! source file: /sfs/fs6/home-geomar/smomw258/UVic_ESCM/2.9/source/common/util.F function indp (value, array, ia) !======================================================================= ! indp = index of nearest data point within "array" corresponding to ! "value". ! inputs: ! value = arbitrary data...same units as elements in "array" ! array = array of data points (must be monotonically increasing) ! ia = dimension of "array" ! output: ! indp = index of nearest data point to "value" ! if "value" is outside the domain of "array" then indp = 1 ! or "ia" depending on whether array(1) or array(ia) is ! closest to "value" ! note: if "array" is dimensioned array(0:ia) in the calling ! program, then the returned index should be reduced ! by one to account for the zero base. ! example: ! let model depths be defined by the following: ! parameter (km=5) ! dimension z(km) ! data z /5.0, 10.0, 50.0, 100.0, 250.0/ ! k1 = indp (12.5, z, km) ! k2 = indp (0.0, z, km) ! k1 would be set to 2, & k2 would be set to 1 so that ! z(k1) would be the nearest data point to 12.5 and z(k2) would ! be the nearest data point to 0.0 !======================================================================= implicit none integer ia, i, ii, indp real value include "stdunits.h" real array(ia) do i=2,ia if (array(i) .lt. array(i-1)) then write (stdout,*) & ' => Error: array must be monotonically increasing in "indp"' &, ' when searching for nearest element to value=',value write (stdout,*) ' array(i) < array(i-1) for i=',i write (stdout,*) ' array(i) for i=1..ia follows:' do ii=1,ia write (stdout,*) 'i=',ii, ' array(i)=',array(ii) enddo stop '=>indp' endif enddo if (value .lt. array(1) .or. value .gt. array(ia)) then if (value .lt. array(1)) indp = 1 if (value .gt. array(ia)) indp = ia return else do i=2,ia if (value .le. array(i)) then indp = i if (array(i)-value .gt. value-array(i-1)) indp = i-1 go to 101 endif enddo 101 continue endif return end subroutine ftc (f, if, jf, xf, yf, c, ic, jc, istart, iend &, jstart, jend, xc, yc, init, work, lenw) !======================================================================= ! "ftc" is a mnemonic for "fine to coarse". ! obtain a coarse grid representation of a fine grid dataset by area ! averaging grid box values on the fine grid which overlay coarse ! grid boxes. note: the coarse grid boxes do not have to contain an ! integral number of fine grid boxes. ! inputs: ! f = data on fine grid ! if = inner dimension of "f" ! jf = outer dimension of "f" ! xf = coordinates for inner dimension of "f" (eg: longitudes) ! yf = coordinates for outer dimension of "f" (eg: latitudes) ! ic = inner dimension of coarse grid "c" ! jc = outer dimension of coarse grid "c" ! istart = starting index along inner dimension of "c" for which ! averaged values are desired ! iend = ending index along inner dimension of "c" for which ! averaged values are desired ! jstart = starting index along outer dimension of "c" for which ! averaged values are desired ! jend = ending index along outer dimension of "c" for which ! averaged values are desired ! xc = coordinates for inner dimension of "c" (eg: longitudes) ! yc = coordinates for outer dimension of "c" (eg: latitudes) ! init = initialize the averaging factors ! "init" should be set = 1 on the first call. ! "init" <> 1 uses the previously computed factors stored ! in "work" array. ! work = work array of averaging factors when "init" <> 1 ! (previously calculated by "ftc" when "init" = 1) ! lenw = size of work array. lenw should be >= 9*max(if,jf) ! output: ! c = coarse grid average of "f" defined over ! ((c(i,j),i=istart,iend),j=jstart,jend) ! work = work array of averaging factors when "init" = 1 ! restrictions: ! fine and coarse grids are assumed rectangular with "xf" and "xc" ! having the same units. "yf" and "yc" must also have the same units ! the coarse domain xc(istart)...xc(iend) must be within ! the fine domain xf(1)...xf(if). similarly, ! yc(jstart)...yc(jend) must be within yf(1)...yf(jf). all ! coordinates must be strictly monotonically increasing. !======================================================================= include "stdunits.h" logical error, show_coord parameter (len=10000, p5=0.5, c0=0.0) dimension iso(0:len), ieo(0:len), jso(0:len), jeo(0:len) &, dx(0:len,2), dy(0:len,2), edgecx(0:len), edgecy(0:len) &, edgefx(0:len), edgefy(0:len) dimension f(if,jf), xf(if), yf(jf) dimension c(ic,jc), xc(ic), yc(jc) dimension work(lenw) write (stdout,*) ' ' write (stdout,*) & ' Averaging data from "fine" to "coarse" grid' !----------------------------------------------------------------------- ! initialize weights or use previously calculated weights !