[1677] | 1 | \magnification =\magstep1 |
---|
| 2 | \count0=90 |
---|
| 3 | %definitions |
---|
| 4 | |
---|
| 5 | %end of definitions |
---|
| 6 | |
---|
| 7 | |
---|
| 8 | \centerline{ Olivier Thual, June 30$^{\rm th}$ 1992} |
---|
| 9 | \bigskip |
---|
| 10 | |
---|
| 11 | \centerline{\bf SIMPLE OCEAN-ATMOSPHERE INTERPOLATION.} |
---|
| 12 | \centerline{\bf PART B: SOFTWARE IMPLEMENATION} |
---|
| 13 | |
---|
| 14 | |
---|
| 15 | \bigskip |
---|
| 16 | |
---|
| 17 | |
---|
| 18 | A set of FORTRAN subroutines constitutes an implementation the ``naive'' |
---|
| 19 | grid-to-grid interpolation method which has been exposed in the previous |
---|
| 20 | Part A of this letter. This implementation is tested for both idealized, |
---|
| 21 | EMERAUDE or OPA grids, masks and scalar fields. These |
---|
| 22 | subroutines can be used in the first version the ocean-atmosphere coupler. |
---|
| 23 | |
---|
| 24 | |
---|
| 25 | |
---|
| 26 | |
---|
| 27 | |
---|
| 28 | \beginsection 1. INTRODUCTION |
---|
| 29 | |
---|
| 30 | Coupling two atmospheric and oceanic general circulation models (AGCM |
---|
| 31 | and OGCM) having two different grids and sea-land masks, requires the |
---|
| 32 | interpolation of fluxes from the atmosphere to the ocean grids and of the |
---|
| 33 | sea surface temperature (SST) in the reverse direction. A simple method |
---|
| 34 | to perform these interpolations have been presented in the previous Epicoa |
---|
| 35 | Letter [1] called ``Simple ocean-atmosphere interpolation. Part A: the method'' as a |
---|
| 36 | particular case of a more general class of interpolations based on |
---|
| 37 | optimization theory (Lagrangian formalism). |
---|
| 38 | |
---|
| 39 | \medskip |
---|
| 40 | |
---|
| 41 | The name of ``naive method'' which has been given to denote one of the simplest |
---|
| 42 | interpolation among this class, comes from the motivations |
---|
| 43 | which have governed its implementation. It was designed with simplicity |
---|
| 44 | requirement and short deadlines in order to reach as quickly as possible a |
---|
| 45 | first version of an ocean-atmosphere coupler. A more ``sovarphisticated |
---|
| 46 | method'' is beeing studied in parallel by Norman BARTH [2]. This method |
---|
| 47 | imposes the conservation of the field integral on each mesh of the coarser |
---|
| 48 | grid, and requires, in order to satisfy these multiple constraints, the |
---|
| 49 | mutiplication by matrices of the coarser grid size square for each |
---|
| 50 | interpolation. |
---|
| 51 | |
---|
| 52 | A lot of the concepts which are used in the ``naive method'', comes from |
---|
| 53 | the ones that are considered in the ``sovarphisticated method'' [3,2], but retain |
---|
| 54 | only the low cost ones. The coupler will offer the possibility of choosing |
---|
| 55 | between the ``naive'' or ``sovarphisticated'' methods, depending on various |
---|
| 56 | constraints (memory space, computer time, efficiency, accuracy, etc...). |
---|
| 57 | Other methods, like the one of Philippe DANDIN [4], will also be pluged into |
---|
| 58 | the coupler. |
---|
| 59 | |
---|
| 60 | |
---|
| 61 | |
---|
| 62 | |
---|
| 63 | |
---|
| 64 | \medskip |
---|
| 65 | |
---|
| 66 | |
---|
| 67 | |
---|
| 68 | |
---|
| 69 | |
---|
| 70 | The ``naive method'' can be summarized in few words: knowing the values |
---|
| 71 | of a field on a source grid, the values on a point of the target grid is |
---|
| 72 | calculated by summing the values if its $L$th closest neighbors, with a |
---|
| 73 | weight which quicky decreases with the interdistance. |
---|
| 74 | |
---|
| 75 | |
---|
| 76 | |
---|
| 77 | \medskip |
---|
| 78 | |
---|
| 79 | In Section 2, I recall the definition of the ``naive method'' in a concise |
---|
| 80 | way. In Section 3, I briefly |
---|
