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C $Header: /u/gcmpack/MITgcm/pkg/kpp/kpp_routines.F,v 1.48 2010/01/20 01:32:50 jmc 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. |
| 10 |
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- 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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C-- o KPP_DOUBLEDIFF - Compute double diffusive contribution to diffusivities |
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|
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c*********************************************************************** |
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|
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SUBROUTINE KPPMIX ( |
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I kmtj, shsq, dvsq, ustar, msk |
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I , bo, bosol |
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#ifdef ALLOW_SALT_PLUME |
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I , boplume,SPDepth |
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#endif /* ALLOW_SALT_PLUME */ |
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I , dbloc, Ritop, coriol |
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I , diffusKzS, diffusKzT |
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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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I , bi, bj, myTime, myIter, myThid ) |
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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 "KPP_PARAMS.h" |
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#ifdef ALLOW_AUTODIFF |
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# include "tamc.h" |
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#endif |
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|
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c input |
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c bi, bj :: Array indices on which to apply calculations |
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c myTime :: Current time in simulation |
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c myIter :: Current iteration number in simulation |
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c myThid :: My Thread Id. number |
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c kmtj (imt) - number of vertical layers on this row |
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c msk (imt) - surface mask (=1 if water, =0 otherwise) |
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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 boplume(imt) - haline 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 diffusKzS(imt,Nr)- background vertical diffusivity for scalars (m^2/s) |
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c diffusKzT(imt,Nr)- background vertical diffusivity for theta (m^2/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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INTEGER bi, bj |
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_RL myTime |
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integer myIter |
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integer myThid |
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integer kmtj (imt ) |
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_RL shsq (imt,Nr) |
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_RL dvsq (imt,Nr) |
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_RL ustar (imt ) |
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_RL bo (imt ) |
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_RL bosol (imt ) |
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#ifdef ALLOW_SALT_PLUME |
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_RL boplume (imt ) |
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_RL SPDepth (imt ) |
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#endif /* ALLOW_SALT_PLUME */ |
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_RL dbloc (imt,Nr) |
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_RL Ritop (imt,Nr) |
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_RL coriol (imt ) |
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_RS msk (imt ) |
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_RL diffusKzS(imt,Nr) |
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_RL diffusKzT(imt,Nr) |
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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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_RL diffus(imt,0:Nrp1,mdiff) |
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_RL ghat (imt,Nr) |
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_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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_RL bfsfc (imt ) |
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_RL casea (imt ) |
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_RL stable (imt ) |
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_RL dkm1 (imt, mdiff) |
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_RL blmc (imt,Nr,mdiff) |
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_RL sigma (imt ) |
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_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, kind=isbyte |
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CADJ STORE dbloc = comlev1_kpp, key=ikppkey, kind=isbyte |
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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 , diffusKzS, diffusKzT |
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I , ikppkey |
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O , diffus, myThid ) |
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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, kind=isbyte |
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CADJ STORE shsq = comlev1_kpp, key=ikppkey, kind=isbyte |
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CADJ STORE ghat = comlev1_kpp, key=ikppkey, kind=isbyte |
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CADJ STORE diffus = comlev1_kpp, key=ikppkey, kind=isbyte |
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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 k=1,Nrp1 |
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do i = 1,imt |
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if(k.ge.kmtj(i)) 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 |
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#ifdef ALLOW_SALT_PLUME |
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I , boplume,SPDepth |
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#endif /* ALLOW_SALT_PLUME */ |
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I , coriol |
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I , ikppkey |
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O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
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I , bi, bj, myTime, myIter, myThid ) |
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|
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CADJ STORE hbl,bfsfc,stable,casea,kbl = comlev1_kpp, |
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CADJ & key=ikppkey, kind=isbyte |
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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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I , myThid ) |
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cph( |
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CADJ STORE dkm1,blmc,ghat = comlev1_kpp, |
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CADJ & key=ikppkey, kind=isbyte |
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CADJ STORE hbl, kbl, diffus, casea = comlev1_kpp, |
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CADJ & key=ikppkey, kind=isbyte |
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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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I , myThid ) |
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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, kind=isbyte |
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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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#ifdef ALLOW_SHELFICE |
