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kpp.f
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subroutine kppmix(
$ dVsq,
$ ustar , Bo , Bosol , alphaDT , betaDS ,
$ Ritop,
$ hbl , kbl,
$ kpp_2d_fields,kpp_const_fields)
IMPLICIT NONE
c.......................................................................
c
c Main driver subroutine for kpp vertical mixing scheme and
c interface to greater ocean model
c
c written by : bill large, june, 6, 1994
c modified by: jan morzel, june, 30, 1994
c bill large, august, 11, 1994
c bill large, november 1994, for 1d code
c
c.......................................................................
c
! Automatically includes parameter.inc
#include "kpp_3d_type.com"
integer km,kmp1,mdiff,ki
parameter (km = NZ, kmp1 = nzp1)!, imt = 1) !NX*NY)
parameter (mdiff = 3) ! number of diffusivities for local arrays
c include 'local_pt.com'
c #include "landsea.com>
c
c input
c real zgrid(kmp1) ! vertical grid (<= 0) (m)
c real hwide(kmp1) ! layer thicknesses (m)
c real Shsq_oned(kmp1) ! (local velocity shear)^2 (m/s)^2
real dVsq(kmp1) ! (velocity shear re sfc)^2 (m/s)^2
real ustar ! surface friction velocity (m/s)
real Bo ! surface turbulent buoy. forcing (m^2/s^3)
real Bosol ! radiative buoyancy forcing (m^2/s^3)
real alphaDT(kmp1) ! alpha * DT across interfaces
real betaDS(kmp1) ! beta * DS across interfaces
c real dbloc_oned(km) ! local delta buoyancy (m/s^2)
real Ritop(km) ! numerator of bulk Richardson Number (m/s)^2
c Ritop = (-z - -zref)* delta buoyancy w/ respect to sfc(m/s^2)
c real Coriol ! Coriolis parameter (s^{-1})
c integer jwtype ! Jerlov water type (1 -- 5)
c logical LRI, LDD, LKPP ! mixing process switches
c real ocdepth
type(kpp_2d_type) :: kpp_2d_fields
type(kpp_const_type) :: kpp_const_fields
c
c output
c visc replaced by kpp_2d_fields%difm (NPK 8/2/2013)
c real visc(0:kmp1) ! vertical viscosity coefficient (m^2/s)
c real difs(0:kmp1) ! vertical scalar diffusivity (m^2/s)
c real dift(0:kmp1) ! vertical temperature diffusivity(m^2/s)
c real ghats(km) ! nonlocal transport (s/m^2)
real hbl ! boundary layer depth (m)
integer kbl ! index of first grid level below hbl
c real Rig_oned(km) ! local Richardson number (NPK diagnostic)
c
c local
real bfsfc ! surface buoyancy forcing (m^2/s^3)
real ws ! momentum velocity scale
real wm ! scalar velocity scale
real caseA ! = 1 in case A; =0 in case B
real stable ! = 1 in stable forcing; =0 in unstable
real dkm1(mdiff) ! boundary layer difs at kbl-1 level
real gat1(mdiff) ! shape function at sigma=1
real dat1(mdiff) ! derivative of shape function at sigma=1
real blmc(km,mdiff) ! boundary layer mixing coefficients
real sigma ! normalized depth (d / hbl)
real Rib(2) ! bulk Richardson number
c WRITE(6,*) 'In kppmix, hwide= ',hwide
c zero the mixing coefficients
DO ki=0,km
kpp_2d_fields%difm(ki) = 0.0
kpp_2d_fields%difs(ki) = 0.0
kpp_2d_fields%dift(ki) = 0.0
END DO
c compute RI and IW interior diffusivities everywhere
IF(kpp_const_fields%LRI) THEN
call ri_iwmix (km,kmp1,kpp_2d_fields,kpp_const_fields)
ENDIF
c add double diffusion if desired
IF(kpp_const_fields%LDD) THEN
call ddmix ( km , kmp1,
$ alphaDT, betaDS , kpp_2d_fields)
ENDIF
c fill the bottom kmp1 coefficients for blmix
kpp_2d_fields%difm(kmp1) = kpp_2d_fields%difm(km)
kpp_2d_fields%difs(kmp1) = kpp_2d_fields%difs(km)
kpp_2d_fields%dift(kmp1) = kpp_2d_fields%dift(km)
c compute boundary layer mixing coefficients ??