| 81 | describe the ``naive method library'', which is the set of FORTRAN |
---|
| 82 | subroutines that I have written to implement the method, and focus on the |
---|
| 83 | visible part of the iceberg that the coupler will need to know. Some basic |
---|
| 84 | tests of this method are presented, showing that there is no trivial bug |
---|
| 85 | left. |
---|
| 86 | |
---|
| 87 | |
---|
| 88 | |
---|
| 89 | |
---|
| 90 | |
---|
| 91 | |
---|
| 92 | |
---|
| 93 | |
---|
| 94 | |
---|
| 95 | \beginsection 2. THE NAIVE METHOD |
---|
| 96 | |
---|
| 97 | In Part A of this letter [1] general considerations about grid-to-grid |
---|
| 98 | interpolation have been presented, and a ``simple ocean-atmosphere method'' have be |
---|
| 99 | presented in this general framework. Here I only present the materials |
---|
| 100 | necessary to its implementation. |
---|
| 101 | |
---|
| 102 | |
---|
| 103 | |
---|
| 104 | \beginsection 2.1 Interpolation without constraints (SST) |
---|
| 105 | |
---|
| 106 | Let $(b_j), j=1,N^b$ be the SST (sea surface temperature) on the ocean grid |
---|
| 107 | B, defined by the points $(r^b_j), j=1,N^b$. Only the umasked points are |
---|
| 108 | considered in this definition of the grids and the following formula. The |
---|
| 109 | values $(a_i), i=1,N^a$ of the SST on the atmospheric grid A, defined by |
---|
| 110 | the points $(r^a_i), i=1,N^a$, are given, in the naive method, by: |
---|
| 111 | $$ |
---|
| 112 | a_i={1\over Z^b( r^a_i)} \sum_{m\in J(r_i^a)} b_i \; |
---|
| 113 | \phi\left( {\left| r_j^b-r_i^a\right| \over \sigma_b } \right) |
---|
| 114 | \eqno(2.1)\; , |
---|
| 115 | $$ |
---|
| 116 | where $J(r)=\{j_1(r), j_2(r), ..., j_{L^b}(r)\}$ is the set containing the |
---|
| 117 | indices of the $L^b$ closest neighbors $r_m^b$ in grid B, of a point $r$ |
---|
| 118 | located anywhere, and the normalizing function $Z^b$, defined for all grids |
---|
| 119 | points of the gird A is: |
---|
| 120 | $$ |
---|
| 121 | Z^b( r^a_i)= \sum_{m\in J(r_i^a)} |
---|
| 122 | \phi\left( {\left| r_j^b-r_i^a\right| \over \sigma_b } \right) \; . |
---|
| 123 | \eqno(2.2) |
---|
| 124 | $$ |
---|
| 125 | |
---|
| 126 | |
---|
| 127 | |
---|
| 128 | In its present implementation the weight function $\phi$ is a gaussian: |
---|
| 129 | $$ |
---|
| 130 | \phi(u) = e^{-u^2 \over 2} |
---|
| 131 | \eqno(2.3) \;. |
---|
| 132 | $$ |
---|
| 133 | |
---|
| 134 | The variance $ \sigma_b$ is of the order one or two times the average |
---|
| 135 | mesh size of the grid B. Other choices of the weight functions are |
---|
| 136 | discussed below. |
---|
| 137 | |
---|
| 138 | |
---|
| 139 | |
---|
| 140 | |
---|
| 141 | |
---|
| 142 | |
---|
| 143 | |
---|
| 144 | |
---|
| 145 | |
---|
| 146 | |
---|
| 147 | |
---|
| 148 | \beginsection 2.2 Summary of the Lagrangian formalism |
---|
| 149 | |
---|
| 150 | As explained in Part A [1], the extension of the above grid-to-grid |
---|
| 151 | interpolation to an interpolation with constraints can be defined through a |
---|
| 152 | formalism in which a Lagrangian functionnal is to be minimized under |
---|
| 153 | these constraints. |
---|
| 154 | |
---|
| 155 | |
---|
| 156 | |
---|
| 157 | In this formalism, both the source grid A (on which $N^a$ values $a_i$ are |
---|
| 158 | known) and the target grid B (on which $N^b$ values $b_i$ are to be found) |
---|
| 159 | are associated to an interpolation which reads: |
---|
| 160 | |
---|
| 161 | $$ |
---|
| 162 | f(r)= \sum_{i=1}^{N^a} a_i \varphi_i(r) |
---|
| 163 | \eqno(2.4) |
---|
| 164 | $$ |
---|
| 165 | for grid A, which is made of $N^a$ grid points, and |
---|
| 166 | $$ |
---|
| 167 | g(r)= \sum_{j=1}^{N^b} b_j \psi_j(r) |
---|
| 168 | \eqno(2.5) |
---|
| 169 | $$ |
---|
| 170 | for grid B, which is made of $N^b$ grid points. |
---|
| 171 | |
---|
| 172 | |
---|