----------------------------------------------------------------------- if (init .eq. 1) then error = .false. write (stdout,*) & ' (initializing the averaging weights)' write (stdout,*) ' ' ! test to verify that array sizes do not exceed limits if (if .gt. len .or. jf .gt. len) then i = max(if,jf) write (stdout,*) '=>Error: increase "len" in "ftc" to ',i stop '=>ftc' endif if (lenw .lt. 9*max(if,jf)) then write (stdout,*) '=>Error: increase size of "work" array', & ' to at least ',9*max(if,jf),' for calls to "ftc"' error = .true. endif ! verify that the "coarse" grid lies within the "fine" grid if (xf(1) .gt. xc(istart) .or. xf(if) .lt. xc(iend)) then write (stdout,*) & '=>Warning: Coarse grid "xc" is outside "fine" grid "xf".' if (xf(1) .gt. xc(istart)) then write (stdout,*) ' xc(',istart,') .lt. xf(1)' endif if (xf(if) .lt. xc(iend)) then write (stdout,*) ' xc(',iend,') .gt. xf(',if,')' endif endif if (yf(1) .gt. yc(jstart) .or. yf(jf) .lt. yc(jend)) then write (stdout,*) & '=>Warning: Coarse grid "yc" is outside "fine" grid "yf".' if (yf(1) .gt. yc(jstart)) then write (stdout,*) ' yc(',jstart,') .lt. yf(1)' endif if (yf(jf) .lt. yc(jend)) then write (stdout,*) ' yc(',jend,') .gt. yf(',jf,')' endif endif ! construct edges of "coarse" grid boxes do i=1,ic-1 edgecx(i) = p5*(xc(i) + xc(i+1)) enddo edgecx(0) = xc(1) - (edgecx(1) - xc(1)) edgecx(ic) = xc(ic) + (xc(ic) - edgecx(ic-1)) do j=1,jc-1 edgecy(j) = p5*(yc(j) + yc(j+1)) enddo edgecy(0) = yc(1) - (edgecy(1) - yc(1)) edgecy(jc) = yc(jc) + (yc(jc) - edgecy(jc-1)) ! construct edges of "fine" grid boxes do i=1,if-1 edgefx(i) = p5*(xf(i) + xf(i+1)) enddo edgefx(0) = xf(1) - (edgefx(1) - xf(1)) edgefx(if) = xf(if) + (xf(if) - edgefx(if-1)) do j=1,jf-1 edgefy(j) = p5*(yf(j) + yf(j+1)) enddo edgefy(0) = yf(1) - (edgefy(1) - yf(1)) edgefy(jf) = yf(jf) + (yf(jf) - edgefy(jf-1)) ! calculate "dx" and "dy" for the "fine" grid boxes do i=1,if dx(i,1) = edgefx(i) - edgefx(i-1) dx(i,2) = dx(i,1) enddo dx(0,1) = dx(1,1) dx(0,2) = dx(1,2) do j=1,jf dy(j,1) = edgefy(j) - edgefy(j-1) dy(j,2) = dy(j,1) enddo dy(0,1) = dy(1,1) dy(0,2) = dy(1,2) ! modify "dx" and "dy" for possibly partial "fine" grid boxes ! near the edges of each coarse grid box. ! "ii" is the index of the fine grid box which contains the ! eastern edge of coarse grid box with index "i". ! dx(ii,1) is the portion of the fine grid box to the west of the ! edge and dx(ii,2) is the portion to the east. similarly, ! dy(jj,1) is to the south and dy(jj,2) is to the north of the ! northern edge of coarse box with index "j". ! note: edgefx and edgefy are zero based and need the -1 when ! using "indp" do i=0,ic ii = indp (edgecx(i), edgefx, if+1) - 1 frac = abs(edgecx(i) - edgefx(ii)) if (edgefx(ii) .lt. edgecx(i)) then ii = ii + 1 dx(ii,2) = (edgefx(min(if,ii)) - edgefx(ii-1)) - frac dx(ii,1) = frac else dx(ii,2) = frac dx(ii,1) = (edgefx(ii) - edgefx(max(ii-1,0))) - frac endif ieo(i) = min(if,max(1,ii)) enddo do i=1,ic iso(i) = max(1,ieo(i-1)) enddo iso(0) = ieo(0) do j=0,jc jj = indp (edgecy(j), edgefy, jf+1) - 1 frac = abs(edgecy(j) - edgefy(jj)) if (edgefy(jj) .lt. edgecy(j)) then jj = jj + 1 dy(jj,2) = (edgefy(min(jf,jj)) - edgefy(jj-1)) - frac dy(jj,1) = frac else dy(jj,2) = frac dy(jj,1) = (edgefy(jj) - edgefy(max(jj-1,0))) - frac endif jeo(j) = min(jf,max(1,jj)) enddo do j=1,jc jso(j) = max(1,jeo(j-1)) enddo jso(0) = jeo(0) ! store the weights into the "work" array indx = 1 do j=0,jc work(indx) = jso(j) work(indx+1) = jeo(j) indx = indx + 2 enddo do i=0,ic work(indx) = iso(i) work(indx+1) = ieo(i) indx = indx + 2 enddo do j=0,jf work(indx) = dy(j,1) work(indx+1) = dy(j,2) indx = indx + 2 enddo do i=0,if work(indx) = dx(i,1) work(indx+1) = dx(i,2) indx = indx + 2 enddo ! verify that coarse grid is coarser than the fine grid do j=jstart,jend if ((jso(j) .eq. jso(j+1)) .and. (yc(j) .ge. yf(1)) & .and. (yc(j) .le. yf(jf))) then write (stdout,*) & '=>Warning: "Coarse" grid is finer than "fine" grid' &, ' near yf(',jso(j),') =',yf(jso(j)) &, ' (average may not be accurate)' endif enddo do i=istart,iend if ((iso(i) .eq. iso(i+1)) .and. (xc(i) .ge. xf(1)) & .and. (xc(i) .le. xf(if))) then write (stdout,*) & '=>Warning: "Coarse" grid is finer than "fine" grid' &, ' near xf(',iso(i),') = ',xf(iso(i)) &, ' (average may not be accurate)' endif enddo show_coord = .false. if (error .or. show_coord) then write (stdout,*) & ' Indices for averaging fine grid to coarse grid:' write (stdout,*) & ' (fractional grid boxes are accounted for)' write (stdout,8700) write (stdout,9000) (m,iso(m),ieo(m),m=istart,iend) write (stdout,*) ' ' write (stdout,*) ' Coordinates for coarse grid points "xc" =' write (stdout,8500) xc write (stdout,*) ' Coordinates for fine grid points "xf" =' write (stdout,8500) xf write (stdout,8800) write (stdout,9000) (m,jso(m),jeo(m),m=jstart,jend) write (stdout,*) ' ' write (stdout,*) ' Coordinates for coarse grid points "yc" =' write (stdout,8500) yc write (stdout,*) ' Coordinates for fine grid points "yf" =' write (stdout,8500) yf endif if (error) stop '=>ftc' else write (stdout,*) & ' (using previously initialized averaging weights)' write (stdout,*) ' ' ! extract the weights from the "work" array indx = 1 do j=0,jc jso(j) = nint(work(indx)) jeo(j) = nint(work(indx+1)) indx = indx + 2 enddo do i=0,ic iso(i) = nint(work(indx)) ieo(i) = nint(work(indx+1)) indx = indx + 2 enddo do j=0,jf dy(j,1) = work(indx) dy(j,2) = work(indx+1) indx = indx + 2 enddo do i=0,if dx(i,1) = work(indx) dx(i,2) = work(indx+1) indx = indx + 2 enddo endif !