| 1 |
heimbach |
1.2 |
C $Header: /escher1/cvs/master/mitgcmuv/pkg/kpp/kpp_routines.F,v 1.6 2000/09/11 22:32:53 dimitri Exp $ |
| 2 |
adcroft |
1.1 |
|
| 3 |
|
|
#include "KPP_OPTIONS.h" |
| 4 |
|
|
|
| 5 |
|
|
C-- File kpp_routines.F: subroutines needed to implement |
| 6 |
|
|
C-- KPP vertical mixing scheme |
| 7 |
|
|
C-- Contents |
| 8 |
|
|
C-- o KPPMIX - Main driver and interface routine. |
| 9 |
|
|
C-- o BLDEPTH - Determine oceanic planetary boundary layer depth. |
| 10 |
|
|
C-- o WSCALE - Compute turbulent velocity scales. |
| 11 |
|
|
C-- o RI_IWMIX - Compute interior viscosity diffusivity coefficients. |
| 12 |
|
|
C-- o Z121 - Apply 121 vertical smoothing. |
| 13 |
|
|
C-- o SMOOTH_HORIZ_RS - Apply horizontal smoothing to RS array. |
| 14 |
|
|
C-- o SMOOTH_HORIZ_RL - Apply horizontal smoothing to RL array. |
| 15 |
|
|
C-- o BLMIX - Boundary layer mixing coefficients. |
| 16 |
|
|
C-- o ENHANCE - Enhance diffusivity at boundary layer interface. |
| 17 |
|
|
C-- o STATEKPP - Compute buoyancy-related input arrays. |
| 18 |
|
|
|
| 19 |
|
|
c************************************************************************* |
| 20 |
|
|
|
| 21 |
|
|
SUBROUTINE KPPMIX ( |
| 22 |
|
|
I lri, kmtj, shsq, dvsq, ustar, bo, bosol |
| 23 |
|
|
I , dbloc, Ritop, coriol |
| 24 |
|
|
I , ikey |
| 25 |
|
|
O , diffus |
| 26 |
|
|
U , ghat |
| 27 |
|
|
O , hbl ) |
| 28 |
|
|
|
| 29 |
|
|
c------------------------------------------------------------------------- |
| 30 |
|
|
c |
| 31 |
|
|
c Main driver subroutine for kpp vertical mixing scheme and |
| 32 |
|
|
c interface to greater ocean model |
| 33 |
|
|
c |
| 34 |
|
|
c written by: bill large, june 6, 1994 |
| 35 |
|
|
c modified by: jan morzel, june 30, 1994 |
| 36 |
|
|
c bill large, august 11, 1994 |
| 37 |
|
|
c bill large, january 25, 1995 : "dVsq" and 1d code |
| 38 |
|
|
c detlef stammer, august 1997 : for use with MIT GCM Classic |
| 39 |
|
|
c d. menemenlis, june 1998 : for use with MIT GCM UV |
| 40 |
|
|
c |
| 41 |
|
|
c----------------------------------------------------------------------- |
| 42 |
|
|
|
| 43 |
|
|
IMPLICIT NONE |
| 44 |
|
|
|
| 45 |
|
|
#include "SIZE.h" |
| 46 |
|
|
#include "EEPARAMS.h" |
| 47 |
|
|
#include "PARAMS.h" |
| 48 |
|
|
#include "DYNVARS.h" |
| 49 |
|
|
#include "FFIELDS.h" |
| 50 |
|
|
#include "KPP_PARAMS.h" |
| 51 |
|
|
|
| 52 |
|
|
c input |
| 53 |
|
|
c lri - mixing process switches |
| 54 |
|
|
c kmtj (imt) - number of vertical layers on this row |
| 55 |
|
|
c shsq (imt,Nr) - (local velocity shear)^2 ((m/s)^2) |
| 56 |
|
|
c dvsq (imt,Nr) - (velocity shear re sfc)^2 ((m/s)^2) |
| 57 |
|
|
c ustar (imt) - surface friction velocity (m/s) |
| 58 |
|
|
c bo (imt) - surface turbulent buoy. forcing (m^2/s^3) |
| 59 |
|
|
c bosol (imt) - radiative buoyancy forcing (m^2/s^3) |
| 60 |
|
|
c dbloc (imt,Nr) - local delta buoyancy across interfaces (m/s^2) |
| 61 |
|
|
c dblocSm(imt,Nr) - horizontally smoothed dbloc (m/s^2) |
| 62 |
|
|
c stored in ghat to save space |
| 63 |
|
|
c Ritop (imt,Nr) - numerator of bulk Richardson Number |
| 64 |
|
|
c (zref-z) * delta buoyancy w.r.t. surface ((m/s)^2) |
| 65 |
|
|
c coriol (imt) - Coriolis parameter (1/s) |
| 66 |
|
|
c note: there is a conversion from 2-D to 1-D for input output variables, |
| 67 |
|
|
c e.g., hbl(sNx,sNy) -> hbl(imt), |
| 68 |
|
|
c where hbl(i,j) -> hbl((j-1)*sNx+i) |
| 69 |
|
|
|
| 70 |
|
|
logical lri |
| 71 |
|
|
integer kmtj (imt ) |
| 72 |
|
|
_RS shsq (imt,Nr) |
| 73 |
|
|
_RS dvsq (imt,Nr) |
| 74 |
|
|
_RS ustar (imt ) |
| 75 |
|
|
_RS bo (imt ) |
| 76 |
|
|
_RS bosol (imt ) |
| 77 |
|
|
_RS dbloc (imt,Nr) |
| 78 |
|
|
_RS Ritop (imt,Nr) |
| 79 |
|
|
_RS coriol (imt ) |
| 80 |
|
|
|
| 81 |
|
|
integer ikey |
| 82 |
|
|
|
| 83 |
|
|
c output |
| 84 |
|
|
c diffus (imt,1) - vertical viscosity coefficient (m^2/s) |
| 85 |
|
|
c diffus (imt,2) - vertical scalar diffusivity (m^2/s) |
| 86 |
|
|
c diffus (imt,3) - vertical temperature diffusivity (m^2/s) |
| 87 |
|
|
c ghat (imt) - nonlocal transport coefficient (s/m^2) |
| 88 |
|
|
c hbl (imt) - mixing layer depth (m) |
| 89 |
|
|
|
| 90 |
|
|
_RS diffus(imt,0:Nrp1,mdiff) |
| 91 |
|
|
_RS ghat (imt,Nr) |
| 92 |
|
|
_RS hbl (imt) |
| 93 |
|
|
|
| 94 |
|
|
#ifdef ALLOW_KPP |
| 95 |
|
|
|
| 96 |
|
|
c local |
| 97 |
|
|
c kbl (imt ) - index of first grid level below hbl |
| 98 |
|
|
c bfsfc (imt ) - surface buoyancy forcing (m^2/s^3) |
| 99 |
|
|
c casea (imt ) - 1 in case A; 0 in case B |
| 100 |
|
|
c stable (imt ) - 1 in stable forcing; 0 if unstable |
| 101 |
|
|
c dkm1 (imt, mdiff) - boundary layer diffusivity at kbl-1 level |
| 102 |
|
|
c blmc (imt,Nr,mdiff) - boundary layer mixing coefficients |
| 103 |
|
|
c sigma (imt ) - normalized depth (d / hbl) |
| 104 |
|
|
c Rib (imt,Nr ) - bulk Richardson number |
| 105 |
|
|
|
| 106 |
|
|
integer kbl (imt ) |
| 107 |
|
|
_RS bfsfc (imt ) |
| 108 |
|
|
_RS casea (imt ) |
| 109 |
|
|
_RS stable (imt ) |
| 110 |
|
|
_RS dkm1 (imt, mdiff) |
| 111 |
|
|
_RS blmc (imt,Nr,mdiff) |
| 112 |
|
|
_RS sigma (imt ) |
| 113 |
|
|
_RS Rib (imt,Nr ) |
| 114 |
|
|
|
| 115 |
|
|
integer i, k, md |
| 116 |
|
|
|
| 117 |
|
|
c----------------------------------------------------------------------- |
| 118 |
|
|
c compute interior mixing coefficients everywhere, due to constant |
| 119 |
|
|
c internal wave activity, static instability, and local shear |
| 120 |
|
|
c instability. |
| 121 |
|
|
c (ghat is temporary storage for horizontally smoothed dbloc) |
| 122 |
|
|
c----------------------------------------------------------------------- |
| 123 |
|
|
|
| 124 |
|
|
call Ri_iwmix ( |
| 125 |
|
|
I kmtj, shsq, dbloc, ghat |
| 126 |
|
|
I , ikey |
| 127 |
|
|
O , diffus ) |
| 128 |
|
|
|
| 129 |
|
|
c----------------------------------------------------------------------- |
| 130 |
|
|
c set seafloor values to zero and fill extra "Nrp1" coefficients |
| 131 |
|
|
c for blmix |
| 132 |
|
|
c----------------------------------------------------------------------- |
| 133 |
|
|
|
| 134 |
|
|
do md = 1, mdiff |
| 135 |
|
|
do i = 1,imt |
| 136 |
|
|
do k=kmtj(i),Nrp1 |
| 137 |
|
|
diffus(i,k,md) = 0.0 |
| 138 |
|
|
end do |
| 139 |
|
|
end do |
| 140 |
|
|
end do |
| 141 |
|
|
|
| 142 |
|
|
c----------------------------------------------------------------------- |
| 143 |
|
|
c compute boundary layer mixing coefficients: |
| 144 |
|
|
c |
| 145 |
|
|
c diagnose the new boundary layer depth |
| 146 |
|
|
c----------------------------------------------------------------------- |
| 147 |
|
|
|
| 148 |
|
|
call bldepth ( |
| 149 |
|
|
I kmtj |
| 150 |
|
|
I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
| 151 |
|
|
I , ikey |
| 152 |
|
|
O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
| 153 |
|
|
& ) |
| 154 |
|
|
|
| 155 |
heimbach |
1.2 |
CADJ STORE hbl,bfsfc,stable,casea,kbl = comlev1_kpp, key = ikey |
| 156 |
adcroft |
1.1 |
|
| 157 |
|
|
c----------------------------------------------------------------------- |
| 158 |
|
|
c compute boundary layer diffusivities |
| 159 |
|
|
c----------------------------------------------------------------------- |
| 160 |
|
|
|
| 161 |
|
|
call blmix ( |
| 162 |
|
|
I ustar, bfsfc, hbl, stable, casea, diffus, kbl |
| 163 |
|
|
O , dkm1, blmc, ghat, sigma |
| 164 |
|
|
& ) |
| 165 |
|
|
|
| 166 |
heimbach |
1.2 |
CADJ STORE dkm1,blmc,ghat = comlev1_kpp, key = ikey |
| 167 |
adcroft |
1.1 |
|
| 168 |
|
|
c----------------------------------------------------------------------- |
| 169 |
|
|
c enhance diffusivity at interface kbl - 1 |
| 170 |
|
|
c----------------------------------------------------------------------- |
