mom_ice_shelf_dynamics module reference

Implements a crude placeholder for a later implementation of full ice shelf dynamics.

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Data Types

ice_shelf_dyn_cs	The control structure for the ice shelf dynamics.
loop_bounds_type	A container for loop bounds.

Functions/Subroutines

slope_limiter()	used for flux limiting in advective subroutines Van Leer limiter (source: Wikipedia) The return value is between 0 and 2 [nondim].
quad_area()	Calculate area of quadrilateral.
register_ice_shelf_dyn_restarts()	This subroutine is used to register any fields related to the ice shelf dynamics that should be written to or read from the restart file.
initialize_ice_shelf_dyn()	Initializes shelf model data, parameters and diagnostics.
initialize_diagnostic_fields()
ice_time_step_cfl()	This function returns the global maximum advective timestep that can be taken based on the current ice velocities.
update_ice_shelf()	This subroutine updates the ice shelf velocities, mass, stresses and properties due to the ice shelf dynamics.
ice_shelf_advect()	This subroutine takes the velocity (on the Bgrid) and timesteps h_t = - div (uh) once.
ice_shelf_solve_outer()
ice_shelf_solve_inner()
ice_shelf_advect_thickness_x()
ice_shelf_advect_thickness_y()
shelf_advance_front()
ice_shelf_min_thickness_calve()	Apply a very simple calving law using a minimum thickness rule.
calve_to_mask()
calc_shelf_driving_stress()
init_boundary_values()
cg_action()
cg_action_subgrid_basal()
matrix_diagonal()	returns the diagonal entries of the matrix for a Jacobi preconditioning
cg_diagonal_subgrid_basal()
apply_boundary_values()
calc_shelf_visc()	Update depth integrated viscosity, based on horizontal strain rates, and also update the nonlinear part of the basal traction.
update_od_ffrac()
update_od_ffrac_uncoupled()
bilinear_shape_functions()	This subroutine calculates the gradients of bilinear basis elements that that are centered at the vertices of the cell.
bilinear_shape_fn_grid()	This subroutine calculates the gradients of bilinear basis elements that are centered at the vertices of the cell using a locally orthogoal MOM6 grid.
bilinear_shape_functions_subgrid()
update_velocity_masks()
interpolate_h_to_b()	Interpolate the ice shelf thickness from tracer point to nodal points, subject to a mask.
ice_shelf_dyn_end()	Deallocates all memory associated with the ice shelf dynamics module.
ice_shelf_temp()	This subroutine updates the vertically averaged ice shelf temperature.
ice_shelf_advect_temp_x()
ice_shelf_advect_temp_y()

Detailed Description

Implements a crude placeholder for a later implementation of full ice shelf dynamics.

Type Documentation

type mom_ice_shelf_dynamics/ice_shelf_dyn_cs

The control structure for the ice shelf dynamics.

Type fields

• % id_u_shelf [integer] :: Diagnostic handles.

• % id_v_shelf [integer] :: Diagnostic handles.

• % id_t_shelf [integer] :: Diagnostic handles.

• % id_ground_frac [integer] :: Diagnostic handles.

• % id_col_thick [integer] :: Diagnostic handles.

• % id_od_av [integer] :: Diagnostic handles.

• % id_u_mask [integer] :: Diagnostic handles.

• % id_v_mask [integer] :: Diagnostic handles.

• % id_t_mask [integer] :: Diagnostic handles.

• % u_shelf [real(:,:),pointer] :: the zonal velocity of the ice shelf/sheet on q-points (B grid) [L T-1 ~> m s-1]

• % v_shelf [real(:,:),pointer] :: the meridional velocity of the ice shelf/sheet on q-points (B grid) [L T-1 ~> m s-1]

• % u_face_mask [real(:,:),pointer] :: mask for velocity boundary conditions on the C-grid u-face - this is because the FEM cares about FACES THAT GET INTEGRATED OVER, not vertices. Will represent boundary conditions on computational boundary (or permanent boundary between fast-moving and near-stagnant ice FOR NOW: 1=interior bdry, 0=no-flow boundary, 2=stress bdry condition, 3=inhomogeneous Dirichlet boundary, 4=flux boundary: at these faces a flux will be specified which will override velocities; a homogeneous velocity condition will be specified (this seems to give the solver less difficulty)

• % v_face_mask [real(:,:),pointer] :: A mask for velocity boundary conditions on the C-grid v-face, with valued defined similarly to u_face_mask.

