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C $Header: /u/u3/gcmpack/MITgcm/pkg/kpp/kpp_routines.F,v 1.16 2003/03/21 23:18:28 heimbach Exp $ |
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C $Name: $ |
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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 |
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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 KPP_SMOOTH_HORIZ - Apply horizontal smoothing to KPP array. |
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C-- o SMOOTH_HORIZ - Apply horizontal smoothing to global 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 mytime, mythid |
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I , kmtj, shsq, dvsq, ustar |
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I , bo, bosol, dbloc, Ritop, coriol |
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I , ikppkey |
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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 myTime - current time in simulation |
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c myThid - thread number for this instance of the routine |
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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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_RL mytime |
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integer mythid |
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integer kmtj (imt ) |
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_KPP_RL shsq (imt,Nr) |
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_KPP_RL dvsq (imt,Nr) |
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_KPP_RL ustar (imt ) |
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_KPP_RL bo (imt ) |
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_KPP_RL bosol (imt ) |
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_KPP_RL dbloc (imt,Nr) |
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_KPP_RL Ritop (imt,Nr) |
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_KPP_RL coriol(imt ) |
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|
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integer ikppkey |
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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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_KPP_RL diffus(imt,0:Nrp1,mdiff) |
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_KPP_RL ghat (imt,Nr) |
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_KPP_RL 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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_KPP_RL bfsfc (imt ) |
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_KPP_RL casea (imt ) |
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_KPP_RL stable(imt ) |
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_KPP_RL dkm1 (imt, mdiff) |
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_KPP_RL blmc (imt,Nr,mdiff) |
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_KPP_RL sigma (imt ) |
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_KPP_RL 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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cph( |
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cph these storings avoid recomp. of Ri_iwmix |
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CADJ STORE ghat = comlev1_kpp, key = ikppkey |
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CADJ STORE dbloc = comlev1_kpp, key = ikppkey |
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cph) |
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call Ri_iwmix ( |
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I kmtj, shsq, dbloc, ghat |
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I , ikppkey |
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O , diffus ) |
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|
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cph( |
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cph these storings avoid recomp. of Ri_iwmix |
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cph DESPITE TAFs 'not necessary' warning! |
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CADJ STORE dbloc = comlev1_kpp, key = ikppkey |
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CADJ STORE shsq = comlev1_kpp, key = ikppkey |
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CADJ STORE ghat = comlev1_kpp, key = ikppkey |
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CADJ STORE diffus = comlev1_kpp, key = ikppkey |
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cph) |
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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 mytime, mythid |
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I , kmtj |
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I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
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I , ikppkey |
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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 = ikppkey |
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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, ikppkey |
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& ) |
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cph( |
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CADJ STORE dkm1,blmc,ghat = comlev1_kpp, key = ikppkey |
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CADJ STORE hbl, kbl, diffus, casea = comlev1_kpp, key = ikppkey |
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cph) |
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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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cph( |
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cph avoids recomp. of enhance |
