source: trunk/SRC/Computation/div.pro

;+
;
; @file_comments
; compute the horizontal divergence of a vectors field located on Arakawa C-grid.
;
; @categories
; Calculation
;
; @param UU
; Matrix representing the zonal coordinates (at U point) of a field of vectors
; A 2D (xy), 3D (xyz or yt) or a structure readable by <pro>litchamp</pro> and containing
; a 2D (xy), 3D (xyz or yt) array (4D case is not coded yet).
; note that the dimension of the array must suit the domain dimension.
;
; @param VV
; Matrix representing the meridional coordinates (at V point) of a field of vectors
; A 2D (xy), 3D (xyz or yt) or a structure readable by <pro>litchamp</pro> and containing
; a 2D (xy), 3D (xyz or yt) array (4D case is not coded yet).
; note that the dimension of the array must suit the domain dimension.
;
; @keyword DIREC {type=scalar string}
; Use if you want to call <pro>moyenne</pro> or
; <pro>grossemoyenne</pro> after the div computation
; (stupid ?) with a mean done in the DIREC direction
;
; @keyword MILLION {default=0}{type=scalar: 0 or 1}
; Activate to multiply returned array by 1.e6
;
; @keyword _EXTRA
; Used to declare that this routine accepts inherited keywords
;
; @returns
; the divergence of the input data (with the same size) located at T
;point (see restrictions).
;
; @uses
; <pro>cm_4cal</pro>
; <pro>cm_4data</pro>
; <pro>cm_4mesh</pro>
;
; @restrictions
;
; - Works only for Arakawa C-grid.
; - UU must be on U grid, VV must be on V grid
; - 4D case is not coded yet
; - the common variable jpt is used to differ xyz (jpt=1) and xyt (jpt\=1) cases.
; - U and V arrays are cut in the same geographic domain. Because of the shift between
;   T, U, V and F grids, it is possible that these two arrays do not have the same
;   size and refer to different indexes. In this case, arrays are re-cut on
;   common indexes. To avoid these re-cuts, use the keyword /memeindice in
; <pro>domdef</pro>
; - When computing the divergence, we update, vargrid, varname, varunits and the
;   grid position parameters (firstxt, lastxt, nxt, firstyt, lastyt, nyt).
; - points that cannot be computed (domain boundaries, coastline) are set to NaN
;
; @examples
;
;   IDL> \@tst_initorca2
;   IDL> plt, div(dist(jpi,jpj), dist(jpi,jpj))
;
; @history
; Guillaume Roullet (grlod\@ipsl.jussieu.fr): creation; spring 1998
; Sebastien Masson (smasson\@lodyc.jussieu.fr)
; adaptation to work with a reduce domain; 12/1/2000
;
; @version
; $Id$
;
; @todo
; code the 4D case
;
;-
FUNCTION div, uu, vv, DIREC=direc, MILLION=million, _EXTRA=ex
;
  compile_opt idl2, strictarrsubs
;
@cm_4cal                        ; for jpt
@cm_4data                       ; for varname, vargrid, vardate, varunit, valmask
@cm_4mesh
;
  time1 = systime(1)          ; for key_performance
;
  IF finite(glamu[0])*finite(gphiu[0])*finite(glamv[0])*finite(gphiv[0]) EQ 0 THEN $
     return, report(['This version of div is based on Arakawa C-grid.' $
                     , 'U and V grids must therefore be defined'])
;
  gr = litchamp(uu, /grid)
  IF gr NE '' THEN BEGIN
    IF gr NE 'U' THEN return, report('the first parameter is not located on U grid, but on '+ strtrim(gr, 2) +'grid')
  ENDIF
  gr = litchamp(vv, /grid)
  IF gr NE '' THEN BEGIN
    IF gr NE 'V' THEN return, report('the second parameter is not located on V grid, but on '+ strtrim(gr, 2) +'grid')
  ENDIF
  u = litchamp(uu)
  v = litchamp(vv)
;
  szu = size(u)
  szv = size(v)

  if szu[0] NE szv[0] then return, report('U and V input data must have the same number of dimensions')

