mom_lateral_boundary_diffusion mom_lateral_boundary_diffusion::lateral_boundary_diffusion_cs integer, parameter, public integer, parameter, public mom_lateral_boundary_diffusion::surface surface = -1 Set a value that corresponds to the surface bopundary. boundary_k_range bulk_average fluxes_bulk_method fluxes_layer_method lateral_boundary_diffusion near_boundary_unit_tests mom_neutral_diffusion::neutral_diffusion_calc_coeffs integer, parameter, public integer, parameter, public mom_lateral_boundary_diffusion::bottom bottom = 1 Set a value that corresponds to the bottom boundary. boundary_k_range bulk_average fluxes_bulk_method fluxes_layer_method near_boundary_unit_tests character(len=40) character(len=40) mom_lateral_boundary_diffusion::mdl mdl = "MOM_lateral_boundary_diffusion" Name of this module. lateral_boundary_diffusion_init logical function, public logical function, public mom_lateral_boundary_diffusion::lateral_boundary_diffusion_init (Time, G, param_file, diag, diabatic_CSp, CS) lateral_boundary_diffusion_init Time Time G G param_file param_file diag diag diabatic_CSp diabatic_CSp CS CS Initialization routine that reads runtime parameters and sets up pointers to other control structures that might be needed for lateral boundary diffusion. time Time structure g Grid structure param_file Parameter file structure diag Diagnostics control structure diabatic_csp KPP control structure needed to get BLD cs Lateral boundary mixing control structure mom_diabatic_driver::extract_diabatic_member mdl mom_error_handler::mom_error mom_remapping::remappingdefaultscheme mom_remapping::remappingschemesdoc subroutine, public subroutine, public mom_lateral_boundary_diffusion::lateral_boundary_diffusion (G, GV, US, h, Coef_x, Coef_y, dt, Reg, CS) lateral_boundary_diffusion G G GV GV US US h h Coef_x Coef_x Coef_y Coef_y dt dt Reg Reg CS CS Driver routine for calculating lateral diffusive fluxes near the top and bottom boundaries. Two different methods are available: Method 1: lower order representation, calculate fluxes from bulk layer integrated quantities. Method 2: more straight forward, diffusion is applied layer by layer using only information from neighboring cells. g Grid type gv ocean vertical grid structure us A dimensional unit scaling type h Layer thickness [H ~> m or kg m-2] coef_x dt * Kh * dy / dx at u-points [L2 ~> m2] coef_y dt * Kh * dx / dy at v-points [L2 ~> m2] dt Tracer time step * I_numitts (I_numitts in tracer_hordiff) reg Tracer registry cs Control structure for this module mom_energetic_pbl::energetic_pbl_get_mld fluxes_bulk_method fluxes_layer_method mom_cvmix_kpp::kpp_get_bld surface mom_tracer_hor_diff::tracer_hordiff real function real function mom_lateral_boundary_diffusion::bulk_average (boundary, nk, deg, h, hBLT, phi, ppoly0_E, ppoly0_coefs, method, k_top, zeta_top, k_bot, zeta_bot) bulk_average boundary boundary nk nk deg deg h h hBLT hBLT phi phi ppoly0_E ppoly0_E ppoly0_coefs ppoly0_coefs method method k_top k_top zeta_top zeta_top k_bot k_bot zeta_bot zeta_bot boundary SURFACE or BOTTOM [nondim] nk Number of layers [nondim] deg Degree of polynomial [nondim] h Layer thicknesses [H ~> m or kg m-2] hblt Depth of the boundary layer [H ~> m or kg m-2] phi Scalar quantity ppoly0_e Edge value of polynomial ppoly0_coefs Coefficients of polynomial method Remapping scheme to use k_top Index of the first layer within the boundary zeta_top Fraction of the layer encompassed by the bottom boundary layer (0 if none, 1. if all). For the surface, this is always 0. because integration starts at the surface [nondim] k_bot Index of the last layer within the boundary zeta_bot Fraction