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CADJ STORE blmc = comlev1_kpp, key = ikppkey |
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cph) |
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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 !!!NOTE!!! In shallow (2-level) regions and for shallow mixed layers |
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c (< 1 level), diffusivity blmc can become negative. The max-s below |
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c are a hack until this problem is properly diagnosed and fixed. |
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c----------------------------------------------------------------------- |
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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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diffus(i,k,1) = max ( blmc(i,k,1), viscAr ) |
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diffus(i,k,2) = max ( blmc(i,k,2), diffKrS ) |
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diffus(i,k,3) = max ( blmc(i,k,3), diffKrT ) |
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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 mytime, mythid |
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I , kmtj |
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I , dvsq, dbloc, Ritop, ustar, bo, bosol, coriol |
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I , ikppkey |
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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" |
260 |
#include "EEPARAMS.h" |
261 |
#include "PARAMS.h" |
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#include "KPP_PARAMS.h" |
263 |
#include "FFIELDS.h" |
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|
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c input |
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c------ |
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c myTime : current time in simulation |
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c myThid : thread number for this instance of the routine |
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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 |
274 |
c buoyancy with respect to surface ((m/s)^2) |
275 |
c ustar : surface friction velocity (m/s) |
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c bo : surface turbulent buoyancy forcing (m^2/s^3) |
277 |
c bosol : radiative buoyancy forcing (m^2/s^3) |
278 |
c coriol : Coriolis parameter (1/s) |
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_RL mytime |
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integer mythid |
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integer kmtj(imt) |
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_KPP_RL dvsq (imt,Nr) |
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_KPP_RL dbloc (imt,Nr) |
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_KPP_RL Ritop (imt,Nr) |
285 |
_KPP_RL ustar (imt) |
286 |
_KPP_RL bo (imt) |
287 |
_KPP_RL bosol (imt) |
288 |
_KPP_RL coriol(imt) |
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integer ikppkey |
290 |
|
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c output |
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c-------- |
293 |
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) |
300 |
_KPP_RL hbl (imt) |
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_KPP_RL bfsfc (imt) |
302 |
_KPP_RL stable(imt) |
303 |
_KPP_RL casea (imt) |
304 |
integer kbl (imt) |
305 |
_KPP_RL Rib (imt,Nr) |
306 |
_KPP_RL sigma (imt) |
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|
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#ifdef ALLOW_KPP |
309 |
|
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c local |
311 |
c------- |
312 |
c wm, ws : turbulent velocity scales (m/s) |
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_KPP_RL wm(imt), ws(imt) |
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_RL worka(imt) |
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|
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_KPP_RL bvsq, vtsq, hekman, hmonob, hlimit, tempVar1, tempVar2 |
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integer i, kl |
318 |
|
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_KPP_RL p5 , eins |
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parameter ( p5=0.5, eins=1.0 ) |
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_RL minusone |
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parameter ( minusone=-1.0 ) |
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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, |
328 |
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)) |
332 |
|
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c initialize hbl and kbl to bottomed out values |
334 |
|
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do i = 1, imt |
336 |
Rib(i,1) = 0.0 |
337 |
kbl(i) = max(kmtj(i),1) |
338 |
hbl(i) = -zgrid(kbl(i)) |
339 |
end do |
340 |
|
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do kl = 2, Nr |
342 |
|
343 |
c compute bfsfc = sw fraction at hbf * zgrid |
344 |
|
345 |
do i = 1, imt |
346 |
worka(i) = zgrid(kl) |
347 |
end do |
348 |
call SWFRAC( |
349 |
I imt, hbf, |
350 |
I mytime, mythid, |
351 |
U worka ) |
352 |
|
353 |
do i = 1, imt |
354 |
|
355 |
c use caseA as temporary array |
356 |
|
357 |
casea(i) = -zgrid(kl) |
358 |
|
359 |
c compute bfsfc= Bo + radiative contribution down to hbf * hbl |
360 |
|
361 |
bfsfc(i) = bo(i) + bosol(i)*(1. - worka(i)) |
362 |
stable(i) = p5 + sign(p5,bfsfc(i)) |
363 |
sigma(i) = stable(i) + (1. - stable(i)) * epsilon |
364 |
|
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end do |
366 |
|
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c----------------------------------------------------------------------- |
