Beispiel #1
0
    def test_distribute(self):

        hef_file = get_demo_file("Hintereisferner.shp")
        entity = gpd.GeoDataFrame.from_file(hef_file).iloc[0]

        gdir = oggm.GlacierDirectory(entity, base_dir=self.testdir)
        gis.define_glacier_region(gdir, entity=entity)
        gis.glacier_masks(gdir)
        centerlines.compute_centerlines(gdir)
        geometry.initialize_flowlines(gdir)
        geometry.catchment_area(gdir)
        geometry.catchment_width_geom(gdir)
        geometry.catchment_width_correction(gdir)
        climate.process_histalp_nonparallel([gdir])
        climate.mu_candidates(gdir, div_id=0)
        hef_file = get_demo_file("mbdata_RGI40-11.00897.csv")
        mbdf = pd.read_csv(hef_file).set_index("YEAR")
        t_star, bias, prcp_fac = climate.t_star_from_refmb(gdir, mbdf["ANNUAL_BALANCE"])
        t_star = t_star[-1]
        bias = bias[-1]
        climate.local_mustar_apparent_mb(gdir, tstar=t_star, bias=bias, prcp_fac=prcp_fac)

        # OK. Values from Fischer and Kuhn 2013
        # Area: 8.55
        # meanH = 67+-7
        # Volume = 0.573+-0.063
        # maxH = 242+-13
        inversion.prepare_for_inversion(gdir)

        ref_v = 0.573 * 1e9

        def to_optimize(x):
            glen_a = cfg.A * x[0]
            fs = cfg.FS * x[1]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=fs, glen_a=glen_a)
            return (v - ref_v) ** 2

        import scipy.optimize as optimization

        out = optimization.minimize(to_optimize, [1, 1], bounds=((0.01, 10), (0.01, 10)), tol=1e-1)["x"]
        glen_a = cfg.A * out[0]
        fs = cfg.FS * out[1]
        v, _ = inversion.invert_parabolic_bed(gdir, fs=fs, glen_a=glen_a, write=True)
        np.testing.assert_allclose(ref_v, v)

        inversion.distribute_thickness(gdir, how="per_altitude", add_nc_name=True)
        inversion.distribute_thickness(gdir, how="per_interpolation", add_slope=False, add_nc_name=True)

        grids_file = gdir.get_filepath("gridded_data")
        with netCDF4.Dataset(grids_file) as nc:
            t1 = nc.variables["thickness_per_altitude"][:]
            t2 = nc.variables["thickness_per_interpolation"][:]

        np.testing.assert_allclose(np.sum(t1), np.sum(t2))
        if not HAS_NEW_GDAL:
            np.testing.assert_allclose(np.max(t1), np.max(t2), atol=30)
Beispiel #2
0
def init_hef(reset=False, border=40, invert_with_sliding=True,
             invert_with_rectangular=True):

    from oggm.core.preprocessing import gis, centerlines, geometry
    from oggm.core.preprocessing import climate, inversion
    import oggm
    import oggm.cfg as cfg
    from oggm.utils import get_demo_file

    # test directory
    testdir = os.path.join(cfg.PATHS['test_dir'], 'tmp_border{}'.format(border))
    if not invert_with_sliding:
        testdir += '_withoutslide'
    if not invert_with_rectangular:
        testdir += '_withoutrectangular'
    if not os.path.exists(testdir):
        os.makedirs(testdir)
        reset = True

    # Init
    cfg.initialize()
    cfg.PATHS['dem_file'] = get_demo_file('hef_srtm.tif')
    cfg.PATHS['climate_file'] = get_demo_file('histalp_merged_hef.nc')
    cfg.PARAMS['border'] = border
    cfg.PARAMS['use_optimized_inversion_params'] = True

    hef_file = get_demo_file('Hintereisferner_RGI5.shp')
    entity = gpd.GeoDataFrame.from_file(hef_file).iloc[0]

    gdir = oggm.GlacierDirectory(entity, base_dir=testdir, reset=reset)
    if not gdir.has_file('inversion_params'):
        reset = True
        gdir = oggm.GlacierDirectory(entity, base_dir=testdir, reset=reset)

