def test_sheetflow():
flux = np.array(
[0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.50000000, 1.35677118, 2.18064899, 2.98289061,
3.77167837, 4.55070068, 5.32231777, 6.08818915, 6.34956448,
0.00000000, 0.50000000, 1.64322882, 2.77444053, 3.90022802,
5.01817926, 6.12943159, 7.23518857, 8.33656075, 8.93446352,
0.00000000, 0.50000000, 1.50000000, 2.54491048, 3.60279934,
4.66824237, 5.73835212, 6.81180077, 7.88776947, 8.46568929,
0.00000000, 0.50000000, 1.50000000, 2.50000000, 3.51408202,
4.54190001, 5.58151561, 6.63069288, 7.68748063, 8.25028271,
0.00000000, 0.50000000, 1.50000000, 2.50000000, 3.51408202,
4.54190001, 5.58151561, 6.63069288, 7.68748063, 8.25028271,
0.00000000, 0.50000000, 1.50000000, 2.54491048, 3.60279934,
4.66824237, 5.73835212, 6.81180077, 7.88776947, 8.46568929,
0.00000000, 0.50000000, 1.64322882, 2.77444053, 3.90022802,
5.01817926, 6.12943159, 7.23518857, 8.33656075, 8.93446352,
0.00000000, 0.50000000, 1.35677118, 2.18064899, 2.98289061,
3.77167837, 4.55070068, 5.32231777, 6.08818915, 6.34956448,
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000]
)
mg = RasterModelGrid((NROWS, NCOLS), (DX, DX))
z = (3000. - mg.node_x) * 0.5
mg.at_node['topographic__elevation'] = z
mg.set_closed_boundaries_at_grid_edges(False, True, True, True)
mg.at_node['water__volume_flux_in'] = np.ones_like(z, dtype=float)
pfr = PotentialityFlowRouter(mg, INPUTS)
pfr.route_flow(route_on_diagonals=True)
assert_array_almost_equal(mg.at_node['water__volume_flux_magnitude'], flux)
def test_sheetflow():
flux = np.array([
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.50000000,
1.35677118, 2.18064899, 2.98289061, 3.77167837, 4.55070068, 5.32231777,
6.08818915, 6.34956448, 0.00000000, 0.50000000, 1.64322882, 2.77444053,
3.90022802, 5.01817926, 6.12943159, 7.23518857, 8.33656075, 8.93446352,
0.00000000, 0.50000000, 1.50000000, 2.54491048, 3.60279934, 4.66824237,
5.73835212, 6.81180077, 7.88776947, 8.46568929, 0.00000000, 0.50000000,
1.50000000, 2.50000000, 3.51408202, 4.54190001, 5.58151561, 6.63069288,
7.68748063, 8.25028271, 0.00000000, 0.50000000, 1.50000000, 2.50000000,
3.51408202, 4.54190001, 5.58151561, 6.63069288, 7.68748063, 8.25028271,
0.00000000, 0.50000000, 1.50000000, 2.54491048, 3.60279934, 4.66824237,
5.73835212, 6.81180077, 7.88776947, 8.46568929, 0.00000000, 0.50000000,
1.64322882, 2.77444053, 3.90022802, 5.01817926, 6.12943159, 7.23518857,
8.33656075, 8.93446352, 0.00000000, 0.50000000, 1.35677118, 2.18064899,
2.98289061, 3.77167837, 4.55070068, 5.32231777, 6.08818915, 6.34956448,
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000
])
mg = RasterModelGrid((NROWS, NCOLS), (DX, DX))
z = (3000. - mg.node_x) * 0.5
mg.at_node['topographic__elevation'] = z
mg.set_closed_boundaries_at_grid_edges(False, True, True, True)
