def test_no_thresh():
K = 0.001
U = 0.01
m = 0.5
n = 1.0
threshold = 0.0
dt = 1000
mg = RasterModelGrid(30, 3, xy_spacing=100.0)
mg.set_closed_boundaries_at_grid_edges(True, False, True, False)
z = mg.zeros(at="node")
mg["node"]["topographic__elevation"] = z + np.random.rand(len(z)) / 1000.0
fa = FlowAccumulator(mg)
sp = Spst(mg, K_sp=K, threshold_sp=threshold)
for i in range(100):
fa.run_one_step()
sp.run_one_step(dt)
mg["node"]["topographic__elevation"][mg.core_nodes] += U * dt
actual_slopes = mg.at_node["topographic__steepest_slope"][
mg.core_nodes[1:-1]]
actual_areas = mg.at_node["drainage_area"][mg.core_nodes[1:-1]]
predicted_slopes = (U / (K * (actual_areas**m)))**(1.0 / n)
assert_array_almost_equal(actual_slopes, predicted_slopes)
def test_with_thresh():
K = 0.001
U = 0.01
m = 0.5
n = 1.0
threshold = 1.0
dt = 1000
mg = RasterModelGrid(30, 3, xy_spacing=100.0)
mg.set_closed_boundaries_at_grid_edges(True, False, True, False)
z = mg.zeros(at="node")
mg["node"]["topographic__elevation"] = z + np.random.rand(len(z)) / 1000.0
fa = FlowAccumulator(mg)
sp = Spst(mg, K_sp=K, threshold_sp=threshold)
for i in range(100):
fa.run_one_step()
sp.run_one_step(dt)
mg["node"]["topographic__elevation"][mg.core_nodes] += U * dt
actual_slopes = mg.at_node["topographic__steepest_slope"][
mg.core_nodes[1:-1]]
actual_areas = mg.at_node["drainage_area"][mg.core_nodes[1:-1]]
predicted_slopes_upper = ((U + threshold) / (K *
(actual_areas**m)))**(1.0 / n)
predicted_slopes_lower = ((U + 0.0) / (K * (actual_areas**m)))**(1.0 / n)
# assert actual and predicted slopes are in the correct range for the slopes.
assert np.all(actual_slopes > predicted_slopes_lower)
assert np.all(actual_slopes < predicted_slopes_upper)
def test_with_thresh():
K = 0.001
U = 0.01
m = 0.5
n = 1.0
threshold = 1.0
dt = 1000
mg = RasterModelGrid(30, 3, xy_spacing=100.)
mg.set_closed_boundaries_at_grid_edges(True, False, True, False)
z = mg.zeros(at="node")
mg["node"]["topographic__elevation"] = z + np.random.rand(len(z)) / 1000.
fa = FlowAccumulator(mg)
sp = Spst(mg, K_sp=K, threshold_sp=threshold)
for i in range(100):
fa.run_one_step()
sp.run_one_step(dt)
mg["node"]["topographic__elevation"][mg.core_nodes] += U * dt
actual_slopes = mg.at_node["topographic__steepest_slope"][mg.core_nodes[1:-1]]
actual_areas = mg.at_node["drainage_area"][mg.core_nodes[1:-1]]
predicted_slopes_upper = ((U + threshold) / (K * (actual_areas ** m))) ** (1. / n)
predicted_slopes_lower = ((U + 0.0) / (K * (actual_areas ** m))) ** (1. / n)
# assert actual and predicted slopes are in the correct range for the slopes.
assert np.all(actual_slopes > predicted_slopes_lower)
assert np.all(actual_slopes < predicted_slopes_upper)
def test_no_thresh():
K = 0.001
U = 0.01
m = 0.5
n = 1.0
threshold = 0.0
dt = 1000
mg = RasterModelGrid(30, 3, xy_spacing=100.)
mg.set_closed_boundaries_at_grid_edges(True, False, True, False)
z = mg.zeros(at="node")
mg["node"]["topographic__elevation"] = z + np.random.rand(len(z)) / 1000.
fa = FlowAccumulator(mg)
sp = Spst(mg, K_sp=K, threshold_sp=threshold)
for i in range(100):
fa.run_one_step()
sp.run_one_step(dt)
mg["node"]["topographic__elevation"][mg.core_nodes] += U * dt
actual_slopes = mg.at_node["topographic__steepest_slope"][mg.core_nodes[1:-1]]
actual_areas = mg.at_node["drainage_area"][mg.core_nodes[1:-1]]
predicted_slopes = (U / (K * (actual_areas ** m))) ** (1. / n)
assert_array_almost_equal(actual_slopes, predicted_slopes)
def test_route_to_multiple_error_raised_run_StreamPowerSmoothThresholdEroder():
mg = RasterModelGrid((10, 10))
z = mg.add_zeros("node", "topographic__elevation")
z += mg.x_of_node + mg.y_of_node
sp = StreamPowerSmoothThresholdEroder(mg, K_sp=0.1, use_Q=mg.ones(at="node"))
fa = FlowAccumulator(mg, flow_director="MFD")
fa.run_one_step()
with pytest.raises(NotImplementedError):
sp.run_one_step(10)
def test_route_to_multiple_error_raised_run_StreamPowerSmoothThresholdEroder():
mg = RasterModelGrid((10, 10))
z = mg.add_zeros('node', 'topographic__elevation')
z += mg.x_of_node + mg.y_of_node
sp = StreamPowerSmoothThresholdEroder(mg, K_sp=0.1, use_Q=mg.ones(at='node'))
fa = FlowAccumulator(mg, flow_director='MFD')
fa.run_one_step()
with pytest.raises(NotImplementedError):
sp.run_one_step(10)
class StreamPowerThresholdModel(_ErosionModel):
"""
A StreamPowerThresholdModel computes erosion using a form of the unit
stream power model that represents a threshold using an exponential term.
"""
def __init__(self, input_file=None, params=None):
"""Initialize the StreamPowerThresholdModel."""
# Call ErosionModel's init
super(StreamPowerThresholdModel, 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)
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.params['K_sp'],
threshold_sp=self.params['threshold_sp'])
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)
class BasicDd(ErosionModel):
r"""**BasicDd** model program.