IF(kpp_const_fields%LKPP) THEN
c diagnose the new boundary layer depth
call bldepth (
+ km , kmp1, dVsq,
$ Ritop, ustar , Bo , Bosol,
+ hbl , bfsfc, stable, caseA, kbl ,
$ Rib , sigma, wm , ws , kpp_2d_fields,
+ kpp_const_fields)
c compute boundary layer diffusivities
call blmix (km , mdiff,
$ ustar, bfsfc, hbl , stable, caseA,
$ kbl,
$ gat1 , dat1 , dkm1, blmc,
$ sigma, wm , ws, kpp_2d_fields,kpp_const_fields)
c enhance diffusivity at interface kbl - 1
call enhance (km , mdiff , dkm1,
$ hbl , kbl , caseA,
$ blmc, kpp_2d_fields,kpp_const_fields)
c combine interior and boundary layer coefficients and nonlocal term
do ki= 1,km
if(ki.lt.kbl) then
kpp_2d_fields%difm(ki)=blmc(ki,1)
kpp_2d_fields%difs(ki)=blmc(ki,2)
kpp_2d_fields%dift(ki)=blmc(ki,3)
else
kpp_2d_fields%ghat(ki)=0.
endif
enddo
c For slab, set all values to small numbers
IF (kpp_const_fields%L_SLAB) THEN
kpp_2d_fields%difm(1:NZtmax)=1e-20
kpp_2d_fields%dift(1:NZtmax)=1e-20
kpp_2d_fields%difs(1:NZtmax)=1e-20
ENDIF
c
c NPK 25/9/08. Trap for negative values of diffusivities.
c If negative, set to a background value of 1E-05.
c
c DO 205 ki= 1,km
c DO 206 i = ipt,ipt
c IF (dift(i,ki) .LT. 0) dift(i,ki)=1E-05
c IF (difs(i,ki) .LT. 0) difs(i,ki)=1E-05
c IF (visc(i,ki) .LT. 0) visc(i,ki)=1E-05
c 206 continue
c 205 continue
ENDIF ! of LKPP
return
end
c ********************************************************************
subroutine bldepth (
$ km , kmp1 , dVsq ,
$ Ritop, ustar , Bo , Bosol,
$ hbl , bfsfc, stable, caseA, kbl ,
$ Rib , sigma, wm , ws , kpp_2d_fields, kpp_const_fields)
IMPLICIT NONE
c
c the oceanic planetray boundary layer depth, hbl, is determined as
c the shallowest depth where the bulk richardson number is
c equal to the critical value, Ricr.
c
c bulk richardson numbers are evaluated by computing velocity and
c buoyancy differences between values at zgrid(kl) < 0 and surface
c reference values.
c in this configuration, the reference values are equal to the
c values in the surface layer.
c when using a very fine vertical grid, these values should be
c computed as the vertical average of velocity and buoyancy from
c the surface down to epsilon*zgrid(kl).
c
c when the bulk richardson number at k exceeds Ricr, hbl is
c linearly interpolated between grid levels zgrid(k) and zgrid(k-1).
c
c The water column and the surface forcing are diagnosed for
c stable/ustable forcing conditions, and where hbl is relative
c to grid points (caseA), so that conditional branches can be
c avoided in later subroutines.
c
c
c model
c include 'local_pt.com'
c include 'times.com'
#include "kpp_3d_type.com"
c Necessary for IMPLICIT NONE
real bvsq,cekman,cmonob,cs,cv,epsilon,fekman,fmonob,
+ hbf,hekman,hmin,hmin2,hmonob,hri,Ricr,vtc,vtsq,epsln
integer ka,ksave,ku,kl
integer km,kmp1 ! number of vertical levels
c integer imt ! number of horizontal grid points
c real zgrid(kmp1) ! vertical grid (<= 0) (m)
c real hwide(kmp1) ! layer thicknesses (m)
c
c input
real dVsq(kmp1) ! (velocity shear re sfc)^2 (m/s)^2
c real dbloc(km) ! local delta buoyancy (m/s^2)
real Ritop(km) ! numerator of bulk Richardson Number (m/s)^2
c Ritop = (-z - -zref)* delta buoyancy w/ respect to sfc(m/s^2)
real ustar ! surface friction velocity (m/s)
real Bo ! surface turbulent buoyancy forcing(m^2/s^3)
real Bosol ! radiative buoyancy forcing (m^2/s^3)
c real Coriol ! Coriolis parameter (1/s)
c integer jwtype ! Jerlov water type (1 to 5)
c real ocdepth
type(kpp_2d_type) :: kpp_2d_fields
type(kpp_const_type) :: kpp_const_fields
c
c output
real hbl ! boundary layer depth (m)
real bfsfc ! Bo+radiation absorbed to d=hbf*hbl(m^2/s^3)
real stable ! =1 in stable forcing; =0 unstable
real caseA ! =1 in case A, =0 in case B
integer kbl ! index of first grid level below hbl
c
c local
real Rib(2) ! Bulk Richardson number
real sigma ! normalized depth (d/hbl)
real wm,ws ! turbulent velocity scales (m/s)
real dmo(2) ! Monin-Obukhov Depth
real hek ! Ekman depth
logical LEK, LMO ! flags for MO and Ekman depth checks
c LOGICAL L_INITFLAG
c common /initflag/L_INITFLAG
c save epsln,Ricr,epsilon,cekman,cmonob,cs,cv,hbf
c
data epsln / 1.e-16 /
c data DelVmin / .005 /
data Ricr / 0.30 /
data epsilon / 0.1 /
data cekman / 0.7 /
data cmonob / 1.0 /
data cs / 98.96 /
data cv / 1.6 /
data hbf / 1.0 /
c Set MO and Ekman depth flags
LEK = .true.