• % u_face_mask_bdry [real(:,:),pointer] :: A duplicate copy of u_face_mask?

• % v_face_mask_bdry [real(:,:),pointer] :: A duplicate copy of v_face_mask?

• % u_flux_bdry_val [real(:,:),pointer] :: The ice volume flux per unit face length into the cell through open boundary u-faces (where u_face_mask=4) [Z L T-1 ~> m2 s-1].

• % v_flux_bdry_val [real(:,:),pointer] :: The ice volume flux per unit face length into the cell through open boundary v-faces (where v_face_mask=4) [Z L T-1 ~> m2 s-1]??

• % umask [real(:,:),pointer] :: u-mask on the actual degrees of freedom (B grid) 1=normal node, 3=inhomogeneous boundary node, 0 - no flow node (will also get ice-free nodes)

• % vmask [real(:,:),pointer] :: v-mask on the actual degrees of freedom (B grid) 1=normal node, 3=inhomogeneous boundary node, 0 - no flow node (will also get ice-free nodes)

• % calve_mask [real(:,:),pointer] :: a mask to prevent the ice shelf front from advancing past its initial position (but it may retreat)

• % t_shelf [real(:,:),pointer] :: Vertically integrated temperature in the ice shelf/stream, on corner-points (B grid) [degC].

• % tmask [real(:,:),pointer] :: A mask on tracer points that is 1 where there is ice.

• % ice_visc [real(:,:),pointer] :: Glen’s law ice viscosity, often in [R L4 Z T-1 ~> kg m2 s-1].

• % thickness_bdry_val [real(:,:),pointer] :: The ice thickness at an inflowing boundary [Z ~> m].

• % u_bdry_val [real(:,:),pointer] :: The zonal ice velocity at inflowing boundaries [L yr-1 ~> m yr-1].

• % v_bdry_val [real(:,:),pointer] :: The meridional ice velocity at inflowing boundaries [L yr-1 ~> m yr-1].

• % h_bdry_val [real(:,:),pointer] :: The ice thickness at inflowing boundaries [m].

• % t_bdry_val [real(:,:),pointer] :: The ice temperature at inflowing boundaries [degC].

• % basal_traction [real(:,:),pointer] :: The area integrated nonlinear part of “linearized” basal stress [R Z L2 T-1 ~> kg s-1]. The exact form depends on basal law exponent and/or whether flow is “hybridized” a la Goldberg 2011.

• % od_rt [real(:,:),pointer] :: A running total for calculating OD_av.

• % ground_frac_rt [real(:,:),pointer] :: A running total for calculating ground_frac.

• % od_av [real(:,:),pointer] :: The time average open ocean depth [Z ~> m].

• % ground_frac [real(:,:),pointer] :: Fraction of the time a cell is “exposed”, i.e. the column thickness is below a threshold and interacting with the rock [nondim]. When this is 1, the ice-shelf is grounded.

• % od_rt_counter [integer] :: A counter of the number of contributions to OD_rt.

• % velocity_update_time_step [real] :: The time interval over which to update the ice shelf velocity using the nonlinear elliptic equation, or 0 to update every timestep [T ~> s].

• % elapsed_velocity_time [real] :: The elapsed time since the ice velocities were last updated [T ~> s].

• % g_earth [real] :: The gravitational acceleration [L2 Z-1 T-2 ~> m s-2].

• % density_ice [real] :: A typical density of ice [R ~> kg m-3].

• % gl_regularize [logical] :: Specifies whether to regularize the floatation condition at the grounding line as in Goldberg Holland Schoof 2009.

• % n_sub_regularize [integer] :: partition of cell over which to integrate for interpolated grounding line the (rectangular) is divided into nxn equally-sized rectangles, over which basal contribution is integrated (iterative quadrature)

• % gl_couple [logical] :: whether to let the floatation condition be determined by ocean column thickness means update_OD_ffrac will be called (note: GL_regularize and GL_couple should be exclusive)

• % cfl_factor [real] :: A factor used to limit subcycled advective timestep in uncoupled runs i.e. dt <= CFL_factor * min(dx / u)

• % a_glen_isothermal [real] :: Ice viscosity parameter in Glen’s Law, [Pa-3 s-1].

