sltint.f90

CCSM Research Tools: Community Atmosphere Model (CAM)

!
!   Latitude 3:  Cubic interpolation
!
              fxl = (   - 2.*fb (ii3-1,kk+1,jj+1) &
                        - 3.*fb (ii3  ,kk+1,jj+1) &
                        + 6.*fb (ii3+1,kk+1,jj+1) &
                        -    fb (ii3+2,kk+1,jj+1) )*rdx6(jj+1)
              fxr = (        fb (ii3-1,kk+1,jj+1) &
                        - 6.*fb (ii3  ,kk+1,jj+1) &
                        + 3.*fb (ii3+1,kk+1,jj+1) &
                        + 2.*fb (ii3+2,kk+1,jj+1) )*rdx6(jj+1)
!
              deli = (       fb (ii3+1,kk+1,jj+1) - &
                             fb (ii3  ,kk+1,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,3,3) = fb (ii3  ,kk+1,jj+1)*hl (i,k,3) &
                             + fb (ii3+1,kk+1,jj+1)*hr (i,k,3) &
                             + fxl*dhl(i,k,3) + fxr*dhr(i,k,3)
!
!   Latitude 4:  Linear interpolation
!
              fintx(i,k,4,3) = fb (ii4  ,kk+1,jj+2)*xl (i,k,4) &
                             + fb (ii4+1,kk+1,jj+2)*xr (i,k,4)
!
! Height level 4:  Linear interpolation on inner two latitudes only
!
!!!           fintx(i,k,1,4) = not used
              fintx(i,k,2,4) = fb (ii2  ,kk+2,jj  )*xl (i,k,2) &
                             + fb (ii2+1,kk+2,jj  )*xr (i,k,2)
              fintx(i,k,3,4) = fb (ii3  ,kk+2,jj+1)*xl (i,k,3) &
                             + fb (ii3+1,kk+2,jj+1)*xr (i,k,3)
!!!           fintx(i,k,4,4) = not used
           end do
        end do
!
! The following loop computes x-derivatives for those cases when the
! departure point lies in either the top or bottom interval of the 
! model grid.  In this special case, data are shifted up or down to
! keep the departure point in the middle interval of the 4-point
! stencil.  Therefore, some derivatives that were computed above will 
! be over-written.
!
        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)
!
! TOP interval
!
              if(kdp (i,k) .eq. 1) then
!
! shift levels 4 and 2 data to levels 1 and 3, respectively
!
                 fintx(i,k,2,1) = fintx(i,k,2,4)
                 fintx(i,k,3,1) = fintx(i,k,3,4)
!
                 fintx(i,k,1,3) = fintx(i,k,1,2)
                 fintx(i,k,2,3) = fintx(i,k,2,2)
                 fintx(i,k,3,3) = fintx(i,k,3,2)
                 fintx(i,k,4,3) = fintx(i,k,4,2)
!
! Height level 1 (placed in level 2 of stencil):
!
!   Latitude 1:  Linear interpolation
!
                 fintx(i,k,1,2) = fb (ii1  ,1,jj-1)*xl (i,k,1) &
                                + fb (ii1+1,1,jj-1)*xr (i,k,1)
!
!   Latitude 2:  Cubic interpolation
!
                 fxl = (   - 2.*fb (ii2-1,1,jj  ) &
                           - 3.*fb (ii2  ,1,jj  ) &
                           + 6.*fb (ii2+1,1,jj  ) &
                           -    fb (ii2+2,1,jj  ) )*rdx6(jj)
                 fxr = (        fb (ii2-1,1,jj  ) &
                           - 6.*fb (ii2  ,1,jj  ) &
                           + 3.*fb (ii2+1,1,jj  ) &
                           + 2.*fb (ii2+2,1,jj  ) )*rdx6(jj)
!                                      
                 deli = (       fb (ii2+1,1,jj  ) - &
                                fb (ii2  ,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,2,2) = fb (ii2  ,1,jj  )*hl (i,k,2) &
                                + fb (ii2+1,1,jj  )*hr (i,k,2) &
                                + fxl*dhl(i,k,2) + fxr*dhr(i,k,2)
!