LMO = .true.
c find bulk Richardson number at every grid level find implied hri
c find Monin-Obukvov depth at every grid level find L
c Compare hri, L and hek to give hbl and kbl
c
c note: the reference depth is -epsilon/2.*zgrid(k), but the reference
c u,v,t,s values are simply the surface layer values,
c and not the averaged values from 0 to 2*ref.depth,
c which is necessary for very fine grids(top layer < 2m thickness)
c note: max values when Ricr never satisfied are
c kbl(i)=km and hbl(i) -zgrid(km)
c min values are kbl(i)=2 hbl(i) -zgrid(1)
Vtc = cv * sqrt(0.2/cs/epsilon) / kpp_const_fields%vonk**2 / Ricr
c indices for array Rib(i,k), the bulk Richardson number.
ka = 1
ku = 2
c initialize hbl and kbl to bottomed out values
Rib(ka) = 0.0
dmo(ka) = -kpp_2d_fields%zm(kmp1)
kbl = km
hbl = -kpp_2d_fields%zm(km)
c Coriol(i) = 2. * (twopi/86164.) * sin(2.5*twopi/360.)
hek = cekman * ustar /
+ (abs(kpp_2d_fields%f) + epsln)
do 200 kl = 2,km
c compute bfsfc = sw fraction at hbf * zgrid
c To optimize the code choose the "swfrac_opt" ?
c call swfrac(imt,hbf,zgrid(kl),jwtype,bfsfc)
c Replaces the IF test at the beginning of the swfrac_opt
c subroutine. The value will be stored in kpp_2d_field%swfrac
c thereafter (see below).
if (kpp_const_fields%ntime .le. 1 .and. kl.eq.2) then
call swfrac_opt(hbf,
+ kpp_2d_fields,kpp_const_fields)
endif
IF(kbl.ge.km) THEN
c WRITE(6,*) 'kbl = ',kbl
c use caseA as temporary array for next call to wscale
caseA = -kpp_2d_fields%zm(kl)
c compute bfsfc= Bo + radiative contribution down to hbf * hbl
bfsfc = Bo
$ + Bosol * (1. - kpp_2d_fields%swfrac(kl))
stable = 0.5 + SIGN( 0.5, bfsfc+epsln )
sigma = stable * 1. + (1.-stable) * epsilon
c WRITE(6,*) 'sigma = ',sigma
c WRITE(6,*) 'hbl = ',hbl
c WRITE(6,*) 'ustar = ',ustar
c WRITE(6,*) 'bfsfc = ',bfsfc
ENDIF
c compute velocity scales at sigma, for hbl= caseA = -zgrid(kl)
c WRITE(6,*) 'kbl = ',kbl
c WRITE(6,*) 'sigma = ',sigma
c WRITE(6,*) 'hbl = ',hbl
c WRITE(6,*) 'ustar = ',ustar
c WRITE(6,*) 'bfsfc = ',bfsfc
c WRITE(6,*) 'wscale(',sigma,hbl,ustar,bfsfc
call wscale(sigma, caseA, ustar, bfsfc, wm,ws,kpp_const_fields)
IF(kbl.ge.km) THEN
c compute the turbulent shear contribution to Rib
bvsq =0.5*
$ (kpp_2d_fields%dbloc(kl-1) /
$ (kpp_2d_fields%zm(kl-1)-kpp_2d_fields%zm(kl))+
$ kpp_2d_fields%dbloc(kl) /
$ (kpp_2d_fields%zm(kl)-kpp_2d_fields%zm(kl+1)))
Vtsq = -kpp_2d_fields%zm(kl) * ws * sqrt(abs(bvsq)) * Vtc
c compute bulk Richardson number at new level, dunder
Rib(ku) = Ritop(kl) / (dVsq(kl)+Vtsq+epsln)
Rib(ku) = MAX( Rib(ku), Rib(ka) + epsln)
c linear interpolate to find hbl where Rib = Ricr
hri = -kpp_2d_fields%zm(kl-1) +
+ (kpp_2d_fields%zm(kl-1)-kpp_2d_fields%zm(kl)) *
$ (Ricr - Rib(ka)) / (Rib(ku)-Rib(ka))
c compute the Monin Obukov length scale
c fmonob = stable(i) * LMO
fmonob = stable * 1.0
dmo(ku) = cmonob * ustar * ustar
+ * ustar
> / kpp_const_fields%vonk / (abs(bfsfc) + epsln)
dmo(ku) = fmonob * dmo(ku) - (1.-fmonob) *
+ kpp_2d_fields%zm(kmp1)
if(dmo(ku).le.(-kpp_2d_fields%zm(kl))) then
hmonob =(dmo(ku)-dmo(ka))/(kpp_2d_fields%zm(kl-1)-
+ kpp_2d_fields%zm(kl))
hmonob =(dmo(ku)+hmonob*kpp_2d_fields%zm(kl)) /
+ (1.-hmonob)
else
hmonob = -kpp_2d_fields%zm(kmp1)
endif
c compute the Ekman depth
c fekman = stable(i) * LEK
fekman = stable * 1.0
hekman = fekman * hek - (1.-fekman) *
+ kpp_2d_fields%zm(kmp1)
c compute boundary layer depth
hmin = MIN(hri, hmonob, hekman, -kpp_2d_fields%ocdepth)
c WRITE(6,*) 'hri=',hri,'hmonob=',hmonob,'hekman=',hekman
if(hmin .lt. -kpp_2d_fields%zm(kl) ) then
c
c Code below added by SJW 09/07/04 to solve problems where hek
c less than zgrid(kl-1) giving negative diffusions
c if this occurs to often then we need to rethink this fix
c
c Modified by NPK 25/09/08 to include Monin-Obukov depth as well.