• % n_glen [real] :: Nonlinearity exponent in Glen’s Law.

• % eps_glen_min [real] :: Min. strain rate to avoid infinite Glen’s law viscosity, [year-1].

• % c_basal_friction [real] :: Coefficient in sliding law tau_b = C u^(n_basal_fric), in units= Pa (m yr-1)-(n_basal_fric)

• % n_basal_fric [real] :: Exponent in sliding law tau_b = C u^(m_slide)

• % density_ocean_avg [real] :: A typical ocean density [R ~> kg m-3]. This does not affect ocean circulation or thermodynamics. It is used to estimate the gravitational driving force at the shelf front (until we think of a better way to do it, but any difference will be negligible).

• % thresh_float_col_depth [real] :: The water column depth over which the shelf if considered to be floating.

• % moving_shelf_front [logical] :: Specify whether to advance shelf front (and calve).

• % calve_to_mask [logical] :: If true, calve off the ice shelf when it passes the edge of a mask.

• % min_thickness_simple_calve [real] :: min. ice shelf thickness criteria for calving [Z ~> m].

• % cg_tolerance [real] :: The tolerance in the CG solver, relative to initial residual, that determines when to stop the conjugate gradient iterations.

• % nonlinear_tolerance [real] :: The fractional nonlinear tolerance, relative to the initial error, that sets when to stop the iterative velocity solver.

• % cg_max_iterations [integer] :: The maximum number of iterations that can be used in the CG solver.

• % nonlin_solve_err_mode [integer] :: 1: exit vel solve based on nonlin residual 2: exit based on “fixed point” metric (|u - u_last| / |u| < tol) where | | is infty-norm

• % debug [logical] :: If true, write verbose checksums for debugging purposes and use reproducible sums.

• % module_is_initialized [logical] :: True if this module has been initialized.

• % diag [type(diag_ctrl),pointer] :: A structure that is used to control diagnostic output.

type mom_ice_shelf_dynamics/loop_bounds_type

A container for loop bounds.

Type fields

• % ish [integer,private] :: Loop bounds.

• % ieh [integer,private] :: Loop bounds.

• % jsh [integer,private] :: Loop bounds.

• % jeh [integer,private] :: Loop bounds.

Function/Subroutine Documentation

function mom_ice_shelf_dynamics/slope_limiter(num, denom) [real]

used for flux limiting in advective subroutines Van Leer limiter (source: Wikipedia) The return value is between 0 and 2 [nondim].

Parameters

• num :: [in] The numerator of the ratio used in the Van Leer slope limiter

• denom :: [in] The denominator of the ratio used in the Van Leer slope limiter

Called from

ice_shelf_advect_temp_x ice_shelf_advect_temp_y ice_shelf_advect_thickness_x ice_shelf_advect_thickness_y

function mom_ice_shelf_dynamics/quad_area(X, Y) [real]

Calculate area of quadrilateral.

Parameters

• x :: [in] The x-positions of the vertices of the quadrilateral [L ~> m].

• y :: [in] The y-positions of the vertices of the quadrilateral [L ~> m].

Called from

bilinear_shape_functions

subroutine mom_ice_shelf_dynamics/register_ice_shelf_dyn_restarts(G, param_file, CS, restart_CS)

This subroutine is used to register any fields related to the ice shelf dynamics that should be written to or read from the restart file.

Parameters

• g :: [inout] The grid type describing the ice shelf grid.

• param_file :: [in] A structure to parse for run-time parameters

• cs :: A pointer to the ice shelf dynamics control structure

• restart_cs :: A pointer to the restart control structure.

Call to

mom_error_handler::mom_error

subroutine mom_ice_shelf_dynamics/initialize_ice_shelf_dyn(param_file, Time, ISS, CS, G, US, diag, new_sim, solo_ice_sheet_in)

Initializes shelf model data, parameters and diagnostics.

Parameters

• param_file :: [in] A structure to parse for run-time parameters

• time :: [inout] The clock that that will indicate the model time

• iss :: [in] A structure with elements that describe the ice-shelf state

• cs :: A pointer to the ice shelf dynamics control structure

• g :: [inout] The grid type describing the ice shelf grid.

• us :: [in] A structure containing unit conversion factors

• diag :: [in] A structure that is used to regulate the diagnostic output.

