C-----------------------------------------------------------------------
SUBROUTINE POLATEV1(IPOPT,KGDSI,KGDSO,MI,MO,KM,IBI,LI,UI,VI,
& NO,RLAT,RLON,CROT,SROT,IBO,LO,UO,VO,IRET)
C$$$ SUBPROGRAM DOCUMENTATION BLOCK
C
C SUBPROGRAM: POLATEV1 INTERPOLATE VECTOR FIELDS (BICUBIC)
C PRGMMR: IREDELL ORG: W/NMC23 DATE: 96-04-10
C
C ABSTRACT: THIS SUBPROGRAM PERFORMS BICUBIC INTERPOLATION
C FROM ANY GRID TO ANY GRID FOR SCALAR FIELDS.
C BITMAPS ARE NOW ALLOWED EVEN WHEN INVALID POINTS ARE WITHIN
C THE BICUBIC TEMPLATE PROVIDED THE MINIMUM WEIGHT IS REACHED.
C OPTIONS ALLOW CHOICES BETWEEN STRAIGHT BICUBIC (IPOPT(1)=0)
C AND CONSTRAINED BICUBIC (IPOPT(1)=1) WHERE THE VALUE IS
C CONFINED WITHIN THE RANGE OF THE SURROUNDING 16 POINTS.
C ANOTHER OPTION IS THE MINIMUM PERCENTAGE FOR MASK,
C I.E. PERCENT VALID INPUT DATA REQUIRED TO MAKE OUTPUT DATA,
C (IPOPT(2)) WHICH DEFAULTS TO 50 (IF IPOPT(2)=-1).
C BILINEAR USED WITHIN ONE GRID LENGTH OF BOUNDARIES.
C ONLY HORIZONTAL INTERPOLATION IS PERFORMED.
C THE GRIDS ARE DEFINED BY THEIR GRID DESCRIPTION SECTIONS
C (PASSED IN INTEGER FORM AS DECODED BY SUBPROGRAM W3FI63).
C THE CURRENT CODE RECOGNIZES THE FOLLOWING PROJECTIONS:
C (KGDS(1)=000) EQUIDISTANT CYLINDRICAL
C (KGDS(1)=001) MERCATOR CYLINDRICAL
C (KGDS(1)=003) LAMBERT CONFORMAL CONICAL
C (KGDS(1)=004) GAUSSIAN CYLINDRICAL (SPECTRAL NATIVE)
C (KGDS(1)=005) POLAR STEREOGRAPHIC AZIMUTHAL
C (KGDS(1)=202) ROTATED EQUIDISTANT CYLINDRICAL (ETA NATIVE)
C WHERE KGDS COULD BE EITHER INPUT KGDSI OR OUTPUT KGDSO.
C THE INPUT AND OUTPUT VECTORS ARE ROTATED SO THAT THEY ARE
C EITHER RESOLVED RELATIVE TO THE DEFINED GRID
C IN THE DIRECTION OF INCREASING X AND Y COORDINATES
C OR RESOLVED RELATIVE TO EASTERLY AND NORTHERLY DIRECTIONS,
C AS DESIGNATED BY THEIR RESPECTIVE GRID DESCRIPTION SECTIONS.
C AS AN ADDED BONUS THE NUMBER OF OUTPUT GRID POINTS
C AND THEIR LATITUDES AND LONGITUDES ARE ALSO RETURNED
C ALONG WITH THEIR VECTOR ROTATION PARAMETERS.
C ON THE OTHER HAND, THE OUTPUT CAN BE A SET OF STATION POINTS
C IF KGDSO(1)<0, IN WHICH CASE THE NUMBER OF POINTS
C AND THEIR LATITUDES AND LONGITUDES MUST BE INPUT
C ALONG WITH THEIR VECTOR ROTATION PARAMETERS.
C OUTPUT BITMAPS WILL ONLY BE CREATED WHEN THE OUTPUT GRID
C EXTENDS OUTSIDE OF THE DOMAIN OF THE INPUT GRID.
