def test_latitudes():
ell = Ellipsoid('GRS80')
lat = np.arange(-90, 90, 0.1, dtype=float)
sph_lat, _, sph_radius = geodetic_to_spherical(lat,
lon=0.0,
height=0.0,
ell=ell)
np.testing.assert_array_almost_equal(ell.geocentric_latitude(lat),
sph_lat,
decimal=8)
reduced_latitude = np.degrees(
np.arctan(np.tan(np.radians(sph_lat)) / (1 - ell.f)))
np.testing.assert_array_almost_equal(ell.reduced_latitude(lat),
reduced_latitude,
decimal=8)
# compare with series from
# J. P. Snyder, Map projections - a working manual, 1926, page 16
latr = np.radians(lat)
s2lat = (ell.e2 / 3 + 31 * ell.e2**2 / 180 +
59 * ell.e2**3 / 560) * np.sin(2 * latr)
s4lat = (17 * ell.e2**2 / 360 + 61 * ell.e2**3 / 1260) * np.sin(4 * latr)
s6lat = (383 * ell.e2**3 / 45360) * np.sin(6 * latr)
authalic_latitude = np.degrees(latr - s2lat + s4lat - s6lat)
np.testing.assert_array_almost_equal(ell.authalic_latitude(lat),
authalic_latitude,
decimal=6)
def test_gravity():
lat, lon, r = geodetic_to_spherical(latitude,
longitude,
0.0,
ell=ell,
degrees=True)
gravity_model = model.gravity(lat, lon, r, degrees=True) * 1e5
gravity_test = data.gravity_ell.values
np.testing.assert_almost_equal(gravity_model, gravity_test)
def test_height_anomaly_ell():
lat, lon, r = geodetic_to_spherical(latitude,
longitude,
0.0,
ell=ell,
degrees=True)
ha_model = model.height_anomaly_ell(lat, lon, r, degrees=True)
ha_test = data.height_anomaly_ell.values
np.testing.assert_almost_equal(ha_model, ha_test)
def test_gravitational_potential():
lat, lon, r = geodetic_to_spherical(latitude,
longitude,
0.0,
ell=ell,
degrees=True)
pot_model = model.gravitational_potential.potential(lat,
lon,
r,
degrees=True)
pot_test = data.potential_ell.values
np.testing.assert_almost_equal(pot_model, pot_test, 6)
def test_gradient():
lat, lon, r = geodetic_to_spherical(latitude, longitude, radius0, ell=ell)
# rad, lon, lat, total
gradient_model = model._gravitational.gradient(lat, lon, r)
r_derivative_model = model._gravitational.r_derivative(lat, lon, r)
lon_derivative_model = model._gravitational.lon_derivative(lat, lon, r)
lat_derivative_model = model._gravitational.lat_derivative(lat, lon, r)
np.testing.assert_almost_equal(gradient_model[0].value,
r_derivative_model.value)
np.testing.assert_almost_equal(gradient_model[1].value,
lon_derivative_model.value)
np.testing.assert_almost_equal(gradient_model[2].value,
lat_derivative_model.value)
def test_radiuses():
ell = Ellipsoid('GRS80')
# geodetic latitude
lat = np.arange(-90, 90, 0.1, dtype=float)
x, y, _ = geodetic_to_cartesian(lat, lon=0.0, height=0.0, ell=ell)
np.testing.assert_array_almost_equal(ell.circle_radius(lat),
np.sqrt(x**2 + y**2),
decimal=5)
sph_lat, _, sph_radius = geodetic_to_spherical(lat,
lon=0.0,
height=0.0,
ell=ell)
np.testing.assert_array_almost_equal(ell.polar_equation(sph_lat),
sph_radius,
decimal=5)
def test_surface_gravity_potential():
ell = LevelEllipsoid('GRS80')
# geodetic latitude
lat = np.arange(-90, 90, 0.1, dtype=float)
rlat, _, u = transform.geodetic_to_ellipsoidal(lat=lat,
lon=0.0, height=0.0, ell=ell)
gravity_potential_0 = ell.gravity_potential(rlat, u)
np.testing.assert_almost_equal(
ell.surface_potential,
gravity_potential_0, decimal=5)
geoclat, _, radius = transform.geodetic_to_spherical(lat=lat,
lon=0.0, height=0.0, ell=ell)
gravity_potential_sph_0 = ell.gravity_potential_sph(geoclat, radius)
np.testing.assert_almost_equal(
ell.surface_potential,
gravity_potential_sph_0, decimal=5)
np.testing.assert_almost_equal(
gravity_potential_sph_0,
gravity_potential_0, decimal=5)
def test_height_anomaly_ell():
lat, lon, r = geodetic_to_spherical(latitude, longitude, radius0, ell=ell)
ha_model = model.height_anomaly_ell(lat, lon, r)
ha_test = data.height_anomaly_ell.values
np.testing.assert_almost_equal(ha_model.value, ha_test)
def test_gravity_anomaly_sa():
lat, lon, r = geodetic_to_spherical(latitude, longitude, radius0, ell=ell)
gravity_anom_model = model.gravity_anomaly_sa(lat, lon, r).to('mGal')
gravity_anom_test = data.gravity_anomaly_sa.values
np.testing.assert_almost_equal(gravity_anom_model.value, gravity_anom_test)
def test_gravitational_potential():
lat, lon, r = geodetic_to_spherical(latitude, longitude, radius0, ell=ell)
pot_model = model.gravitational_potential.potential(lat, lon, r)
pot_test = data.potential_ell.values
np.testing.assert_almost_equal(pot_model.value, pot_test, 6)
