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C $Header: /escher1/cvs/master/mitgcmuv/pkg/kpp/kpp_routines.F,v 1.6 2000/09/11 22:32:53 dimitri Exp $ |
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|
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#include "KPP_OPTIONS.h" |
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|
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C-- File kpp_routines.F: subroutines needed to implement |
| 6 |
C-- KPP vertical mixing scheme |
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C-- Contents |
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C-- o KPPMIX - Main driver and interface routine. |
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C-- o BLDEPTH - Determine oceanic planetary boundary layer depth. |
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C-- o WSCALE - Compute turbulent velocity scales. |
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C-- o RI_IWMIX - Compute interior viscosity diffusivity coefficients. |
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C-- o Z121 - Apply 121 vertical smoothing. |
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C-- o SMOOTH_HORIZ_RS - Apply horizontal smoothing to RS array. |
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C-- o SMOOTH_HORIZ_RL - Apply horizontal smoothing to RL array. |
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C-- o BLMIX - Boundary layer mixing coefficients. |
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C-- o ENHANCE - Enhance diffusivity at boundary layer interface. |
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C-- o STATEKPP - Compute buoyancy-related input arrays. |
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|
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c************************************************************************* |
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|
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SUBROUTINE KPPMIX ( |
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I lri, kmtj, shsq, dvsq, ustar, bo, bosol |
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I , dbloc, Ritop, coriol |
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I , ikey |
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O , diffus |
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U , ghat |
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O , hbl ) |
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|
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c------------------------------------------------------------------------- |
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c |
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c Main driver subroutine for kpp vertical mixing scheme and |
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c interface to greater ocean model |
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c |
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c written by: bill large, june 6, 1994 |
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c modified by: jan morzel, june 30, 1994 |
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c bill large, august 11, 1994 |
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c bill large, january 25, 1995 : "dVsq" and 1d code |
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c detlef stammer, august 1997 : for use with MIT GCM Classic |
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c d. menemenlis, june 1998 : for use with MIT GCM UV |
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c |
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c----------------------------------------------------------------------- |
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|
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IMPLICIT NONE |
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|
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "DYNVARS.h" |
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#include "FFIELDS.h" |
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#include "KPP_PARAMS.h" |
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|
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c input |
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c lri - mixing process switches |
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c kmtj (imt) - number of vertical layers on this row |
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c shsq (imt,Nr) - (local velocity shear)^2 ((m/s)^2) |
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c dvsq (imt,Nr) - (velocity shear re sfc)^2 ((m/s)^2) |
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c ustar (imt) - surface friction velocity (m/s) |
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c bo (imt) - surface turbulent buoy. forcing (m^2/s^3) |
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c bosol (imt) - radiative buoyancy forcing (m^2/s^3) |
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c dbloc (imt,Nr) - local delta buoyancy across interfaces (m/s^2) |
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c dblocSm(imt,Nr) - horizontally smoothed dbloc (m/s^2) |
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c stored in ghat to save space |
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c Ritop (imt,Nr) - numerator of bulk Richardson Number |
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c (zref-z) * delta buoyancy w.r.t. surface ((m/s)^2) |
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c coriol (imt) - Coriolis parameter (1/s) |
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c note: there is a conversion from 2-D to 1-D for input output variables, |
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c e.g., hbl(sNx,sNy) -> hbl(imt), |
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c where hbl(i,j) -> hbl((j-1)*sNx+i) |
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|
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logical lri |
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integer kmtj (imt ) |
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_RS shsq (imt,Nr) |
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_RS dvsq (imt,Nr) |
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_RS ustar (imt ) |
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_RS bo (imt ) |
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_RS bosol (imt ) |
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_RS dbloc (imt,Nr) |
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_RS Ritop (imt,Nr) |
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_RS coriol (imt ) |
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|
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integer ikey |
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|
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c output |
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c diffus (imt,1) - vertical viscosity coefficient (m^2/s) |
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c diffus (imt,2) - vertical scalar diffusivity (m^2/s) |
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c diffus (imt,3) - vertical temperature diffusivity (m^2/s) |
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c ghat (imt) - nonlocal transport coefficient (s/m^2) |
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c hbl (imt) - mixing layer depth (m) |
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|
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_RS diffus(imt,0:Nrp1,mdiff) |
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_RS ghat (imt,Nr) |
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_RS hbl (imt) |
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|
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#ifdef ALLOW_KPP |
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|
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c local |
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c kbl (imt ) - index of first grid level below hbl |
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c bfsfc (imt ) - surface buoyancy forcing (m^2/s^3) |
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c casea (imt ) - 1 in case A; 0 in case B |
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c stable (imt ) - 1 in stable forcing; 0 if unstable |
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c dkm1 (imt, mdiff) - boundary layer diffusivity at kbl-1 level |