• new_sim :: [in] If true this is a new simulation, otherwise has been started from a restart file.

• solo_ice_sheet_in :: [in] If present, this indicates whether a solo ice-sheet driver.

Call to

ice_shelf_solve_outer mom_error_handler::mom_error mom_error_handler::mom_mesg mom_domains::to_all update_od_ffrac_uncoupled update_velocity_masks

subroutine mom_ice_shelf_dynamics/initialize_diagnostic_fields(CS, ISS, G, US, Time)

Parameters

• cs :: [inout] A pointer to the ice shelf control structure

• iss :: [in] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• time :: [in] The current model time

Call to

ice_shelf_solve_outer

function mom_ice_shelf_dynamics/ice_time_step_cfl(CS, ISS, G) [real]

This function returns the global maximum advective timestep that can be taken based on the current ice velocities. Because it involves finding a global minimum, it can be surprisingly expensive.

Parameters

• cs :: [inout] The ice shelf dynamics control structure

• iss :: [inout] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

Return

undefined :: The maximum permitted timestep based on the ice velocities [T ~> s].

Called from

mom_ice_shelf::solo_step_ice_shelf

subroutine mom_ice_shelf_dynamics/update_ice_shelf(CS, ISS, G, US, time_step, Time, ocean_mass, coupled_grounding, must_update_vel)

This subroutine updates the ice shelf velocities, mass, stresses and properties due to the ice shelf dynamics.

Parameters

• cs :: [inout] The ice shelf dynamics control structure

• iss :: [inout] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• time_step :: [in] time step [T ~> s]

• time :: [in] The current model time

• ocean_mass :: [in] If present this is the mass per unit area

• coupled_grounding :: [in] If true, the grounding line is determined by coupled ice-ocean dynamics

• must_update_vel :: [in] Always update the ice velocities if true.

Call to

mom_diag_mediator::disable_averaging mom_diag_mediator::enable_averages ice_shelf_advect ice_shelf_solve_outer ice_shelf_temp update_od_ffrac update_od_ffrac_uncoupled

subroutine mom_ice_shelf_dynamics/ice_shelf_advect(CS, ISS, G, time_step, Time)

This subroutine takes the velocity (on the Bgrid) and timesteps h_t = - div (uh) once. Additionally, it will update the volume of ice in partially-filled cells, and update hmask accordingly.

Parameters

• cs :: [inout] The ice shelf dynamics control structure

• iss :: [inout] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

• time_step :: [in] time step [T ~> s]

• time :: [in] The current model time

Call to

calve_to_mask ice_shelf_advect_thickness_x ice_shelf_advect_thickness_y ice_shelf_min_thickness_calve mom_error_handler::mom_error shelf_advance_front update_velocity_masks

Called from

update_ice_shelf

subroutine mom_ice_shelf_dynamics/ice_shelf_solve_outer(CS, ISS, G, US, u_shlf, v_shlf, iters, time)

Parameters

• cs :: [inout] The ice shelf dynamics control structure

• iss :: [in] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• u_shlf :: [inout] The zonal ice shelf velocity at vertices [L T-1 ~> m s-1]

• v_shlf :: [inout] The meridional ice shelf velocity at vertices [L T-1 ~> m s-1]

• iters :: [out] The number of iterations used in the solver.

• time :: [in] The current model time

Call to

apply_boundary_values bilinear_shape_fn_grid bilinear_shape_functions_subgrid calc_shelf_driving_stress calc_shelf_visc cg_action ice_shelf_solve_inner interpolate_h_to_b mom_error_handler::mom_mesg

Called from

initialize_diagnostic_fields initialize_ice_shelf_dyn update_ice_shelf

subroutine mom_ice_shelf_dynamics/ice_shelf_solve_inner(CS, ISS, G, US, u_shlf, v_shlf, taudx, taudy, H_node, float_cond, hmask, conv_flag, iters, time, Phi, Phisub)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• iss :: [in] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• u_shlf :: [inout] The zonal ice shelf velocity at vertices [L T-1 ~> m s-1]

• v_shlf :: [inout] The meridional ice shelf velocity at vertices [L T-1 ~> m s-1]

• taudx :: [in] The x-direction driving stress [R L3 Z T-2 ~> kg m s-2]

• taudy :: [in] The y-direction driving stress [R L3 Z T-2 ~> kg m s-2]

• h_node :: [in] The ice shelf thickness at nodal (corner)

• float_cond :: [in] An array indicating where the ice

• hmask :: [in] A mask indicating which tracer points are

• conv_flag :: [out] A flag indicating whether (1) or not (0) the iterations have converged to the specified tolerance

• iters :: [out] The number of iterations used in the solver.