c Richardson depth is sometimes calculated to be huge (> 1E10) when
c Ritop is negative or very small and so is not always helpful in
c this scenario.
c
if (.not. kpp_2d_fields%l_initflag) then
if (hmin .lt. -kpp_2d_fields%zm(kl-1)) then
hmin2=MIN(hri,hmonob,-kpp_2d_fields%ocdepth)
if (hmin2 .lt. -kpp_2d_fields%zm(kl)) THEN
c write(6,*) 'Setting hmin=',
c & hmin2,'from hek? ',hekman,
c & 'hri=',hri,'hmonob=',hmonob
hmin=hmin2
c else
c write(6,*) 'Leaving hmin=hek ',hekman,
c & 'as hmonob= ',hmonob,'and hri= ',hri
endif
endif
endif
hbl = hmin
kbl = kl
c if(hmin.ge. hmonob) write(6,*) 'MO ',kl,hmin, hmonob,
c & hri
c if(hmin.ge. hekman) write(6,*) 'EK ',kl,hmin, hekman,
c & hri
endif
ENDIF !kbl
! Save hekman for use with Ekman pumping code in ocn.f
! IF (kpp_const_fields%L_EKMAN_PUMP)
! c kpp_2d_fields%hekman = hekman
ksave = ka
ka = ku
ku = ksave
200 continue
call swfrac(-1.0,hbl,kpp_2d_fields,bfsfc)
bfsfc = Bo + Bosol * (1. - bfsfc)
stable = 0.5 + SIGN( 0.5, bfsfc)
bfsfc = bfsfc + stable * epsln !ensures bfsfc never=0
c determine caseA and caseB
caseA = 0.5 +
$ SIGN( 0.5,-kpp_2d_fields%zm(kbl) -0.5*
+ kpp_2d_fields%hm(kbl) -hbl)
return
end
c *********************************************************************
subroutine wscale(sigma, hbl, ustar, bfsfc,
$ wm , ws, kpp_const_fields)
IMPLICIT NONE
c
c compute turbulent velocity scales.
c use a 2D-lookup table for wm and ws as functions of ustar and
c zetahat (=vonk*sigma*hbl*bfsfc).
c
c
! Automatically includes parameter.inc!
#include "kpp_3d_type.com"
c
c Necessary for IMPLICIT NONE (NPK 11/2/13)
INTEGER ni,nj,i,iz,izp1,j,ju,jup1
REAL am,as,c1,c2,c3,cm,cs,epsln,fzfrac,ucube,udiff,ufrac,
+ usta,wam,was,wbm,wbs,zdiff,zetas,zfrac,zetam
c
TYPE(kpp_const_type) :: kpp_const_fields
c
c lookup table
parameter ( ni = 890, ! number of values for zehat
$ nj = 48) ! number of values for ustar
c real wmt(0:ni+1,0:nj+1) ! lookup table for wm
c real wst(0:ni+1,0:nj+1) ! lookup table for ws
real deltaz ! delta zehat in table
real deltau ! delta ustar in table
real zmin,zmax ! zehat limits for table
real umin,umax ! ustar limits for table
c logical firstf
c save deltaz,deltau,zmin,zmax,umin,umax,firstf
c
data zmin,zmax / -4.e-7, 0.0 / ! m3/s3
data umin,umax / 0. , .04 / ! m/s
c data firstf / .true. /
c model
c include 'local_pt.com'
c integer imt ! number of horizontal grid points
c input
real sigma ! normalized depth (d/hbl)
real hbl ! boundary layer depth (m)
real ustar ! surface friction velocity (m/s)
real bfsfc ! total surface buoyancy flux (m^2/s^3)
c output
real wm,ws ! turbulent velocity scales at sigma
c local
real zehat ! = zeta * ustar**3
real zeta ! = stability parameter d/L
c save epsln,c1,am,cm,c2,zetam,as,cs,c3,zetas,vonk
data epsln / 1.0e-20/
data c1 / 5.0 /
data am,cm,c2,zetam / 1.257 , 8.380 , 16.0 , - 0.2 /
data as,cs,c3,zetas / -28.86 , 98.96 , 16.0 , - 1.0 /
c data vonk / 0.40 /
c
c construct the wm and ws lookup tables
c
c Moved to a separate subroutine for openMP compatability
c NPK 13/2/2013.