----------------------------------------------------------------------- ! average the "fine" grid to the "coarse" grid !----------------------------------------------------------------------- do m=jstart,jend do i=istart,iend weight = c0 sum = c0 do j=jso(m),jeo(m) indy = 2 if (j .eq. jeo(m)) indy = 1 wty = dy(j,indy) do ii=iso(i),ieo(i) indx = 2 if (ii .eq. ieo(i)) indx = 1 area = dx(ii,indx)*wty weight = weight + area sum = sum + f(ii,j)*area enddo enddo c(i,m) = sum/weight enddo enddo return 8500 format (1x,10g11.4) 8700 format (/' Along the 1st dimension, the form is (Coarse grid' &,' point "xc": range of fine grid points "xf" to average)'/) 8800 format (/' Along the 2nd dimension, the form is (Coarse grid' &,' point "yc": range of fine grid points "yf" to average)'/) 9000 format (5(1x,'(',i4,': ',i4,' to ',i4,')'),/) end subroutine ctf (c, ic, jc, xc, yc, f, if, jf, istart, iend &, jstart, jend, xf, yf, init, work, lenw) !======================================================================= ! "ctf" is a mnemonic for "coarse to fine". ! obtain a fine grid representation of a coarse grid dataset by ! linear interpolation of grid box values on the coarse grid to grid ! boxes on the fine grid. ! inputs: ! c = coarse grid data ! ic = inner dimension of coarse grid "c" ! jc = outer dimension of coarse grid "c" ! xc = coordinates for inner dimension of "c" (eg: longitudes) ! yc = coordinates for outer dimension of "c" (eg: latitudes) ! if = inner dimension of "f" ! jf = outer dimension of "f" ! xf = coordinates for inner dimension of "f" (eg: longitudes) ! yf = coordinates for outer dimension of "f" (eg: latitudes) ! istart = starting index along inner dimension of "f" for which ! interpolated values are desired ! iend = ending index along inner dimension of "f" for which ! interpolated values are desired ! jstart = starting index along outer dimension of "f" for which ! interpolated values are desired ! jend = ending index along outer dimension of "f" for which ! interpolated values are desired ! init = initialize the interpolation factors ! "init" should be set = 1 on the first call. ! "init" <> 1 uses the previously computed factors stored ! in "work" array. ! work = work array of interpolation factors when "init" <> 1 ! (previously calculated by "ctf" when "init" = 1) ! lenw = size of work array. lenw should be >= 8*max(if,jf) ! output: ! f = interpolated data on fine grid defined over ! ((f(i,j),i=istart,iend),j=jstart,jend) ! work = work array of interpolation factors when "init" = 1 ! restrictions: ! fine and coarse grids are assumed rectangular with "xf" and "xc" ! having the same units. "yf" and "yc" must also have the same units ! the fine domain xf(istart)...xf(iend) must be within ! the coarse domain xc(1)...xc(ic). Similarly, ! and yc(js)...yc(je) must be within yf(1)...yf(jf). all coordinates ! must be strictly monotonically increasing. !======================================================================= include "stdunits.h" logical error, show_coord parameter (len=10000, p5=0.5, c0=0.0) dimension indxi(len), indxj(len), dnorth(len), dsouth(len) &, deast(len), dwest(len), width(len), height(len) dimension f(if,jf), xf(if), yf(jf) dimension c(ic,jc), xc(ic), yc(jc) dimension work(lenw) write (stdout,*) ' ' write (stdout,*) & ' Interpolating data from "coarse" to "fine" grid' !----------------------------------------------------------------------- ! initialize weights or use previously calculated weights !