| 171 |
|
|
|
| 172 |
|
|
call enhance ( |
| 173 |
|
|
I dkm1, hbl, kbl, diffus, casea |
| 174 |
|
|
U , ghat |
| 175 |
|
|
O , blmc ) |
| 176 |
|
|
|
| 177 |
|
|
c----------------------------------------------------------------------- |
| 178 |
|
|
c combine interior and boundary layer coefficients and nonlocal term |
| 179 |
|
|
c----------------------------------------------------------------------- |
| 180 |
|
|
|
| 181 |
|
|
do k = 1, Nr |
| 182 |
|
|
do i = 1, imt |
| 183 |
|
|
if (k .lt. kbl(i)) then |
| 184 |
|
|
do md = 1, mdiff |
| 185 |
|
|
diffus(i,k,md) = blmc(i,k,md) |
| 186 |
|
|
end do |
| 187 |
|
|
else |
| 188 |
|
|
ghat(i,k) = 0. |
| 189 |
|
|
endif |
| 190 |
|
|
end do |
| 191 |
|
|
end do |
| 192 |
|
|
|
| 193 |
|
|
#endif /* ALLOW_KPP */ |
| 194 |
|
|
|
| 195 |
|
|
return |
| 196 |
|
|
end |
| 197 |
|
|
|
| 198 |
|
|
c************************************************************************* |
| 199 |
|
|
|
| 200 |
|
|
subroutine bldepth ( |
| 201 |
|
|
I kmtj |
| 202 |
|
|
I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
| 203 |
|
|
I , ikey |
| 204 |
|
|
O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
| 205 |
|
|
& ) |
| 206 |
|
|
|
| 207 |
|
|
c the oceanic planetary boundary layer depth, hbl, is determined as |
| 208 |
|
|
c the shallowest depth where the bulk Richardson number is |
| 209 |
|
|
c equal to the critical value, Ricr. |
| 210 |
|
|
c |
| 211 |
|
|
c bulk Richardson numbers are evaluated by computing velocity and |
| 212 |
|
|
c buoyancy differences between values at zgrid(kl) < 0 and surface |
| 213 |
|
|
c reference values. |
| 214 |
|
|
c in this configuration, the reference values are equal to the |
| 215 |
|
|
c values in the surface layer. |
| 216 |
|
|
c when using a very fine vertical grid, these values should be |
| 217 |
|
|
c computed as the vertical average of velocity and buoyancy from |
| 218 |
|
|
c the surface down to epsilon*zgrid(kl). |
| 219 |
|
|
c |
| 220 |
|
|
c when the bulk Richardson number at k exceeds Ricr, hbl is |
| 221 |
|
|
c linearly interpolated between grid levels zgrid(k) and zgrid(k-1). |
| 222 |
|
|
c |
| 223 |
|
|
c The water column and the surface forcing are diagnosed for |
| 224 |
|
|
c stable/ustable forcing conditions, and where hbl is relative |
| 225 |
|
|
c to grid points (caseA), so that conditional branches can be |
| 226 |
|
|
c avoided in later subroutines. |
| 227 |
|
|
c |
| 228 |
|
|
IMPLICIT NONE |
| 229 |
|
|
|
| 230 |
|
|
#include "SIZE.h" |
| 231 |
|
|
#include "EEPARAMS.h" |
| 232 |
|
|
#include "PARAMS.h" |
| 233 |
|
|
#include "KPP_PARAMS.h" |
| 234 |
|
|
#include "FFIELDS.h" |
| 235 |
|
|
|
| 236 |
|
|
c input |
| 237 |
|
|
c------ |
| 238 |
|
|
c kmtj : number of vertical layers |
| 239 |
|
|
c dvsq : (velocity shear re sfc)^2 ((m/s)^2) |
| 240 |
|
|
c dbloc : local delta buoyancy across interfaces (m/s^2) |
| 241 |
|
|
c Ritop : numerator of bulk Richardson Number |
| 242 |
|
|
c =(z-zref)*dbsfc, where dbsfc=delta |
| 243 |
|
|
c buoyancy with respect to surface ((m/s)^2) |
| 244 |
|
|
c ustar : surface friction velocity (m/s) |
| 245 |
|
|
c bo : surface turbulent buoyancy forcing (m^2/s^3) |
| 246 |
|
|
c bosol : radiative buoyancy forcing (m^2/s^3) |
| 247 |
|
|
c coriol : Coriolis parameter (1/s) |
| 248 |
|
|
integer kmtj(imt) |
| 249 |
|
|
_RS dvsq (imt,Nr) |
| 250 |
|
|
_RS dbloc (imt,Nr) |
| 251 |
|
|
_RS Ritop (imt,Nr) |
| 252 |
|
|
_RS ustar (imt) |
| 253 |
|
|
_RS bo (imt) |
| 254 |
|
|
_RS bosol (imt) |
| 255 |
|
|
_RS coriol (imt) |
| 256 |
|
|
integer ikey |
| 257 |
|
|
|
| 258 |
|
|
c output |
| 259 |
|
|
c-------- |
| 260 |
|
|
c hbl : boundary layer depth (m) |
| 261 |
|
|
c bfsfc : Bo+radiation absorbed to d=hbf*hbl (m^2/s^3) |
| 262 |
|
|
c stable : =1 in stable forcing; =0 unstable |
| 263 |
|
|
c casea : =1 in case A, =0 in case B |
| 264 |
|
|
c kbl : -1 of first grid level below hbl |
| 265 |
|
|
c Rib : Bulk Richardson number |
| 266 |
|
|
c sigma : normalized depth (d/hbl) |
| 267 |
|
|
_RS hbl (imt) |
| 268 |
|
|
_RS bfsfc (imt) |
| 269 |
|
|
_RS stable (imt) |
| 270 |
|
|
_RS casea (imt) |
| 271 |
|
|
integer kbl (imt) |
| 272 |
|
|
_RS Rib (imt,Nr) |
| 273 |
|
|
_RS sigma (imt) |
| 274 |
|
|
|
| 275 |
|
|
#ifdef ALLOW_KPP |
| 276 |
|
|
|
| 277 |
|
|
c local |
| 278 |
|
|
c------- |
| 279 |
|
|
c wm, ws : turbulent velocity scales (m/s) |
| 280 |
|
|
c zwork : depth work array |
| 281 |
|
|
_RS wm(imt), ws(imt) |
| 282 |
|
|
_RS zwork(imt) |
| 283 |
|
|
|
| 284 |
heimbach |
1.2 |
_RS bvsq, vtsq, hekman, hmonob, hlimit |
| 285 |
adcroft |
1.1 |
integer i, kl |
| 286 |
|
|
|
| 287 |
heimbach |
1.2 |
_RS p5 , eins , m1 |
| 288 |
|
|
parameter (p5=0.5, eins=1.0, m1=-1.0 ) |
| 289 |
adcroft |
1.1 |
|
| 290 |
|
|
crg intermediate result in RL to avoid overflow in adjoint |
| 291 |
|
|
_RL dpshear2 |
| 292 |
|
|
#ifdef KPP_TEST_DENOM |
| 293 |
|
|
_RL dhelp |
| 294 |
|
|
#endif |
| 295 |
|
|
|
| 296 |
|
|
c find bulk Richardson number at every grid level until > Ricr |
| 297 |
|
|
c |
| 298 |
|
|
c note: the reference depth is -epsilon/2.*zgrid(k), but the reference |
| 299 |
|
|
c u,v,t,s values are simply the surface layer values, |
| 300 |
|
|
c and not the averaged values from 0 to 2*ref.depth, |
| 301 |
|
|
c which is necessary for very fine grids(top layer < 2m thickness) |
| 302 |
|
|
c note: max values when Ricr never satisfied are |
| 303 |
|
|
c kbl(i)=kmtj(i) and hbl(i)=-zgrid(kmtj(i)) |
| 304 |
|
|
|
| 305 |
|
|
c initialize hbl and kbl to bottomed out values |
| 306 |
|
|
|
| 307 |
|
|
do i = 1, imt |
| 308 |
|
|
Rib(i,1) = 0.0 |
| 309 |
|
|
kbl(i) = max(kmtj(i),1) |
| 310 |
|
|
hbl(i) = -zgrid(kbl(i)) |
| 311 |
|
|
end do |
| 312 |
|
|
|
| 313 |
|
|
do kl = 2, Nr |
| 314 |
|
|
|
| 315 |
|
|
c compute bfsfc = sw fraction at hbf * zgrid |
| 316 |
|
|
|
| 317 |
|
|
do i = 1, imt |
| 318 |
|
|
zwork(i) = zgrid(kl) |
| 319 |
|
|
end do |
| 320 |
|
|
call SWFRAC( |
| 321 |
|
|
I imt, hbf, zwork, |
| 322 |
|
|
O bfsfc) |
| 323 |
|
|
|
| 324 |
|
|
do i = 1, imt |
| 325 |
|
|
|
| 326 |
|
|
c use caseA as temporary array |
| 327 |
|
|
|
| 328 |
|
|
casea(i) = -zgrid(kl) |
| 329 |
|
|
|
| 330 |
|
|
c compute bfsfc= Bo + radiative contribution down to hbf * hbl |
| 331 |
|
|
|
| 332 |
|
|
bfsfc(i) = bo(i) + bosol(i)*(1. - bfsfc(i)) |
| 333 |
|
|
stable(i) = p5 + sign(p5,bfsfc(i)) |
| 334 |
|
|
sigma(i) = stable(i) + (1. - stable(i)) * epsilon |
| 335 |
|
|
|
| 336 |
|
|
end do |
| 337 |
|
|
|
| 338 |
|
|
c----------------------------------------------------------------------- |
| 339 |
|
|
c compute velocity scales at sigma, for hbl= caseA = -zgrid(kl) |
| 340 |
|
|
c----------------------------------------------------------------------- |
| 341 |
|
|
|
| 342 |
|
|
call wscale ( |
| 343 |
|
|
I sigma, casea, ustar, bfsfc, |
| 344 |
|
|
O wm, ws ) |
| 345 |
|
|
|
| 346 |
|
|
do i = 1, imt |
| 347 |
|
|
|
| 348 |
|
|
c----------------------------------------------------------------------- |
| 349 |
|
|
c compute the turbulent shear contribution to Rib |
| 350 |
|
|
c----------------------------------------------------------------------- |
| 351 |
|
|
|
| 352 |
|
|
bvsq = p5 * |
| 353 |
|
|
1 ( dbloc(i,kl-1) / (zgrid(kl-1)-zgrid(kl ))+ |
| 354 |
|
|
2 dbloc(i,kl ) / (zgrid(kl )-zgrid(kl+1))) |
| 355 |
|
|
|
| 356 |
|
|
if (bvsq .eq. 0.) then |
| 357 |
|
|
vtsq = 0.0 |
| 358 |
|
|
else |
| 359 |
|
|
vtsq = -zgrid(kl) * ws(i) * sqrt(abs(bvsq)) * Vtc |
| 360 |
|
|
endif |
| 361 |
|
|
|
| 362 |
|
|
c compute bulk Richardson number at new level |
| 363 |
|
|
c note: Ritop needs to be zero on land and ocean bottom |