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C when there is shelfice on top (msk(i)=0), reset the boundary layer |
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C mixing coefficients blmc to pure Ri-number based mixing |
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blmc(i,k,1) = max ( blmc(i,k,1)*msk(i), |
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& diffus(i,k,1) ) |
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blmc(i,k,2) = max ( blmc(i,k,2)*msk(i), |
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& diffus(i,k,2) ) |
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blmc(i,k,3) = max ( blmc(i,k,3)*msk(i), |
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& diffus(i,k,3) ) |
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#endif /* not ALLOW_SHELFICE */ |
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diffus(i,k,1) = max ( blmc(i,k,1), viscArNr(1) ) |
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diffus(i,k,2) = max ( blmc(i,k,2), diffusKzS(i,Nr) ) |
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diffus(i,k,3) = max ( blmc(i,k,3), diffusKzT(i,Nr) ) |
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else |
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ghat(i,k) = 0. _d 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 ( |
| 267 |
I kmtj |
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I , dvsq, dbloc, Ritop, ustar, bo, bosol |
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#ifdef ALLOW_SALT_PLUME |
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I , boplume,SPDepth |
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#endif /* ALLOW_SALT_PLUME */ |
| 272 |
I , coriol |
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I , ikppkey |
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O , hbl, bfsfc, stable, casea, kbl, Rib, sigma |
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I , bi, bj, myTime, myIter, myThid ) |
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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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#ifdef ALLOW_AUTODIFF |
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# include "tamc.h" |
| 306 |
#endif |
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|
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c input |
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c------ |
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c bi, bj :: Array indices on which to apply calculations |
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c myTime :: Current time in simulation |
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c myIter :: Current iteration number in simulation |
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c myThid :: My Thread Id. number |
| 314 |
c kmtj : number of vertical layers |
| 315 |
c dvsq : (velocity shear re sfc)^2 ((m/s)^2) |
| 316 |
c dbloc : local delta buoyancy across interfaces (m/s^2) |
| 317 |
c Ritop : numerator of bulk Richardson Number |
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c =(z-zref)*dbsfc, where dbsfc=delta |
| 319 |
c buoyancy with respect to surface ((m/s)^2) |
| 320 |
c ustar : surface friction velocity (m/s) |
| 321 |
c bo : surface turbulent buoyancy forcing (m^2/s^3) |
| 322 |
c bosol : radiative buoyancy forcing (m^2/s^3) |
| 323 |
c boplume : haline buoyancy forcing (m^2/s^3) |
| 324 |
c coriol : Coriolis parameter (1/s) |
| 325 |
INTEGER bi, bj |
| 326 |
_RL myTime |
| 327 |
integer myIter |
| 328 |
integer myThid |
| 329 |
integer kmtj(imt) |
| 330 |
_RL dvsq (imt,Nr) |
| 331 |
_RL dbloc (imt,Nr) |
| 332 |
_RL Ritop (imt,Nr) |
| 333 |
_RL ustar (imt) |
| 334 |
_RL bo (imt) |
| 335 |
_RL bosol (imt) |
| 336 |
_RL coriol (imt) |
| 337 |
integer ikppkey |
| 338 |
#ifdef ALLOW_SALT_PLUME |
| 339 |
_RL boplume (imt) |
| 340 |
_RL SPDepth (imt) |
| 341 |
#endif /* ALLOW_SALT_PLUME */ |
| 342 |
|
| 343 |
c output |
| 344 |
c-------- |
| 345 |
c hbl : boundary layer depth (m) |
| 346 |
c bfsfc : Bo+radiation absorbed to d=hbf*hbl (m^2/s^3) |
| 347 |
c stable : =1 in stable forcing; =0 unstable |
| 348 |
c casea : =1 in case A, =0 in case B |
| 349 |
c kbl : -1 of first grid level below hbl |
| 350 |
c Rib : Bulk Richardson number |
| 351 |
c sigma : normalized depth (d/hbl) |
| 352 |
_RL hbl (imt) |
| 353 |
_RL bfsfc (imt) |
| 354 |
_RL stable (imt) |
| 355 |
_RL casea (imt) |
| 356 |
integer kbl(imt) |
| 357 |
_RL Rib (imt,Nr) |
| 358 |
_RL sigma (imt) |
| 359 |
|
| 360 |
#ifdef ALLOW_KPP |
| 361 |
|
| 362 |
c local |
| 363 |
c------- |
| 364 |
c wm, ws : turbulent velocity scales (m/s) |
| 365 |
_RL wm(imt), ws(imt) |
| 366 |
_RL worka(imt) |
| 367 |
_RL bvsq, vtsq, hekman, hmonob, hlimit, tempVar1, tempVar2 |
| 368 |
integer i, kl |
| 369 |
|
| 370 |
_RL p5 , eins |
| 371 |
parameter ( p5=0.5, eins=1.0 ) |
| 372 |
_RL minusone |
| 373 |
parameter ( minusone=-1.0 ) |
| 374 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 375 |
integer kkppkey |
| 376 |
#endif |
| 377 |
|
| 378 |
#ifdef ALLOW_DIAGNOSTICS |
| 379 |
c KPPBFSFC - Bo+radiation absorbed to d=hbf*hbl + plume (m^2/s^3) |
| 380 |
_RL KPPBFSFC(imt,Nr) |
| 381 |
_RL KPPRi(imt,Nr) |
| 382 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 383 |
|
| 384 |
c find bulk Richardson number at every grid level until > Ricr |
| 385 |
c |
| 386 |
c note: the reference depth is -epsilon/2.*zgrid(k), but the reference |
| 387 |
c u,v,t,s values are simply the surface layer values, |
| 388 |
c and not the averaged values from 0 to 2*ref.depth, |
| 389 |
c which is necessary for very fine grids(top layer < 2m thickness) |
| 390 |
c note: max values when Ricr never satisfied are |
| 391 |
c kbl(i)=kmtj(i) and hbl(i)=-zgrid(kmtj(i)) |
| 392 |
|
| 393 |
c initialize hbl and kbl to bottomed out values |
| 394 |
|
| 395 |
do i = 1, imt |
| 396 |
Rib(i,1) = 0. _d 0 |
| 397 |
kbl(i) = max(kmtj(i),1) |
| 398 |
hbl(i) = -zgrid(kbl(i)) |
| 399 |
end do |
| 400 |
|
| 401 |
#ifdef ALLOW_DIAGNOSTICS |
| 402 |
do kl = 1, Nr |
| 403 |
do i = 1, imt |
| 404 |
KPPBFSFC(i,kl) = 0. _d 0 |
| 405 |
KPPRi(i,kl) = 0. _d 0 |
| 406 |
enddo |
| 407 |
enddo |
| 408 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 409 |
|
| 410 |
do kl = 2, Nr |
| 411 |
|
| 412 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 413 |
kkppkey = (ikppkey-1)*Nr + kl |
| 414 |
#endif |
| 415 |
|
| 416 |
c compute bfsfc = sw fraction at hbf * zgrid |
| 417 |
|
| 418 |
do i = 1, imt |
| 419 |
worka(i) = zgrid(kl) |
| 420 |
end do |
| 421 |
CADJ store worka = comlev1_kpp_k, key = kkppkey, kind=isbyte |
| 422 |
call SWFRAC( |
| 423 |
I imt, hbf, |
| 424 |
U worka, |
| 425 |
I myTime, myIter, myThid ) |
| 426 |
CADJ store worka = comlev1_kpp_k, key = kkppkey, kind=isbyte |
| 427 |
|
| 428 |
do i = 1, imt |
| 429 |
|
| 430 |
c use caseA as temporary array |
| 431 |
|
| 432 |
casea(i) = -zgrid(kl) |
| 433 |
|
| 434 |
c compute bfsfc= Bo + radiative contribution down to hbf * hbl |
| 435 |
|
| 436 |
bfsfc(i) = bo(i) + bosol(i)*(1. - worka(i)) |
| 437 |
|
| 438 |
end do |
| 439 |
#ifdef ALLOW_SALT_PLUME |
| 440 |
c compute bfsfc = plume fraction at hbf * zgrid |
| 441 |
IF ( useSALT_PLUME ) THEN |
| 442 |
do i = 1, imt |
| 443 |
worka(i) = zgrid(kl) |
| 444 |
enddo |
| 445 |
call SALT_PLUME_FRAC( |
| 446 |
I imt, hbf,SPDepth, |
| 447 |
U worka, |
| 448 |
I myTime, myIter, myThid) |
| 449 |
do i = 1, imt |
| 450 |
bfsfc(i) = bfsfc(i) + boplume(i)*(1. - worka(i)) |
| 451 |
enddo |
| 452 |
ENDIF |
| 453 |
#endif /* ALLOW_SALT_PLUME */ |
| 454 |
|
| 455 |
#ifdef ALLOW_DIAGNOSTICS |
| 456 |
do i = 1, imt |
| 457 |
KPPBFSFC(i,kl) = bfsfc(i) |
| 458 |
enddo |
| 459 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 460 |
|
| 461 |
do i = 1, imt |
| 462 |
stable(i) = p5 + sign(p5,bfsfc(i)) |
| 463 |
sigma(i) = stable(i) + (1. - stable(i)) * epsilon |
| 464 |
enddo |
| 465 |
|
| 466 |
c----------------------------------------------------------------------- |
| 467 |
c compute velocity scales at sigma, for hbl= caseA = -zgrid(kl) |
| 468 |
c----------------------------------------------------------------------- |
| 469 |
|
| 470 |
call wscale ( |
| 471 |
I sigma, casea, ustar, bfsfc, |
| 472 |
O wm, ws, myThid ) |
| 473 |
CADJ store ws = comlev1_kpp_k, key = kkppkey, kind=isbyte |
| 474 |
|
| 475 |
do i = 1, imt |
| 476 |
|
| 477 |
c----------------------------------------------------------------------- |
| 478 |
c compute the turbulent shear contribution to Rib |
