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C Copyright 1981-2007 ECMWF
C
C Licensed under the GNU Lesser General Public License which
C incorporates the terms and conditions of version 3 of the GNU
C General Public License.
C See LICENSE and gpl-3.0.txt for details.
C
SUBROUTINE HWTSLSM
X (KLEN,KSCHEME,KLA,PDLAT,PLATIN,PDLO0,PDLO1,PDLO2,PDLO3,NEIGH,
X LSMOLD,LSMNEW,PWTS)
C
C---->
C**** HWTSLSM
C
C Purpose
C -------
C
C This routine accepts a vector of points and calculates the
C interpolation weightings for each point suitable for the
C horizontal interpolation.
C
C
C Interface
C ---------
C
C CALL HWTSLSM
C X (KLEN,KSCHEME,KLA,PDLAT,PLATIN,PDLO0,PDLO1,PDLO2,PDLO3,NEIGH,
C X LSMOLD,LSMNEW,PWTS)
C
C
C Input parameters
C ----------------
C
C KLEN - Number of points along the vector.
C KSCHEME - Flag showing interpolation scheme to use for point
C 0 = 12-point
C 1 = 4-point bilinear
C 2 = nearest neighbour
C KLA - Latitude number in original field of latitude north of
C point in the vector.
C PDLAT - Meridian linear weight.
C PLATIN - Gaussian latitudes.
C PDLO0 - Zonal linear weight for the latitude of point 5.
C PDLO1 - Zonal linear weight for the latitude of point 1.
C PDLO2 - Zonal linear weight for the latitude of point 3.
C PDLO3 - Zonal linear weight for the latitude of point 11.
C NEIGH - List of indices in the original field of neighbouring
C point values.
C LSMOLD - Array of land-sea mask values ( a reduced gaussian
C field which matches the reduced gaussian field to be
C used for interpolation)
C LSMNEW - Vector of land-sea mask values for the input points
C
C
C Output parameters
C -----------------
C
C PWTS - Weights for interpolation.
C
C Common block usage
C ------------------
C
C None.
C
C
C Method
C ------
C
C Numbering of the points (I is the interpolation point):
C
C 13 5 6 14
C
C 7 1 2 8
C (I)
C 9 3 4 10
C
C 15 11 12 16
C
C
C Externals
C ---------
C
C None.
C
C
C Reference
C ---------
C
C ECMWF Meteorological Bulletin M1.6/7
C IFS Documentation
C Part VI: Technical and Computational Procedures (CY21R4)
C March 2000
C Section 2.3
C
C
C Comments
C --------
C
C None.
C
C
C Author
C ------
C
C J.D.Chambers ECMWF March 2001
C
C
C Modifications
C -------------
C
C None.
C
C----<
C -----------------------------------------------------------------|
C* Definition of variables.
C -----------------------------------------------------------------|
C
IMPLICIT NONE
C
C Parameters
C
INTEGER JP12PT, JP4PT, JPNEARN
PARAMETER (JP12PT = 0)
PARAMETER (JP4PT = 1)
PARAMETER (JPNEARN = 2)
C
C Function arguments
C
INTEGER KLEN, KSCHEME(KLEN), KLA(KLEN)
REAL PDLAT(KLEN), PLATIN(*)
REAL PDLO0(KLEN), PDLO1(KLEN), PDLO2(KLEN), PDLO3(KLEN)
REAL LSMNEW(KLEN)
INTEGER NEIGH(12,*)
REAL LSMOLD(*),PWTS(12,*)
C
C Local variables
C
INTEGER NEXT, LOOP
INTEGER ILA0G, ILA1G, ILA2G, ILA3G
INTEGER IMKOUT, IMKIN1, IMKIN2, IMKIN3, IMKIN4, IMKIN5, IMKIN6
INTEGER IMKIN7, IMKIN8, IMKIN9, IMKIN10, IMKIN11, IMKIN12
REAL ZDLAT, ZDY, ZDY10, ZDY21, ZDY32
REAL ZDLO, ZDLO1, ZDLO2, ZDLO3, ZWXN0, ZWXN1, ZWXN2, ZWXN3
REAL ZWY0, ZWY1, ZWY2, ZWY3