| 173 | |
---|
| 174 | If we impose that the equality of the integrals of the two functions $f$ |
---|
| 175 | and $g$ (fluxes) on the two respective domains that the two grids are |
---|
| 176 | covering, a constrained interpolation method is defined by the |
---|
| 177 | minimization of the Lagrangian: |
---|
| 178 | $$ |
---|
| 179 | L(b_1,b_2,...,b_{N^b}) = \int [f(r)-g(r)]^2 \; dr + |
---|
| 180 | \lambda \int [f(r)-g(r)] \; dr |
---|
| 181 | \eqno(2.6) |
---|
| 182 | $$ |
---|
| 183 | subject to the constraints $ \int [f(r)-g(r)] \; dr =0$. |
---|
| 184 | |
---|
| 185 | With the matrix notations $B=(b_j)$, $A=(a_i)$, $H=(\int \psi_j dr)$, $G=(\int |
---|
| 186 | \varphi_i dr)$ and $V=(\int \psi_m \psi_j dr)$, where $i=1,N^a$ and $j$ |
---|
| 187 | or $m=1,N^b$, the solution of the minimization of $L$, subject to the |
---|
| 188 | constraint $HB=GA$, is given by $B=B^*-\lambda |
---|
| 189 | V^{-1}H$, where $B^*= V^{-1}UA$ is the solution without constraint and |
---|
| 190 | $\lambda$, the Lagragian multiplicator, is given by |
---|
| 191 | $$ |
---|
| 192 | \lambda= { HB^*-GA \over HV^{-1}H} |
---|
| 193 | \eqno(2.7) \;. |
---|
| 194 | $$ |
---|
| 195 | |
---|
| 196 | |
---|
| 197 | |
---|
| 198 | The solution with constraints reads, in its final form |
---|
| 199 | $$ |
---|
| 200 | \eqalign{ |
---|
| 201 | B=& B^* -{ HB^* - GA \over HV^{-1}H } V^{-1}H \cr |
---|
| 202 | =& V^{-1}UA- {HV^{-1}UA - GA\over HV^{-1}H} V^{-1}H } |
---|
| 203 | \eqno(2.8) \;. |
---|
| 204 | $$ |
---|
| 205 | (NB: this expression |
---|
| 206 | and Equation 2.6 gives the errata of Equations 4.4, 4.6 and 4.7 of the first |
---|
| 207 | version {\bf 0615} of the Part A |
---|
| 208 | of this letter, now revised [1]). |
---|
| 209 | |
---|
| 210 | \beginsection 2.3 Interpolation with one constraint (Flux) |
---|
| 211 | |
---|
| 212 | The easiest implementation of the above interpolation with constraint is |
---|
| 213 | obtained when $V$ is the unity matrix, that is when the interpolation |
---|
| 214 | associated with the target grid is the ``closest neighbor'' interpolation |
---|
| 215 | (see Part A [1] for details). |
---|
| 216 | |
---|
| 217 | |
---|
| 218 | |
---|
| 219 | The above naive method, combined with this global conservation constraint |
---|
| 220 | of the integrals over the two domains (total fluxes) read: |
---|
| 221 | |
---|
| 222 | $$ |
---|
| 223 | b_j=b^*_j - \lambda h_j |
---|
| 224 | \eqno(2.9) |
---|
| 225 | $$ |
---|
| 226 | where the unconstrained solution is |
---|
| 227 | $$ |
---|
| 228 | b^*_j={1\over Z^a( r^b_j)} \sum_{m\in I(r_j^b)} a_i |
---|
| 229 | \phi\left( {\left| r_i^a-r_j^b\right| \over \sigma_a } \right) |
---|
| 230 | \eqno(2.10)\; , |
---|
| 231 | $$ |
---|
| 232 | and the Lagrangian multiplier is given by |
---|
| 233 | $$ |
---|
| 234 | \lambda = {\sum_{j=1}^{N^b} h_j b^*_j - \sum_{i=1}^{N^a} g_i a^*_i |
---|
| 235 | \over \sum_{j=1}^{N^b} h_j h_j } |
---|
| 236 | \eqno(2.11) |
---|
| 237 | $$ |
---|
| 238 | where $I(r)=\{i_1(r), i_2(r), ..., i_{L^b}(r)\}$ is the set containing the indices |
---|
| 239 | of the $L^a$ closest neighbors $r_m^a$ in grid A, of a point $r$ located |
---|
| 240 | anywhere, and the normalizing function $Z^a$, defined for all grids points |
---|
| 241 | of the gird B is: |
---|
| 242 | $$ |
---|
| 243 | Z^a( r^b_j)= \sum_{m\in I(r_j^b)} |
---|
| 244 | \phi\left( {\left| r_i^a-r_j^b\right| \over \sigma_a } \right) \; . |
---|
| 245 | \eqno(2.12) |
---|
| 246 | $$ |
---|
| 247 | |
---|
| 248 | |
---|
| 249 | |
---|
| 250 | In the above expressions, $h_j$ is the area of the grid B meshes (see Part |
---|
| 251 | A [1]) and |
---|
| 252 | $$ |
---|
| 253 | g_i= \int {1\over Z^a( r)} \phi\left( {\left|r- r_i^a\right| \over \sigma_a |
---|
| 254 | }\right)\; dr |
---|
| 255 | \eqno(2.12) |
---|
| 256 | $$ |
---|
| 257 | |