368 |
c compute velocity scales at sigma, for hbl= caseA = -zgrid(kl) |
369 |
c----------------------------------------------------------------------- |
370 |
|
371 |
call wscale ( |
372 |
I sigma, casea, ustar, bfsfc, |
373 |
O wm, ws ) |
374 |
|
375 |
do i = 1, imt |
376 |
|
377 |
c----------------------------------------------------------------------- |
378 |
c compute the turbulent shear contribution to Rib |
379 |
c----------------------------------------------------------------------- |
380 |
|
381 |
bvsq = p5 * |
382 |
1 ( dbloc(i,kl-1) / (zgrid(kl-1)-zgrid(kl ))+ |
383 |
2 dbloc(i,kl ) / (zgrid(kl )-zgrid(kl+1))) |
384 |
|
385 |
if (bvsq .eq. 0.) then |
386 |
vtsq = 0.0 |
387 |
else |
388 |
vtsq = -zgrid(kl) * ws(i) * sqrt(abs(bvsq)) * Vtc |
389 |
endif |
390 |
|
391 |
c compute bulk Richardson number at new level |
392 |
c note: Ritop needs to be zero on land and ocean bottom |
393 |
c points so that the following if statement gets triggered |
394 |
c correctly; otherwise, hbl might get set to (big) negative |
395 |
c values, that might exceed the limit for the "exp" function |
396 |
c in "SWFRAC" |
397 |
|
398 |
c |
399 |
c rg: assignment to double precision variable to avoid overflow |
400 |
c ph: test for zero nominator |
401 |
c |
402 |
|
403 |
tempVar1 = dvsq(i,kl) + vtsq |
404 |
tempVar2 = max(tempVar1, phepsi) |
405 |
Rib(i,kl) = Ritop(i,kl) / tempVar2 |
406 |
|
407 |
end do |
408 |
end do |
409 |
|
410 |
cph( |
411 |
cph without this store, there is a recomputation error for |
412 |
cph rib in adbldepth (probably partial recomputation problem) |
413 |
CADJ store Rib = comlev1_kpp |
414 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy),Nr /) |
415 |
cph) |
416 |
|
417 |
do kl = 2, Nr |
418 |
do i = 1, imt |
419 |
if (kbl(i).eq.kmtj(i) .and. Rib(i,kl).gt.Ricr) kbl(i) = kl |
420 |
end do |
421 |
end do |
422 |
|
423 |
CADJ store kbl = comlev1_kpp |
424 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
425 |
|
426 |
do i = 1, imt |
427 |
kl = kbl(i) |
428 |
c linearly interpolate to find hbl where Rib = Ricr |
429 |
if (kl.gt.1 .and. kl.lt.kmtj(i)) then |
430 |
tempVar1 = (Rib(i,kl)-Rib(i,kl-1)) |
431 |
hbl(i) = -zgrid(kl-1) + (zgrid(kl-1)-zgrid(kl)) * |
432 |
1 (Ricr - Rib(i,kl-1)) / tempVar1 |
433 |
endif |
434 |
end do |
435 |
|
436 |
CADJ store hbl = comlev1_kpp |
437 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
438 |
|
439 |
c----------------------------------------------------------------------- |
440 |
c find stability and buoyancy forcing for boundary layer |
441 |
c----------------------------------------------------------------------- |
442 |
|
443 |
do i = 1, imt |
444 |
worka(i) = hbl(i) |
445 |
end do |
446 |
call SWFRAC( |
447 |
I imt, minusone, |
448 |
I mytime, mythid, |
449 |
U worka ) |
450 |
|
451 |
do i = 1, imt |
452 |
bfsfc(i) = bo(i) + bosol(i) * (1. - worka(i)) |
453 |
end do |
454 |
CADJ store bfsfc = comlev1_kpp |
455 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
456 |
|
457 |
c-- ensure bfsfc is never 0 |
458 |
do i = 1, imt |
459 |
stable(i) = p5 + sign( p5, bfsfc(i) ) |
460 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
461 |
end do |
462 |
|
463 |
cph( |
464 |
cph added stable to store list to avoid extensive recomp. |
465 |
CADJ store bfsfc, stable = comlev1_kpp |
466 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
467 |
cph) |
468 |
|
469 |
c----------------------------------------------------------------------- |
470 |
c check hbl limits for hekman or hmonob |
471 |
c ph: test for zero nominator |
472 |
c----------------------------------------------------------------------- |
473 |
|
474 |
do i = 1, imt |
475 |
if (bfsfc(i) .gt. 0.0) then |
476 |
hekman = cekman * ustar(i) / max(abs(Coriol(i)),phepsi) |
477 |
hmonob = cmonob * ustar(i)*ustar(i)*ustar(i) |
478 |
& / vonk / bfsfc(i) |
479 |
hlimit = stable(i) * min(hekman,hmonob) |
480 |
& + (stable(i)-1.) * zgrid(Nr) |
481 |
hbl(i) = min(hbl(i),hlimit) |
482 |
end if |
483 |
end do |
484 |
CADJ store hbl = comlev1_kpp |
485 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
486 |
|
487 |
do i = 1, imt |
488 |
hbl(i) = max(hbl(i),minKPPhbl) |
489 |
kbl(i) = kmtj(i) |
490 |
end do |
491 |
|
492 |
CADJ store hbl = comlev1_kpp |
493 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
494 |
|
495 |
c----------------------------------------------------------------------- |
496 |
c find new kbl |
497 |
c----------------------------------------------------------------------- |
498 |
|
499 |
do kl = 2, Nr |
500 |
do i = 1, imt |
501 |
if ( kbl(i).eq.kmtj(i) .and. (-zgrid(kl)).gt.hbl(i) ) then |
502 |
kbl(i) = kl |
503 |
endif |
504 |
end do |
505 |
end do |
506 |
|
507 |
c----------------------------------------------------------------------- |
508 |
c find stability and buoyancy forcing for final hbl values |
509 |
c----------------------------------------------------------------------- |
510 |
|
511 |
do i = 1, imt |
512 |
worka(i) = hbl(i) |
513 |
end do |
514 |
call SWFRAC( |
515 |
I imt, minusone, |
516 |
I mytime, mythid, |
517 |
U worka ) |
518 |
|
519 |
do i = 1, imt |
520 |
bfsfc(i) = bo(i) + bosol(i) * (1. - worka(i)) |
521 |
end do |
522 |
CADJ store bfsfc = comlev1_kpp |
523 |
CADJ & , key = ikppkey, shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
524 |
|
525 |
c-- ensures bfsfc is never 0 |
526 |
do i = 1, imt |
527 |
stable(i) = p5 + sign( p5, bfsfc(i) ) |
528 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
529 |
end do |
530 |
|
531 |
c----------------------------------------------------------------------- |
532 |
c determine caseA and caseB |
533 |
c----------------------------------------------------------------------- |
534 |
|
535 |
do i = 1, imt |
536 |
casea(i) = p5 + |
537 |
1 sign(p5, -zgrid(kbl(i)) - p5*hwide(kbl(i)) - hbl(i)) |
538 |
end do |
539 |
|
540 |
#endif /* ALLOW_KPP */ |
541 |
|
542 |
return |
