| 1 | ! $Id: disvert.F90 2153 2014-11-24 15:18:11Z emillour $ |
|---|
| 2 | |
|---|
| 3 | SUBROUTINE disvert() |
|---|
| 4 | |
|---|
| 5 | #ifdef CPP_IOIPSL |
|---|
| 6 | use ioipsl, only: getin |
|---|
| 7 | #else |
|---|
| 8 | USE ioipsl_getincom, only: getin |
|---|
| 9 | #endif |
|---|
| 10 | use new_unit_m, only: new_unit |
|---|
| 11 | use assert_m, only: assert |
|---|
| 12 | |
|---|
| 13 | IMPLICIT NONE |
|---|
| 14 | |
|---|
| 15 | include "dimensions.h" |
|---|
| 16 | include "paramet.h" |
|---|
| 17 | include "comvert.h" |
|---|
| 18 | include "comconst.h" |
|---|
| 19 | include "iniprint.h" |
|---|
| 20 | include "logic.h" |
|---|
| 21 | |
|---|
| 22 | !------------------------------------------------------------------------------- |
|---|
| 23 | ! Purpose: Vertical distribution functions for LMDZ. |
|---|
| 24 | ! Triggered by the levels number llm. |
|---|
| 25 | !------------------------------------------------------------------------------- |
|---|
| 26 | ! Read in "comvert.h": |
|---|
| 27 | |
|---|
| 28 | ! pa !--- vertical coordinate is close to a PRESSURE COORDINATE FOR P |
|---|
| 29 | ! < 0.3 * pa (relative variation of p on a model level is < 0.1 %) |
|---|
| 30 | |
|---|
| 31 | ! preff !--- REFERENCE PRESSURE (101325 Pa) |
|---|
| 32 | ! Written in "comvert.h": |
|---|
| 33 | ! ap(llm+1), bp(llm+1) !--- Ap, Bp HYBRID COEFFICIENTS AT INTERFACES |
|---|
| 34 | ! aps(llm), bps(llm) !--- Ap, Bp HYBRID COEFFICIENTS AT MID-LAYERS |
|---|
| 35 | ! dpres(llm) !--- PRESSURE DIFFERENCE FOR EACH LAYER |
|---|
| 36 | ! presnivs(llm) !--- PRESSURE AT EACH MID-LAYER |
|---|
| 37 | ! scaleheight !--- VERTICAL SCALE HEIGHT (Earth: 8kms) |
|---|
| 38 | ! nivsig(llm+1) !--- SIGMA INDEX OF EACH LAYER INTERFACE |
|---|
| 39 | ! nivsigs(llm) !--- SIGMA INDEX OF EACH MID-LAYER |
|---|
| 40 | !------------------------------------------------------------------------------- |
|---|
| 41 | ! Local variables: |
|---|
| 42 | REAL sig(llm+1), dsig(llm) |
|---|
| 43 | REAL sig0(llm+1), zz(llm+1) |
|---|
| 44 | REAL zk, zkm1, dzk1, dzk2, z, k0, k1 |
|---|
| 45 | |
|---|
| 46 | INTEGER l, unit |
|---|
| 47 | REAL dsigmin |
|---|
| 48 | REAL vert_scale,vert_dzmin,vert_dzlow,vert_z0low,vert_dzmid,vert_z0mid,vert_h_mid,vert_dzhig,vert_z0hig,vert_h_hig |
|---|
| 49 | |
|---|
| 50 | REAL alpha, beta, deltaz |
|---|
| 51 | REAL x |
|---|
| 52 | character(len=*),parameter :: modname="disvert" |
|---|
| 53 | |
|---|
| 54 | character(len=24):: vert_sampling |
|---|
| 55 | ! (allowed values are "param", "tropo", "strato" and "read") |
|---|
| 56 | |
|---|
| 57 | !----------------------------------------------------------------------- |
|---|
| 58 | |
|---|
| 59 | WRITE(lunout,*) TRIM(modname)//" starts" |
|---|
| 60 | |
|---|
| 61 | ! default scaleheight is 8km for earth |
|---|
| 62 | scaleheight=8. |
|---|
| 63 | |
|---|
| 64 | vert_sampling = merge("strato", "tropo ", ok_strato) ! default value |