---|
| 258 | In the present implementation of the software, these coefficients have been |
---|
| 259 | approximated by the surface of the meshes, i.e., $g_i$ is |
---|
| 260 | the surface of the set of all the points which admit $r_i^a$ as their |
---|
| 261 | closest neighbor. This is as if the closest neighbor |
---|
| 262 | interpolation were chosen in the constraint, while another interpolation is |
---|
| 263 | chosen in the quadratic term of the Lagrangain. |
---|
| 264 | However, in the future evolution of the |
---|
| 265 | software, more elabored values of $g_i$ will be possible. |
---|
| 266 | |
---|
| 267 | |
---|
| 268 | |
---|
| 269 | |
---|
| 270 | |
---|
| 271 | \vfill\eject |
---|
| 272 | |
---|
| 273 | |
---|
| 274 | |
---|
| 275 | |
---|
| 276 | |
---|
| 277 | |
---|
| 278 | |
---|
| 279 | |
---|
| 280 | |
---|
| 281 | \beginsection 3. IMPLEMENTATION OF THE METHOD |
---|
| 282 | |
---|
| 283 | The above method have been implemented through a set of FORTRAN subroutines |
---|
| 284 | which constitutes the ``naive method library''. Some practical details |
---|
| 285 | are given in view of its use in the coupler, or for testing purposes. |
---|
| 286 | A first set of basic tests |
---|
| 287 | is shown, and the future evolution of this library is hinted. |
---|
| 288 | |
---|
| 289 | |
---|
| 290 | |
---|
| 291 | \beginsection 3.1 The ``naive method library'' |
---|
| 292 | |
---|
| 293 | The directory |
---|
| 294 | {\tt greenh@cerfacs.fr:/usr1/pub/numlab/naiv} contains a software |
---|
| 295 | environment and a set of subroutines constituting the current |
---|
| 296 | implementation of the ``naive'' grid-to-grid interpolation method. These |
---|
| 297 | FORTRAN subroutines have been written following the DOCTOR norm [5, 6]. |
---|
| 298 | A main program performs various tests of these subroutines, and give |
---|
| 299 | examples of the use of theses subroutines. |
---|
| 300 | |
---|
| 301 | |
---|
| 302 | |
---|
| 303 | \bigskip |
---|
| 304 | |
---|
| 305 | |
---|
| 306 | |
---|
| 307 | The initialization of the grids, the masks and the fields is dependant of the |
---|
| 308 | atmospheric and oceanic GCMs to be coupled, and will communicated by |
---|
| 309 | them to the coupler independantly of the interpolation task. However, the |
---|
| 310 | present library also contains subroutines which generates academic grids, |
---|
| 311 | masks or fields for testing purposes, and, so far, the initialization of a |
---|
| 312 | 128x64 EMERAUDE grid, a 228x94 OPA-Pacific grid and some EMERAUDE |
---|
| 313 | fluxes. Extension to other realistic grids for testing purposes are planned. |
---|
| 314 | |
---|
| 315 | |
---|
| 316 | \beginsection 3.2 A first draft for a manual |
---|
| 317 | |
---|
| 318 | This library is written is such a way that only a few items |
---|
| 319 | need to be visible from the coupler. The names of these subroutines |
---|
| 320 | start with {\tt NA}. These high level subroutines call basic subroutines |
---|
| 321 | with, most of the time, |
---|
| 322 | a name starting with {\tt PL}. |
---|
| 323 | A very preliminary draft is given through the name of these |
---|
| 324 | subroutines. |
---|
| 325 | |
---|
| 326 | |
---|
| 327 | \medskip |
---|
| 328 | \medskip |
---|
| 329 | \noindent{\bf Include files} |
---|
| 330 | \medskip |
---|
| 331 | |
---|
| 332 | These are, at first, three include files containing the commons which |
---|
| 333 | describe the grids: |
---|
| 334 | |
---|
| 335 | |
---|
| 336 | |
---|
| 337 | \medskip |
---|
| 338 | |
---|
| 339 | \item{}{\tt NAGRA.H}, containing the common for the arrays of grid A (e.g. |
---|
| 340 | atmsopheric). |
---|
| 341 | |
---|
| 342 | |
---|
| 343 | |
---|
| 344 | \medskip |
---|
| 345 | |
---|
| 346 | \item{}{\tt NAGRB.H}, containing the common for the arrays grid B (e.g. |
