def test_can_run_with_hex():
"""Test that model can run with hex model grid."""
# Set up a 5x5 grid with open boundaries and low initial elevations.
mg = HexModelGrid(7, 7)
z = mg.add_zeros('node', 'topographic__elevation')
z[:] = 0.01 * mg.x_of_node
# Create a D8 flow handler
fa = FlowAccumulator(mg, flow_director='FlowDirectorSteepest')
# Parameter values for test 1
U = 0.001
dt = 10.0
# Create the Space component...
sp = Space(mg,
K_sed=0.00001,
K_br=0.00000000001,
F_f=0.5,
phi=0.1,
H_star=1.,
v_s=0.001,
m_sp=0.5,
n_sp=1.0,
sp_crit_sed=0,
sp_crit_br=0)
# ... and run it to steady state.
for i in range(2000):
fa.run_one_step()
sp.run_one_step(dt=dt)
z[mg.core_nodes] += U * dt
def test_mass_conserve_with_depression_finder_Space(grid2, H, solver,
depression_finder, phi,
v_s, H_star, dt):
grid2.at_node["soil__depth"][:] = H
assert grid2.status_at_node[1] == grid2.BC_NODE_IS_FIXED_VALUE
z_init = grid2.at_node["topographic__elevation"].copy()
if depression_finder is None:
fa = FlowAccumulator(grid2)
else:
fa = FlowAccumulator(grid2,
depression_finder=depression_finder,
routing="D4")
fa.run_one_step()
ed = Space(grid2, solver=solver, phi=phi, v_s=v_s, H_star=H_star)
ed.run_one_step(dt)
# see above test for notes.
dH = grid2.at_node["soil__depth"][:] - H
dH *= 1 - phi
dBr = grid2.at_node["bedrock__elevation"] - (z_init - H)
mass_change = dH + dBr
# assert that the mass loss over the surface is exported through the one
# outlet.
net_change = mass_change[grid2.core_nodes].sum() + (
ed.sediment_influx[1] * dt / grid2.cell_area_at_node[11])
assert_array_almost_equal(net_change, 0.0, decimal=10)
def test_can_run_with_hex():
"""Test that model can run with hex model grid."""
# Set up a 5x5 grid with open boundaries and low initial elevations.
mg = HexModelGrid(7, 7)
z = mg.add_zeros("node", "topographic__elevation")
z[:] = 0.01 * mg.x_of_node
# Create a D8 flow handler
fa = FlowAccumulator(mg, flow_director="FlowDirectorSteepest")
# Parameter values for test 1
U = 0.001
dt = 10.0
# Create the Space component...
sp = Space(
mg,
K_sed=0.00001,
K_br=0.00000000001,
F_f=0.5,
phi=0.1,
H_star=1.,
v_s=0.001,
m_sp=0.5,
n_sp=1.0,
sp_crit_sed=0,
sp_crit_br=0,
)
# ... and run it to steady state.
for i in range(2000):
fa.run_one_step()
sp.run_one_step(dt=dt)
z[mg.core_nodes] += U * dt
def test_soil_field_already_on_grid():
"""
Test that an existing soil grid field is not changed by instantiating
SPACE.
"""
# set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), xy_spacing=10.0)
z = mg.add_zeros("topographic__elevation", at="node")
br = mg.add_zeros("bedrock__elevation", at="node")
soil = mg.add_zeros("soil__depth", at="node")
soil += 1.0 # add 1m of soil everywehre
mg["node"]["topographic__elevation"] += (
mg.node_y / 10000 + mg.node_x / 10000 + np.random.rand(len(mg.node_y)) / 10000
)
mg.set_closed_boundaries_at_grid_edges(
bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True,
)
mg.set_watershed_boundary_condition_outlet_id(
0, mg["node"]["topographic__elevation"], -9999.0
)
br[:] = z[:] - soil[:]
# Create a D8 flow handler
FlowAccumulator(mg, flow_director="D8")
# Instantiate SPACE
sp = Space(
mg,
K_sed=0.01,
K_br=0.01,
F_f=0.0,
phi=0.0,
v_s=0.001,
m_sp=0.5,
n_sp=1.0,
sp_crit_sed=0,
sp_crit_br=0,
solver="basic",
)
# ensure that 'soil__depth' field is everywhere equal to 1.0 m.
testing.assert_array_equal(
np.ones(mg.number_of_nodes),
sp._soil__depth,
err_msg="SPACE soil depth field test failed",
verbose=True,
)
def __init__(self, input_file=None, params=None):
"""Initialize the HybridAlluviumModel."""
# Call ErosionModel's init
super(HybridAlluviumModel, self).__init__(input_file=input_file,
params=params)
# Instantiate a FlowRouter and DepressionFinderAndRouter components
self.flow_router = FlowRouter(self.grid, **self.params)
self.lake_filler = DepressionFinderAndRouter(self.grid, **self.params)
#make area_field and/or discharge_field depending on discharge_method
if self.params['discharge_method'] is not None:
if self.params['discharge_method'] == 'area_field':
area_field = self.grid.at_node['drainage_area']
discharge_field = None
elif self.params['discharge_method'] == 'discharge_field':
discharge_field = self.grid.at_node['surface_water__discharge']
area_field = None
else:
raise (KeyError)
else:
area_field = None
discharge_field = None
# Instantiate a HybridAlluvium component
self.eroder = Space(self.grid,
K_sed=self.params['K_sed'],
K_br=self.params['K_br'],
F_f=self.params['F_f'],
phi=self.params['phi'],
H_star=self.params['H_star'],
v_s=self.params['v_s'],
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
sp_crit_sed=self.params['sp_crit_sed'],
sp_crit_br=self.params['sp_crit_br'],
method=self.params['method'],
discharge_method=self.params['discharge_method'],
area_field=area_field,
discharge_field=discharge_field)
def test_mass_conserve_all_closed_Space(grid, H, solver, phi, v_s, H_star, dt):
grid.at_node["soil__depth"][:] = H
z_init = grid.at_node["topographic__elevation"].copy()
fa = FlowAccumulator(grid)
fa.run_one_step()
ed = Space(grid, solver=solver, phi=phi, v_s=v_s, H_star=H_star)
ed.run_one_step(dt)
# in space, everything is either bedrock or sediment. check for
# conservation.
dH = grid.at_node["soil__depth"][:] - H
# sediment is defined as having a porosity so all changes (up or down )
# must be adjusted to mass.
dH *= 1 - phi
dBr = grid.at_node["bedrock__elevation"] - (z_init - H)
mass_change = dH + dBr
assert_array_almost_equal(mass_change.sum(), 0.0, decimal=10)
def test_br_field_already_on_grid():
"""
Test that an existing bedrock elevation grid field is not changed by
instantiating SPACE.
