mom_lateral_mixing_coeffs module reference

Variable mixing coefficients.

Data Types

varmix_cs

Variable mixing coefficients.

Functions/Subroutines

`calc_depth_function()`	Calculates the non-dimensional depth functions.
`calc_resoln_function()`	Calculates and stores the non-dimensional resolution functions.
`calc_sqg_struct()`	Calculates and stores functions of SQG mode.
`calc_slope_functions()`	Calculates and stores functions of isopycnal slopes, e.g.
`calc_visbeck_coeffs_old()`	Calculates factors used when setting diffusivity coefficients similar to Visbeck et al., 1997.
`calc_eady_growth_rate_2d()`	Calculates the Eady growth rate (2D fields) for use in MEKE and the Visbeck schemes.
`calc_slope_functions_using_just_e()`	The original calc_slope_function() that calculated slopes using interface positions only, not accounting for density variations.
`calc_qg_slopes()`	Calculates and returns isopycnal slopes with wider halos for use in finding QG viscosity.
`calc_qg_leith_viscosity()`	Calculates the Leith Laplacian and bi-harmonic viscosity coefficients.
`varmix_init()`	Initializes the variables mixing coefficients container.
`varmix_end()`	Destructor for VarMix control structure.

Detailed Description

This module provides a container for various factors used in prescribing diffusivities, that are a function of the state (in particular the stratification and isoneutral slopes).

The resolution function

The resolution function is expressed in terms of the ratio of grid-spacing to deformation radius. The square of the resolution parameter is

\[R^2 = \frac{L_d^2}{\Delta^2} = \frac{ c_g^2 }{ f^2 \Delta^2 + c_g \beta \Delta^2 }\]

where the grid spacing is calculated as

\[\Delta^2 = \Delta x^2 + \Delta y^2 .\]

Todo

Check this reference to Bob on/off paper. The resolution function used in scaling diffusivities ([38]) is

\[r(\Delta,L_d) = \frac{1}{1+(\alpha R)^p}\]

The resolution function can be applied independently to thickness diffusion (module mom_thickness_diffuse()), tracer diffusion (mom_tracer_hordiff) lateral viscosity (), tracer diffusion (mom_tracer_hordiff) lateral viscosity (mom_hor_visc()).).

Robert Hallberg, 2013: Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects. Ocean Modelling, 71, pp 92-103. http://dx.doi.org/10.1016/j.ocemod.2013.08.007

Symbol	Module parameter
	`USE_VARIABLE_MIXING`
	`RESOLN_SCALED_KH`
	`RESOLN_SCALED_KHTH`
	`RESOLN_SCALED_KHTR`
\(\alpha\)	`KH_RES_SCALE_COEF` (for thickness and tracer diffusivity)
\(p\)	`KH_RES_FN_POWER` (for thickness and tracer diffusivity)
\(\alpha\)	`VISC_RES_SCALE_COEF` (for lateral viscosity)
\(p\)	`VISC_RES_FN_POWER` (for lateral viscosity)
	`GILL_EQUATORIAL_LD`

Visbeck diffusivity

This module also calculates factors used in setting the thickness diffusivity similar to a Visbeck et al., 1997, scheme. The factors are combined in mom_thickness_diffuse::thickness_diffuse but calculated in this module.but calculated in this module.

\[\kappa_h = \alpha_s L_s^2 S N\]

where \(S\) is the magnitude of the isoneutral slope and \(N\) is the Brunt-Vaisala frequency.

Visbeck, Marshall, Haine and Spall, 1997: Specification of Eddy Transfer Coefficients in Coarse-Resolution Ocean Circulation Models. J. Phys. Oceanogr. http://dx.doi.org/10.1175/1520-0485(1997)027%3C0381:SOETCI%3E2.0.CO;2

Symbol	Module parameter
	`USE_VARIABLE_MIXING`
\(\alpha_s\)	`KHTH_SLOPE_CFF` (for `mom_thickness_diffuse()` module) module)
\(\alpha_s\)	`KHTR_SLOPE_CFF` (for mom_tracer_hordiff module)
\(L_{s}\)	`VISBECK_L_SCALE`
\(S_{max}\)	`VISBECK_MAX_SLOPE`

Vertical structure function for KhTh

The thickness diffusivity can be prescribed a vertical distribution with the shape of the equivalent barotropic velocity mode. The structure function is stored in the control structure for this module (varmix_cs()) but is calculated using subroutines in ) but is calculated using subroutines in mom_wave_speed()..