of the layer encompassed by the surface boundary layer (0 if none, 1. if all). For the bottom boundary layer, this is always 1. because integration starts at the bottom [nondim] mom_remapping::average_value_ppoly bottom mom_error_handler::mom_error surface fluxes_bulk_method real function real function mom_lateral_boundary_diffusion::harmonic_mean (h1, h2) harmonic_mean h1 h1 h2 h2 Calculate the harmonic mean of two quantities See Harmonic Mean. h1 Scalar quantity h2 Scalar quantity fluxes_bulk_method fluxes_layer_method subroutine, public subroutine, public mom_lateral_boundary_diffusion::boundary_k_range (boundary, nk, h, hbl, k_top, zeta_top, k_bot, zeta_bot) boundary_k_range boundary boundary nk nk h h hbl hbl k_top k_top zeta_top zeta_top k_bot k_bot zeta_bot zeta_bot Find the k-index range corresponding to the layers that are within the boundary-layer region. boundary SURFACE or BOTTOM [nondim] nk Number of layers [nondim] h Layer thicknesses of the column [H ~> m or kg m-2] hbl Thickness of the boundary layer [H ~> m or kg m-2] If surface, with respect to zbl_ref = 0. If bottom, with respect to zbl_ref = SUM(h) k_top Index of the first layer within the boundary zeta_top Distance from the top of a layer to the intersection of the top extent of the boundary layer (0 at top, 1 at bottom) [nondim] k_bot Index of the last layer within the boundary zeta_bot Distance of the lower layer to the boundary layer depth (0 at top, 1 at bottom) [nondim] bottom mom_error_handler::mom_error surface fluxes_bulk_method fluxes_layer_method near_boundary_unit_tests mom_neutral_diffusion::neutral_diffusion_calc_coeffs subroutine subroutine mom_lateral_boundary_diffusion::fluxes_layer_method (boundary, nk, deg, h_L, h_R, hbl_L, hbl_R, area_L, area_R, phi_L, phi_R, ppoly0_coefs_L, ppoly0_coefs_R, ppoly0_E_L, ppoly0_E_R, method, khtr_u, F_layer, linear_decay) fluxes_layer_method boundary boundary nk nk deg deg h_L h_L h_R h_R hbl_L hbl_L hbl_R hbl_R area_L area_L area_R area_R phi_L phi_L phi_R phi_R ppoly0_coefs_L ppoly0_coefs_L ppoly0_coefs_R ppoly0_coefs_R ppoly0_E_L ppoly0_E_L ppoly0_E_R ppoly0_E_R method method khtr_u khtr_u F_layer F_layer linear_decay linear_decay Calculate the lateral boundary diffusive fluxes using the layer by layer method. See Along layer approach (Method #1). boundary Which boundary layer SURFACE or BOTTOM [nondim] nk Number of layers [nondim] deg order of the polynomial reconstruction [nondim] h_l Layer thickness (left) [H ~> m or kg m-2] h_r Layer thickness (right) [H ~> m or kg m-2] hbl_l Thickness of the boundary boundary layer (left) [H ~> m or kg m-2] hbl_r Thickness of the boundary boundary layer (right) [H ~> m or kg m-2] area_l Area of the horizontal grid (left) [L2 ~> m2] area_r Area of the horizontal grid (right) [L2 ~> m2] phi_l Tracer values (left) [conc] phi_r Tracer values (right) [conc] ppoly0_coefs_l Tracer reconstruction (left) [conc] ppoly0_coefs_r Tracer reconstruction (right) [conc] ppoly0_e_l Polynomial edge values (left) [nondim] ppoly0_e_r Polynomial edge values (right) [nondim] method Method of polynomial integration [nondim] khtr_u Horizontal diffusivities times delta t at a velocity point [L2 ~> m2] f_layer Layerwise diffusive flux at U- or V-point [H L2 conc ~> m3 conc] linear_decay If True, apply a linear transition at the base of the boundary layer mom_remapping::average_value_ppoly bottom boundary_k_range harmonic_mean surface lateral_boundary_diffusion near_boundary_unit_tests subroutine subroutine mom_lateral_boundary_diffusion::fluxes_bulk_method (boundary, nk, deg, h_L, h_R, hbl_L, hbl_R, area_L, area_R, phi_L, phi_R, ppoly0_coefs_L, ppoly0_coefs_R, ppoly0_E_L, ppoly0_E_R, method, khtr_u, F_bulk, F_layer, F_limit, linear_decay) fluxes_bulk_method boundary boundary nk nk deg deg h_L h_L h_R h_R hbl_L hbl_L hbl_R hbl_R area_L area_L area_R area_R phi_L phi_L phi_R phi_R ppoly0_coefs_L ppoly0_coefs_L ppoly0_coefs_R ppoly0_coefs_R ppoly0_E_L ppoly0_E_L ppoly0_E_R ppoly0_E_R method method khtr_u khtr_u F_bulk F_bulk F_layer F_layer F_limit F_limit linear_decay linear_decay Apply the lateral boundary diffusive fluxes calculated from a 'bulk model' See Bulk layer approach (Method #2). boundary Which boundary layer SURFACE or BOTTOM [nondim] nk Number of layers [nondim] deg order of the polynomial reconstruction [nondim] h_l Layer thickness (left) [H ~> m or kg m-2] h_r Layer thickness (right) [H ~> m or kg m-2] hbl_l Thickness of the boundary boundary layer (left) [H ~> m or kg m-2] hbl_r Thickness of the boundary boundary layer (left) [H ~> m or kg m-2] area_l Area of the horizontal grid (left) [L2 ~> m2] area_r Area of the horizontal grid (right) [L2 ~> m2] phi_l Tracer values (left) [conc] phi_r Tracer values (right) [conc] ppoly0_coefs_l Tracer reconstruction (left) [conc] ppoly0_coefs_r Tracer reconstruction (right) [conc] ppoly0_e_l Polynomial edge values (left) [nondim] ppoly0_e_r Polynomial edge values (right) [nondim] method Method of polynomial integration [nondim] khtr_u Horizontal diffusivities times delta t at a velocity point [L2 ~> m2] f_bulk The bulk mixed layer lateral flux [H L2 conc ~> m3 conc] f_layer Layerwise diffusive flux at U- or V-point [H L2 conc ~> m3 conc] f_limit If True, apply a limiter linear_decay If True, apply a linear transition at the base of the boundary layer bottom boundary_k_range bulk_average harmonic_mean surface lateral_boundary_diffusion near_boundary_unit_tests logical function, public logical function, public mom_lateral_boundary_diffusion::near_boundary_unit_tests (verbose) near_boundary_unit_tests verbose verbose Unit tests for near-boundary horizontal mixing. verbose If true, output additional information for debugging unit tests bottom boundary_k_range fluxes_bulk_method fluxes_layer_method surface test_boundary_k_range test_layer_fluxes mom_unit_tests::unit_tests logical function logical function mom_lateral_boundary_diffusion::test_layer_fluxes (verbose, nk, test_name, F_calc, F_ans) test_layer_fluxes verbose verbose nk nk test_name test_name F_calc F_calc F_ans F_ans Returns true if output of near-boundary unit tests does not match correct computed values and conditionally writes results to stream. verbose If true, write results to stdout test_name Brief description of the unit test nk Number of layers f_calc Fluxes of the unitless tracer from the algorithm [s^-1] f_ans Fluxes of the unitless tracer calculated by hand [s^-1] near_boundary_unit_tests logical function logical function mom_lateral_boundary_diffusion::test_boundary_k_range (k_top, zeta_top, k_bot, zeta_bot, k_top_ans, zeta_top_ans, k_bot_ans, zeta_bot_ans, test_name, verbose) test_boundary_k_range k_top k_top zeta_top zeta_top k_bot k_bot zeta_bot zeta_bot k_top_ans k_top_ans zeta_top_ans zeta_top_ans k_bot_ans k_bot_ans zeta_bot_ans zeta_bot_ans test_name test_name verbose verbose Return true if output of unit tests for boundary_k_range does not match answers. k_top Index of cell containing top of boundary zeta_top Nondimension position k_bot Index of cell containing bottom of boundary zeta_bot Nondimension position k_top_ans Index of cell containing top of boundary zeta_top_ans Nondimension position k_bot_ans Index of cell containing bottom of boundary zeta_bot_ans Nondimension position test_name Name of the unit test