"""
#set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), 10.0)
z = mg.add_zeros('node', 'topographic__elevation')
br = mg.add_zeros('node', 'bedrock__elevation')
br += 1. #make bedrock elevation 5m below surface
soil = mg.add_zeros('node', 'soil__depth')
mg['node']['topographic__elevation'] += mg.node_y / 10000 \
+ mg.node_x / 10000 \
+ np.random.rand(len(mg.node_y)) / 10000
mg.set_closed_boundaries_at_grid_edges(bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True)
mg.set_watershed_boundary_condition_outlet_id(
0, mg['node']['topographic__elevation'], -9999.)
z[:] = br[:] + soil[:]
# Create a D8 flow handler
fa = FlowAccumulator(mg, flow_director='D8')
#Instantiate SPACE
sp = Space(mg,
K_sed=0.01,
K_br=0.01,
F_f=0.0,
phi=0.0,
v_s=0.001,
m_sp=0.5,
n_sp=1.0,
sp_crit_sed=0,
sp_crit_br=0,
solver='basic')
#ensure that 'bedrock__elevation' field is everywhere equal to 1.0 m.
testing.assert_array_equal(np.ones(mg.number_of_nodes),
sp.bedrock__elevation,
err_msg='SPACE bedrock field test failed',
verbose=True)
def test_bad_solver_name():
"""
Test that any solver name besides 'basic' and 'adaptive' raises an error.
"""
# set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), xy_spacing=10.0)
z = mg.add_zeros("topographic__elevation", at="node")
br = mg.add_zeros("bedrock__elevation", at="node")
soil = mg.add_zeros("soil__depth", at="node")
mg["node"]["topographic__elevation"] += (
mg.node_y / 10000 + mg.node_x / 10000 + np.random.rand(len(mg.node_y)) / 10000
)
mg.set_closed_boundaries_at_grid_edges(
bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True,
)
mg.set_watershed_boundary_condition_outlet_id(
0, mg["node"]["topographic__elevation"], -9999.0
)
br[:] = z[:] - soil[:]
# Create a D8 flow handler
FlowAccumulator(mg, flow_director="D8")
# try to instantiate SPACE using a wrong solver name
with pytest.raises(ValueError):
Space(
mg,
K_sed=0.01,
K_br=0.01,
F_f=0.0,
phi=0.0,
v_s=0.001,
m_sp=0.5,
n_sp=1.0,
sp_crit_sed=0,
sp_crit_br=0,
solver="something_else",
)
def test_route_to_multiple_error_raised():
mg = RasterModelGrid((10, 10))
z = mg.add_zeros('node', 'topographic__elevation')
z += mg.x_of_node + mg.y_of_node
fa = FlowAccumulator(mg, flow_director='MFD')
fa.run_one_step()
with pytest.raises(NotImplementedError):
Space(mg,
K_sed=0.1,
K_br=0.1,
F_f=0.5,
phi=0.1,
H_star=1.,
v_s=0.001,
m_sp=1.0,
n_sp=0.5,
sp_crit_sed=0,
sp_crit_br=0)
class BasicHySa(ErosionModel):
"""
A BasicHySa computes erosion using linear diffusion, hybrid alluvium,
and Q~A.
It creates soil through weathering and fluvial bedrock erosion,
and consideres soil thickness in calculating hillslope diffusion.
"""
def __init__(self,
input_file=None,
params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicSa."""
# Call ErosionModel's init
super(BasicHySa,
self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
self.K_br = self.get_parameter_from_exponent('K_rock_sp')
self.K_sed = self.get_parameter_from_exponent('K_sed_sp')
linear_diffusivity = (
self._length_factor**2.) * self.get_parameter_from_exponent(
'linear_diffusivity') # has units length^2/time
v_sc = self.get_parameter_from_exponent(
'v_sc') # normalized settling velocity. Unitless.
linear_diffusivity = (
self._length_factor**2.) * self.get_parameter_from_exponent(
'linear_diffusivity') # has units length^2/time
try:
initial_soil_thickness = (self._length_factor) * self.params[
'initial_soil_thickness'] # has units length
except KeyError:
initial_soil_thickness = 1.0 # default value
soil_transport_decay_depth = (self._length_factor) * self.params[
'soil_transport_decay_depth'] # has units length
max_soil_production_rate = (self._length_factor) * self.params[
'max_soil_production_rate'] # has units length per time
soil_production_decay_depth = (self._length_factor) * self.params[
'soil_production_decay_depth'] # has units length
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(
self.grid,
flow_director='D8',
depression_finder=DepressionFinderAndRouter)
#set methods and fields. K's and sp_crits need to be field names
method = 'simple_stream_power'
discharge_method = 'discharge_field'
area_field = None
discharge_field = 'surface_water__discharge'
# Instantiate a SPACE component
self.eroder = Space(self.grid,
K_sed=self.K_sed,
K_br=self.K_br,
F_f=self.params['F_f'],
phi=self.params['phi'],
H_star=self.params['H_star'],
v_s=v_sc,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
method=method,
discharge_method=discharge_method,
area_field=area_field,
discharge_field=discharge_field,
solver=self.params['solver'])
# Create soil thickness (a.k.a. depth) field
if 'soil__depth' in self.grid.at_node:
soil_thickness = self.grid.at_node['soil__depth']
else:
soil_thickness = self.grid.add_zeros('node', 'soil__depth')
# Create bedrock elevation field
if 'bedrock__elevation' in self.grid.at_node:
bedrock_elev = self.grid.at_node['bedrock__elevation']
else:
bedrock_elev = self.grid.add_zeros('node', 'bedrock__elevation')
# Set soil thickness and bedrock elevation
try:
initial_soil_thickness = self.params['initial_soil_thickness']
except KeyError:
initial_soil_thickness = 1.0 # default value
soil_thickness[:] = initial_soil_thickness
bedrock_elev[:] = self.z - initial_soil_thickness
# Instantiate diffusion and weathering components
self.diffuser = DepthDependentDiffuser(
self.grid,
linear_diffusivity=linear_diffusivity,
soil_transport_decay_depth=soil_transport_decay_depth)
self.weatherer = ExponentialWeatherer(
self.grid,
max_soil_production_rate=max_soil_production_rate,
soil_production_decay_depth=soil_production_decay_depth)
self.grid.at_node['soil__depth'][:] = \
self.grid.at_node['topographic__elevation'] - \
self.grid.at_node['bedrock__elevation']
def run_one_step(self, dt):
"""
Advance model for one time-step of duration dt.