| 479 |
c----------------------------------------------------------------------- |
| 480 |
|
| 481 |
bvsq = p5 * |
| 482 |
1 ( dbloc(i,kl-1) / (zgrid(kl-1)-zgrid(kl ))+ |
| 483 |
2 dbloc(i,kl ) / (zgrid(kl )-zgrid(kl+1))) |
| 484 |
|
| 485 |
if (bvsq .eq. 0. _d 0) then |
| 486 |
vtsq = 0. _d 0 |
| 487 |
else |
| 488 |
vtsq = -zgrid(kl) * ws(i) * sqrt(abs(bvsq)) * Vtc |
| 489 |
endif |
| 490 |
|
| 491 |
c compute bulk Richardson number at new level |
| 492 |
c note: Ritop needs to be zero on land and ocean bottom |
| 493 |
c points so that the following if statement gets triggered |
| 494 |
c correctly; otherwise, hbl might get set to (big) negative |
| 495 |
c values, that might exceed the limit for the "exp" function |
| 496 |
c in "SWFRAC" |
| 497 |
|
| 498 |
c |
| 499 |
c rg: assignment to double precision variable to avoid overflow |
| 500 |
c ph: test for zero nominator |
| 501 |
c |
| 502 |
|
| 503 |
tempVar1 = dvsq(i,kl) + vtsq |
| 504 |
tempVar2 = max(tempVar1, phepsi) |
| 505 |
Rib(i,kl) = Ritop(i,kl) / tempVar2 |
| 506 |
#ifdef ALLOW_DIAGNOSTICS |
| 507 |
KPPRi(i,kl) = Rib(i,kl) |
| 508 |
#endif |
| 509 |
|
| 510 |
end do |
| 511 |
end do |
| 512 |
|
| 513 |
#ifdef ALLOW_DIAGNOSTICS |
| 514 |
CALL DIAGNOSTICS_FILL(KPPBFSFC,'KPPbfsfc',0,Nr,2,bi,bj,myThid) |
| 515 |
CALL DIAGNOSTICS_FILL(KPPRi ,'KPPRi ',0,Nr,2,bi,bj,myThid) |
| 516 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 517 |
|
| 518 |
cph( |
| 519 |
cph without this store, there is a recomputation error for |
| 520 |
cph rib in adbldepth (probably partial recomputation problem) |
| 521 |
CADJ store Rib = comlev1_kpp |
| 522 |
CADJ & , key=ikppkey, kind=isbyte, |
| 523 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy),Nr /) |
| 524 |
cph) |
| 525 |
|
| 526 |
do kl = 2, Nr |
| 527 |
do i = 1, imt |
| 528 |
if (kbl(i).eq.kmtj(i) .and. Rib(i,kl).gt.Ricr) kbl(i) = kl |
| 529 |
end do |
| 530 |
end do |
| 531 |
|
| 532 |
CADJ store kbl = comlev1_kpp |
| 533 |
CADJ & , key=ikppkey, kind=isbyte, |
| 534 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 535 |
|
| 536 |
do i = 1, imt |
| 537 |
kl = kbl(i) |
| 538 |
c linearly interpolate to find hbl where Rib = Ricr |
| 539 |
if (kl.gt.1 .and. kl.lt.kmtj(i)) then |
| 540 |
tempVar1 = (Rib(i,kl)-Rib(i,kl-1)) |
| 541 |
hbl(i) = -zgrid(kl-1) + (zgrid(kl-1)-zgrid(kl)) * |
| 542 |
1 (Ricr - Rib(i,kl-1)) / tempVar1 |
| 543 |
endif |
| 544 |
end do |
| 545 |
|
| 546 |
CADJ store hbl = comlev1_kpp |
| 547 |
CADJ & , key=ikppkey, kind=isbyte, |
| 548 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 549 |
|
| 550 |
c----------------------------------------------------------------------- |
| 551 |
c find stability and buoyancy forcing for boundary layer |
| 552 |
c----------------------------------------------------------------------- |
| 553 |
|
| 554 |
do i = 1, imt |
| 555 |
worka(i) = hbl(i) |
| 556 |
end do |
| 557 |
CADJ store worka = comlev1_kpp |
| 558 |
CADJ & , key=ikppkey, kind=isbyte, |
| 559 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 560 |
call SWFRAC( |
| 561 |
I imt, minusone, |
| 562 |
U worka, |
| 563 |
I myTime, myIter, myThid ) |
| 564 |
CADJ store worka = comlev1_kpp |
| 565 |
CADJ & , key=ikppkey, kind=isbyte, |
| 566 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 567 |
|
| 568 |
do i = 1, imt |
| 569 |
bfsfc(i) = bo(i) + bosol(i) * (1. - worka(i)) |
| 570 |
end do |
| 571 |
|
| 572 |
#ifdef ALLOW_SALT_PLUME |
| 573 |
IF ( useSALT_PLUME ) THEN |
| 574 |
do i = 1, imt |
| 575 |
worka(i) = hbl(i) |
| 576 |
enddo |
| 577 |
call SALT_PLUME_FRAC( |
| 578 |
I imt,minusone,SPDepth, |
| 579 |
U worka, |
| 580 |
I myTime, myIter, myThid ) |
| 581 |
do i = 1, imt |
| 582 |
bfsfc(i) = bfsfc(i) + boplume(i) * (1. - worka(i)) |
| 583 |
enddo |
| 584 |
ENDIF |
| 585 |
#endif /* ALLOW_SALT_PLUME */ |
| 586 |
CADJ store bfsfc = comlev1_kpp |
| 587 |
CADJ & , key=ikppkey, kind=isbyte, |
| 588 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 589 |
|
| 590 |
c-- ensure bfsfc is never 0 |
| 591 |
do i = 1, imt |
| 592 |
stable(i) = p5 + sign( p5, bfsfc(i) ) |
| 593 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
| 594 |
end do |
| 595 |
|
| 596 |
cph( |
| 597 |
cph added stable to store list to avoid extensive recomp. |
| 598 |
CADJ store bfsfc, stable = comlev1_kpp |
| 599 |
CADJ & , key=ikppkey, kind=isbyte, |
| 600 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 601 |
cph) |
| 602 |
|
| 603 |
c----------------------------------------------------------------------- |
| 604 |
c check hbl limits for hekman or hmonob |
| 605 |
c ph: test for zero nominator |
| 606 |
c----------------------------------------------------------------------- |
| 607 |
|
| 608 |
IF ( LimitHblStable ) THEN |
| 609 |
do i = 1, imt |
| 610 |
if (bfsfc(i) .gt. 0.0) then |
| 611 |
hekman = cekman * ustar(i) / max(abs(Coriol(i)),phepsi) |
| 612 |
hmonob = cmonob * ustar(i)*ustar(i)*ustar(i) |
| 613 |
& / vonk / bfsfc(i) |
| 614 |
hlimit = stable(i) * min(hekman,hmonob) |
| 615 |
& + (stable(i)-1.) * zgrid(Nr) |
| 616 |
hbl(i) = min(hbl(i),hlimit) |
| 617 |
end if |
| 618 |
end do |
| 619 |
ENDIF |
| 620 |
|
| 621 |
CADJ store hbl = comlev1_kpp |
| 622 |
CADJ & , key=ikppkey, kind=isbyte, |
| 623 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 624 |
|
| 625 |
do i = 1, imt |
| 626 |
hbl(i) = max(hbl(i),minKPPhbl) |
| 627 |
kbl(i) = kmtj(i) |
| 628 |
end do |
| 629 |
|
| 630 |
CADJ store hbl = comlev1_kpp |
| 631 |
CADJ & , key=ikppkey, kind=isbyte, |
| 632 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 633 |
|
| 634 |
c----------------------------------------------------------------------- |
| 635 |
c find new kbl |
| 636 |
c----------------------------------------------------------------------- |
| 637 |
|
| 638 |
do kl = 2, Nr |
| 639 |
do i = 1, imt |
| 640 |
if ( kbl(i).eq.kmtj(i) .and. (-zgrid(kl)).gt.hbl(i) ) then |
| 641 |
kbl(i) = kl |
| 642 |
endif |
| 643 |
end do |
| 644 |
end do |
| 645 |
|
| 646 |
c----------------------------------------------------------------------- |
| 647 |
c find stability and buoyancy forcing for final hbl values |
| 648 |
c----------------------------------------------------------------------- |
| 649 |
|
| 650 |
do i = 1, imt |
| 651 |
worka(i) = hbl(i) |
| 652 |
end do |
| 653 |
CADJ store worka = comlev1_kpp |
| 654 |
CADJ & , key=ikppkey, kind=isbyte, |
| 655 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 656 |
call SWFRAC( |
| 657 |
I imt, minusone, |
| 658 |
U worka, |
| 659 |
I myTime, myIter, myThid ) |
| 660 |
CADJ store worka = comlev1_kpp |
| 661 |
CADJ & , key=ikppkey, kind=isbyte, |
| 662 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 663 |
|
| 664 |
do i = 1, imt |
| 665 |
bfsfc(i) = bo(i) + bosol(i) * (1. - worka(i)) |
| 666 |
end do |
| 667 |
|
| 668 |
#ifdef ALLOW_SALT_PLUME |
| 669 |
IF ( useSALT_PLUME ) THEN |
| 670 |
do i = 1, imt |
| 671 |
worka(i) = hbl(i) |
| 672 |
enddo |
| 673 |
call SALT_PLUME_FRAC( |
| 674 |
I imt,minusone,SPDepth, |
| 675 |
U worka, |
| 676 |
I myTime, myIter, myThid ) |
| 677 |
do i = 1, imt |
| 678 |
bfsfc(i) = bfsfc(i) + boplume(i) * (1. - worka(i)) |
| 679 |
enddo |
| 680 |
ENDIF |
| 681 |
#endif /* ALLOW_SALT_PLUME */ |
| 682 |
CADJ store bfsfc = comlev1_kpp |
| 683 |
CADJ & , key=ikppkey, kind=isbyte, |
| 684 |
CADJ & shape = (/ (sNx+2*OLx)*(sNy+2*OLy) /) |
| 685 |
|
| 686 |
c-- ensures bfsfc is never 0 |
| 687 |
do i = 1, imt |
| 688 |
stable(i) = p5 + sign( p5, bfsfc(i) ) |
| 689 |
bfsfc(i) = sign(eins,bfsfc(i))*max(phepsi,abs(bfsfc(i))) |
| 690 |
end do |
| 691 |
|
| 692 |
c----------------------------------------------------------------------- |
| 693 |
c determine caseA and caseB |
| 694 |
c----------------------------------------------------------------------- |
| 695 |
|
| 696 |
do i = 1, imt |
| 697 |
casea(i) = p5 + |
| 698 |
1 sign(p5, -zgrid(kbl(i)) - p5*hwide(kbl(i)) - hbl(i)) |
| 699 |
end do |
| 700 |
|
| 701 |
#endif /* ALLOW_KPP */ |
| 702 |
|
| 703 |
return |
| 704 |
end |
| 705 |
|
| 706 |
c************************************************************************* |
| 707 |
|
| 708 |
subroutine wscale ( |
| 709 |
I sigma, hbl, ustar, bfsfc, |
| 710 |
O wm, ws, |
| 711 |
I myThid ) |
| 712 |
|
| 713 |
c compute turbulent velocity scales. |
| 714 |
c use a 2D-lookup table for wm and ws as functions of ustar and |
| 715 |
c zetahat (=vonk*sigma*hbl*bfsfc). |
| 716 |
c |
| 717 |
c note: the lookup table is only used for unstable conditions |
| 718 |