This model program evolves a topographic surface, :math:`\eta`, with the
following governing equation:
.. math::
\frac{\partial \eta}{\partial t} = -\left(KQ^{m}S^{n}
- \omega_{ct}\left(1-e^{-KQ^{m}S^{n}/\omega_{ct}}\right)\right)
+ D\nabla^2 \eta
where :math:`Q` is the local stream discharge and :math:`S` is the local
slope, :math:`m` and :math:`n` are the discharge and slope exponent
parameters, :math:`K` is the erodibility by water, :math:`D` is the
regolith transport efficiency, and :math:`\omega_{ct}` is the critical
stream power needed for erosion to occur. :math:`\omega_{ct}` changes
through time as it increases with cumulative incision depth:
.. math::
\omega_{ct}\left(x,y,t\right) = \mathrm{max}\left(\omega_c +
b D_I\left(x, y, t\right), \omega_c \right)
where :math:`\omega_c` is the threshold when no incision has taken place,
:math:`b` is the rate at which the threshold increases with incision depth,
and :math:`D_I` is the cumulative incision depth at location
:math:`\left(x,y\right)` and time :math:`t`.
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``
"""
_required_fields = ["topographic__elevation"]
def __init__(self,
clock,
grid,
m_sp=0.5,
n_sp=1.0,
water_erodibility=0.0001,
regolith_transport_parameter=0.1,
water_erosion_rule__threshold=0.01,
water_erosion_rule__thresh_depth_derivative=0.0,
**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.
water_erosion_rule__threshold : float, optional
Erosion rule threshold when no erosion has occured
(:math:`\omega_c`). Default is 0.01.
water_erosion_rule__thresh_depth_derivative : float, optional
Rate of increase of water erosion threshold as increased incision
occurs (:math:`b`). Default is 0.0.
**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
-------
BasicDd : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicDd**. 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, BasicDd
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
Construct the model.
>>> model = BasicDd(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)
# Get Parameters and convert units if necessary:
self.m = m_sp
self.n = n_sp
self.K = water_erodibility
if float(self.n) != 1.0:
raise ValueError("Model only supports n equals 1.")
# threshold has units of Length per Time which is what
# StreamPowerSmoothThresholdEroder expects
self.threshold_value = water_erosion_rule__threshold
# Create a field for the (initial) erosion threshold
self.threshold = self.grid.add_zeros("node",
"water_erosion_rule__threshold")
self.threshold[:] = self.threshold_value
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
m_sp=self.m,
n_sp=self.n,
K_sp=self.K,
threshold_sp=self.threshold,
discharge_field="surface_water__discharge",
erode_flooded_nodes=self._erode_flooded_nodes,
)
# Get the parameter for rate of threshold increase with erosion depth
self.thresh_change_per_depth = (
water_erosion_rule__thresh_depth_derivative)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(
self.grid, linear_diffusivity=regolith_transport_parameter)
def update_erosion_threshold_values(self):
r"""Update the erosion threshold at each node based on cumulative
incision so far using:
.. math::
\omega_{ct}\left(x,y,t\right) = \mathrm{max}\left(\omega_c + \\
b D_I\left(x, y, t\right), \omega_c \right)
where :math:`\omega_c` is the threshold when no incision has taken
place, :math:`b` is the rate at which the threshold increases with
incision depth, and :math:`D_I` is the cumulative incision depth at
location :math:`\left(x,y\right)` and time :math:`t`.
"""
# Set the erosion threshold.
#
# Note that a minus sign is used because cum ero depth is negative for
# erosion, positive for deposition.
# The second line handles the case where there is growth, in which case
# we want the threshold to stay at its initial value rather than
# getting smaller.
cum_ero = self.grid.at_node["cumulative_elevation_change"]
cum_ero[:] = (self.z -
self.grid.at_node["initial_topographic__elevation"])
self.threshold[:] = self.threshold_value - (
self.thresh_change_per_depth * cum_ero)
self.threshold[
self.threshold < self.threshold_value] = self.threshold_value
def run_one_step(self, step):
"""Advance model **BasicDd** 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 detachment-limited, threshold-modified erosion 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)
# Calculate the new threshold values given cumulative erosion
self.update_erosion_threshold_values()
# 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:
self.eroder.K = (self.K * self.boundary_handlers["PrecipChanger"].
get_erodibility_adjustment_factor())
self.eroder.run_one_step(step)
# Do some soil creep
self.diffuser.run_one_step(step)
# Finalize the run_one_step_method
self.finalize__run_one_step(step)
class BasicRtTh(TwoLithologyErosionModel):
r"""**BasicRtTh** model program.
This model program combines the :py:class:`BasicRt` and :py:class:`BasicTh`
programs by allowing for two lithologies, an "upper" layer and a "lower"
layer, and permitting the use of an smooth erosion threshold for each
lithology. Given a spatially varying contact zone elevation,
:math:`\eta_C(x,y))`, model **BasicRtTh** evolves a topographic surface
described by :math:`\eta` with the following governing equations:
.. math::
\frac{\partial \eta}{\partial t} = -\left[\omega
- \omega_c (1 - e^{-\omega /\omega_c}) \right]
+ D\nabla^2 \eta
\omega = K(\eta, \eta_C) Q^{m} S^{n}
K(\eta, \eta_C ) = w K_1 + (1 - w) K_2,
\omega_c(\eta, \eta_C ) = w \omega_{c1} + (1 - w) \omega_{c2}
w = \frac{1}{1+\exp \left( -\frac{(\eta -\eta_C )}{W_c}\right)}
where :math:`Q` is the local stream discharge, :math:`S` is the local
slope, :math:`m` and :math:`n` are the discharge and slope exponent
parameters, :math:`W_c` is the contact-zone width, :math:`K_1` and
:math:`K_2` are the erodabilities of the upper and lower lithologies,
:math:`\omega_{c1}` and :math:`\omega_{c2}` are the erosion thresholds of
the upper and lower lithologies, and :math:`D` is the regolith transport
\parameter. :math:`w` is a weight used to calculate the effective
erodibility :math:`K(\eta, \eta_C)` based on the depth to the contact zone
and the width of the contact zone. :math:`\omega` is the erosion rate that
would be calculated without the use of a threshold and as the threshold
increases the erosion rate smoothly transitions between zero and
:math:`\omega`.
The weight :math:`w` promotes smoothness in the solution of erodibility at
a given point. When the surface elevation is at the contact elevation, the
erodibility is the average of :math:`K_1` and :math:`K_2`; above and below
the contact, the erodibility approaches the value of :math:`K_1` and
:math:`K_2` at a rate related to the contact zone width. Thus, to make a
very sharp transition, use a small value for the contact zone width.
