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matthewhoffmanmatthewhoffman
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Add thickness advection version of horizontal_advection test
This is identical to the horizontal_advection test of a passive tracer, but Gaussian bump is applied to thickness field and tracer advection is not considered. This isolates the analysis to a single advection call; if there are issues with the thickness advection, we presumably cannot expect tracer advection to converge properly. It might have been possible to create an argument to toggle between versions, but it was easier (and arguably less confusing) to just make a copy. This uses a Gaussian bump of 1000 m sitting on top of a 1000 m base layer in a doubly periodic mesh. This ensures a margin-less domain, which would avoid the issue of advection degrading to 1st order at margins.
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‎compass/landice/tests/mesh_convergence/__init__.py

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from compass.landice.tests.mesh_convergence.horizontal_advection import (
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HorizontalAdvection,
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)
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from compass.landice.tests.mesh_convergence.horizontal_advection_thickness import ( # noqa
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HorizontalAdvectionThickness,
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)
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from compass.testgroup import TestGroup
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@@ -17,4 +20,5 @@ def __init__(self, mpas_core):
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super().__init__(mpas_core=mpas_core, name='mesh_convergence')
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self.add_test_case(HorizontalAdvection(test_group=self))
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self.add_test_case(HorizontalAdvectionThickness(test_group=self))
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self.add_test_case(Halfar(test_group=self))

‎compass/landice/tests/mesh_convergence/horizontal_advection_thickness/__init__.py

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from compass.landice.tests.mesh_convergence.conv_test_case import ConvTestCase
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from compass.landice.tests.mesh_convergence.horizontal_advection_thickness.analysis import ( # noqa
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Analysis,
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)
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from compass.landice.tests.mesh_convergence.horizontal_advection_thickness.init import ( # noqa
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Init,
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)
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class HorizontalAdvectionThickness(ConvTestCase):
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"""
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A test case for testing horizontal advection of thickness in MALI with
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planar, doubly periodic meshes
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"""
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def __init__(self, test_group):
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"""
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Create test case for creating a MALI mesh
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Parameters
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----------
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test_group : compass.landice.tests.mesh_convergence.MeshConvergence
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The landice test group that this test case belongs to
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"""
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super().__init__(test_group=test_group,
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name='horizontal_advection_thickness')
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self.add_step(Analysis(test_case=self, resolutions=self.resolutions))
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def create_init(self, resolution):
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"""
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Child class must override this to return an instance of a
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ConvInit step
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Parameters
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----------
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resolution : int
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The resolution of the test case
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Returns
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-------
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init : compass.landice.tests.mesh_convergence.conv_init.ConvInit
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The init step object
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"""
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return Init(test_case=self, resolution=resolution)
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def create_analysis(self, resolutions):
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"""
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Child class must override this to return an instance of a
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ConvergenceInit step
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Parameters
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----------
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resolutions : list of int
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The resolutions of the other steps in the test case
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Returns
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-------
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analysis : compass.landice.tests.mesh_convergence.conv_analysis.ConvAnalysis # noqa
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The init step object
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"""
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return Analysis(test_case=self, resolutions=resolutions)

‎compass/landice/tests/mesh_convergence/horizontal_advection_thickness/analysis.py

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import warnings
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import matplotlib.pyplot as plt
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import numpy as np
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import xarray as xr
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from compass.landice.tests.mesh_convergence.conv_analysis import ConvAnalysis
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class Analysis(ConvAnalysis):
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"""
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A step for visualizing the output from the advection convergence test case
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"""
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def __init__(self, test_case, resolutions):
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"""
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Create the step
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Parameters
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----------
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test_case : compass.TestCase
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The test case this step belongs to
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resolutions : list of int
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The resolutions of the meshes that have been run
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"""
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super().__init__(test_case=test_case, resolutions=resolutions)
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self.resolutions = resolutions
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self.add_output_file('convergence.png')
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def run(self):
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"""
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Run this step of the test case
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"""
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plt.switch_backend('Agg')
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resolutions = self.resolutions
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ncells_list = list()
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errors = list()
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for res in resolutions:
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rms_error, ncells = self.rmse(res, variable='thickness')
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ncells_list.append(ncells)
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errors.append(rms_error)
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ncells = np.array(ncells_list)
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errors = np.array(errors)
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p = np.polyfit(np.log10(ncells), np.log10(errors), 1)
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conv = abs(p[0]) * 2.0
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error_fit = ncells**p[0] * 10**p[1]
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plt.loglog(ncells, error_fit, 'k')
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plt.loglog(ncells, errors, 'or')
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plt.annotate('Order of Convergence = {}'.format(np.round(conv, 3)),
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xycoords='axes fraction', xy=(0.3, 0.95), fontsize=14)
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plt.xlabel('Number of Grid Cells', fontsize=14)
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plt.ylabel('L2 Norm', fontsize=14)
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section = self.config['mesh_convergence']
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duration = section.getfloat('duration')
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plt.title(f'Thickness horizontal advection convergence test,'
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f'{duration} yrs')
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plt.savefig('convergence.png', bbox_inches='tight', pad_inches=0.1)
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section = self.config['horizontal_advection']
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conv_thresh = section.getfloat('conv_thresh')
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conv_max = section.getfloat('conv_max')
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if conv < conv_thresh:
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raise ValueError(f'order of convergence '
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f' {conv} < min tolerence {conv_thresh}')
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if conv > conv_max:
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warnings.warn(f'order of convergence '
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f'{conv} > max tolerence {conv_max}')
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def rmse(self, resolution, variable):
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"""
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Compute the RMSE for a given resolution
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Parameters
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----------
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resolution : int
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The resolution of the (uniform) mesh in km
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variable : str
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The name of a variable in the output file to analyze.
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Returns
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-------
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rms_error : float
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The root-mean-squared error
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ncells : int
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The number of cells in the mesh
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"""
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res_tag = '{}km'.format(resolution)
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ds = xr.open_dataset('{}_output.nc'.format(res_tag))
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init = ds[variable].isel(Time=0)
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final = ds[variable].isel(Time=-1)
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diff = final - init
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rms_error = np.sqrt((diff**2).mean()).values
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ncells = ds.sizes['nCells']
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return rms_error, ncells

