!
! $Id: grid_noro.F 2199 2015-02-09 08:59:05Z idelkadi $
!
c
c
      SUBROUTINE grid_noro(imdep, jmdep, xdata, ydata, zdata,
     .             imar, jmar, x, y,
     .             zphi,zmea,zstd,zsig,zgam,zthe,
     .             zpic,zval,mask)
c=======================================================================
c (F. Lott) (voir aussi z.x. Li, A. Harzallah et L. Fairhead)
c
c      Compute the Parameters of the SSO scheme as described in
c      LOTT & MILLER (1997) and LOTT(1999).
c      Target points are on a rectangular grid:
c      iim+1 latitudes including North and South Poles;
c      jjm+1 longitudes, with periodicity jjm+1=1.
c      aux poles.  At the poles the fields value is repeated
c      jjm+1 time.
c      The parameters a,b,c,d represent the limite of the target
c      gridpoint region. The means over this region are calculated
c      from USN data, ponderated by a weight proportional to the 
c      surface occupated by the data inside the model gridpoint area.
c      In most circumstances, this weight is the ratio between the
c      surface of the USN gridpoint area and the surface of the
c      model gridpoint area. 
c
c           (c)
c        ----d-----
c        | . . . .|
c        |        |
c     (b)a . * . .b(a)
c        |        |
c        | . . . .|
c        ----c-----
c           (d)
C=======================================================================
c INPUT:
c        imdep, jmdep: dimensions X and Y input field
c        xdata, ydata: coordinates X and Y input field
c        zdata: Input field
c        In this version it is assumed that the entry data come from
c        the USNavy dataset: imdep=iusn=2160, jmdep=jusn=1080.
c OUTPUT:
c        imar, jmar: dimensions X and Y Output field
c        x, y: ccordinates  X and Y Output field.
c             zmea:  Mean orographie   
c             zstd:  Standard deviation
c             zsig:  Slope
c             zgam:  Anisotropy
c             zthe:  Orientation of the small axis
c             zpic:  Maximum altitude
c             zval:  Minimum altitude
C=======================================================================

      IMPLICIT NONE 
      
      INTEGER,PARAMETER :: iusn=2160,jusn=1080,iext=216
      REAL,PARAMETER :: epsfra = 1.e-5
#include "dimensions.h"
	  REAL xusn(iusn+2*iext),yusn(jusn+2)	
      REAL zusn(iusn+2*iext,jusn+2)

      INTEGER imdep, jmdep
      REAL xdata(imdep),ydata(jmdep) 
      REAL zdata(imdep,jmdep)
c
      INTEGER imar, jmar
  
C INTERMEDIATE FIELDS  (CORRELATIONS OF OROGRAPHY GRADIENT)

      REAL ztz(iim+1,jjm+1),zxtzx(iim+1,jjm+1)
      REAL zytzy(iim+1,jjm+1),zxtzy(iim+1,jjm+1)
      REAL weight(iim+1,jjm+1)