---|
| 347 | ocean). |
---|
| 348 | |
---|
| 349 | |
---|
| 350 | |
---|
| 351 | \medskip |
---|
| 352 | |
---|
| 353 | \item{}{\tt NAGAB.H}, containing the commons for the weight arrays used |
---|
| 354 | in the grid-to-grid interpolations. |
---|
| 355 | |
---|
| 356 | |
---|
| 357 | |
---|
| 358 | \medskip |
---|
| 359 | \medskip |
---|
| 360 | \noindent{\bf Grid initializations subroutines} |
---|
| 361 | \medskip |
---|
| 362 | |
---|
| 363 | The two first sets of commons of {\tt NAGRA.H} and {\tt NABRB.H}, for grid |
---|
| 364 | A and grid B, can be initialized by the subroutines: |
---|
| 365 | |
---|
| 366 | |
---|
| 367 | |
---|
| 368 | \medskip |
---|
| 369 | |
---|
| 370 | \item{} {\tt NAGRDA }, to initialize idealized A grids. |
---|
| 371 | |
---|
| 372 | |
---|
| 373 | |
---|
| 374 | \medskip |
---|
| 375 | |
---|
| 376 | \item{} {\tt NAGRDB }, to initialize idealized B grids. |
---|
| 377 | |
---|
| 378 | |
---|
| 379 | |
---|
| 380 | \medskip |
---|
| 381 | |
---|
| 382 | \item{} {\tt NAGMRO }, to initialize the A grid from the EMERAUDE |
---|
| 383 | 128x64 global grid. |
---|
| 384 | |
---|
| 385 | |
---|
| 386 | |
---|
| 387 | \medskip |
---|
| 388 | |
---|
| 389 | \item{} {\tt NAGOPA}, to initialize idealized B grid from the OPA |
---|
| 390 | 226x94 Pacific grid. |
---|
| 391 | |
---|
| 392 | |
---|
| 393 | |
---|
| 394 | |
---|
| 395 | \medskip |
---|
| 396 | \medskip |
---|
| 397 | \noindent{\bf Interpolations subroutines} |
---|
| 398 | \medskip |
---|
| 399 | |
---|
| 400 | The last set of common, in {\tt NAGAB.H} are calculated in the subourtine: |
---|
| 401 | |
---|
| 402 | \medskip |
---|
| 403 | |
---|
| 404 | \item{} {\tt NASET(amesh,bmesh)}, |
---|
| 405 | to initialize the weight arrays of the interpolation, given the variances |
---|
| 406 | of the weight functions {\tt amesh} and {\tt amesh}. |
---|
| 407 | |
---|
| 408 | |
---|
| 409 | \medskip |
---|
| 410 | |
---|
| 411 | |
---|
| 412 | |
---|
| 413 | Once the three initialisations are done, the grid A to grid B, and grid B to |
---|
| 414 | grid A interpolations are performed by the two subroutines: |
---|
| 415 | |
---|
| 416 | |
---|
| 417 | |
---|
| 418 | \medskip |
---|
| 419 | |
---|
| 420 | |
---|
| 421 | |
---|
| 422 | \item{} {\tt NASST(ssta,sstb)}, to interpolate a field from grid B to |
---|
| 423 | grid A without constraint |
---|
| 424 | (e.g. the SST). |
---|
| 425 | |
---|
| 426 | \medskip |
---|
| 427 | |
---|
| 428 | \item{} {\tt NAFLUX(fluxb,fluxa)}, to interpolate a field from grid A to |
---|
| 429 | grid B while conserving |
---|
| 430 | its average between the two unmasked domains (e.g., fluxes). |
---|
| 431 | |
---|
| 432 | \medskip |
---|
| 433 | \medskip |
---|
| 434 | \noindent{\bf Basic subroutines} |
---|
| 435 | \medskip |
---|
| 436 | |
---|
| 437 | These suboutines are called by the higher level subroutines, and need not to |
---|
| 438 | be known by the first time user: |
---|
| 439 | |
---|
| 440 | |
---|
| 441 | {\tt |
---|
| 442 | PLDIS2.f PLGPRI.f PLGRDU.f PLQQT.f PLSCAR.f PLSST.f PLVISU.f |
---|
| 443 | |
---|
| 444 | |
---|
| 445 | PLFLUX.f PLGRDC.f PLINS.f PLRHAL.f PLSORT.f PLSTAT.f |
---|
| 446 | |
---|
| 447 | |
---|
| 448 | PLGAUS.f PLGRDP.f PLMASQ.f PLRHO.f PLSSPH.f PLTMRO.f |
---|
| 449 | |
---|
| 450 | |
---|
| 451 | IMPR.f IMPRI.f |
---|
| 452 | } |
---|
| 453 | |
---|
| 454 | \medskip |
---|
| 455 | \medskip |
---|
| 456 | \noindent{\bf Testing subroutines} |
---|
| 457 | \medskip |
---|
| 458 | |
---|
| 459 | |
---|
| 460 | Examples of the use of these ``coupler-visible'' subroutines (with names |
---|
| 461 | starting by {\tt NA}), or of the ``basic'' subroutines (with names starting by PL) |
---|
| 462 | can be found in several test performing subroutines: |
---|
| 463 | |
---|
| 464 | \medskip |
---|
| 465 | |
---|