C THE OUTPUT FIELD IS SET TO 0 WHERE THE OUTPUT BITMAP IS OFF.
C
C PROGRAM HISTORY LOG:
C 96-04-10 IREDELL
C 1999-04-08 IREDELL SPLIT IJKGDS INTO TWO PIECES
C 2000-02-07 GILBERT ENSURE THAT VECTOR COMPONENTS ARE ROTATED
C TO THE GRID ORIENTATION.
C 2001-06-18 IREDELL INCLUDE MINIMUM MASK PERCENTAGE OPTION
C 2002-01-17 IREDELL SAVE DATA FROM LAST CALL FOR OPTIMIZATION
C 2007-05-22 IREDELL EXTRAPOLATE UP TO HALF A GRID CELL
C 2007-10-30 IREDELL CORRECT NORTH POLE INDEXING PROBLEM,
C UNIFY MASKED AND NON-MASKED ALGORITHMS,
C AND SAVE WEIGHTS FOR PERFORMANCE.
C
C USAGE: CALL POLATEV1(IPOPT,KGDSI,KGDSO,MI,MO,KM,IBI,LI,UI,VI,
C & NO,RLAT,RLON,CROT,SROT,IBO,LO,UO,VO,IRET)
C
C INPUT ARGUMENT LIST:
C IPOPT - INTEGER (20) INTERPOLATION OPTIONS
C IPOPT(1)=0 FOR STRAIGHT BICUBIC;
C IPOPT(1)=1 FOR CONSTRAINED BICUBIC WHERE VALUE IS
C CONFINED WITHIN THE RANGE OF THE SURROUNDING 4 POINTS.
C IPOPT(2) IS MINIMUM PERCENTAGE FOR MASK
C (DEFAULTS TO 50 IF IPOPT(2)=-1)
C KGDSI - INTEGER (200) INPUT GDS PARAMETERS AS DECODED BY W3FI63
C KGDSO - INTEGER (200) OUTPUT GDS PARAMETERS
C (KGDSO(1)<0 IMPLIES RANDOM STATION POINTS)
C MI - INTEGER SKIP NUMBER BETWEEN INPUT GRID FIELDS IF KM>1
C OR DIMENSION OF INPUT GRID FIELDS IF KM=1
C MO - INTEGER SKIP NUMBER BETWEEN OUTPUT GRID FIELDS IF KM>1
C OR DIMENSION OF OUTPUT GRID FIELDS IF KM=1
C KM - INTEGER NUMBER OF FIELDS TO INTERPOLATE
C IBI - INTEGER (KM) INPUT BITMAP FLAGS
C LI - LOGICAL*1 (MI,KM) INPUT BITMAPS (IF SOME IBI(K)=1)
C UI - REAL (MI,KM) INPUT U-COMPONENT FIELDS TO INTERPOLATE
C VI - REAL (MI,KM) INPUT V-COMPONENT FIELDS TO INTERPOLATE
C NO - INTEGER NUMBER OF OUTPUT POINTS (ONLY IF KGDSO(1)<0)
C RLAT - REAL (NO) OUTPUT LATITUDES IN DEGREES (IF KGDSO(1)<0)
C RLON - REAL (NO) OUTPUT LONGITUDES IN DEGREES (IF KGDSO(1)<0)
C CROT - REAL (NO) VECTOR ROTATION COSINES (IF KGDSO(1)<0)
C SROT - REAL (NO) VECTOR ROTATION SINES (IF KGDSO(1)<0)
C (UGRID=CROT*UEARTH-SROT*VEARTH;
C VGRID=SROT*UEARTH+CROT*VEARTH)
C
C OUTPUT ARGUMENT LIST:
C NO - INTEGER NUMBER OF OUTPUT POINTS (ONLY IF KGDSO(1)>=0)
C RLAT - REAL (MO) OUTPUT LATITUDES IN DEGREES (IF KGDSO(1)>=0)