C CORRELATIONS OF USN OROGRAPHY GRADIENTS

      REAL zxtzxusn(iusn+2*iext,jusn+2),zytzyusn(iusn+2*iext,jusn+2)
      REAL zxtzyusn(iusn+2*iext,jusn+2)
      REAL x(imar+1),y(jmar),zphi(imar+1,jmar)
      REAL zmea(imar+1,jmar),zstd(imar+1,jmar)
      REAL zmea0(imar+1,jmar) ! GK211005 (CG)
      REAL zsig(imar+1,jmar),zgam(imar+1,jmar),zthe(imar+1,jmar)
      REAL zpic(imar+1,jmar),zval(imar+1,jmar)
cxxx PB     integer mask(imar+1,jmar)
      real mask(imar+1,jmar), mask_tmp(imar+1,jmar)
      real num_tot(2200,1100),num_lan(2200,1100)
c
      REAL a(2200),b(2200),c(1100),d(1100)
      logical masque_lu
      INTEGER i,j,ii,jj
      REAL xpi, rad, zdeltay, masque
      REAL zdeltax, zlenx, zleny, xincr
      REAL zbordnor, zbordsud, weighy, zbordest, zbordoue, weighx
      REAL zllmmea, zllmstd, zllmsig, zllmgam, zllmpic, zllmval
      REAL zllmthe, zminthe
      REAL xk, xl, xm, xp, xq, xw
      REAL zmeanor, zmeasud, zstdnor, zstdsud, zsignor, zsigsud
      REAL zweinor, zweisud, zpicnor, zpicsud, zvalnor, zvalsud
c
      print *,' parametres de l orographie a l echelle sous maille' 
      xpi=acos(-1.)
      rad    = 6 371 229.
      zdeltay=2.*xpi/REAL(jusn)*rad
c
c utilise-t'on un masque lu?
c
      masque_lu = .true.
      if (maxval(mask) == -99999 .and. minval(mask) == -99999) then
        masque_lu= .false.
        masque = 0.0
      endif
      write(*,*)'Masque lu', masque_lu
c
c  quelques tests de dimensions:
c    
c
      if(iim.ne.imar) STOP 'Problem dim. x'
      if(jjm.ne.jmar-1) STOP 'Problem dim. y'
      IF (imar.GT.2200 .OR. jmar.GT.1100) THEN
         PRINT*, 'imar or jmar too big', imar, jmar
         CALL ABORT_GCM("GRID_NORO", "", 1)
      ENDIF

      IF(imdep.ne.iusn.or.jmdep.ne.jusn)then
         print *,' imdep or jmdep bad dimensions:',imdep,jmdep
         call abort_gcm("grid_noro", "", 1)
      ENDIF

      IF(imar+1.ne.iim+1.or.jmar.ne.jjm+1)THEN
        print *,' imar or jmar bad dimensions:',imar,jmar
        call abort_gcm("grid_noro", "", 1)
      ENDIF


c      print *,'xdata:',xdata
c      print *,'ydata:',ydata
c      print *,'x:',x
c      print *,'y:',y
c
C  EXTENSION OF THE USN DATABASE TO POCEED COMPUTATIONS AT
C  BOUNDARIES:
c
      DO j=1,jusn
        yusn(j+1)=ydata(j)
      DO i=1,iusn
        zusn(i+iext,j+1)=zdata(i,j)
        xusn(i+iext)=xdata(i)
      ENDDO
      DO i=1,iext
        zusn(i,j+1)=zdata(iusn-iext+i,j)
        xusn(i)=xdata(iusn-iext+i)-2.*xpi
        zusn(iusn+iext+i,j+1)=zdata(i,j)
        xusn(iusn+iext+i)=xdata(i)+2.*xpi
      ENDDO
      ENDDO

        yusn(1)=ydata(1)+(ydata(1)-ydata(2))
        yusn(jusn+2)=ydata(jusn)+(ydata(jusn)-ydata(jusn-1))
       DO i=1,iusn/2+iext
        zusn(i,1)=zusn(i+iusn/2,2)
        zusn(i+iusn/2+iext,1)=zusn(i,2)
        zusn(i,jusn+2)=zusn(i+iusn/2,jusn+1)
        zusn(i+iusn/2+iext,jusn+2)=zusn(i,jusn+1)
       ENDDO
c  
c COMPUTE LIMITS OF MODEL GRIDPOINT AREA
C     ( REGULAR GRID)
c
      a(1) = x(1) - (x(2)-x(1))/2.0
      b(1) = (x(1)+x(2))/2.0
      DO i = 2, imar
         a(i) = b(i-1)
         b(i) = (x(i)+x(i+1))/2.0
      ENDDO
      a(imar+1) = b(imar)
      b(imar+1) = x(imar+1) + (x(imar+1)-x(imar))/2.0