| 364 |
|
|
c points so that the following if statement gets triggered |
| 365 |
|
|
c correctly; otherwise, hbl might get set to (big) negative |
| 366 |
|
|
c values, that might exceed the limit for the "exp" function |
| 367 |
|
|
c in "SWFRAC" |
| 368 |
|
|
|
| 369 |
|
|
c |
| 370 |
|
|
c rg: assignment to double precision variable to avoid overflow |
| 371 |
|
|
c ph: test for zero nominator |
| 372 |
|
|
c |
| 373 |
|
|
#ifdef KPP_TEST_DENOM |
| 374 |
|
|
ctl replace |
| 375 |
|
|
dpshear2 = dvsq(i,kl) + vtsq |
| 376 |
|
|
dpshear2 = max(dpshear2, phepsi) |
| 377 |
|
|
Rib(i,kl) = Ritop(i,kl) / dpshear2 |
| 378 |
|
|
ctl end-replace |
| 379 |
|
|
#else |
| 380 |
|
|
dpshear2 = dvsq(i,kl) + vtsq + epsln |
| 381 |
|
|
Rib(i,kl) = Ritop(i,kl) / dpshear2 |
| 382 |
|
|
#endif |
| 383 |
|
|
end do |
| 384 |
|
|
end do |
| 385 |
|
|
|
| 386 |
|
|
do kl = 2, Nr |
| 387 |
|
|
do i = 1, imt |
| 388 |
|
|
if (kbl(i).eq.kmtj(i) .and. Rib(i,kl).gt.Ricr) kbl(i) = kl |
| 389 |
|
|
end do |
| 390 |
|
|
end do |
| 391 |
|
|
|
| 392 |
heimbach |
1.2 |
CADJ store kbl = comlev1_kpp |
| 393 |
adcroft |
1.1 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 394 |
|
|
|
| 395 |
|
|
do i = 1, imt |
| 396 |
|
|
kl = kbl(i) |
| 397 |
|
|
|
| 398 |
|
|
c linearly interpolate to find hbl where Rib = Ricr |
| 399 |
|
|
|
| 400 |
|
|
if (kl.gt.1 .and. kl.lt.kmtj(i)) then |
| 401 |
|
|
#ifdef KPP_TEST_DENOM |
| 402 |
|
|
dhelp = (Rib(i,kl)-Rib(i,kl-1)) |
| 403 |
|
|
hbl(i) = -zgrid(kl-1) + (zgrid(kl-1)-zgrid(kl)) * |
| 404 |
|
|
1 (Ricr - Rib(i,kl-1)) / dhelp |
| 405 |
|
|
#else |
| 406 |
|
|
hbl(i) = -zgrid(kl-1) + (zgrid(kl-1)-zgrid(kl)) * |
| 407 |
|
|
1 (Ricr - Rib(i,kl-1)) / (Rib(i,kl)-Rib(i,kl-1)) |
| 408 |
|
|
#endif |
| 409 |
|
|
endif |
| 410 |
|
|
end do |
| 411 |
|
|
|
| 412 |
heimbach |
1.2 |
CADJ store hbl = comlev1_kpp |
| 413 |
adcroft |
1.1 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 414 |
|
|
|
| 415 |
|
|
c----------------------------------------------------------------------- |
| 416 |
|
|
c find stability and buoyancy forcing for boundary layer |
| 417 |
|
|
c----------------------------------------------------------------------- |
| 418 |
|
|
|
| 419 |
|
|
call SWFRAC( |
| 420 |
heimbach |
1.2 |
I imt, m1, hbl, |
| 421 |
adcroft |
1.1 |
O bfsfc) |
| 422 |
|
|
|
| 423 |
heimbach |
1.2 |
CADJ store bfsfc = comlev1_kpp |
| 424 |
|
|
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 425 |
|
|
|
| 426 |
adcroft |
1.1 |
do i = 1, imt |
| 427 |
|
|
bfsfc(i) = bo(i) + bosol(i) * (1. - bfsfc(i)) |
| 428 |
|
|
stable(i) = p5 + sign( p5, bfsfc(i) ) |
| 429 |
|
|
|
| 430 |
|
|
#ifdef KPP_TEST_DENOM |
| 431 |
|
|
ctl add |
| 432 |
heimbach |
1.2 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
| 433 |
adcroft |
1.1 |
ctl end-add |
| 434 |
|
|
#else |
| 435 |
|
|
c-- ensures bfsfc is never 0 |
| 436 |
|
|
bfsfc(i) = bfsfc(i) + stable(i) * epsln |
| 437 |
|
|
#endif |
| 438 |
|
|
|
| 439 |
|
|
end do |
| 440 |
|
|
|
| 441 |
|
|
c----------------------------------------------------------------------- |
| 442 |
|
|
c check hbl limits for hekman or hmonob |
| 443 |
|
|
c ph: test for zero nominator |
| 444 |
|
|
c----------------------------------------------------------------------- |
| 445 |
|
|
|
| 446 |
|
|
do i = 1, imt |
| 447 |
|
|
if (bfsfc(i) .gt. 0.0) then |
| 448 |
|
|
#ifdef KPP_TEST_DENOM |
| 449 |
|
|
ctl replace |
| 450 |
|
|
hekman = cekman * ustar(i) / max(abs(Coriol(i)),phepsi) |
| 451 |
|
|
ctl end-replace |
| 452 |
|
|
#else |
| 453 |
|
|
hekman = cekman * ustar(i) / (abs(coriol(i))+epsln) |
| 454 |
|
|
#endif |
| 455 |
|
|
hmonob = cmonob * ustar(i)*ustar(i)*ustar(i) |
| 456 |
|
|
& / vonk / bfsfc(i) |
| 457 |
|
|
hlimit = stable(i) * min(hekman,hmonob) |
| 458 |
|
|
& + (stable(i)-1.) * zgrid(Nr) |
| 459 |
|
|
hbl(i) = min(hbl(i),hlimit) |
| 460 |
|
|
hbl(i) = max(hbl(i),minKPPhbl) |
| 461 |
|
|
endif |
| 462 |
|
|
kbl(i) = kmtj(i) |
| 463 |
|
|
end do |
| 464 |
|
|
|
| 465 |
heimbach |
1.2 |
CADJ store hbl = comlev1_kpp |
| 466 |
adcroft |
1.1 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 467 |
|
|
|
| 468 |
|
|
c----------------------------------------------------------------------- |
| 469 |
|
|
c find new kbl |
| 470 |
|
|
c----------------------------------------------------------------------- |
| 471 |
|
|
|
| 472 |
|
|
do kl = 2, Nr |
| 473 |
|
|
do i = 1, imt |
| 474 |
|
|
if ( kbl(i).eq.kmtj(i) .and. (-zgrid(kl)).gt.hbl(i) ) then |
| 475 |
|
|
kbl(i) = kl |
| 476 |
|
|
endif |
| 477 |
|
|
end do |
| 478 |
|
|
end do |
| 479 |
|
|
|
| 480 |
|
|
c----------------------------------------------------------------------- |
| 481 |
|
|
c find stability and buoyancy forcing for final hbl values |
| 482 |
|
|
c----------------------------------------------------------------------- |
| 483 |
|
|
|
| 484 |
|
|
call SWFRAC( |
| 485 |
heimbach |
1.2 |
I imt, m1, hbl, |
| 486 |
adcroft |
1.1 |
O bfsfc) |
| 487 |
|
|
|
| 488 |
heimbach |
1.2 |
CADJ store bfsfc = comlev1_kpp |
| 489 |
|
|
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 490 |
|
|
|
| 491 |
adcroft |
1.1 |
do i = 1, imt |
| 492 |
|
|
bfsfc(i) = bo(i) + bosol(i) * (1. - bfsfc(i)) |
| 493 |
|
|
stable(i) = p5 + sign( p5, bfsfc(i) ) |
| 494 |
|
|
#ifdef KPP_TEST_DENOM |
| 495 |
|
|
ctl add |
| 496 |
heimbach |
1.2 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
| 497 |
adcroft |
1.1 |
ctl end-add |
| 498 |
|
|
#else |
| 499 |
|
|
c-- ensures bfsfc is never 0 |
| 500 |
|
|
bfsfc(i) = bfsfc(i) + stable(i) * epsln |
| 501 |
|
|
#endif |
| 502 |
|
|
end do |
| 503 |
|
|
|
| 504 |
|
|
c----------------------------------------------------------------------- |
| 505 |
|
|
c determine caseA and caseB |
| 506 |
|
|
c----------------------------------------------------------------------- |
| 507 |
|
|
|
| 508 |
|
|
do i = 1, imt |
| 509 |
|
|
casea(i) = p5 + |
| 510 |
|
|
1 sign(p5, -zgrid(kbl(i)) - p5*hwide(kbl(i)) - hbl(i)) |
| 511 |
|
|
end do |
| 512 |
|
|
|
| 513 |
|
|
#endif /* ALLOW_KPP */ |
| 514 |
|
|
|
| 515 |
|
|
return |
| 516 |
|
|
end |
| 517 |
|
|
|
| 518 |
|
|
c************************************************************************* |
| 519 |
|
|
|
| 520 |
|
|
subroutine wscale ( |
| 521 |
|
|
I sigma, hbl, ustar, bfsfc, |
| 522 |
|
|
O wm, ws ) |
| 523 |
|
|
|
| 524 |
|
|
c compute turbulent velocity scales. |
| 525 |
|
|
c use a 2D-lookup table for wm and ws as functions of ustar and |
| 526 |
|
|
c zetahat (=vonk*sigma*hbl*bfsfc). |
| 527 |
|
|
c |
| 528 |
|
|
c note: the lookup table is only used for unstable conditions |
| 529 |
|
|
c (zehat.le.0), in the stable domain wm (=ws) gets computed |
| 530 |
|
|
c directly. |
| 531 |
|
|
c |
| 532 |
|
|
IMPLICIT NONE |
| 533 |
|
|
|
| 534 |
|
|
#include "SIZE.h" |
| 535 |
|
|
#include "KPP_PARAMS.h" |
| 536 |
|
|
|
| 537 |
|
|
c input |
| 538 |
|
|
c------ |
| 539 |
|
|
c sigma : normalized depth (d/hbl) |
| 540 |
|
|
c hbl : boundary layer depth (m) |
| 541 |
|
|
c ustar : surface friction velocity (m/s) |
| 542 |
|
|
c bfsfc : total surface buoyancy flux (m^2/s^3) |
| 543 |
|
|
_RS sigma(imt) |
| 544 |
|
|
_RS hbl (imt) |
| 545 |
|
|
_RS ustar(imt) |
| 546 |
|
|
_RS bfsfc(imt) |
| 547 |
|
|
|
| 548 |
|
|
c output |
| 549 |
|
|
c-------- |
| 550 |
|
|
c wm, ws : turbulent velocity scales at sigma |
| 551 |
|
|
_RS wm(imt), ws(imt) |
| 552 |
|
|
|
| 553 |
|
|
#ifdef ALLOW_KPP |
| 554 |
|
|
|
| 555 |
|
|
c local |
| 556 |
|
|
c------ |
| 557 |
|
|
c zehat : = zeta * ustar**3 |
| 558 |
|
|
_RS zehat |
| 559 |
|
|
|
| 560 |
|
|
integer iz, izp1, ju, i, jup1 |
| 561 |
|
|
_RS udiff, zdiff, zfrac, ufrac, fzfrac, wam, wbm, was, wbs, u3 |