mg.at_node['water__unit_flux_in'] = np.ones_like(z, dtype=float)
pfr = PotentialityFlowRouter(mg, INPUTS)
pfr.route_flow(route_on_diagonals=True)
assert_array_almost_equal(mg.at_node['water__discharge'], flux)
#z = np.sqrt(mg.node_x**2 + mg.node_y**2) #z = mg.node_x + mg.node_y #val_to_replace_with = z.reshape((nrows,ncols))[3,3] #z.reshape((nrows,ncols))[2:5,:] = val_to_replace_with mg.at_node['topographic__elevation'] = z #mg.set_fixed_value_boundaries_at_grid_edges(True, True, True, True) mg.set_closed_boundaries_at_grid_edges(True, True, True, False) figure(3) imshow_node_grid(mg, mg.node_boundary_status) mg.at_node['water__volume_flux_in'] = np.ones_like(z) pfr = PotentialityFlowRouter(mg, 'pot_fr_params.txt') pfr.route_flow(route_on_diagonals=True) figure(1) imshow_node_grid(mg, 'water__volume_flux_magnitude') figure(2) imshow_node_grid(mg, 'topographic__elevation') out_sum = np.sum(mg.at_node['water__volume_flux_magnitude'].reshape((nrows,ncols))[-3,:]) print(out_sum) print(np.sum(mg.at_node['water__volume_flux_in']), np.sum(mg.at_node['water__volume_flux_magnitude'][mg.boundary_nodes])) print(out_sum - np.sum(mg.at_node['water__volume_flux_in'])) show() print(mg.at_node['water__volume_flux_magnitude'].reshape((nrows,ncols))) print(np.sum(mg.at_node['water__volume_flux_magnitude'].reshape((nrows,ncols)),axis=0)/3.)
def test_in_network():
# a valley network produced by stream power:
z = np.array([3.12900830e-04, 3.66462671e-04, 9.44438515e-04,
1.45006772e-04, 1.91406099e-04, 4.42053204e-04,
2.99818052e-04, 5.45267467e-04, 4.12129514e-04,
7.43816953e-04, 1.59251681e-04, 7.39577249e+01,
6.68718419e+01, 2.95535987e+01, 7.69715256e+01,
4.61083179e+01, 5.70611522e+01, 6.99664564e+01,
8.29355817e+01, 5.85563532e-04, 2.60300016e-04,
8.99636726e+01, 1.11946320e+02, 5.16553709e+01,
1.38432251e+02, 1.02903579e+02, 1.27601424e+02,
8.59469601e+01, 4.77495429e+01, 8.00781223e-04,
4.13095981e-04, 7.41309307e+01, 1.31747968e+02,
1.11724617e+02, 1.71687943e+02, 1.93482716e+02,
1.61044205e+02, 1.34775824e+02, 7.63077925e+01,
8.85837646e-04, 6.94907676e-04, 5.53654246e+01,
9.95405009e+01, 1.81345288e+02, 1.88975196e+02,
1.78104180e+02, 1.75231160e+02, 1.14932425e+02,
5.12018382e+01, 1.26501797e-04, 8.34527300e-04,
8.80562940e+01, 1.24009142e+02, 1.55635807e+02,
1.56683637e+02, 1.62398410e+02, 1.04070282e+02,
6.99665030e+01, 6.41256897e+01, 5.50951003e-04,
2.02545919e-04, 3.05799760e+01, 5.02285119e+01,
8.31442034e+01, 1.75898080e+02, 1.80095770e+02,
1.23416767e+02, 6.97604901e+01, 3.04864568e+01,
4.42047775e-04, 5.75778629e-04, 8.13990441e+01,
1.17362500e+02, 1.35317452e+02, 1.78842796e+02,
9.65391990e+01, 1.16520146e+02, 1.59289373e+02,
8.29784784e+01, 4.21911459e-04, 7.83145812e-04,
8.44510235e+01, 6.85512072e+01, 3.99258990e+01,
9.07740020e+01, 4.47116751e+01, 1.05333999e+02,