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``
- ``lithology_contact__elevation``
"""
_required_fields = [
"topographic__elevation",
"lithology_contact__elevation",
]
def __init__(
self,
clock,
grid,
water_erosion_rule_upper__threshold=1.0,
water_erosion_rule_lower__threshold=1.0,
**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_upper : float, optional
Water erodibility of the upper layer (:math:`K_{1}`). Default is
0.001.
water_erodibility_lower : float, optional
Water erodibility of the upper layer (:math:`K_{2}`). Default is
0.0001.
water_erosion_rule_upper__threshold : float, optional.
Erosion threshold of the upper layer (:math:`\omega_{c1}`). Default
is 1.
water_erosion_rule_lower__threshold: float, optional.
Erosion threshold of the upper layer (:math:`\omega_{c2}`). Default
is 1.
contact_zone__width : float, optional
Thickness of the contact zone (:math:`W_c`). Default is 1.
regolith_transport_parameter : float, optional
Regolith transport efficiency (:math:`D`). Default is 0.1.
**kwargs :
Keyword arguments to pass to :py:class:`TwoLithologyErosionModel`.
Importantly these arguments specify the precipitator and the runoff
generator that control the generation of surface water discharge
(:math:`Q`).
Returns
-------
BasicRtTh : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicRtTh**. 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, constant
>>> from terrainbento import Clock, BasicRtTh
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = constant(grid, "lithology_contact__elevation", value=-10.)
Construct the model.
>>> model = BasicRtTh(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(BasicRtTh, self).__init__(clock, grid, **kwargs)
if float(self.n) != 1.0:
raise ValueError("Model only supports n equals 1.")
# verify correct fields are present.
self._verify_fields(self._required_fields)
# Save the threshold values for rock and till
self.rock_thresh = water_erosion_rule_lower__threshold
self.till_thresh = water_erosion_rule_upper__threshold
# Set up rock-till boundary and associated grid fields.
self._setup_rock_and_till_with_threshold()
# Instantiate a StreamPowerSmoothThresholdEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.erody,
threshold_sp=self.threshold,
m_sp=self.m,
n_sp=self.n,
use_Q="surface_water__discharge",
)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(
self.grid, linear_diffusivity=self.regolith_transport_parameter
)
def run_one_step(self, step):
"""Advance model **BasicRtTh** 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. Updates the spatially variable erodibility and threshold values
based on the relative distance between the topographic surface and
the lithology contact.
5. Calculates detachment-limited erosion by water.
6. Calculates topographic change by linear diffusion.
7. 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)
# Get IDs of flooded nodes, if any
if self.flow_accumulator.depression_finder is None:
flooded = []
else:
flooded = np.where(
self.flow_accumulator.depression_finder.flood_status == 3
)[0]
# Update the erodibility and threshold field
self._update_erodibility_and_threshold_fields()
# Do some erosion (but not on the flooded nodes)
self.eroder.run_one_step(step, flooded_nodes=flooded)
# Do some soil creep
self.diffuser.run_one_step(step)
# Finalize the run_one_step_method
self.finalize__run_one_step(step)
class BasicDdSt(_StochasticErosionModel):
"""
A BasicDdSt computes erosion using (1) unit
stream power with a threshold, (2) linear nhillslope diffusion, and
(3) generation of a random sequence of runoff events across a topographic
surface.
Examples
--------
>>> from erosion_model import StochasticRainDepthDepThresholdModel
>>> my_pars = {}
>>> my_pars['dt'] = 1.0
>>> my_pars['run_duration'] = 1.0
>>> my_pars['infiltration_capacity'] = 1.0
>>> my_pars['K_sp'] = 1.0
>>> my_pars['threshold_sp'] = 1.0
>>> my_pars['linear_diffusivity'] = 0.01
>>> my_pars['mean_storm_duration'] = 0.002
>>> my_pars['mean_interstorm_duration'] = 0.008
>>> my_pars['mean_storm_depth'] = 0.025
>>> srt = StochasticRainDepthDepThresholdModel(params=my_pars)
Warning: no DEM specified; creating 4x5 raster grid
"""
def __init__(self,
input_file=None,
params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicDdSt."""
# Call ErosionModel's init
super(BasicDdSt,
self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
# Get Parameters:
K_sp = self.get_parameter_from_exponent('K_stochastic_sp')
linear_diffusivity = (
self._length_factor**2.) * self.get_parameter_from_exponent(
'linear_diffusivity') # has units length^2/time
# threshold has units of Length per Time which is what
# StreamPowerSmoothThresholdEroder expects
self.threshold_value = self._length_factor * self.get_parameter_from_exponent(
'erosion__threshold') # has units length/time
# Get the parameter for rate of threshold increase with erosion depth
self.thresh_change_per_depth = self.params['thresh_change_per_depth']
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(
self.grid,
flow_director='D8',
depression_finder=DepressionFinderAndRouter)
# instantiate rain generator
self.instantiate_rain_generator()
# Add a field for discharge
if 'surface_water__discharge' not in self.grid.at_node:
self.grid.add_zeros('node', 'surface_water__discharge')
self.discharge = self.grid.at_node['surface_water__discharge']
# Get the infiltration-capacity parameter
infiltration_capacity = (self._length_factor) * self.params[
'infiltration_capacity'] # has units length per time
self.infilt = infiltration_capacity
# Keep a reference to drainage area
self.area = self.grid.at_node['drainage_area']
# Run flow routing and lake filler
self.flow_router.run_one_step()
# Create a field for the (initial) erosion threshold
self.threshold = self.grid.add_zeros('node', 'erosion__threshold')
self.threshold[:] = self.threshold_value
# Get the parameter for rate of threshold increase with erosion depth
self.thresh_change_per_depth = self.params['thresh_change_per_depth']
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
K_sp=K_sp,
use_Q=self.discharge,
threshold_sp=self.threshold)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(self.grid,
linear_diffusivity=linear_diffusivity)
def calc_runoff_and_discharge(self):
"""Calculate runoff rate and discharge; return runoff."""
if self.rain_rate > 0.0 and self.infilt > 0.0:
runoff = self.rain_rate - (
self.infilt * (1.0 - np.exp(-self.rain_rate / self.infilt)))
if runoff < 0:
runoff = 0
else:
runoff = self.rain_rate
self.discharge[:] = runoff * self.area
return runoff
def update_threshold_field(self):
"""Update the threshold based on cumulative erosion depth."""
cum_ero = self.grid.at_node['cumulative_erosion__depth']
cum_ero[:] = (self.z -
self.grid.at_node['initial_topographic__elevation'])
self.threshold[:] = (self.threshold_value -
(self.thresh_change_per_depth * cum_ero))
self.threshold[self.threshold < self.threshold_value] = \
self.threshold_value
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]
# Handle water erosion
self.handle_water_erosion_with_threshold(dt, flooded)
# Do some soil creep
self.diffuser.run_one_step(dt)
# calculate model time
self.model_time += dt
# Lower outlet
self.update_outlet(dt)
# Check walltime
self.check_walltime()
def handle_water_erosion_with_threshold(self, dt, flooded):
"""Handle water erosion.