C RLON - REAL (MO) OUTPUT LONGITUDES IN DEGREES (IF KGDSO(1)>=0)
C CROT - REAL (NO) VECTOR ROTATION COSINES (IF KGDSO(1)>=0)
C SROT - REAL (NO) VECTOR ROTATION SINES (IF KGDSO(1)>=0)
C (UGRID=CROT*UEARTH-SROT*VEARTH;
C VGRID=SROT*UEARTH+CROT*VEARTH)
C IBO - INTEGER (KM) OUTPUT BITMAP FLAGS
C LO - LOGICAL*1 (MO,KM) OUTPUT BITMAPS (ALWAYS OUTPUT)
C UO - REAL (MO,KM) OUTPUT U-COMPONENT FIELDS INTERPOLATED
C VO - REAL (MO,KM) OUTPUT V-COMPONENT FIELDS INTERPOLATED
C IRET - INTEGER RETURN CODE
C 0 SUCCESSFUL INTERPOLATION
C 2 UNRECOGNIZED INPUT GRID OR NO GRID OVERLAP
C 3 UNRECOGNIZED OUTPUT GRID
C
C SUBPROGRAMS CALLED:
C GDSWIZ GRID DESCRIPTION SECTION WIZARD
C IJKGDS0 SET UP PARAMETERS FOR IJKGDS1
C (IJKGDS1) RETURN FIELD POSITION FOR A GIVEN GRID POINT
C (MOVECT) MOVE A VECTOR ALONG A GREAT CIRCLE
C POLFIXV MAKE MULTIPLE POLE VECTOR VALUES CONSISTENT
C
C ATTRIBUTES:
C LANGUAGE: FORTRAN 77
C
C$$$
IMPLICIT NONE
INTEGER,INTENT(IN):: IPOPT(20),KGDSI(200),KGDSO(200),MI,MO,KM
INTEGER,INTENT(IN):: IBI(KM)
LOGICAL*1,INTENT(IN):: LI(MI,KM)
REAL,INTENT(IN):: UI(MI,KM),VI(MI,KM)
INTEGER,INTENT(INOUT):: NO
REAL,INTENT(INOUT):: RLAT(MO),RLON(MO),CROT(MO),SROT(MO)
INTEGER,INTENT(OUT):: IBO(KM)
LOGICAL*1,INTENT(OUT):: LO(MO,KM)
REAL,INTENT(OUT):: UO(MO,KM),VO(MO,KM)
INTEGER,INTENT(OUT):: IRET
REAL XPTS(MO),YPTS(MO)
INTEGER IJX(4),IJY(4)
REAL WX(4),WY(4)
INTEGER IJKGDSA(20)
REAL,PARAMETER:: FILL=-9999.
INTEGER MCON,MP,N,I,J,K,NK,NV,IJKGDS1
REAL PMP,XIJ,YIJ,XF,YF,U,V,W,DUM,UMIN,UMAX,VMIN,VMAX
REAL XPTI(MI),YPTI(MI),RLOI(MI),RLAI(MI),CROI(MI),SROI(MI)
REAL CM,SM,UROT,VROT
INTEGER,SAVE:: KGDSIX(200)=-1,KGDSOX(200)=-1,NOX=-1,IRETX=-1
INTEGER,ALLOCATABLE,SAVE:: NXY(:,:,:),NC(:)
REAL,ALLOCATABLE,SAVE:: RLATX(:),RLONX(:),CROTX(:),SROTX(:)
REAL,ALLOCATABLE,SAVE:: WXY(:,:,:),CXY(:,:,:),SXY(:,:,:)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C SET PARAMETERS
IRET=0
MCON=IPOPT(1)
MP=IPOPT(2)
IF(MP.EQ.-1.OR.MP.EQ.0) MP=50
IF(MP.LT.0.OR.MP.GT.100) IRET=32
PMP=MP*0.01
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C SAVE OR SKIP WEIGHT COMPUTATION
IF(IRET.EQ.0.AND.(KGDSO(1).LT.0.OR.