c
deltaz = (zmax-zmin)/(ni+1)
deltau = (umax-umin)/(nj+1)
c use lookup table for zehat < zmax ONLY; otherwise use stable formulae
c WRITE(6,*) 'vonk = ',vonk
c WRITE(6,*) 'sigma = ',sigma
c WRITE(6,*) 'hbl = ',hbl
c WRITE(6,*) 'bfsfc = ',bfsfc
c WRITE(6,*) 'zehat = ',vonk,sigma,hbl,bfsfc
zehat = kpp_const_fields%vonk * sigma * hbl * bfsfc
IF (zehat .le. zmax) THEN
zdiff = zehat-zmin
iz = int( zdiff/deltaz )
iz = min( iz , ni )
iz = max( iz , 0 )
izp1=iz+1
udiff = ustar-umin
ju = int( udiff/deltau)
ju = min( ju , nj )
ju = max( ju , 0 )
jup1=ju+1
zfrac = zdiff/deltaz - float(iz)
ufrac = udiff/deltau - float(ju)
fzfrac= 1.-zfrac
wam = (fzfrac) * kpp_const_fields%wmt(iz,jup1) +
+ zfrac*kpp_const_fields%wmt(izp1,jup1)
wbm = (fzfrac) * kpp_const_fields%wmt(iz,ju ) +
+ zfrac*kpp_const_fields%wmt(izp1,ju )
wm = (1.-ufrac)* wbm + ufrac*wam
was = (fzfrac) * kpp_const_fields%wst(iz,jup1) +
+ zfrac*kpp_const_fields%wst(izp1,jup1)
wbs = (fzfrac) * kpp_const_fields%wst(iz,ju ) +
+ zfrac*kpp_const_fields%wst(izp1,ju )
ws = (1.-ufrac)* wbs + ufrac*was
ELSE
ucube = ustar**3
wm = kpp_const_fields%vonk * ustar * ucube /
+ (ucube + c1 * zehat)
ws = wm
ENDIF
return
end
c **********************************************************************
subroutine ri_iwmix (km,kmp1,kpp_2d_fields,kpp_const_fields)
implicit none
c
c compute interior viscosity diffusivity coefficients due to
c shear instability (dependent on a local richardson number)
c and due to background internal wave activity.
c
c input
c include 'local_pt.com'
! Automatically includes parameter.inc!
#include "kpp_3d_type.com"
TYPE(kpp_2d_type) :: kpp_2d_fields
TYPE(kpp_const_type) :: kpp_const_fields
integer km,kmp1 ! number of vertical levels
c integer imt ! number of horizontal grid points
c real Shsq(kmp1) ! (local velocity shear)^2 (m/s)^2
c real dbloc(km) ! local delta buoyancy (m/s^2)
c real zgrid(kmp1) ! vertical grid (<= 0) (m)
c output
c real visc(0:kmp1) ! vertical viscosivity coefficient (m^2/s)
c real difs(0:kmp1) ! vertical scalar diffusivity (m^2/s)
c real dift(0:kmp1) ! vertical temperature diffusivity (m^2/s)
c real Rig(km) ! local Richardson number
c local variables
c real Rig,Rigg ! local richardson number
real Rigg
real fri,fcon ! function of Rig
real ratio
real epsln,Riinfty,Ricon,difm0,difs0,difmiw,difsiw,difmcon,
& difscon,c1,c0
c integer i,ki,mr,mRi
INTEGER ki,mRi,j
c save epsln,Riinfty,Ricon,difm0,difs0,difmcon,difscon,
c & difmiw,difsiw,c1
data epsln / 1.e-16 / ! a small number
data Riinfty / 0.8 / ! LMD default was = 0.7
data Ricon / -0.2 / ! note: exp was repl by multiplication
IF (kpp_const_fields%L_SLAB) THEN
data difm0 / 0.000005 / ! max visc due to shear instability
data difs0 / 0.000005 / ! max diff .. .. .. ..