"""
# Route flow
self.flow_router.run_one_step()
# Get IDs of flooded nodes, if any
flooded = np.where(
self.flow_router.depression_finder.flood_status == 3)[0]
#print('There are ' + str(len(flooded)) + ' flooded nodes')
# Do some erosion (but not on the flooded nodes)
# (if we're varying K through time, update that first)
if self.opt_var_precip:
erode_factor = self.pc.get_erodibility_adjustment_factor(
self.model_time)
self.eroder.K_sed = self.K_sed * erode_factor
self.eroder.K_br = self.K_br * erode_factor
self.eroder.run_one_step(dt, flooded_nodes=flooded)
# We must also now erode the bedrock where relevant. If water erosion
# into bedrock has occurred, the bedrock elevation will be higher than
# the actual elevation, so we simply re-set bedrock elevation to the
# lower of itself or the current elevation.
b = self.grid.at_node['bedrock__elevation']
b[:] = np.minimum(b, self.grid.at_node['topographic__elevation'])
# Calculate regolith-production rate
self.weatherer.calc_soil_prod_rate()
# Generate and move soil around
self.diffuser.run_one_step(dt)
# calculate model time
self.model_time += dt
# Lower outlet
self.update_outlet(dt)
# Check walltime
self.check_walltime()
# Check stability
self.check_stability()
def check_stability(self):
"""Check stability and exit if unstable."""
fields = self.grid.at_node.keys()
for f in fields:
if (np.any(np.isnan(self.grid.at_node[f]))
or np.any(np.isinf(self.grid.at_node[f]))):
# model is unstable, write message and exit.
with open('model_failed.txt', 'w') as f:
f.write('This model run became unstable\n')
exit
def __init__(self,
input_file=None,
params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicSa."""
# Call ErosionModel's init
super(BasicHySa,
self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
self.K_br = self.get_parameter_from_exponent('K_rock_sp')
self.K_sed = self.get_parameter_from_exponent('K_sed_sp')
linear_diffusivity = (
self._length_factor**2.) * self.get_parameter_from_exponent(
'linear_diffusivity') # has units length^2/time
v_sc = self.get_parameter_from_exponent(
'v_sc') # normalized settling velocity. Unitless.
linear_diffusivity = (
self._length_factor**2.) * self.get_parameter_from_exponent(
'linear_diffusivity') # has units length^2/time
try:
initial_soil_thickness = (self._length_factor) * self.params[
'initial_soil_thickness'] # has units length
except KeyError:
initial_soil_thickness = 1.0 # default value
soil_transport_decay_depth = (self._length_factor) * self.params[
'soil_transport_decay_depth'] # has units length
max_soil_production_rate = (self._length_factor) * self.params[
'max_soil_production_rate'] # has units length per time
soil_production_decay_depth = (self._length_factor) * self.params[
'soil_production_decay_depth'] # has units length
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(
self.grid,
flow_director='D8',
depression_finder=DepressionFinderAndRouter)
#set methods and fields. K's and sp_crits need to be field names
method = 'simple_stream_power'
discharge_method = 'discharge_field'
area_field = None
discharge_field = 'surface_water__discharge'
# Instantiate a SPACE component
self.eroder = Space(self.grid,
K_sed=self.K_sed,
K_br=self.K_br,
F_f=self.params['F_f'],
phi=self.params['phi'],
H_star=self.params['H_star'],
v_s=v_sc,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
method=method,
discharge_method=discharge_method,
area_field=area_field,
discharge_field=discharge_field,
solver=self.params['solver'])
# Create soil thickness (a.k.a. depth) field
if 'soil__depth' in self.grid.at_node:
soil_thickness = self.grid.at_node['soil__depth']
else:
soil_thickness = self.grid.add_zeros('node', 'soil__depth')
# Create bedrock elevation field
if 'bedrock__elevation' in self.grid.at_node:
bedrock_elev = self.grid.at_node['bedrock__elevation']
else:
bedrock_elev = self.grid.add_zeros('node', 'bedrock__elevation')
# Set soil thickness and bedrock elevation
try:
initial_soil_thickness = self.params['initial_soil_thickness']
except KeyError:
initial_soil_thickness = 1.0 # default value
soil_thickness[:] = initial_soil_thickness
bedrock_elev[:] = self.z - initial_soil_thickness
# Instantiate diffusion and weathering components
self.diffuser = DepthDependentDiffuser(
self.grid,
linear_diffusivity=linear_diffusivity,
soil_transport_decay_depth=soil_transport_decay_depth)
self.weatherer = ExponentialWeatherer(
self.grid,
max_soil_production_rate=max_soil_production_rate,
soil_production_decay_depth=soil_production_decay_depth)
self.grid.at_node['soil__depth'][:] = \
self.grid.at_node['topographic__elevation'] - \
self.grid.at_node['bedrock__elevation']
def __init__(
self,
clock,
grid,
m_sp=0.5,
n_sp=1.0,
water_erodibility_sediment=0.001,
water_erodibility_rock=0.0001,
regolith_transport_parameter=0.1,
settling_velocity=0.001,
sediment_porosity=0.3,
fraction_fines=0.5,
roughness__length_scale=0.5,
solver="basic",
soil_production__maximum_rate=0.001,
soil_production__decay_depth=0.5,
soil_transport_decay_depth=0.5,
sp_crit_br=0,
sp_crit_sed=0,
**kwargs
):
"""
Parameters
----------
clock : terrainbento Clock instance
grid : landlab model grid instance
The grid must have all required fields.
m_sp : float, optional
Drainage area exponent (:math:`m`). Default is 0.5.
n_sp : float, optional
Slope exponent (:math:`n`). Default is 1.0.
water_erodibility : float, optional
Water erodibility (:math:`K`). Default is 0.0001.
regolith_transport_parameter : float, optional
Regolith transport efficiency (:math:`D`). Default is 0.1.
settling_velocity : float, optional
Normalized settling velocity of entrained sediment (:math:`V_s`).
Default is 0.001.
sediment_porosity : float, optional
Sediment porosity (:math:`\phi`). Default is 0.3.
fraction_fines : float, optional
Fraction of fine sediment that is permanently detached
(:math:`F_f`). Default is 0.5.
roughness__length_scale : float, optional
Bedrock roughness length scale. Default is 0.5.
solver : str, optional
Solver option to pass to the Landlab
`Space <https://landlab.readthedocs.io/en/master/reference/components/space.html>`_
component. Default is "basic".
soil_production__maximum_rate : float, optional
Maximum rate of soil production (:math:`P_{0}`). Default is 0.001.
soil_production__decay_depth : float, optional
Decay depth for soil production (:math:`H_{s}`). Default is 0.5.
soil_transport_decay_depth : float, optional
Decay depth for soil transport (:math:`H_{0}`). Default is 0.5.
