| 1 | ;+ |
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| 2 | ; |
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| 3 | ; @file_comments |
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| 4 | ; compute the gradient of a variable located on Arakawa C-grid. |
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| 5 | ; |
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| 6 | ; @categories |
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| 7 | ; Calculation |
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| 8 | ; |
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| 9 | ; @param FIELD |
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| 10 | ; The field for which we want to compute the gradient. A 2D (xy), |
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| 11 | ; 3D (xyz or yt) or 4D (xyzt) array or a structure readable by |
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| 12 | ; <pro>litchamp</pro> and containing a 2D (xy), 3D (xyz or yt) or 4D (xyzt) array. |
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| 13 | ; Note that the dimension of the array must suit the domain dimension. |
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| 14 | ; |
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| 15 | ; @param DIREC {type=scalar string} |
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| 16 | ; the gradient direction: 'x', 'y', 'z' |
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| 17 | ; |
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| 18 | ; @keyword MILLION {default=0}{type=scalar: 0 or 1} |
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| 19 | ; Activate to multiply returned array by 1.e6 |
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| 20 | ; |
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| 21 | ; @keyword _EXTRA |
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| 22 | ; Used to declare that this routine accepts inherited keywords |
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| 23 | ; |
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| 24 | ; @returns |
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| 25 | ; the gradient of the input data with the same size 2D, 3D or 4D |
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| 26 | ; array, located on the appropriate grid (see restrictions) |
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| 27 | ; |
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| 28 | ; @uses |
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| 29 | ; cm_4cal |
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| 30 | ; cm_4data |
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| 31 | ; cm_4mesh |
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| 32 | ; |
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| 33 | ; @restrictions |
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| 34 | ; - Works only for Arakawa C-grid. |
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| 35 | ; - When computing the gradient, the result is not on the same grid point |
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| 36 | ; than the input data. In consequence, we update, vargrid and the grid position |
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| 37 | ; parameters (firstx[tuvf], lastx[tuvf], nx[tuvf], firsty[tuvf], lasty[tuvf], |
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| 38 | ; ny[tuvf], firstz[tw], lastz[tw], nz[tw]). |
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| 39 | ; - points that cannot be computed (domain boundaries, coastline) are set to NaN |
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| 40 | ; - the common variable jpt is used to differ xyz (jpt=1) and xyt (jpt\=1) cases. |
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| 41 | ; |
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| 42 | ; @examples |
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| 43 | ; IDL> \@tst_initorca2 |
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| 44 | ; IDL> plt, grad({arr:gphit,g:'T'}, 'x') |
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| 45 | ; IDL> plt, grad({arr:gphit,g:'T'}, 'y') |
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| 46 | ; |
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| 47 | ; @history |
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| 48 | ; Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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| 49 | ; |
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| 50 | ; @version |
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| 51 | ; $Id$ |
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| 52 | ; |
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| 53 | ;- |
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| 54 | ; |
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| 55 | FUNCTION grad, field, direc, MILLION = million, _EXTRA = ex |
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| 56 | ; |
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| 57 | compile_opt idl2, strictarrsubs |
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| 58 | ; |
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| 59 | @cm_4cal ; for jpt |
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| 60 | @cm_4data ; for varname, vargrid, vardate, varunit, valmask |
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| 61 | @cm_4mesh |
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| 62 | ; |
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| 63 | time1 = systime(1) ; for key_performance |
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| 64 | ;------------------------------------------------------------ |
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| 65 | ; |
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| 66 | IF finite(glamu[0])*finite(gphiu[0])*finite(glamv[0])*finite(gphiv[0]) EQ 0 THEN $ |
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| 67 | return, report(['This version of grad is based on Arakawa C-grid.' $ |