& ANY(KGDSI.NE.KGDSIX).OR.ANY(KGDSO.NE.KGDSOX))) THEN
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C COMPUTE NUMBER OF OUTPUT POINTS AND THEIR LATITUDES AND LONGITUDES.
IF(KGDSO(1).GE.0) THEN
CALL GDSWIZ(KGDSO, 0,MO,FILL,XPTS,YPTS,RLON,RLAT,NO,
& 1,CROT,SROT)
IF(NO.EQ.0) IRET=3
ENDIF
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C LOCATE INPUT POINTS
CALL GDSWIZ(KGDSI,-1,NO,FILL,XPTS,YPTS,RLON,RLAT,NV,0,DUM,DUM)
IF(IRET.EQ.0.AND.NV.EQ.0) IRET=2
CALL GDSWIZ(KGDSI, 0,MI,FILL,XPTI,YPTI,RLOI,RLAI,NV,1,CROI,SROI)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C ALLOCATE AND SAVE GRID DATA
KGDSIX=KGDSI
KGDSOX=KGDSO
IF(NOX.NE.NO) THEN
IF(NOX.GE.0) DEALLOCATE(RLATX,RLONX,CROTX,SROTX,NC,
& NXY,WXY,CXY,SXY)
ALLOCATE(RLATX(NO),RLONX(NO),CROTX(NO),SROTX(NO),NC(NO),
& NXY(4,4,NO),WXY(4,4,NO),CXY(4,4,NO),SXY(4,4,NO))
NOX=NO
ENDIF
IRETX=IRET
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C COMPUTE WEIGHTS
IF(IRET.EQ.0) THEN
CALL IJKGDS0(KGDSI,IJKGDSA)
C$OMP PARALLEL DO
C$OMP&PRIVATE(N,XIJ,YIJ,IJX,IJY,XF,YF,J,I,WX,WY,CM,SM)
DO N=1,NO
RLONX(N)=RLON(N)
RLATX(N)=RLAT(N)
CROTX(N)=CROT(N)
SROTX(N)=SROT(N)
XIJ=XPTS(N)
YIJ=YPTS(N)
IF(XIJ.NE.FILL.AND.YIJ.NE.FILL) THEN
IJX(1:4)=FLOOR(XIJ-1)+(/0,1,2,3/)
IJY(1:4)=FLOOR(YIJ-1)+(/0,1,2,3/)
XF=XIJ-IJX(2)
YF=YIJ-IJY(2)
DO J=1,4
DO I=1,4
NXY(I,J,N)=IJKGDS1(IJX(I),IJY(J),IJKGDSA)
ENDDO
ENDDO
IF(MINVAL(NXY(1:4,1:4,N)).GT.0) THEN
C BICUBIC WHERE 16-POINT STENCIL IS AVAILABLE
NC(N)=1
WX(1)=XF*(1-XF)*(2-XF)/(-6.)
WX(2)=(XF+1)*(1-XF)*(2-XF)/2.
WX(3)=(XF+1)*XF*(2-XF)/2.
WX(4)=(XF+1)*XF*(1-XF)/(-6.)
WY(1)=YF*(1-YF)*(2-YF)/(-6.)
WY(2)=(YF+1)*(1-YF)*(2-YF)/2.
WY(3)=(YF+1)*YF*(2-YF)/2.
WY(4)=(YF+1)*YF*(1-YF)/(-6.)