**kwargs :
Keyword arguments to pass to :py:class:`ErosionModel`. Importantly
these arguments specify the precipitator and the runoff generator
that control the generation of surface water discharge (:math:`Q`).
Returns
-------
BasicHySa : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicHySa**. For more detailed examples, including
steady-state test examples, see the terrainbento tutorials.
To begin, import the model class.
>>> from landlab import RasterModelGrid
>>> from landlab.values import random
>>> from terrainbento import Clock, BasicHySa
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicHySa(clock, grid)
Running the model with ``model.run()`` would create output, so here we
will just run it one step.
>>> model.run_one_step(1.)
>>> model.model_time
1.0
"""
# Call ErosionModel"s init
super().__init__(clock, grid, **kwargs)
# verify correct fields are present.
self._verify_fields(self._required_fields)
soil_thickness = self.grid.at_node["soil__depth"]
bedrock_elev = self.grid.add_zeros("node", "bedrock__elevation")
bedrock_elev[:] = self.z - soil_thickness
self.m = m_sp
self.n = n_sp
self.K_br = water_erodibility_rock
self.K_sed = water_erodibility_sediment
# Instantiate a SPACE component
self.eroder = Space(
self.grid,
K_sed=self.K_sed,
K_br=self.K_br,
sp_crit_br=sp_crit_br,
sp_crit_sed=sp_crit_sed,
F_f=fraction_fines,
phi=sediment_porosity,
H_star=roughness__length_scale,
v_s=settling_velocity,
m_sp=self.m,
n_sp=self.n,
discharge_field="surface_water__discharge",
solver=solver,
)
# Instantiate diffusion and weathering components
self.weatherer = ExponentialWeatherer(
self.grid,
soil_production__maximum_rate=soil_production__maximum_rate,
soil_production__decay_depth=soil_production__decay_depth,
)
self.diffuser = DepthDependentDiffuser(
self.grid,
linear_diffusivity=regolith_transport_parameter,
soil_transport_decay_depth=soil_transport_decay_depth,
)
self.grid.at_node["soil__depth"][:] = (
self.grid.at_node["topographic__elevation"]
- self.grid.at_node["bedrock__elevation"]
)
class BasicHySa(ErosionModel):
r"""**BasicHySa** program.
This model program combines :py:class:`BasicHy` and :py:class:`BasicSa` to
evolve a topographic surface described by :math:`\eta` with the following
governing equation:
.. math::
\eta = \eta_b + H
\frac{\partial H}{\partial t} = P_0 \exp (-H/H_s)
+ \frac{V_s Q_s}{Q(A)\left(1 - \phi \right)}
- K_s Q(A)^{m}S^{n} (1 - e^{-H/H_*})
-\nabla q_h
\frac{\partial \eta_b}{\partial t} = -P_0 \exp (-H/H_s)
- K_r Q(A)^{m}S^{n} e^{-H/H_*}
Q_s = \int_0^A \left(K_s Q(A)^{m}S^{n} (1-e^{-H/H_*})
+ K_r (1-F_f) Q(A)^{m}S^{n} e^{-H/H_*}
- \frac{V_s Q_s}{Q(A)}\right) dA
where :math:`\eta_b` is the bedrock elevation, :math:`H` is the soil depth,
:math:`P_0` is the maximum soil production rate, :math:`H_s` is the soil
production decay depth, :math:`V_s` is effective sediment settling
velocity, :math:`Q_s` is volumetric fluvial sediment flux, :math:`A` is the
local drainage area, :math:`Q`, is the local discharge, :math:`S` is the
local slope, :math:`\phi` is sediment porosity, :math:`F_f` is the fraction
of fine sediment, :math:`K_r` and :math:`K_s` are rock and sediment
erodibility respectively, :math:`m` and :math:`n` are the discharge and
slope exponent parameters, :math:`H_*` is the bedrock roughness length
scale, and :math:`r` is a runoff rate. Hillslope sediment flux per unit
width :math:`q_h` is given by:
.. math::
q_h = -D H^* \left[1-\exp \left( -\frac{H}{H_0} \right) \right]
\nabla \eta.
where :math:`D` is soil diffusivity and :math:`H_0` is the soil transport
depth scale.
Refer to
`Barnhart et al. (2019) <https://doi.org/10.5194/gmd-12-1267-2019>`_
Table 5 for full list of parameter symbols, names, and dimensions.
The following at-node fields must be specified in the grid:
- ``topographic__elevation``
- ``soil__depth``
"""
_required_fields = ["topographic__elevation", "soil__depth"]
def __init__(
self,
clock,
grid,
m_sp=0.5,
n_sp=1.0,
water_erodibility_sediment=0.001,
water_erodibility_rock=0.0001,
regolith_transport_parameter=0.1,
settling_velocity=0.001,
sediment_porosity=0.3,
fraction_fines=0.5,
roughness__length_scale=0.5,
solver="basic",
soil_production__maximum_rate=0.001,
soil_production__decay_depth=0.5,
soil_transport_decay_depth=0.5,
sp_crit_br=0,
sp_crit_sed=0,
**kwargs
):
"""
Parameters
----------
clock : terrainbento Clock instance
grid : landlab model grid instance
The grid must have all required fields.
m_sp : float, optional
Drainage area exponent (:math:`m`). Default is 0.5.
n_sp : float, optional
Slope exponent (:math:`n`). Default is 1.0.
water_erodibility : float, optional
Water erodibility (:math:`K`). Default is 0.0001.
regolith_transport_parameter : float, optional
Regolith transport efficiency (:math:`D`). Default is 0.1.
settling_velocity : float, optional
Normalized settling velocity of entrained sediment (:math:`V_s`).
Default is 0.001.
sediment_porosity : float, optional
Sediment porosity (:math:`\phi`). Default is 0.3.
fraction_fines : float, optional
Fraction of fine sediment that is permanently detached
(:math:`F_f`). Default is 0.5.
roughness__length_scale : float, optional
Bedrock roughness length scale. Default is 0.5.
solver : str, optional
Solver option to pass to the Landlab
`Space <https://landlab.readthedocs.io/en/master/reference/components/space.html>`_
component. Default is "basic".
soil_production__maximum_rate : float, optional
Maximum rate of soil production (:math:`P_{0}`). Default is 0.001.
soil_production__decay_depth : float, optional
Decay depth for soil production (:math:`H_{s}`). Default is 0.5.
soil_transport_decay_depth : float, optional
Decay depth for soil transport (:math:`H_{0}`). Default is 0.5.