| 466 | \item{} {\tt NATFX(fluxb,fluxa)}: |
---|
| 467 | call {\tt NAFLUX} and visualizes the fields. |
---|
| 468 | |
---|
| 469 | \medskip |
---|
| 470 | |
---|
| 471 | \item{} {\tt NATST(ssta,sstb)}: call {\tt NASST} and visualizes the fields. |
---|
| 472 | |
---|
| 473 | \medskip |
---|
| 474 | |
---|
| 475 | \item{} {\tt NATES1(flda,fldb,fldaa)}: calls |
---|
| 476 | {\tt NASST} and then {\tt NAFLUX}, visualizes the fields, and compares the |
---|
| 477 | intial and final fields. |
---|
| 478 | |
---|
| 479 | \medskip |
---|
| 480 | |
---|
| 481 | \item{} {\tt NATES2(flda,fldb,fldaa)}: calls |
---|
| 482 | {\tt NAFLUX} and then {\tt NASST}, and compares the |
---|
| 483 | intial and final fields. |
---|
| 484 | \medskip |
---|
| 485 | |
---|
| 486 | \item{} {\tt NATES3(flda,fldb,fldaa,kvisuo}: calls |
---|
| 487 | {\tt NAFLUX} and then {\tt NASST} and visualizes the fields in a way that |
---|
| 488 | allows animations. |
---|
| 489 | Typically, the influence of the variance of the weight functions can be |
---|
| 490 | studied with this subroutine, through animation of the error field. |
---|
| 491 | |
---|
| 492 | \medskip |
---|
| 493 | \medskip |
---|
| 494 | |
---|
| 495 | These testing subroutines assume |
---|
| 496 | that the grids and the interpolation coefficients have already been |
---|
| 497 | initialized. |
---|
| 498 | |
---|
| 499 | |
---|
| 500 | |
---|
| 501 | \beginsection 3.3 Tests of the grid-to-grid interpolation |
---|
| 502 | |
---|
| 503 | Various tests have been performed to check that the library of subroutines of |
---|
| 504 | was free of trivial tests. However, systematic tests of the performance of |
---|
| 505 | the ``naive method'' and its sensibility to its adjustable parameters (shape |
---|
| 506 | and variance of the weight functions, number of neighbours, relative |
---|
| 507 | positions of the masks, ...) still remain to be done. |
---|
| 508 | |
---|
| 509 | |
---|
| 510 | |
---|
| 511 | \medskip |
---|
| 512 | |
---|
| 513 | In the following tests, the weight function $\phi$ |
---|
| 514 | is a Gaussian, with a uniform |
---|
| 515 | variance on a given grid. |
---|
| 516 | |
---|
| 517 | \medskip |
---|
| 518 | |
---|
| 519 | |
---|
| 520 | |
---|
| 521 | The most trivial test was to check that with a one neighbour interpolation, |
---|
| 522 | and the same grid, the interpolation was giving the same field. |
---|
| 523 | |
---|
| 524 | |
---|
| 525 | |
---|
| 526 | \medskip |
---|
| 527 | |
---|
| 528 | |
---|
| 529 | |
---|
| 530 | The second test has been made with an analytically generated field $f(x,y)=$ |
---|
| 531 | $\cos (k1 x)$ $\cos(k_2 y)$ interpolation forward (NAFLUX) an backward |
---|
| 532 | (NASST) between a cartesian square grid and a polar disk grid, with |
---|
| 533 | non-coincident masks. Figure show an example in which |
---|
| 534 | small neighbour number has been given |
---|
| 535 | to the naive method. This test shows that the original field is well |
---|
| 536 | recovered, excepted, of course, in the regions where the mask are far from |
---|
| 537 | coincidence. |
---|
| 538 | |
---|
| 539 | \medskip |
---|
| 540 | |
---|
| 541 | |
---|
| 542 | |
---|
| 543 | |
---|
| 544 | |
---|
| 545 | The third test uses two grids of very different resolutions, with a mask |
---|
| 546 | defined by an analytical curve. The case of a circle is shown on Figure 2, |
---|
| 547 | and more complex contour should be used in future tests of this kind. |
---|
| 548 | |
---|
| 549 | \medskip |
---|
| 550 | |
---|
| 551 | |
---|
| 552 | |
---|
| 553 | |
---|
| 554 | |
---|
| 555 | The fourth test (Figure 3) studies the interpolation between an |
---|
| 556 | analytically defined field $f(x,y)$ on the masked EMERAUDE grid |
---|
| 557 | (Atmospheric GCM) and the unmasked Pacific OPA (Ocean GCM). In the |
---|