This function takes the place of the _BaseSt function of the name
handle_water_erosion_with_threshold in order to handle water erosion
correctly for model BasicDdSt.
"""
# (if we're varying precipitation parameters through time, update them)
if self.opt_var_precip:
self.intermittency_factor, self.mean_storm__intensity = self.pc.get_current_precip_params(
self.model_time)
# If we're handling duration deterministically, as a set fraction of
# time step duration, calculate a rainfall intensity. Otherwise,
# assume it's already been calculated.
if not self.opt_stochastic_duration:
self.rain_rate = np.random.exponential(self.mean_storm__intensity)
dt_water = dt * self.intermittency_factor
else:
dt_water = dt
# Calculate discharge field
area = self.grid.at_node['drainage_area']
if self.rain_rate > 0.0 and self.infilt > 0.0:
runoff = self.rain_rate - (
self.infilt * (1.0 - np.exp(-self.rain_rate / self.infilt)))
else:
runoff = self.rain_rate
self.discharge[:] = runoff * area
# Handle water erosion:
#
# If we are running stochastic duration, then self.rain_rate will
# have been calculated already. It might be zero, in which case we
# are between storms, so we don't do water erosion.
#
# If we're NOT doing stochastic duration, then we'll run water
# erosion for one or more sub-time steps, each with its own
# randomly drawn precipitation intensity.
#
if self.opt_stochastic_duration and self.rain_rate > 0.0:
self.update_threshold_field()
runoff = self.calc_runoff_and_discharge()
self.eroder.run_one_step(dt, flooded_nodes=flooded)
elif not self.opt_stochastic_duration:
dt_water = ((dt * self.intermittency_factor) /
float(self.n_sub_steps))
for i in range(self.n_sub_steps):
self.rain_rate = \
self.rain_generator.generate_from_stretched_exponential(
self.scale_factor, self.shape_factor)
self.update_threshold_field()
runoff = self.calc_runoff_and_discharge()
self.eroder.run_one_step(dt_water, flooded_nodes=flooded)
class BasicChRtTh(_ErosionModel):
"""
A BasicChRt model computes erosion using cubic diffusion, basic stream
power with two rock units, and Q~A.
"""
def __init__(self,
input_file=None,
params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicChRt model."""
# Call ErosionModel's init
super(BasicChRtTh,
self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
contact_zone__width = (self._length_factor) * self.params[
'contact_zone__width'] # has units length
self.K_rock_sp = self.get_parameter_from_exponent('K_rock_sp')
self.K_till_sp = self.get_parameter_from_exponent('K_till_sp')
rock_erosion__threshold = self.get_parameter_from_exponent(
'rock_erosion__threshold')
till_erosion__threshold = self.get_parameter_from_exponent(
'till_erosion__threshold')
linear_diffusivity = (
self._length_factor**
2.) * self.get_parameter_from_exponent('linear_diffusivity')
# Set up rock-till
self.setup_rock_and_till(self.params['rock_till_file__name'],
self.K_rock_sp, self.K_till_sp,
rock_erosion__threshold,
till_erosion__threshold, contact_zone__width)
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(
self.grid,
flow_director='D8',
depression_finder=DepressionFinderAndRouter)
# Instantiate a StreamPowerSmoothThresholdEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.erody,
threshold_sp=self.threshold,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'])
# Instantiate a LinearDiffuser component
self.diffuser = TaylorNonLinearDiffuser(
self.grid,
linear_diffusivity=linear_diffusivity,
slope_crit=self.params['slope_crit'],
nterms=7)
def setup_rock_and_till(self, file_name, rock_erody, till_erody,
rock_thresh, till_thresh, contact_width):
"""Set up lithology handling for two layers with different erodibility.
Parameters
----------
file_name : string
Name of arc-ascii format file containing elevation of contact
position at each grid node (or NODATA)
rock_erody : float
Water erosion coefficient for bedrock
till_erody : float
Water erosion coefficient for till
rock_thresh : float
Water erosion threshold for bedrock
till_thresh : float
Water erosion threshold for till
contact_width : float [L]
Characteristic width of the interface zone between rock and till
Read elevation of rock-till contact from an esri-ascii format file
containing the basal elevation value at each node, create a field for
erodibility.
"""
from landlab.io import read_esri_ascii
# Read input data on rock-till contact elevation
read_esri_ascii(file_name,
grid=self.grid,
name='rock_till_contact__elevation',
halo=1)
# Get a reference to the rock-till field
self.rock_till_contact = self.grid.at_node[
'rock_till_contact__elevation']
# Create field for erodibility
if 'substrate__erodibility' in self.grid.at_node:
self.erody = self.grid.at_node['substrate__erodibility']
else:
self.erody = self.grid.add_zeros('node', 'substrate__erodibility')
# Create field for threshold values
if 'erosion__threshold' in self.grid.at_node:
self.threshold = self.grid.at_node['erosion__threshold']
else:
self.threshold = self.grid.add_zeros('node', 'erosion__threshold')
# Create array for erodibility weighting function
self.erody_wt = np.zeros(self.grid.number_of_nodes)
# Read the erodibility value of rock and till
self.rock_erody = rock_erody
self.till_erody = till_erody
# Read the threshold values for rock and till
self.rock_thresh = rock_thresh
self.till_thresh = till_thresh
# Read and remember the contact zone characteristic width
self.contact_width = contact_width
def update_erodibility_and_threshold_fields(self):
"""Update erodibility and threshold at each node based on elevation
relative to contact elevation.
To promote smoothness in the solution, the erodibility at a given point
(x,y) is set as follows:
1. Take the difference between elevation, z(x,y), and contact
elevation, b(x,y): D(x,y) = z(x,y) - b(x,y). This number could
be positive (if land surface is above the contact), negative
(if we're well within the rock), or zero (meaning the rock-till
contact is right at the surface).
