def METHOD_NAME():
    # We're going to load up a simple AMR grid and check its volume
    # calculations and path length calculations.
    # Note that we are setting it up to have depth of 1000 maximum, which
    # means our volume will be that of a shell 1000 wide, starting at r of
    # outer_radius - 1000.
    ds = fake_amr_ds(geometry="internal_geographic")
    ds.outer_radius = ds.quan(5000.0, "code_length")
    axes = ["latitude", "longitude", "depth"]
    for i, axis in enumerate(axes):
        dd = ds.all_data()
        fi = ("index", axis)
        fd = ("index", f"d{axis}")
        ma = np.argmax(dd[fi])
        assert_equal(dd[fi][ma] + dd[fd][ma] / 2.0, ds.domain_right_edge[i].d)
        mi = np.argmin(dd[fi])
        assert_equal(dd[fi][mi] - dd[fd][mi] / 2.0, ds.domain_left_edge[i].d)
        assert_equal(dd[fd].max(), (ds.domain_width / ds.domain_dimensions)[i].d)
    inner_r = ds.outer_radius - ds.domain_right_edge[2]
    outer_r = ds.outer_radius
    assert_equal(dd["index", "dtheta"], dd["index", "dlatitude"] * np.pi / 180.0)
    assert_equal(dd["index", "dphi"], dd["index", "dlongitude"] * np.pi / 180.0)
    assert_rel_equal(
        dd[("index", "cell_volume")].sum(dtype="float64"),
        (4.0 / 3.0) * np.pi * (outer_r**3 - inner_r**3),
        10,
    )
    assert_equal(dd["index", "path_element_depth"], dd["index", "ddepth"])
    assert_equal(dd["index", "path_element_depth"], dd["index", "dr"])
    # Note that latitude corresponds to theta, longitude to phi
    assert_equal(
        dd["index", "path_element_latitude"],
        dd["index", "r"] * dd["index", "dlatitude"] * np.pi / 180.0,
    )
    assert_equal(
        dd["index", "path_element_longitude"],
        (
            dd["index", "r"]
            * dd["index", "dlongitude"]
            * np.pi
            / 180.0
            * np.sin((dd["index", "latitude"] + 90.0) * np.pi / 180.0)
        ),
    )
    # We also want to check that our radius is correct
    assert_equal(dd["index", "r"], -1.0 * dd["index", "depth"] + ds.outer_radius)