|---|
| 65 | call getin('vert_sampling', vert_sampling) |
|---|
| 66 | WRITE(lunout,*) TRIM(modname)//' vert_sampling = ' // vert_sampling |
|---|
| 67 | if (llm==39 .and. vert_sampling=="strato") then |
|---|
| 68 | dsigmin=0.3 ! Vieille option par défaut pour CMIP5 |
|---|
| 69 | else |
|---|
| 70 | dsigmin=1. |
|---|
| 71 | endif |
|---|
| 72 | call getin('dsigmin', dsigmin) |
|---|
| 73 | WRITE(LUNOUT,*) trim(modname), 'Discretisation verticale DSIGMIN=',dsigmin |
|---|
| 74 | |
|---|
| 75 | |
|---|
| 76 | select case (vert_sampling) |
|---|
| 77 | case ("param") |
|---|
| 78 | ! On lit les options dans sigma.def: |
|---|
| 79 | OPEN(99, file='sigma.def', status='old', form='formatted') |
|---|
| 80 | READ(99, *) scaleheight ! hauteur d'echelle 8. |
|---|
| 81 | READ(99, *) deltaz ! epaiseur de la premiere couche 0.04 |
|---|
| 82 | READ(99, *) beta ! facteur d'acroissement en haut 1.3 |
|---|
| 83 | READ(99, *) k0 ! nombre de couches dans la transition surf |
|---|
| 84 | READ(99, *) k1 ! nombre de couches dans la transition haute |
|---|
| 85 | CLOSE(99) |
|---|
| 86 | alpha=deltaz/(llm*scaleheight) |
|---|
| 87 | write(lunout, *)trim(modname),':scaleheight, alpha, k0, k1, beta', & |
|---|
| 88 | scaleheight, alpha, k0, k1, beta |
|---|
| 89 | |
|---|
| 90 | alpha=deltaz/tanh(1./k0)*2. |
|---|
| 91 | zkm1=0. |
|---|
| 92 | sig(1)=1. |
|---|
| 93 | do l=1, llm |
|---|
| 94 | sig(l+1)=(cosh(l/k0))**(-alpha*k0/scaleheight) & |
|---|
| 95 | *exp(-alpha/scaleheight*tanh((llm-k1)/k0) & |
|---|
| 96 | *beta**(l-(llm-k1))/log(beta)) |
|---|
| 97 | zk=-scaleheight*log(sig(l+1)) |
|---|
| 98 | |
|---|
| 99 | dzk1=alpha*tanh(l/k0) |
|---|
| 100 | dzk2=alpha*tanh((llm-k1)/k0)*beta**(l-(llm-k1))/log(beta) |
|---|
| 101 | write(lunout, *)l, sig(l+1), zk, zk-zkm1, dzk1, dzk2 |
|---|
| 102 | zkm1=zk |
|---|
| 103 | enddo |
|---|
| 104 | |
|---|
| 105 | sig(llm+1)=0. |
|---|
| 106 | |
|---|
| 107 | bp(: llm) = EXP(1. - 1. / sig(: llm)**2) |
|---|
| 108 | bp(llmp1) = 0. |
|---|
| 109 | |
|---|
| 110 | ap = pa * (sig - bp) |
|---|
| 111 | case("sigma") |
|---|
| 112 | DO l = 1, llm |
|---|
| 113 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
|---|
| 114 | dsig(l) = dsigmin + 7.0 * SIN(x)**2 |
|---|
| 115 | ENDDO |
|---|
| 116 | dsig = dsig / sum(dsig) |
|---|
| 117 | sig(llm+1) = 0. |
|---|
| 118 | DO l = llm, 1, -1 |
|---|
| 119 | sig(l) = sig(l+1) + dsig(l) |
|---|
| 120 | ENDDO |
|---|
| 121 | |
|---|
| 122 | bp(1)=1. |
|---|
| 123 | bp(2: llm) = sig(2:llm) |
|---|
| 124 | bp(llmp1) = 0. |
|---|
| 125 | ap(:)=0. |
|---|
| 126 | case("tropo") |
|---|
| 127 | DO l = 1, llm |
|---|
| 128 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
|---|
| 129 | dsig(l) = dsigmin + 7.0 * SIN(x)**2 |
|---|
| 130 | ENDDO |
|---|
| 131 | dsig = dsig / sum(dsig) |
|---|
| 132 | sig(llm+1) = 0. |
|---|
| 133 | DO l = llm, 1, -1 |
|---|
| 134 | sig(l) = sig(l+1) + dsig(l) |