      c(1) = y(1) - (y(2)-y(1))/2.0
      d(1) = (y(1)+y(2))/2.0
      DO j = 2, jmar-1
         c(j) = d(j-1)
         d(j) = (y(j)+y(j+1))/2.0
      ENDDO
      c(jmar) = d(jmar-1)
      d(jmar) = y(jmar) + (y(jmar)-y(jmar-1))/2.0
c
c  initialisations:
c
      DO i = 1, imar+1
      DO j = 1, jmar
         weight(i,j) = 0.0
         zxtzx(i,j)  = 0.0
         zytzy(i,j)  = 0.0
         zxtzy(i,j)  = 0.0
         ztz(i,j)    = 0.0
         zmea(i,j)   = 0.0
         zpic(i,j)  =-1.E+10
         zval(i,j)  = 1.E+10
      ENDDO
      ENDDO
c
c  COMPUTE SLOPES CORRELATIONS ON USN GRID
c
         DO j = 1,jusn+2 
         DO i = 1, iusn+2*iext
            zytzyusn(i,j)=0.0
            zxtzxusn(i,j)=0.0
            zxtzyusn(i,j)=0.0
         ENDDO
         ENDDO


         DO j = 2,jusn+1 
            zdeltax=zdeltay*cos(yusn(j))
         DO i = 2, iusn+2*iext-1
            zytzyusn(i,j)=(zusn(i,j+1)-zusn(i,j-1))**2/zdeltay**2
            zxtzxusn(i,j)=(zusn(i+1,j)-zusn(i-1,j))**2/zdeltax**2
            zxtzyusn(i,j)=(zusn(i,j+1)-zusn(i,j-1))/zdeltay
     *                   *(zusn(i+1,j)-zusn(i-1,j))/zdeltax
         ENDDO
         ENDDO
c
c  SUMMATION OVER GRIDPOINT AREA
c 
      zleny=xpi/REAL(jusn)*rad
      xincr=xpi/2./REAL(jusn)
       DO ii = 1, imar+1
       DO jj = 1, jmar
       num_tot(ii,jj)=0.
       num_lan(ii,jj)=0.
c        PRINT *,' iteration ii jj:',ii,jj
         DO j = 2,jusn+1 
c         DO j = 3,jusn 
            zlenx=zleny*cos(yusn(j))
            zdeltax=zdeltay*cos(yusn(j))
            zbordnor=(c(jj)-yusn(j)+xincr)*rad
            zbordsud=(yusn(j)-d(jj)+xincr)*rad
            weighy=AMAX1(0.,
     *             amin1(zbordnor,zbordsud,zleny))
         IF(weighy.ne.0)THEN
         DO i = 2, iusn+2*iext-1
            zbordest=(xusn(i)-a(ii)+xincr)*rad*cos(yusn(j))
            zbordoue=(b(ii)+xincr-xusn(i))*rad*cos(yusn(j))
            weighx=AMAX1(0.,
     *             amin1(zbordest,zbordoue,zlenx))
            IF(weighx.ne.0)THEN
            num_tot(ii,jj)=num_tot(ii,jj)+1.0
            if(zusn(i,j).ge.1.)num_lan(ii,jj)=num_lan(ii,jj)+1.0
            weight(ii,jj)=weight(ii,jj)+weighx*weighy
            zxtzx(ii,jj)=zxtzx(ii,jj)+zxtzxusn(i,j)*weighx*weighy
            zytzy(ii,jj)=zytzy(ii,jj)+zytzyusn(i,j)*weighx*weighy
            zxtzy(ii,jj)=zxtzy(ii,jj)+zxtzyusn(i,j)*weighx*weighy
            ztz(ii,jj)  =ztz(ii,jj)  +zusn(i,j)*zusn(i,j)*weighx*weighy
c mean
            zmea(ii,jj) =zmea(ii,jj)+zusn(i,j)*weighx*weighy
c peacks
            zpic(ii,jj)=amax1(zpic(ii,jj),zusn(i,j))
c valleys
            zval(ii,jj)=amin1(zval(ii,jj),zusn(i,j))
            ENDIF
         ENDDO
         ENDIF
         ENDDO
       ENDDO
       ENDDO
c
c  COMPUTE PARAMETERS NEEDED BY THE LOTT & MILLER (1997) AND
C  LOTT (1999) SSO SCHEME.
c
      zllmmea=0.
      zllmstd=0.
      zllmsig=0.
      zllmgam=0.
      zllmpic=0.
      zllmval=0.
      zllmthe=0.
      zminthe=0.
c     print 100,' '
c100  format(1X,A1,'II JJ',4X,'H',8X,'SD',8X,'SI',3X,'GA',3X,'TH') 
       DO ii = 1, imar+1
       DO jj = 1, jmar
         IF (weight(ii,jj) .NE. 0.0) THEN
c  Mask
cXXX           if(num_lan(ii,jj)/num_tot(ii,jj).ge.0.5)then
cXXX             mask(ii,jj)=1
cXXX           else
cXXX             mask(ii,jj)=0
cXXX           ENDIF
             if (.not. masque_lu) then
               mask(ii,jj) = num_lan(ii,jj)/num_tot(ii,jj)
             endif
c  Mean Orography:
           zmea (ii,jj)=zmea (ii,jj)/weight(ii,jj)
           zxtzx(ii,jj)=zxtzx(ii,jj)/weight(ii,jj)
           zytzy(ii,jj)=zytzy(ii,jj)/weight(ii,jj)
           zxtzy(ii,jj)=zxtzy(ii,jj)/weight(ii,jj)
           ztz(ii,jj)  =ztz(ii,jj)/weight(ii,jj)
c  Standard deviation:
           zstd(ii,jj)=sqrt(AMAX1(0.,ztz(ii,jj)-zmea(ii,jj)**2))
         ELSE
            PRINT*, 'probleme,ii,jj=', ii,jj
         ENDIF
       ENDDO
       ENDDO