c (zehat.le.0), in the stable domain wm (=ws) gets computed |
| 719 |
c directly. |
| 720 |
c |
| 721 |
IMPLICIT NONE |
| 722 |
|
| 723 |
#include "SIZE.h" |
| 724 |
#include "KPP_PARAMS.h" |
| 725 |
|
| 726 |
c input |
| 727 |
c------ |
| 728 |
c sigma : normalized depth (d/hbl) |
| 729 |
c hbl : boundary layer depth (m) |
| 730 |
c ustar : surface friction velocity (m/s) |
| 731 |
c bfsfc : total surface buoyancy flux (m^2/s^3) |
| 732 |
c myThid : thread number for this instance of the routine |
| 733 |
integer myThid |
| 734 |
_RL sigma(imt) |
| 735 |
_RL hbl (imt) |
| 736 |
_RL ustar(imt) |
| 737 |
_RL bfsfc(imt) |
| 738 |
|
| 739 |
c output |
| 740 |
c-------- |
| 741 |
c wm, ws : turbulent velocity scales at sigma |
| 742 |
_RL wm(imt), ws(imt) |
| 743 |
|
| 744 |
#ifdef ALLOW_KPP |
| 745 |
|
| 746 |
c local |
| 747 |
c------ |
| 748 |
c zehat : = zeta * ustar**3 |
| 749 |
_RL zehat |
| 750 |
|
| 751 |
integer iz, izp1, ju, i, jup1 |
| 752 |
_RL udiff, zdiff, zfrac, ufrac, fzfrac, wam |
| 753 |
_RL wbm, was, wbs, u3, tempVar |
| 754 |
|
| 755 |
c----------------------------------------------------------------------- |
| 756 |
c use lookup table for zehat < zmax only; otherwise use |
| 757 |
c stable formulae |
| 758 |
c----------------------------------------------------------------------- |
| 759 |
|
| 760 |
do i = 1, imt |
| 761 |
zehat = vonk*sigma(i)*hbl(i)*bfsfc(i) |
| 762 |
|
| 763 |
if (zehat .le. zmax) then |
| 764 |
|
| 765 |
zdiff = zehat - zmin |
| 766 |
iz = int( zdiff / deltaz ) |
| 767 |
iz = min( iz, nni ) |
| 768 |
iz = max( iz, 0 ) |
| 769 |
izp1 = iz + 1 |
| 770 |
|
| 771 |
udiff = ustar(i) - umin |
| 772 |
ju = int( udiff / deltau ) |
| 773 |
ju = min( ju, nnj ) |
| 774 |
ju = max( ju, 0 ) |
| 775 |
jup1 = ju + 1 |
| 776 |
|
| 777 |
zfrac = zdiff / deltaz - float(iz) |
| 778 |
ufrac = udiff / deltau - float(ju) |
| 779 |
|
| 780 |
fzfrac= 1. - zfrac |
| 781 |
wam = fzfrac * wmt(iz,jup1) + zfrac * wmt(izp1,jup1) |
| 782 |
wbm = fzfrac * wmt(iz,ju ) + zfrac * wmt(izp1,ju ) |
| 783 |
wm(i) = (1.-ufrac) * wbm + ufrac * wam |
| 784 |
|
| 785 |
was = fzfrac * wst(iz,jup1) + zfrac * wst(izp1,jup1) |
| 786 |
wbs = fzfrac * wst(iz,ju ) + zfrac * wst(izp1,ju ) |
| 787 |
ws(i) = (1.-ufrac) * wbs + ufrac * was |
| 788 |
|
| 789 |
else |
| 790 |
|
| 791 |
u3 = ustar(i) * ustar(i) * ustar(i) |
| 792 |
tempVar = u3 + conc1 * zehat |
| 793 |
wm(i) = vonk * ustar(i) * u3 / tempVar |
| 794 |
ws(i) = wm(i) |
| 795 |
|
| 796 |
endif |
| 797 |
|
| 798 |
end do |
| 799 |
|
| 800 |
#endif /* ALLOW_KPP */ |
| 801 |
|
| 802 |
return |
| 803 |
end |
| 804 |
|
| 805 |
c************************************************************************* |
| 806 |
|
| 807 |
subroutine Ri_iwmix ( |
| 808 |
I kmtj, shsq, dbloc, dblocSm, |
| 809 |
I diffusKzS, diffusKzT, |
| 810 |
I ikppkey, |
| 811 |
O diffus, |
| 812 |
I myThid ) |
| 813 |
|
| 814 |
c compute interior viscosity diffusivity coefficients due |
| 815 |
c to shear instability (dependent on a local Richardson number), |
| 816 |
c to background internal wave activity, and |
| 817 |
c to static instability (local Richardson number < 0). |
| 818 |
|
| 819 |
IMPLICIT NONE |
| 820 |
|
| 821 |
#include "SIZE.h" |
| 822 |
#include "EEPARAMS.h" |
| 823 |
#include "PARAMS.h" |
| 824 |
#include "KPP_PARAMS.h" |
| 825 |
#ifdef ALLOW_AUTODIFF |
| 826 |
# include "AUTODIFF_PARAMS.h" |
| 827 |
# include "tamc.h" |
| 828 |
#endif |
| 829 |
|
| 830 |
c input |
| 831 |
c kmtj (imt) number of vertical layers on this row |
| 832 |
c shsq (imt,Nr) (local velocity shear)^2 ((m/s)^2) |
| 833 |
c dbloc (imt,Nr) local delta buoyancy (m/s^2) |
| 834 |
c dblocSm(imt,Nr) horizontally smoothed dbloc (m/s^2) |
| 835 |
c diffusKzS(imt,Nr)- background vertical diffusivity for scalars (m^2/s) |
| 836 |
c diffusKzT(imt,Nr)- background vertical diffusivity for theta (m^2/s) |
| 837 |
c myThid :: My Thread Id. number |
| 838 |
integer kmtj (imt) |
| 839 |
_RL shsq (imt,Nr) |
| 840 |
_RL dbloc (imt,Nr) |
| 841 |
_RL dblocSm (imt,Nr) |
| 842 |
_RL diffusKzS(imt,Nr) |
| 843 |
_RL diffusKzT(imt,Nr) |
| 844 |
integer ikppkey |
| 845 |
integer myThid |
| 846 |
|
| 847 |
c output |
| 848 |
c diffus(imt,0:Nrp1,1) vertical viscosivity coefficient (m^2/s) |
| 849 |
c diffus(imt,0:Nrp1,2) vertical scalar diffusivity (m^2/s) |
| 850 |
c diffus(imt,0:Nrp1,3) vertical temperature diffusivity (m^2/s) |
| 851 |
_RL diffus(imt,0:Nrp1,3) |
| 852 |
|
| 853 |
#ifdef ALLOW_KPP |
| 854 |
|
| 855 |
c local variables |
| 856 |
c Rig local Richardson number |
| 857 |
c fRi, fcon function of Rig |
| 858 |
_RL Rig |
| 859 |
_RL fRi, fcon |
| 860 |
_RL ratio |
| 861 |
integer i, ki, kp1 |
| 862 |
_RL c1, c0 |
| 863 |
|
| 864 |
#ifdef ALLOW_KPP_VERTICALLY_SMOOTH |
| 865 |
integer mr |
| 866 |
CADJ INIT kpp_ri_tape_mr = common, 1 |
| 867 |
#endif |
| 868 |
|
| 869 |
c constants |
| 870 |
c1 = 1. _d 0 |
| 871 |
c0 = 0. _d 0 |
| 872 |
|
| 873 |
c----------------------------------------------------------------------- |
| 874 |
c compute interior gradient Ri at all interfaces ki=1,Nr, (not surface) |
| 875 |
c use diffus(*,*,1) as temporary storage of Ri to be smoothed |
| 876 |
c use diffus(*,*,2) as temporary storage for Brunt-Vaisala squared |
| 877 |
c set values at bottom and below to nearest value above bottom |
| 878 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 879 |
C break data flow dependence on diffus |
| 880 |
diffus(1,1,1) = 0.0 |
| 881 |
|
| 882 |
do ki = 1, Nr |
| 883 |
do i = 1, imt |
| 884 |
diffus(i,ki,1) = 0. |
| 885 |
diffus(i,ki,2) = 0. |
| 886 |
diffus(i,ki,3) = 0. |
| 887 |
enddo |
| 888 |
enddo |
| 889 |
#endif |
| 890 |
|
| 891 |
|
| 892 |
do ki = 1, Nr |
| 893 |
do i = 1, imt |
| 894 |
if (kmtj(i) .LE. 1 ) then |
| 895 |
diffus(i,ki,1) = 0. |
| 896 |
diffus(i,ki,2) = 0. |
| 897 |
elseif (ki .GE. kmtj(i)) then |
| 898 |
diffus(i,ki,1) = diffus(i,ki-1,1) |
| 899 |
diffus(i,ki,2) = diffus(i,ki-1,2) |
| 900 |
else |
| 901 |
diffus(i,ki,1) = dblocSm(i,ki) * (zgrid(ki)-zgrid(ki+1)) |
| 902 |
& / max( Shsq(i,ki), phepsi ) |
| 903 |
diffus(i,ki,2) = dbloc(i,ki) / (zgrid(ki)-zgrid(ki+1)) |
| 904 |
endif |
| 905 |
end do |
| 906 |
end do |
| 907 |
CADJ store diffus = comlev1_kpp, key=ikppkey, kind=isbyte |
| 908 |
|
| 909 |
c----------------------------------------------------------------------- |
| 910 |
c vertically smooth Ri |
| 911 |
#ifdef ALLOW_KPP_VERTICALLY_SMOOTH |
| 912 |
do mr = 1, num_v_smooth_Ri |
| 913 |
|
| 914 |
CADJ store diffus(:,:,1) = kpp_ri_tape_mr |
| 915 |
CADJ & , key=mr, shape=(/ (sNx+2*OLx)*(sNy+2*OLy),Nr+2 /) |
| 916 |
|
| 917 |
call z121 ( |
| 918 |
U diffus(1,0,1), |
| 919 |
I myThid ) |
| 920 |
end do |
| 921 |
#endif |
| 922 |
|
| 923 |
c----------------------------------------------------------------------- |
| 924 |
c after smoothing loop |
| 925 |
|
| 926 |
do ki = 1, Nr |
| 927 |
do i = 1, imt |
| 928 |
|
| 929 |
c evaluate f of Brunt-Vaisala squared for convection, store in fcon |
| 930 |
|
| 931 |
Rig = max ( diffus(i,ki,2) , BVSQcon ) |
| 932 |
ratio = min ( (BVSQcon - Rig) / BVSQcon, c1 ) |
| 933 |
fcon = c1 - ratio * ratio |
| 934 |
fcon = fcon * fcon * fcon |
| 935 |
|
| 936 |
c evaluate f of smooth Ri for shear instability, store in fRi |
| 937 |
|
| 938 |
Rig = max ( diffus(i,ki,1), c0 ) |
| 939 |
ratio = min ( Rig / Riinfty , c1 ) |
| 940 |
fRi = c1 - ratio * ratio |
| 941 |
fRi = fRi * fRi * fRi |
| 942 |
|
| 943 |
c ---------------------------------------------------------------------- |
| 944 |
c evaluate diffusivities and viscosity |
| 945 |
c mixing due to internal waves, and shear and static instability |
| 946 |
|
| 947 |
kp1 = MIN(ki+1,Nr) |
| 948 |
#ifdef EXCLUDE_KPP_SHEAR_MIX |
| 949 |
diffus(i,ki,1) = viscArNr(1) |
| 950 |
diffus(i,ki,2) = diffusKzS(i,kp1) |
| 951 |
diffus(i,ki,3) = diffusKzT(i,kp1) |
| 952 |
#else /* EXCLUDE_KPP_SHEAR_MIX */ |
| 953 |
# ifdef ALLOW_AUTODIFF |
| 954 |
if ( inAdMode ) then |
| 955 |
diffus(i,ki,1) = viscArNr(1) |
| 956 |
diffus(i,ki,2) = diffusKzS(i,kp1) |
| 957 |
diffus(i,ki,3) = diffusKzT(i,kp1) |
| 958 |
else |
| 959 |
# else /* ALLOW_AUTODIFF */ |
| 960 |
if ( .TRUE. ) then |
| 961 |
# endif /* ALLOW_AUTODIFF */ |
| 962 |
diffus(i,ki,1) = viscArNr(1) + fcon*difmcon + fRi*difm0 |
| 963 |
diffus(i,ki,2) = diffusKzS(i,kp1)+fcon*difscon+fRi*difs0 |
| 964 |
diffus(i,ki,3) = diffusKzT(i,kp1)+fcon*diftcon+fRi*dift0 |
| 965 |
endif |
| 966 |
#endif /* EXCLUDE_KPP_SHEAR_MIX */ |
| 967 |
end do |
| 968 |
end do |
| 969 |
|
| 970 |