| 562 |
|
|
_RL dum |
| 563 |
|
|
|
| 564 |
|
|
c----------------------------------------------------------------------- |
| 565 |
|
|
c use lookup table for zehat < zmax only; otherwise use |
| 566 |
|
|
c stable formulae |
| 567 |
|
|
c----------------------------------------------------------------------- |
| 568 |
|
|
|
| 569 |
|
|
do i = 1, imt |
| 570 |
|
|
zehat = vonk*sigma(i)*hbl(i)*bfsfc(i) |
| 571 |
|
|
|
| 572 |
|
|
if (zehat .le. zmax) then |
| 573 |
|
|
|
| 574 |
|
|
zdiff = zehat - zmin |
| 575 |
|
|
iz = int( zdiff / deltaz ) |
| 576 |
|
|
iz = min( iz, nni ) |
| 577 |
|
|
iz = max( iz, 0 ) |
| 578 |
|
|
izp1 = iz + 1 |
| 579 |
|
|
|
| 580 |
|
|
udiff = ustar(i) - umin |
| 581 |
|
|
ju = int( udiff / deltau ) |
| 582 |
|
|
ju = min( ju, nnj ) |
| 583 |
|
|
ju = max( ju, 0 ) |
| 584 |
|
|
jup1 = ju + 1 |
| 585 |
|
|
|
| 586 |
|
|
zfrac = zdiff / deltaz - float(iz) |
| 587 |
|
|
ufrac = udiff / deltau - float(ju) |
| 588 |
|
|
|
| 589 |
|
|
fzfrac= 1. - zfrac |
| 590 |
|
|
wam = fzfrac * wmt(iz,jup1) + zfrac * wmt(izp1,jup1) |
| 591 |
|
|
wbm = fzfrac * wmt(iz,ju ) + zfrac * wmt(izp1,ju ) |
| 592 |
|
|
wm(i) = (1.-ufrac) * wbm + ufrac * wam |
| 593 |
|
|
|
| 594 |
|
|
was = fzfrac * wst(iz,jup1) + zfrac * wst(izp1,jup1) |
| 595 |
|
|
wbs = fzfrac * wst(iz,ju ) + zfrac * wst(izp1,ju ) |
| 596 |
|
|
ws(i) = (1.-ufrac) * wbs + ufrac * was |
| 597 |
|
|
|
| 598 |
|
|
else |
| 599 |
|
|
|
| 600 |
|
|
u3 = ustar(i) * ustar(i) * ustar(i) |
| 601 |
|
|
dum = u3 + conc1 * zehat |
| 602 |
|
|
wm(i) = vonk * ustar(i) * u3 / dum |
| 603 |
|
|
ws(i) = wm(i) |
| 604 |
|
|
|
| 605 |
|
|
endif |
| 606 |
|
|
|
| 607 |
|
|
end do |
| 608 |
|
|
|
| 609 |
|
|
#endif /* ALLOW_KPP */ |
| 610 |
|
|
|
| 611 |
|
|
return |
| 612 |
|
|
end |
| 613 |
|
|
|
| 614 |
|
|
c************************************************************************* |
| 615 |
|
|
|
| 616 |
|
|
subroutine Ri_iwmix ( |
| 617 |
|
|
I kmtj, shsq, dbloc, dblocSm |
| 618 |
|
|
I , ikey |
| 619 |
|
|
O , diffus ) |
| 620 |
|
|
|
| 621 |
|
|
c compute interior viscosity diffusivity coefficients due |
| 622 |
|
|
c to shear instability (dependent on a local Richardson number), |
| 623 |
|
|
c to background internal wave activity, and |
| 624 |
|
|
c to static instability (local Richardson number < 0). |
| 625 |
|
|
|
| 626 |
|
|
IMPLICIT NONE |
| 627 |
|
|
|
| 628 |
|
|
#include "SIZE.h" |
| 629 |
|
|
#include "EEPARAMS.h" |
| 630 |
|
|
#include "PARAMS.h" |
| 631 |
|
|
#include "KPP_PARAMS.h" |
| 632 |
|
|
|
| 633 |
|
|
c input |
| 634 |
|
|
c kmtj (imt) number of vertical layers on this row |
| 635 |
|
|
c shsq (imt,Nr) (local velocity shear)^2 ((m/s)^2) |
| 636 |
|
|
c dbloc (imt,Nr) local delta buoyancy (m/s^2) |
| 637 |
|
|
c dblocSm(imt,Nr) horizontally smoothed dbloc (m/s^2) |
| 638 |
|
|
integer kmtj (imt) |
| 639 |
|
|
_RS shsq (imt,Nr) |
| 640 |
|
|
_RS dbloc (imt,Nr) |
| 641 |
|
|
_RS dblocSm(imt,Nr) |
| 642 |
|
|
integer ikey |
| 643 |
|
|
|
| 644 |
|
|
c output |
| 645 |
|
|
c diffus(imt,0:Nrp1,1) vertical viscosivity coefficient (m^2/s) |
| 646 |
|
|
c diffus(imt,0:Nrp1,2) vertical scalar diffusivity (m^2/s) |
| 647 |
|
|
c diffus(imt,0:Nrp1,3) vertical temperature diffusivity (m^2/s) |
| 648 |
|
|
_RS diffus(imt,0:Nrp1,3) |
| 649 |
|
|
|
| 650 |
|
|
#ifdef ALLOW_KPP |
| 651 |
|
|
|
| 652 |
|
|
c local variables |
| 653 |
|
|
c Rig local Richardson number |
| 654 |
|
|
c fRi, fcon function of Rig |
| 655 |
|
|
_RS Rig |
| 656 |
|
|
_RS fRi, fcon |
| 657 |
|
|
_RS ratio |
| 658 |
|
|
integer i, ki, mr |
| 659 |
|
|
_RS c1, c0 |
| 660 |
|
|
|
| 661 |
|
|
c constants |
| 662 |
|
|
c1 = 1.0 |
| 663 |
|
|
c0 = 0.0 |
| 664 |
|
|
|
| 665 |
|
|
c----------------------------------------------------------------------- |
| 666 |
|
|
c compute interior gradient Ri at all interfaces ki=1,Nr, (not surface) |
| 667 |
|
|
c use diffus(*,*,1) as temporary storage of Ri to be smoothed |
| 668 |
|
|
c use diffus(*,*,2) as temporary storage for Brunt-Vaisala squared |
| 669 |
|
|
c set values at bottom and below to nearest value above bottom |
| 670 |
|
|
|
| 671 |
|
|
do ki = 1, Nr |
| 672 |
|
|
do i = 1, imt |
| 673 |
|
|
if (kmtj(i) .EQ. 0 ) then |
| 674 |
|
|
diffus(i,ki,1) = 0. |
| 675 |
|
|
diffus(i,ki,2) = 0. |
| 676 |
|
|
elseif (ki .GE. kmtj(i)) then |
| 677 |
|
|
diffus(i,ki,1) = diffus(i,ki-1,1) |
| 678 |
|
|
diffus(i,ki,2) = diffus(i,ki-1,2) |
| 679 |
|
|
else |
| 680 |
|
|
diffus(i,ki,1) = dblocSm(i,ki) * (zgrid(ki)-zgrid(ki+1)) |
| 681 |
|
|
#ifdef KPP_TEST_DENOM |
| 682 |
|
|
& / max( Shsq(i,ki), phepsi ) |
| 683 |
|
|
#else |
| 684 |
|
|
& / ( shsq(i,ki) + epsln ) |
| 685 |
|
|
#endif |
| 686 |
|
|
diffus(i,ki,2) = dbloc(i,ki) / (zgrid(ki)-zgrid(ki+1)) |
| 687 |
|
|
endif |
| 688 |
|
|
end do |
| 689 |
|
|
end do |
| 690 |
|
|
|
| 691 |
|
|
c----------------------------------------------------------------------- |
| 692 |
|
|
c vertically smooth Ri |
| 693 |
|
|
|
| 694 |
|
|
do mr = 1, num_v_smooth_Ri |
| 695 |
heimbach |
1.2 |
|
| 696 |
|
|
CADJ store diffus(:,:,1) = comlev1_kpp_sm |
| 697 |
|
|
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy),Nr+2 /) |
| 698 |
|
|
|
| 699 |
adcroft |
1.1 |
call z121 ( |
| 700 |
|
|
U diffus(1,0,1)) |
| 701 |
|
|
end do |
| 702 |
|
|
|
| 703 |
heimbach |
1.2 |
CADJ store diffus = comlev1_kpp |
| 704 |
adcroft |
1.1 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy),Nr+2,3 /) |
| 705 |
|
|
|
| 706 |
|
|
c----------------------------------------------------------------------- |
| 707 |
|
|
c after smoothing loop |
| 708 |
|
|
|
| 709 |
|
|
do ki = 1, Nr |
| 710 |
|
|
do i = 1, imt |
| 711 |
|
|
|
| 712 |
|
|
c evaluate f of Brunt-Vaisala squared for convection, store in fcon |
| 713 |
|
|
|
| 714 |
|
|
Rig = max ( diffus(i,ki,2) , BVSQcon ) |
| 715 |
|
|
ratio = min ( (BVSQcon - Rig) / BVSQcon, c1 ) |
| 716 |
|
|
fcon = c1 - ratio * ratio |
| 717 |
|
|
fcon = fcon * fcon * fcon |
| 718 |
|
|
|
| 719 |
|
|
c evaluate f of smooth Ri for shear instability, store in fRi |
| 720 |
|
|
|
| 721 |
|
|
Rig = max ( diffus(i,ki,1), c0 ) |
| 722 |
|
|
ratio = min ( Rig / Riinfty , c1 ) |
| 723 |
|
|
fRi = c1 - ratio * ratio |
| 724 |
|
|
fRi = fRi * fRi * fRi |
| 725 |
|
|
|
| 726 |
|
|
c ---------------------------------------------------------------------- |
| 727 |
|
|
c evaluate diffusivities and viscosity |
| 728 |
|
|
c mixing due to internal waves, and shear and static instability |
| 729 |
|
|
|
| 730 |
|
|
diffus(i,ki,1) = viscAr + fcon * difmcon + fRi * difm0 |
| 731 |
|
|
diffus(i,ki,2) = diffKrS + fcon * difscon + fRi * difs0 |
| 732 |
heimbach |
1.2 |
diffus(i,ki,3) = diffKrT + fcon * difscon + fRi * difs0 |
| 733 |
adcroft |
1.1 |
|
| 734 |
|
|
end do |
| 735 |
|
|
end do |
| 736 |
|
|
|
| 737 |
|
|
c ------------------------------------------------------------------------ |
| 738 |
|
|
c set surface values to 0.0 |
| 739 |
|
|
|
| 740 |
|
|
do i = 1, imt |
| 741 |
|
|
diffus(i,0,1) = c0 |
| 742 |
|
|
diffus(i,0,2) = c0 |
| 743 |
|
|
diffus(i,0,3) = c0 |
| 744 |
|
|
end do |
| 745 |
|
|
|
| 746 |
|
|
#endif /* ALLOW_KPP */ |
| 747 |
|
|
|
| 748 |
|
|
return |
| 749 |
|
|
end |
| 750 |
|
|
|
| 751 |
|
|
c************************************************************************* |
| 752 |
|
|
|
| 753 |
|
|
subroutine z121 ( |
| 754 |
|
|
U v ) |
| 755 |
|
|
|
| 756 |
|
|
c Apply 121 smoothing in k to 2-d array V(i,k=1,Nr) |
| 757 |
|
|
c top (0) value is used as a dummy |
| 758 |
|
|
c bottom (Nrp1) value is set to input value from above. |
| 759 |
|
|
|
| 760 |
heimbach |
1.2 |
c Note that it is important to exclude from the smoothing any points |