**kwargs :
Keyword arguments to pass to :py:class:`ErosionModel`. Importantly
these arguments specify the precipitator and the runoff generator
that control the generation of surface water discharge (:math:`Q`).
Returns
-------
BasicHySa : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicHySa**. For more detailed examples, including
steady-state test examples, see the terrainbento tutorials.
To begin, import the model class.
>>> from landlab import RasterModelGrid
>>> from landlab.values import random
>>> from terrainbento import Clock, BasicHySa
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicHySa(clock, grid)
Running the model with ``model.run()`` would create output, so here we
will just run it one step.
>>> model.run_one_step(1.)
>>> model.model_time
1.0
"""
# Call ErosionModel"s init
super().__init__(clock, grid, **kwargs)
# verify correct fields are present.
self._verify_fields(self._required_fields)
soil_thickness = self.grid.at_node["soil__depth"]
bedrock_elev = self.grid.add_zeros("node", "bedrock__elevation")
bedrock_elev[:] = self.z - soil_thickness
self.m = m_sp
self.n = n_sp
self.K_br = water_erodibility_rock
self.K_sed = water_erodibility_sediment
# Instantiate a SPACE component
self.eroder = Space(
self.grid,
K_sed=self.K_sed,
K_br=self.K_br,
sp_crit_br=sp_crit_br,
sp_crit_sed=sp_crit_sed,
F_f=fraction_fines,
phi=sediment_porosity,
H_star=roughness__length_scale,
v_s=settling_velocity,
m_sp=self.m,
n_sp=self.n,
discharge_field="surface_water__discharge",
solver=solver,
)
# Instantiate diffusion and weathering components
self.weatherer = ExponentialWeatherer(
self.grid,
soil_production__maximum_rate=soil_production__maximum_rate,
soil_production__decay_depth=soil_production__decay_depth,
)
self.diffuser = DepthDependentDiffuser(
self.grid,
linear_diffusivity=regolith_transport_parameter,
soil_transport_decay_depth=soil_transport_decay_depth,
)
self.grid.at_node["soil__depth"][:] = (
self.grid.at_node["topographic__elevation"]
- self.grid.at_node["bedrock__elevation"]
)
def run_one_step(self, step):
"""Advance model **BasicHySa** for one time-step of duration step.
The **run_one_step** method does the following:
1. Creates rain and runoff, then directs and accumulates flow.
2. Assesses the location, if any, of flooded nodes where erosion should
not occur.
3. Assesses if a :py:mod:`PrecipChanger` is an active boundary handler
and if so, uses it to modify the erodibility by water.
4. Calculates erosion and deposition by water.
5. Calculates topographic change by linear diffusion.
6. Finalizes the step using the :py:mod:`ErosionModel` base class
function **finalize__run_one_step**. This function updates all
boundary handlers handlers by ``step`` and increments model time by
``step``.
Parameters
----------
step : float
Increment of time for which the model is run.
"""
# create and move water
self.create_and_move_water(step)
# Do some erosion (but not on the flooded nodes)
# (if we're varying K through time, update that first)
if "PrecipChanger" in self.boundary_handlers:
erode_factor = self.boundary_handlers[
"PrecipChanger"
].get_erodibility_adjustment_factor()
self.eroder.K_sed = self.K_sed * erode_factor
self.eroder.K_br = self.K_br * erode_factor
self.eroder.run_one_step(step)
# We must also now erode the bedrock where relevant. If water erosion
# into bedrock has occurred, the bedrock elevation will be higher than
# the actual elevation, so we simply re-set bedrock elevation to the
# lower of itself or the current elevation.
b = self.grid.at_node["bedrock__elevation"]
b[:] = np.minimum(b, self.grid.at_node["topographic__elevation"])
# Calculate regolith-production rate
self.weatherer.calc_soil_prod_rate()
# Generate and move soil around
self.diffuser.run_one_step(step)
# Finalize the run_one_step_method
self.finalize__run_one_step(step)
# Check stability
self.check_stability()
def check_stability(self):
"""Check model stability and exit if unstable."""
fields = self.grid.at_node.keys()
for f in fields:
if np.any(np.isnan(self.grid.at_node[f])) or np.any(
np.isinf(self.grid.at_node[f])
):
raise SystemExit(
"terrainbento ModelHySa: Model became unstable"
)
def test_matches_bedrock_alluvial_solution():
"""
Test that model matches the bedrock-alluvial analytical solution
for slope/area relationship at steady state:
S=((U * v_s * (1 - F_f)) / (K_sed * A^m) + U / (K_br * A^m))^(1/n).
Also test that the soil depth everywhere matches the bedrock-alluvial
analytical solution at steady state:
H = -H_star * ln(1 - (v_s / (K_sed / (K_br * (1 - F_f)) + v_s))).
"""
# set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), xy_spacing=10.0)
z = mg.add_zeros("node", "topographic__elevation")
br = mg.add_zeros("node", "bedrock__elevation")
soil = mg.add_zeros("node", "soil__depth")
mg["node"]["topographic__elevation"] += (
mg.node_y / 100000 + mg.node_x / 100000 + np.random.rand(len(mg.node_y)) / 10000
)
mg.set_closed_boundaries_at_grid_edges(
bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True,
)
mg.set_watershed_boundary_condition_outlet_id(
0, mg["node"]["topographic__elevation"], -9999.
)
soil[:] += 0. # initial condition of no soil depth.
br[:] = z[:]
z[:] += soil[:]
# Instantiate DepressionFinderAndRouter
df = DepressionFinderAndRouter(mg)
# Create a D8 flow handler
fa = FlowAccumulator(
mg, flow_director="D8", depression_finder="DepressionFinderAndRouter"
)
# Parameter values for detachment-limited test
K_br = 0.02
K_sed = 0.02
U = 0.0001
dt = 1.0
F_f = 0.2 # all detached rock disappears; detachment-ltd end-member
m_sp = 0.5
n_sp = 1.0
v_s = 0.25
H_star = 0.1
# Instantiate the Space component...
sp = Space(
mg,
K_sed=K_sed,
K_br=K_br,
F_f=F_f,
phi=0.0,
H_star=H_star,
v_s=v_s,
m_sp=m_sp,
n_sp=n_sp,
sp_crit_sed=0,
sp_crit_br=0,
)