| 558 | forward interpolation (NAFLUX), the trace of the EMERAUDE mask can be |
---|
| 559 | seen on the unmasked OPA domain. In the backward direction (NASST), the |
---|
| 560 | original field is well recovered on the tropical Pacific, and, of course, |
---|
| 561 | meaninless far from this region. |
---|
| 562 | |
---|
| 563 | |
---|
| 564 | |
---|
| 565 | The last test (Figure 4) deals with a realistic flux field (stress $\tau_ x$ |
---|
| 566 | in the longitudinal direction) of EMERAUDE and shows it interpolation on |
---|
| 567 | the Pacific OPA masked grid. Comparison with Philippe Dandin's |
---|
| 568 | interpolation's method is under progress. |
---|
| 569 | |
---|
| 570 | |
---|
| 571 | |
---|
| 572 | \beginsection 3.4 Future developments |
---|
| 573 | |
---|
| 574 | In the present state of the ``naive method library'', |
---|
| 575 | the coupler-visible items are |
---|
| 576 | ready to be used in the coupler. However, they are at the |
---|
| 577 | stage of a $\beta$-release, and will be improved by furthers tunings. The |
---|
| 578 | possibility of choosing weight functions which shape and variance can vary |
---|
| 579 | with the index of the grid point will be given. This will allow, for instance, |
---|
| 580 | to use ``non-smoothing'' function, e.g. the functions associated to the |
---|
| 581 | spectral method used on the grid [7]. This will also allow to pay special |
---|
| 582 | attention to land-sea regions, or implement interpolation method based on |
---|
| 583 | ``wavelet decomposition''. |
---|
| 584 | |
---|
| 585 | |
---|
| 586 | |
---|
| 587 | %The calculation of the grid surface elements is not yet properly |
---|
| 588 | %implemented for spherical grids. |
---|
| 589 | |
---|
| 590 | |
---|
| 591 | |
---|
| 592 | \beginsection 4. CONCLUSION |
---|
| 593 | |
---|
| 594 | The present letter can be considered as a first draft of a user manual of |
---|
| 595 | the ``naive method''. A concise presentation |
---|
| 596 | of the method has been presented, |
---|
| 597 | as well ot its possible future evolution. Pratical details for the |
---|
| 598 | use of the ``naive method library'' have been given in the spirit of its |
---|
| 599 | integration into the coupler. The names of testing subroutines which can be |
---|
| 600 | read as examples have been given. |
---|
| 601 | |
---|
| 602 | |
---|
| 603 | |
---|
| 604 | Further steps need to be done in order to reach a clean version of this |
---|
| 605 | ``naive method library'', with a more complete user manual. However, these |
---|
| 606 | first steps in the organisation of a sofware product, with the respect of |
---|
| 607 | the DOCTOR norm, the separation between subroutines ``visible'' from a |
---|
| 608 | calling code, with a minimal list of argument and extensive use of |
---|
| 609 | commons, and ``basic'' subroutines free of commons, can be helpfull for |
---|
| 610 | the organization of our future software development. Such an organization |
---|
| 611 | is also found in the ``Spectral Interface Library'' [8]. |
---|
| 612 | |
---|
| 613 | |
---|
| 614 | |
---|
| 615 | \beginsection Acknowledgments |
---|
| 616 | |
---|
| 617 | I thank Dominique ASTRUC for helping to use his visualization software [9] |
---|
| 618 | with which the Figure have been produced. |
---|
| 619 | |
---|
| 620 | |
---|
| 621 | |
---|
| 622 | |
---|
| 623 | \beginsection REFERENCES |
---|
| 624 | |
---|
| 625 | |
---|
| 626 | \def\ref{\parskip 12pt \leftskip 20pt \parindent -20pt} |
---|
| 627 | \def\endref{\parskip 0pt \leftskip 0pt \parindent 20pt} |
---|
| 628 | |
---|
| 629 | |
---|
| 630 | \ref |
---|
| 631 | |
---|
| 632 | [1] |
---|
| 633 | O. THUAL, Simple ocean-atmosphere interpolation. Part A: the method, |
---|
| 634 | {\it Epicoa \ } {\bf 0315} (1992). |
---|
| 635 | |
---|
| 636 | |
---|
| 637 | |