| 761 |
adcroft |
1.1 |
c that are outside the range of the K(Ri) scheme, ie. >0.8, or <0.0. |
| 762 |
heimbach |
1.2 |
c Otherwise, there is interference with other physics, especially |
| 763 |
adcroft |
1.1 |
c penetrative convection. |
| 764 |
|
|
|
| 765 |
|
|
IMPLICIT NONE |
| 766 |
|
|
#include "SIZE.h" |
| 767 |
|
|
#include "KPP_PARAMS.h" |
| 768 |
|
|
|
| 769 |
|
|
c input/output |
| 770 |
|
|
c------------- |
| 771 |
|
|
c v : 2-D array to be smoothed in Nrp1 direction |
| 772 |
|
|
_RS v(imt,0:Nrp1) |
| 773 |
|
|
|
| 774 |
|
|
#ifdef ALLOW_KPP |
| 775 |
|
|
|
| 776 |
|
|
c local |
| 777 |
|
|
_RS zwork, zflag |
| 778 |
heimbach |
1.2 |
_RS KRi_range(1:Nrp1) |
| 779 |
adcroft |
1.1 |
integer i, k, km1, kp1 |
| 780 |
|
|
|
| 781 |
heimbach |
1.2 |
_RS p0 , p25 , p5 , p2 |
| 782 |
|
|
parameter ( p0 = 0.0, p25 = 0.25, p5 = 0.5, p2 = 2.0 ) |
| 783 |
|
|
|
| 784 |
|
|
KRi_range(Nrp1) = p0 |
| 785 |
adcroft |
1.1 |
|
| 786 |
heimbach |
1.2 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 787 |
|
|
C-- dummy assignment to end declaration part for TAMC |
| 788 |
|
|
i = 0 |
| 789 |
|
|
|
| 790 |
|
|
C-- HPF directive to help TAMC |
| 791 |
|
|
CHPF$ INDEPENDENT |
| 792 |
|
|
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 793 |
adcroft |
1.1 |
do i = 1, imt |
| 794 |
|
|
|
| 795 |
|
|
v(i,Nrp1) = v(i,Nr) |
| 796 |
|
|
|
| 797 |
|
|
do k = 1, Nr |
| 798 |
|
|
KRi_range(k) = p5 + SIGN(p5,v(i,k)) |
| 799 |
|
|
KRi_range(k) = KRi_range(k) * |
| 800 |
|
|
& ( p5 + SIGN(p5,(Riinfty-v(i,k))) ) |
| 801 |
|
|
end do |
| 802 |
|
|
|
| 803 |
|
|
zwork = KRi_range(1) * v(i,1) |
| 804 |
|
|
v(i,1) = p2 * v(i,1) + |
| 805 |
|
|
& KRi_range(1) * KRi_range(2) * v(i,2) |
| 806 |
|
|
zflag = p2 + KRi_range(1) * KRi_range(2) |
| 807 |
|
|
v(i,1) = v(i,1) / zflag |
| 808 |
|
|
|
| 809 |
heimbach |
1.2 |
CADJ INIT z121tape = common, Nr |
| 810 |
adcroft |
1.1 |
do k = 2, Nr |
| 811 |
heimbach |
1.2 |
CADJ STORE v(i,k), zwork = z121tape |
| 812 |
adcroft |
1.1 |
km1 = k - 1 |
| 813 |
|
|
kp1 = k + 1 |
| 814 |
|
|
zflag = v(i,k) |
| 815 |
|
|
v(i,k) = p2 * v(i,k) + |
| 816 |
|
|
& KRi_range(k) * KRi_range(kp1) * v(i,kp1) + |
| 817 |
|
|
& KRi_range(k) * zwork |
| 818 |
|
|
zwork = KRi_range(k) * zflag |
| 819 |
|
|
zflag = p2 + KRi_range(k)*(KRi_range(kp1)+KRi_range(km1)) |
| 820 |
|
|
v(i,k) = v(i,k) / zflag |
| 821 |
|
|
end do |
| 822 |
|
|
|
| 823 |
|
|
end do |
| 824 |
|
|
|
| 825 |
|
|
#endif /* ALLOW_KPP */ |
| 826 |
|
|
|
| 827 |
|
|
return |
| 828 |
|
|
end |
| 829 |
|
|
|
| 830 |
|
|
c************************************************************************* |
| 831 |
|
|
|
| 832 |
|
|
subroutine smooth_horiz_rs ( |
| 833 |
|
|
I k, bi, bj, |
| 834 |
|
|
I fld_in, |
| 835 |
|
|
O fld_out ) |
| 836 |
|
|
|
| 837 |
|
|
c Apply horizontal smoothing to RS 2-D array |
| 838 |
|
|
|
| 839 |
|
|
IMPLICIT NONE |
| 840 |
|
|
#include "SIZE.h" |
| 841 |
|
|
#include "KPP_PARAMS.h" |
| 842 |
|
|
|
| 843 |
|
|
c input |
| 844 |
|
|
c k, bi, bj : array indices |
| 845 |
|
|
c fld_in : 2-D array to be smoothed |
| 846 |
|
|
integer k, bi, bj |
| 847 |
|
|
_RS fld_in(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 848 |
|
|
|
| 849 |
|
|
c output |
| 850 |
|
|
c fld_out : smoothed 2-D array |
| 851 |
|
|
_RS fld_out(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 852 |
|
|
|
| 853 |
|
|
#ifdef ALLOW_KPP |
| 854 |
|
|
|
| 855 |
|
|
c local |
| 856 |
|
|
integer i, j, im1, ip1, jm1, jp1 |
| 857 |
|
|
_RS tempVar |
| 858 |
|
|
_RS fld_tmp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 859 |
|
|
|
| 860 |
|
|
integer imin , imax |
| 861 |
|
|
parameter( imin=1-OLx+1, imax=sNx+OLx-1 ) |
| 862 |
|
|
|
| 863 |
|
|
integer jmin , jmax |
| 864 |
|
|
parameter( jmin=1-OLy+1, jmax=sNy+OLy-1 ) |
| 865 |
|
|
|
| 866 |
|
|
_RS p0 , p5 , p25 , p125 , p0625 |
| 867 |
|
|
parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
| 868 |
|
|
|
| 869 |
|
|
DO j = jmin, jmax |
| 870 |
|
|
jm1 = j-1 |
| 871 |
|
|
jp1 = j+1 |
| 872 |
|
|
DO i = imin, imax |
| 873 |
|
|
im1 = i-1 |
| 874 |
|
|
ip1 = i+1 |
| 875 |
|
|
tempVar = |
| 876 |
|
|
& p25 * pMask(i ,j ,k,bi,bj) + |
| 877 |
|
|
& p125 * ( pMask(im1,j ,k,bi,bj) + |
| 878 |
|
|
& pMask(ip1,j ,k,bi,bj) + |
| 879 |
|
|
& pMask(i ,jm1,k,bi,bj) + |
| 880 |
|
|
& pMask(i ,jp1,k,bi,bj) ) + |
| 881 |
|
|
& p0625 * ( pMask(im1,jm1,k,bi,bj) + |
| 882 |
|
|
& pMask(im1,jp1,k,bi,bj) + |
| 883 |
|
|
& pMask(ip1,jm1,k,bi,bj) + |
| 884 |
|
|
& pMask(ip1,jp1,k,bi,bj) ) |
| 885 |
|
|
IF ( tempVar .GE. p25 ) THEN |
| 886 |
|
|
fld_tmp(i,j) = ( |
| 887 |
|
|
& p25 * fld_in(i ,j )*pMask(i ,j ,k,bi,bj) + |
| 888 |
|
|
& p125 *(fld_in(im1,j )*pMask(im1,j ,k,bi,bj) + |
| 889 |
|
|
& fld_in(ip1,j )*pMask(ip1,j ,k,bi,bj) + |
| 890 |
|
|
& fld_in(i ,jm1)*pMask(i ,jm1,k,bi,bj) + |
| 891 |
|
|
& fld_in(i ,jp1)*pMask(i ,jp1,k,bi,bj))+ |
| 892 |
|
|
& p0625*(fld_in(im1,jm1)*pMask(im1,jm1,k,bi,bj) + |
| 893 |
|
|
& fld_in(im1,jp1)*pMask(im1,jp1,k,bi,bj) + |
| 894 |
|
|
& fld_in(ip1,jm1)*pMask(ip1,jm1,k,bi,bj) + |
| 895 |
|
|
& fld_in(ip1,jp1)*pMask(ip1,jp1,k,bi,bj))) |
| 896 |
|
|
& / tempVar |
| 897 |
|
|
ELSE |
| 898 |
|
|
fld_tmp(i,j) = fld_in(i,j) |
| 899 |
|
|
ENDIF |
| 900 |
|
|
ENDDO |
| 901 |
|
|
ENDDO |
| 902 |
|
|
|
| 903 |
|
|
c transfer smoothed field to output array |
| 904 |
|
|
DO j = jmin, jmax |
| 905 |
|
|
DO i = imin, imax |
| 906 |
|
|
fld_out(i,j) = fld_tmp(i,j) |
| 907 |
|
|
ENDDO |
| 908 |
|
|
ENDDO |
| 909 |
|
|
|
| 910 |
|
|
c set output array edges to input field values |
| 911 |
|
|
DO j = jmin, jmax |
| 912 |
|
|
DO i = 1-OLx, imin-1 |
| 913 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 914 |
|
|
END DO |
| 915 |
|
|
DO i = imax+1, sNx+OLx |
| 916 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 917 |
|
|
END DO |
| 918 |
|
|
END DO |
| 919 |
|
|
DO i = 1-OLx, sNx+OLx |
| 920 |
|
|
DO j = 1-OLy, jmin-1 |
| 921 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 922 |
|
|
END DO |
| 923 |
|
|
DO j = jmax+1, sNy+OLy |
| 924 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 925 |
|
|
END DO |
| 926 |
|
|
END DO |
| 927 |
|
|
|
| 928 |
|
|
#endif /* ALLOW_KPP */ |
| 929 |
|
|
|
| 930 |
|
|
return |
| 931 |
|
|
end |
| 932 |
|
|
|
| 933 |
|
|
c************************************************************************* |
| 934 |
|
|
|
| 935 |
|
|
subroutine smooth_horiz_rl ( |
| 936 |
|
|
I k, bi, bj, |
| 937 |
|
|
I fld_in, |
| 938 |
|
|
O fld_out ) |
| 939 |
|
|
|
| 940 |
|
|
c Apply horizontal smoothing to RL 2-D array |
| 941 |
|
|
|
| 942 |
|
|
IMPLICIT NONE |
| 943 |
|
|
#include "SIZE.h" |
| 944 |
|
|
#include "KPP_PARAMS.h" |
| 945 |
|
|
|
| 946 |
|
|
c input |
| 947 |
|
|
c k, bi, bj : array indices |
| 948 |
|
|
c fld_in : 2-D array to be smoothed |
| 949 |
|
|
integer k, bi, bj |
| 950 |
|
|
_RL fld_in(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 951 |
|
|
|
| 952 |
|
|
c output |
| 953 |
|
|
c fld_out : smoothed 2-D array |
| 954 |
|
|
_RL fld_out(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 955 |
|
|
|
| 956 |
|
|
#ifdef ALLOW_KPP |
| 957 |
|
|
|
| 958 |
|
|
c local |
| 959 |
|
|
integer i, j, im1, ip1, jm1, jp1 |
| 960 |
|
|
_RL tempVar |
| 961 |
|
|
_RL fld_tmp(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 962 |
|
|
|
| 963 |
|
|
integer imin , imax |
| 964 |
|
|
parameter( imin=1-OLx+1, imax=sNx+OLx-1 ) |
| 965 |
|
|
|
| 966 |
|
|
integer jmin , jmax |
| 967 |
|
|
parameter( jmin=1-OLy+1, jmax=sNy+OLy-1 ) |
| 968 |
|
|
|
| 969 |
|
|
_RS p0 , p5 , p25 , p125 , p0625 |
| 970 |
|
|
parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
| 971 |
|
|
|
| 972 |