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c blmc (imt,Nr,mdiff) - boundary layer mixing coefficients |
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c sigma (imt ) - normalized depth (d / hbl) |
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c Rib (imt,Nr ) - bulk Richardson number |
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|
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integer kbl (imt ) |
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_RS bfsfc (imt ) |
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_RS casea (imt ) |
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_RS stable (imt ) |
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_RS dkm1 (imt, mdiff) |
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_RS blmc (imt,Nr,mdiff) |
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_RS sigma (imt ) |
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_RS Rib (imt,Nr ) |
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|
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integer i, k, md |
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|
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c----------------------------------------------------------------------- |
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c compute interior mixing coefficients everywhere, due to constant |
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c internal wave activity, static instability, and local shear |
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c instability. |
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c (ghat is temporary storage for horizontally smoothed dbloc) |
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c----------------------------------------------------------------------- |
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|
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call Ri_iwmix ( |
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I kmtj, shsq, dbloc, ghat |
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I , ikey |
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O , diffus ) |
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|
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c----------------------------------------------------------------------- |
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c set seafloor values to zero and fill extra "Nrp1" coefficients |
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c for blmix |
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c----------------------------------------------------------------------- |
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|
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do md = 1, mdiff |
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do i = 1,imt |
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do k=kmtj(i),Nrp1 |
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diffus(i,k,md) = 0.0 |
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end do |
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end do |
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end do |
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|
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c----------------------------------------------------------------------- |
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c compute boundary layer mixing coefficients: |
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c |
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c diagnose the new boundary layer depth |
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c----------------------------------------------------------------------- |
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|
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call bldepth ( |
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I kmtj |
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I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
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I , ikey |
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O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
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& ) |
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|
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CADJ STORE hbl,bfsfc,stable,casea,kbl = comlev1_kpp, key = ikey |
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|
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c----------------------------------------------------------------------- |
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c compute boundary layer diffusivities |
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c----------------------------------------------------------------------- |
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|
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call blmix ( |
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I ustar, bfsfc, hbl, stable, casea, diffus, kbl |
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O , dkm1, blmc, ghat, sigma |
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& ) |
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|
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CADJ STORE dkm1,blmc,ghat = comlev1_kpp, key = ikey |
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|
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c----------------------------------------------------------------------- |
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c enhance diffusivity at interface kbl - 1 |
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c----------------------------------------------------------------------- |
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|
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call enhance ( |
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I dkm1, hbl, kbl, diffus, casea |
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U , ghat |
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O , blmc ) |
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|
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c----------------------------------------------------------------------- |
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c combine interior and boundary layer coefficients and nonlocal term |
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c----------------------------------------------------------------------- |
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|
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do k = 1, Nr |
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do i = 1, imt |
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if (k .lt. kbl(i)) then |
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do md = 1, mdiff |
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diffus(i,k,md) = blmc(i,k,md) |
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end do |
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else |
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ghat(i,k) = 0. |
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endif |
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end do |
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end do |
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|
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#endif /* ALLOW_KPP */ |
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|
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return |
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end |
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|
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c************************************************************************* |
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|
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subroutine bldepth ( |
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I kmtj |
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I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
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I , ikey |
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O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
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& ) |
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|