# ... and run it to steady state (10000x1-year timesteps).
for i in range(10000):
fa.run_one_step()
flooded = np.where(df.flood_status == 3)[0]
sp.run_one_step(dt=dt, flooded_nodes=flooded)
br[mg.core_nodes] += U * dt # m
soil[0] = 0. # enforce 0 soil depth at boundary to keep lowering steady
z[:] = br[:] + soil[:]
# compare numerical and analytical slope solutions
num_slope = mg.at_node["topographic__steepest_slope"][mg.core_nodes]
analytical_slope = np.power(
(
(U * v_s * (1 - F_f))
/ (K_sed * np.power(mg.at_node["drainage_area"][mg.core_nodes], m_sp))
)
+ (U / (K_br * np.power(mg.at_node["drainage_area"][mg.core_nodes], m_sp))),
1. / n_sp,
)
# test for match with analytical slope-area relationship
testing.assert_array_almost_equal(
num_slope,
analytical_slope,
decimal=8,
err_msg="SPACE bedrock-alluvial slope-area test failed",
verbose=True,
)
# compare numerical and analytical soil depth solutions
num_h = mg.at_node["soil__depth"][mg.core_nodes]
analytical_h = -H_star * np.log(1 - (v_s / (K_sed / (K_br * (1 - F_f)) + v_s)))
# test for match with analytical sediment depth
testing.assert_array_almost_equal(
num_h,
analytical_h,
decimal=5,
err_msg="SPACE bedrock-alluvial soil thickness test failed",
verbose=True,
)
F_f = 0.
phi = 0.
H_star = 1.
v_s = 5.0
m_sp = 0.5
n_sp = 1.0
sp_crit_sed = 0.
sp_crit_br = 0.
#Instantiate SPACE model with chosen parameters
sp = Space(mg,
K_sed=K_sed,
K_br=K_br,
F_f=F_f,
phi=phi,
H_star=H_star,
v_s=v_s,
m_sp=m_sp,
n_sp=n_sp,
sp_crit_sed=sp_crit_sed,
sp_crit_br=sp_crit_br,
method='simple_stream_power')
##Run time loop###########################################################
#Set model timestep
timestep = 1.0 #years
#Set elapsed time to zero
elapsed_time = 0
#Set model run time
run_time = 100000 #years
def test_matches_transport_solution():
"""
Test that model matches the transport-limited analytical solution
for slope/area relationship at steady state: S=((U * v_s) / (K_sed * A^m)
+ U / (K_sed * A^m))^(1/n).
Also test that model matches the analytical solution for steady-state
sediment flux: Qs = U * A * (1 - phi).
"""
# set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), xy_spacing=10.0)
z = mg.add_zeros("node", "topographic__elevation")
br = mg.add_zeros("node", "bedrock__elevation")
soil = mg.add_zeros("node", "soil__depth")
mg["node"]["topographic__elevation"] += (
mg.node_y / 100000 + mg.node_x / 100000 +
np.random.rand(len(mg.node_y)) / 10000)
mg.set_closed_boundaries_at_grid_edges(
bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True,
)
mg.set_watershed_boundary_condition_outlet_id(
0, mg["node"]["topographic__elevation"], -9999.0)
soil[:] += 100.0 # initial soil depth of 100 m
br[:] = z[:]
z[:] += soil[:]
# Instantiate DepressionFinderAndRouter
df = DepressionFinderAndRouter(mg)
# Create a D8 flow handler
fa = FlowAccumulator(mg,
flow_director="D8",
depression_finder="DepressionFinderAndRouter")
# Parameter values for detachment-limited test
K_sed = 0.01
U = 0.0001
dt = 1.0
F_f = 1.0 # all detached rock disappears; detachment-ltd end-member
m_sp = 0.5
n_sp = 1.0
v_s = 0.5
phi = 0.5
# Instantiate the Space component...
sp = Space(
mg,
K_sed=K_sed,
K_br=0.01,
F_f=F_f,
phi=phi,
H_star=1.0,
v_s=v_s,
m_sp=m_sp,
n_sp=n_sp,
sp_crit_sed=0,
sp_crit_br=0,
)
# ... and run it to steady state (5000x1-year timesteps).
for i in range(5000):
fa.run_one_step()
flooded = np.where(df.flood_status == 3)[0]
sp.run_one_step(dt=dt, flooded_nodes=flooded)
br[mg.core_nodes] += U * dt # m
soil[
0] = 100.0 # enforce constant soil depth at boundary to keep lowering steady
z[:] = br[:] + soil[:]
# compare numerical and analytical slope solutions
num_slope = mg.at_node["topographic__steepest_slope"][mg.core_nodes]
analytical_slope = np.power(
((U * v_s * (1 - phi)) /
(K_sed * np.power(mg.at_node["drainage_area"][mg.core_nodes], m_sp)))
+
((U * (1 - phi)) /
(K_sed * np.power(mg.at_node["drainage_area"][mg.core_nodes], m_sp))),
1.0 / n_sp,
)
# test for match with analytical slope-area relationship
testing.assert_array_almost_equal(
num_slope,
analytical_slope,
decimal=8,
err_msg="SPACE transport-limited slope-area test failed",
verbose=True,
)
# compare numerical and analytical sediment flux solutions
num_sedflux = mg.at_node["sediment__flux"][mg.core_nodes]
analytical_sedflux = U * mg.at_node["drainage_area"][mg.core_nodes] * (1 -
phi)
# test for match with anakytical sediment flux
testing.assert_array_almost_equal(
num_sedflux,
analytical_sedflux,
decimal=8,
err_msg="SPACE transport-limited sediment flux test failed",
verbose=True,
)
def test_matches_detachment_solution():
"""
Test that model matches the detachment-limited analytical solution
for slope/area relationship at steady state: S=(U/K_br)^(1/n)*A^(-m/n).
"""
# set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), xy_spacing=10.0)
z = mg.add_zeros("node", "topographic__elevation")
br = mg.add_zeros("node", "bedrock__elevation")
soil = mg.add_zeros("node", "soil__depth")
mg["node"]["topographic__elevation"] += (
mg.node_y / 10000 + mg.node_x / 10000 + np.random.rand(len(mg.node_y)) / 10000
)
mg.set_closed_boundaries_at_grid_edges(
bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True,
)
mg.set_watershed_boundary_condition_outlet_id(
0, mg["node"]["topographic__elevation"], -9999.
