sltint.f90

CCSM Research Tools: Community Atmosphere Model (CAM)

#include <misc.h>
#include <params.h>
subroutine sltint(kdim    ,ikcnst  ,jcen    ,fb      ,lam     , &
                  rdphi   ,rdz     ,lbasdy  ,wdz     ,xl      , &
                  xr      ,wgt1x   ,wgt2x   ,wgt3x   ,wgt4x   , &
                  hl      ,hr      ,dhl     ,dhr     ,ys      , &
                  yn      ,wgt1y   ,wgt2y   ,wgt3y   ,wgt4y   , &
                  hs      ,hn      ,dhs     ,dhn     ,wgt1z   , &
                  wgt2z   ,wgt3z   ,wgt4z   ,hb      ,ht      , &
                  dhb     ,dht     ,idp     ,jdp     ,kdp     , &
                  kkdp    ,lhrzint ,lvrtint ,limdrh  ,limdrv  , &
                  fdp     ,nlon    )
!
!-----------------------------------------------------------------------
!
! Purpose:
! Interpolate field to departure points using Hermite or Lagrange
! Cubic interpolation
!
! Author:  J. Olson
!
!-----------------------------------------------------------------------
!
! $Id: sltint.F90,v 1.3 2000/06/14 19:32:12 erik Exp $
! $Author: erik $
!
!-----------------------------------------------------------------------

  use precision
  use pmgrid
#if (!defined CRAY)
  use srchutil, only: wheneq
#endif
  implicit none

!----------------------------- Parameters ------------------------------
!
  integer, parameter :: ppdy = 4 ! length of interpolation grid stencil
  integer, parameter :: ppdz = 4 ! length of interp. grid stencil in z
!
!------------------------------Arguments--------------------------------
!
  integer , intent(in)   :: kdim                ! vertical dimension
  integer , intent(in)   :: ikcnst              ! constituent index
  integer , intent(in)   :: jcen                ! index of latitude in extended grid

  real(r8), intent(in)   :: fb(plond,kdim*ikcnst,beglatex:endlatex) ! input field
  real(r8), intent(in)   :: lam   (plond,platd) ! longitude coordinates of model grid
  real(r8), intent(in)   :: rdphi (plon,plev)   ! reciprocal of y-interval
  real(r8), intent(in)   :: rdz   (plon,plev)   ! reciprocal of z-interval
  real(r8), intent(in)   :: lbasdy(4,2,platd)   ! basis functions for lat deriv est.
  real(r8), intent(in)   :: wdz   (4,2,kdim)    ! basis functions for vert deriv est.
  real(r8), intent(in)   :: xl    (plon,plev,4) ! weight for x-interpolants (left)
  real(r8), intent(in)   :: xr    (plon,plev,4) ! weight for x-interpolants (right)
  real(r8), intent(in)   :: wgt1x (plon,plev,4) ! weight for x-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt2x (plon,plev,4) ! weight for x-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt3x (plon,plev,4) ! weight for x-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt4x (plon,plev,4) ! weight for x-interpolants (Lag Cubic)
  real(r8), intent(in)   :: hl    (plon,plev,4) ! weight for x-interpolants (Hermite)
  real(r8), intent(in)   :: hr    (plon,plev,4) ! weight for x-interpolants (Hermite)
  real(r8), intent(in)   :: dhl   (plon,plev,4) ! weight for x-interpolants (Hermite)
  real(r8), intent(in)   :: dhr   (plon,plev,4) ! weight for x-interpolants (Hermite)

  real(r8), intent(in)   :: ys    (plon,plev)   ! weight for y-interpolants (south)
  real(r8), intent(in)   :: yn    (plon,plev)   ! weight for y-interpolants (north)
  real(r8), intent(in)   :: wgt1y (plon,plev)   ! weight for y-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt2y (plon,plev)   ! weight for y-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt3y (plon,plev)   ! weight for y-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt4y (plon,plev)   ! weight for y-interpolants (Lag Cubic)
  real(r8), intent(in)   :: hs    (plon,plev)   ! weight for y-interpolants (Hermite)
  real(r8), intent(in)   :: hn    (plon,plev)   ! weight for y-interpolants (Hermite)
  real(r8), intent(in)   :: dhs   (plon,plev)   ! weight for y-interpolants (Hermite)
  real(r8), intent(in)   :: dhn   (plon,plev)   ! weight for y-interpolants (Hermite)

  real(r8), intent(in)   :: wgt1z (plon,plev)   ! weight for z-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt2z (plon,plev)   ! weight for z-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt3z (plon,plev)   ! weight for z-interpolants (Lag Cubic)
  real(r8), intent(in)   :: wgt4z (plon,plev)   ! weight for z-interpolants (Lag Cubic)
  real(r8), intent(in)   :: hb    (plon,plev)   ! weight for z-interpolants (Hermite)
  real(r8), intent(in)   :: ht    (plon,plev)   ! weight for z-interpolants (Hermite)
  real(r8), intent(in)   :: dhb   (plon,plev)   ! weight for z-interpolants (Hermite)
  real(r8), intent(in)   :: dht   (plon,plev)   ! weight for z-interpolants (Hermite)