    if not reset:
        return gdir

    gis.define_glacier_region(gdir, entity=entity)
    gis.glacier_masks(gdir)
    centerlines.compute_centerlines(gdir)
    centerlines.compute_downstream_lines(gdir)
    geometry.initialize_flowlines(gdir)
    centerlines.compute_downstream_bedshape(gdir)
    geometry.catchment_area(gdir)
    geometry.catchment_intersections(gdir)
    geometry.catchment_width_geom(gdir)
    geometry.catchment_width_correction(gdir)
    climate.process_histalp_nonparallel([gdir])
    climate.mu_candidates(gdir, div_id=0)
    mbdf = gdir.get_ref_mb_data()['ANNUAL_BALANCE']
    res = climate.t_star_from_refmb(gdir, mbdf)
    climate.local_mustar_apparent_mb(gdir, tstar=res['t_star'][-1],
                                     bias=res['bias'][-1],
                                     prcp_fac=res['prcp_fac'])

    inversion.prepare_for_inversion(gdir, add_debug_var=True,
                                    invert_with_rectangular=invert_with_rectangular)
    ref_v = 0.573 * 1e9

    if invert_with_sliding:
        def to_optimize(x):
            # For backwards compat
            _fd = 1.9e-24 * x[0]
            glen_a = (cfg.N+2) * _fd / 2.
            fs = 5.7e-20 * x[1]
            v, _ = inversion.mass_conservation_inversion(gdir, fs=fs,
                                                         glen_a=glen_a)
            return (v - ref_v)**2

        out = optimization.minimize(to_optimize, [1, 1],
                                    bounds=((0.01, 10), (0.01, 10)),
                                    tol=1e-4)['x']
        _fd = 1.9e-24 * out[0]
        glen_a = (cfg.N+2) * _fd / 2.
        fs = 5.7e-20 * out[1]
        v, _ = inversion.mass_conservation_inversion(gdir, fs=fs,
                                                     glen_a=glen_a,
                                                     write=True)
    else:
        def to_optimize(x):
            glen_a = cfg.A * x[0]
            v, _ = inversion.mass_conservation_inversion(gdir, fs=0.,
                                                         glen_a=glen_a)
            return (v - ref_v)**2

        out = optimization.minimize(to_optimize, [1],
                                    bounds=((0.01, 10),),
                                    tol=1e-4)['x']
        glen_a = cfg.A * out[0]
        fs = 0.
        v, _ = inversion.mass_conservation_inversion(gdir, fs=fs,
                                                     glen_a=glen_a,
                                                     write=True)
    d = dict(fs=fs, glen_a=glen_a)
    d['factor_glen_a'] = out[0]
    try:
        d['factor_fs'] = out[1]
    except IndexError:
        d['factor_fs'] = 0.
    gdir.write_pickle(d, 'inversion_params')

    # filter
    inversion.filter_inversion_output(gdir)

    inversion.distribute_thickness(gdir, how='per_altitude',
                                   add_nc_name=True)
    inversion.distribute_thickness(gdir, how='per_interpolation',
                                   add_slope=False, smooth=False,
                                   add_nc_name=True)

    return gdir
Beispiel #3
0
def init_hef(reset=False,
             border=40,
             invert_with_sliding=True,
             invert_with_rectangular=True):

    from oggm.core.preprocessing import gis, centerlines, geometry
    from oggm.core.preprocessing import climate, inversion
    import oggm
    import oggm.cfg as cfg
    from oggm.utils import get_demo_file

    # test directory
    testdir = os.path.join(cfg.PATHS['test_dir'],
                           'tmp_border{}'.format(border))
    if not invert_with_sliding:
        testdir += '_withoutslide'
    if not invert_with_rectangular:
        testdir += '_withoutrectangular'
    if not os.path.exists(testdir):
        os.makedirs(testdir)
        reset = True

    # Init
    cfg.initialize()
    cfg.PATHS['dem_file'] = get_demo_file('hef_srtm.tif')
    cfg.PATHS['climate_file'] = get_demo_file('histalp_merged_hef.nc')
    cfg.PARAMS['border'] = border

    hef_file = get_demo_file('Hintereisferner_RGI5.shp')
    entity = gpd.GeoDataFrame.from_file(hef_file).iloc[0]

    gdir = oggm.GlacierDirectory(entity, base_dir=testdir, reset=reset)
    if not gdir.has_file('inversion_params'):
        reset = True
        gdir = oggm.GlacierDirectory(entity, base_dir=testdir, reset=reset)