|---|
| 135 | ENDDO |
|---|
| 136 | |
|---|
| 137 | bp(1)=1. |
|---|
| 138 | bp(2: llm) = EXP(1. - 1. / sig(2: llm)**2) |
|---|
| 139 | bp(llmp1) = 0. |
|---|
| 140 | |
|---|
| 141 | ap(1)=0. |
|---|
| 142 | ap(2: llm + 1) = pa * (sig(2: llm + 1) - bp(2: llm + 1)) |
|---|
| 143 | case("strato") |
|---|
| 144 | DO l = 1, llm |
|---|
| 145 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
|---|
| 146 | dsig(l) =(dsigmin + 7. * SIN(x)**2) & |
|---|
| 147 | *(0.5*(1.-tanh(1.*(x-asin(1.))/asin(1.))))**2 |
|---|
| 148 | ENDDO |
|---|
| 149 | dsig = dsig / sum(dsig) |
|---|
| 150 | sig(llm+1) = 0. |
|---|
| 151 | DO l = llm, 1, -1 |
|---|
| 152 | sig(l) = sig(l+1) + dsig(l) |
|---|
| 153 | ENDDO |
|---|
| 154 | |
|---|
| 155 | bp(1)=1. |
|---|
| 156 | bp(2: llm) = EXP(1. - 1. / sig(2: llm)**2) |
|---|
| 157 | bp(llmp1) = 0. |
|---|
| 158 | |
|---|
| 159 | ap(1)=0. |
|---|
| 160 | ap(2: llm + 1) = pa * (sig(2: llm + 1) - bp(2: llm + 1)) |
|---|
| 161 | case("strato_correct") |
|---|
| 162 | !================================================================== |
|---|
| 163 | ! Fredho 2014/05/18, Saint-Louis du Senegal |
|---|
| 164 | ! Cette version de la discretisation strato est corrige au niveau |
|---|
| 165 | ! du passage des sig aux ap, bp |
|---|
| 166 | ! la version precedente donne un coude dans l'epaisseur des couches |
|---|
| 167 | ! vers la tropopause |
|---|
| 168 | !================================================================== |
|---|
| 169 | |
|---|
| 170 | |
|---|
| 171 | DO l = 1, llm |
|---|
| 172 | x = 2*asin(1.) * (l - 0.5) / (llm + 1) |
|---|
| 173 | dsig(l) =(dsigmin + 7. * SIN(x)**2) & |
|---|
| 174 | *(0.5*(1.-tanh(1.*(x-asin(1.))/asin(1.))))**2 |
|---|
| 175 | ENDDO |
|---|
| 176 | dsig = dsig / sum(dsig) |
|---|
| 177 | sig0(llm+1) = 0. |
|---|
| 178 | DO l = llm, 1, -1 |
|---|
| 179 | sig0(l) = sig0(l+1) + dsig(l) |
|---|
| 180 | ENDDO |
|---|
| 181 | sig=racinesig(sig0) |
|---|
| 182 | |
|---|
| 183 | bp(1)=1. |
|---|
| 184 | bp(2:llm)=EXP(1.-1./sig(2: llm)**2) |
|---|
| 185 | bp(llmp1)=0. |
|---|
| 186 | |
|---|
| 187 | ap(1)=0. |
|---|
| 188 | ap(2:llm)=pa*(sig(2:llm)-bp(2:llm)) |
|---|
| 189 | ap(llm+1)=0. |
|---|
| 190 | |
|---|
| 191 | CASE("strato_custom0") |
|---|
| 192 | !======================================================= |
|---|
| 193 | ! Version Transitoire |
|---|
| 194 | ! custumize strato distribution with specific alpha & beta values and function |
|---|
| 195 | ! depending on llm (experimental and temporary)! |
|---|
| 196 | SELECT CASE (llm) |
|---|
| 197 | CASE(55) |
|---|
| 198 | alpha=0.45 |
|---|
| 199 | beta=4.0 |
|---|
| 200 | CASE(63) |
|---|
| 201 | alpha=0.45 |
|---|
| 202 | beta=5.0 |
|---|
| 203 | CASE(71) |
|---|
| 204 | alpha=3.05 |
|---|
| 205 | beta=65. |
|---|
| 206 | CASE(79) |
|---|
| 207 | alpha=3.20 |
|---|
| 208 | ! alpha=2.05 ! FLOTT 79 (PLANTE) |
|---|
| 209 | beta=70. |
|---|
| 210 | END SELECT |