2. Define a smoothing function as:
$F(D) = 1 / (1 + exp(-D/D*))$
This sigmoidal function has the property that F(0) = 0.5,
F(D >> D*) = 1, and F(-D << -D*) = 0.
Here, D* describes the characteristic width of the "contact
zone", where the effective erodibility is a mixture of the two.
If the surface is well above this contact zone, then F = 1. If
it's well below the contact zone, then F = 0.
3. Set the erodibility using F:
$K = F K_till + (1-F) K_rock$
So, as F => 1, K => K_till, and as F => 0, K => K_rock. In
between, we have a weighted average.
4. Threshold values are set similarly.
Translating these symbols into variable names:
z = self.elev
b = self.rock_till_contact
D* = self.contact_width
F = self.erody_wt
K_till = self.till_erody
K_rock = self.rock_erody
"""
# Update the erodibility weighting function (this is "F")
D_over_D_star = ((self.z[self.data_nodes] -
self.rock_till_contact[self.data_nodes]) /
self.contact_width)
# truncate D_over_D star to remove potential for overflow in exponent
D_over_D_star[D_over_D_star < -100.0] = -100.0
D_over_D_star[D_over_D_star > 100.0] = 100.0
self.erody_wt[self.data_nodes] = (1.0 / (1.0 + np.exp(-D_over_D_star)))
# (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.till_erody = self.K_till_sp * erode_factor
self.rock_erody = self.K_rock_sp * erode_factor
# Calculate the effective erodibilities using weighted averaging
self.erody[:] = (self.erody_wt * self.till_erody +
(1.0 - self.erody_wt) * self.rock_erody)
# Calculate the effective thresholds using weighted averaging
self.threshold[:] = (self.erody_wt * self.till_thresh +
(1.0 - self.erody_wt) * self.rock_thresh)
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]
# Update the erodibility and threshold field
self.update_erodibility_and_threshold_fields()
# Do some erosion (but not on the flooded nodes)
self.eroder.run_one_step(dt, flooded_nodes=flooded)
# Do some soil creep
self.diffuser.run_one_step(dt,
dynamic_dt=True,
if_unstable='raise',
courant_factor=0.1)
# calculate model time
self.model_time += dt
# Lower outlet
self.update_outlet(dt)
# Check walltime
self.check_walltime()
class BasicTh(ErosionModel):
"""
A BasicTh computes erosion using linear diffusion, stream
power with a smoothed threshold, and Q~A.
"""
def __init__(self,
input_file=None,
params=None,
BaselevelHandlerClass=None):
"""Initialize the LinDifSPThresholdModel."""
# Call ErosionModel's init
super(BasicTh,
self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
# Get Parameters and convert units if necessary:
K_sp = self.get_parameter_from_exponent('K_sp', raise_error=False)
K_ss = self.get_parameter_from_exponent('K_ss', raise_error=False)
linear_diffusivity = (
self._length_factor**2.) * self.get_parameter_from_exponent(
'linear_diffusivity') # has units length^2/time
# threshold has units of Length per Time which is what
# StreamPowerSmoothThresholdEroder expects
threshold = self._length_factor * self.get_parameter_from_exponent(
'erosion__threshold') # has units length/time
# check that a stream power and a shear stress parameter have not both been given
if K_sp != None and K_ss != None:
raise ValueError('A parameter for both K_sp and K_ss has been'
'provided. Only one of these may be provided')
elif K_sp != None or K_ss != None:
if K_sp != None:
self.K = K_sp
else:
self.K = (self._length_factor**(
1. / 3.)) * K_ss # K_ss has units Lengtg^(1/3) per Time
else:
raise ValueError('A value for K_sp or K_ss must be provided.')
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(
self.grid,
flow_director='D8',
depression_finder=DepressionFinderAndRouter)
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.K,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
threshold_sp=threshold)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(self.grid,
linear_diffusivity=linear_diffusivity)
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]
# Do some erosion (but not on the flooded nodes)
# (if we're varying K through time, update that first)
if self.opt_var_precip:
self.eroder.K = (
self.K *
self.pc.get_erodibility_adjustment_factor(self.model_time))
self.eroder.run_one_step(dt, flooded_nodes=flooded)
# Do some soil creep
self.diffuser.run_one_step(dt)
# calculate model time
self.model_time += dt
# Lower outlet
self.update_outlet(dt)
# Check walltime
self.check_walltime()
class BasicDdVs(_ErosionModel):
"""
A BasicDdVs computes erosion using linear diffusion,
"smoothly thresholded" stream power in which the threshold increases with
cumulative erosion depth, and Q ~ A exp( -b S / A).
"VSA" stands for "variable source area".
"""
def __init__(self, input_file=None, params=None,
BaselevelHandlerClass=None):
"""Initialize the VSADepthDepThresholdModel."""
# Call ErosionModel's init
super(BasicDdVs, self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
self.K_sp = self.get_parameter_from_exponent('K_sp')
linear_diffusivity = (self._length_factor**2.)*self.get_parameter_from_exponent('linear_diffusivity') # has units length^2/time
recharge_rate = (self._length_factor)*self.params['recharge_rate'] # has units length per time
soil_thickness = (self._length_factor)*self.params['initial_soil_thickness'] # has units length
K_hydraulic_conductivity = (self._length_factor)*self.params['K_hydraulic_conductivity'] # has units length per time
self.threshold_value = self._length_factor*self.get_parameter_from_exponent('erosion__threshold') # has units length/time
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(self.grid,
flow_director='D8',
depression_finder = DepressionFinderAndRouter)
# Add a field for effective drainage area
if 'effective_drainage_area' in self.grid.at_node:
self.eff_area = self.grid.at_node['effective_drainage_area']
else:
self.eff_area = self.grid.add_zeros('node',
'effective_drainage_area')
# Get the effective-area parameter
self.sat_param = (K_hydraulic_conductivity*soil_thickness*self.grid.dx)/(recharge_rate)
# Create a field for the (initial) erosion threshold
self.threshold = self.grid.add_zeros('node', 'erosion__threshold')
self.threshold[:] = self.threshold_value
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(self.grid,
use_Q=self.eff_area,
K_sp=self.K_sp,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
threshold_sp=self.threshold)
# Get the parameter for rate of threshold increase with erosion depth
self.thresh_change_per_depth = self.params['thresh_change_per_depth']
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(self.grid,
linear_diffusivity = linear_diffusivity)
def calc_effective_drainage_area(self):
"""Calculate and store effective drainage area.