c ------------------------------------------------------------------------ |
| 971 |
c set surface values to 0.0 |
| 972 |
|
| 973 |
do i = 1, imt |
| 974 |
diffus(i,0,1) = c0 |
| 975 |
diffus(i,0,2) = c0 |
| 976 |
diffus(i,0,3) = c0 |
| 977 |
end do |
| 978 |
|
| 979 |
#endif /* ALLOW_KPP */ |
| 980 |
|
| 981 |
return |
| 982 |
end |
| 983 |
|
| 984 |
c************************************************************************* |
| 985 |
|
| 986 |
subroutine z121 ( |
| 987 |
U v, |
| 988 |
I myThid ) |
| 989 |
|
| 990 |
c Apply 121 smoothing in k to 2-d array V(i,k=1,Nr) |
| 991 |
c top (0) value is used as a dummy |
| 992 |
c bottom (Nrp1) value is set to input value from above. |
| 993 |
|
| 994 |
c Note that it is important to exclude from the smoothing any points |
| 995 |
c that are outside the range of the K(Ri) scheme, ie. >0.8, or <0.0. |
| 996 |
c Otherwise, there is interference with other physics, especially |
| 997 |
c penetrative convection. |
| 998 |
|
| 999 |
IMPLICIT NONE |
| 1000 |
#include "SIZE.h" |
| 1001 |
#include "KPP_PARAMS.h" |
| 1002 |
|
| 1003 |
c input/output |
| 1004 |
c------------- |
| 1005 |
c v : 2-D array to be smoothed in Nrp1 direction |
| 1006 |
c myThid: thread number for this instance of the routine |
| 1007 |
integer myThid |
| 1008 |
_RL v(imt,0:Nrp1) |
| 1009 |
|
| 1010 |
#ifdef ALLOW_KPP |
| 1011 |
|
| 1012 |
c local |
| 1013 |
_RL zwork, zflag |
| 1014 |
_RL KRi_range(1:Nrp1) |
| 1015 |
integer i, k, km1, kp1 |
| 1016 |
|
| 1017 |
_RL p0 , p25 , p5 , p2 |
| 1018 |
parameter ( p0 = 0.0, p25 = 0.25, p5 = 0.5, p2 = 2.0 ) |
| 1019 |
|
| 1020 |
KRi_range(Nrp1) = p0 |
| 1021 |
|
| 1022 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 1023 |
C-- dummy assignment to end declaration part for TAMC |
| 1024 |
i = 0 |
| 1025 |
|
| 1026 |
C-- HPF directive to help TAMC |
| 1027 |
CHPF$ INDEPENDENT |
| 1028 |
CADJ INIT z121tape = common, Nr |
| 1029 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 1030 |
|
| 1031 |
do i = 1, imt |
| 1032 |
|
| 1033 |
k = 1 |
| 1034 |
CADJ STORE v(i,k) = z121tape |
| 1035 |
v(i,Nrp1) = v(i,Nr) |
| 1036 |
|
| 1037 |
do k = 1, Nr |
| 1038 |
KRi_range(k) = p5 + SIGN(p5,v(i,k)) |
| 1039 |
KRi_range(k) = KRi_range(k) * |
| 1040 |
& ( p5 + SIGN(p5,(Riinfty-v(i,k))) ) |
| 1041 |
end do |
| 1042 |
|
| 1043 |
zwork = KRi_range(1) * v(i,1) |
| 1044 |
v(i,1) = p2 * v(i,1) + |
| 1045 |
& KRi_range(1) * KRi_range(2) * v(i,2) |
| 1046 |
zflag = p2 + KRi_range(1) * KRi_range(2) |
| 1047 |
v(i,1) = v(i,1) / zflag |
| 1048 |
|
| 1049 |
do k = 2, Nr |
| 1050 |
CADJ STORE v(i,k), zwork = z121tape |
| 1051 |
km1 = k - 1 |
| 1052 |
kp1 = k + 1 |
| 1053 |
zflag = v(i,k) |
| 1054 |
v(i,k) = p2 * v(i,k) + |
| 1055 |
& KRi_range(k) * KRi_range(kp1) * v(i,kp1) + |
| 1056 |
& KRi_range(k) * zwork |
| 1057 |
zwork = KRi_range(k) * zflag |
| 1058 |
zflag = p2 + KRi_range(k)*(KRi_range(kp1)+KRi_range(km1)) |
| 1059 |
v(i,k) = v(i,k) / zflag |
| 1060 |
end do |
| 1061 |
|
| 1062 |
end do |
| 1063 |
|
| 1064 |
#endif /* ALLOW_KPP */ |
| 1065 |
|
| 1066 |
return |
| 1067 |
end |
| 1068 |
|
| 1069 |
c************************************************************************* |
| 1070 |
|
| 1071 |
subroutine smooth_horiz ( |
| 1072 |
I k, bi, bj, |
| 1073 |
U fld, |
| 1074 |
I myThid ) |
| 1075 |
|
| 1076 |
c Apply horizontal smoothing to global _RL 2-D array |
| 1077 |
|
| 1078 |
IMPLICIT NONE |
| 1079 |
#include "SIZE.h" |
| 1080 |
#include "GRID.h" |
| 1081 |
#include "KPP_PARAMS.h" |
| 1082 |
|
| 1083 |
c input |
| 1084 |
c bi, bj : array indices |
| 1085 |
c k : vertical index used for masking |
| 1086 |
c myThid : thread number for this instance of the routine |
| 1087 |
INTEGER myThid |
| 1088 |
integer k, bi, bj |
| 1089 |
|
| 1090 |
c input/output |
| 1091 |
c fld : 2-D array to be smoothed |
| 1092 |
_RL fld( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
| 1093 |
|
| 1094 |
#ifdef ALLOW_KPP |
| 1095 |
|
| 1096 |
c local |
| 1097 |
integer i, j, im1, ip1, jm1, jp1 |
| 1098 |
_RL tempVar |
| 1099 |
_RL fld_tmp( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
| 1100 |
|
| 1101 |
integer imin , imax , jmin , jmax |
| 1102 |
parameter(imin=2-OLx, imax=sNx+OLx-1, jmin=2-OLy, jmax=sNy+OLy-1) |
| 1103 |
|
| 1104 |
_RL p0 , p5 , p25 , p125 , p0625 |
| 1105 |
parameter( p0=0.0, p5=0.5, p25=0.25, p125=0.125, p0625=0.0625 ) |
| 1106 |
|
| 1107 |
DO j = jmin, jmax |
| 1108 |
jm1 = j-1 |
| 1109 |
jp1 = j+1 |
| 1110 |
DO i = imin, imax |
| 1111 |
im1 = i-1 |
| 1112 |
ip1 = i+1 |
| 1113 |
tempVar = |
| 1114 |
& p25 * maskC(i ,j ,k,bi,bj) + |
| 1115 |
& p125 * ( maskC(im1,j ,k,bi,bj) + |
| 1116 |
& maskC(ip1,j ,k,bi,bj) + |
| 1117 |
& maskC(i ,jm1,k,bi,bj) + |
| 1118 |
& maskC(i ,jp1,k,bi,bj) ) + |
| 1119 |
& p0625 * ( maskC(im1,jm1,k,bi,bj) + |
| 1120 |
& maskC(im1,jp1,k,bi,bj) + |
| 1121 |
& maskC(ip1,jm1,k,bi,bj) + |
| 1122 |
& maskC(ip1,jp1,k,bi,bj) ) |
| 1123 |
IF ( tempVar .GE. p25 ) THEN |
| 1124 |
fld_tmp(i,j) = ( |
| 1125 |
& p25 * fld(i ,j )*maskC(i ,j ,k,bi,bj) + |
| 1126 |
& p125 *(fld(im1,j )*maskC(im1,j ,k,bi,bj) + |
| 1127 |
& fld(ip1,j )*maskC(ip1,j ,k,bi,bj) + |
| 1128 |
& fld(i ,jm1)*maskC(i ,jm1,k,bi,bj) + |
| 1129 |
& fld(i ,jp1)*maskC(i ,jp1,k,bi,bj))+ |
| 1130 |
& p0625*(fld(im1,jm1)*maskC(im1,jm1,k,bi,bj) + |
| 1131 |
& fld(im1,jp1)*maskC(im1,jp1,k,bi,bj) + |
| 1132 |
& fld(ip1,jm1)*maskC(ip1,jm1,k,bi,bj) + |
| 1133 |
& fld(ip1,jp1)*maskC(ip1,jp1,k,bi,bj))) |
| 1134 |
& / tempVar |
| 1135 |
ELSE |
| 1136 |
fld_tmp(i,j) = fld(i,j) |
| 1137 |
ENDIF |
| 1138 |
ENDDO |
| 1139 |
ENDDO |
| 1140 |
|
| 1141 |
c transfer smoothed field to output array |
| 1142 |
DO j = jmin, jmax |
| 1143 |
DO i = imin, imax |
| 1144 |
fld(i,j) = fld_tmp(i,j) |
| 1145 |
ENDDO |
| 1146 |
ENDDO |
| 1147 |
|
| 1148 |
#endif /* ALLOW_KPP */ |
| 1149 |
|
| 1150 |
return |
| 1151 |
end |
| 1152 |
|
| 1153 |
c************************************************************************* |
| 1154 |
|
| 1155 |
subroutine blmix ( |
| 1156 |
I ustar, bfsfc, hbl, stable, casea, diffus, kbl |
| 1157 |
O , dkm1, blmc, ghat, sigma, ikppkey |
| 1158 |
I , myThid ) |
| 1159 |
|
| 1160 |
c mixing coefficients within boundary layer depend on surface |
| 1161 |
c forcing and the magnitude and gradient of interior mixing below |
| 1162 |
c the boundary layer ("matching"). |
| 1163 |
c |
| 1164 |
c caution: if mixing bottoms out at hbl = -zgrid(Nr) then |
| 1165 |
c fictitious layer at Nrp1 is needed with small but finite width |
| 1166 |
c hwide(Nrp1) (eg. epsln = 1.e-20). |
| 1167 |
c |
| 1168 |
IMPLICIT NONE |
| 1169 |
|
| 1170 |
#include "SIZE.h" |
| 1171 |
#include "KPP_PARAMS.h" |
| 1172 |
#ifdef ALLOW_AUTODIFF |
| 1173 |
# include "tamc.h" |
| 1174 |
#endif |
| 1175 |
|
| 1176 |
c input |
| 1177 |
c ustar (imt) surface friction velocity (m/s) |
| 1178 |
c bfsfc (imt) surface buoyancy forcing (m^2/s^3) |
| 1179 |
c hbl (imt) boundary layer depth (m) |
| 1180 |
c stable(imt) = 1 in stable forcing |
| 1181 |
c casea (imt) = 1 in case A |
| 1182 |
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
| 1183 |
c kbl (imt) -1 of first grid level below hbl |
| 1184 |
c myThid thread number for this instance of the routine |
| 1185 |
integer myThid |
| 1186 |
_RL ustar (imt) |
| 1187 |
_RL bfsfc (imt) |
| 1188 |
_RL hbl (imt) |
| 1189 |
_RL stable(imt) |
| 1190 |
_RL casea (imt) |
| 1191 |
_RL diffus(imt,0:Nrp1,mdiff) |
| 1192 |
integer kbl(imt) |
| 1193 |
|
| 1194 |
c output |
| 1195 |
c dkm1 (imt,mdiff) boundary layer difs at kbl-1 level |
| 1196 |
c blmc (imt,Nr,mdiff) boundary layer mixing coefficients (m^2/s) |
| 1197 |
c ghat (imt,Nr) nonlocal scalar transport |
| 1198 |
c sigma(imt) normalized depth (d / hbl) |
| 1199 |
_RL dkm1 (imt,mdiff) |
| 1200 |
_RL blmc (imt,Nr,mdiff) |
| 1201 |
_RL ghat (imt,Nr) |
| 1202 |
_RL sigma(imt) |
| 1203 |
integer ikppkey |
| 1204 |
|
| 1205 |
#ifdef ALLOW_KPP |
| 1206 |
|
| 1207 |
c local |
| 1208 |
c gat1*(imt) shape function at sigma = 1 |
| 1209 |
c dat1*(imt) derivative of shape function at sigma = 1 |
| 1210 |
c ws(imt), wm(imt) turbulent velocity scales (m/s) |
| 1211 |
_RL gat1m(imt), gat1s(imt), gat1t(imt) |
| 1212 |
_RL dat1m(imt), dat1s(imt), dat1t(imt) |
| 1213 |
_RL ws(imt), wm(imt) |
| 1214 |
integer i, kn, ki |
| 1215 |
_RL R, dvdzup, dvdzdn, viscp |
| 1216 |
_RL difsp, diftp, visch, difsh, difth |
| 1217 |
_RL f1, sig, a1, a2, a3, delhat |
| 1218 |
_RL Gm, Gs, Gt |
| 1219 |
_RL tempVar |
| 1220 |
|
| 1221 |
_RL p0 , eins |
| 1222 |
parameter (p0=0.0, eins=1.0) |