    if not reset:
        return gdir

    gis.define_glacier_region(gdir, entity=entity)
    gis.glacier_masks(gdir)
    centerlines.compute_centerlines(gdir)
    centerlines.compute_downstream_lines(gdir)
    geometry.initialize_flowlines(gdir)
    geometry.catchment_area(gdir)
    geometry.catchment_intersections(gdir)
    geometry.catchment_width_geom(gdir)
    geometry.catchment_width_correction(gdir)
    climate.process_histalp_nonparallel([gdir])
    climate.mu_candidates(gdir, div_id=0)
    mbdf = gdir.get_ref_mb_data()['ANNUAL_BALANCE']
    res = climate.t_star_from_refmb(gdir, mbdf)
    climate.local_mustar_apparent_mb(gdir,
                                     tstar=res['t_star'][-1],
                                     bias=res['bias'][-1],
                                     prcp_fac=res['prcp_fac'])

    inversion.prepare_for_inversion(
        gdir,
        add_debug_var=True,
        invert_with_rectangular=invert_with_rectangular)
    ref_v = 0.573 * 1e9

    if invert_with_sliding:

        def to_optimize(x):
            # For backwards compat
            _fd = 1.9e-24 * x[0]
            glen_a = (cfg.N + 2) * _fd / 2.
            fs = 5.7e-20 * x[1]
            v, _ = inversion.mass_conservation_inversion(gdir,
                                                         fs=fs,
                                                         glen_a=glen_a)
            return (v - ref_v)**2

        out = optimization.minimize(to_optimize, [1, 1],
                                    bounds=((0.01, 10), (0.01, 10)),
                                    tol=1e-4)['x']
        _fd = 1.9e-24 * out[0]
        glen_a = (cfg.N + 2) * _fd / 2.
        fs = 5.7e-20 * out[1]
        v, _ = inversion.mass_conservation_inversion(gdir,
                                                     fs=fs,
                                                     glen_a=glen_a,
                                                     write=True)
    else:

        def to_optimize(x):
            glen_a = cfg.A * x[0]
            v, _ = inversion.mass_conservation_inversion(gdir,
                                                         fs=0.,
                                                         glen_a=glen_a)
            return (v - ref_v)**2

        out = optimization.minimize(to_optimize, [1],
                                    bounds=((0.01, 10), ),
                                    tol=1e-4)['x']
        glen_a = cfg.A * out[0]
        fs = 0.
        v, _ = inversion.mass_conservation_inversion(gdir,
                                                     fs=fs,
                                                     glen_a=glen_a,
                                                     write=True)
    d = dict(fs=fs, glen_a=glen_a)
    d['factor_glen_a'] = out[0]
    try:
        d['factor_fs'] = out[1]
    except IndexError:
        d['factor_fs'] = 0.
    gdir.write_pickle(d, 'inversion_params')

    # filter
    inversion.filter_inversion_output(gdir)

    inversion.distribute_thickness(gdir, how='per_altitude', add_nc_name=True)
    inversion.distribute_thickness(gdir,
                                   how='per_interpolation',
                                   add_slope=False,
                                   smooth=False,
                                   add_nc_name=True)

    return gdir
Beispiel #4
0
def init_hef(reset=False, border=40, invert_with_sliding=True):

    # test directory
    testdir = TESTDIR_BASE + '_border{}'.format(border)
    if not invert_with_sliding:
        testdir += '_withoutslide'
    if not os.path.exists(testdir):
        os.makedirs(testdir)
        reset = True
    if not os.path.exists(os.path.join(testdir, 'RGI40-11.00897')):
        reset = True
    if not os.path.exists(os.path.join(testdir, 'RGI40-11.00897',
                                       'inversion_params.pkl')):
        reset = True

    # Init
    cfg.initialize()
    cfg.set_divides_db(get_demo_file('HEF_divided.shp'))
    cfg.PATHS['dem_file'] = get_demo_file('hef_srtm.tif')
    cfg.PATHS['climate_file'] = get_demo_file('histalp_merged_hef.nc')
    cfg.PARAMS['border'] = border