verbose If true always print output near_boundary_unit_tests Calculates and applies diffusive fluxes as a parameterization of lateral mixing (non-neutral) by mesoscale eddies near the top and bottom (to be implemented) boundary layers of the ocean. The LBD framework accounts for the effects of diabatic mesoscale fluxes within surface and bottom boundary layers. Unlike the equivalent adiabatic fluxes, which is applied along neutral density surfaces, LBD is purely horizontal. The bottom boundary layer fluxes remain to be implemented, although most of the steps needed to do so have already been added and tested. Boundary lateral diffusion can be applied using one of the three methods: Method #1: Along layer (default); Method #2: Bulk layer; A brief summary of these methods is provided below. This is the recommended and more straight forward method where diffusion is applied layer by layer using only information from neighboring cells. Step #1: compute vertical indices containing boundary layer (boundary_k_range). For the TOP boundary layer, these are: k_top, k_bot, zeta_top, zeta_bot Step #2: calculate the diffusive flux at each layer: \[ F_{k} = -KHTR \times h_{eff}(k) \times (\phi_R(k) - \phi_L(k)), \] where h_eff is the harmonic mean of the layer thickness in the left and right columns. This method does not require a limiter since KHTR is already limted based on a diffusive CFL condition prior to the call of this module. Step #3: option to linearly decay the flux from k_bot_min to k_bot_max: If LBD_LINEAR_TRANSITION = True and k_bot_diff > 1, the diffusive flux will decay linearly between the top interface of the layer containing the minimum boundary layer depth (k_bot_min) and the lower interface of the layer containing the maximum layer depth (k_bot_max). Apply the lateral boundary diffusive fluxes calculated from a 'bulk model'.This is a lower order representation (Kraus-Turner like approach) which assumes that eddies are acting along well mixed layers (i.e., eddies do not know care about vertical tracer gradients within the boundary layer). Step #1: compute vertical indices containing boundary layer (boundary_k_range). For the TOP boundary layer, these are: k_top, k_bot, zeta_top, zeta_bot Step #2: compute bulk averages (thickness weighted) tracer averages (phi_L and phi_R), then calculate the bulk diffusive flux (F_{bulk}): \[ F_{bulk} = -KHTR \times h_{eff} \times (\phi_R - \phi_L), \] where h_eff is the harmonic mean of the boundary layer depth in the left and right columns ( \[ HBL_L \] and \[ HBL_R \], respectively). Step #3: decompose F_bulk onto individual layers: \[ F_{layer}(k) = F_{bulk} \times h_{frac}(k) , \] where h_{frac} is \[ h_{frac}(k) = h_u(k) \times \frac{1}{\sum(h_u)}. \] h_u is the harmonic mean of thicknesses at each layer. Special care (layer reconstruction) must be taken at k_min = min(k_botL, k_bot_R). Step #4: option to linearly decay the flux from k_bot_min to k_bot_max: If LBD_LINEAR_TRANSITION = True and k_bot_diff > 1, the diffusive flux will decay linearly between the top interface of the layer containing the minimum boundary layer depth (k_bot_min) and the lower interface of the layer containing the maximum layer depth (k_bot_max). Step #5: limit the tracer flux so that 1) only down-gradient fluxes are applied, and 2) the flux cannot be larger than F_max, which is defined using the tracer gradient: \[ F_{max} = -0.2 \times [(V_R(k) \times \phi_R(k)) - (V_L(k) \times \phi_L(k))], \] where V is the cell volume. Why 0.2? t=0 t=inf 0 .2 0 1 0 .2.2.2 0 .2 The harmonic mean (HM) betwen h1 and h2 is defined as: \[ HM = \frac{2 \times h1 \times h2}{h1 + h2} \]