;------------------------------------------------------------
; We find common points between U and V
;------------------------------------------------------------
  indicexu = (lindgen(jpi))[firstxu:firstxu+nxu-1]
  indicexv = (lindgen(jpi))[firstxv:firstxv+nxv-1]
  indicex = inter(indicexu, indicexv)
  indiceyu = (lindgen(jpj))[firstyu:firstyu+nyu-1]
  indiceyv = (lindgen(jpj))[firstyv:firstyv+nyv-1]
  indicey = inter(indiceyu, indiceyv)
  nx = n_elements(indicex)
  ny = n_elements(indicey)
  indice2d = lindgen(jpi, jpj)
  indice2d = indice2d[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1]
;----------------------------------------------------------------------------
  vargrid = 'T'
  varname = 'div'
  IF keyword_set(million) THEN varunits = '1.e6*'+varunit+'/m' ELSE varunits = varunit+'/m'
  IF keyword_set(million) THEN scale = 1.e6 ELSE scale = 1.
  if n_elements(valmask) EQ 0 THEN valmask = 1.e20
  firstxt = indicex[0] & lastxt = indicex[0]+nx-1 & nxt = nx
  firstyt = indicey[0] & lastyt = indicey[0]+ny-1 & nyt = ny
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
  case 1 of
;----------------------------------------------------------------------------
;xyz
;----------------------------------------------------------------------------
    szu[0] EQ 3 AND jpt EQ 1:BEGIN
;------------------------------------------------------------
; extraction of U and V on the appropriated domain
;------------------------------------------------------------
      case 1 of
        szu[1] EQ nxu AND szu[2] EQ nyu AND $
           szv[1] EQ nxv AND szv[2] EQ nyv:BEGIN
          case 1 of
            nxu NE nx:if indicex[0] EQ firstxu then u = u[0:nx-1, *, *] ELSE u = u[1: nx, *, *]
            nxv NE nx:if indicex[0] EQ firstxv then v = v[0:nx-1, *, *] ELSE v = v[1: nx, *, *]
            nyu NE ny:if indicey[0] EQ firstyu then u = u[*, 0:ny-1, *] ELSE u = u[*, 1: ny, *]
            nyv NE ny:if indicey[0] EQ firstyv then v = v[*, 0:ny-1, *] ELSE v = v[*, 1: ny, *]
            ELSE :
          endcase
        END
        szu[1] EQ jpi AND szu[2] EQ jpj AND $
           szv[1] EQ jpi AND szv[2] EQ jpj:BEGIN
          u = u[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *]
          v = v[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *]
        END
        ELSE:return $
           , report(['We cannot find re-cut on common indexes (see restriction un the header.).' $
                     , 'To avoid this problem, read the full domain' $
                     , 'or use the keyword /memeindice in domdef when defining the zoom area'])
      ENDCASE
;------------------------------------------------------------
; divergence computation
;------------------------------------------------------------
      zu = (e2u[indice2d])[*]#replicate(1., nzt)
      landu = where((umask())[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, firstzt:lastzt] EQ 0)
      if landu[0] NE -1 then zu[temporary(landu)] = !values.f_nan
      zu = temporary(u) * temporary(zu)
;
      zv = (e1v[indice2d])[*]#replicate(1., nzt)
      landv = where((vmask())[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, firstzt:lastzt] EQ 0)
      if landv[0] NE -1 then zv[temporary(landv)] = !values.f_nan
      zv = temporary(v) * temporary(zv)
;
      zdiv = (scale / (e1t[indice2d]*e2t[indice2d]))[*]#replicate(1., nzt)
      zdiv = ( zu - shift(zu, 1, 0, 0) + zv - shift(zv, 0, 1, 0) ) * temporary(zdiv)
;------------------------------------------------------------
; Edging put at !values.f_nan
;------------------------------------------------------------
      if  NOT keyword_set(key_periodic) OR nx NE jpi then begin
        zdiv[0, *, *] = !values.f_nan
        zdiv[nx-1, *, *] = !values.f_nan
      endif
      zdiv[*, 0, *] = !values.f_nan
      zdiv[*, ny-1, *] = !values.f_nan
;
      land = where(tmask[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, firstzt:lastzt] EQ 0)
      if land[0] NE -1 then zdiv[temporary(land)] = valmask
      if keyword_set(direc) then  zdiv = moyenne(zdiv, direc, /nan)
    END
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
;xyt
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
    szu[0] EQ 3 AND jpt GT 1:BEGIN
;------------------------------------------------------------
; extraction of U and V on the appropriated domain
;------------------------------------------------------------
      case 1 of
        szu[1] EQ nxu AND szu[2] EQ nyu AND $
           szv[1] EQ nxv AND szv[2] EQ nyv:BEGIN
          case 1 of
            nxu NE nx:if indicex[0] EQ firstxu then u = u[0:nx-1, *, *] ELSE u = u[1: nx, *, *]
            nxv NE nx:if indicex[0] EQ firstxv then v = v[0:nx-1, *, *] ELSE v = v[1: nx, *, *]
            nyu NE ny:if indicey[0] EQ firstyu then u = u[*, 0:ny-1, *] ELSE u = u[*, 1: ny, *]
            nyv NE ny:if indicey[0] EQ firstyv then v = v[*, 0:ny-1, *] ELSE v = v[*, 1: ny, *]
            ELSE :
          endcase
        END
        szu[1] EQ jpi AND szu[2] EQ jpj AND $
           szv[1] EQ jpi AND szv[2] EQ jpj:BEGIN
          u = u[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *]
          v = v[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *]
        END
        ELSE:return, -1
      endcase
;------------------------------------------------------------
; divergence computation
;------------------------------------------------------------
      zu = e2u[indice2d]
      landu = where((umask())[indice2d+jpi*jpj*firstzt] EQ 0)
      if landu[0] NE -1 then zu[temporary(landu)] = !values.f_nan
      zu = (temporary(zu))[*]#replicate(1., jpt)
      zu = temporary(u) * temporary(zu)
;
      zv = e1v[indice2d]
      landv = where((vmask())[indice2d+jpi*jpj*firstzt] EQ 0)
      if landv[0] NE -1 then zv[temporary(landv)] = !values.f_nan
      zv = (temporary(zv))[*]#replicate(1., jpt)
      zv = temporary(v) * temporary(zv)
;
      zdiv = (scale / (e1t[indice2d]*e2t[indice2d]))[*]#replicate(1., jpt)
      zdiv = ( zu - shift(zu, 1, 0, 0) + zv - shift(zv, 0, 1, 0) ) * temporary(zdiv)
;------------------------------------------------------------
; Edging put at !values.f_nan
;------------------------------------------------------------
      if  NOT keyword_set(key_periodic) OR nx NE jpi then begin
        zdiv[0, *, *] = !values.f_nan
        zdiv[nx-1, *, *] = !values.f_nan
      endif
      zdiv[*, 0, *] = !values.f_nan
      zdiv[*, ny-1, *] = !values.f_nan
;
      land = where(tmask[indice2d+jpi*jpj*firstzt] EQ 0, cnt)
      if land[0] NE -1 then BEGIN
        land = (temporary(land))#replicate(1L, jpt) + replicate(1L, cnt)#(nx*ny*lindgen(jpt))
        zdiv[temporary(land)] = valmask
      ENDIF
      if keyword_set(direc) then  zdiv = grossemoyenne(zdiv, direc, /nan)
    END
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
;xyzt
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
    szu[0] EQ 4:BEGIN
      return, report('Case not coded contact saxo team or make a do loop!')
    END
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
;xy
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
    szu[0] EQ 2:BEGIN
;------------------------------------------------------------
; extraction of U and V on the appropriated domain
;------------------------------------------------------------
      case 1 of
        szu[1] EQ nxu AND szu[2] EQ nyu AND $
           szv[1] EQ nxv AND szv[2] EQ nyv:BEGIN
          case 1 of
            nxu NE nx:if indicex[0] EQ firstxu then u = u[0:nx-1, *] ELSE u = u[1: nx, *]
            nxv NE nx:if indicex[0] EQ firstxv then v = v[0:nx-1, *] ELSE v = v[1: nx, *]
            nyu NE ny:if indicey[0] EQ firstyu then u = u[*, 0:ny-1] ELSE u = u[*, 1: ny]
            nyv NE ny:if indicey[0] EQ firstyv then v = v[*, 0:ny-1] ELSE v = v[*, 1: ny]
            ELSE :
          endcase
        END
        szu[1] EQ jpi AND szu[2] EQ jpj AND $
           szv[1] EQ jpi AND szv[2] EQ jpj:BEGIN
          u = u[indice2d]
          v = v[indice2d]
        END
        ELSE:return, -1
      endcase
;------------------------------------------------------------
; divergence computation
;------------------------------------------------------------
      zu = e2u[indice2d]
      landu = where((umask())[indice2d+jpi*jpj*firstzt] EQ 0)
      if landu[0] NE -1 then zu[temporary(landu)] = !values.f_nan
      zu = temporary(u) * temporary(zu)