|---|
| 211 | ! Or used values provided by user in def file: |
|---|
| 212 | CALL getin("strato_alpha",alpha) |
|---|
| 213 | CALL getin("strato_beta",beta) |
|---|
| 214 | |
|---|
| 215 | ! Build geometrical distribution |
|---|
| 216 | scaleheight=7. |
|---|
| 217 | zz(1)=0. |
|---|
| 218 | IF (llm==55.OR.llm==63) THEN |
|---|
| 219 | DO l=1,llm |
|---|
| 220 | z=zz(l)/scaleheight |
|---|
| 221 | zz(l+1)=zz(l)+0.03+z*1.5*(1.-TANH(z-0.5))+alpha*(1.+TANH(z-1.5)) & |
|---|
| 222 | +5.0*EXP((l-llm)/beta) |
|---|
| 223 | ENDDO |
|---|
| 224 | ELSEIF (llm==71) THEN !.OR.llm==79) THEN ! FLOTT 79 (PLANTE) |
|---|
| 225 | DO l=1,llm |
|---|
| 226 | z=zz(l) |
|---|
| 227 | zz(l+1)=zz(l)+0.02+0.88*TANH(z/2.5)+alpha*(1.+TANH((z-beta)/15.)) |
|---|
| 228 | ENDDO |
|---|
| 229 | ELSEIF (llm==79) THEN |
|---|
| 230 | DO l=1,llm |
|---|
| 231 | z=zz(l) |
|---|
| 232 | zz(l+1)=zz(l)+0.02+0.80*TANH(z/3.8)+alpha*(1+TANH((z-beta)/17.)) & |
|---|
| 233 | +0.03*TANH(z/.25) |
|---|
| 234 | ENDDO |
|---|
| 235 | ENDIF ! of IF (llm==55.OR.llm==63) ... |
|---|
| 236 | |
|---|
| 237 | |
|---|
| 238 | ! Build sigma distribution |
|---|
| 239 | sig0=EXP(-zz(:)/scaleheight) |
|---|
| 240 | sig0(llm+1)=0. |
|---|
| 241 | ! sig=ridders(sig0) |
|---|
| 242 | sig=racinesig(sig0) |
|---|
| 243 | |
|---|
| 244 | ! Compute ap() and bp() |
|---|
| 245 | bp(1)=1. |
|---|
| 246 | bp(2:llm)=EXP(1.-1./sig(2:llm)**2) |
|---|
| 247 | bp(llm+1)=0. |
|---|
| 248 | ap=pa*(sig-bp) |
|---|
| 249 | |
|---|
| 250 | CASE("strato_custom") |
|---|
| 251 | !=================================================================== |
|---|
| 252 | ! David Cugnet, François Lott, Lionel Guez, Ehouoarn Millour, Fredho |
|---|
| 253 | ! 2014/05 |
|---|
| 254 | ! custumize strato distribution |
|---|
| 255 | ! Al the parameter are given in km assuming a given scalehigh |
|---|
| 256 | vert_scale=7. ! scale hight |
|---|
| 257 | vert_dzmin=0.02 ! width of first layer |
|---|
| 258 | vert_dzlow=1. ! dz in the low atmosphere |
|---|
| 259 | vert_z0low=8. ! height at which resolution recches dzlow |
|---|
| 260 | vert_dzmid=3. ! dz in the mid atmsophere |
|---|
| 261 | vert_z0mid=70. ! height at which resolution recches dzmid |
|---|
| 262 | vert_h_mid=20. ! width of the transition |
|---|
| 263 | vert_dzhig=11. ! dz in the high atmsophere |
|---|
| 264 | vert_z0hig=80. ! height at which resolution recches dz |
|---|
| 265 | vert_h_hig=20. ! width of the transition |
|---|
| 266 | !=================================================================== |
|---|
| 267 | |
|---|
| 268 | call getin('vert_scale',vert_scale) |
|---|
| 269 | call getin('vert_dzmin',vert_dzmin) |
|---|
| 270 | call getin('vert_dzlow',vert_dzlow) |
|---|
| 271 | call getin('vert_z0low',vert_z0low) |
|---|
| 272 | CALL getin('vert_dzmid',vert_dzmid) |
|---|
| 273 | CALL getin('vert_z0mid',vert_z0mid) |
|---|
| 274 | call getin('vert_h_mid',vert_h_mid) |
|---|