| 1223 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 1224 |
integer kkppkey |
| 1225 |
#endif |
| 1226 |
|
| 1227 |
c----------------------------------------------------------------------- |
| 1228 |
c compute velocity scales at hbl |
| 1229 |
c----------------------------------------------------------------------- |
| 1230 |
|
| 1231 |
do i = 1, imt |
| 1232 |
sigma(i) = stable(i) * 1.0 + (1. - stable(i)) * epsilon |
| 1233 |
end do |
| 1234 |
|
| 1235 |
CADJ STORE sigma = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1236 |
call wscale ( |
| 1237 |
I sigma, hbl, ustar, bfsfc, |
| 1238 |
O wm, ws, myThid ) |
| 1239 |
CADJ STORE wm = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1240 |
CADJ STORE ws = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1241 |
|
| 1242 |
do i = 1, imt |
| 1243 |
wm(i) = sign(eins,wm(i))*max(phepsi,abs(wm(i))) |
| 1244 |
ws(i) = sign(eins,ws(i))*max(phepsi,abs(ws(i))) |
| 1245 |
end do |
| 1246 |
CADJ STORE wm = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1247 |
CADJ STORE ws = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1248 |
|
| 1249 |
do i = 1, imt |
| 1250 |
|
| 1251 |
kn = int(caseA(i)+phepsi) *(kbl(i) -1) + |
| 1252 |
$ (1 - int(caseA(i)+phepsi)) * kbl(i) |
| 1253 |
|
| 1254 |
c----------------------------------------------------------------------- |
| 1255 |
c find the interior viscosities and derivatives at hbl(i) |
| 1256 |
c----------------------------------------------------------------------- |
| 1257 |
|
| 1258 |
delhat = 0.5*hwide(kn) - zgrid(kn) - hbl(i) |
| 1259 |
R = 1.0 - delhat / hwide(kn) |
| 1260 |
dvdzup = (diffus(i,kn-1,1) - diffus(i,kn ,1)) / hwide(kn) |
| 1261 |
dvdzdn = (diffus(i,kn ,1) - diffus(i,kn+1,1)) / hwide(kn+1) |
| 1262 |
viscp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
| 1263 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
| 1264 |
|
| 1265 |
dvdzup = (diffus(i,kn-1,2) - diffus(i,kn ,2)) / hwide(kn) |
| 1266 |
dvdzdn = (diffus(i,kn ,2) - diffus(i,kn+1,2)) / hwide(kn+1) |
| 1267 |
difsp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
| 1268 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
| 1269 |
|
| 1270 |
dvdzup = (diffus(i,kn-1,3) - diffus(i,kn ,3)) / hwide(kn) |
| 1271 |
dvdzdn = (diffus(i,kn ,3) - diffus(i,kn+1,3)) / hwide(kn+1) |
| 1272 |
diftp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup)) + |
| 1273 |
1 R * (dvdzdn + abs(dvdzdn)) ) |
| 1274 |
|
| 1275 |
visch = diffus(i,kn,1) + viscp * delhat |
| 1276 |
difsh = diffus(i,kn,2) + difsp * delhat |
| 1277 |
difth = diffus(i,kn,3) + diftp * delhat |
| 1278 |
|
| 1279 |
f1 = stable(i) * conc1 * bfsfc(i) / |
| 1280 |
& max(ustar(i)**4,phepsi) |
| 1281 |
gat1m(i) = visch / hbl(i) / wm(i) |
| 1282 |
dat1m(i) = -viscp / wm(i) + f1 * visch |
| 1283 |
|
| 1284 |
gat1s(i) = difsh / hbl(i) / ws(i) |
| 1285 |
dat1s(i) = -difsp / ws(i) + f1 * difsh |
| 1286 |
|
| 1287 |
gat1t(i) = difth / hbl(i) / ws(i) |
| 1288 |
dat1t(i) = -diftp / ws(i) + f1 * difth |
| 1289 |
|
| 1290 |
end do |
| 1291 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1292 |
CADJ STORE gat1m = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1293 |
CADJ STORE gat1s = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1294 |
CADJ STORE gat1t = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1295 |
CADJ STORE dat1m = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1296 |
CADJ STORE dat1s = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1297 |
CADJ STORE dat1t = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1298 |
#endif |
| 1299 |
do i = 1, imt |
| 1300 |
dat1m(i) = min(dat1m(i),p0) |
| 1301 |
dat1s(i) = min(dat1s(i),p0) |
| 1302 |
dat1t(i) = min(dat1t(i),p0) |
| 1303 |
end do |
| 1304 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1305 |
CADJ STORE dat1m = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1306 |
CADJ STORE dat1s = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1307 |
CADJ STORE dat1t = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1308 |
#endif |
| 1309 |
|
| 1310 |
do ki = 1, Nr |
| 1311 |
|
| 1312 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 1313 |
kkppkey = (ikppkey-1)*Nr + ki |
| 1314 |
#endif |
| 1315 |
|
| 1316 |
c----------------------------------------------------------------------- |
| 1317 |
c compute turbulent velocity scales on the interfaces |
| 1318 |
c----------------------------------------------------------------------- |
| 1319 |
|
| 1320 |
do i = 1, imt |
| 1321 |
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
| 1322 |
sigma(i) = stable(i)*sig + (1.-stable(i))*min(sig,epsilon) |
| 1323 |
end do |
| 1324 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1325 |
CADJ STORE wm = comlev1_kpp_k, key = kkppkey |
| 1326 |
CADJ STORE ws = comlev1_kpp_k, key = kkppkey |
| 1327 |
#endif |
| 1328 |
CADJ STORE sigma = comlev1_kpp_k, key = kkppkey |
| 1329 |
call wscale ( |
| 1330 |
I sigma, hbl, ustar, bfsfc, |
| 1331 |
O wm, ws, myThid ) |
| 1332 |
CADJ STORE wm = comlev1_kpp_k, key = kkppkey |
| 1333 |
CADJ STORE ws = comlev1_kpp_k, key = kkppkey |
| 1334 |
|
| 1335 |
c----------------------------------------------------------------------- |
| 1336 |
c compute the dimensionless shape functions at the interfaces |
| 1337 |
c----------------------------------------------------------------------- |
| 1338 |
|
| 1339 |
do i = 1, imt |
| 1340 |
sig = (-zgrid(ki) + 0.5 * hwide(ki)) / hbl(i) |
| 1341 |
a1 = sig - 2. |
| 1342 |
a2 = 3. - 2. * sig |
| 1343 |
a3 = sig - 1. |
| 1344 |
|
| 1345 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
| 1346 |
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
| 1347 |
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
| 1348 |
|
| 1349 |
c----------------------------------------------------------------------- |
| 1350 |
c compute boundary layer diffusivities at the interfaces |
| 1351 |
c----------------------------------------------------------------------- |
| 1352 |
|
| 1353 |
blmc(i,ki,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
| 1354 |
blmc(i,ki,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
| 1355 |
blmc(i,ki,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
| 1356 |
|
| 1357 |
c----------------------------------------------------------------------- |
| 1358 |
c nonlocal transport term = ghat * <ws>o |
| 1359 |
c----------------------------------------------------------------------- |
| 1360 |
|
| 1361 |
tempVar = ws(i) * hbl(i) |
| 1362 |
ghat(i,ki) = (1.-stable(i)) * cg / max(phepsi,tempVar) |
| 1363 |
|
| 1364 |
end do |
| 1365 |
end do |
| 1366 |
|
| 1367 |
c----------------------------------------------------------------------- |
| 1368 |
c find diffusivities at kbl-1 grid level |
| 1369 |
c----------------------------------------------------------------------- |
| 1370 |
|
| 1371 |
do i = 1, imt |
| 1372 |
sig = -zgrid(kbl(i)-1) / hbl(i) |
| 1373 |
sigma(i) = stable(i) * sig |
| 1374 |
& + (1. - stable(i)) * min(sig,epsilon) |
| 1375 |
end do |
| 1376 |
|
| 1377 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1378 |
CADJ STORE wm = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1379 |
CADJ STORE ws = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1380 |
#endif |
| 1381 |
CADJ STORE sigma = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1382 |
call wscale ( |
| 1383 |
I sigma, hbl, ustar, bfsfc, |
| 1384 |
O wm, ws, myThid ) |
| 1385 |
CADJ STORE wm = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1386 |
CADJ STORE ws = comlev1_kpp, key=ikppkey, kind=isbyte |
| 1387 |
|
| 1388 |
do i = 1, imt |
| 1389 |
sig = -zgrid(kbl(i)-1) / hbl(i) |
| 1390 |
a1 = sig - 2. |
| 1391 |
a2 = 3. - 2. * sig |
| 1392 |
a3 = sig - 1. |
| 1393 |
Gm = a1 + a2 * gat1m(i) + a3 * dat1m(i) |
| 1394 |
Gs = a1 + a2 * gat1s(i) + a3 * dat1s(i) |
| 1395 |
Gt = a1 + a2 * gat1t(i) + a3 * dat1t(i) |
| 1396 |
dkm1(i,1) = hbl(i) * wm(i) * sig * (1. + sig * Gm) |
| 1397 |
dkm1(i,2) = hbl(i) * ws(i) * sig * (1. + sig * Gs) |
| 1398 |
dkm1(i,3) = hbl(i) * ws(i) * sig * (1. + sig * Gt) |
| 1399 |
end do |
| 1400 |
|
| 1401 |
#endif /* ALLOW_KPP */ |
| 1402 |
|
| 1403 |
return |
| 1404 |
end |
| 1405 |
|
| 1406 |
c************************************************************************* |
| 1407 |
|
| 1408 |
subroutine enhance ( |
| 1409 |
I dkm1, hbl, kbl, diffus, casea |
| 1410 |
U , ghat |
| 1411 |
O , blmc |
| 1412 |
& , myThid ) |
| 1413 |
|
| 1414 |
c enhance the diffusivity at the kbl-.5 interface |
| 1415 |
|
| 1416 |
IMPLICIT NONE |