)
br[:] = z[:] - soil[:]
# Create a D8 flow handler
fa = FlowAccumulator(mg, flow_director="D8")
# Parameter values for detachment-limited test
K_br = 0.01
U = 0.0001
dt = 1.0
F_f = 1.0 # all detached rock disappears; detachment-ltd end-member
m_sp = 0.5
n_sp = 1.0
# Instantiate the Space component...
sp = Space(
mg,
K_sed=0.00001,
K_br=K_br,
F_f=F_f,
phi=0.1,
H_star=1.,
v_s=0.001,
m_sp=m_sp,
n_sp=n_sp,
sp_crit_sed=0,
sp_crit_br=0,
)
# ... and run it to steady state (2000x1-year timesteps).
for i in range(2000):
fa.run_one_step()
sp.run_one_step(dt=dt)
z[mg.core_nodes] += U * dt # m
br[mg.core_nodes] = z[mg.core_nodes] - soil[mg.core_nodes]
# compare numerical and analytical slope solutions
num_slope = mg.at_node["topographic__steepest_slope"][mg.core_nodes]
analytical_slope = np.power(U / K_br, 1. / n_sp) * np.power(
mg.at_node["drainage_area"][mg.core_nodes], -m_sp / n_sp
)
# test for match with analytical slope-area relationship
testing.assert_array_almost_equal(
num_slope,
analytical_slope,
decimal=8,
err_msg="SPACE detachment-limited test failed",
verbose=True,
)
def test_matches_bedrock_alluvial_solution():
"""
Test that model matches the bedrock-alluvial analytical solution
for slope/area relationship at steady state:
S=((U * v_s * (1 - F_f)) / (K_sed * A^m) + U / (K_br * A^m))^(1/n).
Also test that the soil depth everywhere matches the bedrock-alluvial
analytical solution at steady state:
H = -H_star * ln(1 - (v_s / (K_sed / (K_br * (1 - F_f)) + v_s))).
"""
#set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), 10.0)
z = mg.add_zeros('node', 'topographic__elevation')
br = mg.add_zeros('node', 'bedrock__elevation')
soil = mg.add_zeros('node', 'soil__depth')
mg['node']['topographic__elevation'] += (
mg.node_y / 100000 + mg.node_x / 100000 +
np.random.rand(len(mg.node_y)) / 10000)
mg.set_closed_boundaries_at_grid_edges(bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True)
mg.set_watershed_boundary_condition_outlet_id(
0, mg['node']['topographic__elevation'], -9999.)
soil[:] += 0. #initial condition of no soil depth.
br[:] = z[:]
z[:] += soil[:]
#Instantiate DepressionFinderAndRouter
df = DepressionFinderAndRouter(mg)
# Create a D8 flow handler
fa = FlowAccumulator(mg,
flow_director='D8',
depression_finder='DepressionFinderAndRouter')
# Parameter values for detachment-limited test
K_br = 0.02
K_sed = 0.02
U = 0.0001
dt = 1.0
F_f = 0.2 #all detached rock disappears; detachment-ltd end-member
m_sp = 0.5
n_sp = 1.0
v_s = 0.25
H_star = 0.1
# Instantiate the Space component...
sp = Space(mg,
K_sed=K_sed,
K_br=K_br,
F_f=F_f,
phi=0.0,
H_star=H_star,
v_s=v_s,
m_sp=m_sp,
n_sp=n_sp,
sp_crit_sed=0,
sp_crit_br=0)
# ... and run it to steady state (10000x1-year timesteps).
for i in range(10000):
fa.run_one_step()
flooded = np.where(df.flood_status == 3)[0]
sp.run_one_step(dt=dt, flooded_nodes=flooded)
br[mg.core_nodes] += U * dt #m
soil[0] = 0. #enforce 0 soil depth at boundary to keep lowering steady
z[:] = br[:] + soil[:]
#compare numerical and analytical slope solutions
num_slope = mg.at_node['topographic__steepest_slope'][mg.core_nodes]
analytical_slope = (np.power(
((U * v_s * (1 - F_f)) /
(K_sed * np.power(mg.at_node['drainage_area'][mg.core_nodes], m_sp)))
+
(U /
(K_br * np.power(mg.at_node['drainage_area'][mg.core_nodes], m_sp))),
1. / n_sp))
#test for match with analytical slope-area relationship
testing.assert_array_almost_equal(
num_slope,
analytical_slope,
decimal=8,
err_msg='SPACE bedrock-alluvial slope-area test failed',
verbose=True)
#compare numerical and analytical soil depth solutions
num_h = mg.at_node['soil__depth'][mg.core_nodes]
analytical_h = -H_star * np.log(1 - (v_s / (K_sed / (K_br *
(1 - F_f)) + v_s)))
#test for match with analytical sediment depth
testing.assert_array_almost_equal(
num_h,
analytical_h,
decimal=5,
err_msg='SPACE bedrock-alluvial soil thickness test failed',
verbose=True)
def test_matches_detachment_solution():
"""
Test that model matches the detachment-limited analytical solution
for slope/area relationship at steady state: S=(U/K_br)^(1/n)*A^(-m/n).
"""
#set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), 10.0)
z = mg.add_zeros('node', 'topographic__elevation')
br = mg.add_zeros('node', 'bedrock__elevation')
soil = mg.add_zeros('node', 'soil__depth')
mg['node']['topographic__elevation'] += mg.node_y / 10000 \
+ mg.node_x / 10000 \
+ np.random.rand(len(mg.node_y)) / 10000
mg.set_closed_boundaries_at_grid_edges(bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True)
mg.set_watershed_boundary_condition_outlet_id(
0, mg['node']['topographic__elevation'], -9999.)
br[:] = z[:] - soil[:]
# Create a D8 flow handler
fa = FlowAccumulator(mg, flow_director='D8')
# Parameter values for detachment-limited test
K_br = 0.01
U = 0.0001
dt = 1.0
F_f = 1.0 #all detached rock disappears; detachment-ltd end-member
m_sp = 0.5
n_sp = 1.0
# Instantiate the Space component...
sp = Space(mg,
K_sed=0.00001,
K_br=K_br,
F_f=F_f,
phi=0.1,
H_star=1.,
v_s=0.001,
m_sp=m_sp,
n_sp=n_sp,
sp_crit_sed=0,
sp_crit_br=0)
