[2] | 1 | ;+ |
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| 2 | ; |
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[142] | 3 | ; @file_comments |
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[314] | 4 | ; Calculate the vertical component of the curl of a vectors field |
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| 5 | ; located on Arakawa C-grid. |
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[2] | 6 | ; |
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[142] | 7 | ; @categories |
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[157] | 8 | ; Calculation |
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[226] | 9 | ; |
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[142] | 10 | ; @param UU |
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[314] | 11 | ; Matrix representing the zonal coordinates (at U point) of a field of vectors |
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[268] | 12 | ; A 2D (xy), 3D (xyz or yt) or a structure readable by <pro>litchamp</pro> and containing |
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[242] | 13 | ; a 2D (xy), 3D (xyz or yt) array (4D case is not coded yet). |
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| 14 | ; Note that the dimension of the array must suit the domain dimension. |
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[2] | 15 | ; |
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[226] | 16 | ; @param VV |
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[314] | 17 | ; Matrix representing the meridional coordinates (at V point) of a field of vectors |
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[268] | 18 | ; A 2D (xy), 3D (xyz or yt) or a structure readable by <pro>litchamp</pro> and containing |
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[242] | 19 | ; a 2D (xy), 3D (xyz or yt) array (4D case is not coded yet). |
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| 20 | ; Note that the dimension of the array must suit the domain dimension. |
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[2] | 21 | ; |
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[167] | 22 | ; @keyword DIREC {type=scalar string} |
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[238] | 23 | ; Use if you want to call <pro>moyenne</pro> or |
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| 24 | ; <pro>grossemoyenne</pro> after the div computation |
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[167] | 25 | ; with a mean done in the DIREC direction |
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| 26 | ; |
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[314] | 27 | ; @keyword MILLION {default=0}{type=scalar: 0 or 1} |
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| 28 | ; Activate to multiply returned array by 1.e6 |
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| 29 | ; |
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| 30 | ; @keyword _EXTRA |
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| 31 | ; Used to declare that this routine accepts inherited keywords |
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| 32 | ; |
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[238] | 33 | ; @returns |
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[314] | 34 | ; the vertical component of the curl of the input data (with the same |
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| 35 | ; size) located at F point (see restrictions) |
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[2] | 36 | ; |
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[142] | 37 | ; @uses |
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[238] | 38 | ; cm_4cal |
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| 39 | ; cm_4data |
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[314] | 40 | ; cm_4mesh |
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[2] | 41 | ; |
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[142] | 42 | ; @restrictions |
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[2] | 43 | ; |
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[226] | 44 | ; - Works only for Arakawa C-grid. |
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[167] | 45 | ; - UU must be on U grid, VV must be on V grid |
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[242] | 46 | ; - 4D case is not coded yet |
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[167] | 47 | ; - the common variable jpt is used to differ xyz (jpt=1) and xyt (jpt\=1) cases. |
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[226] | 48 | ; - U and V arrays are cut in the same geographic domain. Because of the shift between |
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| 49 | ; T, U, V and F grids, it is possible that these two arrays do not have the same |
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| 50 | ; size and refer to different indexes. In this case, arrays are re-cut on |
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[231] | 51 | ; common indexes. To avoid these re-cuts, use the keyword /memeindice in |
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| 52 | ; <pro>domdef</pro> |
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[167] | 53 | ; - When computing the divergence, we update, vargrid, varname, varunits and the |
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| 54 | ; grid position parameters (firstxf, lastxf, nxf, firstyf, lastyf, nyf). |
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[226] | 55 | ; - points that cannot be computed (domain boundaries, coastline) are set to NaN |
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[2] | 56 | ; |
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[167] | 57 | ; @examples |
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[314] | 58 | ; IDL> @tst_initorca2 |
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[167] | 59 | ; IDL> plt, curl(dist(jpi,jpj), dist(jpi,jpj)) |
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[2] | 60 | ; |
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[226] | 61 | ; @history |
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[157] | 62 | ; Guillaume Roullet (grlod\@ipsl.jussieu.fr) |
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[163] | 63 | ; Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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| 64 | ; adaptation to work with a reduce domain |
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| 65 | ; 21/5/1999: missing values at !values.f_nan |
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[226] | 66 | ; |
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[142] | 67 | ; @version |
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| 68 | ; $Id$ |