!   Latitude 3:  Cubic interpolation
!
                 fxl = (   - 2.*fb (ii3-1,1,jj+1) &
                           - 3.*fb (ii3  ,1,jj+1) &
                           + 6.*fb (ii3+1,1,jj+1) &
                           -    fb (ii3+2,1,jj+1) )*rdx6(jj+1)
                 fxr = (        fb (ii3-1,1,jj+1) &
                           - 6.*fb (ii3  ,1,jj+1) &
                           + 3.*fb (ii3+1,1,jj+1) &
                           + 2.*fb (ii3+2,1,jj+1) )*rdx6(jj+1)
!                                      
                 deli = (       fb (ii3+1,1,jj+1) - &
                                fb (ii3  ,1,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  ,1,jj+1)*hl (i,k,3) &
                                + fb (ii3+1,1,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  ,1,jj+2)*xl (i,k,4) &
                                + fb (ii4+1,1,jj+2)*xr (i,k,4)
!
! Height level 3 (placed in level 4 of stencil):
!  Linear interpolation on inner two latitudes only
!
!!!              fintx(i,k,1,4) = not used
                 fintx(i,k,2,4) = fb (ii2  ,3,jj  )*xl (i,k,2) &
                                + fb (ii2+1,3,jj  )*xr (i,k,2)
                 fintx(i,k,3,4) = fb (ii3  ,3,jj+1)*xl (i,k,3) &
                                + fb (ii3+1,3,jj+1)*xr (i,k,3)
!!!              fintx(i,k,4,4) = not used
!
! BOT interval
!
              else if(kdp (i,k) .eq. kdimm1) then
!
! shift levels 1 and 3 data to levels 4 and 2, respectively
!
                 fintx(i,k,2,4) = fintx(i,k,2,1)
                 fintx(i,k,3,4) = fintx(i,k,3,1)
!
                 fintx(i,k,1,2) = fintx(i,k,1,3)
                 fintx(i,k,2,2) = fintx(i,k,2,3)
                 fintx(i,k,3,2) = fintx(i,k,3,3)
                 fintx(i,k,4,2) = fintx(i,k,4,3)
!
! Height level 2 (placed in level 1 of stencil):
!  Linear interpolation on inner two latitudes only
!
!!!              fintx(i,k,1,1) =  not used
                 fintx(i,k,2,1) = fb (ii2  ,kdimm2,jj  )*xl (i,k,2) &
                                + fb (ii2+1,kdimm2,jj  )*xr (i,k,2)
                 fintx(i,k,3,1) = fb (ii3  ,kdimm2,jj+1)*xl (i,k,3) &
                                + fb (ii3+1,kdimm2,jj+1)*xr (i,k,3)
!!!              fintx(i,k,4,1) =  not used
!
! Height level 4 (placed in level 3 of stencil):
!
!   Latitude 1:  Linear interpolation
!
                 fintx(i,k,1,3) = fb (ii1  ,kdim,jj-1)*xl (i,k,1) &
                                + fb (ii1+1,kdim,jj-1)*xr (i,k,1)
!
!   Latitude 2:  Cubic interpolation
!
                 fxl = (   - 2.*fb (ii2-1,kdim,jj  ) &
                           - 3.*fb (ii2  ,kdim,jj  ) &
                           + 6.*fb (ii2+1,kdim,jj  ) &
                           -    fb (ii2+2,kdim,jj  ) )*rdx6(jj)
                 fxr = (        fb (ii2-1,kdim,jj  ) &
                           - 6.*fb (ii2  ,kdim,jj  ) &
                           + 3.*fb (ii2+1,kdim,jj  ) &
                           + 2.*fb (ii2+2,kdim,jj  ) )*rdx6(jj)
!                                          
                 deli = (       fb (ii2+1,kdim,jj  ) - &
                                fb (ii2  ,kdim,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  ,kdim,jj  )*hl (i,k,2) &
                                + fb (ii2+1,kdim,jj  )*hr (i,k,2) &
                                + fxl*dhl(i,k,2) + fxr*dhr(i,k,2)
!