|
|
DO j = jmin, jmax |
| 973 |
|
|
jm1 = j-1 |
| 974 |
|
|
jp1 = j+1 |
| 975 |
|
|
DO i = imin, imax |
| 976 |
|
|
im1 = i-1 |
| 977 |
|
|
ip1 = i+1 |
| 978 |
|
|
tempVar = |
| 979 |
|
|
& p25 * pMask(i ,j ,k,bi,bj) + |
| 980 |
|
|
& p125 * ( pMask(im1,j ,k,bi,bj) + |
| 981 |
|
|
& pMask(ip1,j ,k,bi,bj) + |
| 982 |
|
|
& pMask(i ,jm1,k,bi,bj) + |
| 983 |
|
|
& pMask(i ,jp1,k,bi,bj) ) + |
| 984 |
|
|
& p0625 * ( pMask(im1,jm1,k,bi,bj) + |
| 985 |
|
|
& pMask(im1,jp1,k,bi,bj) + |
| 986 |
|
|
& pMask(ip1,jm1,k,bi,bj) + |
| 987 |
|
|
& pMask(ip1,jp1,k,bi,bj) ) |
| 988 |
|
|
IF ( tempVar .GE. p25 ) THEN |
| 989 |
|
|
fld_tmp(i,j) = ( |
| 990 |
|
|
& p25 * fld_in(i ,j )*pMask(i ,j ,k,bi,bj) + |
| 991 |
|
|
& p125 *(fld_in(im1,j )*pMask(im1,j ,k,bi,bj) + |
| 992 |
|
|
& fld_in(ip1,j )*pMask(ip1,j ,k,bi,bj) + |
| 993 |
|
|
& fld_in(i ,jm1)*pMask(i ,jm1,k,bi,bj) + |
| 994 |
|
|
& fld_in(i ,jp1)*pMask(i ,jp1,k,bi,bj))+ |
| 995 |
|
|
& p0625*(fld_in(im1,jm1)*pMask(im1,jm1,k,bi,bj) + |
| 996 |
|
|
& fld_in(im1,jp1)*pMask(im1,jp1,k,bi,bj) + |
| 997 |
|
|
& fld_in(ip1,jm1)*pMask(ip1,jm1,k,bi,bj) + |
| 998 |
|
|
& fld_in(ip1,jp1)*pMask(ip1,jp1,k,bi,bj))) |
| 999 |
|
|
& / tempVar |
| 1000 |
|
|
ELSE |
| 1001 |
|
|
fld_tmp(i,j) = fld_in(i,j) |
| 1002 |
|
|
ENDIF |
| 1003 |
|
|
ENDDO |
| 1004 |
|
|
ENDDO |
| 1005 |
|
|
|
| 1006 |
|
|
c transfer smoothed field to output array |
| 1007 |
|
|
DO j = jmin, jmax |
| 1008 |
|
|
DO i = imin, imax |
| 1009 |
|
|
fld_out(i,j) = fld_tmp(i,j) |
| 1010 |
|
|
ENDDO |
| 1011 |
|
|
ENDDO |
| 1012 |
|
|
|
| 1013 |
|
|
c set output array edges to input field values |
| 1014 |
|
|
DO j = jmin, jmax |
| 1015 |
|
|
DO i = 1-OLx, imin-1 |
| 1016 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 1017 |
|
|
END DO |
| 1018 |
|
|
DO i = imax+1, sNx+OLx |
| 1019 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 1020 |
|
|
END DO |
| 1021 |
|
|
END DO |
| 1022 |
|
|
DO i = 1-OLx, sNx+OLx |
| 1023 |
|
|
DO j = 1-OLy, jmin-1 |
| 1024 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 1025 |
|
|
END DO |
| 1026 |
|
|
DO j = jmax+1, sNy+OLy |
| 1027 |
|
|
fld_out(i,j) = fld_in(i,j) |
| 1028 |
|
|
END DO |
| 1029 |
|
|
END DO |
| 1030 |
|
|
|
| 1031 |
|
|
#endif /* ALLOW_KPP */ |
| 1032 |
|
|
|
| 1033 |
|
|
return |
| 1034 |
|
|
end |
| 1035 |
|
|
|
| 1036 |
|
|
c************************************************************************* |
| 1037 |
|
|
|
| 1038 |
|
|
subroutine blmix ( |
| 1039 |
|
|
I ustar, bfsfc, hbl, stable, casea, diffus, kbl |
| 1040 |
|
|
O , dkm1, blmc, ghat, sigma |
| 1041 |
|
|
& ) |
| 1042 |
|
|
|
| 1043 |
|
|
c mixing coefficients within boundary layer depend on surface |
| 1044 |
|
|
c forcing and the magnitude and gradient of interior mixing below |
| 1045 |
|
|
c the boundary layer ("matching"). |
| 1046 |
|
|
c |
| 1047 |
|
|
c caution: if mixing bottoms out at hbl = -zgrid(Nr) then |
| 1048 |
|
|
c fictitious layer at Nrp1 is needed with small but finite width |
| 1049 |
|
|
c hwide(Nrp1) (eg. epsln = 1.e-20). |
| 1050 |
|
|
c |
| 1051 |
|
|
IMPLICIT NONE |
| 1052 |
|
|
|
| 1053 |
|
|
#include "SIZE.h" |
| 1054 |
|
|
#include "KPP_PARAMS.h" |
| 1055 |
|
|
|
| 1056 |
|
|
c input |
| 1057 |
|
|
c ustar (imt) surface friction velocity (m/s) |
| 1058 |
|
|
c bfsfc (imt) surface buoyancy forcing (m^2/s^3) |
| 1059 |
|
|
c hbl (imt) boundary layer depth (m) |
| 1060 |
|
|
c stable(imt) = 1 in stable forcing |
| 1061 |
|
|
c casea (imt) = 1 in case A |
| 1062 |
|
|
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
| 1063 |
|
|
c kbl(imt) -1 of first grid level below hbl |
| 1064 |
|
|
_RS ustar (imt) |
| 1065 |
|
|
_RS bfsfc (imt) |
| 1066 |
|
|
_RS hbl (imt) |
| 1067 |
|
|
_RS stable(imt) |
| 1068 |
|
|
_RS casea (imt) |
| 1069 |
|
|
_RS diffus(imt,0:Nrp1,mdiff) |
| 1070 |
|
|
integer kbl(imt) |
| 1071 |
|
|
|
| 1072 |
|
|
c output |
| 1073 |
|
|
c dkm1 (imt,mdiff) boundary layer difs at kbl-1 level |
| 1074 |
|
|
c blmc (imt,Nr,mdiff) boundary layer mixing coefficients (m^2/s) |
| 1075 |
|
|
c ghat (imt,Nr) nonlocal scalar transport |
| 1076 |
|
|
c sigma(imt) normalized depth (d / hbl) |
| 1077 |
|
|
_RS dkm1 (imt,mdiff) |
| 1078 |
|
|
_RS blmc (imt,Nr,mdiff) |
| 1079 |
|
|
_RS ghat (imt,Nr) |
| 1080 |
|
|
_RS sigma(imt) |
| 1081 |
|
|
|
| 1082 |
|
|
#ifdef ALLOW_KPP |
| 1083 |
|
|
|
| 1084 |
|
|
c local |
| 1085 |
heimbach |
1.2 |
c gat1*(imt) shape function at sigma = 1 |
| 1086 |
|
|
c dat1*(imt) derivative of shape function at sigma = 1 |
| 1087 |
adcroft |
1.1 |
c ws(imt), wm(imt) turbulent velocity scales (m/s) |
| 1088 |
heimbach |
1.2 |
_RS gat1m(imt), gat1s(imt), gat1t(imt) |
| 1089 |
|
|
_RS dat1m(imt), dat1s(imt), dat1t(imt) |
| 1090 |
adcroft |
1.1 |
_RS ws(imt), wm(imt) |
| 1091 |
|
|
integer i, kn, ki |
| 1092 |
|
|
_RS R, dvdzup, dvdzdn, viscp |
| 1093 |
|
|
_RS difsp, diftp, visch, difsh, difth |
| 1094 |
|
|
_RS f1, sig, a1, a2, a3, delhat |
| 1095 |
heimbach |
1.2 |
_RS Gm, Gs, Gt |
| 1096 |
|
|
_RL dum |
| 1097 |
adcroft |
1.1 |
|
| 1098 |
heimbach |
1.2 |
_RS p0 , eins |
| 1099 |
|
|
parameter (p0=0.0, eins=1.0) |
| 1100 |
adcroft |
1.1 |
|
| 1101 |
|
|
c----------------------------------------------------------------------- |
| 1102 |
|
|
c compute velocity scales at hbl |
| 1103 |
|
|
c----------------------------------------------------------------------- |
| 1104 |
|
|
|
| 1105 |
|
|
do i = 1, imt |
| 1106 |
|
|
sigma(i) = stable(i) * 1.0 + (1. - stable(i)) * epsilon |
| 1107 |
|
|
end do |
| 1108 |
|
|
|
| 1109 |
|
|
call wscale ( |
| 1110 |
|
|
I sigma, hbl, ustar, bfsfc, |
| 1111 |
|
|
O wm, ws ) |
| 1112 |
|
|
|
| 1113 |
|
|
do i = 1, imt |
| 1114 |
|
|
|
| 1115 |
|
|
kn = int(caseA(i)+phepsi) *(kbl(i) -1) + |
| 1116 |
|
|
$ (1 - int(caseA(i)+phepsi)) * kbl(i) |
| 1117 |
|
|
|
| 1118 |
|
|
c----------------------------------------------------------------------- |
| 1119 |
|
|
c find the interior viscosities and derivatives at hbl(i) |
| 1120 |
|
|
c----------------------------------------------------------------------- |
| 1121 |
|
|
|
| 1122 |
|
|
delhat = 0.5*hwide(kn) - zgrid(kn) - hbl(i) |
| 1123 |
|
|
R = 1.0 - delhat / hwide(kn) |
| 1124 |
|
|
dvdzup = (diffus(i,kn-1,1) - diffus(i,kn ,1)) / hwide(kn) |
| 1125 |
|
|
dvdzdn = (diffus(i,kn ,1) - diffus(i,kn+1,1)) / hwide(kn+1) |
| 1126 |
|
|
viscp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
| 1127 |
|
|
1 R * (dvdzdn + abs(dvdzdn)) ) |
| 1128 |
|
|
|
| 1129 |
|
|
dvdzup = (diffus(i,kn-1,2) - diffus(i,kn ,2)) / hwide(kn) |
| 1130 |
|
|
dvdzdn = (diffus(i,kn ,2) - diffus(i,kn+1,2)) / hwide(kn+1) |
| 1131 |
|
|
difsp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
| 1132 |
|
|
1 R * (dvdzdn + abs(dvdzdn)) ) |
| 1133 |
|
|
|
| 1134 |
|
|
dvdzup = (diffus(i,kn-1,3) - diffus(i,kn ,3)) / hwide(kn) |
| 1135 |
|
|
dvdzdn = (diffus(i,kn ,3) - diffus(i,kn+1,3)) / hwide(kn+1) |
| 1136 |
|
|
diftp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
| 1137 |
|
|
1 R * (dvdzdn + abs(dvdzdn)) ) |
| 1138 |
|
|
|
| 1139 |
|
|
visch = diffus(i,kn,1) + viscp * delhat |
| 1140 |
|
|
difsh = diffus(i,kn,2) + difsp * delhat |
| 1141 |
|
|
difth = diffus(i,kn,3) + diftp * delhat |
| 1142 |
|
|
|
| 1143 |
|
|
#ifdef KPP_TEST_DENOM |
| 1144 |
|
|
ctl replace (Important!!! not phepsi**4 !!!) |
| 1145 |
|
|
f1 = stable(i) * conc1 * bfsfc(i) / |
| 1146 |
|
|
& max(ustar(i)**4,phepsi) |
| 1147 |
heimbach |
1.2 |
wm(i) = sign(eins,wm(i))*max(phepsi,abs(wm(i))) |
| 1148 |
|
|
gat1m(i) = visch / hbl(i) / wm(i) |
| 1149 |
|
|
dat1m(i) = -viscp / wm(i) + f1 * visch |
| 1150 |
adcroft |
1.1 |
#else |
| 1151 |
|
|
f1 = stable(i) * conc1 * bfsfc(i) / (ustar(i)**4+epsln) |