----------------------------------------------------------------------- if (init .eq. 1) then error = .false. write (stdout,*) & ' (initializing interpolation weights)' write (stdout,*) ' ' ! test to verify that array sizes do not exceed limits if (if .gt. len .or. jf .gt. len) then i = max(if,jf) write (stdout,*) '=>Error: increase "len" in "ctf" to ',i error = .true. endif if (lenw .lt. 8*max(if,jf)) then write (stdout,*) '=>Error: increase size of "work" array', & ' to at least ',8*max(if,jf),' for calls to "ctf"' error = .true. endif ! verify that the "fine" grid lies within the "coarse" grid epsilon = 1.e-5 xcminus = xc(1) - epsilon*(xc(2)-xc(1)) xcplus = xc(ic) + epsilon*(xc(ic)-xc(ic-1)) if (xf(istart) .lt. xcminus .or. xf(iend) .gt. xcplus) then error = .true. write (stdout,*) & '=>Warning: "fine" grid outside "coarse" grid in "ctf".' if (xf(istart) .lt. xc(1)) then write (stdout,*) ' xf(',istart,') .lt. xc(1)' endif if (xc(ic) .lt. xf(iend)) then write (stdout,*) ' xf(',iend,') .gt. xc(',ic,')' endif endif ycminus = yc(1) - epsilon*(yc(2)-yc(1)) ycplus = yc(jc) + epsilon*(yc(jc)-yc(jc-1)) if (ycminus .gt. yf(jstart) .or. ycplus .lt. yf(jend)) then error = .true. write (stdout,*) & '=>Warning: "fine" grid outside "coarse" grid in "ctf".' if (yc(1) .gt. yf(jstart)) then write (stdout,*) ' yf(',jstart,') .lt. yc(1)' endif if (yc(jc) .lt. yf(jend)) then write (stdout,*) ' yf(',jend,') .gt. yc(',jc,')' endif endif ! find interpolation factors indx = 1 do j=jstart,jend jj = indp (yf(j), yc, jc) if (yc(jj) .gt. yf(j) .or. jj .eq. jc) jj = jj - 1 indxj(j) = jj dnorth(j) = yc(jj+1) - yf(j) dsouth(j) = yf(j) - yc(jj) height(j) = yc(jj+1) - yc(jj) ! store into "work" array for future use (when "init" <> 1) work(indx) = indxj(j) work(indx+1) = dnorth(j) work(indx+2) = dsouth(j) work(indx+3) = height(j) indx = indx + 4 enddo do i=istart,iend ii = indp (xf(i), xc, ic) if (xc(ii) .gt. xf(i) .or. ii .eq. ic) ii = ii - 1 indxi(i) = ii deast(i) = xc(ii+1) - xf(i) dwest(i) = xf(i) - xc(ii) width(i) = xc(ii+1) - xc(ii) ! store into "work" array for future use (when "init" <> 1) work(indx) = indxi(i) work(indx+1) = deast(i) work(indx+2) = dwest(i) work(indx+3) = width(i) indx = indx + 4 enddo show_coord = .false. if (error .or. show_coord) then write (stdout,*) ' ' write (stdout,*) ' Coordinates for coarse grid points "xc" =' write (stdout,8500) xc write (stdout,*) ' Coordinates for fine grid points "xf" =' write (stdout,8500) xf write (stdout,*) ' Coordinates for coarse grid points "yc" =' write (stdout,8500) yc write (stdout,*) ' Coordinates for fine grid points "yf" =' write (stdout,8500) yf endif if (error) stop '=>ctf' else ! extract previously calculated interpolation weights from "work" write (stdout,*) &' (using previously initialized interpolation weights)' indx = 1 do j=jstart,jend indxj(j) = nint(work(indx)) dnorth(j) = work(indx+1) dsouth(j) = work(indx+2) height(j) = work(indx+3) indx = indx + 4 enddo do i=istart,iend indxi(i) = nint(work(indx)) deast(i) = work(indx+1) dwest(i) = work(indx+2) width(i) = work(indx+3) indx = indx + 4 enddo endif !----------------------------------------------------------------------- ! interpolate data from "coarse" to "fine" grid !----------------------------------------------------------------------- do jj=jstart,jend j = indxj(jj) do ii=istart,iend i = indxi(ii) f(ii,jj) = (c(i,j) *deast(ii)*dnorth(jj) & + c(i+1,j) *dwest(ii)*dnorth(jj) & + c(i,j+1) *deast(ii)*dsouth(jj) & + c(i+1,j+1)*dwest(ii)*dsouth(jj)) / & (width(ii)*height(jj)) enddo enddo return 8500 format (1x,10g11.3) end subroutine extrap (a, land, sor, res, il, jl, maxscn, crit, text &, gtype) !======================================================================= ! utility to extrapolate values into land areas neglecting ! non-uniformity or asymmetry in the grid by solving a simple ! heat eqn: del**2(a) = 0 over land areas using values over ocean ! areas as boundary conditions. ! this alleviates the problem of mismatched land/sea areas due to ! different geometries or resolutions when interpolating between ! atmospheric and ocean model grids. ! the intent is to force reasonable values into land areas ! near coastlines. far from coasts, the extrapolations may not be ! reasonable. ! note: the values over land are used as an initial guess field ! and need to be specified ! inputs: ! a = array with land areas to be filled. land areas contain ! initial guess field. ! land = mask = (0, non zero) to indicate (land, non land) area ! il = number of points along 1st dimension to be filled ! jl = number of points along 2nd dimension to be filled ! maxscn = maximum number of passes allowed in relaxation ! crit = criterion for ending relaxation before "maxscn" limit ! text = character string (up to 15 chars) to identify data ! gtype = grid type = (1,2) to identify (ocean, atmosphere) grid ! sor = scratch area ! res = scratch area ! outputs: ! a = array with extrapolated values in land areas. ! non land areas remain unchanged. !======================================================================= logical done include "stdunits.h" integer gtype character(*) :: text parameter (c0=0.0, p25=0.25) dimension a(il,jl), land(il,jl), res(il,jl), sor(il,jl) !----------------------------------------------------------------------- ! solve a simple Poisson eqn by relaxation to extrapolate data into ! land areas using values over non land areas as boundary values. ! note: successive calls to extrap will require fewer scans because ! the initial guess field over land areas gets better with ! each call. !