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| 69 | ; |
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[226] | 70 | ; @todo |
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[242] | 71 | ; code the 4D case |
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[238] | 72 | ; |
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[2] | 73 | ;- |
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[231] | 74 | ; |
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[314] | 75 | FUNCTION curl, uu, vv, DIREC = direc, MILLION = million, _EXTRA = ex |
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[114] | 76 | ; |
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| 77 | compile_opt idl2, strictarrsubs |
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| 78 | ; |
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[167] | 79 | @cm_4cal ; for jpt |
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| 80 | @cm_4data ; for varname, vargrid, vardate, varunit, valmask |
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[226] | 81 | @cm_4mesh |
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[2] | 82 | ; |
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[314] | 83 | time1 = systime(1) ; for key_performance |
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[167] | 84 | ; |
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| 85 | IF finite(glamu[0])*finite(gphiu[0])*finite(glamv[0])*finite(gphiv[0]) EQ 0 THEN $ |
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[25] | 86 | return, report(['This version of curl is based on Arakawa C-grid.' $ |
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| 87 | , 'U and V grids must therefore be defined']) |
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| 88 | ; |
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[314] | 89 | gr = litchamp(uu, /grid) |
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| 90 | IF gr NE '' THEN BEGIN |
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| 91 | IF gr NE 'U' THEN return, report('the first parameter is not located on U grid, but on '+ strtrim(gr, 2) +'grid') |
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| 92 | ENDIF |
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| 93 | gr = litchamp(vv, /grid) |
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| 94 | IF gr NE '' THEN BEGIN |
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| 95 | IF gr NE 'V' THEN return, report('the second parameter is not located on V grid, but on '+ strtrim(gr, 2) +'grid') |
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| 96 | ENDIF |
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[167] | 97 | u = litchamp(uu) |
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| 98 | v = litchamp(vv) |
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[2] | 99 | |
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[167] | 100 | szu = size(u) |
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| 101 | szv = size(v) |
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[226] | 102 | |
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[167] | 103 | if szu[0] NE szv[0] then return, report('U and V input data must have the same number of dimensions') |
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[2] | 104 | |
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| 105 | ;------------------------------------------------------------ |
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[142] | 106 | ; We find common points between U and V |
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[2] | 107 | ;------------------------------------------------------------ |
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[167] | 108 | indicexu = (lindgen(jpi))[firstxu:firstxu+nxu-1] |
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| 109 | indicexv = (lindgen(jpi))[firstxv:firstxv+nxv-1] |
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| 110 | indicex = inter(indicexu, indicexv) |
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| 111 | indiceyu = (lindgen(jpj))[firstyu:firstyu+nyu-1] |
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| 112 | indiceyv = (lindgen(jpj))[firstyv:firstyv+nyv-1] |
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| 113 | indicey = inter(indiceyu, indiceyv) |
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[226] | 114 | nx = n_elements(indicex) |
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[167] | 115 | ny = n_elements(indicey) |
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| 116 | indice2d = lindgen(jpi, jpj) |
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| 117 | indice2d = indice2d[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1] |
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[2] | 118 | ;---------------------------------------------------------------------------- |
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[167] | 119 | vargrid = 'F' |
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| 120 | varname = 'vorticity' |
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[314] | 121 | IF keyword_set(million) THEN varunits = '1.e6*'+varunit+'/m' ELSE varunits = varunit+'/m' |
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| 122 | IF keyword_set(million) THEN scale = 1.e6 ELSE scale = 1. |
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[167] | 123 | if n_elements(valmask) EQ 0 THEN valmask = 1e20 |
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[314] | 124 | firstxf = indicex[0] & lastxf = indicex[0]+nx-1 & nxf = nx |
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| 125 | firstyf = indicey[0] & lastyf = indicey[0]+ny-1 & nyf = ny |
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[2] | 126 | ;---------------------------------------------------------------------------- |
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[167] | 127 | ;---------------------------------------------------------------------------- |
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| 128 | case 1 of |
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| 129 | ;---------------------------------------------------------------------------- |
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[2] | 130 | ;xyz |
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| 131 | ;---------------------------------------------------------------------------- |
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[226] | 132 | szu[0] EQ 3 AND jpt EQ 1:BEGIN |
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[2] | 133 | ;------------------------------------------------------------ |
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[142] | 134 | ; extraction of U and V on the appropriated domain |
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[2] | 135 | ;------------------------------------------------------------ |