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| 68 | , 'U and V grids must therefore be defined']) |
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| 69 | ; |
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| 70 | res = litchamp(field) |
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| 71 | szres = size(res) |
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| 72 | grille, mask, glam, gphi, gdep, nx, ny, nz $ |
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| 73 | , firstx, firsty, firstz, lastx, lasty, lastz |
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| 74 | ; |
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| 75 | if n_elements(valmask) EQ 0 then valmask = 1.e20 |
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| 76 | varname = 'grad of '+varname |
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| 77 | IF keyword_set(million) THEN varunit = '1.e6*'+varunit+'/m' ELSE varunit = varunit+'/m' |
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| 78 | case strupcase(vargrid) of |
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| 79 | 'T':BEGIN |
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| 80 | case direc of |
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| 81 | 'x':BEGIN |
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| 82 | divi = e1u[firstx:lastx, firsty:lasty] |
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| 83 | newmask = (umask())[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 84 | vargrid = 'U' |
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| 85 | firstxu = firstxt & lastxu = lastxt & nxu = nxt |
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| 86 | firstyu = firstyt & lastyu = lastyt & nyu = nyt |
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| 87 | END |
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| 88 | 'y':BEGIN |
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| 89 | divi = e2v[firstx:lastx, firsty:lasty] |
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| 90 | newmask = (vmask())[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 91 | vargrid = 'V' |
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| 92 | firstxv = firstxt & lastxv = lastxt & nxv = nxt |
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| 93 | firstyv = firstyt & lastyv = lastyt & nyv = nyt |
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| 94 | END |
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| 95 | 'z':BEGIN |
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| 96 | divi = e3w[firstz:lastz] |
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| 97 | newmask = mask |
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| 98 | vargrid = 'W' |
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| 99 | firstzw = firstzt & lastzw = lastzt & nzw = nzt |
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| 100 | END |
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| 101 | ELSE:return, report('Bad definition of direction argument') |
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| 102 | ENDCASE |
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| 103 | END |
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| 104 | 'W':BEGIN |
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| 105 | case direc of |
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| 106 | 'x':BEGIN |
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| 107 | divi = e1u[firstx:lastx, firsty:lasty] |
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| 108 | newmask = (umask())[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 109 | vargrid = 'U' |
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| 110 | firstxu = firstxt & lastxu = lastxt & nxu = nxt |
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| 111 | firstyu = firstyt & lastyu = lastyt & nyu = nyt |
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| 112 | END |
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| 113 | 'y':BEGIN |
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| 114 | divi = e2v[firstx:lastx, firsty:lasty] |
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| 115 | newmask = (vmask())[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 116 | vargrid = 'V' |
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| 117 | firstxv = firstxt & lastxv = lastxt & nxv = nxt |
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| 118 | firstyv = firstyt & lastyv = lastyt & nyv = nyt |
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| 119 | END |
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| 120 | 'z':BEGIN |
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| 121 | divi = e3t[firstz:lastz] |
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| 122 | newmask = mask |
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| 123 | vargrid = 'T' |
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| 124 | firstzt = firstzw & lastzt = lastzw & nzt = nzw |
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| 125 | END |
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| 126 | ELSE:return, report('Bad definition of direction argument') |
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| 127 | endcase |
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| 128 | END |
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| 129 | 'U':BEGIN |
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| 130 | case direc of |
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| 131 | 'x':BEGIN |
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| 132 | divi = (shift(e1t, -1, 0))[firstx:lastx, firsty:lasty] |
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| 133 | newmask = tmask[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 134 | vargrid = 'T' |
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| 135 | firstxt = firstxu & lastxt = lastxu & nxt = nxu |
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| 136 | firstyt = firstyu & lastyt = lastyu & nyt = nyu |
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| 137 | END |
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| 138 | 'y':BEGIN |