Effective drainage area is defined as:
$A_{eff} = A \exp ( \alpha S / A) = A R_r$
where $S$ is downslope-positive steepest gradient, $A$ is drainage
area, $R_r$ is the runoff ratio, and $\alpha$ is the saturation
parameter.
"""
area = self.grid.at_node['drainage_area']
slope = self.grid.at_node['topographic__steepest_slope']
cores = self.grid.core_nodes
self.eff_area[cores] = (area[cores] * (np.exp(-self.sat_param
* slope[cores]
/ area[cores])))
def run_one_step(self, dt):
"""
Advance model for one time-step of duration dt.
"""
# Route flow
self.flow_router.run_one_step()
# Update effective runoff ratio
self.calc_effective_drainage_area()
# Zero out effective area in flooded nodes
self.eff_area[self.flow_router.depression_finder.flood_status==3] = 0.0
# Set the erosion threshold.
#
# Note that a minus sign is used because cum ero depth is negative for
# erosion, positive for deposition.
# The second line handles the case where there is growth, in which case
# we want the threshold to stay at its initial value rather than
# getting smaller.
cum_ero = self.grid.at_node['cumulative_erosion__depth']
cum_ero[:] = (self.z
- self.grid.at_node['initial_topographic__elevation'])
self.threshold[:] = (self.threshold_value
- (self.thresh_change_per_depth
* cum_ero))
self.threshold[self.threshold < self.threshold_value] = \
self.threshold_value
# Do some erosion (but not on the flooded nodes)
# (if we're varying K through time, update that first)
if self.opt_var_precip:
self.eroder.K = (self.K_sp
* self.pc.get_erodibility_adjustment_factor(self.model_time))
self.eroder.run_one_step(dt)
# Do some soil creep
self.diffuser.run_one_step(dt)
# calculate model time
self.model_time += dt
# Lower outlet
self.update_outlet(dt)
# Check walltime
self.check_walltime()
class BasicDdRt(ErosionModel):
"""
A BasicDdRt computes erosion using linear diffusion, stream
power with a smoothed threshold, Q~A, and two lithologies: rock and till.
"""
def __init__(self, input_file=None, params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicDdRt."""
# Call ErosionModel's init
super(BasicDdRt, self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
contact_zone__width = (self._length_factor)*self.params['contact_zone__width'] # has units length
self.K_rock_sp = self.get_parameter_from_exponent('K_rock_sp')
self.K_till_sp = self.get_parameter_from_exponent('K_till_sp')
linear_diffusivity = (self._length_factor**2.)*self.get_parameter_from_exponent('linear_diffusivity')
self.threshold_value = self._length_factor*self.get_parameter_from_exponent('erosion__threshold') # has units length/time
# Set up rock-till
self.setup_rock_and_till(self.params['rock_till_file__name'],
self.K_rock_sp,
self.K_till_sp,
contact_zone__width)
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(self.grid,
flow_director='D8',
depression_finder = DepressionFinderAndRouter)
# Create a field for the (initial) erosion threshold
self.threshold = self.grid.add_zeros('node', 'erosion__threshold')
self.threshold[:] = self.threshold_value
# Instantiate a StreamPowerSmoothThresholdEroder component
self.eroder = StreamPowerSmoothThresholdEroder(self.grid,
K_sp=self.erody,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
threshold_sp=self.threshold)
# Get the parameter for rate of threshold increase with erosion depth
self.thresh_change_per_depth = self.params['thresh_change_per_depth']
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(self.grid,
linear_diffusivity = linear_diffusivity)
def setup_rock_and_till(self, file_name, rock_erody, till_erody,
contact_width):
"""Set up lithology handling for two layers with different erodibility.
Parameters
----------
file_name : string
Name of arc-ascii format file containing elevation of contact
position at each grid node (or NODATA)
rock_erody : float
Water erosion coefficient for bedrock
till_erody : float
Water erosion coefficient for till
contact_width : float [L]
Characteristic width of the interface zone between rock and till
Read elevation of rock-till contact from an esri-ascii format file
containing the basal elevation value at each node, create a field for
erodibility.
"""
from landlab.io import read_esri_ascii
# Read input data on rock-till contact elevation
read_esri_ascii(file_name, grid=self.grid,
name='rock_till_contact__elevation',
halo=1)
# Get a reference to the rock-till field
self.rock_till_contact = self.grid.at_node['rock_till_contact__elevation']
# Create field for erodibility
if 'substrate__erodibility' in self.grid.at_node:
self.erody = self.grid.at_node['substrate__erodibility']
else:
self.erody = self.grid.add_zeros('node', 'substrate__erodibility')
# Create array for erodibility weighting function
self.erody_wt = np.zeros(self.grid.number_of_nodes)
# Read the erodibility value of rock and till
self.rock_erody = rock_erody
self.till_erody = till_erody
# Read and remember the contact zone characteristic width
self.contact_width = contact_width
def update_erodibility_field(self):
"""Update erodibility at each node based on elevation
relative to contact elevation.
To promote smoothness in the solution, the erodibility at a given point
(x,y) is set as follows:
1. Take the difference between elevation, z(x,y), and contact
elevation, b(x,y): D(x,y) = z(x,y) - b(x,y). This number could
be positive (if land surface is above the contact), negative
(if we're well within the rock), or zero (meaning the rock-till
contact is right at the surface).
2. Define a smoothing function as:
$F(D) = 1 / (1 + exp(-D/D*))$
This sigmoidal function has the property that F(0) = 0.5,
F(D >> D*) = 1, and F(-D << -D*) = 0.
Here, D* describes the characteristic width of the "contact
zone", where the effective erodibility is a mixture of the two.
If the surface is well above this contact zone, then F = 1. If
it's well below the contact zone, then F = 0.
3. Set the erodibility using F:
$K = F K_till + (1-F) K_rock$
So, as F => 1, K => K_till, and as F => 0, K => K_rock. In
between, we have a weighted average.
4. Threshold values are assumed to depend on cumulative incision
depth but NOT on lithologic unit (this is obviously a
simplification).