----------------------------------------------------------------------- ! check on the grid type: atmosphere or ocean if (gtype .ne. 1 .and. gtype .ne. 2) then write (stdout,98) gtype stop '=>extrap' endif !----------------------------------------------------------------------- ! set the relaxation coefficient to zero over ocean or air ! relc is somewhat arbitrary !----------------------------------------------------------------------- relc = 0.6 do j=1,jl do i=1,il if (land(i,j) .eq. 0) then sor(i,j) = relc else sor(i,j) = c0 endif enddo enddo !----------------------------------------------------------------------- ! iterate until errors are acceptable. !----------------------------------------------------------------------- n = 0 100 continue resmax = c0 done = .true. n = n + 1 do j=2,jl-1 do i=2,il-1 res(i,j) = p25*(a(i-1,j) + a(i+1,j) + a(i,j-1) + a(i,j+1)) & - a(i,j) enddo enddo do j=2,jl-1 do i=2,il-1 res(i,j) = res(i,j)*sor(i,j) a(i,j) = a(i,j) + res(i,j) absres = abs(res(i,j)) if (absres .gt. crit) done = .false. resmax = max(absres,resmax) enddo enddo !----------------------------------------------------------------------- ! set conditions at edge of grid !----------------------------------------------------------------------- if (gtype .eq. 1) then ! use cyclic or no flux conditions on ocean grids do j=1,jl a(1,j) = a(il-1,j) a(il,j) = a(2,j) enddo elseif (gtype .eq. 2) then ! always put cyclic conditions on atmosphere grids do j=1,jl a(1,j) = a(il-1,j) a(il,j) = a(2,j) enddo endif ! no flux condition at northern and southern boundaries do i=1,il a(i,1) = a(i,2) a(i,jl) = a(i,jl-1) enddo if (.not. done .and. n .le. maxscn) go to 100 write (stdout,99) text, n, resmax 99 format (1x,'==> Extrapolated ',a15,' into land using ',i4 &, ' scans. max residual=', g14.7) 98 format (1x,'==> Error: gtype =',i6,' in extrap') return end subroutine setbcx (a, imt, jmtorkm) !======================================================================= ! set zonal boundary condition on the first index of array "a" for ! every second index. the first index corresponds to the "x" ! or longitude direction. ! input: ! a = array in need of setting the zonal b.c. ! output ! a = array with zonal b.c. set !======================================================================= dimension a(imt,jmtorkm) do k=1,jmtorkm a(1,k) = a(imt-1,k) a(imt,k) = a(2,k) enddo return end subroutine iplot (iarray, im, il, jl) !======================================================================= ! map integer array "iarray" into characters for printing with ! format (a1) to provide a contour map of the integer field. ! note: max number of unique characters = 120 ! inputs: ! iarray = integer array to be plotted ! im = inner dimension of "iarray" ! il = number of points along inner dimension to plot (along x) ! jl = number of points along outer dimension to plot (along y) ! output: prints contour map of "iarray" !======================================================================= include "stdunits.h" dimension iarray(im,jl) character(120) :: levels, lev1 save levels write (stdout,*) ' ' ! set character markers lev1(1:51) = '.abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWX' levels = lev1(1:51)//'YZ0123456789+*-=!@#$%<>[]{}()' ! find range of integers maxint = iarray(1,1) minint = iarray(1,1) do j=1,jl do i=1,il maxint = max(maxint,iarray(i,j)) minint = min(minint,iarray(i,j)) enddo enddo ! show mapping of integers into characters write (stdout,*) ' ' write (stdout,*) & ' "iplot" mapping of integers to characters is as follows:' inc = 3 last = min(minint+80-1,maxint) do i=minint,last,inc ii = i-minint+1 if (i+inc .le. last) then jinc = inc else jinc = last-i+1 endif write (stdout,'(6(1x,i6,a,a,3x))') & (j+minint-1," is printed as ",levels(j:j),j=ii,ii+jinc-1) enddo write (stdout,*) ' ' if (maxint - minint + 1 .gt. 80) then write (stdout,*) & ' => Note: there are ',maxint-minint+1,' integers in the field' write (stdout,*) ' "iplot" cannot uniquely assign ' &,' more than 120 characters for plotting symbols.' write (stdout,*) ' therefore integers are ' &, 'represented by cyclically reusing the list of plotting symbols' write (stdout,*) ' ' endif ! print character representation of integers inc=124 do l=0,il,inc incr = min(inc,il-l) write (stdout,8800) (l+i,i=1,incr,4) do jj=1,jl j = jl+1-jj ! write (stdout,8900) j, (levels(min(80,iarray(l+i,j)-minint+1): ! & min(80,iarray(l+i,j)-minint+1)),i=1,incr) write (stdout,8900) j, & (levels(mod(iarray(l+i,j)-minint+1-1,80)+1: & mod(iarray(l+i,j)-minint+1-1,80)+1),i=1,incr) enddo enddo return 8800 format (/, 2x, 31i4) 8900 format (1x,i3,1x, 124a1) end subroutine imatrx (iarray, im, istrt, iend, jstrt, jend, iform) !