Corrections to cell-averaged density computation

[iangrooms]

This PR builds on mom-ocean#1156 and mom-ocean#1209, implementing a correction to the computation of cell-averaged density in various parts of the model. A description of the parameterization and results can be found in these papers.

The main updates in this PR are the ability to use a new stochastic version of the correction, and the ability to turn on the density correction in the calculation of the mixed layer lateral density gradient in the mixed layer restratification parameterization.
In addition, the code related to this parameterization has been re-factored a bit, along with some small bug fixes.

The parameterization can be toggled on/off in different parts of the code using the following flags:

• USE_STANLEY_PGF turns it on in computation of the pressure gradient force
• USE_STANLEY_ML turns it on in the mixed layer restratification parameterization
• USE_STANLEY_ISO turns it on in the computation of isopycnal slopes in MOM_isopycnal_slopes.F90. This doesn't necessarily turn it on in MOM_thickness_diffuse.F90 though, since MOM_thickness_diffuse.F90 sometimes computes its own isopycnal slopes. See below
• USE_STANLEY_GM turns it on in the computation of isopycnal slopes in GM. Specifically, it sets use_stanley to .TRUE. in these lines of MOM_thickness_diffuse.F90

  MOM6/src/parameterizations/lateral/MOM_thickness_diffuse.F90

  Lines 797 to 798 in 3d62428

  	calc_derivatives = use_EOS .and. (k >= nk_linear) .and. &
  	(find_work .or. .not. present_slope_x .or. CS%use_FGNV_streamfn .or. use_stanley)

  .

The tunable coefficients of the parameterization are controlled by

• STANLEY_COEFF this is the main tunable coefficient, denoted c in the papers linked above. The SGS temperature variance is parameterized as c times squared temperature differences.
• STANLEY_A allows you to tune the amplitude of the noise in the stochastic version. The multiplicative noise is exp(a * chi). With a default of 1.0 you get the stochastic parameterization described in the papers. With a value of 0.0 you get a deterministic parameterization.

[gustavo-marques]

Passing tests in mom_aux and Cheyenne-MOM6-examples.

MOM_input parameters added:

USE_STANLEY_ISO = False         !   [Boolean] default = False
                                ! If true, turn on Stanley SGS T variance parameterization in isopycnal slope
                                ! code.

USE_STANLEY_GM = False          !   [Boolean] default = False
                                ! If true, turn on Stanley SGS T variance parameterization in GM code.

STOCH_EOS = False               !   [Boolean] default = False
                                ! If true, stochastic perturbations are applied to the EOS in the PGF.

STANLEY_COEFF = -1.0            !   [not defined] default = -1.0
                                ! Coefficient correlating the temperature gradient and SGS T variance.

STANLEY_A = 1.0                 !   [not defined] default = 1.0
                                ! Coefficient a which scales chi in stochastic perturbation of the SGS T
                                ! variance.

USE_STANLEY_PGF = False         !   [Boolean] default = False
                               ! If true, turn on Stanley SGS T variance parameterization in PGF code.

USE_STANLEY_ML = False          !   [Boolean] default = False
                                ! If true, turn on Stanley SGS T variance parameterization in ML restrat code.

MOM_input parameters there were removed:

STANLEY_PRM_DET_COEFF = -1.0    !   [nondim] default = -1.0
                                ! The coefficient correlating SGS temperature variance with the mean temperature
                                ! gradient in the deterministic part of the Stanley parameterization. Negative
                                ! values disable the scheme.

PGF_STANLEY_T2_DET_COEFF = -1.0 !   [nondim] default = -1.0
                                ! The coefficient correlating SGS temperature variance with the mean temperature
                                ! gradient in the deterministic part of the Stanley form of the Brankart
                                ! correction. Negative values disable the scheme.