543 |
end |
544 |
|
545 |
c************************************************************************* |
546 |
|
547 |
subroutine wscale ( |
548 |
I sigma, hbl, ustar, bfsfc, |
549 |
O wm, ws ) |
550 |
|
551 |
c compute turbulent velocity scales. |
552 |
c use a 2D-lookup table for wm and ws as functions of ustar and |
553 |
c zetahat (=vonk*sigma*hbl*bfsfc). |
554 |
c |
555 |
c note: the lookup table is only used for unstable conditions |
556 |
c (zehat.le.0), in the stable domain wm (=ws) gets computed |
557 |
c directly. |
558 |
c |
559 |
IMPLICIT NONE |
560 |
|
561 |
#include "SIZE.h" |
562 |
#include "KPP_PARAMS.h" |
563 |
|
564 |
c input |
565 |
c------ |
566 |
c sigma : normalized depth (d/hbl) |
567 |
c hbl : boundary layer depth (m) |
568 |
c ustar : surface friction velocity (m/s) |
569 |
c bfsfc : total surface buoyancy flux (m^2/s^3) |
570 |
_KPP_RL sigma(imt) |
571 |
_KPP_RL hbl (imt) |
572 |
_KPP_RL ustar(imt) |
573 |
_KPP_RL bfsfc(imt) |
574 |
|
575 |
c output |
576 |
c-------- |
577 |
c wm, ws : turbulent velocity scales at sigma |
578 |
_KPP_RL wm(imt), ws(imt) |
579 |
|
580 |
#ifdef ALLOW_KPP |
581 |
|
582 |
c local |
583 |
c------ |
584 |
c zehat : = zeta * ustar**3 |
585 |
_KPP_RL zehat |
586 |
|
587 |
integer iz, izp1, ju, i, jup1 |
588 |
_KPP_RL udiff, zdiff, zfrac, ufrac, fzfrac, wam |
589 |
_KPP_RL wbm, was, wbs, u3, tempVar |
590 |
|
591 |
c----------------------------------------------------------------------- |
592 |
c use lookup table for zehat < zmax only; otherwise use |
593 |
c stable formulae |
594 |
c----------------------------------------------------------------------- |
595 |
|
596 |
do i = 1, imt |
597 |
zehat = vonk*sigma(i)*hbl(i)*bfsfc(i) |
598 |
|
599 |
if (zehat .le. zmax) then |
600 |
|
601 |
zdiff = zehat - zmin |
602 |
iz = int( zdiff / deltaz ) |
603 |
iz = min( iz, nni ) |
604 |
iz = max( iz, 0 ) |
605 |
izp1 = iz + 1 |
606 |
|
607 |
udiff = ustar(i) - umin |
608 |
ju = int( udiff / deltau ) |
609 |
ju = min( ju, nnj ) |
610 |
ju = max( ju, 0 ) |
611 |
jup1 = ju + 1 |
612 |
|
613 |
zfrac = zdiff / deltaz - float(iz) |
614 |
ufrac = udiff / deltau - float(ju) |
615 |
|
616 |
fzfrac= 1. - zfrac |
617 |
wam = fzfrac * wmt(iz,jup1) + zfrac * wmt(izp1,jup1) |
618 |
wbm = fzfrac * wmt(iz,ju ) + zfrac * wmt(izp1,ju ) |
619 |
wm(i) = (1.-ufrac) * wbm + ufrac * wam |
620 |
|
621 |
was = fzfrac * wst(iz,jup1) + zfrac * wst(izp1,jup1) |
622 |
wbs = fzfrac * wst(iz,ju ) + zfrac * wst(izp1,ju ) |
623 |
ws(i) = (1.-ufrac) * wbs + ufrac * was |
624 |
|
625 |
else |
626 |
|
627 |
u3 = ustar(i) * ustar(i) * ustar(i) |
628 |
tempVar = u3 + conc1 * zehat |
629 |
wm(i) = vonk * ustar(i) * u3 / tempVar |
630 |
ws(i) = wm(i) |
631 |
|
632 |
endif |
633 |
|
634 |
end do |
635 |
|
636 |
#endif /* ALLOW_KPP */ |
637 |
|
638 |
return |
639 |
end |
640 |
|
641 |
c************************************************************************* |
642 |
|
643 |
subroutine Ri_iwmix ( |
644 |
I kmtj, shsq, dbloc, dblocSm |
645 |
I , ikppkey |
646 |
O , diffus ) |
647 |
|
648 |
c compute interior viscosity diffusivity coefficients due |
649 |
c to shear instability (dependent on a local Richardson number), |
650 |
c to background internal wave activity, and |
651 |
c to static instability (local Richardson number < 0). |
652 |
|
653 |
IMPLICIT NONE |
654 |
|
655 |
#include "SIZE.h" |
656 |
#include "EEPARAMS.h" |
657 |
#include "PARAMS.h" |
658 |
#include "KPP_PARAMS.h" |
659 |
|
660 |
c input |
661 |
c kmtj (imt) number of vertical layers on this row |
662 |
c shsq (imt,Nr) (local velocity shear)^2 ((m/s)^2) |
663 |
c dbloc (imt,Nr) local delta buoyancy (m/s^2) |
664 |
c dblocSm(imt,Nr) horizontally smoothed dbloc (m/s^2) |
665 |
integer kmtj (imt) |
666 |
_KPP_RL shsq (imt,Nr) |
667 |
_KPP_RL dbloc (imt,Nr) |
668 |
_KPP_RL dblocSm(imt,Nr) |
669 |
integer ikppkey |
670 |
|
671 |
c output |
672 |
c diffus(imt,0:Nrp1,1) vertical viscosivity coefficient (m^2/s) |
673 |
c diffus(imt,0:Nrp1,2) vertical scalar diffusivity (m^2/s) |
674 |
c diffus(imt,0:Nrp1,3) vertical temperature diffusivity (m^2/s) |
675 |
_KPP_RL diffus(imt,0:Nrp1,3) |
676 |
|
677 |
#ifdef ALLOW_KPP |
678 |
|
679 |
c local variables |
680 |
c Rig local Richardson number |
681 |
c fRi, fcon function of Rig |
682 |
_KPP_RL Rig |
683 |
_KPP_RL fRi, fcon |
684 |
_KPP_RL ratio |
685 |
integer i, ki |
686 |
_KPP_RL c1, c0 |
687 |
|
688 |
#ifdef ALLOW_KPP_VERTICALLY_SMOOTH |
689 |
integer mr |
690 |
CADJ INIT kpp_ri_tape_mr = common, 1 |
691 |
#endif |
692 |
|
693 |
c constants |
694 |
c1 = 1.0 |
695 |
c0 = 0.0 |
696 |
|
697 |
c----------------------------------------------------------------------- |
698 |
c compute interior gradient Ri at all interfaces ki=1,Nr, (not surface) |
699 |
c use diffus(*,*,1) as temporary storage of Ri to be smoothed |
700 |
c use diffus(*,*,2) as temporary storage for Brunt-Vaisala squared |
701 |
c set values at bottom and below to nearest value above bottom |
702 |
#ifdef ALLOW_AUTODIFF_TAMC |
703 |
C break data flow dependence on diffus |
704 |
diffus(1,1,1) = 0.0 |
705 |
#endif |
706 |
|
707 |
do ki = 1, Nr |
708 |
do i = 1, imt |
709 |
if (kmtj(i) .LE. 1 ) then |
710 |
diffus(i,ki,1) = 0. |
711 |
diffus(i,ki,2) = 0. |
712 |
elseif (ki .GE. kmtj(i)) then |
713 |
diffus(i,ki,1) = diffus(i,ki-1,1) |
714 |
diffus(i,ki,2) = diffus(i,ki-1,2) |
715 |
else |
716 |
diffus(i,ki,1) = dblocSm(i,ki) * (zgrid(ki)-zgrid(ki+1)) |
717 |
& / max( Shsq(i,ki), phepsi ) |
718 |
diffus(i,ki,2) = dbloc(i,ki) / (zgrid(ki)-zgrid(ki+1)) |
719 |
endif |
720 |
end do |
721 |
end do |
722 |
|
723 |
c----------------------------------------------------------------------- |
724 |
c vertically smooth Ri |
725 |
#ifdef ALLOW_KPP_VERTICALLY_SMOOTH |
726 |
do mr = 1, num_v_smooth_Ri |
727 |
|
728 |
CADJ store diffus(:,:,1) = kpp_ri_tape_mr |
729 |
CADJ & , key=mr, shape=(/ (sNx+2*OLx)*(sNy+2*OLy),Nr+2 /) |
730 |
|
731 |
call z121 ( |
732 |
