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Subsections
Authors: Dimitris Menemenlis and Patrick Heimbach
6.4.2.1 Introduction
The nonlocal KProfile Parameterization (KPP) scheme
of Large et al. [1994] unifies the treatment of a variety of
unresolved processes involved in vertical mixing.
To consider it as one mixing scheme is, in the view of the authors,
somewhat misleading since it consists of several entities
to deal with distinct mixing processes in the ocean's surface
boundary layer, and the interior:
 mixing in the interior is goverened by
shear instability (modeled as function of the local gradient
Richardson number), internal wave activity (assumed constant),
and doublediffusion (not implemented here).
 a boundary layer depth
or hbl is determined
at each grid point, based on a critical value of turbulent
processes parameterized by a bulk Richardson number;
 mixing is strongly enhanced in the boundary layer under the
stabilizing or destabilizing influence of surface forcing
(buoyancy and momentum) enabling boundary layer properties
to penetrate well into the thermocline;
mixing is represented through a polynomial profile whose
coefficients are determined subject to several contraints;
 the boundarylayer profile is made to agree with similarity
theory of turbulence and is matched, in the asymptotic sense
(function and derivative agree at the boundary),
to the interior thus fixing the polynomial coefficients;
matching allows for some fraction of the boundary layer mixing
to affect the interior, and vice versa;
 a ``nonlocal'' term
or ghat
which is independent of the vertical property gradient further
enhances mixing where the water column is unstable
The scheme has been extensively compared to observations
(see e.g. Large et al. [1997]) and is now coomon in many
ocean models.
The current code originates in the NCAR NCOM 1D code
and was kindly provided by Bill Large and Jan Morzel.
It has been adapted first to the MITgcm vector code and
subsequently to the current parallel code.
Adjustment were mainly in conjunction with WRAPPER requirements
(domain decomposition and threading capability), to enable
automatic differentiation of tangent linear and adjoint code
via TAMC.
The following sections will describe the KPP package
configuration and compiling (6.4.2.2),
the settings and choices of runtime parameters
(6.4.2.3),
more detailed description of equations to which these
parameters relate (6.4.2.4),
and key subroutines where they are used (6.4.2.5),
and diagnostics output of KPPderived diffusivities, viscosities
and boundarylayer/mixedlayer depths
(6.4.2.6).
6.4.2.2 KPP configuration and compiling
As with all MITgcm packages, KPP can be turned on or off at compile time
 using the packages.conf file by adding kpp to it,
 or using genmake2 adding
enable=kpp or disable=kpp switches
 Required packages and CPP options:
No additional packages are required, but the MITgcm kernel flag
enabling the penetration of shortwave radiation below
the surface layer needs to be set in CPP_OPTIONS.h
as follows:
#define SHORTWAVE_HEATING
(see Section 3.4).
Parts of the KPP code can be enabled or disabled at compile time
via CPP preprocessor flags. These options are set in
KPP_OPTIONS.h. Table 6.4.2.2 summarizes them.
Table 6.6:
CPP option 
Description 
_KPP_RL 

FRUGAL_KPP 

KPP_SMOOTH_SHSQ 

KPP_SMOOTH_DVSQ 

KPP_SMOOTH_DENS 

KPP_SMOOTH_VISC 

KPP_SMOOTH_DIFF 

KPP_ESTIMATE_UREF 

INCLUDE_DIAGNOSTICS_INTERFACE_CODE 

KPP_GHAT 

EXCLUDE_KPP_SHEAR_MIX 


6.4.2.3 Runtime parameters
Runtime parameters are set in files
data.pkg and data.kpp
which are read in kpp_readparms.F.
Runtime parameters may be broken into 3 categories:
(i) switching on/off the package at runtime,
(ii) required MITgcm flags,
(iii) package flags and parameters.
The KPP package is switched on at runtime by setting
useKPP = .TRUE. in data.pkg.
The following flags/parameters of the MITgcm dynamical
kernel need to be set in conjunction with KPP:
implicitViscosity = .TRUE. 
enable implicit vertical viscosity 
implicitDiffusion = .TRUE. 
enable implicit vertical diffusion 
Table 6.4.2.3 summarizes the
runtime flags that are set in data.pkg, and
their default values.
Table 6.7:
Flag/parameter 
default 
Description 
I/O related parameters 
kpp_freq 
deltaTClock 
Recomputation frequency for KPP fields 
kpp_dumpFreq 
dumpFreq 
Dump frequency of KPP field snapshots 
kpp_taveFreq 
taveFreq 
Averaging and dump frequency of KPP fields 
KPPmixingMaps 
.FALSE. 
include KPP diagnostic maps in STDOUT 
KPPwriteState 
.FALSE. 
write KPP state to file 
KPP_ghatUseTotalDiffus 
.FALSE. 
if .T. compute nonlocal term using total vertical diffusivity 


if .F. use KPP vertical diffusivity 
Genral KPP parameters 
minKPPhbl 
delRc(1) 
Minimum boundary layer depth 
epsilon 
0.1 
nondimensional extent of the surface layer 
vonk 
0.4 
von Karman constant 
dB_dz 
5.2E5 1/s

maximum dB/dz in mixed layer hMix 
concs 
98.96 

concv 
1.8 

Boundary layer parameters (S/R bldepth) 
Ricr 
0.3 
critical bulk Richardson number 
cekman 
0.7 
coefficient for Ekman depth 
cmonob 
1.0 
coefficient for MoninObukhov depth 
concv 
1.8 
ratio of interior to entrainment depth buoyancy frequency 
hbf 
1.0 
fraction of depth to which absorbed solar radiation contributes 


to surface buoyancy forcing 
Vtc 

nondim. coeff. for velocity scale of turbulant velocity shear 


( = function of concv,concs,epsilon,vonk,Ricr) 
Boundary layer mixing parameters (S/R blmix) 
cstar 
10. 
proportionality coefficient for nonlocal transport 
cg 

nondimensional coefficient for countergradient term 


( = function of cstar,vonk,concs,epsilon) 
Interior mixing parameters (S/R Ri_iwmix) 
Riinfty 
0.7 
gradient Richardson number limit for shear instability 
BVDQcon 
0.2E4 1/s