C CORRECT VALUES OF HORIZONTAL SLOPE NEAR THE POLES:

       DO ii = 1, imar+1
         zxtzx(ii,1)=zxtzx(ii,2)
         zxtzx(ii,jmar)=zxtzx(ii,jmar-1)
         zxtzy(ii,1)=zxtzy(ii,2)
         zxtzy(ii,jmar)=zxtzy(ii,jmar-1)
         zytzy(ii,1)=zytzy(ii,2)
         zytzy(ii,jmar)=zytzy(ii,jmar-1)
       ENDDO

C  FILTERS TO SMOOTH OUT FIELDS FOR INPUT INTO SSO SCHEME.

C  FIRST FILTER, MOVING AVERAGE OVER 9 POINTS.

       zmea0(:,:) = zmea(:,:) ! GK211005 (CG) on sauvegarde la topo non lissee
       CALL MVA9(zmea,iim+1,jjm+1)
       CALL MVA9(zstd,iim+1,jjm+1)
       CALL MVA9(zpic,iim+1,jjm+1)
       CALL MVA9(zval,iim+1,jjm+1)
       CALL MVA9(zxtzx,iim+1,jjm+1)
       CALL MVA9(zxtzy,iim+1,jjm+1) 
       CALL MVA9(zytzy,iim+1,jjm+1)
CXXX   Masque prenant en compte maximum de terre
CXXX  On seuil a 10% de terre de terre car en dessous les parametres de surface n'on
CXXX pas de sens (PB)
       mask_tmp= 0.0
       WHERE(mask .GE. 0.1) mask_tmp = 1.