1.04965376e+02, 6.42615041e+01, 8.48184002e-04,
9.92952214e-04, 5.44805365e-04, 6.83657298e-04,
4.27967811e-04, 4.40101095e-04, 5.47248461e-04,
5.77178429e-06, 4.39642103e-04, 4.80194778e-04,
9.24014550e-04])
flux = np.array([0.71259316, 1.83684053, 7.98879336, 9.29556058,
10.55574138, 7.24717075, 7.35872565, 4.50198345,
1.97243029, 0.54929957, 1.71629201, 2.51051881,
2.92200909, 17.86860506, 4.15011452, 8.63568651,
7.26035354, 4.03993054, 2.05376022, 3.22879774,
3.64720173, 2.49610302, 1.96767906, 11.22263014,
2.93014856, 5.64199803, 3.24078038, 4.45203171,
6.62959451, 4.89790426, 6.37085028, 5.61698632,
2.07622910, 5.07309101, 2.93574511, 1.58440439,
2.98059775, 2.89536436, 4.32847468, 7.65823581,
6.75481149, 8.75145535, 6.37428052, 1.86527306,
1.71832016, 2.21381817, 2.14143388, 3.76828344,
9.74905731, 7.61218631, 13.23331816, 3.94223434,
3.12961197, 3.66940158, 4.73780806, 3.63252392,
8.36581084, 10.53572540, 8.04446793, 12.51965897,
12.20119563, 26.49337737, 20.10974987, 11.85575877,
1.84082688, 1.58440439, 4.20691725, 10.24822185,
19.04410064, 10.58826422, 10.25346723, 2.18153267,
2.00375244, 2.51941157, 1.65546848, 5.73599744,
3.04184663, 1.58440439, 2.47361063, 8.29762758,
1.42053367, 1.95945056, 3.39713331, 5.74421869,
4.29959761, 11.13098904, 2.56199932, 2.59397940,
3.16455917, 1.84587679, 0.57901390, 1.94727188,
4.37381176, 5.18582361, 7.70532091, 6.86738229,
6.04728286, 2.94714474, 2.00238426, 0.88296519])
potnt = np.array([0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 3.11607782,
4.55006628, 42.19484548, 4.51089463, 17.74767207,
11.86792011, 5.93094409, 2.26828834, 0.00000000,
0.00000000, 3.44492073, 2.99141368, 86.14598295,
3.22150654, 13.04937646, 4.51470410, 10.17131370,
14.01678016, 0.00000000, 0.00000000, 8.30460195,
2.72370114, 19.70198723, 4.81322624, 2.37203114,
4.76156757, 3.84190283, 5.53509620, 0.00000000,
0.00000000, 16.37964991, 18.32384346, 2.62626616,
3.21546389, 5.36483142, 3.18817287, 5.90189406,
18.67655153, 0.00000000, 0.00000000, 4.00510836,
3.72650973, 5.71530087, 24.27830939, 10.79812183,
29.22832978, 32.48924644, 9.86359775, 0.00000000,
0.00000000, 59.87184966, 154.76673703, 74.08035402,
3.21059221, 2.38746224, 7.36767179, 45.28386960,
44.05471543, 0.00000000, 0.00000000, 3.05098779,
2.45849055, 3.12955437, 1.87486166, 25.11244631,
6.21239887, 1.64106832, 3.28554137, 0.00000000,
0.00000000, 2.36944471, 5.71708702, 13.67642516,
4.71435055, 22.42310636, 3.41364647, 3.49569092,
4.14217802, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000])
mg = RasterModelGrid((NROWS, NCOLS), (DX, DX))
mg.add_field('node', 'topographic__elevation', z)
mg.at_node['water__volume_flux_in'] = DX * DX * np.ones_like(z) * 100. / (
60. * 60. * 24. * 365.25) # remember, flux is /s, so this is a small number!