REAL ZWXNN, ZCXNN, ZWXSS, ZCXSS
REAL ZWXS0, ZWXS1, ZWXS2, ZWXS3
REAL ZWY, ZCY, ZWXN, ZCXN, ZWXS, ZCXS
REAL ZWLSI1, ZWLSI2, ZWLSI3, ZWLSI4, ZWLSI5, ZWLSI6
REAL ZWLSI7, ZWLSI8, ZWLSI9, ZWLSI10, ZWLSI11, ZWLSI12
REAL ZWLSI13, ZWLSI14, ZWLSI15, ZWLSI16, ZWLSI17
REAL ZEPSIL
DATA ZEPSIL/1.E-5/
C
C Inline functions
C
REAL A, B, ADJUST
REAL ALPHA, BETA, GAMMA, DELTA, EPSILON, F2, F3, F4
C
ADJUST(A,B) = 1.0 - INT(B + ZEPSIL)*(1.0 - A)
C
F2(ALPHA,BETA,GAMMA,DELTA,EPSILON) =
X ALPHA * ((1.0 + BETA*GAMMA) *
X (1.0 + DELTA*(GAMMA-2.0)) *
X (1.0 + EPSILON*(GAMMA-3.0))) /
X ((1.0 - 2.0*DELTA) * (1.0 - 3.0*EPSILON))
C
F3(ALPHA,BETA,GAMMA,DELTA,EPSILON) =
X ALPHA * ((1.0 + BETA*GAMMA) *
X (1.0 + DELTA*(GAMMA - 1.0)) *
X (1.0 + EPSILON*(GAMMA - 3.0))) /
X ((1.0 + BETA) * (1.0 - 2.0*EPSILON))
C
F4(ALPHA,BETA,GAMMA,DELTA,EPSILON) =
X ALPHA * ((1.0 + BETA*GAMMA) *
X (1.0 + DELTA*(GAMMA - 1.0)) *
X (1.0 + EPSILON*(GAMMA - 2.0))) /
X ((1.0 + 2.0*BETA) * (1.0 + DELTA))
C
C -----------------------------------------------------------------|
C Process each point in the vector.
C -----------------------------------------------------------------|
C
DO NEXT = 1,KLEN
C
C Clear the weights for the current point
C
DO LOOP = 1, 12
PWTS(LOOP,NEXT) = 0.0
ENDDO
C
C Use appropriate interpolation scheme for the current point
C
C -----------------------------------------------------------------|
C
C Nearest point selection
C
C -----------------------------------------------------------------|
C
IF( KSCHEME(NEXT).EQ.JPNEARN ) THEN
C
DO LOOP = 1, 4
IF( NEIGH(LOOP,NEXT).NE.0 ) PWTS(LOOP,NEXT) = 1.0
ENDDO
C
GOTO 900
C
C -----------------------------------------------------------------|
C
C 4-point interpolation
C
C -----------------------------------------------------------------|
C
ELSE IF( KSCHEME(NEXT).EQ.JP4PT ) THEN
C
C -----------------------------------------------------------------|
C Initialise the lsm weights
C -----------------------------------------------------------------|
C
ZWLSI1 = 1.0
ZWLSI2 = 1.0
ZWLSI3 = 1.0
ZWLSI4 = 1.0
C
ZWLSI14 = 0.0
ZWLSI15 = 0.0
ZWLSI17 = 0.0
C
C Modify the weights according to whether or not the target
C point matches its neighbours
C
IMKOUT = NINT(LSMNEW(NEXT))
C
IMKIN1 = NINT(LSMOLD(NEIGH(1,NEXT)))
IF( IMKIN1.NE.IMKOUT ) ZWLSI1 = 0.0
C
IMKIN2 = NINT(LSMOLD(NEIGH(2,NEXT)))
IF( IMKIN2.NE.IMKOUT ) ZWLSI2 = 0.0
C
IMKIN3 = NINT(LSMOLD(NEIGH(3,NEXT)))
IF( IMKIN3.NE.IMKOUT ) ZWLSI3 = 0.0
C
IMKIN4 = NINT(LSMOLD(NEIGH(4,NEXT)))
IF( IMKIN4.NE.IMKOUT ) ZWLSI4 = 0.0
C
IF( IMKIN1.NE.IMKOUT) ZWLSI1 = 0.0
IF( IMKIN2.NE.IMKOUT) ZWLSI2 = 0.0
IF( IMKIN3.NE.IMKOUT) ZWLSI3 = 0.0
IF( IMKIN4.NE.IMKOUT) ZWLSI4 = 0.0
C
ZWLSI14 = MIN(ZWLSI1 + ZWLSI2, 1.0)
ZWLSI15 = MIN(ZWLSI3 + ZWLSI4, 1.0)
ZWLSI17 = MIN(ZWLSI14 + ZWLSI15, 1.0)
C
ZWLSI1 = ADJUST(ZWLSI1,ZWLSI14)
ZWLSI2 = ADJUST(ZWLSI2,ZWLSI14)
ZWLSI3 = ADJUST(ZWLSI3,ZWLSI15)
ZWLSI4 = ADJUST(ZWLSI4,ZWLSI15)
C
ZWLSI14 = ADJUST(ZWLSI17,ZWLSI14)
ZWLSI15 = ADJUST(ZWLSI17,ZWLSI15)
C
C -----------------------------------------------------------------|
C Weights for bilinear interpolation.