Symbol	Module parameter
	`KHTH_USE_EBT_STRUCT`

Type Documentation

type mom_lateral_mixing_coeffs/varmix_cs

Variable mixing coefficients.

Type fields:

% id_sn_u :: integer Diagnostic identifier.
% id_sn_v :: integer Diagnostic identifier.
% id_l2u :: integer Diagnostic identifier.
% id_l2v :: integer Diagnostic identifier.
% id_res_fn :: integer Diagnostic identifier.
% id_n2_u :: integer Diagnostic identifier.
% id_n2_v :: integer Diagnostic identifier.
% id_s2_u :: integer Diagnostic identifier.
% id_s2_v :: integer Diagnostic identifier.
% id_dzu :: integer Diagnostic identifier.
% id_dzv :: integer Diagnostic identifier.
% id_dzsxn :: integer Diagnostic identifier.
% id_dzsyn :: integer Diagnostic identifier.
% id_rd_dx :: integer Diagnostic identifier.
% id_kh_u_qg :: integer Diagnostic identifier.
% id_kh_v_qg :: integer Diagnostic identifier.
% id_sqg_struct :: integer Diagnostic identifier.
% id_bs_struct :: integer Diagnostic identifier.
% id_khth_struct :: integer Diagnostic identifier.
% id_khtr_struct :: integer Diagnostic identifier.
% id_kdgl90_struct :: integer Diagnostic identifier.
% diag :: type(diag_ctrl), pointer A structure that is used to regulate the timing of diagnostic output.
% initialized :: logical True if this control structure has been initialized.
% use_variable_mixing :: logical If true, use the variable mixing.
% resoln_scaling_used :: logical If true, a resolution function is used somewhere to scale away one of the viscosities or diffusivities when the deformation radius is well resolved.
% resoln_scaled_kh :: logical If true, scale away the Laplacian viscosity when the deformation radius is well resolved.
% resoln_scaled_khth :: logical If true, scale away the thickness diffusivity when the deformation radius is well resolved.
% depth_scaled_khth :: logical If true, KHTH is scaled away when the depth is shallower than a reference depth.
% resoln_scaled_khtr :: logical If true, scale away the tracer diffusivity when the deformation radius is well resolved.
% interpolate_res_fn :: logical If true, interpolate the resolution function to the velocity points from the thickness points; otherwise interpolate the wave speed and calculate the resolution function independently at each point.
% use_stored_slopes :: logical If true, stores isopycnal slopes in this structure.
% resoln_use_ebt :: logical If true, use the equivalent barotropic wave speed instead of the first baroclinic wave speed for calculating the resolution function.
% khth_use_ebt_struct :: logical If true, uses the equivalent barotropic structure as the vertical structure of thickness diffusivity.
% kdgl90_use_ebt_struct :: logical If true, uses the equivalent barotropic structure as the vertical structure of diffusivity in the GL90 scheme.
% kdgl90_use_sqg_struct :: logical If true, uses the surface quasigeostrophic structure as the vertical structure of diffusivity in the GL90 scheme.
% khth_use_sqg_struct :: logical If true, uses the surface quasigeostrophic structure as the vertical structure of thickness diffusivity.
% khtr_use_ebt_struct :: logical If true, uses the equivalent barotropic structure as the vertical structure of tracer diffusivity.
% khtr_use_sqg_struct :: logical If true, uses the surface quasigeostrophic structure as the vertical structure of tracer diffusivity.
% calculate_cg1 :: logical If true, calls
% calculate_rd_dx :: logical If true, calculates Rd/dx and populate CSRd_dx_h. This parameter is set depending on other parameters.
% calculate_res_fns :: logical If true, calculate all the resolution factors. This parameter is set depending on other parameters.
% calculate_depth_fns :: logical If true, calculate all the depth factors. This parameter is set depending on other parameters.