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[167] | 136 | case 1 of |
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| 137 | szu[1] EQ nxu AND szu[2] EQ nyu AND $ |
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[226] | 138 | szv[1] EQ nxv AND szv[2] EQ nyv:BEGIN |
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[167] | 139 | case 1 of |
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| 140 | nxu NE nx:if indicex[0] EQ firstxu then u = u[0:nx-1, *, *] ELSE u = u[1: nx, *, *] |
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| 141 | nxv NE nx:if indicex[0] EQ firstxv then v = v[0:nx-1, *, *] ELSE v = v[1: nx, *, *] |
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| 142 | nyu NE ny:if indicey[0] EQ firstyu then u = u[*, 0:ny-1, *] ELSE u = u[*, 1: ny, *] |
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| 143 | nyv NE ny:if indicey[0] EQ firstyv then v = v[*, 0:ny-1, *] ELSE v = v[*, 1: ny, *] |
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| 144 | ELSE : |
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| 145 | endcase |
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| 146 | END |
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| 147 | szu[1] EQ jpi AND szu[2] EQ jpj AND $ |
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[226] | 148 | szv[1] EQ jpi AND szv[2] EQ jpj:BEGIN |
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[167] | 149 | u = u[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *] |
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| 150 | v = v[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *] |
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| 151 | END |
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| 152 | ELSE:return, -1 |
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| 153 | endcase |
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[2] | 154 | ;------------------------------------------------------------ |
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[167] | 155 | ; curl computation |
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[2] | 156 | ;------------------------------------------------------------ |
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[167] | 157 | coefu = ((e1u[indice2d])[*]#replicate(1., nzt)) $ |
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| 158 | * (umask())[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, firstzt:lastzt] |
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| 159 | landu = where(coefu EQ 0) |
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| 160 | if landu[0] NE -1 then coefu[temporary(landu)] = !values.f_nan |
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[226] | 161 | |
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[167] | 162 | coefv = ((e2v[indice2d])[*]#replicate(1., nzt)) $ |
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| 163 | *(vmask())[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, firstzt:lastzt] |
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| 164 | landv = where(coefv EQ 0) |
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| 165 | if landv[0] NE -1 then coefv[temporary(landv)] = !values.f_nan |
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[2] | 166 | |
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[314] | 167 | tabf = scale * (fmask())[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, firstzt:lastzt] $ |
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[167] | 168 | / ((e1f[indice2d]*e2f[indice2d])[*]#replicate(1., nzt)) |
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| 169 | landf = where(tabf EQ 0) |
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[2] | 170 | ; |
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[167] | 171 | zu = temporary(u) * temporary(coefu) |
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| 172 | zv = temporary(v) * temporary(coefv) |
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[2] | 173 | |
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[167] | 174 | psi = (shift(zv, -1, 0, 0)-zv) + (zu-shift(zu, 0, -1, 0)) |
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| 175 | psi = temporary(tabf) * temporary(psi) |
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[2] | 176 | ;------------------------------------------------------------ |
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[142] | 177 | ; Edging put at !values.f_nan |
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[2] | 178 | ;------------------------------------------------------------ |
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[167] | 179 | if NOT keyword_set(key_periodic) OR nx NE jpi then begin |
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| 180 | psi[0, *, *] = !values.f_nan |
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| 181 | psi[nx-1, *, *] = !values.f_nan |
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| 182 | endif |
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| 183 | psi[*, 0, *] = !values.f_nan |
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| 184 | psi[*, ny-1, *] = !values.f_nan |
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[2] | 185 | ; |
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[167] | 186 | if landf[0] NE -1 then psi[temporary(landf)] = valmask |
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| 187 | if keyword_set(direc) then psi = moyenne(psi, direc, /nan) |
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| 188 | END |
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[2] | 189 | ;---------------------------------------------------------------------------- |
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| 190 | ;---------------------------------------------------------------------------- |
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| 191 | ;xyt |
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| 192 | ;---------------------------------------------------------------------------- |
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| 193 | ;---------------------------------------------------------------------------- |
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[226] | 194 | szu[0] EQ 3 AND jpt GT 1:BEGIN |
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[2] | 195 | ;------------------------------------------------------------ |
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[142] | 196 | ; extraction of U and V on the appropriated domain |
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[2] | 197 | ;------------------------------------------------------------ |
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[167] | 198 | case 1 of |
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| 199 | szu[1] EQ nxu AND szu[2] EQ nyu AND $ |