C -----------------------------------------------------------------|
C
ZWY = ZWLSI15 * (1.0 + ZWLSI14 * (PDLAT(NEXT) - 1.0))
ZCY = 1.0 - ZWY
C
ZWXN = ZWLSI2 * (1.0 + ZWLSI1 * (PDLO1(NEXT) - 1.0))
ZCXN = 1.0 - ZWXN
C
ZWXS = ZWLSI4 * (1.0 + ZWLSI3 * (PDLO2(NEXT) - 1.0))
ZCXS = 1.0 - ZWXS
C
PWTS(1,NEXT) = ZCXN * ZCY
PWTS(2,NEXT) = ZWXN * ZCY
PWTS(3,NEXT) = ZCXS * ZWY
PWTS(4,NEXT) = ZWXS * ZWY
C
GOTO 900
C
C -----------------------------------------------------------------|
C
C 12-point interpolation
C
C -----------------------------------------------------------------|
C
ELSE
C
C -----------------------------------------------------------------|
C Initialise the lsm weights
C -----------------------------------------------------------------|
C
ZWLSI1 = 1.0
ZWLSI2 = 1.0
ZWLSI3 = 1.0
ZWLSI4 = 1.0
ZWLSI5 = 1.0
ZWLSI6 = 1.0
ZWLSI7 = 1.0
ZWLSI8 = 1.0
ZWLSI9 = 1.0
ZWLSI10 = 1.0
ZWLSI11 = 1.0
ZWLSI12 = 1.0
C
ZWLSI13 = 0.0
ZWLSI14 = 0.0
ZWLSI15 = 0.0
ZWLSI16 = 0.0
ZWLSI17 = 0.0
C
C Modify the weights according to whether or not the target
C point matches its neighbours
C
IMKOUT = NINT(LSMNEW(NEXT))
C
IMKIN1 = NINT(LSMOLD(NEIGH(1,NEXT)))
IF( IMKIN1.NE.IMKOUT ) ZWLSI1 = 0.0
C
IMKIN2 = NINT(LSMOLD(NEIGH(2,NEXT)))
IF( IMKIN2.NE.IMKOUT ) ZWLSI2 = 0.0
C
IMKIN3 = NINT(LSMOLD(NEIGH(3,NEXT)))
IF( IMKIN3.NE.IMKOUT ) ZWLSI3 = 0.0
C
IMKIN4 = NINT(LSMOLD(NEIGH(4,NEXT)))
IF( IMKIN4.NE.IMKOUT ) ZWLSI4 = 0.0
C
IMKIN5 = NINT(LSMOLD(NEIGH(5,NEXT)))
IF( IMKIN5.NE.IMKOUT ) ZWLSI5 = 0.0
C
IMKIN6 = NINT(LSMOLD(NEIGH(6,NEXT)))
IF( IMKIN6.NE.IMKOUT ) ZWLSI6 = 0.0
C
IMKIN7 = NINT(LSMOLD(NEIGH(7,NEXT)))
IF( IMKIN7.NE.IMKOUT ) ZWLSI7 = 0.0
C
IMKIN8 = NINT(LSMOLD(NEIGH(8,NEXT)))
IF( IMKIN8.NE.IMKOUT ) ZWLSI8 = 0.0
C
IMKIN9 = NINT(LSMOLD(NEIGH(9,NEXT)))
IF( IMKIN9.NE.IMKOUT ) ZWLSI9 = 0.0
C
IMKIN10 = NINT(LSMOLD(NEIGH(10,NEXT)))
IF( IMKIN10.NE.IMKOUT ) ZWLSI10 = 0.0
C
IMKIN11 = NINT(LSMOLD(NEIGH(11,NEXT)))