    # loop because for some reason indexing wont work
    hef_file = get_demo_file('Hintereisferner.shp')
    rgidf = gpd.GeoDataFrame.from_file(hef_file)
    for index, entity in rgidf.iterrows():
        gdir = oggm.GlacierDirectory(entity, base_dir=testdir, reset=reset)

    if not reset:
        return gdir

    gis.define_glacier_region(gdir, entity=entity)
    gis.glacier_masks(gdir)
    centerlines.compute_centerlines(gdir)
    centerlines.compute_downstream_lines(gdir)
    geometry.initialize_flowlines(gdir)
    geometry.catchment_area(gdir)
    geometry.catchment_width_geom(gdir)
    geometry.catchment_width_correction(gdir)
    climate.distribute_climate_data([gdir])
    climate.mu_candidates(gdir, div_id=0)
    hef_file = get_demo_file('mbdata_RGI40-11.00897.csv')
    mbdf = pd.read_csv(hef_file).set_index('YEAR')
    t_star, bias = climate.t_star_from_refmb(gdir, mbdf['ANNUAL_BALANCE'])
    climate.local_mustar_apparent_mb(gdir, tstar=t_star[-1], bias=bias[-1])

    inversion.prepare_for_inversion(gdir)
    ref_v = 0.573 * 1e9

    if invert_with_sliding:
        def to_optimize(x):
            # For backwards compat
            _fd = 1.9e-24 * x[0]
            glen_a = (cfg.N+2) * _fd / 2.
            fs = 5.7e-20 * x[1]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=fs,
                                                  glen_a=glen_a)
            return (v - ref_v)**2

        import scipy.optimize as optimization
        out = optimization.minimize(to_optimize, [1, 1],
                                    bounds=((0.01, 10), (0.01, 10)),
                                    tol=1e-4)['x']
        _fd = 1.9e-24 * out[0]
        glen_a = (cfg.N+2) * _fd / 2.
        fs = 5.7e-20 * out[1]
        v, _ = inversion.invert_parabolic_bed(gdir, fs=fs,
                                              glen_a=glen_a,
                                              write=True)
    else:
        def to_optimize(x):
            glen_a = cfg.A * x[0]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=0.,
                                                  glen_a=glen_a)
            return (v - ref_v)**2

        import scipy.optimize as optimization
        out = optimization.minimize(to_optimize, [1],
                                    bounds=((0.01, 10),),
                                    tol=1e-4)['x']
        glen_a = cfg.A * out[0]
        fs = 0.
        v, _ = inversion.invert_parabolic_bed(gdir, fs=fs,
                                              glen_a=glen_a,
                                              write=True)
    d = dict(fs=fs, glen_a=glen_a)
    d['factor_glen_a'] = out[0]
    try:
        d['factor_fs'] = out[1]
    except IndexError:
        d['factor_fs'] = 0.
    gdir.write_pickle(d, 'inversion_params')

    inversion.distribute_thickness(gdir, how='per_altitude',
                                   add_nc_name=True)
    inversion.distribute_thickness(gdir, how='per_interpolation',
                                   add_slope=False, smooth=False,
                                   add_nc_name=True)

    return gdir
Beispiel #5
0
def init_hef(reset=False, border=40, invert_with_sliding=True):

    from oggm.core.preprocessing import gis, centerlines, geometry
    from oggm.core.preprocessing import climate, inversion
    import oggm
    import oggm.cfg as cfg
    from oggm.utils import get_demo_file

    # test directory
    testdir = TESTDIR_BASE + "_border{}".format(border)
    if not invert_with_sliding:
        testdir += "_withoutslide"
    if not os.path.exists(testdir):
        os.makedirs(testdir)
        reset = True
    if not os.path.exists(os.path.join(testdir, "RGI40-11.00897")):
        reset = True
    if not os.path.exists(os.path.join(testdir, "RGI40-11.00897", "inversion_params.pkl")):
        reset = True

    # Init
    cfg.initialize()
    cfg.PATHS["dem_file"] = get_demo_file("hef_srtm.tif")
    cfg.PATHS["climate_file"] = get_demo_file("histalp_merged_hef.nc")
    cfg.PARAMS["border"] = border

    hef_file = get_demo_file("Hintereisferner.shp")
    entity = gpd.GeoDataFrame.from_file(hef_file).iloc[0]
    gdir = oggm.GlacierDirectory(entity, base_dir=testdir, reset=reset)

    if not reset:
        return gdir

    gis.define_glacier_region(gdir, entity=entity)
    gis.glacier_masks(gdir)
    centerlines.compute_centerlines(gdir)
    centerlines.compute_downstream_lines(gdir)
    geometry.initialize_flowlines(gdir)
    geometry.catchment_area(gdir)
    geometry.catchment_width_geom(gdir)
    geometry.catchment_width_correction(gdir)
    climate.process_histalp_nonparallel([gdir])
    climate.mu_candidates(gdir, div_id=0)
    hef_file = get_demo_file("mbdata_RGI40-11.00897.csv")
    mbdf = pd.read_csv(hef_file).set_index("YEAR")
    t_star, bias, prcp_fac = climate.t_star_from_refmb(gdir, mbdf["ANNUAL_BALANCE"])
    climate.local_mustar_apparent_mb(gdir, tstar=t_star[-1], bias=bias[-1], prcp_fac=prcp_fac)