!   Latitude 3:  Cubic interpolation
!
                 fxl = (   - 2.*fb (ii3-1,kdim,jj+1) &
                           - 3.*fb (ii3  ,kdim,jj+1) &
                           + 6.*fb (ii3+1,kdim,jj+1) &
                           -    fb (ii3+2,kdim,jj+1) )*rdx6(jj+1)
                 fxr = (        fb (ii3-1,kdim,jj+1) &
                           - 6.*fb (ii3  ,kdim,jj+1) &
                           + 3.*fb (ii3+1,kdim,jj+1) &
                           + 2.*fb (ii3+2,kdim,jj+1) )*rdx6(jj+1)
!                                          
                 deli = (       fb (ii3+1,kdim,jj+1) - &
                                fb (ii3  ,kdim,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,3,3) = fb (ii3  ,kdim,jj+1)*hl (i,k,3) &
                                + fb (ii3+1,kdim,jj+1)*hr (i,k,3) &
                                + fxl*dhl(i,k,3) + fxr*dhr(i,k,3)
!
!   Latitude 4:  Linear interpolation
!
                 fintx(i,k,4,3) = fb (ii4  ,kdim,jj+2)*xl (i,k,4) &
                                + fb (ii4+1,kdim,jj+2)*xr (i,k,4)
              end if
           end do
        end do
!
! PART 2:  y-derivatives
!
        jmin =  1000000
        jmax = -1000000
        do k=1,plev
           do i=1,nlon
              if(jdp(i,k) .lt. jmin) jmin = jdp(i,k)
              if(jdp(i,k) .gt. jmax) jmax = jdp(i,k)
           end do
        end do
!
! Loop over departure latitudes
!
        icount = 0
        do jdpval = jmin,jmax
           do k=1,plev
              call wheneq(nlon    ,jdp(1,k),1       ,jdpval  , &
                          indx    ,nval    )
              icount = icount + nval
!
! y derivatives at the inner height levels (kk = 2,3) needed for
! z-interpolation
!
              do kk  = 2,3
                 do ii = 1,nval
                    i = indx(ii)
                    fbot(i,k,kk) = lbasdy(1,1,jdpval)*fintx(i,k,1,kk) &
                                 + lbasdy(2,1,jdpval)*fintx(i,k,2,kk) &
                                 + lbasdy(3,1,jdpval)*fintx(i,k,3,kk) &
                                 + lbasdy(4,1,jdpval)*fintx(i,k,4,kk)
                    ftop(i,k,kk) = lbasdy(1,2,jdpval)*fintx(i,k,1,kk) &
                                 + lbasdy(2,2,jdpval)*fintx(i,k,2,kk) &
                                 + lbasdy(3,2,jdpval)*fintx(i,k,3,kk) &
                                 + lbasdy(4,2,jdpval)*fintx(i,k,4,kk)
                 end do
              end do
           end do
        end do
        if (icount.ne.nlon*plev) then
           write(*,*)'SLTINT:  Did not complete computations for all departure points'
           call endrun
        end if
!
! Apply SCM0 limiter to derivative estimates.
!
        do kk  = 2,3
           do k=1,plev
              do i=1,nlon
                 deli = ( fintx(i,k,3,kk) - fintx(i,k,2,kk) )*rdphi(i,k)
                 tmp1 = fac*deli
                 tmp2 = abs( tmp1 )
                 if( deli*fbot(i,k,kk)   .le. 0.0  ) fbot(i,k,kk) = 0.
                 if( deli*ftop(i,k,kk)   .le. 0.0  ) ftop(i,k,kk) = 0.
                 if( abs( fbot(i,k,kk) ) .gt. tmp2 ) fbot(i,k,kk) = tmp1
                 if( abs( ftop(i,k,kk) ) .gt. tmp2 ) ftop(i,k,kk) = tmp1
              end do
           end do
        end do
!
! PART 3:  y-interpolants
!
        do k=1,plev
           do i=1,nlon
              finty(i,k,1) = fintx(i,k,2,1)*ys (i,k) &
                           + fintx(i,k,3,1)*yn (i,k)
              finty(i,k,2) = fintx(i,k,2,2)*hs (i,k) + fbot (i,k  ,2)*dhs(i,k) &
                           + fintx(i,k,3,2)*hn (i,k) + ftop (i,k  ,2)*dhn(i,k)
              finty(i,k,3) = fintx(i,k,2,3)*hs (i,k) + fbot (i,k  ,3)*dhs(i,k) &
                           + fintx(i,k,3,3)*hn (i,k) + ftop (i,k  ,3)*dhn(i,k)
              finty(i,k,4) = fintx(i,k,2,4)*ys (i,k) &