‎compass/landice/tests/mesh_convergence/horizontal_advection_thickness/horizontal_advection_thickness.cfg

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# options for planar horizontal advection test case
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[horizontal_advection]
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# Number of vertical levels
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vert_levels = 3
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# ice thickness (m)
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ice_thickness = 1000.0
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# bed elevation (m)
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bed_elevation = 0.0
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# center of the tracer gaussian (km)
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x_center = 0.
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y_center = 0.
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# width of gaussian tracer "blob" (km)
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gaussian_width = 50
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# whether to advect in x, y, or both
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advect_x = True
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advect_y = True
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# convergence threshold below which the test fails
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conv_thresh = 0.6
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# Convergence rate above which a warning is issued
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conv_max = 3.0
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# options for mesh convergence test cases
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[mesh_convergence]
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# a list of resolutions (km) to test
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resolutions = 16, 8, 4, 2

‎compass/landice/tests/mesh_convergence/horizontal_advection_thickness/init.py

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import numpy
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import xarray
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from mpas_tools.io import write_netcdf
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from compass.landice.tests.mesh_convergence.conv_init import ConvInit
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class Init(ConvInit):
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"""
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A step for creating an initial_condition for advection convergence test
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case
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"""
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def __init__(self, test_case, resolution):
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"""
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Create the step
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Parameters
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----------
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test_case : compass.TestCase
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The test case this step belongs to
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resolution : int
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The resolution of the test case
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"""
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super().__init__(test_case=test_case, resolution=resolution)
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self.add_output_file('initial_state.nc')
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def run(self):
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"""
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Run this step of the test case
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"""
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# create the mesh and graph.info
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super().run()
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config = self.config
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section = config['horizontal_advection']
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ice_thickness = section.getfloat('ice_thickness')
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bed_elevation = section.getfloat('bed_elevation')
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x_center = 1e3 * section.getfloat('x_center')
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y_center = 1e3 * section.getfloat('y_center')
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advect_x = section.getboolean('advect_x')
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advect_y = section.getboolean('advect_y')
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gaussian_width = 1e3 * section.getfloat('gaussian_width')
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nVertLevels = section.getint('vert_levels')
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section = config['mesh_convergence']
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duration = section.getfloat('duration') * 3600.0 * 24.0 * 365.0
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ds = xarray.open_dataset('mesh.nc')
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xCell = ds.xCell
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yCell = ds.yCell
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if advect_x:
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x_vel = ds.attrs['x_period'] / duration
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else:
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x_vel = 0.
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if advect_y:
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y_vel = ds.attrs['y_period'] / duration
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else:
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y_vel = 0.
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layerThicknessFractions = xarray.DataArray(
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data=1.0 / nVertLevels * numpy.ones((nVertLevels,)),
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dims=['nVertLevels'])
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# create base layer of uniform thickness over entire domain
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# to ensure no margins
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thickness = ice_thickness * xarray.ones_like(xCell)
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# now add Gaussian bump on top
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# using bump height equal to base height
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dist_sq = (xCell - x_center)**2 + (yCell - y_center)**2
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thickness += ice_thickness * numpy.exp(-0.5 * dist_sq /
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gaussian_width**2)
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thickness = thickness.expand_dims(dim='Time', axis=0)
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bedTopography = bed_elevation * xarray.ones_like(thickness)
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uReconstructX = x_vel * xarray.ones_like(xCell)
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uReconstructX = uReconstructX.expand_dims(dim={"nVertInterfaces":
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nVertLevels + 1},
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axis=1)
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uReconstructX = uReconstructX.expand_dims(dim='Time', axis=0)
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uReconstructY = y_vel * xarray.ones_like(xCell)
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uReconstructY = uReconstructY.expand_dims(dim={"nVertInterfaces":
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nVertLevels + 1},
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axis=1)
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uReconstructY = uReconstructY.expand_dims(dim='Time', axis=0)
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ds['layerThicknessFractions'] = layerThicknessFractions
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ds['thickness'] = thickness
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ds['bedTopography'] = bedTopography
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ds['uReconstructX'] = uReconstructX
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ds['uReconstructY'] = uReconstructY
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write_netcdf(ds, 'initial_state.nc')

‎compass/landice/tests/mesh_convergence/horizontal_advection_thickness/namelist.forward

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config_velocity_solver = 'none'
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config_unrealistic_velocity = 1.0e36
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config_thickness_advection = 'fo'
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config_tracer_advection = 'none'
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config_start_time = '0001-01-01_00:00:00'

‎compass/landice/tests/mesh_convergence/horizontal_advection_thickness/streams.forward

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<streams>
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<stream name="output">
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<var name="uReconstructX"/>
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<var name="uReconstructY"/>
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<var name="thickness"/>
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</stream>
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</streams>

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