| 1417 |
|
| 1418 |
#include "SIZE.h" |
| 1419 |
#include "KPP_PARAMS.h" |
| 1420 |
|
| 1421 |
c input |
| 1422 |
c dkm1(imt,mdiff) bl diffusivity at kbl-1 grid level |
| 1423 |
c hbl(imt) boundary layer depth (m) |
| 1424 |
c kbl(imt) grid above hbl |
| 1425 |
c diffus(imt,0:Nrp1,mdiff) vertical diffusivities (m^2/s) |
| 1426 |
c casea(imt) = 1 in caseA, = 0 in case B |
| 1427 |
c myThid thread number for this instance of the routine |
| 1428 |
integer myThid |
| 1429 |
_RL dkm1 (imt,mdiff) |
| 1430 |
_RL hbl (imt) |
| 1431 |
integer kbl (imt) |
| 1432 |
_RL diffus(imt,0:Nrp1,mdiff) |
| 1433 |
_RL casea (imt) |
| 1434 |
|
| 1435 |
c input/output |
| 1436 |
c nonlocal transport, modified ghat at kbl(i)-1 interface (s/m**2) |
| 1437 |
_RL ghat (imt,Nr) |
| 1438 |
|
| 1439 |
c output |
| 1440 |
c enhanced bound. layer mixing coeff. |
| 1441 |
_RL blmc (imt,Nr,mdiff) |
| 1442 |
|
| 1443 |
#ifdef ALLOW_KPP |
| 1444 |
|
| 1445 |
c local |
| 1446 |
c fraction hbl lies beteen zgrid neighbors |
| 1447 |
_RL delta |
| 1448 |
integer ki, i, md |
| 1449 |
_RL dkmp5, dstar |
| 1450 |
|
| 1451 |
do i = 1, imt |
| 1452 |
ki = kbl(i)-1 |
| 1453 |
if ((ki .ge. 1) .and. (ki .lt. Nr)) then |
| 1454 |
delta = (hbl(i) + zgrid(ki)) / (zgrid(ki) - zgrid(ki+1)) |
| 1455 |
do md = 1, mdiff |
| 1456 |
dkmp5 = casea(i) * diffus(i,ki,md) + |
| 1457 |
1 (1.- casea(i)) * blmc (i,ki,md) |
| 1458 |
dstar = (1.- delta)**2 * dkm1(i,md) |
| 1459 |
& + delta**2 * dkmp5 |
| 1460 |
blmc(i,ki,md) = (1.- delta)*diffus(i,ki,md) |
| 1461 |
& + delta*dstar |
| 1462 |
end do |
| 1463 |
ghat(i,ki) = (1.- casea(i)) * ghat(i,ki) |
| 1464 |
endif |
| 1465 |
end do |
| 1466 |
|
| 1467 |
#endif /* ALLOW_KPP */ |
| 1468 |
|
| 1469 |
return |
| 1470 |
end |
| 1471 |
|
| 1472 |
c************************************************************************* |
| 1473 |
|
| 1474 |
SUBROUTINE STATEKPP ( |
| 1475 |
O RHO1, DBLOC, DBSFC, TTALPHA, SSBETA, |
| 1476 |
I ikppkey, bi, bj, myThid ) |
| 1477 |
c |
| 1478 |
c----------------------------------------------------------------------- |
| 1479 |
c "statekpp" computes all necessary input arrays |
| 1480 |
c for the kpp mixing scheme |
| 1481 |
c |
| 1482 |
c input: |
| 1483 |
c bi, bj = array indices on which to apply calculations |
| 1484 |
c |
| 1485 |
c output: |
| 1486 |
c rho1 = potential density of surface layer (kg/m^3) |
| 1487 |
c dbloc = local buoyancy gradient at Nr interfaces |
| 1488 |
c g/rho{k+1,k+1} * [ drho{k,k+1}-drho{k+1,k+1} ] (m/s^2) |
| 1489 |
c dbsfc = buoyancy difference with respect to the surface |
| 1490 |
c g * [ drho{1,k}/rho{1,k} - drho{k,k}/rho{k,k} ] (m/s^2) |
| 1491 |
c ttalpha= thermal expansion coefficient without 1/rho factor |
| 1492 |
c d(rho) / d(potential temperature) (kg/m^3/C) |
| 1493 |
c ssbeta = salt expansion coefficient without 1/rho factor |
| 1494 |
c d(rho) / d(salinity) (kg/m^3/PSU) |
| 1495 |
c |
| 1496 |
c see also subroutines find_rho.F find_alpha.F find_beta.F |
| 1497 |
c |
| 1498 |
c written by: jan morzel, feb. 10, 1995 (converted from "sigma" version) |
| 1499 |
c modified by: d. menemenlis, june 1998 : for use with MIT GCM UV |
| 1500 |
c |
| 1501 |
|
| 1502 |
c----------------------------------------------------------------------- |
| 1503 |
|
| 1504 |
IMPLICIT NONE |
| 1505 |
|
| 1506 |
#include "SIZE.h" |
| 1507 |
#include "EEPARAMS.h" |
| 1508 |
#include "PARAMS.h" |
| 1509 |
#include "KPP_PARAMS.h" |
| 1510 |
#include "DYNVARS.h" |
| 1511 |
#include "GRID.h" |
| 1512 |
#ifdef ALLOW_AUTODIFF |
| 1513 |
# include "tamc.h" |
| 1514 |
#endif |
| 1515 |
|
| 1516 |
c-------------- Routine arguments ----------------------------------------- |
| 1517 |
INTEGER bi, bj, myThid |
| 1518 |
_RL RHO1 ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
| 1519 |
_RL DBLOC ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nr ) |
| 1520 |
_RL DBSFC ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nr ) |
| 1521 |
_RL TTALPHA( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nrp1 ) |
| 1522 |
_RL SSBETA ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nrp1 ) |
| 1523 |
|
| 1524 |
#ifdef ALLOW_KPP |
| 1525 |
|
| 1526 |
c-------------------------------------------------------------------------- |
| 1527 |
c |
| 1528 |
c local arrays: |
| 1529 |
c |
| 1530 |
c rhok - density of t(k ) & s(k ) at depth k |
| 1531 |
c rhokm1 - density of t(k-1) & s(k-1) at depth k |
| 1532 |
c rho1k - density of t(1 ) & s(1 ) at depth k |
| 1533 |
c work1,2,3 - work arrays for holding horizontal slabs |
| 1534 |
|
| 1535 |
_RL RHOK (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1536 |
_RL RHOKM1(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1537 |
_RL RHO1K (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1538 |
_RL WORK1 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1539 |
_RL WORK2 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1540 |
_RL WORK3 (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 1541 |
|
| 1542 |
INTEGER I, J, K |
| 1543 |
INTEGER ikppkey, kkppkey |
| 1544 |
|
| 1545 |
c calculate density, alpha, beta in surface layer, and set dbsfc to zero |
| 1546 |
|
| 1547 |
kkppkey = (ikppkey-1)*Nr + 1 |
| 1548 |
|
| 1549 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1550 |
CADJ STORE theta(:,:,1,bi,bj) = comlev1_kpp_k, |
| 1551 |
CADJ & key=kkppkey, kind=isbyte |
| 1552 |
CADJ STORE salt (:,:,1,bi,bj) = comlev1_kpp_k, |
| 1553 |
CADJ & key=kkppkey, kind=isbyte |
| 1554 |
#endif /* KPP_AUTODIFF_EXCESSIVE_STORE */ |
| 1555 |
CALL FIND_RHO_2D( |
| 1556 |
I 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, 1, |
| 1557 |
I theta(1-OLx,1-OLy,1,bi,bj), salt(1-OLx,1-OLy,1,bi,bj), |
| 1558 |
O WORK1, |
| 1559 |
I 1, bi, bj, myThid ) |
| 1560 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1561 |
CADJ STORE theta(:,:,1,bi,bj) = comlev1_kpp_k, |
| 1562 |
CADJ & key=kkppkey, kind=isbyte |
| 1563 |
CADJ STORE salt (:,:,1,bi,bj) = comlev1_kpp_k, |
| 1564 |
CADJ & key=kkppkey, kind=isbyte |
| 1565 |
#endif /* KPP_AUTODIFF_EXCESSIVE_STORE */ |
| 1566 |
|
| 1567 |
call FIND_ALPHA( |
| 1568 |
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, 1, 1, |
| 1569 |
O WORK2, myThid ) |
| 1570 |
|
| 1571 |
call FIND_BETA( |
| 1572 |
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, 1, 1, |
| 1573 |
O WORK3, myThid ) |
| 1574 |
|
| 1575 |
DO J = 1-OLy, sNy+OLy |
| 1576 |
DO I = 1-OLx, sNx+OLx |
| 1577 |
RHO1(I,J) = WORK1(I,J) + rhoConst |
| 1578 |
TTALPHA(I,J,1) = WORK2(I,J) |
| 1579 |
SSBETA(I,J,1) = WORK3(I,J) |
| 1580 |
DBSFC(I,J,1) = 0. |
| 1581 |
END DO |
| 1582 |
END DO |
| 1583 |
|
| 1584 |
c calculate alpha, beta, and gradients in interior layers |
| 1585 |
|
| 1586 |
CHPF$ INDEPENDENT, NEW (RHOK,RHOKM1,RHO1K,WORK1,WORK2) |
| 1587 |
DO K = 2, Nr |
| 1588 |
|
| 1589 |
kkppkey = (ikppkey-1)*Nr + k |
| 1590 |
|
| 1591 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1592 |
CADJ STORE theta(:,:,k,bi,bj) = comlev1_kpp_k, |
| 1593 |
CADJ & key=kkppkey, kind=isbyte |
| 1594 |
CADJ STORE salt (:,:,k,bi,bj) = comlev1_kpp_k, |
| 1595 |
CADJ & key=kkppkey, kind=isbyte |
| 1596 |
#endif /* KPP_AUTODIFF_EXCESSIVE_STORE */ |
| 1597 |
CALL FIND_RHO_2D( |
| 1598 |
I 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, k, |
| 1599 |
I theta(1-OLx,1-OLy,k,bi,bj), salt(1-OLx,1-OLy,k,bi,bj), |
| 1600 |
O RHOK, |
| 1601 |
I k, bi, bj, myThid ) |
| 1602 |
|
| 1603 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1604 |
CADJ STORE theta(:,:,k-1,bi,bj) = comlev1_kpp_k, |
| 1605 |
CADJ & key=kkppkey, kind=isbyte |
| 1606 |
CADJ STORE salt (:,:,k-1,bi,bj) = comlev1_kpp_k, |
| 1607 |
CADJ & key=kkppkey, kind=isbyte |
| 1608 |
#endif /* KPP_AUTODIFF_EXCESSIVE_STORE */ |
| 1609 |
CALL FIND_RHO_2D( |
| 1610 |
I 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, k, |
| 1611 |
I theta(1-OLx,1-OLy,k-1,bi,bj),salt(1-OLx,1-OLy,k-1,bi,bj), |
| 1612 |
O RHOKM1, |
| 1613 |
I k-1, bi, bj, myThid ) |
| 1614 |
|
| 1615 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1616 |
CADJ STORE theta(:,:,1,bi,bj) = comlev1_kpp_k, |
| 1617 |
CADJ & key=kkppkey, kind=isbyte |
| 1618 |
CADJ STORE salt (:,:,1,bi,bj) = comlev1_kpp_k, |
| 1619 |
CADJ & key=kkppkey, kind=isbyte |
| 1620 |
#endif /* KPP_AUTODIFF_EXCESSIVE_STORE */ |
| 1621 |
CALL FIND_RHO_2D( |
| 1622 |
I 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, k, |
| 1623 |
I theta(1-OLx,1-OLy,1,bi,bj), salt(1-OLx,1-OLy,1,bi,bj), |
| 1624 |
O RHO1K, |
| 1625 |
I 1, bi, bj, myThid ) |
| 1626 |
|
| 1627 |