  integer , intent(in)   :: idp   (plon,plev,4) ! index of x-coordinate of dep pt
  integer , intent(in)   :: jdp   (plon,plev)   ! index of y-coordinate of dep pt
  integer , intent(in)   :: kdp   (plon,plev)   ! index of z-coordinate of dep pt
  integer , intent(in)   :: kkdp  (plon,plev)   ! index of z-coordinate of dep pt (alt)

  logical , intent(in)   :: lhrzint             ! flag to do horizontal interpolation
  logical , intent(in)   :: lvrtint             ! flag to do vertical   interpolation
  logical , intent(in)   :: limdrh              ! horizontal derivative limiter flag
  logical , intent(in)   :: limdrv              ! vertical   derivative limiter flag
  real(r8), intent(out)  :: fdp(plon,plev)      ! interpolant
  integer , intent(in)   :: nlon                ! number of longitudes for this latitude
!
!---------------------------Local workspace-----------------------------
!
  integer i                           ! |
  integer ii1,ii2,ii3,ii4             ! |
  integer ii,jj,j                     ! |
  integer k                           ! |
  integer kk                          ! |
  integer jmin                        ! |
  integer jmax                        ! | -- indices
  integer jdpval                      ! |
  integer kdpval                      ! |
  integer icount                      ! |
  integer indx(plon)                  ! |
  integer nval                        ! |
  integer kdimm1                      ! |
  integer kdimm2                      ! |
  integer kdimm3                      ! |
!
  real(r8) fac                        ! factor applied in limiter
  real(r8) tmp1                       ! derivative factor
  real(r8) tmp2                       ! abs(tmp1)
  real(r8) deli                       ! linear derivative
  real(r8) dx                         ! delta x
  real(r8) rdx (platd)                ! 1./dx
  real(r8) rdx6(platd)                ! 1./(6*dx)
  real(r8) fxl                        ! left  derivative estimate
  real(r8) fxr                        ! right derivative estimate
!
  real(r8) f1                         ! |
  real(r8) f2                         ! |
  real(r8) f3                         ! |
  real(r8) f4                         ! |
  real(r8) tmptop                     ! | -- work arrays
  real(r8) tmpbot                     ! |
  real(r8) fintx(plon,plev,ppdy,ppdz) ! |
  real(r8) finty(plon,plev     ,ppdz) ! |
  real(r8) fbot (plon,plev,ppdz)      ! |
  real(r8) ftop (plon,plev,ppdz)      ! |
!
!-----------------------------------------------------------------------
!
  fac  = 3.*(1. - 10.*epsilon(fac))
  kdimm1 = kdim - 1
  kdimm2 = kdim - 2
  kdimm3 = kdim - 3
!
  do j = 1,platd
     dx      = lam(nxpt+2,j) - lam(nxpt+1,j)
     rdx (j) = 1./dx
     rdx6(j) = 1./(6.*dx)
  end do
!
!-----------------------------------------------------------------------
!------------------------- Code Description ----------------------------
!
! Each block of code performs a specific interpolation as follows:
!
!  For 3-D (horizontal AND vertical) interpolation:
!
!    10XX loops: Hermite  cubic/linear interpolation in the horizontal
!    20XX loops: Lagrange cubic/linear interpolation in the horizontal
!    30XX loops: Hermite  cubic/linear interpolation in the vertical
!    40XX loops: Lagrange cubic/linear interpolation in the vertical
!
!  For horizontal interpolation only:
!
!    50XX loops: an optimized Lagrange cubic/linear algorithm
!    60XX loops: Hermite cubic/linear interpolation in the horizontal
!
!  For vertical interpolation only:
!
!    70XX loops: an optimized Lagrange cubic/linear algorithm (no
!                Hermite interpolator available)
!
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!
  if( lhrzint .and. lvrtint ) then
!
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!
!    10XX loops: Hermite  cubic/linear interpolation in the horizontal
!
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!
     if( limdrh ) then
!
! PART 1:  x-interpolation
!
! Loop over fields.
! ..x interpolation at each height needed for z interpolation.
! ...x interpolation at each latitude needed for y interpolation.
!
        do k=1,plev
           do i=1,nlon
              ii1 = idp(i,k,1)