U diffus(1,0,1)) |
733 |
end do |
734 |
#endif |
735 |
|
736 |
c----------------------------------------------------------------------- |
737 |
c after smoothing loop |
738 |
|
739 |
do ki = 1, Nr |
740 |
do i = 1, imt |
741 |
|
742 |
c evaluate f of Brunt-Vaisala squared for convection, store in fcon |
743 |
|
744 |
Rig = max ( diffus(i,ki,2) , BVSQcon ) |
745 |
ratio = min ( (BVSQcon - Rig) / BVSQcon, c1 ) |
746 |
fcon = c1 - ratio * ratio |
747 |
fcon = fcon * fcon * fcon |
748 |
|
749 |
c evaluate f of smooth Ri for shear instability, store in fRi |
750 |
|
751 |
Rig = max ( diffus(i,ki,1), c0 ) |
752 |
ratio = min ( Rig / Riinfty , c1 ) |
753 |
fRi = c1 - ratio * ratio |
754 |
fRi = fRi * fRi * fRi |
755 |
|
756 |
c ---------------------------------------------------------------------- |
757 |
c evaluate diffusivities and viscosity |
758 |
c mixing due to internal waves, and shear and static instability |
759 |
|
760 |
diffus(i,ki,1) = viscAr + fcon * difmcon + fRi * difm0 |
761 |
diffus(i,ki,2) = diffKrS + fcon * difscon + fRi * difs0 |
762 |
diffus(i,ki,3) = diffKrT + fcon * difscon + fRi * difs0 |
763 |
|
764 |
end do |
765 |
end do |
766 |
|
767 |
c ------------------------------------------------------------------------ |
768 |
c set surface values to 0.0 |
769 |
|
770 |
do i = 1, imt |
771 |
diffus(i,0,1) = c0 |
772 |
diffus(i,0,2) = c0 |
773 |
diffus(i,0,3) = c0 |
774 |
end do |
775 |
|
776 |
#endif /* ALLOW_KPP */ |
777 |
|
778 |
return |
779 |
end |
780 |
|
781 |
c************************************************************************* |
782 |
|
783 |
subroutine z121 ( |
784 |
U v ) |
785 |
|
786 |
c Apply 121 smoothing in k to 2-d array V(i,k=1,Nr) |
787 |
c top (0) value is used as a dummy |
788 |
c bottom (Nrp1) value is set to input value from above. |
789 |
|
790 |
c Note that it is important to exclude from the smoothing any points |
791 |
c that are outside the range of the K(Ri) scheme, ie. >0.8, or <0.0. |
792 |
c Otherwise, there is interference with other physics, especially |
793 |
c penetrative convection. |
794 |
|
795 |
IMPLICIT NONE |
796 |
#include "SIZE.h" |
797 |
#include "KPP_PARAMS.h" |
798 |
|
799 |
c input/output |
800 |
c------------- |
801 |
c v : 2-D array to be smoothed in Nrp1 direction |
802 |
_KPP_RL v(imt,0:Nrp1) |
803 |
|
804 |
#ifdef ALLOW_KPP |
805 |
|
806 |
c local |
807 |
_KPP_RL zwork, zflag |
808 |
_KPP_RL KRi_range(1:Nrp1) |
809 |
integer i, k, km1, kp1 |
810 |
|
811 |
_KPP_RL p0 , p25 , p5 , p2 |
812 |
parameter ( p0 = 0.0, p25 = 0.25, p5 = 0.5, p2 = 2.0 ) |
813 |
|
814 |
KRi_range(Nrp1) = p0 |
815 |
|
816 |
#ifdef ALLOW_AUTODIFF_TAMC |
817 |
C-- dummy assignment to end declaration part for TAMC |
818 |
i = 0 |
819 |
|
820 |
C-- HPF directive to help TAMC |
821 |
CHPF$ INDEPENDENT |
822 |
CADJ INIT z121tape = common, Nr |
823 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
824 |
|
825 |
do i = 1, imt |
826 |
|
827 |
k = 1 |
828 |
CADJ STORE v(i,k) = z121tape |
829 |
v(i,Nrp1) = v(i,Nr) |
830 |
|
831 |
do k = 1, Nr |
832 |
KRi_range(k) = p5 + SIGN(p5,v(i,k)) |
833 |
KRi_range(k) = KRi_range(k) * |
834 |
& ( p5 + SIGN(p5,(Riinfty-v(i,k))) ) |
835 |
end do |
836 |
|
837 |
zwork = KRi_range(1) * v(i,1) |
838 |
v(i,1) = p2 * v(i,1) + |
839 |
& KRi_range(1) * KRi_range(2) * v(i,2) |
840 |
zflag = p2 + KRi_range(1) * KRi_range(2) |
841 |
v(i,1) = v(i,1) / zflag |
842 |
|
843 |
do k = 2, Nr |
844 |
CADJ STORE v(i,k), zwork = z121tape |
845 |
km1 = k - 1 |
846 |
kp1 = k + 1 |
847 |
zflag = v(i,k) |
848 |
v(i,k) = p2 * v(i,k) + |
849 |
& KRi_range(k) * KRi_range(kp1) * v(i,kp1) + |
850 |
& KRi_range(k) * zwork |
851 |
zwork = KRi_range(k) * zflag |
852 |
zflag = p2 + KRi_range(k)*(KRi_range(kp1)+KRi_range(km1)) |
853 |
v(i,k) = v(i,k) / zflag |
854 |
end do |
855 |
|
856 |
end do |
857 |
|
858 |
#endif /* ALLOW_KPP */ |
859 |
|
860 |
return |
861 |
end |
862 |
|
863 |
c************************************************************************* |
864 |
|
865 |
subroutine kpp_smooth_horiz ( |
866 |
I k, bi, bj, |
867 |
U fld ) |
868 |
|
869 |
c Apply horizontal smoothing to KPP array |
870 |
|
871 |
IMPLICIT NONE |
872 |
#include "SIZE.h" |
873 |
#include "KPP_PARAMS.h" |
874 |
|
875 |
c input |
876 |
c bi, bj : array indices |
877 |
c k : vertical index used for masking |
878 |
integer k, bi, bj |
879 |
|
880 |
c input/output |
881 |
c fld : 2-D array to be smoothed |
882 |
_KPP_RL fld( ibot:itop, jbot:jtop ) |
883 |
|
884 |
#ifdef ALLOW_KPP |
885 |
|
886 |
c local |
887 |
integer i, j, im1, ip1, jm1, jp1 |
888 |
_KPP_RL tempVar |
889 |
_KPP_RL fld_tmp( ibot:itop, jbot:jtop ) |
890 |
|
891 |
integer imin , imax , jmin , jmax |
892 |
parameter( imin=ibot+1, imax=itop-1, jmin=jbot+1, jmax=jtop-1 ) |
893 |
|
894 |
_KPP_RL p0 , p5 , p25 , p125 , p0625 |
895 |
parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
896 |
|
897 |
DO j = jmin, jmax |
898 |
jm1 = j-1 |
899 |
jp1 = j+1 |
900 |
DO i = imin, imax |
901 |
im1 = i-1 |
902 |
ip1 = i+1 |
903 |
tempVar = |
904 |
& p25 * pMask(i ,j ,k,bi,bj) + |
905 |
& p125 * ( pMask(im1,j ,k,bi,bj) + |
906 |
& pMask(ip1,j ,k,bi,bj) + |
907 |
& pMask(i ,jm1,k,bi,bj) + |
908 |
& pMask(i ,jp1,k,bi,bj) ) + |
909 |
& p0625 * ( pMask(im1,jm1,k,bi,bj) + |
910 |
& pMask(im1,jp1,k,bi,bj) + |
911 |
& pMask(ip1,jm1,k,bi,bj) + |
912 |
& pMask(ip1,jp1,k,bi,bj) ) |
913 |
IF ( tempVar .GE. p25 ) THEN |
914 |
fld_tmp(i,j) = ( |
915 |
& p25 * fld(i ,j )*pMask(i ,j ,k,bi,bj) + |
916 |
& p125 *(fld(im1,j )*pMask(im1,j ,k,bi,bj) + |
917 |
& fld(ip1,j )*pMask(ip1,j ,k,bi,bj) + |
918 |
& fld(i ,jm1)*pMask(i ,jm1,k,bi,bj) + |
919 |
& fld(i ,jp1)*pMask(i ,jp1,k,bi,bj))+ |
920 |
& p0625*(fld(im1,jm1)*pMask(im1,jm1,k,bi,bj) + |
921 |
& fld(im1,jp1)*pMask(im1,jp1,k,bi,bj) + |
922 |
& fld(ip1,jm1)*pMask(ip1,jm1,k,bi,bj) + |
923 |
& fld(ip1,jp1)*pMask(ip1,jp1,k,bi,bj))) |
924 |
& / tempVar |
925 |
ELSE |
926 |
fld_tmp(i,j) = fld(i,j) |
927 |
ENDIF |
