regrid_interp regrid_interp::interp_cs_type integer, parameter integer, parameter regrid_interp::degree_1 degree_1 = 1 Interpolant degrees. regridding_set_ppolys integer, parameter integer, parameter regrid_interp::degree_2 degree_2 = 2 Interpolant degrees. regridding_set_ppolys integer, parameter integer, parameter regrid_interp::degree_3 degree_3 = 3 Interpolant degrees. regridding_set_ppolys integer, parameter integer, parameter regrid_interp::degree_4 degree_4 = 4 Interpolant degrees. regridding_set_ppolys integer, parameter, public integer, parameter, public regrid_interp::degree_max degree_max = 5 Interpolant degrees. integer, parameter integer, parameter regrid_interp::interpolation_p1m_h2 interpolation_p1m_h2 = 0 O(h^2) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_p1m_h4 interpolation_p1m_h4 = 1 O(h^2) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_p1m_ih4 interpolation_p1m_ih4 = 2 O(h^2) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_plm interpolation_plm = 3 O(h^2) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_ppm_h4 interpolation_ppm_h4 = 4 O(h^3) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_ppm_ih4 interpolation_ppm_ih4 = 5 O(h^3) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_p3m_ih4ih3 interpolation_p3m_ih4ih3 = 6 O(h^4) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_p3m_ih6ih5 interpolation_p3m_ih6ih5 = 7 O(h^4) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_pqm_ih4ih3 interpolation_pqm_ih4ih3 = 8 O(h^4) interpolation_scheme regridding_set_ppolys integer, parameter integer, parameter regrid_interp::interpolation_pqm_ih6ih5 interpolation_pqm_ih6ih5 = 9 O(h^5) interpolation_scheme regridding_set_ppolys real, parameter, public real, parameter, public regrid_interp::nr_offset nr_offset = 1e-6 When the N-R algorithm produces an estimate that lies outside [0,1], the estimate is set to be equal to the boundary location, 0 or 1, plus or minus an offset, respectively, when the derivative is zero at the boundary [nondim]. get_polynomial_coordinate integer, parameter, public integer, parameter, public regrid_interp::nr_iterations nr_iterations = 8 Maximum number of Newton-Raphson iterations. Newton-Raphson iterations are used to build the new grid by finding the coordinates associated with target densities and interpolations of degree larger than 1. get_polynomial_coordinate coord_slight::rho_interfaces_col real, parameter, public real, parameter, public regrid_interp::nr_tolerance nr_tolerance = 1e-12 Tolerance for Newton-Raphson iterations (stop when increment falls below this) [nondim]. get_polynomial_coordinate coord_slight::rho_interfaces_col subroutine, public subroutine, public regrid_interp::regridding_set_ppolys (CS, densities, n0, h0, ppoly0_E, ppoly0_S, ppoly0_coefs, degree, h_neglect, h_neglect_edge) regridding_set_ppolys CS CS densities densities n0 n0 h0 h0 ppoly0_E ppoly0_E ppoly0_S ppoly0_S ppoly0_coefs ppoly0_coefs degree degree h_neglect h_neglect h_neglect_edge h_neglect_edge Builds an interpolated profile for the densities within each grid cell. It may happen that, given a high-order interpolator, the number of available layers is insufficient (e.g., there are two available layers for a third-order PPM ih4 scheme). In these cases, we resort to the simplest continuous linear scheme (P1M h2). cs Interpolation control structure n0 Number of cells on source grid densities Actual cell densities [A] h0 cell widths on source grid [H] ppoly0_e Edge value of polynomial [A] ppoly0_s Edge slope of polynomial [A H-1] ppoly0_coefs Coefficients of polynomial [A] degree The degree of the polynomials h_neglect A negligibly small width for the purpose of cell reconstructions [H] in the same units as h0. h_neglect_edge A negligibly small width for the purpose of edge value calculations [H] in the same units as h0. degree_1 degree_2 degree_3 degree_4 regrid_edge_values::edge_slopes_implicit_h3 regrid_edge_values::edge_slopes_implicit_h5 interpolation_p1m_h2 interpolation_p1m_h4 interpolation_p1m_ih4 interpolation_p3m_ih4ih3 interpolation_p3m_ih6ih5 interpolation_plm interpolation_ppm_h4 interpolation_ppm_ih4 interpolation_pqm_ih4ih3 interpolation_pqm_ih6ih5 p1m_functions::p1m_boundary_extrapolation p1m_functions::p1m_interpolation p3m_functions::p3m_boundary_extrapolation p3m_functions::p3m_interpolation plm_functions::plm_boundary_extrapolation plm_functions::plm_reconstruction ppm_functions::ppm_boundary_extrapolation ppm_functions::ppm_reconstruction pqm_functions::pqm_boundary_extrapolation_v1 pqm_functions::pqm_reconstruction build_and_interpolate_grid subroutine, public subroutine, public regrid_interp::interpolate_grid (n0, h0, x0, ppoly0_E, ppoly0_coefs, target_values, degree, n1, h1, x1, answers_2018) interpolate_grid n0 n0 h0 h0 x0 x0 ppoly0_E ppoly0_E ppoly0_coefs ppoly0_coefs target_values target_values degree degree n1 n1 h1 h1 x1 x1 answers_2018 answers_2018 Given target values (e.g., density), build new grid based on polynomial. Given the grid 'grid0' and the piecewise polynomial interpolant 'ppoly0' (possibly discontinuous), the coordinates of the new grid 'grid1' are determined by finding the corresponding target interface densities. n0 Number of points on source grid n1 Number of points on target grid h0 Thicknesses of source grid cells [H] x0 Source interface positions [H] ppoly0_e Edge values of interpolating polynomials [A] ppoly0_coefs Coefficients of interpolating polynomials [A] target_values Target values of interfaces [A] degree Degree of interpolating polynomials h1 Thicknesses of target grid cells [H] x1 Target interface positions [H] answers_2018 If true use older, less acccurate expressions. get_polynomial_coordinate build_and_interpolate_grid subroutine, public subroutine, public regrid_interp::build_and_interpolate_grid (CS, densities, n0, h0, x0, target_values, n1, h1, x1, h_neglect, h_neglect_edge) build_and_interpolate_grid CS CS densities densities n0 n0 h0 h0 x0 x0 target_values target_values n1 n1 h1 h1 x1 x1 h_neglect h_neglect h_neglect_edge h_neglect_edge Build a grid by interpolating for target values. cs A control structure for regrid_interp n0 The number of points on the input grid n1 The number of points on the output grid densities Input cell densities [R ~> kg m-3] target_values Target values of interfaces [R ~> kg m-3] h0 Initial cell widths [H] x0 Source interface positions [H] h1 Output cell widths [H] x1 Target interface positions [H] h_neglect A negligibly small width for the purpose of cell reconstructions [H] in the same units as h0. h_neglect_edge A negligibly small width for the purpose of edge value calculations [H] in the same units as h0. interpolate_grid regridding_set_ppolys coord_hycom::build_hycom1_column coord_rho::build_rho_column coord_rho::build_rho_column_iteratively real function real function regrid_interp::get_polynomial_coordinate (N, h, x_g, edge_values, ppoly_coefs, target_value, degree, answers_2018) get_polynomial_coordinate N N h h x_g x_g edge_values edge_values ppoly_coefs ppoly_coefs target_value target_value degree degree answers_2018 answers_2018 Given a target value, find corresponding coordinate for given polynomial. Here, 'ppoly' is assumed to be a piecewise discontinuous polynomial of degree 'degree' throughout the domain defined by 'grid'. A target value is given and we need to determine the corresponding grid coordinate to define the new grid.If the target value is out of range, the grid coordinate is simply set to be equal to one of the boundary coordinates, which results in vanished layers near the boundaries.IT IS ASSUMED THAT THE PIECEWISE POLYNOMIAL IS MONOTONICALLY INCREASING. IF THIS IS NOT THE CASE, THE NEW GRID MAY BE ILL-DEFINED.It is assumed that the number of cells defining 'grid' and 'ppoly' are the same. n Number of grid cells h Grid cell thicknesses [H] x_g Grid interface locations [H] edge_values Edge values of interpolating polynomials [A] ppoly_coefs Coefficients of interpolating polynomials [A] target_value Target value to find position for [A] degree Degree of the interpolating polynomials answers_2018 If true use older, less acccurate expressions. The position of x_g at which target_value is found [H] mom_error_handler::mom_error nr_iterations nr_offset nr_tolerance interpolate_grid integer function integer function regrid_interp::interpolation_scheme (interp_scheme) interpolation_scheme interp_scheme interp_scheme Numeric value of interpolation_scheme corresponding to scheme name. interp_scheme Name of the interpolation scheme Valid values include "P1M_H2", "P1M_H4", "P1M_IH2", "PLM", "PPM_H4", "PPM_IH4", "P3M_IH4IH3", "P3M_IH6IH5", "PQM_IH4IH3", and "PQM_IH6IH5" interpolation_p1m_h2 interpolation_p1m_h4 interpolation_p1m_ih4 interpolation_p3m_ih4ih3 interpolation_p3m_ih6ih5 interpolation_plm interpolation_ppm_h4 interpolation_ppm_ih4 interpolation_pqm_ih4ih3 interpolation_pqm_ih6ih5 mom_error_handler::mom_error mom_string_functions::uppercase set_interp_scheme subroutine, public subroutine, public regrid_interp::set_interp_scheme (CS, interp_scheme) set_interp_scheme CS CS interp_scheme interp_scheme Store the interpolation_scheme value in the interp_CS based on the input string. cs A control structure for regrid_interp interp_scheme Name of the interpolation scheme Valid values include "P1M_H2", "P1M_H4", "P1M_IH2", "PLM", "PPM_H4", "PPM_IH4", "P3M_IH4IH3", "P3M_IH6IH5", "PQM_IH4IH3", and "PQM_IH6IH5" interpolation_scheme mom_regridding::set_regrid_params subroutine, public subroutine, public regrid_interp::set_interp_extrap (CS, extrap) set_interp_extrap CS CS extrap extrap Store the boundary_extrapolation value in the interp_CS. cs A control structure for regrid_interp extrap Indicate whether high-order boundary extrapolation should be used in boundary cells mom_regridding::set_regrid_params Vertical interpolation for regridding.