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UPP_MATH.f
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!> @file
!>
!> @brief upp_math is a collection of UPP subroutines for numerical math functions calculation.
!> @author Jesse Meng @date 2020-05-20
!>
!> dvdxdudy() computes dudy, dvdx, uwnd
!>
!> h2u(), h2v(), u2h(), v2h() interpolate variables between U, V, H, points
!> adopted from UPP subroutine GRIDAVG.f
!>
!> ### Program history log:
!> Date | Programmer | Comments
!> -----|------------|---------
!> 2020-05-20 | Jesse Meng | Initial
!> 2022-06-10 | Wen Meng | Modify dvdxdudy to retrict computation on undefined grids
!> 2023-03-03 | Sam Trahan | Add some missing exchanges (grids that only need i-direction exchanges)
!>
!> @author Jesse Meng @date 2020-05-20
module upp_math
use masks, only: dx, dy
use ctlblk_mod, only: im, jsta_2l, jend_2u, jsta_m, jend_m, spval,&
ista_2l, iend_2u, ista_m, iend_m
use gridspec_mod, only: gridtype
!
implicit none
private
public :: DDVDX, DDUDY, UUAVG
public :: dvdxdudy
public :: H2U, H2V, U2H, V2H
!> DDVDX dv/dx derivative
REAL, ALLOCATABLE :: DDVDX(:,:)
!> DDUDY du/dy derivative
REAL, ALLOCATABLE :: DDUDY(:,:)
!> UUAVG u wind velocity on mass points
REAL, ALLOCATABLE :: UUAVG(:,:)
!
!-------------------------------------------------------------------------------------
!
contains
!
!-------------------------------------------------------------------------------------
!> dvdxdudy() computes dudy, dvdx, uwnd
!>
!> @param[in] uwnd real U horizontal wind component on velocity points
!> @param[in] vwnd real V horizontal wind component on velocity points
!
subroutine dvdxdudy(uwnd,vwnd)
!
implicit none
REAL, dimension(ista_2l:iend_2u,jsta_2l:jend_2u), intent(in) :: UWND, VWND
!
!-- local variables
!--
integer i, j
real r2dx, r2dy
INTEGER, allocatable :: IHE(:),IHW(:)
!Initializing
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
DDVDX(I,J)=SPVAL
DDUDY(I,J)=SPVAL
UUAVG(I,J)=SPVAL
ENDDO
ENDDO
IF(GRIDTYPE == 'A')THEN
!$omp parallel do private(i,j,r2dx,r2dy)
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
IF(VWND(I+1,J)<SPVAL.AND.VWND(I-1,J)<SPVAL.AND. &
UWND(I,J+1)<SPVAL.AND.UWND(I,J-1)<SPVAL.AND. &
UWND(I,J)<SPVAL.AND.VWND(I,J)<SPVAL.AND. &
ABS(DX(I,J))>1.E-5.AND.ABS(DY(I,J))>1.E-5) THEN
R2DX = 1./(2.*DX(I,J))
R2DY = 1./(2.*DY(I,J))
DDVDX(I,J) = (VWND(I+1,J)-VWND(I-1,J))*R2DX
DDUDY(I,J) = (UWND(I,J+1)-UWND(I,J-1))*R2DY
UUAVG(I,J) = UWND(I,J)
END IF
END DO
END DO
ELSE IF (GRIDTYPE == 'E')THEN
allocate(ihw(JSTA_2L:JEND_2U), IHE(JSTA_2L:JEND_2U))
!$omp parallel do private(j)
DO J=JSTA_2L,JEND_2U
IHW(J) = -MOD(J,2)
IHE(J) = IHW(J)+1
ENDDO
!$omp parallel do private(i,j,r2dx,r2dy)
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
IF(VWND(I+IHE(J),J) < SPVAL.AND.VWND(I+IHW(J),J) < SPVAL .AND. &