• time :: [in] The current model time

• phi :: [in] The gradients of bilinear basis elements at Gaussian

• phisub :: [in] Quadrature structure weights at subgridscale

Call to

apply_boundary_values cg_action matrix_diagonal mom_domains::to_all

Called from

ice_shelf_solve_outer

subroutine mom_ice_shelf_dynamics/ice_shelf_advect_thickness_x(CS, G, LB, time_step, hmask, h0, h_after_uflux, uh_ice)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• g :: [in] The grid structure used by the ice shelf.

• lb :: [in] Loop bounds structure.

• time_step :: [in] The time step for this update [T ~> s].

• hmask :: [inout] A mask indicating which tracer points are

• h0 :: [in] The initial ice shelf thicknesses [Z ~> m].

• h_after_uflux :: [inout] The ice shelf thicknesses after

• uh_ice :: [inout] The accumulated zonal ice volume flux [Z L2 ~> m3]

Call to

slope_limiter

Called from

ice_shelf_advect

subroutine mom_ice_shelf_dynamics/ice_shelf_advect_thickness_y(CS, G, LB, time_step, hmask, h0, h_after_vflux, vh_ice)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• g :: [in] The grid structure used by the ice shelf.

• lb :: [in] Loop bounds structure.

• time_step :: [in] The time step for this update [T ~> s].

• hmask :: [inout] A mask indicating which tracer points are

• h0 :: [in] The initial ice shelf thicknesses [Z ~> m].

• h_after_vflux :: [inout] The ice shelf thicknesses after

• vh_ice :: [inout] The accumulated meridional ice volume flux [Z L2 ~> m3]

Call to

slope_limiter

Called from

ice_shelf_advect

subroutine mom_ice_shelf_dynamics/shelf_advance_front(CS, ISS, G, hmask, uh_ice, vh_ice)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• iss :: [inout] A structure with elements that describe the ice-shelf state

• g :: [in] The grid structure used by the ice shelf.

• hmask :: [inout] A mask indicating which tracer points are

• uh_ice :: [inout] The accumulated zonal ice volume flux [Z L2 ~> m3]

• vh_ice :: [inout] The accumulated meridional ice volume flux [Z L2 ~> m3]

Call to

mom_error_handler::is_root_pe mom_error_handler::mom_mesg

Called from

ice_shelf_advect

subroutine mom_ice_shelf_dynamics/ice_shelf_min_thickness_calve(G, h_shelf, area_shelf_h, hmask, thickness_calve, halo)

Apply a very simple calving law using a minimum thickness rule.

Parameters

• g :: [in] The grid structure used by the ice shelf.

• h_shelf :: [inout] The ice shelf thickness [Z ~> m].

• area_shelf_h :: [inout] The area per cell covered by the ice shelf [L2 ~> m2].

• hmask :: [inout] A mask indicating which tracer points are partly or fully covered by an ice-shelf

• thickness_calve :: [in] The thickness at which to trigger calving [Z ~> m].

• halo :: [in] The number of halo points to use. If not present, work on the entire data domain.

Called from

ice_shelf_advect

subroutine mom_ice_shelf_dynamics/calve_to_mask(G, h_shelf, area_shelf_h, hmask, calve_mask)

Parameters

• g :: [in] The grid structure used by the ice shelf.

• h_shelf :: [inout] The ice shelf thickness [Z ~> m].

• area_shelf_h :: [inout] The area per cell covered by the ice shelf [L2 ~> m2].

• hmask :: [inout] A mask indicating which tracer points are partly or fully covered by an ice-shelf

• calve_mask :: [in] A mask that indicates where the ice shelf can exist, and where it will calve.

Called from

ice_shelf_advect

subroutine mom_ice_shelf_dynamics/calc_shelf_driving_stress(CS, ISS, G, US, taudx, taudy, OD)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• iss :: [in] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• od :: [in] ocean floor depth at tracer points [Z ~> m].

