def test_depth_kwarg(self):
nz = 20
zin = 0.5 * nz**-1 + np.arange(nz, dtype=np.float64) / nz
N2 = np.full(nz, 1.)
f0 = 1.
with self.assertRaises(ValueError):
z, def_radius, bc_modes = modes.neutral_modes_from_N2_profile(
zin, N2, f0, depth=zin[-5])
# no error expected
z, def_radius, bc_modes = modes.neutral_modes_from_N2_profile(
zin, N2, f0, depth=1.1)
def test_depth_kwarg(self):
nz = 20
zin = 0.5*nz**-1 + np.arange(nz, dtype=np.float64)/nz
N2 = np.full(nz, 1.)
f0 = 1.
with self.assertRaises(ValueError):
z, def_radius, bc_modes = modes.neutral_modes_from_N2_profile(
zin, N2, f0, depth=zin[-5]
)
# no error expected
z, def_radius, bc_modes = modes.neutral_modes_from_N2_profile(
zin, N2, f0, depth=1.1
)
def test_N2_const_equal_spacing(self):
# prepare a test N^2 profile
nz = 20
depth = 0.5*nz**-1 + np.arange(nz, dtype=np.float64)/nz
N2 = np.full(nz, 1.)
f0 = 1.
z, def_radius, bc_modes = modes.neutral_modes_from_N2_profile(
depth, N2, f0
)
# make sure we got the right number of modes
# NOPE! don't want all the modes and scipy.sparse.linalg.eigs won't
# compute them
#self.assertEqual(nz, len(def_radius))
# make sure the modes themselves have the right structure
self.assertEqual(nz+1, bc_modes.shape[0],
msg='modes array must the right shape')
self.assertTrue(np.all(np.diff(def_radius[1:]) < 0),
msg='modes should be sorted in order of decreasing deformation radius')
nmodes = len(def_radius)
zero_crossings = np.abs(np.diff(np.sign(bc_modes), axis=0)/2).sum(axis=0)
self.assertListEqual(list(range(nmodes)), list(zero_crossings),
msg='modes should have the correct number of zero crossings')
mode_amplitudes = (bc_modes**2).sum(axis=0)
self.assertTrue(np.allclose(np.ones(nmodes), mode_amplitudes),
msg='modes should be normalized to amplitude of 1')
def test_N2_const_equal_spacing(self):
# prepare a test N^2 profile
nz = 20
depth = 0.5 * nz**-1 + np.arange(nz, dtype=np.float64) / nz
N2 = np.full(nz, 1.)
f0 = 1.
z, def_radius, bc_modes = modes.neutral_modes_from_N2_profile(
depth, N2, f0)
self.assertEqual(nz + 1,
bc_modes.shape[0],
msg='modes array must the right shape')
self.assertTrue(
np.all(np.diff(def_radius[1:]) < 0),
msg=
'modes should be sorted in order of decreasing deformation radius')
nmodes = len(def_radius)
zero_crossings = np.abs(np.diff(np.sign(bc_modes), axis=0) /
2).sum(axis=0)
self.assertListEqual(
list(range(nmodes)),
list(zero_crossings),
msg='modes should have the correct number of zero crossings')
mode_amplitudes = (bc_modes**2).sum(axis=0)
self.assertTrue(np.allclose(np.ones(nmodes), mode_amplitudes),
msg='modes should be normalized to amplitude of 1')
def test_neutral_mode_args(self):
nz = 10
N2 = np.zeros(nz)
depth = np.arange(nz)
# check for unequal lengths of arrays
with self.assertRaises(ValueError):
_, _, _ = modes.neutral_modes_from_N2_profile(depth[1:], N2, 1.)
with self.assertRaises(ValueError):
_, _, _ = modes.neutral_modes_from_N2_profile(depth, N2[1:], 1.)
depth_non_monotonic = depth
depth_non_monotonic[0] = 5
# check for non-monotonic profile
with self.assertRaises(ValueError) as cm:
_, _, _ = modes.neutral_modes_from_N2_profile(
depth_non_monotonic, N2, 1.)