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[226] | 200 | szv[1] EQ nxv AND szv[2] EQ nyv:BEGIN |
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[167] | 201 | if nxu NE nx then $ |
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[226] | 202 | if indicex[0] EQ firstxu then u = u[0:nx-1, *, *] ELSE u = u[1: nx, *, *] |
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[167] | 203 | IF nxv NE nx THEN $ |
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| 204 | if indicex[0] EQ firstxv then v = v[0:nx-1, *, *] ELSE v = v[1: nx, *, *] |
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| 205 | IF nyu NE ny THEN $ |
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[226] | 206 | if indicey[0] EQ firstyu then u = u[*, 0:ny-1, *] ELSE u = u[*, 1: ny, *] |
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[167] | 207 | IF nyv NE ny THEN $ |
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| 208 | if indicey[0] EQ firstyv then v = v[*, 0:ny-1, *] ELSE v = v[*, 1: ny, *] |
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| 209 | END |
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| 210 | szu[1] EQ jpi AND szu[2] EQ jpj AND $ |
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[226] | 211 | szv[1] EQ jpi AND szv[2] EQ jpj:BEGIN |
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[167] | 212 | u = u[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *] |
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| 213 | v = v[indicex[0]:indicex[0]+nx-1, indicey[0]:indicey[0]+ny-1, *] |
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| 214 | END |
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[314] | 215 | ELSE:return $ |
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| 216 | , report(['We cannot find re-cut on common indexes (see restriction un the header.).' $ |
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| 217 | , 'To avoid this problem, read the full domain' $ |
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| 218 | , 'or use the keyword /memeindice in domdef when defining the zoom area']) |
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| 219 | ENDCASE |
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[2] | 220 | ;---------------------------------------------------------------------------- |
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[167] | 221 | ; curl computation |
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[2] | 222 | ;---------------------------------------------------------------------------- |
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[167] | 223 | coefu = e1u[indice2d]*(umask())[indice2d+jpi*jpj*firstzt] |
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| 224 | landu = where(coefu EQ 0) |
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| 225 | if landu[0] NE -1 then coefu[temporary(landu)] = !values.f_nan |
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| 226 | coefu = temporary(coefu[*])#replicate(1., jpt) |
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[2] | 227 | ; |
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[167] | 228 | coefv = e2v[indice2d]*(vmask())[indice2d+jpi*jpj*firstzt] |
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| 229 | landv = where(coefv EQ 0) |
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| 230 | if landv[0] NE -1 then coefv[temporary(landv)] = !values.f_nan |
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| 231 | coefv = temporary(coefv[*])#replicate(1., jpt) |
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[2] | 232 | ; |
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[314] | 233 | tabf = scale * (fmask())[indice2d+jpi*jpj*firstzt]/(e1f[indice2d]*e2f[indice2d]) |
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[248] | 234 | tabf = reform(temporary(tabf[*])#replicate(1., jpt), nx, ny, jpt, /overwrite) |
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[167] | 235 | landf = where(tabf EQ 0) |
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[2] | 236 | ; |
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[167] | 237 | zu = temporary(u) * temporary(coefu) |
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| 238 | zv = temporary(v) * temporary(coefv) |
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| 239 | ; |
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| 240 | psi = (shift(zv, -1, 0, 0)-zv) + (zu-shift(zu, 0, -1, 0)) |
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| 241 | psi = temporary(tabf) * temporary(psi) |
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[2] | 242 | ;------------------------------------------------------------ |
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[142] | 243 | ; extraction of U and V on the appropriated domain |
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[2] | 244 | ;------------------------------------------------------------ |
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[167] | 245 | if NOT keyword_set(key_periodic) OR nx NE jpi then begin |
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| 246 | psi[0, *, *] = !values.f_nan |
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| 247 | psi[nx-1, *, *] = !values.f_nan |
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| 248 | endif |
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| 249 | psi[*, 0, *] = !values.f_nan |
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| 250 | psi[*, ny-1, *] = !values.f_nan |
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| 251 | if landf[0] NE -1 then psi[temporary(landf)] = valmask |
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| 252 | if keyword_set(direc) then psi = grossemoyenne(psi, direc, /nan) |
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| 253 | END |
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[2] | 254 | ;---------------------------------------------------------------------------- |
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| 255 | ;---------------------------------------------------------------------------- |
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| 256 | ;xyzt |
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| 257 | ;---------------------------------------------------------------------------- |
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| 258 | ;---------------------------------------------------------------------------- |
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[226] | 259 | szu[0] EQ 4:BEGIN |
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[167] | 260 | return, report('Case not coded contact saxo team or make a do loop!') |
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| 261 | END |
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[2] | 262 | ;---------------------------------------------------------------------------- |