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c the oceanic planetary boundary layer depth, hbl, is determined as |
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c the shallowest depth where the bulk Richardson number is |
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c equal to the critical value, Ricr. |
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c |
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c bulk Richardson numbers are evaluated by computing velocity and |
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c buoyancy differences between values at zgrid(kl) < 0 and surface |
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c reference values. |
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c in this configuration, the reference values are equal to the |
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c values in the surface layer. |
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c when using a very fine vertical grid, these values should be |
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c computed as the vertical average of velocity and buoyancy from |
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c the surface down to epsilon*zgrid(kl). |
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c |
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c when the bulk Richardson number at k exceeds Ricr, hbl is |
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c linearly interpolated between grid levels zgrid(k) and zgrid(k-1). |
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c |
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c The water column and the surface forcing are diagnosed for |
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c stable/ustable forcing conditions, and where hbl is relative |
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c to grid points (caseA), so that conditional branches can be |
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c avoided in later subroutines. |
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c |
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IMPLICIT NONE |
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|
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "KPP_PARAMS.h" |
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#include "FFIELDS.h" |
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|
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c input |
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c------ |
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c kmtj : number of vertical layers |
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c dvsq : (velocity shear re sfc)^2 ((m/s)^2) |
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c dbloc : local delta buoyancy across interfaces (m/s^2) |
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c Ritop : numerator of bulk Richardson Number |
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c =(z-zref)*dbsfc, where dbsfc=delta |
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c buoyancy with respect to surface ((m/s)^2) |
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c ustar : surface friction velocity (m/s) |
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c bo : surface turbulent buoyancy forcing (m^2/s^3) |
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c bosol : radiative buoyancy forcing (m^2/s^3) |
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c coriol : Coriolis parameter (1/s) |
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integer kmtj(imt) |
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_RS dvsq (imt,Nr) |
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_RS dbloc (imt,Nr) |
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_RS Ritop (imt,Nr) |
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_RS ustar (imt) |
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_RS bo (imt) |
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_RS bosol (imt) |
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_RS coriol (imt) |
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integer ikey |
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|
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c output |
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c-------- |
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c hbl : boundary layer depth (m) |
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c bfsfc : Bo+radiation absorbed to d=hbf*hbl (m^2/s^3) |
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c stable : =1 in stable forcing; =0 unstable |
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c casea : =1 in case A, =0 in case B |
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c kbl : -1 of first grid level below hbl |
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c Rib : Bulk Richardson number |
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c sigma : normalized depth (d/hbl) |
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_RS hbl (imt) |
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_RS bfsfc (imt) |
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_RS stable (imt) |
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_RS casea (imt) |
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integer kbl (imt) |
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_RS Rib (imt,Nr) |
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_RS sigma (imt) |
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|
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#ifdef ALLOW_KPP |
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|
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c local |
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c------- |
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c wm, ws : turbulent velocity scales (m/s) |
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c zwork : depth work array |
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_RS wm(imt), ws(imt) |
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_RS zwork(imt) |
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|
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_RS bvsq, vtsq, hekman, hmonob, hlimit |
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integer i, kl |
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|
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_RS p5 , eins , m1 |
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parameter (p5=0.5, eins=1.0, m1=-1.0 ) |
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|
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crg intermediate result in RL to avoid overflow in adjoint |
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_RL dpshear2 |
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#ifdef KPP_TEST_DENOM |
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_RL dhelp |
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#endif |
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|
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c find bulk Richardson number at every grid level until > Ricr |
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c |
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c note: the reference depth is -epsilon/2.*zgrid(k), but the reference |
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c u,v,t,s values are simply the surface layer values, |
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c and not the averaged values from 0 to 2*ref.depth, |
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c which is necessary for very fine grids(top layer < 2m thickness) |
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c note: max values when Ricr never satisfied are |
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c kbl(i)=kmtj(i) and hbl(i)=-zgrid(kmtj(i)) |
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|
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c initialize hbl and kbl to bottomed out values |
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|
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do i = 1, imt |
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Rib(i,1) = 0.0 |
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kbl(i) = max(kmtj(i),1) |
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hbl(i) = -zgrid(kbl(i)) |
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end do |
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|