• taudx :: [inout] X-direction driving stress at q-points [kg L s-2 ~> kg m s-2]

• taudy :: [inout] Y-direction driving stress at q-points [kg L s-2 ~> kg m s-2]

Called from

ice_shelf_solve_outer

subroutine mom_ice_shelf_dynamics/init_boundary_values(CS, G, time, hmask, input_flux, input_thick, new_sim)

Parameters

• cs :: [inout] A pointer to the ice shelf control structure

• g :: [inout] The grid structure used by the ice shelf.

• time :: [in] The current model time

• hmask :: [in] A mask indicating which tracer points are

• input_flux :: [in] The integrated inward ice thickness flux per unit face length [Z L T-1 ~> m2 s-1]

• input_thick :: [in] The ice thickness at boundaries [Z ~> m].

• new_sim :: [in] If present and false, this run is being restarted

subroutine mom_ice_shelf_dynamics/cg_action(uret, vret, u_shlf, v_shlf, Phi, Phisub, umask, vmask, hmask, H_node, ice_visc, float_cond, bathyT, basal_trac, G, US, is, ie, js, je, dens_ratio)

Parameters

• g :: [in] The grid structure used by the ice shelf.

• uret :: [inout] The retarding stresses working at u-points [R L3 Z T-2 ~> kg m s-2].

• vret :: [inout] The retarding stresses working at v-points [R L3 Z T-2 ~> kg m s-2].

• phi :: [in] The gradients of bilinear basis elements at Gaussian

• phisub :: [in] Quadrature structure weights at subgridscale

• u_shlf :: [in] The zonal ice shelf velocity at vertices [L T-1 ~> m s-1]

• v_shlf :: [in] The meridional ice shelf velocity at vertices [L T-1 ~> m s-1]

• umask :: [in] A coded mask indicating the nature of the

• vmask :: [in] A coded mask indicating the nature of the

• h_node :: [in] The ice shelf thickness at nodal (corner)

• hmask :: [in] A mask indicating which tracer points are

• ice_visc :: [in] A field related to the ice viscosity from Glen’s

• float_cond :: [in] An array indicating where the ice

• bathyt :: [in] The depth of ocean bathymetry at tracer points [Z ~> m].

• basal_trac :: [in] A field related to the nonlinear part of the

• dens_ratio :: [in] The density of ice divided by the density of seawater, nondimensional

• us :: [in] A structure containing unit conversion factors

• is :: [in] The starting i-index to work on

• ie :: [in] The ending i-index to work on

• js :: [in] The starting j-index to work on

• je :: [in] The ending j-index to work on

Call to

cg_action_subgrid_basal

Called from

ice_shelf_solve_inner ice_shelf_solve_outer

subroutine mom_ice_shelf_dynamics/cg_action_subgrid_basal(Phisub, H, U, V, bathyT, dens_ratio, Ucontr, Vcontr)

Parameters

• phisub :: [in] Quadrature structure weights at subgridscale

• h :: [in] The ice shelf thickness at nodal (corner) points [Z ~> m].

• u :: [in] The zonal ice shelf velocity at vertices [L T-1 ~> m s-1]

• v :: [in] The meridional ice shelf velocity at vertices [L T-1 ~> m s-1]

• bathyt :: [in] The depth of ocean bathymetry at tracer points [Z ~> m].

• dens_ratio :: [in] The density of ice divided by the density of seawater [nondim]

• ucontr :: [out] The areal average of u-velocities where the ice shelf is grounded, or 0 where it is floating [L T-1 ~> m s-1].

• vcontr :: [out] The areal average of v-velocities where the ice shelf is grounded, or 0 where it is floating [L T-1 ~> m s-1].