| 275 | call getin('vert_dzhig',vert_dzhig) |
|---|
| 276 | call getin('vert_z0hig',vert_z0hig) |
|---|
| 277 | call getin('vert_h_hig',vert_h_hig) |
|---|
| 278 | |
|---|
| 279 | scaleheight=vert_scale ! for consistency with further computations |
|---|
| 280 | ! Build geometrical distribution |
|---|
| 281 | zz(1)=0. |
|---|
| 282 | DO l=1,llm |
|---|
| 283 | z=zz(l) |
|---|
| 284 | zz(l+1)=zz(l)+vert_dzmin+vert_dzlow*TANH(z/vert_z0low)+ & |
|---|
| 285 | & (vert_dzmid-vert_dzlow)* & |
|---|
| 286 | & (TANH((z-vert_z0mid)/vert_h_mid)-TANH((-vert_z0mid)/vert_h_mid)) & |
|---|
| 287 | & +(vert_dzhig-vert_dzmid-vert_dzlow)* & |
|---|
| 288 | & (TANH((z-vert_z0hig)/vert_h_hig)-TANH((-vert_z0hig)/vert_h_hig)) |
|---|
| 289 | ENDDO |
|---|
| 290 | |
|---|
| 291 | |
|---|
| 292 | !=================================================================== |
|---|
| 293 | ! Comment added Fredho 2014/05/18, Saint-Louis, Senegal |
|---|
| 294 | ! From approximate z to ap, bp, so that p=ap+bp*p0 and p/p0=exp(-z/H) |
|---|
| 295 | ! sig0 is p/p0 |
|---|
| 296 | ! sig is an intermediate distribution introduce to estimate bp |
|---|
| 297 | ! 1. sig0=exp(-z/H) |
|---|
| 298 | ! 2. inversion of sig0=(1-pa/p0)*sig+(1-pa/p0)*exp(1-1/sig**2) |
|---|
| 299 | ! 3. bp=exp(1-1/sig**2) |
|---|
| 300 | ! 4. ap deduced from the combination of 2 and 3 so that sig0=ap/p0+bp |
|---|
| 301 | !=================================================================== |
|---|
| 302 | |
|---|
| 303 | sig0=EXP(-zz(:)/vert_scale) |
|---|
| 304 | sig0(llm+1)=0. |
|---|
| 305 | sig=racinesig(sig0) |
|---|
| 306 | bp(1)=1. |
|---|
| 307 | bp(2:llm)=EXP(1.-1./sig(2:llm)**2) |
|---|
| 308 | bp(llm+1)=0. |
|---|
| 309 | ap=pa*(sig-bp) |
|---|
| 310 | |
|---|
| 311 | case("read") |
|---|
| 312 | ! Read "ap" and "bp". First line is skipped (title line). "ap" |
|---|
| 313 | ! should be in Pa. First couple of values should correspond to |
|---|
| 314 | ! the surface, that is : "bp" should be in descending order. |
|---|
| 315 | call new_unit(unit) |
|---|
| 316 | open(unit, file="hybrid.txt", status="old", action="read", & |
|---|
| 317 | position="rewind") |
|---|
| 318 | read(unit, fmt=*) ! skip title line |
|---|
| 319 | do l = 1, llm + 1 |
|---|
| 320 | read(unit, fmt=*) ap(l), bp(l) |
|---|
| 321 | end do |
|---|
| 322 | close(unit) |
|---|
| 323 | call assert(ap(1) == 0., ap(llm + 1) == 0., bp(1) == 1., & |
|---|
| 324 | bp(llm + 1) == 0., "disvert: bad ap or bp values") |
|---|
| 325 | case default |
|---|
| 326 | call abort_gcm("disvert", 'Wrong value for "vert_sampling"', 1) |
|---|
| 327 | END select |
|---|
| 328 | |
|---|
| 329 | DO l=1, llm |
|---|
| 330 | nivsigs(l) = REAL(l) |
|---|
| 331 | ENDDO |
|---|
| 332 | |
|---|
| 333 | DO l=1, llmp1 |
|---|
| 334 | nivsig(l)= REAL(l) |
|---|
| 335 | ENDDO |
|---|
| 336 | |
|---|
| 337 | write(lunout, *) trim(modname),': BP ' |
|---|
| 338 | write(lunout, *) bp |
|---|
