim(ie) = nlonin
iip(ie) = 1
wgtw(ie) = (xin(1)+360._r8 - xout(ie,j)) /dxinwrap
wgte(ie) = (xout(ie,j) - xin(nlonin))/dxinwrap
end do
!
! Loop though output indices finding input indices and weights
!
iiprev = 1
do i=iw,ie
do ii=iiprev,nlonin-1
if (xout(i,j) > xin(ii) .and. xout(i,j) <= xin(ii+1)) then
iim(i) = ii
iip(i) = ii + 1
wgtw(i) = (xin(ii+1) - xout(i,j)) / (xin(ii+1) - xin(ii))
wgte(i) = (xout(i,j) - xin(ii)) / (xin(ii+1) - xin(ii))
goto 60
end if
end do
call wrf_abort ! ('BILIN: Failed to find interp values')
60 iiprev = ii
end do
icount = 0
do i=1,nlonout(j)
if (iim(i) == 0 .or. iip(i) == 0) icount = icount + 1
sum = wgtw(i) + wgte(i)
if (sum < 0.99999_r8 .or. sum > 1.00001_r8) icount = icount + 1
if (wgtw(i) < 0._r8 .or. wgtw(i) > 1._r8) icount = icount + 1
if (wgte(i) < 0._r8 .or. wgte(i) > 1._r8) icount = icount + 1
end do
if (icount > 0) then
write(message,*)'BILIN: j=',j,' Something bad in longitude indices or weights'
call wrf_message( trim(message) )
call wrf_abort !
end if
!
! Do the interpolation, 1st in longitude then latitude
!
do k=1,nlev
do i=1,nlonin
igrid(i) = arrin(i,k,jjm(j))*wgts(j) + arrin(i,k,jjp(j))*wgtn(j)
end do
do i=1,nlonout(j)
arrout(i,k,j) = igrid(iim(i))*wgtw(i) + igrid(iip(i))*wgte(i)
end do
end do
end do
return
end subroutine bilin
subroutine vertinterp(ncol, ncold, nlev, pmid, pout, arrin, arrout)
!-----------------------------------------------------------------------
!
! Purpose:
! Vertically interpolate input array to output pressure level
! Copy values at boundaries.
!
! Method:
!
! Author:
!
!-----------------------------------------------------------------------
implicit none
!------------------------------Arguments--------------------------------
integer , intent(in) :: ncol ! column dimension
integer , intent(in) :: ncold ! declared column dimension
integer , intent(in) :: nlev ! vertical dimension
real(r8), intent(in) :: pmid(ncold,nlev) ! input level pressure levels
real(r8), intent(in) :: pout ! output pressure level
real(r8), intent(in) :: arrin(ncold,nlev) ! input array
real(r8), intent(out) :: arrout(ncold) ! output array (interpolated)
!--------------------------------------------------------------------------
!---------------------------Local variables-----------------------------
integer i,k ! indices
integer kupper(ncold) ! Level indices for interpolation
real(r8) dpu ! upper level pressure difference
real(r8) dpl ! lower level pressure difference
logical found(ncold) ! true if input levels found
logical error ! error flag
!-----------------------------------------------------------------
!
! Initialize index array and logical flags
!
do i=1,ncol
found(i) = .false.
kupper(i) = 1
end do
error = .false.
!
! Store level indices for interpolation.
! If all indices for this level have been found,
! do the interpolation
!
do k=1,nlev-1
do i=1,ncol
if ((.not. found(i)) .and. pmid(i,k)<pout .and. pout<=pmid(i,k+1)) then
found(i) = .true.
kupper(i) = k
end if
end do
end do
!
! If we've fallen through the k=1,nlev-1 loop, we cannot interpolate and
! must extrapolate from the bottom or top data level for at least some
! of the longitude points.
!
do i=1,ncol
if (pout <= pmid(i,1)) then
arrout(i) = arrin(i,1)
else if (pout >= pmid(i,nlev)) then
arrout(i) = arrin(i,nlev)
else if (found(i)) then
dpu = pout - pmid(i,kupper(i))
dpl = pmid(i,kupper(i)+1) - pout