Called from

apply_boundary_values cg_action

subroutine mom_ice_shelf_dynamics/matrix_diagonal(CS, G, US, float_cond, H_node, ice_visc, basal_trac, hmask, dens_ratio, Phisub, u_diagonal, v_diagonal)

returns the diagonal entries of the matrix for a Jacobi preconditioning

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• g :: [in] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• float_cond :: [in] An array indicating where the ice

• h_node :: [in] The ice shelf thickness at nodal

• ice_visc :: [in] A field related to the ice viscosity from Glen’s

• basal_trac :: [in] A field related to the nonlinear part of the

• hmask :: [in] A mask indicating which tracer points are

• dens_ratio :: [in] The density of ice divided by the density of seawater [nondim]

• phisub :: [in] Quadrature structure weights at subgridscale locations for finite element calculations [nondim]

• u_diagonal :: [inout] The diagonal elements of the u-velocity

• v_diagonal :: [inout] The diagonal elements of the v-velocity

Call to

bilinear_shape_fn_grid cg_diagonal_subgrid_basal

Called from

ice_shelf_solve_inner

subroutine mom_ice_shelf_dynamics/cg_diagonal_subgrid_basal(Phisub, H_node, bathyT, dens_ratio, sub_grnd)

Parameters

• phisub :: [in] Quadrature structure weights at subgridscale

• h_node :: [in] The ice shelf thickness at nodal (corner) points [Z ~> m].

• bathyt :: [in] The depth of ocean bathymetry at tracer points [Z ~> m].

• dens_ratio :: [in] The density of ice divided by the density of seawater [nondim]

• sub_grnd :: [out] The weighted fraction of the sub-cell where the ice shelf is grounded [nondim]

Called from

matrix_diagonal

subroutine mom_ice_shelf_dynamics/apply_boundary_values(CS, ISS, G, US, time, Phisub, H_node, ice_visc, basal_trac, float_cond, dens_ratio, u_bdry_contr, v_bdry_contr)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• iss :: [in] A structure with elements that describe the ice-shelf state

• g :: [in] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• time :: [in] The current model time

• phisub :: [in] Quadrature structure weights at subgridscale

• h_node :: [in] The ice shelf thickness at nodal

• ice_visc :: [in] A field related to the ice viscosity from Glen’s

• basal_trac :: [in] A field related to the nonlinear part of the

• float_cond :: [in] An array indicating where the ice

• dens_ratio :: [in] The density of ice divided by the density of seawater, nondimensional

• u_bdry_contr :: [inout] Zonal force contributions due to the

• v_bdry_contr :: [inout] Meridional force contributions due to the

Call to

bilinear_shape_fn_grid cg_action_subgrid_basal

Called from

ice_shelf_solve_inner ice_shelf_solve_outer

subroutine mom_ice_shelf_dynamics/calc_shelf_visc(CS, ISS, G, US, u_shlf, v_shlf)

Update depth integrated viscosity, based on horizontal strain rates, and also update the nonlinear part of the basal traction.

Parameters

• cs :: [inout] A pointer to the ice shelf control structure

• iss :: [in] A structure with elements that describe the ice-shelf state

• g :: [in] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• u_shlf :: [inout] The zonal ice shelf velocity [L T-1 ~> m s-1].

• v_shlf :: [inout] The meridional ice shelf velocity [L T-1 ~> m s-1].

Called from

ice_shelf_solve_outer

subroutine mom_ice_shelf_dynamics/update_od_ffrac(CS, G, US, ocean_mass, find_avg)

Parameters

• cs :: [inout] A pointer to the ice shelf control structure

• g :: [inout] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• ocean_mass :: [in] The mass per unit area of the ocean [kg m-2].

• find_avg :: [in] If true, find the average of OD and ffrac, and reset the underlying running sums to 0.

Called from

update_ice_shelf

subroutine mom_ice_shelf_dynamics/update_od_ffrac_uncoupled(CS, G, h_shelf)

Parameters

• cs :: [inout] A pointer to the ice shelf control structure

• g :: [in] The grid structure used by the ice shelf.

• h_shelf :: [in] the thickness of the ice shelf [Z ~> m].

Called from

initialize_ice_shelf_dyn update_ice_shelf

subroutine mom_ice_shelf_dynamics/bilinear_shape_functions(X, Y, Phi, area)

This subroutine calculates the gradients of bilinear basis elements that that are centered at the vertices of the cell. Values are calculated at points of gaussian quadrature.

Parameters

• x :: [in] The x-positions of the vertices of the quadrilateral [L ~> m].

• y :: [in] The y-positions of the vertices of the quadrilateral [L ~> m].

• phi :: [inout] The gradients of bilinear basis elements at Gaussian quadrature points surrounding the cell vertices [L-1 ~> m-1].

• area :: [out] The quadrilateral cell area [L2 ~> m2].