    inversion.prepare_for_inversion(gdir)
    ref_v = 0.573 * 1e9

    if invert_with_sliding:

        def to_optimize(x):
            # For backwards compat
            _fd = 1.9e-24 * x[0]
            glen_a = (cfg.N + 2) * _fd / 2.0
            fs = 5.7e-20 * x[1]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=fs, glen_a=glen_a)
            return (v - ref_v) ** 2

        out = optimization.minimize(to_optimize, [1, 1], bounds=((0.01, 10), (0.01, 10)), tol=1e-4)["x"]
        _fd = 1.9e-24 * out[0]
        glen_a = (cfg.N + 2) * _fd / 2.0
        fs = 5.7e-20 * out[1]
        v, _ = inversion.invert_parabolic_bed(gdir, fs=fs, glen_a=glen_a, write=True)
    else:

        def to_optimize(x):
            glen_a = cfg.A * x[0]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=0.0, glen_a=glen_a)
            return (v - ref_v) ** 2

        out = optimization.minimize(to_optimize, [1], bounds=((0.01, 10),), tol=1e-4)["x"]
        glen_a = cfg.A * out[0]
        fs = 0.0
        v, _ = inversion.invert_parabolic_bed(gdir, fs=fs, glen_a=glen_a, write=True)
    d = dict(fs=fs, glen_a=glen_a)
    d["factor_glen_a"] = out[0]
    try:
        d["factor_fs"] = out[1]
    except IndexError:
        d["factor_fs"] = 0.0
    gdir.write_pickle(d, "inversion_params")

    inversion.distribute_thickness(gdir, how="per_altitude", add_nc_name=True)
    inversion.distribute_thickness(gdir, how="per_interpolation", add_slope=False, smooth=False, add_nc_name=True)

    return gdir
Beispiel #6
0
def init_hef(reset=False, border=40, invert_with_sliding=True):

    # test directory
    testdir = TESTDIR_BASE + '_border{}'.format(border)
    if not invert_with_sliding:
        testdir += '_withoutslide'
    if not os.path.exists(testdir):
        os.makedirs(testdir)
        reset = True
    if not os.path.exists(os.path.join(testdir, 'RGI40-11.00897')):
        reset = True
    if not os.path.exists(os.path.join(testdir, 'RGI40-11.00897',
                                       'inversion_params.pkl')):
        reset = True

    # Init
    cfg.initialize()
    cfg.set_divides_db(get_demo_file('divides_workflow.shp'))
    cfg.PATHS['dem_file'] = get_demo_file('hef_srtm.tif')
    cfg.PATHS['climate_file'] = get_demo_file('histalp_merged_hef.nc')
    cfg.PARAMS['border'] = border

    hef_file = get_demo_file('Hintereisferner.shp')
    entity = gpd.GeoDataFrame.from_file(hef_file).iloc[0]
    gdir = oggm.GlacierDirectory(entity, base_dir=testdir, reset=reset)

    if not reset:
        return gdir

    gis.define_glacier_region(gdir, entity=entity)
    gis.glacier_masks(gdir)
    centerlines.compute_centerlines(gdir)
    centerlines.compute_downstream_lines(gdir)
    geometry.initialize_flowlines(gdir)
    geometry.catchment_area(gdir)
    geometry.catchment_width_geom(gdir)
    geometry.catchment_width_correction(gdir)
    climate.distribute_climate_data([gdir])
    climate.mu_candidates(gdir, div_id=0)
    hef_file = get_demo_file('mbdata_RGI40-11.00897.csv')
    mbdf = pd.read_csv(hef_file).set_index('YEAR')
    t_star, bias = climate.t_star_from_refmb(gdir, mbdf['ANNUAL_BALANCE'])
    climate.local_mustar_apparent_mb(gdir, tstar=t_star[-1], bias=bias[-1])

    inversion.prepare_for_inversion(gdir)
    ref_v = 0.573 * 1e9

    if invert_with_sliding:
        def to_optimize(x):
            # For backwards compat
            _fd = 1.9e-24 * x[0]
            glen_a = (cfg.N+2) * _fd / 2.
            fs = 5.7e-20 * x[1]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=fs,
                                                  glen_a=glen_a)
            return (v - ref_v)**2