# ... and run it to steady state (2000x1-year timesteps).
for i in range(2000):
fa.run_one_step()
sp.run_one_step(dt=dt)
z[mg.core_nodes] += U * dt #m
br[mg.core_nodes] = z[mg.core_nodes] - soil[mg.core_nodes]
#compare numerical and analytical slope solutions
num_slope = mg.at_node['topographic__steepest_slope'][mg.core_nodes]
analytical_slope = np.power(U / K_br, 1./n_sp) \
* np.power(mg.at_node['drainage_area'][mg.core_nodes], -m_sp / n_sp)
#test for match with analytical slope-area relationship
testing.assert_array_almost_equal(
num_slope,
analytical_slope,
decimal=8,
err_msg='SPACE detachment-limited test failed',
verbose=True)
lm = DepressionFinderAndRouter(mg)
expWeath = ExponentialWeatherer(
mg,
soil_production__maximum_rate=soilProductionRate,
soil_production__decay_depth=soilProductionDecayDepth)
sf = SteepnessFinder(mg, min_drainage_area=1e6)
sp = Space(mg,
K_sed=Kvs,
K_br=Kvb,
F_f=Ff,
phi=phi,
H_star=Hstar,
v_s=vs,
m_sp=m,
n_sp=n,
sp_crit_sed=sp_crit_sedi,
sp_crit_br=sp_crit_bedrock,
solver=solver)
lc = landformClassifier(mg)
DDdiff = DepthDependentDiffuser(mg,
linear_diffusivity=linDiff,
soil_transport_decay_depth=2)
lpj = DynVeg_LpjGuess(LPJGUESS_INPUT_PATH, LPJGUESS_TEMPLATE_PATH,
LPJGUESS_FORCINGS_PATH, LPJGUESS_INS_FILE_TPL,
LPJGUESS_BIN, LPJGUESS_CO2FILE, LPJGUESS_FORCINGS_STRING)
def test_matches_transport_solution():
"""
Test that model matches the transport-limited analytical solution
for slope/area relationship at steady state: S=((U * v_s) / (K_sed * A^m)
+ U / (K_sed * A^m))^(1/n).
Also test that model matches the analytical solution for steady-state
sediment flux: Qs = U * A * (1 - phi).
"""
#set up a 5x5 grid with one open outlet node and low initial elevations.
nr = 5
nc = 5
mg = RasterModelGrid((nr, nc), 10.0)
z = mg.add_zeros('node', 'topographic__elevation')
br = mg.add_zeros('node', 'bedrock__elevation')
soil = mg.add_zeros('node', 'soil__depth')
mg['node']['topographic__elevation'] += mg.node_y / 100000 \
+ mg.node_x / 100000 \
+ np.random.rand(len(mg.node_y)) / 10000
mg.set_closed_boundaries_at_grid_edges(bottom_is_closed=True,
left_is_closed=True,
right_is_closed=True,
top_is_closed=True)
mg.set_watershed_boundary_condition_outlet_id(0,
mg['node']['topographic__elevation'],
-9999.)
soil[:] += 100. #initial soil depth of 100 m
br[:] = z[:]
z[:] += soil[:]
#Instantiate DepressionFinderAndRouter
df = DepressionFinderAndRouter(mg)
# Create a D8 flow handler
fa = FlowAccumulator(mg, flow_director='D8',
depression_finder='DepressionFinderAndRouter')
# Parameter values for detachment-limited test
K_sed = 0.01
U = 0.0001
dt = 1.0
F_f = 1.0 #all detached rock disappears; detachment-ltd end-member
m_sp = 0.5
n_sp = 1.0
v_s = 0.5
phi=0.5
# Instantiate the Space component...
sp = Space(mg, K_sed=K_sed, K_br=0.01,
F_f=F_f, phi=phi, H_star=1., v_s=v_s,
m_sp=m_sp, n_sp=n_sp, sp_crit_sed=0,
sp_crit_br=0)
# ... and run it to steady state (5000x1-year timesteps).
for i in range(5000):
fa.run_one_step()
flooded = np.where(df.flood_status==3)[0]
sp.run_one_step(dt=dt, flooded_nodes=flooded)
br[mg.core_nodes] += U * dt #m
soil[0] = 100. #enforce constant soil depth at boundary to keep lowering steady
z[:] = br[:] + soil[:]
#compare numerical and analytical slope solutions
num_slope = mg.at_node['topographic__steepest_slope'][mg.core_nodes]
analytical_slope = (np.power(((U * v_s) / (K_sed
* np.power(mg.at_node['drainage_area'][mg.core_nodes], m_sp)))
+ (U / (K_sed * np.power(mg.at_node['drainage_area'][mg.core_nodes],
m_sp))), 1./n_sp))
#test for match with analytical slope-area relationship
testing.assert_array_almost_equal(num_slope, analytical_slope,
decimal=8,
err_msg='SPACE transport-limited slope-area test failed',
verbose=True)
#compare numerical and analytical sediment flux solutions
num_sedflux = mg.at_node['sediment__flux'][mg.core_nodes]
analytical_sedflux = (U * mg.at_node['drainage_area'][mg.core_nodes]
* (1 - phi))
#test for match with anakytical sediment flux
testing.assert_array_almost_equal(num_sedflux, analytical_sedflux,
decimal=8,
err_msg='SPACE transport-limited sediment flux test failed',
verbose=True)
class HybridAlluviumModel(_ErosionModel):
"""
A HybridAlluviumModel computes erosion of sediment and bedrock
using dual mass conservation on the bed and in the water column. It
applies exponential entrainment rules to account for bed cover.
"""
def __init__(self, input_file=None, params=None):
"""Initialize the HybridAlluviumModel."""
# Call ErosionModel's init
super(HybridAlluviumModel, self).__init__(input_file=input_file,
params=params)
# Instantiate a FlowRouter and DepressionFinderAndRouter components
self.flow_router = FlowRouter(self.grid, **self.params)
self.lake_filler = DepressionFinderAndRouter(self.grid, **self.params)
#make area_field and/or discharge_field depending on discharge_method
if self.params['discharge_method'] is not None:
if self.params['discharge_method'] == 'area_field':
area_field = self.grid.at_node['drainage_area']
discharge_field = None
elif self.params['discharge_method'] == 'discharge_field':
discharge_field = self.grid.at_node['surface_water__discharge']
area_field = None
else:
raise (KeyError)
else:
area_field = None
discharge_field = None
# Instantiate a HybridAlluvium component
self.eroder = Space(self.grid,
K_sed=self.params['K_sed'],
K_br=self.params['K_br'],
F_f=self.params['F_f'],
phi=self.params['phi'],
H_star=self.params['H_star'],
v_s=self.params['v_s'],
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
sp_crit_sed=self.params['sp_crit_sed'],
sp_crit_br=self.params['sp_crit_br'],
method=self.params['method'],
discharge_method=self.params['discharge_method'],
area_field=area_field,
discharge_field=discharge_field)
def run_one_step(self, dt):
"""
Advance model for one time-step of duration dt.
"""
# Route flow
self.flow_router.run_one_step()
self.lake_filler.map_depressions()
# Get IDs of flooded nodes, if any
flooded = np.where(self.lake_filler.flood_status == 3)[0]
# Do some erosion (but not on the flooded nodes)
self.eroder.run_one_step(dt, flooded_nodes=flooded)