              ii2 = idp(i,k,2)
              ii3 = idp(i,k,3)
              ii4 = idp(i,k,4)
              jj = jdp(i,k)
              kk = kkdp(i,k)
!
! Height level 1:  Linear interpolation on inner two latitudes only
!
!!!           fintx(i,k,1,1) = not used
              fintx(i,k,2,1) = fb (ii2  ,kk-1,jj  )*xl (i,k,2) &
                             + fb (ii2+1,kk-1,jj  )*xr (i,k,2)
              fintx(i,k,3,1) = fb (ii3  ,kk-1,jj+1)*xl (i,k,3) &
                             + fb (ii3+1,kk-1,jj+1)*xr (i,k,3)
!!!           fintx(i,k,4,1) = not used
!
! Height level 2
!
!   Latitude 1:  Linear interpolation
!
              fintx(i,k,1,2) = fb (ii1  ,kk,jj-1)*xl (i,k,1) &
                             + fb (ii1+1,kk,jj-1)*xr (i,k,1)
!
!   Latitude 2:  Cubic interpolation
!
              fxl = (   - 2.*fb (ii2-1,kk,jj) &
                        - 3.*fb (ii2  ,kk,jj) &
                        + 6.*fb (ii2+1,kk,jj) &
                        -    fb (ii2+2,kk,jj) )*rdx6(jj)
              fxr = (        fb (ii2-1,kk,jj) &
                        - 6.*fb (ii2  ,kk,jj) &
                        + 3.*fb (ii2+1,kk,jj) &
                        + 2.*fb (ii2+2,kk,jj) )*rdx6(jj)
!
              deli = (       fb (ii2+1,kk,jj) - &
                             fb (ii2  ,kk,jj) )*rdx(jj)
              tmp1 = fac*deli
              tmp2 = abs( tmp1 )
              if( deli*fxl   .le. 0.0  ) fxl = 0.
              if( deli*fxr   .le. 0.0  ) fxr = 0.
              if( abs( fxl ) .gt. tmp2 ) fxl = tmp1
              if( abs( fxr ) .gt. tmp2 ) fxr = tmp1
!
              fintx(i,k,2,2) = fb (ii2  ,kk,jj)*hl (i,k,2) &
                             + fb (ii2+1,kk,jj)*hr (i,k,2) &
                             + fxl*dhl(i,k,2) + fxr*dhr(i,k,2)
!
!   Latitude 3:  Cubic interpolation
!
              fxl = (   - 2.*fb (ii3-1,kk  ,jj+1) &
                        - 3.*fb (ii3  ,kk  ,jj+1) &
                        + 6.*fb (ii3+1,kk  ,jj+1) &
                        -    fb (ii3+2,kk  ,jj+1) )*rdx6(jj+1)
              fxr = (        fb (ii3-1,kk  ,jj+1) &
                        - 6.*fb (ii3  ,kk  ,jj+1) &
                        + 3.*fb (ii3+1,kk  ,jj+1) &
                        + 2.*fb (ii3+2,kk  ,jj+1) )*rdx6(jj+1)
!
              deli = (       fb (ii3+1,kk  ,jj+1) - &
                             fb (ii3  ,kk  ,jj+1) )*rdx(jj+1)
              tmp1 = fac*deli
              tmp2 = abs( tmp1 )
              if( deli*fxl   .le. 0.0  ) fxl = 0.
              if( deli*fxr   .le. 0.0  ) fxr = 0.
              if( abs( fxl ) .gt. tmp2 ) fxl = tmp1
              if( abs( fxr ) .gt. tmp2 ) fxr = tmp1
!
              fintx(i,k,3,2) = fb (ii3  ,kk  ,jj+1)*hl (i,k,3) &
                             + fb (ii3+1,kk  ,jj+1)*hr (i,k,3) &
                             + fxl*dhl(i,k,3) + fxr*dhr(i,k,3)
!
!   Latitude 4:  Linear interpolation
!
              fintx(i,k,4,2) = fb (ii4  ,kk,jj+2)*xl (i,k,4) &
                             + fb (ii4+1,kk,jj+2)*xr (i,k,4)
!
! Height level 3
!
!   Latitude 1:  Linear interpolation
!
              fintx(i,k,1,3) = fb (ii1  ,kk+1,jj-1)*xl (i,k,1) &
                             + fb (ii1+1,kk+1,jj-1)*xr (i,k,1)
!
!   Latitude 2:  Cubic interpolation
!
              fxl = (   - 2.*fb (ii2-1,kk+1,jj  ) &
                        - 3.*fb (ii2  ,kk+1,jj  ) &
                        + 6.*fb (ii2+1,kk+1,jj  ) &
                        -    fb (ii2+2,kk+1,jj  ) )*rdx6(jj)
              fxr = (        fb (ii2-1,kk+1,jj  ) &
                        - 6.*fb (ii2  ,kk+1,jj  ) &
                        + 3.*fb (ii2+1,kk+1,jj  ) &
                        + 2.*fb (ii2+2,kk+1,jj  ) )*rdx6(jj)
!
              deli = (       fb (ii2+1,kk+1,jj  ) - &
                             fb (ii2  ,kk+1,jj  ) )*rdx(jj)
              tmp1 = fac*deli
              tmp2 = abs( tmp1 )
              if( deli*fxl   .le. 0.0  ) fxl = 0.
              if( deli*fxr   .le. 0.0  ) fxr = 0.
              if( abs( fxl ) .gt. tmp2 ) fxl = tmp1
              if( abs( fxr ) .gt. tmp2 ) fxr = tmp1
!
              fintx(i,k,2,3) = fb (ii2  ,kk+1,jj  )*hl (i,k,2) &
                             + fb (ii2+1,kk+1,jj  )*hr (i,k,2) &
                             + fxl*dhl(i,k,2) + fxr*dhr(i,k,2)