% calculate_eady_growth_rate :: logical If true, calculate all the Eady growth rates. This parameter is set depending on other parameters.
% use_stanley_iso :: logical If true, use Stanley parameterization in MOM_isopycnal_slopes.
% use_simpler_eady_growth_rate :: logical If true, use a simpler method to calculate the Eady growth rate that avoids division by layer thickness. This parameter is set depending on other parameters.
% full_depth_eady_growth_rate :: logical If true, calculate the Eady growth rate based on an average that includes contributions from sea-level changes in its denominator, rather than just the nominal depth of the bathymetry. This only applies when using the model interface heights as a proxy for isopycnal slopes.
% obc_friendly :: logical If true, use only interior data for thickness weighting and to calculate stratification and other fields at open boundary condition faces.
% res_fn_obc_bug :: logical If false, use only interior data for calculating the resolution functions at open boundary condition faces and vertices.
% cropping_distance :: real Distance from surface or bottom to filter out outcropped or incropped interfaces for the Eady growth rate calc [Z ~> m].
% h_min_n2 :: real The minimum vertical distance to use in the denominator of the buoyancy frequency used in the slope calculation [H ~> m or kg m-2].
% sn_u :: real, dimension(:,:), allocatable S*N at u-points [T-1 ~> s-1].
% sn_v :: real, dimension(:,:), allocatable S*N at v-points [T-1 ~> s-1].
% l2u :: real, dimension(:,:), allocatable Length scale^2 at u-points [L2 ~> m2].
% l2v :: real, dimension(:,:), allocatable Length scale^2 at v-points [L2 ~> m2].
% cg1 :: real, dimension(:,:), allocatable The first baroclinic gravity wave speed [L T-1 ~> m s-1].
% res_fn_h :: real, dimension(:,:), allocatable Non-dimensional function of the ratio the first baroclinic deformation radius to the grid spacing at h points [nondim].
% res_fn_q :: real, dimension(:,:), allocatable Non-dimensional function of the ratio the first baroclinic deformation radius to the grid spacing at q points [nondim].
% res_fn_u :: real, dimension(:,:), allocatable Non-dimensional function of the ratio the first baroclinic deformation radius to the grid spacing at u points [nondim].
% res_fn_v :: real, dimension(:,:), allocatable Non-dimensional function of the ratio the first baroclinic deformation radius to the grid spacing at v points [nondim].
% depth_fn_u :: real, dimension(:,:), allocatable Non-dimensional function of the ratio of the depth to a reference depth (maximum 1) at u points [nondim].
% depth_fn_v :: real, dimension(:,:), allocatable Non-dimensional function of the ratio of the depth to a reference depth (maximum 1) at v points [nondim].
% beta_dx2_h :: real, dimension(:,:), allocatable The magnitude of the gradient of the Coriolis parameter times the grid spacing squared at h points [L T-1 ~> m s-1].
% beta_dx2_q :: real, dimension(:,:), allocatable The magnitude of the gradient of the Coriolis parameter times the grid spacing squared at q points [L T-1 ~> m s-1].
% beta_dx2_u :: real, dimension(:,:), allocatable The magnitude of the gradient of the Coriolis parameter times the grid spacing squared at u points [L T-1 ~> m s-1].
% beta_dx2_v :: real, dimension(:,:), allocatable The magnitude of the gradient of the Coriolis parameter times the grid spacing squared at v points [L T-1 ~> m s-1].
% f2_dx2_h :: real, dimension(:,:), allocatable The Coriolis parameter squared times the grid spacing squared at h [L2 T-2 ~> m2 s-2].
% f2_dx2_q :: real, dimension(:,:), allocatable The Coriolis parameter squared times the grid spacing squared at q [L2 T-2 ~> m2 s-2].
% f2_dx2_u :: real, dimension(:,:), allocatable The Coriolis parameter squared times the grid spacing squared at u [L2 T-2 ~> m2 s-2].