       DO ii = 1, imar
       DO jj = 1, jmar
         IF (weight(ii,jj) .NE. 0.0) THEN
c  Coefficients K, L et M:
           xk=(zxtzx(ii,jj)+zytzy(ii,jj))/2.
           xl=(zxtzx(ii,jj)-zytzy(ii,jj))/2.
           xm=zxtzy(ii,jj)
           xp=xk-sqrt(xl**2+xm**2)
           xq=xk+sqrt(xl**2+xm**2)
           xw=1.e-8
           if(xp.le.xw) xp=0.
           if(xq.le.xw) xq=xw
           if(abs(xm).le.xw) xm=xw*sign(1.,xm)
c slope: 
cXXX           zsig(ii,jj)=sqrt(xq)*mask(ii,jj)
cXXXc isotropy:
cXXX           zgam(ii,jj)=xp/xq*mask(ii,jj)
cXXXc angle theta:
cXXX           zthe(ii,jj)=57.29577951*atan2(xm,xl)/2.*mask(ii,jj)
cXXX           zphi(ii,jj)=zmea(ii,jj)*mask(ii,jj)
cXXX           zmea(ii,jj)=zmea(ii,jj)*mask(ii,jj)
cXXX           zpic(ii,jj)=zpic(ii,jj)*mask(ii,jj)
cXXX           zval(ii,jj)=zval(ii,jj)*mask(ii,jj)
cXXX           zstd(ii,jj)=zstd(ii,jj)*mask(ii,jj)
CXX* PB modif pour maque de terre fractionnaire
c slope: 
           zsig(ii,jj)=sqrt(xq)*mask_tmp(ii,jj)
c isotropy:
           zgam(ii,jj)=xp/xq*mask_tmp(ii,jj)
c angle theta:
           zthe(ii,jj)=57.29577951*atan2(xm,xl)/2.*mask_tmp(ii,jj)
           ! GK211005 (CG) ne pas forcement lisser la topo
           ! zphi(ii,jj)=zmea(ii,jj)*mask_tmp(ii,jj)
           zphi(ii,jj)=zmea0(ii,jj)*mask_tmp(ii,jj)
           !
           zmea(ii,jj)=zmea(ii,jj)*mask_tmp(ii,jj)
           zpic(ii,jj)=zpic(ii,jj)*mask_tmp(ii,jj)
           zval(ii,jj)=zval(ii,jj)*mask_tmp(ii,jj)
           zstd(ii,jj)=zstd(ii,jj)*mask_tmp(ii,jj)
c          print 101,ii,jj,
c    *           zmea(ii,jj),zstd(ii,jj),zsig(ii,jj),zgam(ii,jj),
c    *           zthe(ii,jj)
c101  format(1x,2(1x,i2),2(1x,f7.1),1x,f7.4,2x,f4.2,1x,f5.1)     
         ELSE
c           PRINT*, 'probleme,ii,jj=', ii,jj
         ENDIF
      zllmmea=AMAX1(zmea(ii,jj),zllmmea)
      zllmstd=AMAX1(zstd(ii,jj),zllmstd)
      zllmsig=AMAX1(zsig(ii,jj),zllmsig)
      zllmgam=AMAX1(zgam(ii,jj),zllmgam)
      zllmthe=AMAX1(zthe(ii,jj),zllmthe)
      zminthe=amin1(zthe(ii,jj),zminthe)
      zllmpic=AMAX1(zpic(ii,jj),zllmpic)
      zllmval=AMAX1(zval(ii,jj),zllmval)
       ENDDO
       ENDDO
      print *,'  MEAN ORO:',zllmmea
      print *,'  ST. DEV.:',zllmstd
      print *,'  PENTE:',zllmsig
      print *,' ANISOTROP:',zllmgam
      print *,'  ANGLE:',zminthe,zllmthe	
      print *,'  pic:',zllmpic
      print *,'  val:',zllmval
      
C
c gamma and theta a 1. and 0. at poles
c
      DO jj=1,jmar
      zmea(imar+1,jj)=zmea(1,jj)
      zphi(imar+1,jj)=zphi(1,jj)
      zpic(imar+1,jj)=zpic(1,jj)
      zval(imar+1,jj)=zval(1,jj)
      zstd(imar+1,jj)=zstd(1,jj)
      zsig(imar+1,jj)=zsig(1,jj)
      zgam(imar+1,jj)=zgam(1,jj)
      zthe(imar+1,jj)=zthe(1,jj)
      ENDDO


      zmeanor=0.0
      zmeasud=0.0
      zstdnor=0.0
      zstdsud=0.0
      zsignor=0.0
      zsigsud=0.0
      zweinor=0.0
      zweisud=0.0
      zpicnor=0.0
      zpicsud=0.0                                   
      zvalnor=0.0
      zvalsud=0.0 