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| 139 | divi = e2f[firstx:lastx, firsty:lasty] |
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| 140 | newmask = (fmask())[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 141 | vargrid = 'F' |
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| 142 | firstxf = firstxu & lastxf = lastxu & nxf = nxu |
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| 143 | firstyf = firstyu & lastyf = lastyu & nyf = nyu |
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| 144 | END |
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| 145 | 'z':BEGIN |
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| 146 | divi = e3w[firstz:lastz] |
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| 147 | newmask = mask |
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| 148 | vargrid = 'W' |
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| 149 | firstzw = firstzt & lastzw = lastzt & nzw = nzt |
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| 150 | END |
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| 151 | ELSE:return, report('Bad definition of direction argument') |
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| 152 | endcase |
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| 153 | END |
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| 154 | 'V':BEGIN |
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| 155 | case direc of |
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| 156 | 'x':BEGIN |
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| 157 | divi = e1f[firstx:lastx, firsty:lasty] |
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| 158 | newmask = (fmask())[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 159 | vargrid = 'F' |
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| 160 | firstxf = firstxv & lastxf = lastxv & nxf = nxv |
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| 161 | firstyf = firstyv & lastyf = lastyv & nyf = nyv |
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| 162 | END |
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| 163 | 'y':BEGIN |
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| 164 | divi = (shift(e2t, 0, -1))[firstx:lastx, firsty:lasty] |
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| 165 | newmask = tmask[firstx:lastx, firsty:lasty, firstz:lastz] |
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| 166 | vargrid = 'T' |
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| 167 | firstxt = firstxv & lastxt = lastxv & nxt = nxv |
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| 168 | firstyt = firstyv & lastyt = lastyv & nyt = nyv |
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| 169 | END |
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| 170 | 'z':BEGIN |
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| 171 | divi = e3w[firstz:lastz] |
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| 172 | newmask = mask |
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| 173 | vargrid = 'W' |
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| 174 | firstzw = firstzt & lastzw = lastzt & nzw = nzt |
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| 175 | END |
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| 176 | ELSE:return, report('Bad definition of direction argument') |
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| 177 | endcase |
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| 178 | END |
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| 179 | 'F':BEGIN |
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| 180 | ; case direc of |
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| 181 | ; 'x':divi = (shift(e1v, -1, 0))[firstx:lastx, firsty:lasty] |
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| 182 | ; 'y':divi = (shift(e2u, 0, -1))[firstx:lastx, firsty:lasty] |
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| 183 | ; 'z':divi = e3w[firstz:lastz] |
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| 184 | ; ELSE:return, report('Bad definition of direction argument') |
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| 185 | ; endcase |
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| 186 | return, report('F grid: case not coded, please contact SAXO team...') |
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| 187 | END |
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| 188 | ELSE:return, report('Bad definition of vargrid') |
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| 189 | ENDCASE |
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| 190 | IF keyword_set(million) THEN divi = temporary(divi)*1.e-6 |
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| 191 | res = fitintobox(temporary(res)) |
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| 192 | IF n_elements(res) EQ 1 AND res[0] EQ -1 THEN return, res |
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| 193 | case 1 of |
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| 194 | ;---------------------------------------------------------------------------- |
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| 195 | ;xy |
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| 196 | ;---------------------------------------------------------------------------- |
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| 197 | szres[0] EQ 2:BEGIN |
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| 198 | land = where((temporary(mask))[*, *, firstz] EQ 0) |
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| 199 | if land[0] NE -1 then res[temporary(land)] = !values.f_nan |
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| 200 | case direc of |
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| 201 | 'x':BEGIN |
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| 202 | res = (shift(res, -1, 0)-res)/temporary(divi) |
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| 203 | if key_periodic EQ 0 OR nx NE jpi THEN res[nx-1, *] = !values.f_nan |