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| 263 | ;---------------------------------------------------------------------------- |
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| 264 | ;xy |
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| 265 | ;---------------------------------------------------------------------------- |
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| 266 | ;---------------------------------------------------------------------------- |
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[226] | 267 | szu[0] EQ 2:BEGIN |
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[2] | 268 | ;------------------------------------------------------------ |
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| 269 | ;------------------------------------------------------------ |
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[167] | 270 | case 1 of |
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| 271 | szu[1] EQ nxu AND szu[2] EQ nyu AND $ |
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[226] | 272 | szv[1] EQ nxv AND szv[2] EQ nyv:BEGIN |
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[167] | 273 | if nxu NE nx then $ |
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[226] | 274 | if indicex[0] EQ firstxu then u = u[0:nx-1, *] ELSE u = u[1: nx, *] |
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[167] | 275 | IF nxv NE nx THEN $ |
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| 276 | if indicex[0] EQ firstxv then v = v[0:nx-1, *] ELSE v = v[1: nx, *] |
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| 277 | IF nyu NE ny THEN $ |
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[226] | 278 | if indicey[0] EQ firstyu then u = u[*, 0:ny-1] ELSE u = u[*, 1: ny] |
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[167] | 279 | IF nyv NE ny THEN $ |
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| 280 | if indicey[0] EQ firstyv then v = v[*, 0:ny-1] ELSE v = v[*, 1: ny] |
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| 281 | END |
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| 282 | szu[1] EQ jpi AND szu[2] EQ jpj AND $ |
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[226] | 283 | szv[1] EQ jpi AND szv[2] EQ jpj:BEGIN |
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[167] | 284 | u = u[indice2d] |
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| 285 | v = v[indice2d] |
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| 286 | END |
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| 287 | ELSE:return, -1 |
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| 288 | endcase |
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[2] | 289 | ;------------------------------------------------------------ |
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[167] | 290 | ; curl computation |
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[2] | 291 | ;------------------------------------------------------------ |
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[167] | 292 | coefu = e1u[indice2d]*(umask())[indice2d+jpi*jpj*firstzt] |
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| 293 | landu = where(coefu EQ 0) |
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| 294 | if landu[0] NE -1 then coefu[temporary(landu)] = !values.f_nan |
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| 295 | coefv = e2v[indice2d]*(vmask())[indice2d+jpi*jpj*firstzt] |
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| 296 | landv = where(coefv EQ 0) |
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| 297 | if landv[0] NE -1 then coefv[temporary(landv)] = !values.f_nan |
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[314] | 298 | tabf = scale * (fmask())[indice2d+jpi*jpj*firstzt]/(e1f[indice2d]*e2f[indice2d]) |
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[167] | 299 | landf = where(tabf EQ 0) |
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[2] | 300 | ; |
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[167] | 301 | zu = temporary(u) * temporary(coefu) |
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| 302 | zv = temporary(v) * temporary(coefv) |
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[2] | 303 | |
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[167] | 304 | psi = (shift(zv, -1, 0)-zv) + (zu-shift(zu, 0, -1)) |
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| 305 | psi = temporary(tabf) * temporary(psi) |
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[2] | 306 | ;------------------------------------------------------------ |
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[142] | 307 | ; Edging put at !values.f_nan |
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[2] | 308 | ;------------------------------------------------------------ |
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[167] | 309 | if NOT keyword_set(key_periodic) OR nx NE jpi then begin |
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| 310 | psi[0, *] = !values.f_nan |
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| 311 | psi[nx-1, *] = !values.f_nan |
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| 312 | endif |
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| 313 | psi[*, 0] = !values.f_nan |
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| 314 | psi[*, ny-1] = !values.f_nan |
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[2] | 315 | ; |
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[167] | 316 | if landf[0] NE -1 then psi[temporary(landf)] = valmask |
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| 317 | if keyword_set(direc) then psi = moyenne(psi, direc, /nan) |
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| 318 | END |
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| 319 | ;---------------------------------------------------------------------------- |
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| 320 | ;---------------------------------------------------------------------------- |
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| 321 | ELSE:return, report('U and V input arrays must have 2, 3 or 4 dimensions') |
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| 322 | ENDCASE |
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[2] | 323 | ;------------------------------------------------------------ |
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[314] | 324 | if keyword_set(key_performance) THEN print, 'time curl', systime(1)-time1 |
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[2] | 325 | |
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[167] | 326 | return, psi |
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[2] | 327 | end |
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