def test_neutral_mode_OCCA_GulfStream(self):
""" Test profile in the Gulf Stream in the OCCA data set
"""
zN2 = np.array([ -10.00006115, -20.00006114, -30.00006113, -40.00006112,
-50.0000611 , -60.00006109, -70.00256358, -80.01506451,
-90.06006328, -100.20256308, -110.5900682 , -121.51007976,
-133.44509256, -147.10512803, -163.43519352, -183.5678012 ,
-208.72298023, -240.09073926, -278.70109317, -325.30655719,
-380.30712264, -443.70276088, -515.09343642, -593.72659767,
-678.57216844, -768.44015906, -862.11055267, -958.45325725,
-1056.53586028, -1155.72595435, -1255.87608991, -1357.68378579,
-1463.12934261, -1575.64299213, -1699.66489761, -1839.65538686,
-1999.10931291, -2180.15155508, -2383.76440293, -2610.28273438,
-2859.78914881, -3132.29607118, -3427.80347989, -3746.3113517 ,
-4087.81966191, -4452.32838443, -4839.83749199, -5250.34695635,
-5683.85674858])
N2 = np.array([ 4.49013733e-05, 1.32619531e-04, 1.67213349e-04,
1.39980381e-04, 1.08620176e-04, 8.89353316e-05,
7.59696940e-05, 6.85660114e-05, 6.13053056e-05,
4.96623307e-05, 4.26153730e-05, 3.83933836e-05,
3.33244718e-05, 3.14573673e-05, 2.74780120e-05,
2.50869570e-05, 2.35907064e-05, 2.26047540e-05,
2.06309696e-05, 1.93499569e-05, 1.85802260e-05,
1.73887368e-05, 1.49995125e-05, 1.25945779e-05,
1.06210281e-05, 9.69791903e-06, 9.18845407e-06,
7.56655382e-06, 5.00383224e-06, 2.83633215e-06,
1.67170878e-06, 1.19350982e-06, 9.87252978e-07,
9.54096555e-07, 1.05979705e-06, 1.18957478e-06,
1.23432375e-06, 1.22190029e-06, 1.20084648e-06,
1.18287498e-06, 1.14801849e-06, 1.08643614e-06,
9.36511867e-07, 6.17342678e-07, 3.35507108e-07,
3.19646379e-07, 2.60733349e-07, np.nan,
np.nan])
f0 = 9.276710625272244e-05
nz = len(zN2)
kwargs = {'num_eigen': 2, 'init_vector': None, 'num_Lanczos': nz*10, 'iteration': nz*100, 'tolerance': 0}
zphi, Rd, v = modes.neutral_modes_from_N2_profile(
-zN2, N2, f0, **kwargs)
self.assertTrue(np.isclose(Rd[1], 25787.38588731),
msg='Rossby radius should be exact to the solution')
self.assertTrue(np.allclose(np.diff(v[:, 0]), 0.),
msg='The barotropic vertical mode should have all same value')
v1 = np.array([ 0.2287108, 0.22844163, 0.22738221, 0.22538205, 0.22315635, 0.22100572,
0.21890111, 0.21681132, 0.21466035, 0.21249153, 0.21051281, 0.20857709,
0.20653185, 0.20436013, 0.20172795, 0.19864415, 0.19475028, 0.18960952,
0.18268901, 0.17391394, 0.16270843, 0.14845062, 0.13133273, 0.11305419,
0.09473064, 0.07691331, 0.05874788, 0.04009015, 0.02387257, 0.01278873,
0.00637754, 0.00253038, -0.00029387, -0.00275014, -0.00532013, -0.00849032,
-0.01248929, -0.01713441, -0.02220176, -0.02756655, -0.0331077, -0.03857259,
-0.04363333, -0.04770119, -0.05004272, -0.05105026, -0.05168191, -0.05185931])
self.assertTrue(np.allclose(np.absolute(v[:, 1]), np.absolute(v1)),
msg='The amplitude of vertical modes should have the exact elements')
def test_neutral_mode_args(self):
nz = 10
N2 = np.zeros(nz)
depth = np.arange(nz)
# check for unequal lengths of arrays
with self.assertRaises(ValueError):
_, _, _ = modes.neutral_modes_from_N2_profile(
depth[1:], N2, 1.
)
with self.assertRaises(ValueError):
_, _, _ = modes.neutral_modes_from_N2_profile(
depth, N2[1:], 1.