& UWND(I,J+1) < SPVAL .AND.UWND(I,J-1) < SPVAL) THEN
R2DX = 1./(2.*DX(I,J))
R2DY = 1./(2.*DY(I,J))
DDVDX(I,J) = (VWND(I+IHE(J),J)-VWND(I+IHW(J),J))*R2DX
DDUDY(I,J) = (UWND(I,J+1)-UWND(I,J-1))*R2DY
UUAVG(I,J) = 0.25*(UWND(I+IHE(J),J)+UWND(I+IHW(J),J) &
& + UWND(I,J+1)+UWND(I,J-1))
END IF
END DO
END DO
deallocate(ihw, IHE)
ELSE IF (GRIDTYPE == 'B')THEN
!$omp parallel do private(i,j,r2dx,r2dy)
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
R2DX = 1./DX(I,J)
R2DY = 1./DY(I,J)
if(VWND(I, J)==SPVAL .or. VWND(I, J-1)==SPVAL .or. &
VWND(I-1,J)==SPVAL .or. VWND(I-1,J-1)==SPVAL .or. &
UWND(I, J)==SPVAL .or. UWND(I-1,J )==SPVAL .or. &
UWND(I,J-1)==SPVAL .or. UWND(I-1,J-1)==SPVAL) cycle
DDVDX(I,J) = (0.5*(VWND(I,J)+VWND(I,J-1))-0.5*(VWND(I-1,J) &
& + VWND(I-1,J-1)))*R2DX
DDUDY(I,J) = (0.5*(UWND(I,J)+UWND(I-1,J))-0.5*(UWND(I,J-1) &
& + UWND(I-1,J-1)))*R2DY
UUAVG(I,J) = 0.25*(UWND(I-1,J-1)+UWND(I-1,J) &
& + UWND(I, J-1)+UWND(I, J))
END DO
END DO
END IF
end subroutine dvdxdudy
!
!-------------------------------------------------------------------------------------
!
subroutine H2U(ingrid,outgrid)
!
!> H2U() interpolates from H points onto U points
!>
!> @param[in] ingrid Input grid on H points
!> @param[out] outgrid Output grid on U points
!>
!> Author: CHUANG, EMC, Dec. 2010
!
use ctlblk_mod, only: spval, jsta, jend, jsta_m, jend_m, me, num_procs, jm,&
im, jsta_2l, jend_2u, ista, iend, ista_m, iend_m, ista_2l, iend_2u
use gridspec_mod, only: gridtype
implicit none
INCLUDE "mpif.h"
integer:: i,j,ie,iw
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(in)::ingrid
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(out)::outgrid
outgrid=spval
if(GRIDTYPE == 'A')THEN
do j=jsta,jend
do i=ista,iend
outgrid(i,j)=ingrid(i,j)
end do
end do
else IF(GRIDTYPE == 'E')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
IE=I+MOD(J,2)
IW=IE-1
outgrid(i,j)=(ingrid(IW,J)+ingrid(IE,J)+ingrid(I,J+1)+ingrid(I,J-1))/4.0
end do
end do
ELSE IF(GRIDTYPE == 'B')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA,JEND_M
DO I=ISTA,IEND_M
outgrid(i,j)=(ingrid(i,j)+ingrid(i,j+1)+ingrid(i+1,j)+ingrid(i+1,j+1))/4.0
end do
end do
! Fill in boundary points because hysplit fails when 10 m wind has bitmaps
do j=jsta,jend_m
outgrid(iend,j)=outgrid(iend-1,j)
end do
IF(me == (num_procs-1) .and. jend_2u >= jm) then
DO I=ISTA,IEND
outgrid(i,jend) = outgrid(i,jend-1)
END DO
END IF
ELSE IF(GRIDTYPE == 'C')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA,JEND
DO I=ISTA,IEND_M
outgrid(i,j)=(ingrid(i,j)+ingrid(i+1,j))/2.0
end do
end do
end if
end subroutine H2U
!
!-------------------------------------------------------------------------------------
!
subroutine H2V(ingrid,outgrid)
!
!> H2V() interpolates from H points onto V points
!>
!> @param[in] ingrid Input grid on H points.
!> @param[out] outgrid Output grid on V points.