% f2_dx2_v :: real, dimension(:,:), allocatable The Coriolis parameter squared times the grid spacing squared at v [L2 T-2 ~> m2 s-2].
% rd_dx_h :: real, dimension(:,:), allocatable Deformation radius over grid spacing [nondim].
% slope_x :: real, dimension(:,:,:), allocatable Zonal isopycnal slope [Z L-1 ~> nondim].
% slope_y :: real, dimension(:,:,:), allocatable Meridional isopycnal slope [Z L-1 ~> nondim].
% ebt_struct :: real, dimension(:,:,:), allocatable EBT vertical structure to scale diffusivities with [nondim].
% sqg_struct :: real, dimension(:,:,:), allocatable SQG vertical structure to scale diffusivities with [nondim].
% bs_struct :: real, dimension(:,:,:), allocatable Vertical structure function used in backscatter [nondim].
% khth_struct :: real, dimension(:,:,:), allocatable Vertical structure function used in thickness diffusivity [nondim].
% khtr_struct :: real, dimension(:,:,:), allocatable Vertical structure function used in tracer diffusivity [nondim].
% kdgl90_struct :: real, dimension(:,:,:), allocatable Vertical structure function used in GL90 diffusivity [nondim].
% bs_ebt_power :: real Power to raise EBT vertical structure to. Default 0.0.
% sqg_expo :: real Exponent for SQG vertical structure [nondim]. Default 1.0.
% interpolated_sqg_struct :: logical If true, interpolate properties to velocity points and then interpolate the buoyancy frequencies and layer thicknesses back to tracer points when calculating the SQG vertical structure.
% bs_use_sqg_struct :: logical If true, use sqg_stuct for backscatter vertical structure.
% laplac3_const_u :: real, dimension(:,:), allocatable Laplacian metric-dependent constants at u-points [L3 ~> m3].
% laplac3_const_v :: real, dimension(:,:), allocatable Laplacian metric-dependent constants at u-points [L3 ~> m3].
% kh_u_qg :: real, dimension(:,:,:), allocatable QG Leith GM coefficient at u-points [L2 T-1 ~> m2 s-1].
% kh_v_qg :: real, dimension(:,:,:), allocatable QG Leith GM coefficient at v-points [L2 T-1 ~> m2 s-1].
% use_visbeck :: logical Use Visbeck formulation for thickness diffusivity.
% varmix_ktop :: integer Top layer to start downward integrals.
% visbeck_l_scale :: real Fixed length scale in Visbeck formula [L ~> m], or if negative a scaling factor [nondim] relating this length scale squared to the cell area.
% eady_gr_d_scale :: real Depth over which to average SN [Z ~> m].
% res_coef_khth :: real A coefficient [nondim] that determines the function of resolution, used for thickness and tracer mixing, as: F = 1 / (1 + (Res_coef_khth*Ld/dx)^Res_fn_power)
% res_coef_visc :: real A coefficient [nondim] that determines the function of resolution, used for lateral viscosity, as: F = 1 / (1 + (Res_coef_visc*Ld/dx)^Res_fn_power)
% depth_scaled_khth_h0 :: real The depth above which KHTH is linearly scaled away [Z ~> m].
% depth_scaled_khth_exp :: real The exponent used in the depth dependent scaling function for KHTH [nondim].
% kappa_smooth :: real A diffusivity for smoothing T/S in vanished layers [H Z T-1 ~> m2 s-1 or kg m-1 s-1].
% res_fn_power_khth :: integer The power of dx/Ld in the KhTh resolution function. Any positive integer power may be used, but even powers and especially 2 are coded to be more efficient.
% res_fn_power_visc :: integer The power of dx/Ld in the Kh resolution function. Any positive integer power may be used, but even powers and especially 2 are coded to be more efficient.
% visbeck_s_max :: real Upper bound on slope used in Eady growth rate [Z L-1 ~> nondim].
% use_qg_leith_gm :: logical If true, uses the QG Leith viscosity as the GM coefficient.
% use_beta_in_qg_leith :: logical If true, includes the beta term in the QG Leith GM coefficient.
% wave_speed :: type(wave_speed_cs) Wave speed control structure.
% pass_cg1 :: type(group_pass_type) For group halo pass.
% debug :: logical If true, write out checksums of data for debugging.