IF( IMKIN11.NE.IMKOUT ) ZWLSI11 = 0.0
C
IMKIN12 = NINT(LSMOLD(NEIGH(12,NEXT)))
IF( IMKIN12.NE.IMKOUT ) ZWLSI12 = 0.0
C
ZWLSI13 = MIN(ZWLSI5+ZWLSI6 ,1.0)
ZWLSI14 = MIN(ZWLSI7+ZWLSI1+ZWLSI2+ZWLSI8 ,1.0)
ZWLSI15 = MIN(ZWLSI9+ZWLSI3+ZWLSI4+ZWLSI10 ,1.0)
ZWLSI16 = MIN(ZWLSI11+ZWLSI12 ,1.0)
ZWLSI17 = MIN(ZWLSI13+ZWLSI14+ZWLSI15+ZWLSI16,1.0)
C
ZWLSI1 = ADJUST(ZWLSI1,ZWLSI14)
ZWLSI2 = ADJUST(ZWLSI2,ZWLSI14)
ZWLSI3 = ADJUST(ZWLSI3,ZWLSI15)
ZWLSI4 = ADJUST(ZWLSI4,ZWLSI15)
ZWLSI5 = ADJUST(ZWLSI5,ZWLSI13)
ZWLSI6 = ADJUST(ZWLSI6,ZWLSI13)
ZWLSI7 = ADJUST(ZWLSI7,ZWLSI14)
ZWLSI8 = ADJUST(ZWLSI8,ZWLSI14)
ZWLSI9 = ADJUST(ZWLSI9,ZWLSI15)
ZWLSI10 = ADJUST(ZWLSI10,ZWLSI15)
ZWLSI11 = ADJUST(ZWLSI11,ZWLSI16)
ZWLSI12 = ADJUST(ZWLSI12,ZWLSI16)
C
ZWLSI13 = ADJUST(ZWLSI13,ZWLSI17)
ZWLSI14 = ADJUST(ZWLSI14,ZWLSI17)
ZWLSI15 = ADJUST(ZWLSI15,ZWLSI17)
ZWLSI16 = ADJUST(ZWLSI16,ZWLSI17)
C
C Setup latitude numbers for the 4 rows.
C
ILA1G = KLA(NEXT)
ILA0G = ILA1G - 1
ILA2G = ILA1G + 1
ILA3G = ILA1G + 2
C
C Setup the weights between rows.
C
ZDLAT = PDLAT(NEXT)
ZDY = ZDLAT * (PLATIN(ILA2G) - PLATIN(ILA1G))
ZDY10 = PLATIN(ILA1G) - PLATIN(ILA0G)
ZDY21 = PLATIN(ILA2G) - PLATIN(ILA1G)
ZDY32 = PLATIN(ILA3G) - PLATIN(ILA2G)
C
C -----------------------------------------------------------------|
C Polynomial in x-direction.
C -----------------------------------------------------------------|
C
C Northern parallel
C
ZDLO1 = PDLO1(NEXT)
ZWXN1 = F2(ZWLSI1,ZWLSI7,ZDLO1,ZWLSI2,ZWLSI8)
ZWXN2 = F3(ZWLSI2,ZWLSI7,ZDLO1,ZWLSI1,ZWLSI8)
ZWXN3 = F4(ZWLSI8,ZWLSI7,ZDLO1,ZWLSI1,ZWLSI2)
ZWXN0 = 1.0 - ZWXN1 - ZWXN2 - ZWXN3
C
C Southern parallel
C
ZDLO2 = PDLO2(NEXT)
ZWXS1 = F2(ZWLSI3,ZWLSI9,ZDLO2,ZWLSI4,ZWLSI10)
ZWXS2 = F3(ZWLSI4,ZWLSI9,ZDLO2,ZWLSI3,ZWLSI10)
ZWXS3 = F4(ZWLSI10,ZWLSI9,ZDLO2,ZWLSI3,ZWLSI4)
ZWXS0 = 1.0 - ZWXS1 - ZWXS2 - ZWXS3
C
C -----------------------------------------------------------------|
C Polynomial in y-direction.