data difmiw / 0.000001 / ! background/internal waves visc(m^2/s)
data difsiw / 0.000001 / ! .. .. .. diff(m^2/s)
ELSE
data difm0 / 0.005 /
data difs0 / 0.005 /
data difmiw / 0.0001 /
data difsiw / 0.00001 /
ENDIF
data difmcon / 0.0000 / ! max visc for convection (m^2/s)
data difscon / 0.0000 / ! max diff for convection (m^2/s)
data c1/ 1.0/
data c0/ 0.0/
data mRi/ 1 / ! number of vertical smoothing passes
c
c compute interior gradient Ri at all interfaces, except surface
c-----------------------------------------------------------------------
c compute interior gradient Ri at all interfaces ki=1,km, (not surface)
c use visc(imt,ki=1,km) as temporary storage to be smoothed
c use dift(imt,ki=1,km) as temporary storage of unsmoothed Ri
c use difs(imt,ki=1,km) as dummy in smoothing call
do 110 ki = 1, km
c WRITE(6,*) ki
c WRITE(6,*) 'Shsq(ki) = ',Shsq(ki)
kpp_2d_fields%Rig(ki) = kpp_2d_fields%dbloc(ki) *
+ (kpp_2d_fields%zm(ki)-kpp_2d_fields%zm(ki+1))/
$ (kpp_2d_fields%Shsq(ki) + epsln)
kpp_2d_fields%dift(ki) = kpp_2d_fields%Rig(ki)
kpp_2d_fields%difm(ki) = kpp_2d_fields%dift(ki)
110 continue
c-----------------------------------------------------------------------
c vertically smooth Ri mRi times
do j = 1,mRi
call z121(kmp1,c0,Riinfty,kpp_2d_fields%difm,
+ kpp_2d_fields%difs)
enddo
c-----------------------------------------------------------------------
c after smoothing loop
DO ki = 1, km
c evaluate f of unsmooth Ri (fri) for convection store in fcon
c evaluate f of smooth Ri (fri) for shear instability store in fri
Rigg = AMAX1( kpp_2d_fields%dift(ki) , Ricon )
ratio = AMIN1( (Ricon-Rigg)/Ricon , c1 )
fcon = (c1 - ratio*ratio)
fcon = fcon * fcon * fcon
Rigg = AMAX1( kpp_2d_fields%difm(ki) , c0 )
ratio = AMIN1( Rigg/Riinfty , c1 )
fri = (c1 - ratio*ratio)
fri = fri * fri * fri
c if(i.eq.1)write(6,*)ki,dift(i,ki),visc(i,ki),Rigg,ratio,fri,
c + fcon
c ************************ Overwrite with Gent's PP **********
c fcon = 0.0
c Rigg = AMAX1( dift(i,ki) , c0 )
c fri = c1 / (c1 + 10. * Rigg )
c difm0 = 0.1 * fri
c difs0 = 0.1 * fri * fri
c ************************ Overwrite with original PP
c fcon = 0.0
c Rigg = AMAX1( dift(i,ki) , c0 )
c fri = c1 / (c1 + 5. * Rigg )
c difm0 = 0.01 * fri
c difs0 = (difmiw + fri * difm0)
c ----------------------------------------------------------------------
c evaluate diffusivities and viscosity
c mixing due to internal waves, and shear and static instability
kpp_2d_fields%difm(ki) =
+ (difmiw + fcon * difmcon + fri * difm0)
kpp_2d_fields%difs(ki) =
+ (difsiw + fcon * difscon + fri * difs0)
kpp_2d_fields%dift(ki) = kpp_2d_fields%difs(ki)
END DO
c ------------------------------------------------------------------------
c set surface values to 0.0
kpp_2d_fields%difm(0) = c0
kpp_2d_fields%dift(0) = c0
kpp_2d_fields%difs(0) = c0
return
end
c *********************************************************************
Subroutine z121 (kmp1,vlo,vhi,V,w)
IMPLICIT NONE
c Necessary for IMPLICIT NONE (NPK 11/2/13)
INTEGER kmp1
REAL vlo,vhi,tmp,wait
INTEGER k,km
c Apply 121 smoothing in k to 2-d array V(i,k=1,km)
c top (0) value is used as a dummy
c bottom (kmp1) value is set to input value from above.
c input
c include 'local_pt.com'
real V(0:kmp1) ! 2-D array to be smoothed in kmp1 direction
real w(0:kmp1) ! 2-D array of internal weights to be computed
km = kmp1 - 1
w(0) = 0.0
w(kmp1) = 0.0
V(0) = 0.0
V(kmp1) = 0.0
do k=1,km
if((V(k).lt.vlo).or.(V(k).gt.vhi)) then
w(k) = 0.0
c w(i,k) = 1.0
else
w(k) = 1.0
endif
enddo
do k=1,km
tmp = V(k)
V(k) = w(k-1)*V(0)+2.*V(k)+w(k+1)*V(k+1)
wait = w(k-1) + 2.0 + w(k+1)
V(k) = V(k) / wait
V(0) = tmp
enddo
return
end
c *********************************************************************
subroutine ddmix (km, kmp1,
+ alphaDT,betaDS,kpp_2d_fields)
IMPLICIT NONE
c
c Rrho dependent interior flux parameterization.
c Add double-diffusion diffusivities to Ri-mix values at blending
c interface and below.
c
c input
! Automatically includes parameter.inc!
#include "kpp_3d_type.com"
c include 'local_pt.com'
c Necessary for IMPLICIT NONE (NPK 11/2/13)
integer km,kmp1,ki
real dsfmax,rrho0
real alphaDT(kmp1) ! alpha * DT across interfaces
real betaDS(kmp1) ! beta * DS across interfaces
c real zgrid(kmp1)
TYPE(kpp_2d_type) :: kpp_2d_fields
c output
c real visc(0:kmp1) ! interior viscosity (m^2/s)
c real dift(0:kmp1) ! interior thermal diffusivity (m^2/s)
c real difs(0:kmp1) ! interior scalar diffusivity (m^2/s)
c
c local
real Rrho ! dd parameter
real diffdd ! double diffusion diffusivity scale
real prandtl ! prandtl number
c save Rrho0,dsfmax
data Rrho0 / 1.9 / ! Rp=(alpha*delT)/(beta*delS)
data dsfmax / 1.0e-4 / ! .0001 m2/s
DO ki= 1, km
c salt fingering case
if((alphaDT(ki).gt.betaDS(ki)).and.(betaDS(ki).gt.0.)) then
Rrho = MIN(alphaDT(ki) / betaDS(ki) , Rrho0)
diffdd = 1.0-((Rrho-1)/(Rrho0-1))**2
diffdd = dsfmax*diffdd*diffdd*diffdd
kpp_2d_fields%dift(ki) = kpp_2d_fields%dift(ki) + diffdd *
+ 0.8 / Rrho
kpp_2d_fields%difs(ki) = kpp_2d_fields%difs(ki) + diffdd
c diffusive convection
else if ((alphaDT(ki).lt.0.0).and.(betaDS(ki).lt.0.0).and.