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| 204 | if vargrid EQ 'T' OR vargrid EQ 'V' then res = shift(temporary(res), 1, 0) |
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| 205 | END |
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| 206 | 'y':BEGIN |
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| 207 | res = (shift(res, 0, -1)-res)/temporary(divi) |
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| 208 | res[*, ny-1] = !values.f_nan |
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| 209 | if vargrid EQ 'T' OR vargrid EQ 'U' then res = shift(temporary(res), 0, 1) |
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| 210 | END |
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| 211 | ELSE:return, report('Bad definition of direction argument for the type of array') |
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| 212 | ENDCASE |
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| 213 | land = where((temporary(newmask))[*, *, firstz] EQ 0) |
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| 214 | if land[0] NE -1 then res[temporary(land)] = valmask |
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| 215 | END |
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| 216 | ;---------------------------------------------------------------------------- |
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| 217 | ;xyt |
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| 218 | ;---------------------------------------------------------------------------- |
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| 219 | szres[0] EQ 3 AND jpt NE 1:BEGIN |
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| 220 | land = where((temporary(mask))[*, *, firstz] EQ 0, cnt) |
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| 221 | if land[0] NE -1 then BEGIN |
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| 222 | land = (temporary(land))#replicate(1L, jpt) + replicate(1L, cnt)#(nx*ny*lindgen(jpt)) |
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| 223 | res[temporary(land)] = !values.f_nan |
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| 224 | ENDIF |
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| 225 | divi = (temporary(divi))[*]#replicate(1., jpt) |
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| 226 | case direc of |
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| 227 | 'x':BEGIN |
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| 228 | res = (shift(res, -1, 0, 0)-res)/temporary(divi) |
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| 229 | if key_periodic EQ 0 OR nx NE jpi THEN res[nx-1, *, *] = !values.f_nan |
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| 230 | if vargrid EQ 'T' OR vargrid EQ 'V' then res = shift(temporary(res), 1, 0, 0) |
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| 231 | END |
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| 232 | 'y':BEGIN |
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| 233 | res = (shift(res, 0, -1, 0)-res)/temporary(divi) |
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| 234 | res[*, ny-1, *] = !values.f_nan |
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| 235 | if vargrid EQ 'T' OR vargrid EQ 'U' then res = shift(temporary(res), 0, 1, 0) |
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| 236 | END |
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| 237 | ELSE:return, report('Bad definition of direction argument for the type of array') |
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| 238 | ENDCASE |
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| 239 | land = where((temporary(newmask))[*, *, firstz] EQ 0, cnt) |
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| 240 | if land[0] NE -1 then BEGIN |
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| 241 | land = (temporary(land))#replicate(1L, jpt) + replicate(1L, cnt)#(nx*ny*lindgen(jpt)) |
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| 242 | res[temporary(land)] = valmask |
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| 243 | ENDIF |
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| 244 | END |
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| 245 | ;---------------------------------------------------------------------------- |
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| 246 | ;xyz |
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| 247 | ;---------------------------------------------------------------------------- |
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| 248 | szres[0] EQ 3 AND jpt EQ 1:BEGIN |
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| 249 | land = where(mask EQ 0) |
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| 250 | if land[0] NE -1 then res[temporary(land)] = !values.f_nan |
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| 251 | case direc OF |
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| 252 | 'x':BEGIN |
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| 253 | divi = (temporary(divi))[*]#replicate(1., nz) |
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| 254 | res = (shift(res, -1, 0, 0)-res)/temporary(divi) |
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| 255 | if key_periodic EQ 0 OR nx NE jpi THEN res[nx-1, *, *] = !values.f_nan |
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| 256 | if vargrid EQ 'T' OR vargrid EQ 'V' then res = shift(temporary(res), 1, 0, 0) |
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| 257 | END |
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| 258 | 'y':BEGIN |
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| 259 | divi = (temporary(divi))[*]#replicate(1., nz) |
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| 260 | res = (shift(res, 0, -1, 0)-res)/temporary(divi) |
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| 261 | res[*, ny-1, *] = !values.f_nan |
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| 262 | if vargrid EQ 'T' OR vargrid EQ 'U' then res = shift(temporary(res), 0, 1, 0) |
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| 263 | END |