C -----------------------------------------------------------------|
C
ZWY1 = ZWLSI14*((1.0 + ZWLSI13*(ZDY + ZDY10 - 1.0)) *
X (1.0 + ZWLSI15*(ZDY - ZDY21 - 1.0)) *
X (1.0 + ZWLSI16*(ZDY - ZDY21 - ZDY32 - 1.0))) /
X ((1.0 + ZWLSI13*(ZDY10 - 1.0)) *
X (1.0 + ZWLSI15*( -ZDY21 - 1.0)) *
X (1.0 + ZWLSI16*( -ZDY21 - ZDY32 - 1.0)))
ZWY2 = ZWLSI15*((1.0 + ZWLSI13*(ZDY + ZDY10 - 1.0)) *
X (1.0 + ZWLSI14*(ZDY - 1.0)) *
X (1.0 + ZWLSI16*(ZDY - ZDY21 - ZDY32 - 1.0))) /
X ((1.0 + ZWLSI13*(ZDY10 + ZDY21 - 1.0)) *
X (1.0 + ZWLSI14*(ZDY21 - 1.0)) *
X (1.0 + ZWLSI16*( -ZDY32 - 1.0)))
ZWY3 = ZWLSI16*((1.0 + ZWLSI13*(ZDY + ZDY10 - 1.0)) *
X (1.0 + ZWLSI14*(ZDY - 1.0)) *
X (1.0 + ZWLSI15*(ZDY - ZDY21 - 1.0))) /
X ((1.0 + ZWLSI13*(ZDY10 + ZDY21 + ZDY32 - 1.0)) *
X (1.0 + ZWLSI14*(ZDY21 + ZDY32 - 1.0)) *
X (1.0 + ZWLSI15*(ZDY32 - 1.0)))
ZWY0 = 1.0 - ZWY1 - ZWY2 - ZWY3
C
C -----------------------------------------------------------------|
C Linear parts for extreme rows.
C -----------------------------------------------------------------|
C
C Northernmost
C
ZDLO = PDLO0(NEXT)
ZWXNN = ZWLSI6 * (1.0 + ZWLSI5 * (ZDLO - 1.0))
ZCXNN = 1.0 - ZWXNN
C
C Southernmost
C
ZDLO3 = PDLO3(NEXT)
ZWXSS = ZWLSI12 * (1.0 + ZWLSI11 * (ZDLO3 - 1.0))
ZCXSS = 1.0 - ZWXSS
C
C -----------------------------------------------------------------|
C Weights for 12 points interpolation.
C -----------------------------------------------------------------|
C
PWTS( 1,NEXT) = ZWXN1 * ZWY1
PWTS( 2,NEXT) = ZWXN2 * ZWY1
PWTS( 3,NEXT) = ZWXS1 * ZWY2
PWTS( 4,NEXT) = ZWXS2 * ZWY2
PWTS( 5,NEXT) = ZCXNN * ZWY0
PWTS( 6,NEXT) = ZWXNN * ZWY0
PWTS( 7,NEXT) = ZWXN0 * ZWY1
PWTS( 8,NEXT) = ZWXN3 * ZWY1
PWTS( 9,NEXT) = ZWXS0 * ZWY2
PWTS(10,NEXT) = ZWXS3 * ZWY2
PWTS(11,NEXT) = ZCXSS * ZWY3
PWTS(12,NEXT) = ZWXSS * ZWY3
C
GOTO 900
C
ENDIF
C
C -----------------------------------------------------------------|
C End of processing for current point in vector.
C -----------------------------------------------------------------|
C
900 CONTINUE
C
ENDDO
C
RETURN
END
|