[source]

Function/Subroutine Documentation

subroutine mom_lateral_mixing_coeffs/calc_depth_function(G, CS)

Calculates the non-dimensional depth functions.

Parameters:

g :: [in] Ocean grid structure
cs :: [inout] Variable mixing control structure

Call to:

mom_error_handler::mom_error

Called from:

mom::step_mom mom::step_offline

[source]

subroutine mom_lateral_mixing_coeffs/calc_resoln_function(h, tv, G, GV, US, CS, MEKE, OBC, dt)

Calculates and stores the non-dimensional resolution functions.

Parameters:

g :: [inout] Ocean grid structure
gv :: [in] Vertical grid structure
h :: h [in] Layer thickness [H ~> m or kg m-2]
tv :: tv [in] Thermodynamic variables
us :: [in] A dimensional unit scaling type
cs :: [inout] Variable mixing control structure
meke :: [in] MEKE struct
obc :: Open boundaries control structure
dt :: dt [in] Time increment [T ~> s]

Call to:

calc_sqg_struct mom_error_handler::mom_error mom_diag_mediator::query_averaging_enabled mom_wave_speed::wave_speed

Called from:

mom::step_mom mom::step_offline

[source]

subroutine mom_lateral_mixing_coeffs/calc_sqg_struct(h, tv, G, GV, US, CS, dt, MEKE, OBC)

Calculates and stores functions of SQG mode.

Parameters:

g :: [inout] Ocean grid structure
gv :: [in] Vertical grid structure
us :: [in] A dimensional unit scaling type
h :: h [in] Layer thickness [H ~> m or kg m-2]
tv :: tv [in] Thermodynamic variables
dt :: dt [in] Time increment [T ~> s]
cs :: [inout] Variable mixing control struct
meke :: [in] MEKE struct
obc :: Open boundaries control structure

Call to:

mom_isopycnal_slopes::calc_isoneutral_slopes mom_eos::eos_domain mom_error_handler::mom_error mom_diag_mediator::query_averaging_enabled

Called from:

calc_resoln_function

[source]

subroutine mom_lateral_mixing_coeffs/calc_slope_functions(h, tv, dt, G, GV, US, CS, OBC)

Calculates and stores functions of isopycnal slopes, e.g. Sx, Sy, S*N, mostly used in the Visbeck et al. style scaling of diffusivity.

Parameters:

g :: [inout] Ocean grid structure
gv :: [in] Vertical grid structure
us :: [in] A dimensional unit scaling type
h :: h [inout] Layer thickness [H ~> m or kg m-2]
tv :: tv [in] Thermodynamic variables
dt :: dt [in] Time increment [T ~> s]
cs :: [inout] Variable mixing control structure
obc :: Open boundaries control structure

Call to:

calc_eady_growth_rate_2d mom_isopycnal_slopes::calc_isoneutral_slopes calc_slope_functions_using_just_e calc_visbeck_coeffs_old mom_error_handler::mom_error mom_diag_mediator::query_averaging_enabled

[source]

subroutine mom_lateral_mixing_coeffs/calc_visbeck_coeffs_old(h, slope_x, slope_y, N2_u, N2_v, G, GV, US, CS, OBC)

Calculates factors used when setting diffusivity coefficients similar to Visbeck et al., 1997. This is on older implementation that is susceptible to large values of Eady growth rate for incropping layers.

Parameters:

g :: [inout] Ocean grid structure
gv :: [in] Vertical grid structure
h :: h [in] Layer thickness [H ~> m or kg m-2]
slope_x :: slope_x [in] Zonal isoneutral slope [Z L-1 ~> nondim]
n2_u :: [in] Buoyancy (Brunt-Vaisala) frequency at u-points [L2 Z-2 T-2 ~> s-2]
slope_y :: slope_y [in] Meridional isoneutral slope [Z L-1 ~> nondim]
n2_v :: [in] Buoyancy (Brunt-Vaisala) frequency at v-points [L2 Z-2 T-2 ~> s-2]
us :: [in] A dimensional unit scaling type
cs :: [inout] Variable mixing control structure
obc :: Open boundaries control structure.

Call to:

mom_error_handler::mom_error mom_diag_mediator::query_averaging_enabled

Called from:

calc_slope_functions

[source]

subroutine mom_lateral_mixing_coeffs/calc_eady_growth_rate_2d(CS, G, GV, US, h, e, dzu, dzv, dzSxN, dzSyN, SN_u, SN_v)

Calculates the Eady growth rate (2D fields) for use in MEKE and the Visbeck schemes.