$ (alphaDT(ki).lt.betaDS(ki)) ) then
Rrho = alphaDT(ki) / betaDS(ki)
diffdd = 1.5e-6*9.0*0.101*exp(4.6*exp(-0.54*(1/Rrho-1)))
prandtl = 0.15*Rrho
if (Rrho.gt.0.5) prandtl = (1.85-0.85/Rrho)*Rrho
kpp_2d_fields%dift(ki) = kpp_2d_fields%dift(ki) + diffdd
kpp_2d_fields%difs(ki) = kpp_2d_fields%difs(ki) +
+ prandtl*diffdd
endif
ENDDO
return
end
c *********************************************************************
subroutine blmix
$ (km , mdiff ,
$ ustar, bfsfc, hbl , stable, caseA,
$ kbl ,
$ gat1 , dat1 , dkm1, blmc,
$ sigma, wm, ws, kpp_2d_fields,kpp_const_fields)
c mixing coefficients within boundary layer depend on surface
c forcing and the magnitude and gradient of interior mixing below
c the boundary layer ("matching").
IMPLICIT NONE
CAUTION if mixing bottoms out at hbl = -zgrid(km) THEN
c fictious layer kmp1 is needed with small but finite width (eg. 1.e-10)
c model
c include 'local_pt.com'
! Automatically includes parameter.inc!
#include "kpp_3d_type.com"
TYPE(kpp_2d_type) :: kpp_2d_fields
TYPE(kpp_const_type) :: kpp_const_fields
integer km !,kmp1 ! number of vertical levels
c integer imt ! number of horizontal grid points
integer mdiff ! number of viscosities + diffusivities
c real zgrid(kmp1) ! vertical grid (<=0) (m)
c real hwide(kmp1) ! layer thicknesses (m)
c
c input
real ustar ! surface friction velocity (m/s)
real bfsfc ! surface buoyancy forcing (m^2/s^3)
real hbl ! boundary layer depth (m)
real stable ! = 1 in stable forcing
real caseA ! = 1 in case A
c real visc(imt,0:kmp1) ! vertical viscosity coefficient (m^2/s)
c real difs(imt,0:kmp1) ! vertical scalar diffusivity (m^2/s)
c real dift(imt,0:kmp1) ! vertical temperature diffusivity (m^2/s)
integer kbl ! index of first grid level below hbl
c
c output
real gat1(mdiff)
real dat1(mdiff)
real dkm1(mdiff) ! boundary layer difs at kbl-1 level
real blmc(km,mdiff) ! boundary layer mixing coefficients(m^2/s)
c real ghats(km) ! nonlocal scalar transport
c
c local
real sigma ! normalized depth (d / hbl)
real ws, wm ! turbulent velocity scales (m/s)
c None of these were previously declared ... (NPK 6/2/13)
real a1,a2,a3,am,as,c1,c2,c3,cg,cm,cs,cstar,delhat,difsh,
+ difsp,difth,diftp,dvdzup,epsln,f1,gm,gs,
+ dvdzdn,epsilon,gt,r,visch,viscp,zetam,sig,
+ zetas
integer ki,kn
c save epsln,epsilon,c1,am,cm,c2,zetam,as,cs,c3,zetas,
c $ cstar
data epsln / 1.e-20 /
data epsilon / 0.1 /
data c1 / 5.0 /
data am,cm,c2,zetam / 1.257 , 8.380, 16.0, - 0.2 / !7-24-92
data as,cs,c3,zetas / -28.86 , 98.96 , 16.0, - 1.0 /
data cstar / 5. /
c
cg = cstar * kpp_const_fields%vonk *
+ (cs * kpp_const_fields%vonk * epsilon)**(1./3.)