pfr = PotentialityFlowRouter(mg, INPUTS)
pfr.route_flow(return_components=True)
assert_array_almost_equal(mg.at_node['water__volume_flux_magnitude'], flux)
assert_array_almost_equal(mg.at_node['potentiality_field'][mg.core_nodes],
potnt[mg.core_nodes])
def test_in_network():
# a valley network produced by stream power:
z = np.array([
3.12900830e-04, 3.66462671e-04, 9.44438515e-04, 1.45006772e-04,
1.91406099e-04, 4.42053204e-04, 2.99818052e-04, 5.45267467e-04,
4.12129514e-04, 7.43816953e-04, 1.59251681e-04, 7.39577249e+01,
6.68718419e+01, 2.95535987e+01, 7.69715256e+01, 4.61083179e+01,
5.70611522e+01, 6.99664564e+01, 8.29355817e+01, 5.85563532e-04,
2.60300016e-04, 8.99636726e+01, 1.11946320e+02, 5.16553709e+01,
1.38432251e+02, 1.02903579e+02, 1.27601424e+02, 8.59469601e+01,
4.77495429e+01, 8.00781223e-04, 4.13095981e-04, 7.41309307e+01,
1.31747968e+02, 1.11724617e+02, 1.71687943e+02, 1.93482716e+02,
1.61044205e+02, 1.34775824e+02, 7.63077925e+01, 8.85837646e-04,
6.94907676e-04, 5.53654246e+01, 9.95405009e+01, 1.81345288e+02,
1.88975196e+02, 1.78104180e+02, 1.75231160e+02, 1.14932425e+02,
5.12018382e+01, 1.26501797e-04, 8.34527300e-04, 8.80562940e+01,
1.24009142e+02, 1.55635807e+02, 1.56683637e+02, 1.62398410e+02,
1.04070282e+02, 6.99665030e+01, 6.41256897e+01, 5.50951003e-04,
2.02545919e-04, 3.05799760e+01, 5.02285119e+01, 8.31442034e+01,
1.75898080e+02, 1.80095770e+02, 1.23416767e+02, 6.97604901e+01,
3.04864568e+01, 4.42047775e-04, 5.75778629e-04, 8.13990441e+01,
1.17362500e+02, 1.35317452e+02, 1.78842796e+02, 9.65391990e+01,
1.16520146e+02, 1.59289373e+02, 8.29784784e+01, 4.21911459e-04,
7.83145812e-04, 8.44510235e+01, 6.85512072e+01, 3.99258990e+01,
9.07740020e+01, 4.47116751e+01, 1.05333999e+02, 1.04965376e+02,
6.42615041e+01, 8.48184002e-04, 9.92952214e-04, 5.44805365e-04,
6.83657298e-04, 4.27967811e-04, 4.40101095e-04, 5.47248461e-04,
5.77178429e-06, 4.39642103e-04, 4.80194778e-04, 9.24014550e-04
])
flux = np.array([
0.71259316, 1.83684053, 7.98879336, 9.29556058, 10.55574138,
7.24717075, 7.35872565, 4.50198345, 1.97243029, 0.54929957, 1.71629201,
2.51051881, 2.92200909, 17.86860506, 4.15011452, 8.63568651,
7.26035354, 4.03993054, 2.05376022, 3.22879774, 3.64720173, 2.49610302,
1.96767906, 11.22263014, 2.93014856, 5.64199803, 3.24078038,
4.45203171, 6.62959451, 4.89790426, 6.37085028, 5.61698632, 2.07622910,
5.07309101, 2.93574511, 1.58440439, 2.98059775, 2.89536436, 4.32847468,
7.65823581, 6.75481149, 8.75145535, 6.37428052, 1.86527306, 1.71832016,
2.21381817, 2.14143388, 3.76828344, 9.74905731, 7.61218631,
13.23331816, 3.94223434, 3.12961197, 3.66940158, 4.73780806,
3.63252392, 8.36581084, 10.53572540, 8.04446793, 12.51965897,
12.20119563, 26.49337737, 20.10974987, 11.85575877, 1.84082688,
1.58440439, 4.20691725, 10.24822185, 19.04410064, 10.58826422,
10.25346723, 2.18153267, 2.00375244, 2.51941157, 1.65546848,
5.73599744, 3.04184663, 1.58440439, 2.47361063, 8.29762758, 1.42053367,
1.95945056, 3.39713331, 5.74421869, 4.29959761, 11.13098904,