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do kl = 2, Nr |
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|
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c compute bfsfc = sw fraction at hbf * zgrid |
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|
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do i = 1, imt |
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zwork(i) = zgrid(kl) |
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end do |
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call SWFRAC( |
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I imt, hbf, zwork, |
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O bfsfc) |
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|
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do i = 1, imt |
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|
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c use caseA as temporary array |
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|
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casea(i) = -zgrid(kl) |
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|
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c compute bfsfc= Bo + radiative contribution down to hbf * hbl |
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|
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bfsfc(i) = bo(i) + bosol(i)*(1. - bfsfc(i)) |
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stable(i) = p5 + sign(p5,bfsfc(i)) |
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sigma(i) = stable(i) + (1. - stable(i)) * epsilon |
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|
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end do |
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|
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c----------------------------------------------------------------------- |
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c compute velocity scales at sigma, for hbl= caseA = -zgrid(kl) |
| 340 |
c----------------------------------------------------------------------- |
| 341 |
|
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call wscale ( |
| 343 |
I sigma, casea, ustar, bfsfc, |
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O wm, ws ) |
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|
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do i = 1, imt |
| 347 |
|
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c----------------------------------------------------------------------- |
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c compute the turbulent shear contribution to Rib |
| 350 |
c----------------------------------------------------------------------- |
| 351 |
|
| 352 |
bvsq = p5 * |
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1 ( dbloc(i,kl-1) / (zgrid(kl-1)-zgrid(kl ))+ |
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2 dbloc(i,kl ) / (zgrid(kl )-zgrid(kl+1))) |
| 355 |
|
| 356 |
if (bvsq .eq. 0.) then |
| 357 |
vtsq = 0.0 |
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else |
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vtsq = -zgrid(kl) * ws(i) * sqrt(abs(bvsq)) * Vtc |
| 360 |
endif |
| 361 |
|
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c compute bulk Richardson number at new level |
| 363 |
c note: Ritop needs to be zero on land and ocean bottom |
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c points so that the following if statement gets triggered |
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c correctly; otherwise, hbl might get set to (big) negative |
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c values, that might exceed the limit for the "exp" function |
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c in "SWFRAC" |
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|
| 369 |
c |
| 370 |
c rg: assignment to double precision variable to avoid overflow |
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c ph: test for zero nominator |
| 372 |
c |
| 373 |
#ifdef KPP_TEST_DENOM |
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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 |
CADJ store kbl = comlev1_kpp |
| 393 |
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 |
CADJ store hbl = comlev1_kpp |
| 413 |
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 |
I imt, m1, hbl, |
| 421 |
O bfsfc) |
| 422 |
|
| 423 |
CADJ store bfsfc = comlev1_kpp |
| 424 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 425 |
|
| 426 |
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 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
| 433 |
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 |
CADJ store hbl = comlev1_kpp |
| 466 |
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 |
I imt, m1, hbl, |
| 486 |
O bfsfc) |
| 487 |
|
| 488 |
CADJ store bfsfc = comlev1_kpp |
| 489 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 490 |
|
| 491 |
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 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
| 497 |
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 |
|
| 696 |
CADJ store diffus(:,:,1) = comlev1_kpp_sm |
| 697 |
CADJ & , key = ikey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy),Nr+2 /) |
| 698 |
|
| 699 |
call z121 ( |
| 700 |
U diffus(1,0,1)) |
| 701 |
end do |
| 702 |
|
| 703 |
CADJ store diffus = comlev1_kpp |
| 704 |
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 |
diffus(i,ki,3) = diffKrT + fcon * difscon + fRi * difs0 |
| 733 |
|
| 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 |
c Note that it is important to exclude from the smoothing any points |
| 761 |
c that are outside the range of the K(Ri) scheme, ie. >0.8, or <0.0. |
| 762 |
c Otherwise, there is interference with other physics, especially |
| 763 |
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 |
_RS KRi_range(1:Nrp1) |
| 779 |
integer i, k, km1, kp1 |
| 780 |
|
| 781 |
_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 |
|
| 786 |
#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 |
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 |
CADJ INIT z121tape = common, Nr |
| 810 |
do k = 2, Nr |
| 811 |
CADJ STORE v(i,k), zwork = z121tape |
| 812 |
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 |
c gat1*(imt) shape function at sigma = 1 |
| 1086 |
c dat1*(imt) derivative of shape function at sigma = 1 |
| 1087 |
c ws(imt), wm(imt) turbulent velocity scales (m/s) |
| 1088 |
_RS gat1m(imt), gat1s(imt), gat1t(imt) |
| 1089 |
_RS dat1m(imt), dat1s(imt), dat1t(imt) |
| 1090 |
_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 |
_RS Gm, Gs, Gt |
| 1096 |
_RL dum |
| 1097 |
|
| 1098 |
_RS p0 , eins |
| 1099 |
parameter (p0=0.0, eins=1.0) |
| 1100 |
|
| 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 |
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 |
#else |
| 1151 |
f1 = stable(i) * conc1 * bfsfc(i) / (ustar(i)**4+epsln) |
| 1152 |
gat1m(i) = visch / hbl(i) / (wm(i)+epsln) |
| 1153 |
dat1m(i) = -viscp / (wm(i)+epsln) + f1 * visch |
| 1154 |
#endif |
| 1155 |
dat1m(i) = min(dat1m(i),p0) |
| 1156 |
|
| 1157 |
#ifdef KPP_TEST_DENOM |
| 1158 |
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 |
#else |
| 1162 |
gat1s(i) = difsh / hbl(i) / (ws(i)+epsln) |
| 1163 |
dat1s(i) = -difsp / (ws(i)+epsln) + f1 * difsh |
| 1164 |
#endif |
| 1165 |
dat1s(i) = min(dat1s(i),p0) |
| 1166 |
|
| 1167 |
#ifdef KPP_TEST_DENOM |
| 1168 |
gat1t(i) = difth / hbl(i) / ws(i) |
| 1169 |
dat1t(i) = -diftp / ws(i) + f1 * difth |
| 1170 |
#else |
| 1171 |
gat1t(i) = difth / hbl(i) / (ws(i)+epsln) |
| 1172 |
dat1t(i) = -diftp / (ws(i)+epsln) + f1 * difth |
| 1173 |
#endif |
| 1174 |
dat1t(i) = min(dat1t(i),p0) |
| 1175 |
|
| 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 |
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 |
|
| 1206 |
c----------------------------------------------------------------------- |
| 1207 |
c compute boundary layer diffusivities at the interfaces |
| 1208 |
c----------------------------------------------------------------------- |
| 1209 |
|
| 1210 |
blmc(i,ki,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
| 1211 |
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 |
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 |
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 |
CHPF$ INDEPENDENT, NEW (RHOK,RHOKM1,RHO1K,WORK1,WORK2) |
| 1443 |
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 |
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