928 |
ENDDO |
929 |
ENDDO |
930 |
|
931 |
c transfer smoothed field to output array |
932 |
DO j = jmin, jmax |
933 |
DO i = imin, imax |
934 |
fld(i,j) = fld_tmp(i,j) |
935 |
ENDDO |
936 |
ENDDO |
937 |
|
938 |
#endif /* ALLOW_KPP */ |
939 |
|
940 |
return |
941 |
end |
942 |
|
943 |
c************************************************************************* |
944 |
|
945 |
subroutine smooth_horiz ( |
946 |
I k, bi, bj, |
947 |
U fld ) |
948 |
|
949 |
c Apply horizontal smoothing to global _RL 2-D array |
950 |
|
951 |
IMPLICIT NONE |
952 |
#include "SIZE.h" |
953 |
#include "KPP_PARAMS.h" |
954 |
|
955 |
c input |
956 |
c bi, bj : array indices |
957 |
c k : vertical index used for masking |
958 |
integer k, bi, bj |
959 |
|
960 |
c input/output |
961 |
c fld : 2-D array to be smoothed |
962 |
_RL fld( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
963 |
|
964 |
#ifdef ALLOW_KPP |
965 |
|
966 |
c local |
967 |
integer i, j, im1, ip1, jm1, jp1 |
968 |
_RL tempVar |
969 |
_RL fld_tmp( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
970 |
|
971 |
integer imin , imax , jmin , jmax |
972 |
parameter(imin=2-OLx, imax=sNx+OLx-1, jmin=2-OLy, jmax=sNy+OLy-1) |
973 |
|
974 |
_RL p0 , p5 , p25 , p125 , p0625 |
975 |
parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
976 |
|
977 |
DO j = jmin, jmax |
978 |
jm1 = j-1 |
979 |
jp1 = j+1 |
980 |
DO i = imin, imax |
981 |
im1 = i-1 |
982 |
ip1 = i+1 |
983 |
tempVar = |
984 |
& p25 * pMask(i ,j ,k,bi,bj) + |
985 |
& p125 * ( pMask(im1,j ,k,bi,bj) + |
986 |
& pMask(ip1,j ,k,bi,bj) + |
987 |
& pMask(i ,jm1,k,bi,bj) + |
988 |
& pMask(i ,jp1,k,bi,bj) ) + |
989 |
& p0625 * ( pMask(im1,jm1,k,bi,bj) + |
990 |
& pMask(im1,jp1,k,bi,bj) + |
991 |
& pMask(ip1,jm1,k,bi,bj) + |
992 |
& pMask(ip1,jp1,k,bi,bj) ) |
993 |
IF ( tempVar .GE. p25 ) THEN |
994 |
fld_tmp(i,j) = ( |
995 |
& p25 * fld(i ,j )*pMask(i ,j ,k,bi,bj) + |
996 |
& p125 *(fld(im1,j )*pMask(im1,j ,k,bi,bj) + |
997 |
& fld(ip1,j )*pMask(ip1,j ,k,bi,bj) + |
998 |
& fld(i ,jm1)*pMask(i ,jm1,k,bi,bj) + |
999 |
& fld(i ,jp1)*pMask(i ,jp1,k,bi,bj))+ |
1000 |
& p0625*(fld(im1,jm1)*pMask(im1,jm1,k,bi,bj) + |
1001 |
& fld(im1,jp1)*pMask(im1,jp1,k,bi,bj) + |
1002 |
& fld(ip1,jm1)*pMask(ip1,jm1,k,bi,bj) + |
1003 |
& fld(ip1,jp1)*pMask(ip1,jp1,k,bi,bj))) |
1004 |
& / tempVar |
1005 |
ELSE |
1006 |
fld_tmp(i,j) = fld(i,j) |
1007 |
ENDIF |
1008 |
ENDDO |
1009 |
ENDDO |
1010 |
|
1011 |
c transfer smoothed field to output array |
1012 |
DO j = jmin, jmax |
1013 |
DO i = imin, imax |
1014 |
fld(i,j) = fld_tmp(i,j) |
1015 |
ENDDO |
1016 |
ENDDO |
1017 |
|
1018 |
#endif /* ALLOW_KPP */ |
1019 |
|
1020 |
return |
1021 |
end |
1022 |
|
1023 |
c************************************************************************* |
1024 |
|
1025 |
subroutine blmix ( |
1026 |
I ustar, bfsfc, hbl, stable, casea, diffus, kbl |
1027 |
O , dkm1, blmc, ghat, sigma, ikppkey |
1028 |
& ) |
1029 |
|
1030 |
c mixing coefficients within boundary layer depend on surface |
1031 |
c forcing and the magnitude and gradient of interior mixing below |
1032 |
c the boundary layer ("matching"). |
1033 |
c |
1034 |
c caution: if mixing bottoms out at hbl = -zgrid(Nr) then |
1035 |
c fictitious layer at Nrp1 is needed with small but finite width |
1036 |
c hwide(Nrp1) (eg. epsln = 1.e-20). |
1037 |
c |
1038 |
IMPLICIT NONE |
1039 |
|
1040 |
#include "SIZE.h" |
1041 |
#include "KPP_PARAMS.h" |
1042 |
|
1043 |
c input |
1044 |
c ustar (imt) surface friction velocity (m/s) |
1045 |
c bfsfc (imt) surface buoyancy forcing (m^2/s^3) |
1046 |
c hbl (imt) boundary layer depth (m) |
1047 |
c stable(imt) = 1 in stable forcing |
1048 |
c casea (imt) = 1 in case A |
1049 |
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
1050 |
c kbl(imt) -1 of first grid level below hbl |
1051 |
_KPP_RL ustar (imt) |
1052 |
_KPP_RL bfsfc (imt) |
1053 |
_KPP_RL hbl (imt) |
1054 |
_KPP_RL stable(imt) |
1055 |
_KPP_RL casea (imt) |
1056 |
_KPP_RL diffus(imt,0:Nrp1,mdiff) |
1057 |
integer kbl(imt) |
1058 |
|
1059 |
c output |
1060 |
c dkm1 (imt,mdiff) boundary layer difs at kbl-1 level |
1061 |
c blmc (imt,Nr,mdiff) boundary layer mixing coefficients (m^2/s) |
1062 |
c ghat (imt,Nr) nonlocal scalar transport |
1063 |
c sigma(imt) normalized depth (d / hbl) |
1064 |
_KPP_RL dkm1 (imt,mdiff) |
1065 |
_KPP_RL blmc (imt,Nr,mdiff) |
1066 |
_KPP_RL ghat (imt,Nr) |
1067 |
_KPP_RL sigma(imt) |
1068 |
integer ikppkey |
1069 |
|
1070 |
#ifdef ALLOW_KPP |
1071 |
|
1072 |
c local |
1073 |
c gat1*(imt) shape function at sigma = 1 |
1074 |
c dat1*(imt) derivative of shape function at sigma = 1 |
1075 |
c ws(imt), wm(imt) turbulent velocity scales (m/s) |
1076 |
_KPP_RL gat1m(imt), gat1s(imt), gat1t(imt) |
1077 |
_KPP_RL dat1m(imt), dat1s(imt), dat1t(imt) |
1078 |
_KPP_RL ws(imt), wm(imt) |
1079 |
integer i, kn, ki |
1080 |
_KPP_RL R, dvdzup, dvdzdn, viscp |
1081 |
_KPP_RL difsp, diftp, visch, difsh, difth |
1082 |
_KPP_RL f1, sig, a1, a2, a3, delhat |
1083 |
_KPP_RL Gm, Gs, Gt |
1084 |
_KPP_RL tempVar |
1085 |
|
1086 |
_KPP_RL p0 , eins |
1087 |
parameter (p0=0.0, eins=1.0) |
1088 |
|
1089 |
c----------------------------------------------------------------------- |
1090 |
c compute velocity scales at hbl |
1091 |
c----------------------------------------------------------------------- |
1092 |
|
1093 |
do i = 1, imt |
1094 |
sigma(i) = stable(i) * 1.0 + (1. - stable(i)) * epsilon |
1095 |
end do |
1096 |
|
1097 |
call wscale ( |
1098 |
I sigma, hbl, ustar, bfsfc, |
1099 |
O wm, ws ) |
1100 |
|
1101 |
do i = 1, imt |
1102 |
wm(i) = sign(eins,wm(i))*max(phepsi,abs(wm(i))) |
1103 |
ws(i) = sign(eins,ws(i))*max(phepsi,abs(ws(i))) |
1104 |
end do |
1105 |
CADJ STORE wm = comlev1_kpp, key = ikppkey |
1106 |
CADJ STORE ws = comlev1_kpp, key = ikppkey |
1107 |
|
1108 |
do i = 1, imt |
1109 |
|
1110 |
kn = int(caseA(i)+phepsi) *(kbl(i) -1) + |
1111 |
$ (1 - int(caseA(i)+phepsi)) * kbl(i) |
1112 |
|
1113 |