!>
!> Author: CHUANG, EMC, Dec. 2010
!
use ctlblk_mod, only: spval, jsta, jend, jsta_m, jend_m, im, jsta_2l, jend_2u,&
ista, iend, ista_m, iend_m, ista_2l, iend_2u
use gridspec_mod, only: gridtype
implicit none
INCLUDE "mpif.h"
integer:: i,j,ie,iw
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(in)::ingrid
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(out)::outgrid
outgrid=spval
if(GRIDTYPE == 'A')THEN
do j=jsta,jend
do i=ista,iend
outgrid(i,j)=ingrid(i,j)
end do
end do
else IF(GRIDTYPE == 'E')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
IE=I+MOD(J,2)
IW=IE-1
outgrid(i,j)=(ingrid(IW,J)+ingrid(IE,J)+ingrid(I,J+1)+ingrid(I,J-1))/4.0
end do
end do
ELSE IF(GRIDTYPE == 'B')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA,JEND_M
DO I=ISTA,IEND_M
outgrid(i,j)=(ingrid(i,j)+ingrid(i,j+1)+ingrid(i+1,j)+ingrid(i+1,j+1))/4.0
end do
end do
ELSE IF(GRIDTYPE == 'C')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA,JEND_M
DO I=ISTA,IEND
outgrid(i,j)=(ingrid(i,j)+ingrid(i,j+1))/2.0
end do
end do
end if
end subroutine H2V
!
!-------------------------------------------------------------------------------------
!
subroutine U2H(ingrid,outgrid)
!
!> U2H() interpolates from U points onto H points
!>
!> @param[in] ingrid Input grid on U points.
!> @param[out] outgrid Output grid on H points.
!>
!> Author: CHUANG, EMC, Dec. 2010
!
use ctlblk_mod, only: spval, jsta, jend, jsta_m, jend_m, im, jsta_2l, jend_2u,&
ista, iend, ista_m, iend_m, ista_2l, iend_2u
use gridspec_mod, only: gridtype
implicit none
INCLUDE "mpif.h"
integer:: i,j,ie,iw
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(in)::ingrid
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(out)::outgrid
outgrid=spval
if(GRIDTYPE == 'A')THEN
do j=jsta,jend
do i=ista,iend
outgrid(i,j)=ingrid(i,j)
end do
end do
else IF(GRIDTYPE == 'E')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
IE=I+MOD(J+1,2)
IW=IE-1
outgrid(i,j)=(ingrid(IW,J)+ingrid(IE,J)+ingrid(I,J+1)+ingrid(I,J-1))/4.0
end do
end do
ELSE IF(GRIDTYPE == 'B')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
outgrid(i,j)=(ingrid(i-1,j-1)+ingrid(i,j-1)+ingrid(i-1,j)+ingrid(i,j))/4.0
end do
end do
ELSE IF(GRIDTYPE == 'C')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA,JEND
DO I=ISTA_M,IEND
outgrid(i,j)=(ingrid(i-1,j)+ingrid(i,j))/2.0
end do
end do
end if
end subroutine U2H
!
!-------------------------------------------------------------------------------------
!
subroutine V2H(ingrid,outgrid)
!
!> V2H() interpolates from V points onto H points
!>
!> @param[in] ingrid Input grid on V points.
!> @param[out] outgrid Output grid on H points.
!>
!> Author: CHUANG, EMC, Dec. 2010
!
use ctlblk_mod, only: spval, jsta, jend, jsta_m, jend_m, im, jsta_2l, jend_2u,&
ista, iend, ista_m, iend_m, ista_2l, iend_2u
use gridspec_mod, only: gridtype
implicit none
INCLUDE "mpif.h"
integer:: i,j,ie,iw
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(in)::ingrid
real,dimension(ISTA_2L:IEND_2U,JSTA_2L:JEND_2U),intent(out)::outgrid
outgrid=spval
if(GRIDTYPE == 'A')THEN
do j=jsta,jend
do i=ista,iend
outgrid(i,j)=ingrid(i,j)
end do
end do
else IF(GRIDTYPE == 'E')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
IE=I+MOD(J,2)
IW=IE-1
outgrid(i,j)=(ingrid(IW,J)+ingrid(IE,J)+ingrid(I,J+1)+ingrid(I,J-1))/4.0
end do
end do
ELSE IF(GRIDTYPE == 'B')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA_M,JEND_M
DO I=ISTA_M,IEND_M
outgrid(i,j)=(ingrid(i-1,j-1)+ingrid(i,j-1)+ingrid(i-1,j)+ingrid(i,j))/4.0
end do
end do
ELSE IF(GRIDTYPE == 'C')THEN
call exch(ingrid(ista_2l,jsta_2l))
DO J=JSTA_M,JEND
DO I=ISTA,IEND
outgrid(i,j)=(ingrid(i,j-1)+ingrid(i,j))/2.0
end do
end do
end if
end subroutine V2H
!
!-------------------------------------------------------------------------------------
!
end module upp_math