Parameters:

cs :: [inout] Variable mixing coefficients
g :: [in] Ocean grid structure
gv :: [in] Vertical grid structure
us :: [in] A dimensional unit scaling type
h :: h [in] Interface height [Z ~> m]
e :: e [in] Interface height [Z ~> m]
dzu :: dzu [in] dz at u-points [Z ~> m]
dzv :: dzv [in] dz at v-points [Z ~> m]
dzsxn :: [in] dz Sx N at u-points [Z T-1 ~> m s-1]
dzsyn :: [in] dz Sy N at v-points [Z T-1 ~> m s-1]
sn_u :: [inout] SN at u-points [T-1 ~> s-1]
sn_v :: [inout] SN at v-points [T-1 ~> s-1]

Called from:

calc_slope_functions

[source]

subroutine mom_lateral_mixing_coeffs/calc_slope_functions_using_just_e(h, G, GV, US, CS, e)

The original calc_slope_function() that calculated slopes using interface positions only, not accounting for density variations.

Parameters:

g :: [inout] Ocean grid structure
gv :: [in] Vertical grid structure
h :: h [inout] Layer thickness [H ~> m or kg m-2]
us :: [in] A dimensional unit scaling type
cs :: [inout] Variable mixing control structure
e :: e [in] Interface position [Z ~> m]

Call to:

mom_error_handler::mom_error

Called from:

calc_slope_functions

[source]

subroutine mom_lateral_mixing_coeffs/calc_qg_slopes(h, tv, dt, G, GV, US, slope_x, slope_y, CS, OBC)

Calculates and returns isopycnal slopes with wider halos for use in finding QG viscosity.

Parameters:

g :: [in] Ocean grid structure
gv :: [in] Vertical grid structure
us :: [in] A dimensional unit scaling type
h :: h [in] Layer thickness [H ~> m or kg m-2]
tv :: tv [in] Thermodynamic variables
dt :: dt [in] Time increment [T ~> s]
slope_x :: slope_x [inout] Isopycnal slope in i-dir [Z L-1 ~> nondim]
slope_y :: slope_y [inout] Isopycnal slope in j-dir [Z L-1 ~> nondim]
cs :: [in] Variable mixing control structure
obc :: Open boundaries control structure

Call to:

mom_isopycnal_slopes::calc_isoneutral_slopes mom_error_handler::mom_error

Called from:

mom_hor_visc::horizontal_viscosity

[source]

subroutine mom_lateral_mixing_coeffs/calc_qg_leith_viscosity(CS, G, GV, US, h, dz, k, div_xx_dx, div_xx_dy, slope_x, slope_y, vort_xy_dx, vort_xy_dy)

Calculates the Leith Laplacian and bi-harmonic viscosity coefficients.

Parameters:

cs :: [inout] Variable mixing coefficients
g :: [in] Ocean grid structure
gv :: [in] The ocean’s vertical grid structure.
us :: [in] A dimensional unit scaling type
h :: h [in] Layer thickness [H ~> m or kg m-2]
dz :: dz [in] Layer vertical extents [Z ~> m]
k :: k [in] Layer for which to calculate vorticity magnitude
div_xx_dx :: div_xx_dx [in] x-derivative of horizontal divergence (d/dx(du/dx + dv/dy)) [L-1 T-1 ~> m-1 s-1]
div_xx_dy :: div_xx_dy [in] y-derivative of horizontal divergence (d/dy(du/dx + dv/dy)) [L-1 T-1 ~> m-1 s-1]
slope_x :: slope_x [inout] Isopycnal slope in i-dir [Z L-1 ~> nondim]
slope_y :: slope_y [inout] Isopycnal slope in j-dir [Z L-1 ~> nondim]
vort_xy_dx :: vort_xy_dx [inout] x-derivative of vertical vorticity (d/dx(dv/dx - du/dy)) [L-1 T-1 ~> m-1 s-1]
vort_xy_dy :: vort_xy_dy [inout] y-derivative of vertical vorticity (d/dy(dv/dx - du/dy)) [L-1 T-1 ~> m-1 s-1]

Called from: