KPP mixing

The k-profile parameterization (KPP) [13] is relatively complex and only the parameters that are routinely changed are shown here in the namelist. It is possible to change other parameters by editing the KPP module, but this should not be necessary and is discouraged. As described previously, KPP utilizes enhanced diffusion for convection so implicit vertical mixing must be enabled and diffusion must be specified as the convection method. Note that the constants convect_diff, convect_visc are used for convection within KPP.

A recent change to the KPP implementation is to allow a depth dependent background diffusivity κ and viscosity ν. The form of this dependence is

κ = κ_1 + κ_2 arctan((z - d)/L) (3.1)

Table: KPP namelist

&vmix_kpp_nml	LANL default	CESM1 default	Valid values	KPP mixing
bckgrnd_vdc1	0.1	0.1		base background vertical diffusivity (cm2/s)
bckgrnd_vdc2	0.0	0.0		variation in background vertical diffusivity (cm2/s)
bckgrnd_vdc_eq (CESM1 only)	N/A	resolution- and option-dependent value determined by CESM1 scripts		equatorial diffusivity (Gregg)
bckgrnd_vdc_psim (CESM1 only)	N/A	resolution- and option-dependent value determined by CESM1 scripts		maximum PSI induced diffusivity (MacKinnon)
bckgrnd_vdc_ban (CESM1 only)	N/A	resolution- and option-dependent value determined by CESM1 scripts		Banda Sea diffusivity (Gordon)
bckgrnd_vdc_dpth	250000.0	250000.0		depth (cm) at which background vertical diffusivity is vdc1
bckgrnd_vdc_linv	0.000045	0.000045		inverse of the length scale (1/L in cm-1) over which diffusivity transition takes place
Prandtl	10.0	10.0		(unitless) ratio of background vertical viscosity and diffusivity
rich_mix	50.0	50.0		Coefficient for Richardson-number function
lrich	.true.	.true.	.true., .false.	use Richardson-number for interior mixing
ldbl_diff	.false.	.false.	.true., .false.	add double-diffusive parameterization
lshort_wave	.false.	.false.	.true., .false.	use penetrative shortwave forcing
lcheckekmo	.false.	.false.	.true., .false.	check whether boundary layer exceeds Ekman or Monin-Obukhov limit
num_v_smooth_Ri	1	1		Number of passes to smooth Richardson number
lhoriz_varying_bckgrnd (CESM1 only)	N/A	.true.	.true., .false.
llangmuir (CESM1 only)	N/A	.false.	.true., .false.	flag to activate Langmuir parameterization
linertial (CESM1 only)	N/A	.false.	.true., .false.	flag to activate inertial mixing parameterization
/

ν = (PR)κ (3.2)

where z is the model depth, d is the depth at which κ reaches κ_1, L is a length scale over which the transition between κ_1 and κ_2 takes place and Pr is the Prandtl number. If a constant diffusivity and viscosity are required, simply set vdc2 to zero and vdc1 to the appropriate diffusivity.