Translating these symbols into variable names:
z = self.elev
b = self.rock_till_contact
D* = self.contact_width
F = self.erody_wt
K_till = self.till_erody
K_rock = self.rock_erody
"""
# Update the erodibility weighting function (this is "F")
self.erody_wt[self.data_nodes] = (1.0
/ (1.0
+ np.exp(-(self.z[self.data_nodes] - self.rock_till_contact[self.data_nodes])
/ self.contact_width)))
# (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.till_erody = self.K_till_sp * erode_factor
self.rock_erody = self.K_rock_sp * erode_factor
# Calculate the effective erodibilities using weighted averaging
self.erody[:] = (self.erody_wt * self.till_erody
+ (1.0 - self.erody_wt) * self.rock_erody)
def update_erosion_threshold_values(self):
"""Updates the erosion threshold at each node based on cumulative
erosion so far."""
# Set the erosion threshold.
#
# Note that a minus sign is used because cum ero depth is negative for
# erosion, positive for deposition.
# The second line handles the case where there is growth, in which case
# we want the threshold to stay at its initial value rather than
# getting smaller.
cum_ero = self.grid.at_node['cumulative_erosion__depth']
cum_ero[:] = (self.z
- self.grid.at_node['initial_topographic__elevation'])
self.threshold[:] = (self.threshold_value
- (self.thresh_change_per_depth
* cum_ero))
self.threshold[self.threshold < self.threshold_value] = \
self.threshold_value
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]
# Update the erodibility and threshold field
self.update_erodibility_field()
# Calculate the new threshold values given cumulative erosion
self.update_erosion_threshold_values()
# Do some erosion (but not on the flooded nodes)
self.eroder.run_one_step(dt, flooded_nodes=flooded)
# Do some soil creep
self.diffuser.run_one_step(dt)
# calculate model time
self.model_time += dt
# Lower outlet
self.update_outlet(dt)
# Check walltime
self.check_walltime()
class BasicDd(_ErosionModel):
"""
A BasicDd computes erosion using linear diffusion, stream
power with a smoothed threshold that is proportional to
depth, and Q~A.
"""
def __init__(self,
input_file=None,
params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicDd."""
# Call ErosionModel's init
super(BasicDd,
self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
# Get Parameters and convert units if necessary:
K_sp = self.get_parameter_from_exponent('K_sp', raise_error=False)
K_ss = self.get_parameter_from_exponent('K_ss', raise_error=False)
linear_diffusivity = (
self._length_factor**2.) * self.get_parameter_from_exponent(
'linear_diffusivity') # has units length^2/time
# threshold has units of Length per Time which is what
# StreamPowerSmoothThresholdEroder expects
self.threshold_value = self._length_factor * self.get_parameter_from_exponent(
'erosion__threshold') # has units length/time
# check that a stream power and a shear stress parameter have not both been given
if K_sp != None and K_ss != None:
raise ValueError('A parameter for both K_sp and K_ss has been'
'provided. Only one of these may be provided')
elif K_sp != None or K_ss != None:
if K_sp != None:
self.K = K_sp
else:
self.K = (self._length_factor**(
1. / 3.)) * K_ss # K_ss has units Lengtg^(1/3) per Time
else:
raise ValueError('A value for K_sp or K_ss must be provided.')
# Instantiate a FlowAccumulator with DepressionFinderAndRouter using D8 method
self.flow_router = FlowAccumulator(
self.grid,
flow_director='D8',
depression_finder=DepressionFinderAndRouter)
# Create a field for the (initial) erosion threshold
self.threshold = self.grid.add_zeros('node', 'erosion__threshold')
self.threshold[:] = self.threshold_value
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'],
K_sp=self.K,
threshold_sp=self.threshold)
# Get the parameter for rate of threshold increase with erosion depth
self.thresh_change_per_depth = self.params['thresh_change_per_depth']
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(self.grid,
linear_diffusivity=linear_diffusivity)
def update_erosion_threshold_values(self):
"""Updates the erosion threshold at each node based on cumulative
erosion so far."""
# Set the erosion threshold.
#
# Note that a minus sign is used because cum ero depth is negative for
# erosion, positive for deposition.
# The second line handles the case where there is growth, in which case
# we want the threshold to stay at its initial value rather than
# getting smaller.
cum_ero = self.grid.at_node['cumulative_erosion__depth']
cum_ero[:] = (self.z -
self.grid.at_node['initial_topographic__elevation'])
self.threshold[:] = (self.threshold_value -
(self.thresh_change_per_depth * cum_ero))
self.threshold[self.threshold < self.threshold_value] = \
self.threshold_value
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]
# Calculate the new threshold values given cumulative erosion
self.update_erosion_threshold_values()
# Do some erosion (but not on the flooded nodes)
# (if we're varying K through time, update that first)
if self.opt_var_precip:
self.eroder.K = (
self.K *
self.pc.get_erodibility_adjustment_factor(self.model_time))
self.eroder.run_one_step(dt, flooded_nodes=flooded)
# Do some soil creep
self.diffuser.run_one_step(dt)
# calculate model time
self.model_time += dt
# Lower outlet
self.update_outlet(dt)
# Check walltime
self.check_walltime()
class StreamPowerVarThresholdModel(_ErosionModel):
"""
A StreamPowerVarThresholdModel computes erosion using a form of the unit
stream power model that represents a threshold using an exponential term.
The threshold value itself depends on incision depth below an initial
reference surface. This is meant to mimic coarsening of sediment in the
channel with progressive incision, similar to the model of
Gran et al. (2013)
"""
def __init__(self, input_file=None, params=None):
"""Initialize the StreamPowerVarThresholdModel."""
# Call ErosionModel's init
super(StreamPowerVarThresholdModel, 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)
# Create a field for the (initial) erosion threshold
self.threshold = self.grid.add_zeros('node', 'erosion__threshold')
self.threshold[:] = self.params['threshold_sp']
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.params['K_sp'],
threshold_sp=self.threshold)
# Get the parameter for rate of threshold increase with erosion depth
self.thresh_change_per_depth = self.params['thresh_change_per_depth']
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]
# Set the erosion threshold.
#
# Note that a minus sign is used because cum ero depth is negative for
# erosion, positive for deposition.
# The second line handles the case where there is growth, in which case
# we want the threshold to stay at its initial value rather than
# getting smaller.
cum_ero = self.grid.at_node['cumulative_erosion__depth']
cum_ero[:] = (self.z
- self.grid.at_node['initial_topographic__elevation'])
self.threshold[:] = (self.params['threshold_sp']
- (self.thresh_change_per_depth
* cum_ero))
self.threshold[self.threshold < self.params['threshold_sp']] = \
self.params['threshold_sp']
# Do some erosion (but not on the flooded nodes)
self.eroder.run_one_step(dt, flooded_nodes=flooded)
class BasicThVs(ErosionModel):
r"""**BasicThVs** model program.