      DO ii=1,imar
      zweinor=zweinor+              weight(ii,   1)
      zweisud=zweisud+              weight(ii,jmar)
      zmeanor=zmeanor+zmea(ii,   1)*weight(ii,   1)
      zmeasud=zmeasud+zmea(ii,jmar)*weight(ii,jmar)
      zstdnor=zstdnor+zstd(ii,   1)*weight(ii,   1)
      zstdsud=zstdsud+zstd(ii,jmar)*weight(ii,jmar)
      zsignor=zsignor+zsig(ii,   1)*weight(ii,   1)
      zsigsud=zsigsud+zsig(ii,jmar)*weight(ii,jmar)
      zpicnor=zpicnor+zpic(ii,   1)*weight(ii,   1)
      zpicsud=zpicsud+zpic(ii,jmar)*weight(ii,jmar)
      zvalnor=zvalnor+zval(ii,   1)*weight(ii,   1)
      zvalsud=zvalsud+zval(ii,jmar)*weight(ii,jmar)
      ENDDO

      DO ii=1,imar+1
      zmea(ii,   1)=zmeanor/zweinor
      zmea(ii,jmar)=zmeasud/zweisud
      zphi(ii,   1)=zmeanor/zweinor
      zphi(ii,jmar)=zmeasud/zweisud
      zpic(ii,   1)=zpicnor/zweinor
      zpic(ii,jmar)=zpicsud/zweisud
      zval(ii,   1)=zvalnor/zweinor
      zval(ii,jmar)=zvalsud/zweisud
      zstd(ii,   1)=zstdnor/zweinor
      zstd(ii,jmar)=zstdsud/zweisud
      zsig(ii,   1)=zsignor/zweinor
      zsig(ii,jmar)=zsigsud/zweisud
      zgam(ii,   1)=1.
      zgam(ii,jmar)=1.
      zthe(ii,   1)=0.
      zthe(ii,jmar)=0.
      ENDDO

      RETURN
      END

      SUBROUTINE MVA9(X,IMAR,JMAR)
      IMPLICIT NONE
C MAKE A MOVING AVERAGE OVER 9 GRIDPOINTS OF THE X FIELDS
      INTEGER IMAR,JMAR
      REAL X(IMAR,JMAR),XF(IMAR,JMAR)
      real WEIGHTpb(-1:1,-1:1)
      INTEGER I,J,IS,JS
      REAL SUM


      SUM=0.
      DO IS=-1,1
        DO JS=-1,1
          WEIGHTpb(IS,JS)=1./REAL((1+IS**2)*(1+JS**2))
          SUM=SUM+WEIGHTpb(IS,JS)
        ENDDO
      ENDDO
      
c     WRITE(*,*) 'MVA9 ', IMAR, JMAR
c     WRITE(*,*) 'MVA9 ', WEIGHTpb
c     WRITE(*,*) 'MVA9 SUM ', SUM
      DO IS=-1,1
        DO JS=-1,1
          WEIGHTpb(IS,JS)=WEIGHTpb(IS,JS)/SUM
        ENDDO
      ENDDO

      DO J=2,JMAR-1
        DO I=2,IMAR-1
          XF(I,J)=0.
          DO IS=-1,1
            DO JS=-1,1
              XF(I,J)=XF(I,J)+X(I+IS,J+JS)*WEIGHTpb(IS,JS)
            ENDDO
          ENDDO
        ENDDO
      ENDDO

      DO J=2,JMAR-1
        XF(1,J)=0.
        IS=IMAR-1
        DO JS=-1,1 
          XF(1,J)=XF(1,J)+X(IS,J+JS)*WEIGHTpb(-1,JS)
        ENDDO
        DO IS=0,1 
          DO JS=-1,1 
            XF(1,J)=XF(1,J)+X(1+IS,J+JS)*WEIGHTpb(IS,JS)
          ENDDO
        ENDDO
        XF(IMAR,J)=XF(1,J)
      ENDDO

      DO I=1,IMAR
        XF(I,1)=XF(I,2)
        XF(I,JMAR)=XF(I,JMAR-1)
      ENDDO

      DO I=1,IMAR
        DO J=1,JMAR
          X(I,J)=XF(I,J)
        ENDDO
      ENDDO

      RETURN
      END