======================================================================= ! integer matrix print with various formats ! inputs: ! iarray = integer array to be printed ! im = the 1st dimension of array ! istrt = starting index along 1st dimension for plot ! iend = ending index along 1st dimension for plot ! jstrt = starting index along 2nd dimension for plot ! jend = ending index along 2nd dimension for plot ! note: if jstrt and jend are negative then the vertical ! y-axis is inverted. ! iform = format designator: 1 => format (i1) ! 2 => format (i2) ! 3 => format (i3) ! 4 => format (i4) ! output: print integer "iarray" with user format control !======================================================================= include "stdunits.h" dimension iarray(im,1000) ! choose the plotting domain js = min(abs(jstrt),abs(jend)) je = max(abs(jstrt),abs(jend)) is = min(abs(istrt),abs(iend)) ie = max(abs(istrt),abs(iend)) il = ie-is+1 write (stdout,*) ' ' if (iform .eq. 1) then ! use I1 format to print the integer array inc=120 do l=0,il,inc incr = min(inc,il-l) write (stdout,8800) (l+i+is-1,i=1,incr,4) do jj=js,je if (jstrt .lt. 0 .or. jend .lt. 0) then j = je - (jj-js) else j = jj endif write (stdout,8900) j, (iarray(l+i+is-1,j),i=1,incr) enddo enddo elseif (iform .eq. 2) then ! use I2 format to print the integer array inc=60 do l=0,il,inc incr = min(inc,il-l) write (stdout,9000) (l+i+is-1,i=1,incr,2) do jj=js,je if (jstrt .lt. 0 .or. jend .lt. 0) then j = je - (jj-js) else j = jj endif write (stdout,9200) j, (iarray(l+i+is-1,j),i=1,incr) enddo enddo elseif (iform .eq. 3) then ! use I3 format to print the integer array inc=40 do l=0,il,inc incr = min(inc,il-l) write (stdout,9400) (l+i+is-1,i=1,incr,2) do jj=js,je if (jstrt .lt. 0 .or. jend .lt. 0) then j = je - (jj-js) else j = jj endif write (stdout,9500) j, (iarray(l+i+is-1,j),i=1,incr) enddo enddo elseif (iform .eq. 4) then ! use I4 format to print the integer array inc=30 do l=0,il,inc incr = min(inc,il-l) write (stdout,9600) (l+i+is-1,i=1,incr,2) do jj=js,je if (jstrt .lt. 0 .or. jend .lt. 0) then j = je - (jj-js) else j = jj endif write (stdout,9700) j, (iarray(l+i+is-1,j),i=1,incr) enddo enddo endif return 8800 format (/, 2x, 30i4) 8900 format (1x,i3,1x, 120i1) 9000 format (/, 3x, 30i4) 9200 format (1x,i3,1x, 60i2) 9400 format (/,/,/,2x,20i6/) 9500 format (1x,i3,1x,40i3) 9600 format (/,/,/,1x,20i8/) 9700 format (1x,i3,1x,30i4) end subroutine matrix (array, irdim, istrt, im, jstrt, jm, scale) !======================================================================= ! matrix is a general two-dimensional array printing routine, ! input: ! array = the array to be printed ! irdim = the 1st dimension of array ! istrt = the 1st element of the 1st dimension to be printed ! im = the last element of the 1st dimension to be printed ! jstrt = the 1st element of the 2nd dimension to be printed ! jm = the last element of the 2nd dimension to be printed ! the 2nd dimension is printed in reverse order if both ! jstrt & jm are negative ! scale = a scaling factor by which array is divided before ! printing. (if this is zero, no scaling is done.) ! if scale=0, 10 columns are printed across in e format ! if scale>0, 20 columns are printed across in f format ! output: print "array" as a matrix !======================================================================= include "stdunits.h" parameter (c0=0.0, c1=1.0) dimension array(irdim,1000) if (jstrt*jm .lt. 0) then write (stdout,999) jstrt, jm stop '=>matrix' endif ! allow for inversion of 2nd dimension if (jm .lt. 0) then js = -jm je = -jstrt jinc = -1 else js = jstrt je = jm jinc = 1 endif if (scale .eq. c0) then do is=istrt,im,10 ie = min(is + 9,im) write (stdout,9001) (i, i=is,ie) do l=js,je,jinc write (stdout,9002) l, (array(i,l),i=is,ie) enddo write (stdout,'(/)') enddo else scaler = c1/scale do is=istrt,im,20 ie = min(is + 19,im) write (stdout,9003) (i, i=is,ie) do l=js,je,jinc write (stdout,9004) l, (array(i,l)*scaler,i=is,ie) enddo write (stdout,'(/)') enddo endif return 999 format (1x,'jstrt=',i5,' jm=',i5,' in matrix') 9001 format(10i13) 9002 format(1x,i2,10(1pe13.5)) 9003 format(3x,20i6) 9004 format(1x,i3,1x,20f6.2) end subroutine scope (array, im, il, jl, text) !======================================================================= ! scope interrogates "array" for the min, max (with respective ! locations), and simple unweighted average ! inputs: ! array = the array to be interrogated ! im = the inner dimension of "array" ! il = the number of points along the inner dimension to consider ! jl = the number of points along the inner dimension to consider ! text = descriptive text (up to 15 chars) to be printed ! output: prints min, max (with locations), and average of "array" !