#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1628 |
CADJ STORE rhok (:,:) = comlev1_kpp_k, |
| 1629 |
CADJ & key=kkppkey, kind=isbyte |
| 1630 |
CADJ STORE rhokm1(:,:) = comlev1_kpp_k, |
| 1631 |
CADJ & key=kkppkey, kind=isbyte |
| 1632 |
CADJ STORE rho1k (:,:) = comlev1_kpp_k, |
| 1633 |
CADJ & key=kkppkey, kind=isbyte |
| 1634 |
#endif /* KPP_AUTODIFF_EXCESSIVE_STORE */ |
| 1635 |
|
| 1636 |
call FIND_ALPHA( |
| 1637 |
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, K, K, |
| 1638 |
O WORK1, myThid ) |
| 1639 |
|
| 1640 |
call FIND_BETA( |
| 1641 |
I bi, bj, 1-OLx, sNx+OLx, 1-OLy, sNy+OLy, K, K, |
| 1642 |
O WORK2, myThid ) |
| 1643 |
|
| 1644 |
DO J = 1-OLy, sNy+OLy |
| 1645 |
DO I = 1-OLx, sNx+OLx |
| 1646 |
TTALPHA(I,J,K) = WORK1 (I,J) |
| 1647 |
SSBETA(I,J,K) = WORK2 (I,J) |
| 1648 |
DBLOC(I,J,K-1) = gravity * (RHOK(I,J) - RHOKM1(I,J)) / |
| 1649 |
& (RHOK(I,J) + rhoConst) |
| 1650 |
DBSFC(I,J,K) = gravity * (RHOK(I,J) - RHO1K (I,J)) / |
| 1651 |
& (RHOK(I,J) + rhoConst) |
| 1652 |
END DO |
| 1653 |
END DO |
| 1654 |
|
| 1655 |
END DO |
| 1656 |
|
| 1657 |
c compute arrays for K = Nrp1 |
| 1658 |
DO J = 1-OLy, sNy+OLy |
| 1659 |
DO I = 1-OLx, sNx+OLx |
| 1660 |
TTALPHA(I,J,Nrp1) = TTALPHA(I,J,Nr) |
| 1661 |
SSBETA(I,J,Nrp1) = SSBETA(I,J,Nr) |
| 1662 |
DBLOC(I,J,Nr) = 0. |
| 1663 |
END DO |
| 1664 |
END DO |
| 1665 |
|
| 1666 |
#ifdef ALLOW_DIAGNOSTICS |
| 1667 |
IF ( useDiagnostics ) THEN |
| 1668 |
CALL DIAGNOSTICS_FILL(DBSFC ,'KPPdbsfc',0,Nr,2,bi,bj,myThid) |
| 1669 |
CALL DIAGNOSTICS_FILL(DBLOC ,'KPPdbloc',0,Nr,2,bi,bj,myThid) |
| 1670 |
ENDIF |
| 1671 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 1672 |
|
| 1673 |
#endif /* ALLOW_KPP */ |
| 1674 |
|
| 1675 |
RETURN |
| 1676 |
END |
| 1677 |
|
| 1678 |
|
| 1679 |
c************************************************************************* |
| 1680 |
|
| 1681 |
SUBROUTINE KPP_DOUBLEDIFF ( |
| 1682 |
I TTALPHA, SSBETA, |
| 1683 |
U kappaRT, |
| 1684 |
U kappaRS, |
| 1685 |
I ikppkey, imin, imax, jmin, jmax, bi, bj, myThid ) |
| 1686 |
c |
| 1687 |
c----------------------------------------------------------------------- |
| 1688 |
c "KPP_DOUBLEDIFF" adds the double diffusive contributions |
| 1689 |
C as Rrho-dependent parameterizations to kappaRT and kappaRS |
| 1690 |
c |
| 1691 |
c input: |
| 1692 |
c bi, bj = array indices on which to apply calculations |
| 1693 |
c imin, imax, jmin, jmax = array boundaries |
| 1694 |
c ikppkey = key for TAMC/TAF automatic differentiation |
| 1695 |
c myThid = thread id |
| 1696 |
c |
| 1697 |
c ttalpha= thermal expansion coefficient without 1/rho factor |
| 1698 |
c d(rho) / d(potential temperature) (kg/m^3/C) |
| 1699 |
c ssbeta = salt expansion coefficient without 1/rho factor |
| 1700 |
c d(rho) / d(salinity) (kg/m^3/PSU) |
| 1701 |
c output: updated |
| 1702 |
c kappaRT/S :: background diffusivities for temperature and salinity |
| 1703 |
c |
| 1704 |
c written by: martin losch, sept. 15, 2009 |
| 1705 |
c |
| 1706 |
|
| 1707 |
c----------------------------------------------------------------------- |
| 1708 |
|
| 1709 |
IMPLICIT NONE |
| 1710 |
|
| 1711 |
#include "SIZE.h" |
| 1712 |
#include "EEPARAMS.h" |
| 1713 |
#include "PARAMS.h" |
| 1714 |
#include "KPP_PARAMS.h" |
| 1715 |
#include "DYNVARS.h" |
| 1716 |
#include "GRID.h" |
| 1717 |
#ifdef ALLOW_AUTODIFF |
| 1718 |
# include "tamc.h" |
| 1719 |
#endif |
| 1720 |
|
| 1721 |
c-------------- Routine arguments ----------------------------------------- |
| 1722 |
INTEGER ikppkey, imin, imax, jmin, jmax, bi, bj, myThid |
| 1723 |
|
| 1724 |
_RL TTALPHA( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nrp1 ) |
| 1725 |
_RL SSBETA ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nrp1 ) |
| 1726 |
_RL KappaRT( 1-Olx:sNx+Olx, 1-Oly:sNy+Oly, Nr ) |
| 1727 |
_RL KappaRS( 1-Olx:sNx+Olx, 1-Oly:sNy+Oly, Nr ) |
| 1728 |
|
| 1729 |
|
| 1730 |
#ifdef ALLOW_KPP |
| 1731 |
|
| 1732 |
C-------------------------------------------------------------------------- |
| 1733 |
C |
| 1734 |
C local variables |
| 1735 |
C I,J,K :: loop indices |
| 1736 |
C kkppkey :: key for TAMC/TAF automatic differentiation |
| 1737 |
C |
| 1738 |
INTEGER I, J, K |
| 1739 |
INTEGER kkppkey |
| 1740 |
C alphaDT :: d\rho/d\theta * d\theta |
| 1741 |
C betaDS :: d\rho/dsalt * dsalt |
| 1742 |
C Rrho :: "density ratio" R_{\rho} = \alpha dT/dz / \beta dS/dz |
| 1743 |
C nuddt/s :: double diffusive diffusivities |
| 1744 |
C numol :: molecular diffusivity |
| 1745 |
C rFac :: abbreviation for 1/(R_{\rho0}-1) |
| 1746 |
|
| 1747 |
_RL alphaDT ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
| 1748 |
_RL betaDS ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
| 1749 |
_RL nuddt ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
| 1750 |
_RL nudds ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy ) |
| 1751 |
_RL Rrho |
| 1752 |
_RL numol, rFac, nutmp |
| 1753 |
INTEGER Km1 |
| 1754 |
|
| 1755 |
C set some constants here |
| 1756 |
numol = 1.5 _d -06 |
| 1757 |
rFac = 1. _d 0 / (Rrho0 - 1. _d 0 ) |
| 1758 |
C |
| 1759 |
kkppkey = (ikppkey-1)*Nr + 1 |
| 1760 |
|
| 1761 |
CML#ifdef KPP_AUTODIFF_EXCESSIVE_STORE |
| 1762 |
CMLCADJ STORE theta(:,:,1,bi,bj) = comlev1_kpp_k, |
| 1763 |
CMLCADJ & key=kkppkey, kind=isbyte |
| 1764 |
CMLCADJ STORE salt (:,:,1,bi,bj) = comlev1_kpp_k, |
| 1765 |
CMLCADJ & key=kkppkey, kind=isbyte |
| 1766 |
CML#endif /* KPP_AUTODIFF_EXCESSIVE_STORE */ |
| 1767 |
|
| 1768 |
DO K = 1, Nr |
| 1769 |
Km1 = MAX(K-1,1) |
| 1770 |
DO J = 1-Oly, sNy+Oly |
| 1771 |
DO I = 1-Olx, sNx+Olx |
| 1772 |
alphaDT(I,J) = ( theta(I,J,Km1,bi,bj)-theta(I,J,K,bi,bj) ) |
| 1773 |
& * 0.5 _d 0 * ABS( TTALPHA(I,J,Km1) + TTALPHA(I,J,K) ) |
| 1774 |
betaDS(I,J) = ( salt(I,J,Km1,bi,bj)-salt(I,J,K,bi,bj) ) |
| 1775 |
& * 0.5 _d 0 * ( SSBETA(I,J,Km1) + SSBETA(I,J,K) ) |
| 1776 |
nuddt(I,J) = 0. _d 0 |
| 1777 |
nudds(I,J) = 0. _d 0 |
| 1778 |
ENDDO |
| 1779 |
ENDDO |
| 1780 |
IF ( K .GT. 1 ) THEN |
| 1781 |
DO J = jMin, jMax |
| 1782 |
DO I = iMin, iMax |
| 1783 |
Rrho = 0. _d 0 |
| 1784 |
C Now we have many different cases |
| 1785 |
C a. alphaDT > 0 and betaDS > 0 => salt fingering |
| 1786 |
C (salinity destabilizes) |
| 1787 |
IF ( alphaDT(I,J) .GT. betaDS(I,J) |
| 1788 |
& .AND. betaDS(I,J) .GT. 0. _d 0 ) THEN |
| 1789 |
Rrho = MIN( alphaDT(I,J)/betaDS(I,J), Rrho0 ) |
| 1790 |
C Large et al. 1994, eq. 31a |
| 1791 |
C nudds(I,J) = dsfmax * ( 1. _d 0 - (Rrho - 1. _d 0) * rFac )**3 |
| 1792 |
nutmp = ( 1. _d 0 - (Rrho - 1. _d 0) * rFac ) |
| 1793 |
nudds(I,J) = dsfmax * nutmp * nutmp * nutmp |
| 1794 |
C Large et al. 1994, eq. 31c |
| 1795 |
nuddt(I,J) = 0.7 _d 0 * nudds(I,J) |
| 1796 |
ELSEIF ( alphaDT(I,J) .LT. 0. _d 0 |
| 1797 |
& .AND. betaDS(I,J) .LT. 0. _d 0 |
| 1798 |
& .AND.alphaDT(I,J) .GT. betaDS(I,J) ) THEN |
| 1799 |
C b. alphaDT < 0 and betaDS < 0 => semi-convection, diffusive convection |
| 1800 |
C (temperature destabilizes) |
| 1801 |
C for Rrho >= 1 the water column is statically unstable and we never |
| 1802 |
C reach this point |
| 1803 |
Rrho = alphaDT(I,J)/betaDS(I,J) |
| 1804 |
C Large et al. 1994, eq. 32 |
| 1805 |
nuddt(I,J) = numol * 0.909 _d 0 |
| 1806 |
& * exp ( 4.6 _d 0 * exp ( |
| 1807 |
& - 5.4 _d 0 * ( 1. _d 0/Rrho - 1. _d 0 ) ) ) |
| 1808 |
CMLC or |
| 1809 |
CMLC Large et al. 1994, eq. 33 |
| 1810 |
CML nuddt(I,J) = numol * 8.7 _d 0 * Rrho**1.1 |
| 1811 |
C Large et al. 1994, eqs. 34 |
| 1812 |
nudds(I,J) = nuddt(I,J) * MAX( 0.15 _d 0 * Rrho, |
| 1813 |
& 1.85 _d 0 * Rrho - 0.85 _d 0 ) |
| 1814 |
ELSE |
| 1815 |
C Do nothing, because in this case the water colume is unstable |
| 1816 |
C => double diffusive processes are negligible and mixing due |
| 1817 |
C to shear instability will dominate |
| 1818 |
ENDIF |
| 1819 |
ENDDO |
| 1820 |
ENDDO |
| 1821 |
C ENDIF ( K .GT. 1 ) |
| 1822 |
ENDIF |
| 1823 |
C |
| 1824 |
DO J = 1-Oly, sNy+Oly |
| 1825 |
DO I = 1-Olx, sNx+Olx |
| 1826 |
kappaRT(I,J,K) = kappaRT(I,J,K) + nuddt(I,J) |
| 1827 |
kappaRS(I,J,K) = kappaRS(I,J,K) + nudds(I,J) |
| 1828 |
ENDDO |
| 1829 |
ENDDO |
| 1830 |
#ifdef ALLOW_DIAGNOSTICS |
| 1831 |
IF ( useDiagnostics ) THEN |
| 1832 |
CALL DIAGNOSTICS_FILL(nuddt,'KPPnuddt',k,1,2,bi,bj,myThid) |
| 1833 |
CALL DIAGNOSTICS_FILL(nudds,'KPPnudds',k,1,2,bi,bj,myThid) |
| 1834 |
ENDIF |
| 1835 |
#endif /* ALLOW_DIAGNOSTICS */ |
| 1836 |
C end of K-loop |
| 1837 |
ENDDO |
| 1838 |
#endif /* ALLOW_KPP */ |
| 1839 |
|
| 1840 |
RETURN |
| 1841 |
END |
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