)
depth_non_monotonic = depth
depth_non_monotonic[0] = 5
# check for non-monotonic profile
with self.assertRaises(ValueError) as cm:
_, _, _ = modes.neutral_modes_from_N2_profile(
depth_non_monotonic, N2, 1.
)
def test_neutral_mode_OCCA_GulfStream(self):
""" Test profile in the Gulf Stream in the OCCA data set
"""
zN2 = np.array([
-10.00006115, -20.00006114, -30.00006113, -40.00006112,
-50.0000611, -60.00006109, -70.00256358, -80.01506451,
-90.06006328, -100.20256308, -110.5900682, -121.51007976,
-133.44509256, -147.10512803, -163.43519352, -183.5678012,
-208.72298023, -240.09073926, -278.70109317, -325.30655719,
-380.30712264, -443.70276088, -515.09343642, -593.72659767,
-678.57216844, -768.44015906, -862.11055267, -958.45325725,
-1056.53586028, -1155.72595435, -1255.87608991, -1357.68378579,
-1463.12934261, -1575.64299213, -1699.66489761, -1839.65538686,
-1999.10931291, -2180.15155508, -2383.76440293, -2610.28273438,
-2859.78914881, -3132.29607118, -3427.80347989, -3746.3113517,
-4087.81966191, -4452.32838443, -4839.83749199, -5250.34695635,
-5683.85674858
])
N2 = np.array([
4.49013733e-05, 1.32619531e-04, 1.67213349e-04, 1.39980381e-04,
1.08620176e-04, 8.89353316e-05, 7.59696940e-05, 6.85660114e-05,
6.13053056e-05, 4.96623307e-05, 4.26153730e-05, 3.83933836e-05,
3.33244718e-05, 3.14573673e-05, 2.74780120e-05, 2.50869570e-05,
2.35907064e-05, 2.26047540e-05, 2.06309696e-05, 1.93499569e-05,
1.85802260e-05, 1.73887368e-05, 1.49995125e-05, 1.25945779e-05,
1.06210281e-05, 9.69791903e-06, 9.18845407e-06, 7.56655382e-06,
5.00383224e-06, 2.83633215e-06, 1.67170878e-06, 1.19350982e-06,
9.87252978e-07, 9.54096555e-07, 1.05979705e-06, 1.18957478e-06,
1.23432375e-06, 1.22190029e-06, 1.20084648e-06, 1.18287498e-06,
1.14801849e-06, 1.08643614e-06, 9.36511867e-07, 6.17342678e-07,
3.35507108e-07, 3.19646379e-07, 2.60733349e-07, np.nan, np.nan
])
f0 = 9.276710625272244e-05
nz = len(zN2)
kwargs = {
'num_eigen': 2,
'init_vector': None,
'num_Lanczos': nz * 10,
'iteration': nz * 100,
'tolerance': 0
}
zphi, Rd, v = modes.neutral_modes_from_N2_profile(
-zN2, N2, f0, **kwargs)
self.assertTrue(np.isclose(Rd[1], 25787.38588731),
msg='Rossby radius should be exact to the solution')
self.assertTrue(
np.allclose(np.diff(v[:, 0]), 0.),
msg='The barotropic vertical mode should have all same value')
v1 = np.array([
0.2287108, 0.22844163, 0.22738221, 0.22538205, 0.22315635,
0.22100572, 0.21890111, 0.21681132, 0.21466035, 0.21249153,
0.21051281, 0.20857709, 0.20653185, 0.20436013, 0.20172795,
0.19864415, 0.19475028, 0.18960952, 0.18268901, 0.17391394,
0.16270843, 0.14845062, 0.13133273, 0.11305419, 0.09473064,
0.07691331, 0.05874788, 0.04009015, 0.02387257, 0.01278873,
0.00637754, 0.00253038, -0.00029387, -0.00275014, -0.00532013,
-0.00849032, -0.01248929, -0.01713441, -0.02220176, -0.02756655,
-0.0331077, -0.03857259, -0.04363333, -0.04770119, -0.05004272,
-0.05105026, -0.05168191, -0.05185931
])
self.assertTrue(
np.allclose(np.absolute(v[:, 1]), np.absolute(v1)),
msg='The amplitude of vertical modes should have the exact elements'
)