        out = optimization.minimize(to_optimize, [1, 1],
                                    bounds=((0.01, 10), (0.01, 10)),
                                    tol=1e-4)['x']
        _fd = 1.9e-24 * out[0]
        glen_a = (cfg.N+2) * _fd / 2.
        fs = 5.7e-20 * out[1]
        v, _ = inversion.invert_parabolic_bed(gdir, fs=fs,
                                              glen_a=glen_a,
                                              write=True)
    else:
        def to_optimize(x):
            glen_a = cfg.A * x[0]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=0.,
                                                  glen_a=glen_a)
            return (v - ref_v)**2

        out = optimization.minimize(to_optimize, [1],
                                    bounds=((0.01, 10),),
                                    tol=1e-4)['x']
        glen_a = cfg.A * out[0]
        fs = 0.
        v, _ = inversion.invert_parabolic_bed(gdir, fs=fs,
                                              glen_a=glen_a,
                                              write=True)
    d = dict(fs=fs, glen_a=glen_a)
    d['factor_glen_a'] = out[0]
    try:
        d['factor_fs'] = out[1]
    except IndexError:
        d['factor_fs'] = 0.
    gdir.write_pickle(d, 'inversion_params')

    inversion.distribute_thickness(gdir, how='per_altitude',
                                   add_nc_name=True)
    inversion.distribute_thickness(gdir, how='per_interpolation',
                                   add_slope=False, smooth=False,
                                   add_nc_name=True)

    return gdir
Beispiel #7
0
    def test_distribute(self):

        hef_file = get_demo_file('Hintereisferner.shp')
        entity = gpd.GeoDataFrame.from_file(hef_file).iloc[0]

        gdir = oggm.GlacierDirectory(entity, base_dir=self.testdir)
        gis.define_glacier_region(gdir, entity=entity)
        gis.glacier_masks(gdir)
        centerlines.compute_centerlines(gdir)
        geometry.initialize_flowlines(gdir)
        geometry.catchment_area(gdir)
        geometry.catchment_width_geom(gdir)
        geometry.catchment_width_correction(gdir)
        climate.distribute_climate_data([gdir])
        climate.mu_candidates(gdir, div_id=0)
        hef_file = get_demo_file('mbdata_RGI40-11.00897.csv')
        mbdf = pd.read_csv(hef_file).set_index('YEAR')
        t_star, bias = climate.t_star_from_refmb(gdir, mbdf['ANNUAL_BALANCE'])
        t_star = t_star[-1]
        bias = bias[-1]
        climate.local_mustar_apparent_mb(gdir, tstar=t_star, bias=bias)

        # OK. Values from Fischer and Kuhn 2013
        # Area: 8.55
        # meanH = 67+-7
        # Volume = 0.573+-0.063
        # maxH = 242+-13
        inversion.prepare_for_inversion(gdir)

        ref_v = 0.573 * 1e9

        def to_optimize(x):
            glen_a = cfg.A * x[0]
            fs = cfg.FS * x[1]
            v, _ = inversion.invert_parabolic_bed(gdir, fs=fs, glen_a=glen_a)
            return (v - ref_v)**2

        import scipy.optimize as optimization
        out = optimization.minimize(to_optimize, [1, 1],
                                    bounds=((0.01, 10), (0.01, 10)),
                                    tol=1e-1)['x']
        glen_a = cfg.A * out[0]
        fs = cfg.FS * out[1]
        v, _ = inversion.invert_parabolic_bed(gdir,
                                              fs=fs,
                                              glen_a=glen_a,
                                              write=True)
        np.testing.assert_allclose(ref_v, v)

        inversion.distribute_thickness(gdir,
                                       how='per_altitude',
                                       add_nc_name=True)
        inversion.distribute_thickness(gdir,
                                       how='per_interpolation',
                                       add_slope=False,
                                       add_nc_name=True)

        grids_file = gdir.get_filepath('gridded_data')
        with netCDF4.Dataset(grids_file) as nc:
            t1 = nc.variables['thickness_per_altitude'][:]
            t2 = nc.variables['thickness_per_interpolation'][:]

        np.testing.assert_allclose(np.sum(t1), np.sum(t2))
        if not HAS_NEW_GDAL:
            np.testing.assert_allclose(np.max(t1), np.max(t2), atol=30)