| 339 | write(lunout, *) trim(modname),': AP ' |
|---|
| 340 | write(lunout, *) ap |
|---|
| 341 | |
|---|
| 342 | write(lunout, *) 'Niveaux de pressions approximatifs aux centres des' |
|---|
| 343 | write(lunout, *)'couches calcules pour une pression de surface =', preff |
|---|
| 344 | write(lunout, *) 'et altitudes equivalentes pour une hauteur d echelle de ' |
|---|
| 345 | write(lunout, *) scaleheight,' km' |
|---|
| 346 | DO l = 1, llm |
|---|
| 347 | dpres(l) = bp(l) - bp(l+1) |
|---|
| 348 | presnivs(l) = 0.5 *( ap(l)+bp(l)*preff + ap(l+1)+bp(l+1)*preff ) |
|---|
| 349 | write(lunout, *)'PRESNIVS(', l, ')=', presnivs(l), ' Z ~ ', & |
|---|
| 350 | log(preff/presnivs(l))*scaleheight & |
|---|
| 351 | , ' DZ ~ ', scaleheight*log((ap(l)+bp(l)*preff)/ & |
|---|
| 352 | max(ap(l+1)+bp(l+1)*preff, 1.e-10)) |
|---|
| 353 | ENDDO |
|---|
| 354 | |
|---|
| 355 | write(lunout, *) trim(modname),': PRESNIVS ' |
|---|
| 356 | write(lunout, *) presnivs |
|---|
| 357 | |
|---|
| 358 | CONTAINS |
|---|
| 359 | |
|---|
| 360 | !------------------------------------------------------------------------------- |
|---|
| 361 | ! |
|---|
| 362 | FUNCTION ridders(sig) RESULT(sg) |
|---|
| 363 | ! |
|---|
| 364 | !------------------------------------------------------------------------------- |
|---|
| 365 | IMPLICIT NONE |
|---|
| 366 | !------------------------------------------------------------------------------- |
|---|
| 367 | ! Purpose: Search for s solving (Pa/Preff)*s+(1-Pa/Preff)*EXP(1-1./s**2)=sg |
|---|
| 368 | ! Notes: Uses Ridders' method, quite robust. Initial bracketing: 0<=sg<=1. |
|---|
| 369 | ! Reference: Ridders, C. F. J. "A New Algorithm for Computing a Single Root of a |
|---|
| 370 | ! Real Continuous Function" IEEE Trans. Circuits Systems 26, 979-980, 1979 |
|---|
| 371 | !------------------------------------------------------------------------------- |
|---|
| 372 | ! Arguments: |
|---|
| 373 | REAL, INTENT(IN) :: sig(:) |
|---|
| 374 | REAL :: sg(SIZE(sig)) |
|---|
| 375 | !------------------------------------------------------------------------------- |
|---|
| 376 | ! Local variables: |
|---|
| 377 | INTEGER :: it, ns, maxit |
|---|
| 378 | REAL :: c1, c2, x1, x2, x3, x4, f1, f2, f3, f4, s, xx, distrib |
|---|
| 379 | !------------------------------------------------------------------------------- |
|---|
| 380 | ns=SIZE(sig); maxit=9999 |
|---|
| 381 | c1=Pa/Preff; c2=1.-c1 |
|---|
| 382 | DO l=1,ns |
|---|
| 383 | xx=HUGE(1.) |
|---|
| 384 | x1=0.0; f1=distrib(x1,c1,c2,sig(l)) |
|---|
| 385 | x2=1.0; f2=distrib(x2,c1,c2,sig(l)) |
|---|
| 386 | DO it=1,maxit |
|---|
| 387 | x3=0.5*(x1+x2); f3=distrib(x3,c1,c2,sig(l)) |
|---|
| 388 | s=SQRT(f3**2-f1*f2); IF(s==0.) EXIT |
|---|
| 389 | x4=x3+(x3-x1)*(SIGN(1.,f1-f2)*f3/s); IF(ABS(10.*LOG(x4-xx))<=1E-5) EXIT |
|---|
| 390 | xx=x4; f4=distrib(x4,c1,c2,sig(l)); IF(f4==0.) EXIT |
|---|