======================================================================= character(*) :: text dimension array(im,jl) umax = array(1,1) umin = array(1,1) iumax = 1 jumax = 1 iumin = 1 jumin = 1 sum = 0.0 do j=1,jl do i=1,il sum = sum + array(i,j) if (array(i,j) .gt. umax) then umax = array(i,j) iumax = i jumax = j endif if (array(i,j) .lt. umin) then umin = array(i,j) iumin = i jumin = j endif enddo enddo avg = sum/(il*jl) write (*,9200) text, il, jl, iumin, jumin, umin, iumax, jumax &, umax, avg return 9200 format (1x,'Scope: ',a15,': il=',i4,', jl=',i4 &,', min(',i4,',',i4,')=',g10.3,', max(',i4,',',i4,')=',g10.3 &,', avg=',g10.3/) end subroutine sum1st (a, imt, jmt, text) !======================================================================= ! inputs: ! a = the array to be interrogated ! imt = the 1st dimension of "a" ! imt = the 2nd dimension of "a" ! text = descriptive text to be printed ! output: sums the first index of array "a" for each 2nd index !======================================================================= character(*) :: text dimension a(imt,jmt) print *,' ' print *,text big = abs(a(1,1)) imax = 0 jmax = 0 do j=1,jmt sum = 0.0 do i=1,imt sum = sum + a(i,j) if (abs(a(i,j)) .gt. big) then big = abs(a(i,j)) imax = i jmax = j endif enddo if (sum .ne. 0.0) then write (*,'(a,i4,a,e14.7)') & '2nd index=',j,'. sum over 1st index =',sum endif enddo if (imax .ne. 0 .and. jmax .ne. 0) then write (*,*) ' biggest=',a(imax,jmax),' at i=',imax,' j=',jmax else write (*,*) ' ---field is a constant =', a(1,1) endif return end subroutine plot (array, im, istrt, iend, jstrt, jend &, zmin, zmax, nbin, title) !======================================================================= ! "plot" contours "array" by dividing the array values into bins, ! assigning a character to each bin, and printing the characters to ! produce a contour map. ! The inner (1st) dimension is plotted horizontally (x-axis) and the ! outer (2nd) dimension is plotted vertically (y-axis) and can be ! inverted. ! inputs: ! array = the array to be contoured ! im = the inner dimension of "array" ! istrt = starting index along 1st dimension for plot ! iend = ending index along 1st dimension for plot ! jstrt = starting index along 2nd dimension for plot ! jend = ending index along 2nd dimension for plot ! note: if jstrt and jend are negative then the vertical ! y-axis is inverted. ! zmin = the minimum value to plot ! zmax = the maximum value to plot ! note: if zmin=zmax then then min and max of "array" ! is used. ! nbin = the number of bins between zmin and zmax ! title = descriptive text string ! output: contours "array" !======================================================================= parameter (maxbin=52, ncols=124) character(*) :: title dimension array(im,1000), bin(maxbin,3) character(maxbin) :: c, cc character(1) :: line(ncols) data c/'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'/ save c ! choose the plotting domain js = min(abs(jstrt),abs(jend)) je = max(abs(jstrt),abs(jend)) is = min(abs(istrt),abs(iend)) ie = max(abs(istrt),abs(iend)) il = ie-is+1 ! set the max and min if (zmax .eq. zmin) then big = array(is,js) sml = array(is,js) do j=js,je do i=is,ie if (array(i,j) .gt. big) big = array(i,j) if (array(i,j) .lt. sml) sml = array(i,j) enddo enddo else big = max(zmin,zmax) sml = min(zmin,zmax) endif ! set up the discretization into bins write (*,*) ' ' write (*,*) ' => contour bins for: ', title delta = (big-sml)/max(1,abs(nbin)) limit = min(maxbin,max(1,abs(nbin))) do n=1,limit bin(n,1) = sml + (n-1)*delta bin(n,2) = sml + n*delta bin(n,3) = 0.5*(bin(n,1)+bin(n,2)) cc(n:n) = c(n:n) if (n .eq. 1) cc(n:n) = '-' if (n .ge. max(1,abs(nbin)) .or. n .eq. maxbin) cc(n:n) = '+' if (bin(n,1) .le. 0.0 .and. bin(n,2) .gt. 0.0) cc(n:n) = '.' if (n .lt. limit) then write (*,'(1x,a,a,g10.3,a,g10.3,a,g10.3,a)') cc(n:n) &, ' = ', bin(n,3) &, ', (', bin(n,1),' <= x < ', bin(n,2),')' else write (*,'(1x,a,a,g10.3,a,g10.3,a,g10.3,a)') cc(n:n) &, ' = ', bin(n,3) &, ', (', bin(n,1),' <= x <=', bin(n,2),')' endif enddo if (abs(nbin) .gt. maxbin) then write (*,*) & ' => Note: numbers larger than this are also plotted as +' endif ! plot the character representation of the bins write (*,*) ' ' do l=0,il,ncols incr = min(ncols,il-l) write (*,8800) (l+i+is-1,i=1,incr,4) do jj=js,je if (jstrt .lt. 0 .or. jend .lt. 0) then j = jj else j = je - (jj-js) endif do i=1,incr k = min(ifix((array(l+i+is-1,j) - sml)/delta) + 1, limit) line(i) = cc(k:k) enddo write (*,8900) j, (line(i),i=1,incr) enddo enddo return 8800 format (/, 2x, 31i4) 8900 format (1x,i3,1x, 124a1) end subroutine print_checksum (a, im, jm, text) dimension a(im,jm) character(*) :: text sum = checksum (a, im, jm) print *, text, sum return end function checksum (a, im, jm) implicit none integer i, im, j, jm real checksum, sum, a(im,jm) sum = 0.0 do j=1,jm do i=1,im sum = sum + abs(a(i,j)) enddo enddo checksum = sum return end subroutine wrufio (iounit, array, len) !