| 1152 |
heimbach |
1.2 |
gat1m(i) = visch / hbl(i) / (wm(i)+epsln) |
| 1153 |
|
|
dat1m(i) = -viscp / (wm(i)+epsln) + f1 * visch |
| 1154 |
adcroft |
1.1 |
#endif |
| 1155 |
heimbach |
1.2 |
dat1m(i) = min(dat1m(i),p0) |
| 1156 |
adcroft |
1.1 |
|
| 1157 |
|
|
#ifdef KPP_TEST_DENOM |
| 1158 |
heimbach |
1.2 |
ws(i) = sign(eins,ws(i))*max(phepsi,abs(ws(i))) |
| 1159 |
|
|
gat1s(i) = difsh / hbl(i) / ws(i) |
| 1160 |
|
|
dat1s(i) = -difsp / ws(i) + f1 * difsh |
| 1161 |
adcroft |
1.1 |
#else |
| 1162 |
heimbach |
1.2 |
gat1s(i) = difsh / hbl(i) / (ws(i)+epsln) |
| 1163 |
|
|
dat1s(i) = -difsp / (ws(i)+epsln) + f1 * difsh |
| 1164 |
adcroft |
1.1 |
#endif |
| 1165 |
heimbach |
1.2 |
dat1s(i) = min(dat1s(i),p0) |
| 1166 |
adcroft |
1.1 |
|
| 1167 |
|
|
#ifdef KPP_TEST_DENOM |
| 1168 |
heimbach |
1.2 |
gat1t(i) = difth / hbl(i) / ws(i) |
| 1169 |
|
|
dat1t(i) = -diftp / ws(i) + f1 * difth |
| 1170 |
adcroft |
1.1 |
#else |
| 1171 |
heimbach |
1.2 |
gat1t(i) = difth / hbl(i) / (ws(i)+epsln) |
| 1172 |
|
|
dat1t(i) = -diftp / (ws(i)+epsln) + f1 * difth |
| 1173 |
adcroft |
1.1 |
#endif |
| 1174 |
heimbach |
1.2 |
dat1t(i) = min(dat1t(i),p0) |
| 1175 |
adcroft |
1.1 |
|
| 1176 |
|
|
end do |
| 1177 |
|
|
|
| 1178 |
|
|
do ki = 1, Nr |
| 1179 |
|
|
|
| 1180 |
|
|
c----------------------------------------------------------------------- |
| 1181 |
|
|
c compute turbulent velocity scales on the interfaces |
| 1182 |
|
|
c----------------------------------------------------------------------- |
| 1183 |
|
|
|
| 1184 |
|
|
do i = 1, imt |
| 1185 |
|
|
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
| 1186 |
|
|
sigma(i) = stable(i)*sig + (1.-stable(i))*min(sig,epsilon) |
| 1187 |
|
|
end do |
| 1188 |
|
|
call wscale ( |
| 1189 |
|
|
I sigma, hbl, ustar, bfsfc, |
| 1190 |
|
|
O wm, ws ) |
| 1191 |
|
|
|
| 1192 |
|
|
c----------------------------------------------------------------------- |
| 1193 |
|
|
c compute the dimensionless shape functions at the interfaces |
| 1194 |
|
|
c----------------------------------------------------------------------- |
| 1195 |
|
|
|
| 1196 |
|
|
do i = 1, imt |
| 1197 |
|
|
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
| 1198 |
|
|
a1 = sig - 2. |
| 1199 |
|
|
a2 = 3. - 2. * sig |
| 1200 |
|
|
a3 = sig - 1. |
| 1201 |
|
|
|
| 1202 |
heimbach |
1.2 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
| 1203 |
|
|
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
| 1204 |
|
|
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
| 1205 |
adcroft |
1.1 |
|
| 1206 |
|
|
c----------------------------------------------------------------------- |
| 1207 |
|
|
c compute boundary layer diffusivities at the interfaces |
| 1208 |
|
|
c----------------------------------------------------------------------- |
| 1209 |
|
|
|
| 1210 |
heimbach |
1.2 |
blmc(i,ki,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
| 1211 |
adcroft |
1.1 |
blmc(i,ki,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
| 1212 |
|
|
blmc(i,ki,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
| 1213 |
|
|
|
| 1214 |
|
|
c----------------------------------------------------------------------- |
| 1215 |
|
|
c nonlocal transport term = ghat * <ws>o |
| 1216 |
|
|
c----------------------------------------------------------------------- |
| 1217 |
|
|
#ifdef KPP_TEST_DENOM |
| 1218 |
|
|
dum = ws(i) * hbl(i) |
| 1219 |
|
|
ctl replace |
| 1220 |
|
|
ghat(i,ki) = (1.-stable(i)) * cg / max(phepsi,dum) |
| 1221 |
|
|
ctl end-replace |
| 1222 |
|
|
#else |
| 1223 |
|
|
dum = ws(i) * hbl(i) + epsln |
| 1224 |
|
|
ghat(i,ki) = (1. - stable(i)) * cg / dum |
| 1225 |
|
|
#endif |
| 1226 |
|
|
|
| 1227 |
|
|
end do |
| 1228 |
|
|
end do |
| 1229 |
|
|
|
| 1230 |
|
|
c----------------------------------------------------------------------- |
| 1231 |
|
|
c find diffusivities at kbl-1 grid level |
| 1232 |
|
|
c----------------------------------------------------------------------- |
| 1233 |
|
|
|
| 1234 |
|
|
do i = 1, imt |
| 1235 |
|
|
sig = -zgrid(kbl(i)-1) / hbl(i) |
| 1236 |
|
|
sigma(i) = stable(i) * sig |
| 1237 |
|
|
& + (1. - stable(i)) * min(sig,epsilon) |
| 1238 |
|
|
end do |
| 1239 |
|
|
|
| 1240 |
|
|
call wscale ( |
| 1241 |
|
|
I sigma, hbl, ustar, bfsfc, |
| 1242 |
|
|
O wm, ws ) |
| 1243 |
|
|
|
| 1244 |
|
|
do i = 1, imt |
| 1245 |
|
|
sig = -zgrid(kbl(i)-1) / hbl(i) |
| 1246 |
|
|
a1 = sig - 2. |
| 1247 |
|
|
a2 = 3. - 2. * sig |
| 1248 |
|
|
a3 = sig - 1. |
| 1249 |
heimbach |
1.2 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
| 1250 |
|
|
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
| 1251 |
|
|
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
| 1252 |
|
|
dkm1(i,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
| 1253 |
adcroft |
1.1 |
dkm1(i,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
| 1254 |
|
|
dkm1(i,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
| 1255 |
|
|
end do |
| 1256 |
|
|
|
| 1257 |
|
|
#endif /* ALLOW_KPP */ |
| 1258 |
|
|
|
| 1259 |
|
|
return |
| 1260 |
|
|
end |
| 1261 |
|
|
|
| 1262 |
|
|
c************************************************************************* |
| 1263 |
|
|
|
| 1264 |
|
|
subroutine enhance ( |
| 1265 |
|
|
I dkm1, hbl, kbl, diffus, casea |
| 1266 |
|
|
U , ghat |
| 1267 |
|
|
O , blmc |
| 1268 |
|
|
& ) |
| 1269 |
|
|
|
| 1270 |
|
|
c enhance the diffusivity at the kbl-.5 interface |
| 1271 |
|
|
|
| 1272 |
|
|
IMPLICIT NONE |
| 1273 |
|
|
|
| 1274 |
|
|
#include "SIZE.h" |
| 1275 |
|
|
#include "KPP_PARAMS.h" |
| 1276 |
|
|
|
| 1277 |
|
|
c input |
| 1278 |
|
|
c dkm1(imt,mdiff) bl diffusivity at kbl-1 grid level |
| 1279 |
|
|
c hbl(imt) boundary layer depth (m) |
| 1280 |
|
|
c kbl(imt) grid above hbl |
| 1281 |
|
|
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
| 1282 |
|
|
c casea(imt) = 1 in caseA, = 0 in case B |
| 1283 |
|
|
_RS dkm1 (imt,mdiff) |
| 1284 |
|
|
_RS hbl (imt) |
| 1285 |
|
|
integer kbl (imt) |
| 1286 |
|
|
_RS diffus(imt,0:Nrp1,mdiff) |
| 1287 |
|
|
_RS casea (imt) |
| 1288 |
|
|
|
| 1289 |
|
|
c input/output |
| 1290 |
|
|
c nonlocal transport, modified ghat at kbl(i)-1 interface (s/m**2) |
| 1291 |
|
|
_RS ghat (imt,Nr) |
| 1292 |
|
|
|
| 1293 |
|
|
c output |
| 1294 |
|
|
c enhanced bound. layer mixing coeff. |
| 1295 |
|
|
_RS blmc (imt,Nr,mdiff) |
| 1296 |
|
|
|
| 1297 |
|
|
#ifdef ALLOW_KPP |
| 1298 |
|
|
|
| 1299 |
|
|
c local |
| 1300 |
|
|
c fraction hbl lies beteen zgrid neighbors |
| 1301 |
|
|
_RS delta |
| 1302 |
|
|
integer ki, i, md |
| 1303 |
|
|
_RS dkmp5, dstar |
| 1304 |
|
|
|
| 1305 |
|
|
do i = 1, imt |
| 1306 |
|
|
ki = kbl(i)-1 |
| 1307 |
|
|
if ((ki .ge. 1) .and. (ki .lt. Nr)) then |
| 1308 |
|
|
delta = (hbl(i) + zgrid(ki)) / (zgrid(ki) - zgrid(ki+1)) |
| 1309 |
|
|
do md = 1, mdiff |
| 1310 |
|
|
dkmp5 = casea(i) * diffus(i,ki,md) + |
| 1311 |
|
|
1 (1.- casea(i)) * blmc (i,ki,md) |
| 1312 |
|
|
dstar = (1.- delta)**2 * dkm1(i,md) |
| 1313 |
|
|
& + delta**2 * dkmp5 |
| 1314 |
|
|
blmc(i,ki,md) = (1.- delta)*diffus(i,ki,md) |
| 1315 |
|
|
& + delta*dstar |
| 1316 |
|
|
end do |
| 1317 |
|
|
ghat(i,ki) = (1.- casea(i)) * ghat(i,ki) |
| 1318 |
|
|
endif |
| 1319 |
|
|
end do |
| 1320 |
|
|
|
| 1321 |
|
|
#endif /* ALLOW_KPP */ |
| 1322 |
|
|
|
| 1323 |
|
|
return |
| 1324 |
|
|
end |
| 1325 |
|
|
|
| 1326 |
|
|
c************************************************************************* |
| 1327 |
|
|
|
| 1328 |
|
|
SUBROUTINE STATEKPP ( |
| 1329 |
|
|
I bi, bj, myThid, |
| 1330 |
|
|
O RHO1, DBLOC, DBSFC, TTALPHA, SSBETA) |
| 1331 |
|
|
c |
| 1332 |
|
|
c----------------------------------------------------------------------- |