      zv = e1v[indice2d]
      landv = where((vmask())[indice2d+jpi*jpj*firstzt] EQ 0)
      if landv[0] NE -1 then zv[temporary(landv)] = !values.f_nan
      zv = temporary(v) * temporary(zv)

      zdiv = scale / (e1t[indice2d]*e2t[indice2d])
      zdiv = ( zu - shift(zu, 1, 0) + zv - shift(zv, 0, 1) ) * temporary(zdiv)
;------------------------------------------------------------
; Edging put at !values.f_nan
;------------------------------------------------------------
      if  NOT keyword_set(key_periodic) OR nx NE jpi then begin
        zdiv[0, *] = !values.f_nan
        zdiv[nx-1, *] = !values.f_nan
      endif
      zdiv[*, 0] = !values.f_nan
      zdiv[*, ny-1] = !values.f_nan
;
      land =  where(tmask[indice2d+jpi*jpj*firstzt] EQ 0)
      if land[0] NE -1 then zdiv[temporary(land)] = valmask
      if keyword_set(direc) then zdiv = moyenne(zdiv, direc, /nan)
    END
;----------------------------------------------------------------------------
;----------------------------------------------------------------------------
    ELSE:return, report('U and V input arrays must have 2, 3 or 4 dimensions')
  ENDCASE
;------------------------------------------------------------
  if keyword_set(key_performance) THEN print, 'time div', systime(1)-time1

  return, zdiv
end