This model program combines models :py:class:`BasicTh` and
:py:class:`BasicVs`. It evolves a topographic surface described by :
math:`\eta` with the following governing equations:
.. math::
\frac{\partial \eta}{\partial t} = -\left(K A_{eff}^{m}S^{n}
- \omega_{c}\left(1-e^{-KA_{eff}^{m}S^{n}/\omega_{c}}\right)\right)
+ D\nabla^2 \eta
A_{eff} = A \exp \left( -\frac{-\alpha S}{A}\right)
\alpha = \frac{K_{sat} H dx}{R_m}
where :math:`Q` is the local stream discharge, :math:`S` is the local slope,
:math:`m` and :math:`n` are the discharge and slope exponent parameters,
:math:`K` is the erodibility by water, :math:`\omega_c` is the critical
stream power needed for erosion to occur, and :math:`D` is the regolith
transport parameter.
:math:`\alpha` is the saturation area scale used for transforming area into
effective area :math:`A_{eff}`. It is given as a function of the saturated
hydraulic conductivity :math:`K_{sat}`, the soil thickness :math:`H`, the
grid spacing :math:`dx`, and the recharge rate, :math:`R_m`.
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=0.0001,
regolith_transport_parameter=0.1,
hydraulic_conductivity=0.1,
water_erosion_rule__threshold=0.01,
**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.
water_erosion_rule__threshold : float, optional
Erosion rule threshold when no erosion has occured
(:math:`\omega_c`). Default is 0.01.
hydraulic_conductivity : float, optional
Hydraulic conductivity (:math:`K_{sat}`). Default is 0.1.
**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
-------
BasicThVs : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicThVs**. 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, BasicThVs
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicThVs(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)
# ensure Precipitator and RunoffGenerator are vanilla
self._ensure_precip_runoff_are_vanilla(vsa_precip=True)
# verify correct fields are present.
self._verify_fields(self._required_fields)
self.m = m_sp
self.n = n_sp
self.K = water_erodibility
if float(self.n) != 1.0:
raise ValueError("Model only supports n = 1.")
# Get the effective-area parameter
self._Kdx = hydraulic_conductivity * self.grid.dx
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.K,
m_sp=self.m,
n_sp=self.n,
threshold_sp=water_erosion_rule__threshold,
discharge_field="surface_water__discharge",
erode_flooded_nodes=self._erode_flooded_nodes,
)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(
self.grid, linear_diffusivity=regolith_transport_parameter)
def _calc_effective_drainage_area(self):
"""Calculate and store effective drainage area."""
area = self.grid.at_node["drainage_area"]
slope = self.grid.at_node["topographic__steepest_slope"]
cores = self.grid.core_nodes
sat_param = (self._Kdx * self.grid.at_node["soil__depth"] /
self.grid.at_node["rainfall__flux"])
eff_area = area[cores] * (np.exp(
-sat_param[cores] * slope[cores] / area[cores]))
self.grid.at_node["surface_water__discharge"][cores] = eff_area
def run_one_step(self, step):
"""Advance model **BasicThVs** for one time-step of duration step.
The **run_one_step** method does the following:
1. Directs flow, accumulates drainage area, and calculates effective
drainage area.
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 detachment-limited erosion 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)
# Update effective runoff ratio
self._calc_effective_drainage_area()
# Zero out effective area in flooded nodes
if self._erode_flooded_nodes:
flooded_nodes = []
else:
flood_status = self.grid.at_node["flood_status_code"]
flooded_nodes = np.nonzero(flood_status == _FLOODED)[0]
self.grid.at_node["surface_water__discharge"][flooded_nodes] = 0.0
# 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:
self.eroder.K = (self.K * self.boundary_handlers["PrecipChanger"].
get_erodibility_adjustment_factor())
self.eroder.run_one_step(step)
# Do some soil creep
self.diffuser.run_one_step(step)
# Finalize the run_one_step_method
self.finalize__run_one_step(step)
class BasicTh(ErosionModel):
r"""**BasicTh** model program.
This model program evolves a topographic surface described by :math:`\eta`
with the following governing equation:
.. math::
\frac{\partial \eta}{\partial t} = -\left(K Q^{m}S^{n}
- \omega_c\left(1-e^{-KQ^{m}S^{n}/\omega_c}\right)\right)
+ D\nabla^2 \eta
where :math:`Q` is the local stream discharge, :math:`S` is the local
slope, :math:`m` and :math:`n` are the discharge and slope exponent
parameters, :math:`K` is the erodibility by water, :math:`\omega_c` is the
critical stream power needed for erosion to occur and :math:`D` is the
regolith transport efficiency.
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``
"""
_required_fields = ["topographic__elevation"]
def __init__(
self,
clock,
grid,
m_sp=0.5,
n_sp=1.0,
water_erodibility=0.0001,
regolith_transport_parameter=0.1,
water_erosion_rule__threshold=0.01,
**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.
water_erosion_rule__threshold : float, optional
Erosion rule threshold when no erosion has occured
(:math:`\omega_c`). Default is 0.01.
**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
-------
BasicTh : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicTh**. 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, BasicTh
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
Construct the model.
>>> model = BasicTh(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(BasicTh, self).__init__(clock, grid, **kwargs)
# verify correct fields are present.
self._verify_fields(self._required_fields)
# Get Parameters and convert units if necessary:
self.m = m_sp
self.n = n_sp
self.K = water_erodibility
if float(self.n) != 1.0:
raise ValueError("Model only supports n equals 1.")
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.K,
m_sp=self.m,
n_sp=self.n,
threshold_sp=water_erosion_rule__threshold,
use_Q="surface_water__discharge",
)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(
self.grid, linear_diffusivity=regolith_transport_parameter
)
def run_one_step(self, step):
"""Advance model **BasicTh** 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 detachment-limited, threshold-modified erosion 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)
# Get IDs of flooded nodes, if any
if self.flow_accumulator.depression_finder is None:
flooded = []
else:
flooded = np.where(
self.flow_accumulator.depression_finder.flood_status == 3
)[0]
# 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:
self.eroder.K = (
self.K
* self.boundary_handlers[
"PrecipChanger"
].get_erodibility_adjustment_factor()
)
self.eroder.run_one_step(step, flooded_nodes=flooded)
# Do some soil creep
self.diffuser.run_one_step(step)
# Finalize the run_one_step_method
self.finalize__run_one_step(step)