c----------------------------------------------------------------------- |
1114 |
c find the interior viscosities and derivatives at hbl(i) |
1115 |
c----------------------------------------------------------------------- |
1116 |
|
1117 |
delhat = 0.5*hwide(kn) - zgrid(kn) - hbl(i) |
1118 |
R = 1.0 - delhat / hwide(kn) |
1119 |
dvdzup = (diffus(i,kn-1,1) - diffus(i,kn ,1)) / hwide(kn) |
1120 |
dvdzdn = (diffus(i,kn ,1) - diffus(i,kn+1,1)) / hwide(kn+1) |
1121 |
viscp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
1122 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
1123 |
|
1124 |
dvdzup = (diffus(i,kn-1,2) - diffus(i,kn ,2)) / hwide(kn) |
1125 |
dvdzdn = (diffus(i,kn ,2) - diffus(i,kn+1,2)) / hwide(kn+1) |
1126 |
difsp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
1127 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
1128 |
|
1129 |
dvdzup = (diffus(i,kn-1,3) - diffus(i,kn ,3)) / hwide(kn) |
1130 |
dvdzdn = (diffus(i,kn ,3) - diffus(i,kn+1,3)) / hwide(kn+1) |
1131 |
diftp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
1132 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
1133 |
|
1134 |
visch = diffus(i,kn,1) + viscp * delhat |
1135 |
difsh = diffus(i,kn,2) + difsp * delhat |
1136 |
difth = diffus(i,kn,3) + diftp * delhat |
1137 |
|
1138 |
f1 = stable(i) * conc1 * bfsfc(i) / |
1139 |
& max(ustar(i)**4,phepsi) |
1140 |
gat1m(i) = visch / hbl(i) / wm(i) |
1141 |
dat1m(i) = -viscp / wm(i) + f1 * visch |
1142 |
dat1m(i) = min(dat1m(i),p0) |
1143 |
|
1144 |
gat1s(i) = difsh / hbl(i) / ws(i) |
1145 |
dat1s(i) = -difsp / ws(i) + f1 * difsh |
1146 |
dat1s(i) = min(dat1s(i),p0) |
1147 |
|
1148 |
gat1t(i) = difth / hbl(i) / ws(i) |
1149 |
dat1t(i) = -diftp / ws(i) + f1 * difth |
1150 |
dat1t(i) = min(dat1t(i),p0) |
1151 |
|
1152 |
end do |
1153 |
|
1154 |
do ki = 1, Nr |
1155 |
|
1156 |
c----------------------------------------------------------------------- |
1157 |
c compute turbulent velocity scales on the interfaces |
1158 |
c----------------------------------------------------------------------- |
1159 |
|
1160 |
do i = 1, imt |
1161 |
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
1162 |
sigma(i) = stable(i)*sig + (1.-stable(i))*min(sig,epsilon) |
1163 |
end do |
1164 |
call wscale ( |
1165 |
I sigma, hbl, ustar, bfsfc, |
1166 |
O wm, ws ) |
1167 |
|
1168 |
c----------------------------------------------------------------------- |
1169 |
c compute the dimensionless shape functions at the interfaces |
1170 |
c----------------------------------------------------------------------- |
1171 |
|
1172 |
do i = 1, imt |
1173 |
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
1174 |
a1 = sig - 2. |
1175 |
a2 = 3. - 2. * sig |
1176 |
a3 = sig - 1. |
1177 |
|
1178 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
1179 |
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
1180 |
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
1181 |
|
1182 |
c----------------------------------------------------------------------- |
1183 |
c compute boundary layer diffusivities at the interfaces |
1184 |
c----------------------------------------------------------------------- |
1185 |
|
1186 |
blmc(i,ki,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
1187 |
blmc(i,ki,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
1188 |
blmc(i,ki,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
1189 |
|
1190 |
c----------------------------------------------------------------------- |
1191 |
c nonlocal transport term = ghat * <ws>o |
1192 |
c----------------------------------------------------------------------- |
1193 |
|
1194 |
tempVar = ws(i) * hbl(i) |
1195 |
ghat(i,ki) = (1.-stable(i)) * cg / max(phepsi,tempVar) |
1196 |
|
1197 |
end do |
1198 |
end do |
1199 |
|
1200 |
c----------------------------------------------------------------------- |
1201 |
c find diffusivities at kbl-1 grid level |
1202 |
c----------------------------------------------------------------------- |
1203 |
|
1204 |
do i = 1, imt |
1205 |
sig = -zgrid(kbl(i)-1) / hbl(i) |
1206 |
sigma(i) = stable(i) * sig |
1207 |
& + (1. - stable(i)) * min(sig,epsilon) |
1208 |
end do |
1209 |
|
1210 |
call wscale ( |
1211 |
I sigma, hbl, ustar, bfsfc, |
1212 |
O wm, ws ) |
1213 |
|
1214 |
do i = 1, imt |
1215 |
sig = -zgrid(kbl(i)-1) / hbl(i) |
1216 |
a1 = sig - 2. |
1217 |
a2 = 3. - 2. * sig |
1218 |
a3 = sig - 1. |
1219 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
1220 |
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
1221 |
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
1222 |
dkm1(i,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
1223 |
dkm1(i,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
1224 |
dkm1(i,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
1225 |
end do |
1226 |
|
1227 |
#endif /* ALLOW_KPP */ |
1228 |
|
1229 |
return |
1230 |
end |
1231 |
|
1232 |
c************************************************************************* |
1233 |
|
1234 |
subroutine enhance ( |
1235 |
I dkm1, hbl, kbl, diffus, casea |
1236 |
U , ghat |
1237 |
O , blmc |
1238 |
& ) |
1239 |
|
1240 |
c enhance the diffusivity at the kbl-.5 interface |
1241 |
|
1242 |
IMPLICIT NONE |
1243 |
|
1244 |
#include "SIZE.h" |
1245 |
#include "KPP_PARAMS.h" |
1246 |
|
1247 |
c input |
1248 |
c dkm1(imt,mdiff) bl diffusivity at kbl-1 grid level |
1249 |
c hbl(imt) boundary layer depth (m) |
1250 |
c kbl(imt) grid above hbl |
1251 |
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
1252 |
c casea(imt) = 1 in caseA, = 0 in case B |
1253 |
_KPP_RL dkm1 (imt,mdiff) |
1254 |
_KPP_RL hbl (imt) |
1255 |
integer kbl (imt) |
1256 |
_KPP_RL diffus(imt,0:Nrp1,mdiff) |
1257 |
_KPP_RL casea (imt) |
1258 |
|
1259 |
c input/output |
1260 |
c nonlocal transport, modified ghat at kbl(i)-1 interface (s/m**2) |
1261 |
_KPP_RL ghat (imt,Nr) |
1262 |
|
1263 |
c output |
1264 |
c enhanced bound. layer mixing coeff. |