Call to

quad_area

subroutine mom_ice_shelf_dynamics/bilinear_shape_fn_grid(G, i, j, Phi)

This subroutine calculates the gradients of bilinear basis elements that are centered at the vertices of the cell using a locally orthogoal MOM6 grid. Values are calculated at points of gaussian quadrature.

Parameters

• g :: [in] The grid structure used by the ice shelf.

• i :: [in] The i-index in the grid to work on.

• j :: [in] The j-index in the grid to work on.

• phi :: [inout] The gradients of bilinear basis elements at Gaussian quadrature points surrounding the cell vertices [L-1 ~> m-1].

Called from

apply_boundary_values ice_shelf_solve_outer matrix_diagonal

subroutine mom_ice_shelf_dynamics/bilinear_shape_functions_subgrid(Phisub, nsub)

Parameters

• phisub :: [inout] Quadrature structure weights at subgridscale

• nsub :: [in] The number of subgridscale quadrature locations in each direction

Called from

ice_shelf_solve_outer

subroutine mom_ice_shelf_dynamics/update_velocity_masks(CS, G, hmask, umask, vmask, u_face_mask, v_face_mask)

Parameters

• cs :: [in] A pointer to the ice shelf dynamics control structure

• g :: [inout] The grid structure used by the ice shelf.

• hmask :: [in] A mask indicating which tracer points are

• umask :: [out] A coded mask indicating the nature of the

• vmask :: [out] A coded mask indicating the nature of the

• u_face_mask :: [out] A coded mask for velocities at the C-grid u-face

• v_face_mask :: [out] A coded mask for velocities at the C-grid v-face

Call to

mom_domains::to_all

Called from

ice_shelf_advect initialize_ice_shelf_dyn

subroutine mom_ice_shelf_dynamics/interpolate_h_to_b(G, h_shelf, hmask, H_node)

Interpolate the ice shelf thickness from tracer point to nodal points, subject to a mask.

Parameters

• g :: [inout] The grid structure used by the ice shelf.

• h_shelf :: [in] The ice shelf thickness at tracer points [Z ~> m].

• hmask :: [in] A mask indicating which tracer points are

• h_node :: [inout] The ice shelf thickness at nodal (corner)

Called from

ice_shelf_solve_outer

subroutine mom_ice_shelf_dynamics/ice_shelf_dyn_end(CS)

Deallocates all memory associated with the ice shelf dynamics module.

Parameters

cs :: A pointer to the ice shelf dynamics control structure

Called from

mom_ice_shelf::ice_shelf_end

subroutine mom_ice_shelf_dynamics/ice_shelf_temp(CS, ISS, G, US, time_step, melt_rate, Time)

This subroutine updates the vertically averaged ice shelf temperature.

Parameters

• cs :: [inout] A pointer to the ice shelf control structure

• iss :: [in] A structure with elements that describe the ice-shelf state

• g :: [inout] The grid structure used by the ice shelf.

• us :: [in] A structure containing unit conversion factors

• time_step :: [in] The time step for this update [T ~> s].

• melt_rate :: [in] basal melt rate [R Z T-1 ~> kg m-2 s-1]

• time :: [in] The current model time

Call to

ice_shelf_advect_temp_x ice_shelf_advect_temp_y

Called from

update_ice_shelf

subroutine mom_ice_shelf_dynamics/ice_shelf_advect_temp_x(CS, G, time_step, hmask, h0, h_after_uflux)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• g :: [inout] The grid structure used by the ice shelf.

• time_step :: [in] The time step for this update [T ~> s].

• hmask :: [in] A mask indicating which tracer points are

• h0 :: [in] The initial ice shelf thicknesses [Z ~> m].

• h_after_uflux :: [inout] The ice shelf thicknesses after

Call to

slope_limiter

Called from

ice_shelf_temp

subroutine mom_ice_shelf_dynamics/ice_shelf_advect_temp_y(CS, G, time_step, hmask, h_after_uflux, h_after_vflux)

Parameters

• cs :: [in] A pointer to the ice shelf control structure

• g :: [in] The grid structure used by the ice shelf.

• time_step :: [in] The time step for this update [T ~> s].

• hmask :: [in] A mask indicating which tracer points are

• h_after_uflux :: [in] The ice shelf thicknesses after

• h_after_vflux :: [inout] The ice shelf thicknesses after

Call to

slope_limiter

Called from

ice_shelf_temp