ELSE
C BILINEAR ELSEWHERE NEAR THE EDGE OF THE GRID
NC(N)=2
WX(1)=0
WX(2)=(1-XF)
WX(3)=XF
WX(4)=0
WY(1)=0
WY(2)=(1-YF)
WY(3)=YF
WY(4)=0
ENDIF
DO J=1,4
DO I=1,4
WXY(I,J,N)=WX(I)*WY(J)
IF(NXY(I,J,N).GT.0) THEN
CALL MOVECT(RLAI(NXY(I,J,N)),RLOI(NXY(I,J,N)),
& RLAT(N),RLON(N),CM,SM)
CXY(I,J,N)=CM*CROI(NXY(I,J,N))+SM*SROI(NXY(I,J,N))
SXY(I,J,N)=SM*CROI(NXY(I,J,N))-CM*SROI(NXY(I,J,N))
ENDIF
ENDDO
ENDDO
ELSE
NC(N)=0
ENDIF
ENDDO
ENDIF
ENDIF
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C INTERPOLATE OVER ALL FIELDS
IF(IRET.EQ.0.AND.IRETX.EQ.0) THEN
IF(KGDSO(1).GE.0) THEN
NO=NOX
DO N=1,NO
RLON(N)=RLONX(N)
RLAT(N)=RLATX(N)
CROT(N)=CROTX(N)
SROT(N)=SROTX(N)
ENDDO
ENDIF
C$OMP PARALLEL DO
C$OMP&PRIVATE(NK,K,N,U,V,W,UMIN,UMAX,VMIN,VMAX,UROT,VROT,J,I)
DO NK=1,NO*KM
K=(NK-1)/NO+1
N=NK-NO*(K-1)
IF(NC(N).GT.0) THEN
U=0
V=0
W=0
IF(MCON.GT.0) UMIN=HUGE(UMIN)
IF(MCON.GT.0) UMAX=-HUGE(UMAX)
IF(MCON.GT.0) VMIN=HUGE(VMIN)
IF(MCON.GT.0) VMAX=-HUGE(VMAX)
DO J=NC(N),5-NC(N)
DO I=NC(N),5-NC(N)
IF(NXY(I,J,N).GT.0) THEN
IF(IBI(K).EQ.0.OR.LI(NXY(I,J,N),K)) THEN
UROT=CXY(I,J,N)*UI(NXY(I,J,N),K)-
& SXY(I,J,N)*VI(NXY(I,J,N),K)
VROT=SXY(I,J,N)*UI(NXY(I,J,N),K)+
& CXY(I,J,N)*VI(NXY(I,J,N),K)
U=U+WXY(I,J,N)*UROT
V=V+WXY(I,J,N)*VROT
W=W+WXY(I,J,N)
IF(MCON.GT.0) UMIN=MIN(UMIN,UROT)
IF(MCON.GT.0) UMAX=MAX(UMAX,UROT)
IF(MCON.GT.0) VMIN=MIN(VMIN,VROT)
IF(MCON.GT.0) VMAX=MAX(VMAX,VROT)
ENDIF
ENDIF
ENDDO
ENDDO
LO(N,K)=W.GE.PMP
IF(LO(N,K)) THEN
UROT=CROT(N)*U-SROT(N)*V
VROT=SROT(N)*U+CROT(N)*V
UO(N,K)=UROT/W
VO(N,K)=VROT/W
IF(MCON.GT.0) UO(N,K)=MIN(MAX(UO(N,K),UMIN),UMAX)
IF(MCON.GT.0) VO(N,K)=MIN(MAX(VO(N,K),VMIN),VMAX)
ELSE
UO(N,K)=0.
VO(N,K)=0.
ENDIF
ELSE
LO(N,K)=.FALSE.
UO(N,K)=0.
VO(N,K)=0.
ENDIF
ENDDO
DO K=1,KM
IBO(K)=IBI(K)
IF(.NOT.ALL(LO(1:NO,K))) IBO(K)=1
ENDDO
IF(KGDSO(1).EQ.0) CALL POLFIXV(NO,MO,KM,RLAT,RLON,IBO,LO,UO,VO)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ELSE
IF(IRET.EQ.0) IRET=IRETX
IF(KGDSO(1).GE.0) NO=0
ENDIF
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
END