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| 264 | 'z':BEGIN |
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| 265 | divi = replicate(1., nx*ny)#(temporary(divi))[*] |
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| 266 | if nx EQ 1 OR ny EQ 1 then res = reform(res, nx, ny, nz, /overwrite) |
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| 267 | if vargrid EQ 'W' THEN BEGIN |
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| 268 | res = (shift(res, 0, 0, 1)-res)/temporary(divi) |
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| 269 | res[*, *, 0] = !values.f_nan |
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| 270 | ENDIF ELSE BEGIN |
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| 271 | res = (res-shift(res, 0, 0, -1))/temporary(divi) |
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| 272 | res[*, *, nz-1] = !values.f_nan |
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| 273 | ENDELSE |
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| 274 | END |
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| 275 | ENDCASE |
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| 276 | land = where(temporary(newmask) EQ 0) |
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| 277 | if land[0] NE -1 then res[temporary(land)] = valmask |
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| 278 | END |
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| 279 | ;---------------------------------------------------------------------------- |
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| 280 | ;xyzt |
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| 281 | ;---------------------------------------------------------------------------- |
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| 282 | szres[0] EQ 4:BEGIN |
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| 283 | land = where(temporary(mask) EQ 0, cnt) |
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| 284 | if land[0] NE -1 then BEGIN |
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| 285 | land = (temporary(land))#replicate(1L, jpt) + replicate(1L, cnt)#(nx*ny*nz*lindgen(jpt)) |
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| 286 | res[temporary(land)] = !values.f_nan |
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| 287 | ENDIF |
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| 288 | case direc OF |
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| 289 | 'x':BEGIN |
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| 290 | divi = (temporary(divi))[*]#replicate(1., nz*jpt) |
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| 291 | res = (shift(res, -1, 0, 0, 0)-res)/temporary(divi) |
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| 292 | if key_periodic EQ 0 OR nx NE jpi THEN res[nx-1, *, *, *] = !values.f_nan |
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| 293 | if vargrid EQ 'T' OR vargrid EQ 'V' then res = shift(temporary(res), 1, 0, 0, 0) |
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| 294 | END |
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| 295 | 'y':BEGIN |
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| 296 | divi = (temporary(divi))[*]#replicate(1., nz*jpt) |
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| 297 | res = (shift(res, 0, -1, 0, 0)-res)/temporary(divi) |
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| 298 | res[*, ny-1, *, *] = !values.f_nan |
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| 299 | if vargrid EQ 'T' OR vargrid EQ 'U' then res = shift(temporary(res), 0, 1, 0, 0) |
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| 300 | END |
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| 301 | 'z':BEGIN |
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| 302 | divi = replicate(1., nx*ny)#(temporary(divi))[*] |
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| 303 | divi = (temporary(divi))[*]#replicate(1L, jpt) |
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| 304 | if nx EQ 1 OR ny EQ 1 then res = reform(res, nx, ny, nz, jpt, /overwrite) |
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| 305 | if vargrid EQ 'W' THEN BEGIN |
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| 306 | res = (shift(res, 0, 0, 1, 0)-res)/temporary(divi) |
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| 307 | res[*, *, 0, *] = !values.f_nan |
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| 308 | ENDIF ELSE BEGIN |
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| 309 | res = (res-shift(res, 0, 0, -1, 0))/temporary(divi) |
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| 310 | res[*, *, nz-1, *] = !values.f_nan |
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| 311 | ENDELSE |
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| 312 | END |
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| 313 | ENDCASE |
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| 314 | land = where(newmask EQ 0, cnt) |
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| 315 | if land[0] NE -1 then BEGIN |
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| 316 | land = (temporary(land))#replicate(1L, jpt) + replicate(1L, cnt)#(nx*ny*nz*lindgen(jpt)) |
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| 317 | res[temporary(land)] = valmask |
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| 318 | ENDIF |
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| 319 | END |
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| 320 | ELSE:return, report('input array must have 2, 3 or 4 dimensions') |
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| 321 | ENDCASE |
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| 322 | |
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| 323 | if keyword_set(key_performance) THEN print, 'time curl', systime(1)-time1 |
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| 324 | |
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| 325 | return, res |
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| 326 | END |
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