| 1333 |
|
|
c "statekpp" computes all necessary input arrays |
| 1334 |
|
|
c for the kpp mixing scheme |
| 1335 |
|
|
c |
| 1336 |
|
|
c input: |
| 1337 |
|
|
c bi, bj = array indices on which to apply calculations |
| 1338 |
|
|
c |
| 1339 |
|
|
c output: |
| 1340 |
|
|
c rho1 = potential density of surface layer (kg/m^3) |
| 1341 |
|
|
c dbloc = local buoyancy gradient at Nr interfaces |
| 1342 |
|
|
c g/rho{k+1,k+1} * [ drho{k,k+1}-drho{k+1,k+1} ] (m/s^2) |
| 1343 |
|
|
c dbsfc = buoyancy difference with respect to the surface |
| 1344 |
|
|
c g * [ drho{1,k}/rho{1,k} - drho{k,k}/rho{k,k} ] (m/s^2) |
| 1345 |
|
|
c ttalpha= thermal expansion coefficient without 1/rho factor |
| 1346 |
|
|
c d(rho) / d(potential temperature) (kg/m^3/C) |
| 1347 |
|
|
c ssbeta = salt expansion coefficient without 1/rho factor |
| 1348 |
|
|
c d(rho) / d(salinity) (kg/m^3/PSU) |
| 1349 |
|
|
c |
| 1350 |
|
|
c see also subroutines find_rho.F find_alpha.F find_beta.F |
| 1351 |
|
|
c |
| 1352 |
|
|
c written by: jan morzel, feb. 10, 1995 (converted from "sigma" version) |
| 1353 |
|
|
c modified by: d. menemenlis, june 1998 : for use with MIT GCM UV |
| 1354 |
|
|
c |
| 1355 |
|
|
c----------------------------------------------------------------------- |
| 1356 |
|
|
|
| 1357 |
|
|
IMPLICIT NONE |
| 1358 |
|
|
|
| 1359 |
|
|
#include "SIZE.h" |
| 1360 |
|
|
#include "EEPARAMS.h" |
| 1361 |
|
|
#include "PARAMS.h" |
| 1362 |
|
|
#include "KPP_PARAMS.h" |
| 1363 |
|
|
|
| 1364 |
|
|
c-------------- Routine arguments ----------------------------------------- |
| 1365 |
|
|
INTEGER bi, bj, myThid |
| 1366 |
|
|
#ifdef FRUGAL_KPP |
| 1367 |
|
|
_RS RHO1 (sNx,sNy) |
| 1368 |
|
|
_RS DBLOC (sNx,sNy,Nr) |
| 1369 |
|
|
_RS DBSFC (sNx,sNy,Nr) |
| 1370 |
|
|
_RS TTALPHA(sNx,sNy,Nrp1) |
| 1371 |
|
|
_RS SSBETA (sNx,sNy,Nrp1) |
| 1372 |
|
|
#else |
| 1373 |
|
|
_RS RHO1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1374 |
|
|
_RS DBLOC (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 1375 |
|
|
_RS DBSFC (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
| 1376 |
|
|
_RS TTALPHA(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nrp1) |
| 1377 |
|
|
_RS SSBETA (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nrp1) |
| 1378 |
|
|
#endif |
| 1379 |
|
|
|
| 1380 |
|
|
#ifdef ALLOW_KPP |
| 1381 |
|
|
|
| 1382 |
|
|
c-------------------------------------------------------------------------- |
| 1383 |
|
|
c |
| 1384 |
|
|
c local arrays: |
| 1385 |
|
|
c |
| 1386 |
|
|
c rhok - density of t(k ) & s(k ) at depth k |
| 1387 |
|
|
c rhokm1 - density of t(k-1) & s(k-1) at depth k |
| 1388 |
|
|
c rho1k - density of t(1 ) & s(1 ) at depth k |
| 1389 |
|
|
c work1, work2 - work arrays for holding horizontal slabs |
| 1390 |
|
|
|
| 1391 |
|
|
_RL RHOK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1392 |
|
|
_RL RHOKM1(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1393 |
|
|
_RL RHO1K (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1394 |
|
|
_RL WORK1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1395 |
|
|
_RL WORK2 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1396 |
|
|
_RL WORK3 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1397 |
|
|
INTEGER I, J, K |
| 1398 |
|
|
|
| 1399 |
|
|
c calculate density, alpha, beta in surface layer, and set dbsfc to zero |
| 1400 |
|
|
|
| 1401 |
|
|
call FIND_RHO( |
| 1402 |
|
|
#ifdef FRUGAL_KPP |
| 1403 |
|
|
I bi, bj, 1, sNx, 1, sNy, 1, 1, eosType, |
| 1404 |
|
|
#else |
| 1405 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, 1, 1, eosType, |
| 1406 |
|
|
#endif |
| 1407 |
|
|
O WORK1, |
| 1408 |
|
|
I myThid ) |
| 1409 |
|
|
|
| 1410 |
|
|
call FIND_ALPHA( |
| 1411 |
|
|
#ifdef FRUGAL_KPP |
| 1412 |
|
|
I bi, bj, 1, sNx, 1, sNy, 1, 1, eosType, |
| 1413 |
|
|
#else |
| 1414 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, 1, 1, eosType, |
| 1415 |
|
|
#endif |
| 1416 |
|
|
O WORK2 ) |
| 1417 |
|
|
|
| 1418 |
|
|
call FIND_BETA( |
| 1419 |
|
|
#ifdef FRUGAL_KPP |
| 1420 |
|
|
I bi, bj, 1, sNx, 1, sNy, 1, 1, eosType, |
| 1421 |
|
|
#else |
| 1422 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, 1, 1, eosType, |
| 1423 |
|
|
#endif |
| 1424 |
|
|
O WORK3 ) |
| 1425 |
|
|
|
| 1426 |
|
|
#ifdef FRUGAL_KPP |
| 1427 |
|
|
DO J = 1, sNy |
| 1428 |
|
|
DO I = 1, sNx |
| 1429 |
|
|
#else |
| 1430 |
|
|
DO J = 1-OLy, sNy+OLy |
| 1431 |
|
|
DO I = 1-OLx, sNx+OLx |
| 1432 |
|
|
#endif |
| 1433 |
|
|
RHO1(I,J) = WORK1(I,J) + rhonil |
| 1434 |
|
|
TTALPHA(I,J,1) = WORK2(I,J) |
| 1435 |
|
|
SSBETA(I,J,1) = WORK3(I,J) |
| 1436 |
|
|
DBSFC(I,J,1) = 0. |
| 1437 |
|
|
END DO |
| 1438 |
|
|
END DO |
| 1439 |
|
|
|
| 1440 |
|
|
c calculate alpha, beta, and gradients in interior layers |
| 1441 |
|
|
|
| 1442 |
heimbach |
1.2 |
CHPF$ INDEPENDENT, NEW (RHOK,RHOKM1,RHO1K,WORK1,WORK2) |
| 1443 |
adcroft |
1.1 |
DO K = 2, Nr |
| 1444 |
|
|
|
| 1445 |
|
|
call FIND_RHO( |
| 1446 |
|
|
#ifdef FRUGAL_KPP |
| 1447 |
|
|
I bi, bj, 1, sNx, 1, sNy, K, K, eosType, |
| 1448 |
|
|
#else |
| 1449 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, K, K, eosType, |
| 1450 |
|
|
#endif |
| 1451 |
|
|
O RHOK, |
| 1452 |
|
|
I myThid ) |
| 1453 |
|
|
|
| 1454 |
|
|
call FIND_RHO( |
| 1455 |
|
|
#ifdef FRUGAL_KPP |
| 1456 |
|
|
I bi, bj, 1, sNx, 1, sNy, K-1, K, eosType, |
| 1457 |
|
|
#else |
| 1458 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, K-1, K, eosType, |
| 1459 |
|
|
#endif |
| 1460 |
|
|
O RHOKM1, |
| 1461 |
|
|
I myThid ) |
| 1462 |
|
|
|
| 1463 |
|
|
call FIND_RHO( |
| 1464 |
|
|
#ifdef FRUGAL_KPP |
| 1465 |
|
|
I bi, bj, 1, sNx, 1, sNy, 1, K, eosType, |
| 1466 |
|
|
#else |
| 1467 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, 1, K, eosType, |
| 1468 |
|
|
#endif |
| 1469 |
|
|
O RHO1K, |
| 1470 |
|
|
I myThid ) |
| 1471 |
|
|
|
| 1472 |
|
|
call FIND_ALPHA( |
| 1473 |
|
|
#ifdef FRUGAL_KPP |
| 1474 |
|
|
I bi, bj, 1, sNx, 1, sNy, K, K, eosType, |
| 1475 |
|
|
#else |
| 1476 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, K, K, eosType, |
| 1477 |
|
|
#endif |
| 1478 |
|
|
O WORK1 ) |
| 1479 |
|
|
|
| 1480 |
|
|
call FIND_BETA( |
| 1481 |
|
|
#ifdef FRUGAL_KPP |
| 1482 |
|
|
I bi, bj, 1, sNx, 1, sNy, K, K, eosType, |
| 1483 |
|
|
#else |
| 1484 |
|
|
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, K, K, eosType, |
| 1485 |
|
|
#endif |
| 1486 |
|
|
O WORK2 ) |
| 1487 |
|
|
|
| 1488 |
|
|
#ifdef FRUGAL_KPP |
| 1489 |
|
|
DO J = 1, sNy |
| 1490 |
|
|
DO I = 1, sNx |
| 1491 |
|
|
#else |
| 1492 |
|
|
DO J = 1-OLy, sNy+OLy |
| 1493 |
|
|
DO I = 1-OLx, sNx+OLx |
| 1494 |
|
|
#endif |
| 1495 |
|
|
TTALPHA(I,J,K) = WORK1 (I,J) |
| 1496 |
|
|
SSBETA(I,J,K) = WORK2 (I,J) |
| 1497 |
|
|
DBLOC(I,J,K-1) = gravity * (RHOK(I,J) - RHOKM1(I,J)) / |
| 1498 |
|
|
& (RHOK(I,J) + rhonil) |
| 1499 |
|
|
DBSFC(I,J,K) = gravity * (RHOK(I,J) - RHO1K (I,J)) / |
| 1500 |
|
|
& (RHOK(I,J) + rhonil) |
| 1501 |
|
|
END DO |
| 1502 |
|
|
END DO |
| 1503 |
|
|
|
| 1504 |
|
|
END DO |
| 1505 |
|
|
|
| 1506 |
|
|
c compute arrays for K = Nrp1 |
| 1507 |
|
|
#ifdef FRUGAL_KPP |
| 1508 |
|
|
DO J = 1, sNy |
| 1509 |
|
|
DO I = 1, sNx |
| 1510 |
|
|
#else |
| 1511 |
|
|
DO J = 1-OLy, sNy+OLy |
| 1512 |
|
|
DO I = 1-OLx, sNx+OLx |
| 1513 |
|
|
#endif |
| 1514 |
|
|
TTALPHA(I,J,Nrp1) = TTALPHA(I,J,Nr) |
| 1515 |
|
|
SSBETA(I,J,Nrp1) = SSBETA(I,J,Nr) |
| 1516 |
|
|
DBLOC(I,J,Nr) = 0. |
| 1517 |
|
|
END DO |
| 1518 |
|
|
END DO |
| 1519 |
|
|
|
| 1520 |
|
|
#endif /* ALLOW_KPP */ |
| 1521 |
|
|
|
| 1522 |
|
|
RETURN |
| 1523 |
|
|
END |
Parent Directory
| 
Revision Log
| 
Revision Graph