BruntVäisalä squared 
difm0 
0.005 m
/s 
viscosity max. due to shear instability 
difs0 
0.005 m
/s 
tracer diffusivity max. due to shear instability 
dift0 
0.005 m
/s 
heat diffusivity max. due to shear instability 
difmcon 
0.1 
viscosity due to convective instability 
difscon 
0.1 
tracer diffusivity due to convective instability 
diftcon 
0.1 
heat diffusivity due to convective instability 
Doublediffusive mixing parameters (S/R ddmix) 
Rrho0 
not used 
limit for double diffusive density ratio 
dsfmax 
not used 
maximum diffusivity in case of salt fingering 

6.4.2.4 Equations and key routines
We restrict ourselves to writing out only the essential equations
that relate to main processes and parameters mentioned above.
We closely follow the notation of Large et al. [1994].
Toplevel routine.
Intermediatelevel routine
The vertical fluxes
of momentum and tracer properties
is composed of a gradientflux term (proportional to
the vertical property divergence
), and
a ``nonlocal'' term
that enhances the
gradientflux mixing coefficient

(6.23) 
In practice, the routine peforms the following tasks:
 compute velocity scales at hbl
 find the interior viscosities and derivatives at hbl
 compute turbulent velocity scales on the interfaces
 compute the dimensionless shape functions at the interfaces
 compute boundary layer diffusivities at the interfaces
 compute nonlocal transport term
 find diffusivities at kbl1 grid level
Compute interior viscosity and diffusivity coefficients due to
 shear instability (dependent on a local gradient Richardson number),
 to background internal wave activity, and
 to static instability (local Richardson number
0).
TO BE CONTINUED.
The oceanic planetary boundary layer depth, hbl, is determined as
the shallowest depth where the bulk Richardson number is
equal to the critical value, Ricr.
Bulk Richardson numbers are evaluated by computing velocity and
buoyancy differences between values at zgrid(kl) < 0 and surface
reference values.
In this configuration, the reference values are equal to the
values in the surface layer.
When using a very fine vertical grid, these values should be
computed as the vertical average of velocity and buoyancy from
the surface down to epsilon*zgrid(kl).
When the bulk Richardson number at k exceeds Ricr, hbl is
linearly interpolated between grid levels zgrid(k) and zgrid(k1).
The water column and the surface forcing are diagnosed for
stable/ustable forcing conditions, and where hbl is relative
to grid points (caseA), so that conditional branches can be
avoided in later subroutines.
TO BE CONTINUED.
Add contribution to net diffusivity/viscosity from
KPP diffusivity/viscosity.
TO BE CONTINUED.
Add non local KPP transport term (ghat) to diffusive
temperature/salinity/passive tracer flux.
The nonlocal transport term is nonzero only for scalars
in unstable (convective) forcing conditions.
TO BE CONTINUED.
TO BE CONTINUED.
TO BE CONTINUED.
6.4.2.5 Flow chart
C !CALLING SEQUENCE:
c ...
c kpp_calc (TOP LEVEL ROUTINE)
c 
c  statekpp: o compute all EOS/densityrelated arrays
c  o uses S/R FIND_ALPHA, FIND_BETA, FIND_RHO
c 
c  kppmix
c   ri_iwmix (compute interior mixing coefficients due to constant
c   internal wave activity, static instability,
c   and local shear instability).
c  
c   bldepth (diagnose boundary layer depth)
c  
c   blmix (compute boundary layer diffusivities)
c  
c   enhance (enhance diffusivity at interface kbl  1)
c  o
c 
c  swfrac
c o
6.4.2.6 KPP diagnostics
Diagnostics output is available via the diagnostics package
(see Section 7.1).
Available output fields are summarized here:

<Name>Levsgrid< Units >< Tile (max=80c)

KPPviscA 23 SM m^2/s KPP vertical eddy viscosity coefficient
KPPdiffS 23 SM m^2/s Vertical diffusion coefficient for salt & tracers
KPPdiffT 23 SM m^2/s Vertical diffusion coefficient for heat
KPPghat  23 SM s/m^2 Nonlocal transport coefficient
KPPhbl  1 SM m KPP boundary layer depth, bulk Ri criterion
KPPmld  1 SM m Mixed layer depth, dT=.8degC density criterion
KPPfrac  1 SM  Shortwave flux fraction penetrating mixing layer
lab_sea:
natl_box:
6.4.2.9 Experiments and tutorials that use kpp
 Labrador Sea experiment, in lab_sea verification directory
Next: 6.4.3 GGL90: a TKE
Up: 6.4 Ocean Packages
Previous: 6.4.1 GMREDI: GentMcWilliams/Redi SGS
Contents
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Massachusetts Institute of Technology 
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