c compute velocity scales at hbl
sigma = stable * 1.0 + (1.-stable) * epsilon
c WRITE(6,*) 'wscale(',sigma,hbl,ustar,bfsfc
call wscale(sigma, hbl, ustar, bfsfc,wm,ws,kpp_const_fields)
kn = ifix(caseA+epsln) *(kbl -1) +
$ (1-ifix(caseA+epsln)) * kbl
c find the interior viscosities and derivatives at hbl(i)
delhat = 0.5*kpp_2d_fields%hm(kn)-kpp_2d_fields%zm(kn) -
+ hbl
R = 1.0 - delhat / kpp_2d_fields%hm(kn)
c WRITE(6,*) 'kn = ',kn
c WRITE(6,*) 'kpp_2d_fields%difm(kn-1) =',kpp_2d_fields%difm(kn-1)
c WRITE(6,*) 'kpp_2d_fields%difm(kn) =',kpp_2d_fields%difm(kn)
c WRITE(6,*) 'kpp_2d_fields%hm(kn) = ',kpp_2d_fields%hm(kn)
c WRITE(6,*) 'kpp_2d_fields%hm(kn+1) =',kpp_2d_fields%hm(kn+1)
dvdzup = (kpp_2d_fields%difm(kn-1) - kpp_2d_fields%difm(kn)) /
+ kpp_2d_fields%hm(kn)
dvdzdn = (kpp_2d_fields%difm(kn) - kpp_2d_fields%difm(kn+1))
+ / kpp_2d_fields%hm(kn+1)
viscp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup))+
$ R * (dvdzdn + abs(dvdzdn)) )
dvdzup = (kpp_2d_fields%difs(kn-1) - kpp_2d_fields%difs(kn)) /
+ kpp_2d_fields%hm(kn)
dvdzdn = (kpp_2d_fields%difs(kn) - kpp_2d_fields%difs(kn+1))
+ / kpp_2d_fields%hm(kn+1)
difsp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup))+
$ R * (dvdzdn + abs(dvdzdn)) )
dvdzup = (kpp_2d_fields%dift(kn-1) - kpp_2d_fields%dift(kn)) /
+ kpp_2d_fields%hm(kn)
dvdzdn = (kpp_2d_fields%dift(kn) - kpp_2d_fields%dift(kn+1))
+ / kpp_2d_fields%hm(kn+1)
diftp = 0.5 * ( (1.-R) * (dvdzup + abs(dvdzup))+
$ R * (dvdzdn + abs(dvdzdn)) )
c
visch = kpp_2d_fields%difm(kn) + viscp * delhat
difsh = kpp_2d_fields%difs(kn) + difsp * delhat
difth = kpp_2d_fields%dift(kn) + diftp * delhat
c
f1 = stable * c1 * bfsfc / (ustar**4+epsln)
gat1(1) = visch / hbl / (wm+epsln)
dat1(1) = -viscp / (wm+epsln) + f1 * visch
dat1(1) = min(dat1(1),0.)
gat1(2) = difsh / hbl / (ws+epsln)
dat1(2) = -difsp / (ws+epsln) + f1 * difsh
dat1(2) = min(dat1(2),0.)
gat1(3) = difth / hbl / (ws+epsln)
dat1(3) = -diftp / (ws+epsln) + f1 * difth
dat1(3) = min(dat1(3),0.)
c Turn off interior matching here
c gat1(i,1) = 0.0001
c gat1(i,2) = 0.00001
c gat1(i,3) = 0.00001
c do m=1,3
c dat1(i,m) = 0.0
c enddo
c
do 300 ki = 1,km
c
c compute turbulent velocity scales on the interfaces
c
sig = (-kpp_2d_fields%zm(ki) + 0.5 *
+ kpp_2d_fields%hm(ki)) / hbl
sigma = stable*sig + (1.-stable)*AMIN1(sig,epsilon)
call wscale(sigma, hbl, ustar, bfsfc,wm,ws,kpp_const_fields)
c
c compute the dimensionless shape functions at the interfaces
c
sig = (-kpp_2d_fields%zm(ki) + 0.5 *
+ kpp_2d_fields%hm(ki)) / hbl
a1 = sig - 2.
a2 = 3.-2.*sig
a3 = sig - 1.
c
Gm = a1 + a2 * gat1(1) + a3 * dat1(1)
Gs = a1 + a2 * gat1(2) + a3 * dat1(2)
Gt = a1 + a2 * gat1(3) + a3 * dat1(3)
c
c compute boundary layer diffusivities at the interfaces
c
blmc(ki,1) = hbl * wm * sig * (1. + sig * Gm)
blmc(ki,2) = hbl * ws * sig * (1. + sig * Gs)
blmc(ki,3) = hbl * ws * sig * (1. + sig * Gt)
c
c nonlocal transport term = ghats * <ws>o
kpp_2d_fields%ghat(ki) = (1.-stable) * cg / (ws*hbl+epsln)
300 continue
c find diffusivities at kbl-1 grid level
sig = -kpp_2d_fields%zm(kbl-1) / hbl
sigma = stable * sig + (1.-stable) * AMIN1(sig,epsilon)
c
call wscale(sigma, hbl, ustar, bfsfc, wm, ws,kpp_const_fields)
c
sig = -kpp_2d_fields%zm(kbl-1) / hbl
a1= sig - 2.
a2 = 3.-2.*sig
a3 = sig - 1.
Gm = a1 + a2 * gat1(1) + a3 * dat1(1)
Gs = a1 + a2 * gat1(2) + a3 * dat1(2)
Gt = a1 + a2 * gat1(3) + a3 * dat1(3)
dkm1(1) = hbl * wm * sig * (1. + sig * Gm)
dkm1(2) = hbl * ws * sig * (1. + sig * Gs)
dkm1(3) = hbl * ws * sig * (1. + sig * Gt)
return
end
c ******************************************************************