1265 |
_KPP_RL blmc (imt,Nr,mdiff) |
1266 |
|
1267 |
#ifdef ALLOW_KPP |
1268 |
|
1269 |
c local |
1270 |
c fraction hbl lies beteen zgrid neighbors |
1271 |
_KPP_RL delta |
1272 |
integer ki, i, md |
1273 |
_KPP_RL dkmp5, dstar |
1274 |
|
1275 |
do i = 1, imt |
1276 |
ki = kbl(i)-1 |
1277 |
if ((ki .ge. 1) .and. (ki .lt. Nr)) then |
1278 |
delta = (hbl(i) + zgrid(ki)) / (zgrid(ki) - zgrid(ki+1)) |
1279 |
do md = 1, mdiff |
1280 |
dkmp5 = casea(i) * diffus(i,ki,md) + |
1281 |
1 (1.- casea(i)) * blmc (i,ki,md) |
1282 |
dstar = (1.- delta)**2 * dkm1(i,md) |
1283 |
& + delta**2 * dkmp5 |
1284 |
blmc(i,ki,md) = (1.- delta)*diffus(i,ki,md) |
1285 |
& + delta*dstar |
1286 |
end do |
1287 |
ghat(i,ki) = (1.- casea(i)) * ghat(i,ki) |
1288 |
endif |
1289 |
end do |
1290 |
|
1291 |
#endif /* ALLOW_KPP */ |
1292 |
|
1293 |
return |
1294 |
end |
1295 |
|
1296 |
c************************************************************************* |
1297 |
|
1298 |
SUBROUTINE STATEKPP ( |
1299 |
I bi, bj, myThid, |
1300 |
O RHO1, DBLOC, DBSFC, TTALPHA, SSBETA) |
1301 |
c |
1302 |
c----------------------------------------------------------------------- |
1303 |
c "statekpp" computes all necessary input arrays |
1304 |
c for the kpp mixing scheme |
1305 |
c |
1306 |
c input: |
1307 |
c bi, bj = array indices on which to apply calculations |
1308 |
c |
1309 |
c output: |
1310 |
c rho1 = potential density of surface layer (kg/m^3) |
1311 |
c dbloc = local buoyancy gradient at Nr interfaces |
1312 |
c g/rho{k+1,k+1} * [ drho{k,k+1}-drho{k+1,k+1} ] (m/s^2) |
1313 |
c dbsfc = buoyancy difference with respect to the surface |
1314 |
c g * [ drho{1,k}/rho{1,k} - drho{k,k}/rho{k,k} ] (m/s^2) |
1315 |
c ttalpha= thermal expansion coefficient without 1/rho factor |
1316 |
c d(rho) / d(potential temperature) (kg/m^3/C) |
1317 |
c ssbeta = salt expansion coefficient without 1/rho factor |
1318 |
c d(rho) / d(salinity) (kg/m^3/PSU) |
1319 |
c |
1320 |
c see also subroutines find_rho.F find_alpha.F find_beta.F |
1321 |
c |
1322 |
c written by: jan morzel, feb. 10, 1995 (converted from "sigma" version) |
1323 |
c modified by: d. menemenlis, june 1998 : for use with MIT GCM UV |
1324 |
c |
1325 |
c----------------------------------------------------------------------- |
1326 |
|
1327 |
IMPLICIT NONE |
1328 |
|
1329 |
#include "SIZE.h" |
1330 |
#include "EEPARAMS.h" |
1331 |
#include "PARAMS.h" |
1332 |
#include "KPP_PARAMS.h" |
1333 |
#include "DYNVARS.h" |
1334 |
|
1335 |
c-------------- Routine arguments ----------------------------------------- |
1336 |
INTEGER bi, bj, myThid |
1337 |
_KPP_RL RHO1 ( ibot:itop, jbot:jtop ) |
1338 |
_KPP_RL DBLOC ( ibot:itop, jbot:jtop, Nr ) |
1339 |
_KPP_RL DBSFC ( ibot:itop, jbot:jtop, Nr ) |
1340 |
_KPP_RL TTALPHA( ibot:itop, jbot:jtop, Nrp1 ) |
1341 |
_KPP_RL SSBETA ( ibot:itop, jbot:jtop, Nrp1 ) |
1342 |
|
1343 |
#ifdef ALLOW_KPP |
1344 |
|
1345 |
c-------------------------------------------------------------------------- |
1346 |
c |
1347 |
c local arrays: |
1348 |
c |
1349 |
c rhok - density of t(k ) & s(k ) at depth k |
1350 |
c rhokm1 - density of t(k-1) & s(k-1) at depth k |
1351 |
c rho1k - density of t(1 ) & s(1 ) at depth k |
1352 |
c work1, work2 - work arrays for holding horizontal slabs |
1353 |
|
1354 |
_RL RHOK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1355 |
_RL RHOKM1(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1356 |
_RL RHO1K (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1357 |
_RL WORK1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1358 |
_RL WORK2 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1359 |
_RL WORK3 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
1360 |
INTEGER I, J, K |
1361 |
|
1362 |
c calculate density, alpha, beta in surface layer, and set dbsfc to zero |
1363 |
|
1364 |
call FIND_RHO( |
1365 |
I bi, bj, ibot, itop, jbot, jtop, 1, 1, |
1366 |
I theta, salt, |
1367 |
O WORK1, |
1368 |
I myThid ) |
1369 |
|
1370 |
call FIND_ALPHA( |
1371 |
I bi, bj, ibot, itop, jbot, jtop, 1, 1, |
1372 |
O WORK2 ) |
1373 |
|
1374 |
call FIND_BETA( |
1375 |
I bi, bj, ibot, itop, jbot, jtop, 1, 1, |
1376 |
O WORK3 ) |
1377 |
|
1378 |
DO J = jbot, jtop |
1379 |
DO I = ibot, itop |
1380 |
RHO1(I,J) = WORK1(I,J) + rhoConst |
1381 |
TTALPHA(I,J,1) = WORK2(I,J) |
1382 |
SSBETA(I,J,1) = WORK3(I,J) |
1383 |
DBSFC(I,J,1) = 0. |
1384 |
END DO |
1385 |
END DO |
1386 |
|
1387 |
c calculate alpha, beta, and gradients in interior layers |
1388 |
|
1389 |
CHPF$ INDEPENDENT, NEW (RHOK,RHOKM1,RHO1K,WORK1,WORK2) |
1390 |
DO K = 2, Nr |
1391 |
|
1392 |
call FIND_RHO( |
1393 |
I bi, bj, ibot, itop, jbot, jtop, K, K, |
1394 |
I theta, salt, |
1395 |
O RHOK, |
1396 |
I myThid ) |
1397 |
|
1398 |
call FIND_RHO( |
1399 |
I bi, bj, ibot, itop, jbot, jtop, K-1, K, |
1400 |
I theta, salt, |
1401 |
O RHOKM1, |
1402 |
I myThid ) |
1403 |
|
1404 |
call FIND_RHO( |
1405 |
I bi, bj, ibot, itop, jbot, jtop, 1, K, |
1406 |
I theta, salt, |
1407 |
O RHO1K, |
1408 |
I myThid ) |
1409 |
|
1410 |
call FIND_ALPHA( |
1411 |
I bi, bj, ibot, itop, jbot, jtop, K, K, |
1412 |
O WORK1 ) |
1413 |
|
1414 |
call FIND_BETA( |
1415 |
I bi, bj, ibot, itop, jbot, jtop, K, K, |
1416 |
O WORK2 ) |
1417 |
|
1418 |
DO J = jbot, jtop |
1419 |
DO I = ibot, itop |
1420 |
TTALPHA(I,J,K) = WORK1 (I,J) |
1421 |
SSBETA(I,J,K) = WORK2 (I,J) |
1422 |
DBLOC(I,J,K-1) = gravity * (RHOK(I,J) - RHOKM1(I,J)) / |
1423 |
& (RHOK(I,J) + rhoConst) |
1424 |
DBSFC(I,J,K) = gravity * (RHOK(I,J) - RHO1K (I,J)) / |
1425 |
& (RHOK(I,J) + rhoConst) |
1426 |
END DO |
1427 |
END DO |
1428 |
|
1429 |
END DO |
1430 |
|
1431 |
c compute arrays for K = Nrp1 |
1432 |
DO J = jbot, jtop |
1433 |
DO I = ibot, itop |
1434 |
TTALPHA(I,J,Nrp1) = TTALPHA(I,J,Nr) |
1435 |
SSBETA(I,J,Nrp1) = SSBETA(I,J,Nr) |
1436 |
DBLOC(I,J,Nr) = 0. |
1437 |
END DO |
1438 |
END DO |
1439 |
|
1440 |
#endif /* ALLOW_KPP */ |
1441 |
|
1442 |
RETURN |
1443 |
END |