======================================================================= ! write unformatted fortran i/o ! input: ! iounit = fortran unit number ! array = array to be written to "iounit" ! len = length of array ! output: writes to unit "iounit" !======================================================================= implicit none integer iounit, l, len real array(len) write (iounit) array return end subroutine rdufio (iounit, array, len) !======================================================================= ! read unformatted fortran i/o ! input: ! iounit = fortran unit number ! array = array to be read from "iounit" ! len = length of array ! output: none !======================================================================= implicit none integer iounit, len real array(len) read (iounit) array return end subroutine tranlon (c, ic, il, jl, t, cx, fx, ifl, tx) !----------------------------------------------------------------------- ! grid interpolators in MOM require the grid coordinates to be ! monotonic. when the prime meridian lies within the model grid, ! global datasets (e.g. Scripps topography) must be translated in ! longitude to remove the jump in ! longitudes (358.5 359.5, 0.5, 1.5) across the meridian before ! interpolating to the model grid. This is only of concern in ! limited domain grids (e.g. Atlantic basin) that contain the ! prime meridian. ! translate longitudes "cx" to "tx" so that tx(i) i=1..ic ! completely encloses model longitudes fx(i) i=1..ifl ! note that "tx" may extend beyond 360 degrees to contain "fx". ! use same mapping to translate data in "c" ! input: ! c = original data array ! t = temp array for translating data ! cx = original data longitudes ! tx = translated data longitudes ! fx = model longitudes ! output ! c = translated data array !----------------------------------------------------------------------- implicit none integer iw, ic, il, jl, ifl, indp, i, im1, j real c(ic,jl), t(ic), tx(ic), cx(ic), fx(ifl) !----------------------------------------------------------------------- ! find the index of the 1st model grid point on the data grid !----------------------------------------------------------------------- iw = indp (fx(1), cx, ic) if (cx(iw) .gt. fx(1)) iw = max(1,iw-1) !----------------------------------------------------------------------- ! translate data longitudes so that tx(1) = cx(iw), tx(2) = cx(iw+1) !----------------------------------------------------------------------- do i=1,ic tx(i) = cx(mod(i+iw-2,il) + 1) im1 = max(1,i-1) if (tx(i) .lt. tx(im1)) tx(i) = tx(i) + 360.0 enddo if (fx(ifl) .gt. tx(ic)) then write (6,997) iw, ic, ifl write (6,998) 'tx= ',(tx(i),i=1,ic) write (6,998) 'fx= ',(fx(i),i=1,ifl) stop endif !----------------------------------------------------------------------- ! translate data to match translated longitudes !----------------------------------------------------------------------- do j=1,jl do i=1,ic t(i) = c(mod(i+iw-2,il) + 1,j) enddo do i=1,ic c(i,j) = t(i) enddo enddo return 997 format (1x, ' ===> tx(ic) < fx(ifl) in tranlon. iw=',i6, 1 ' il=',i6,' ifl=',i6) 998 format (1x,a4,(5x,10e11.4)) end subroutine areatot (data, dmsk, tot) !======================================================================= ! calculate the area weighted total of data ! input: ! data = data to be totalled ! dmsk = data mask ! output: ! tot = area weighted total of the data !======================================================================= implicit none integer i, j, land real sl, el, fx, tot include "size.h" include "param.h" include "pconst.h" include "stdunits.h" include "grdvar.h" real data(imt,jmt), dmsk(imt,jmt) tot = 0.0 do j=2,jmtm1 fx = cst(j)*dyt(j) do i=2,imtm1 tot = tot + data(i,j)*dxt(i)*fx*dmsk(i,j) enddo enddo return end subroutine areaavg (data, dmsk, avg) !======================================================================= ! calculate the area weighted average of data ! input: ! data = data to be averaged ! dmsk = data mask ! output: ! avg = area weighted average of the data !======================================================================= implicit none integer i, j real fx, tarea, tdata, area, avg include "size.h" include "param.h" include "pconst.h" include "stdunits.h" include "grdvar.h" real data(imt,jmt), dmsk(imt,jmt) tarea = 0.0 tdata = 0.0 avg = 0.0 do j=2,jmtm1 fx = cst(j)*dyt(j) do i=2,imtm1 area = dxt(i)*fx*dmsk(i,j) tarea = tarea + area tdata = tdata + data(i,j)*area enddo enddo if (tarea .ne. 0.0) avg = tdata/tarea return end