2.56199932, 2.59397940, 3.16455917, 1.84587679, 0.57901390, 1.94727188,
4.37381176, 5.18582361, 7.70532091, 6.86738229, 6.04728286, 2.94714474,
2.00238426, 0.88296519
])
potnt = np.array([
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 3.11607782,
4.55006628, 42.19484548, 4.51089463, 17.74767207, 11.86792011,
5.93094409, 2.26828834, 0.00000000, 0.00000000, 3.44492073, 2.99141368,
86.14598295, 3.22150654, 13.04937646, 4.51470410, 10.17131370,
14.01678016, 0.00000000, 0.00000000, 8.30460195, 2.72370114,
19.70198723, 4.81322624, 2.37203114, 4.76156757, 3.84190283,
5.53509620, 0.00000000, 0.00000000, 16.37964991, 18.32384346,
2.62626616, 3.21546389, 5.36483142, 3.18817287, 5.90189406,
18.67655153, 0.00000000, 0.00000000, 4.00510836, 3.72650973,
5.71530087, 24.27830939, 10.79812183, 29.22832978, 32.48924644,
9.86359775, 0.00000000, 0.00000000, 59.87184966, 154.76673703,
74.08035402, 3.21059221, 2.38746224, 7.36767179, 45.28386960,
44.05471543, 0.00000000, 0.00000000, 3.05098779, 2.45849055,
3.12955437, 1.87486166, 25.11244631, 6.21239887, 1.64106832,
3.28554137, 0.00000000, 0.00000000, 2.36944471, 5.71708702,
13.67642516, 4.71435055, 22.42310636, 3.41364647, 3.49569092,
4.14217802, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,
0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000
])
mg = RasterModelGrid((NROWS, NCOLS), (DX, DX))
mg.add_field('node', 'topographic__elevation', z)
mg.at_node['water__unit_flux_in'] = DX * DX * np.ones_like(z) * 100. / (
60. * 60. * 24. * 365.25
) # remember, flux is /s, so this is a small number!
pfr = PotentialityFlowRouter(mg, INPUTS)
pfr.route_flow(return_components=True)
assert_array_almost_equal(mg.at_node['water__discharge'], flux)
assert_array_almost_equal(mg.at_node['flow__potential'][mg.core_nodes],
potnt[mg.core_nodes])
#Set boundary conditions
mg.set_closed_boundaries_at_grid_edges(True, True, True, False)
mg.set_fixed_value_boundaries_at_grid_edges(False, False, False, True)
inlet_node = np.array((mg.number_of_node_columns + 1))
mg.at_node['water__volume_flux_in'].fill(0.)
mg.at_node['water__volume_flux_in'][inlet_node] = 1.
pfr = PotentialityFlowRouter(mg, 'pot_fr_params.txt')
interior_nodes = mg.core_nodes
# do the loop
for i in xrange(2000):
if i%50==0:
print('loop '+str(i))
mg.at_node['topographic__elevation'][inlet_node] = 1.
pfr.route_flow(route_on_diagonals=True)
#imshow(mg, 'water__volume_flux_magnitude')
#show()
kd = mg.at_node['water__volume_flux_magnitude'] # 0.01 m2 per year
# dt = np.nanmin(0.2*mg.dx*mg.dx/kd) # CFL condition
dt = 0.5
g = mg.calculate_gradients_at_active_links(mg.at_node['topographic__elevation'])
map_link_end_node_max_value_to_link(mg, 'water__volume_flux_magnitude')
kd_link = 1.e6*mg.at_link['water__volume_flux_magnitude'][mg.active_links]
qs = -kd_link*g
dqsdx = mg.calculate_flux_divergence_at_nodes(qs)
dzdt = -dqsdx
mg.at_node['topographic__elevation'][interior_nodes] += dzdt[interior_nodes]*dt
figure(1)
imshow_node_grid(mg, 'topographic__elevation')