| 391 | IF(SIGN(f3,f4)/=f3) THEN; x1=x3; f1=f3; x2=xx; f2=f4 |
|---|
| 392 | ELSE IF(SIGN(f1,f4)/=f1) THEN; x2=xx; f2=f4 |
|---|
| 393 | ELSE IF(SIGN(f2,f4)/=f2) THEN; x1=xx; f1=f4 |
|---|
| 394 | ELSE; CALL abort_gcm("ridders",'Algorithm failed (which is odd...') |
|---|
| 395 | END IF |
|---|
| 396 | IF(ABS(10.*LOG(ABS(x2-x1)))<=1E-5) EXIT !--- ERROR ON SIG <= 0.01m |
|---|
| 397 | END DO |
|---|
| 398 | IF(it==maxit+1) WRITE(lunout,'(a,i3)')'WARNING in ridder: failed to converg& |
|---|
| 399 | &e for level ',l |
|---|
| 400 | sg(l)=xx |
|---|
| 401 | END DO |
|---|
| 402 | sg(1)=1.; sg(ns)=0. |
|---|
| 403 | |
|---|
| 404 | END FUNCTION ridders |
|---|
| 405 | |
|---|
| 406 | FUNCTION racinesig(sig) RESULT(sg) |
|---|
| 407 | ! |
|---|
| 408 | !------------------------------------------------------------------------------- |
|---|
| 409 | IMPLICIT NONE |
|---|
| 410 | !------------------------------------------------------------------------------- |
|---|
| 411 | ! Fredho 2014/05/18 |
|---|
| 412 | ! Purpose: Search for s solving (Pa/Preff)*sg+(1-Pa/Preff)*EXP(1-1./sg**2)=s |
|---|
| 413 | ! Notes: Uses Newton Raphson search |
|---|
| 414 | !------------------------------------------------------------------------------- |
|---|
| 415 | ! Arguments: |
|---|
| 416 | REAL, INTENT(IN) :: sig(:) |
|---|
| 417 | REAL :: sg(SIZE(sig)) |
|---|
| 418 | !------------------------------------------------------------------------------- |
|---|
| 419 | ! Local variables: |
|---|
| 420 | INTEGER :: it, ns, maxit |
|---|
| 421 | REAL :: c1, c2, x1, x2, x3, x4, f1, f2, f3, f4, s, xx, distrib |
|---|
| 422 | !------------------------------------------------------------------------------- |
|---|
| 423 | ns=SIZE(sig); maxit=100 |
|---|
| 424 | c1=Pa/Preff; c2=1.-c1 |
|---|
| 425 | DO l=2,ns-1 |
|---|
| 426 | sg(l)=sig(l) |
|---|
| 427 | DO it=1,maxit |
|---|
| 428 | f1=exp(1-1./sg(l)**2)*(1.-c1) |
|---|
| 429 | sg(l)=sg(l)-(c1*sg(l)+f1-sig(l))/(c1+2*f1*sg(l)**(-3)) |
|---|
| 430 | ENDDO |
|---|
| 431 | ! print*,'SSSSIG ',sig(l),sg(l),c1*sg(l)+exp(1-1./sg(l)**2)*(1.-c1) |
|---|
| 432 | ENDDO |
|---|
| 433 | sg(1)=1.; sg(ns)=0. |
|---|
| 434 | |
|---|
| 435 | END FUNCTION racinesig |
|---|
| 436 | |
|---|
| 437 | |
|---|
| 438 | |
|---|
| 439 | |
|---|
| 440 | END SUBROUTINE disvert |
|---|
| 441 | |
|---|
| 442 | !------------------------------------------------------------------------------- |
|---|
| 443 | |
|---|
| 444 | FUNCTION distrib(x,c1,c2,x0) RESULT(res) |
|---|
| 445 | ! |
|---|
| 446 | !------------------------------------------------------------------------------- |
|---|
| 447 | ! Arguments: |
|---|
| 448 | REAL, INTENT(IN) :: x, c1, c2, x0 |
|---|
| 449 | REAL :: res |
|---|
| 450 | !------------------------------------------------------------------------------- |
|---|
| 451 | res=c1*x+c2*EXP(1-1/(x**2))-x0 |
|---|
| 452 | |
|---|
| 453 | END FUNCTION distrib |
|---|
| 454 | |
|---|
| 455 | |
|---|