---|
| 638 | [2] |
---|
| 639 | N. H. BARTH, A Conservative Scheme for Passing Variables Between |
---|
| 640 | Coupled Models of the Ocean an Atmosphere |
---|
| 641 | {\it Technical Report \ }, CERFACS (1992). |
---|
| 642 | |
---|
| 643 | |
---|
| 644 | |
---|
| 645 | [3] |
---|
| 646 | O. THUAL, Gathering information for a coupler, |
---|
| 647 | {\it Epicoa \ } {\bf 0119} (1992). |
---|
| 648 | |
---|
| 649 | |
---|
| 650 | |
---|
| 651 | |
---|
| 652 | [4] |
---|
| 653 | P. DANDIN, th\`ese de doctorat, in preparation (1992). |
---|
| 654 | |
---|
| 655 | |
---|
| 656 | |
---|
| 657 | [5] J. CLOCHARD, Norme de codage ``DOCTOR'' pour le projet ARPEGE,{\it Note de |
---|
| 658 | travail ``AREPEGE''} {\bf No. 4} (1988). |
---|
| 659 | |
---|
| 660 | |
---|
| 661 | |
---|
| 662 | [6] J. K. GIBSON, The Doctor system - A DOCumentary ORiented programming |
---|
| 663 | system, {\it ECMWF Technical Memorandum} {\bf No. 52} (1982). |
---|
| 664 | |
---|
| 665 | |
---|
| 666 | [7] P. BERNARDET, private communication (1992). |
---|
| 667 | |
---|
| 668 | [8] O. THUAL, Spectral Interfaces Library Version 2.2, CERFACS (1990). |
---|
| 669 | |
---|
| 670 | |
---|
| 671 | [9] D. ASTRUC, Visuo: manuel de l'utilisateur, {\it Internal Report} |
---|
| 672 | (1990). |
---|
| 673 | |
---|
| 674 | \endref |
---|
| 675 | |
---|
| 676 | |
---|
| 677 | \vfill\eject |
---|
| 678 | \centerline{ Exchange of Projects and Ideas for Coupling Ocean and |
---|
| 679 | Atmosphere (Epicoa)} |
---|
| 680 | \centerline{ Appendix to Olivier Thual(8) , June 30$^{\rm th}$ 1992} |
---|
| 681 | \bigskip |
---|
| 682 | |
---|
| 683 | |
---|
| 684 | \centerline{\bf SOURCE OF THE NAIVE METHOD LIBRARY} |
---|
| 685 | \bigskip |
---|
| 686 | |
---|
| 687 | \centerline{ Version naiv01, 92 06 30 } |
---|
| 688 | |
---|
| 689 | |
---|
| 690 | |
---|
| 691 | \bigskip \bigskip |
---|
| 692 | |
---|
| 693 | This version is contained in {\tt |
---|
| 694 | greenh@cerfacs.fr:/usr1/pub/numlab/naiv/cnaiv01} |
---|
| 695 | |
---|
| 696 | \bigskip \bigskip |
---|
| 697 | |
---|
| 698 | |
---|
| 699 | |
---|
| 700 | \beginsection 1. Include files |
---|
| 701 | |
---|
| 702 | {\tt |
---|
| 703 | |
---|
| 704 | NAGAB.H NAGRA.H NAGRB.H |
---|
| 705 | |
---|
| 706 | |
---|
| 707 | } |
---|
| 708 | |
---|
| 709 | \beginsection 2. Main Program |
---|
| 710 | |
---|
| 711 | |
---|
| 712 | |
---|
| 713 | {\tt |
---|
| 714 | |
---|
| 715 | ANAIV.f |
---|
| 716 | |
---|
| 717 | } |
---|
| 718 | |
---|
| 719 | |
---|
| 720 | |
---|
| 721 | \beginsection 3. Coupler visible subroutines {\tt NA - - - -} |
---|
| 722 | |
---|
| 723 | |
---|
| 724 | |
---|
| 725 | {\tt |
---|
| 726 | |
---|
| 727 | NAFLUX.f NAGMRO.f NAGRA.H NAGRDA.f NASET.f NATES1.f NATES3.f NATST.f |
---|
| 728 | |
---|
| 729 | |
---|
| 730 | NAGAB.H NAGOPA.f NAGRB.H NAGRDB.f NASST.f NATES2.f NATFX.f |
---|
| 731 | |
---|
| 732 | |
---|
| 733 | |
---|
| 734 | } |
---|
| 735 | |
---|
| 736 | |
---|
| 737 | |
---|
| 738 | \beginsection 4. Basic subroutines {\tt PL - - - -} |
---|
| 739 | |
---|
| 740 | |
---|
| 741 | |
---|
| 742 | {\tt |
---|
| 743 | |
---|
| 744 | PLDIS2.f PLGPRI.f PLGRDU.f PLQQT.f PLSCAR.f PLSST.f PLVISU.f |
---|
| 745 | |
---|
| 746 | |
---|
| 747 | PLFLUX.f PLGRDC.f PLINS.f PLRHAL.f PLSORT.f PLSTAT.f |
---|
| 748 | |
---|
| 749 | |
---|
| 750 | PLGAUS.f PLGRDP.f PLMASQ.f PLRHO.f PLSSPH.f PLTMRO.f |
---|
| 751 | |
---|
| 752 | |
---|
| 753 | |
---|
| 754 | |
---|
| 755 | } |
---|
| 756 | |
---|
| 757 | |
---|
| 758 | |
---|
| 759 | \beginsection 5. Subroutine stolen from outside |
---|
| 760 | |
---|
| 761 | |
---|
| 762 | |
---|
| 763 | {\tt |
---|
| 764 | |
---|
| 765 | IMPR.f IMPRI.f |
---|
| 766 | |
---|
| 767 | |
---|
| 768 | } |
---|
| 769 | |
---|
| 770 | |
---|
| 771 | |
---|
| 772 | \end |
---|
| 773 | |
---|
| 774 | |
---|
| 775 | |
---|