class BasicSa(ErosionModel):
r"""**BasicSa** model program.
This model program explicitly resolves a soil layer. This soil layer is
produced by weathering that decays exponentially with soil thickness and
hillslope transport is soil-depth dependent. Given a spatially varying soil
thickness :math:`H` and a spatially varying bedrock elevation
:math:`\eta_b`, model **BasicSa** evolves a topographic surface described
by :math:`\eta` with the following governing equations:
.. math::
\eta = \eta_b + H
\frac{\partial H}{\partial t} = P_0 \exp (-H/H_s)
- \delta (H) K A^{M} S^{N}
- \nabla q_h
\frac{\partial \eta_b}{\partial t} = -P_0 \exp (-H/H_s)
- (1 - \delta (H) ) K Q^{m} S^{N}
q_h = -D H^* \left[1-\exp \left( -\frac{H}{H_0} \right) \right] \nabla \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:`D` is the regolith transport
parameter, :math:`H` is the regolith thickness, :math:`H_s` is the sediment
production decay depth, :math:`P_0` is the maximum sediment production
rate, and :math:`H_0` is the sediment transport decay depth. :math:`q_s`
represents the hillslope sediment flux per unit width.
The function :math:`\delta (H)` is used to indicate that water erosion will
act on soil where it exists, and on the underlying lithology where soil is
absent. To achieve this, :math:`\delta (H)` is defined to equal 1 when
:math:`H > 0` (meaning soil is present), and 0 if :math:`H = 0` (meaning
the underlying parent material is exposed).
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,
soil_production__maximum_rate=0.001,
soil_production__decay_depth=0.5,
soil_transport_decay_depth=0.5,
**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.
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
-------
BasicSa : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicSa**. 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, BasicSa
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicSa(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
# Instantiate a FastscapeEroder component
self.eroder = FastscapeEroder(
self.grid,
K_sp=self.K,
m_sp=self.m,
n_sp=self.n,
discharge_field="surface_water__discharge",
erode_flooded_nodes=self._erode_flooded_nodes,
)
soil_thickness = self.grid.at_node["soil__depth"]
bedrock_elev = self.grid.add_zeros("node", "bedrock__elevation")
bedrock_elev[:] = self.z - soil_thickness
# 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,
)
def run_one_step(self, step):
"""Advance model **BasicSa** 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 erosion by water.
5. Produces soil and calculates soil depth with exponential weathering.
6. Calculates topographic change by depth-dependent 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)
# 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)
# 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)
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
class BasicVsSa(_ErosionModel):
"""
A BasicVsSa computes erosion using depth-dependent linear diffusion, basic
stream power, and Q ~ A exp( -c H S / A); H = soil thickness.
This "c" parameter has dimensions of length, and is defined as
c = K dx / R, where K is saturated hydraulic conductivity, dx is grid
spacing, and R is recharge.
"""
def __init__(self, input_file=None, params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicVsSa."""
# Call ErosionModel's init
super(BasicVsSa, self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
# Get Parameters and convert units if necessary:
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
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
recharge_rate = (self._length_factor)*self.params['recharge_rate'] # has units length per time
K_hydraulic_conductivity = (self._length_factor)*self.params['K_hydraulic_conductivity'] # has units length per time
# 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')
soil_thickness[:] = initial_soil_thickness
bedrock_elev[:] = self.z - initial_soil_thickness
# 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-length parameter
self.sat_len = (K_hydraulic_conductivity*self.grid.dx)/(recharge_rate)
# Instantiate a FastscapeEroder component
self.eroder = StreamPowerEroder(self.grid,
use_Q=self.eff_area,
K_sp=self.K_sp,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'])
# Instantiate a DepthDependentDiffuser component
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)
def calc_effective_drainage_area(self):
"""Calculate and store effective drainage area.
Effective drainage area is defined as:
$A_{eff} = A \exp ( c H S / A) = A R_r$
where $H$ is soil thickness, $S$ is downslope-positive steepest
gradient, $A$ is drainage area, $R_r$ is the runoff ratio, and $c$ is
the saturation length parameter.
"""
area = self.grid.at_node['drainage_area']
slope = self.grid.at_node['topographic__steepest_slope']
soil = self.grid.at_node['soil__depth']
cores = self.grid.core_nodes
self.eff_area[cores] = (area[cores] * (np.exp(-self.sat_len
* soil[cores]
* 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
# 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)
# 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()
# 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 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"
)
class BasicSa(ErosionModel):
"""
A BasicSa computes erosion using linear diffusion, basic
stream power, and Q~A.
It creates soil through weathering 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(BasicSa,
self).__init__(input_file=input_file,
params=params,
BaselevelHandlerClass=BaselevelHandlerClass)
# Get Parameters and convert units if necessary:
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
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)
# Instantiate a FastscapeEroder component
self.eroder = FastscapeEroder(self.grid,
K_sp=self.K_sp,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'])
# 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
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)
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_sp *
self.pc.get_erodibility_adjustment_factor(self.model_time))
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()
class BasicRtSa(ErosionModel):
"""
A BasicSaRt computes erosion using linear diffusion, basic
stream power with rock and till layers, and Q~A.
It creates soil through weathering and consideres soil thickness
in calculating hillslope diffusion.
"""
def __init__(self,
input_file=None,
params=None,
BaselevelHandlerClass=None):
"""Initialize the BasicSaRt."""
# Call ErosionModel's init
super(BasicSaRt,
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')
# 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)
# Instantiate a FastscapeEroder component
self.eroder = FastscapeEroder(self.grid,
K_sp=self.erody,
m_sp=self.params['m_sp'],
n_sp=self.params['n_sp'])
# 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._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
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)
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)
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.
Some considerations here:
1. We could represent the contact between two layers either as a
depth below present land surface, or as an altitude. Using a
depth would allow for vertical motion, because for a fixed
surface, the depth remains constant while the altitude changes.
But the depth must be updated every time the surface is eroded
or aggrades. Using an altitude avoids having to update the
contact position every time the surface erodes or aggrades, but
any tectonic motion would need to be applied to the contact
position as well. Here we'll use the altitude approach because
this model was originally written for an application with lots
of erosion expected but no tectonics.
"""
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.
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 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 field
self.update_erodibility_field()
# Do some erosion (but not on the flooded nodes)
self.eroder.run_one_step(dt,
flooded_nodes=flooded,
K_if_used=self.erody)
# 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()
class BasicSaVs(ErosionModel):
r"""**BasicSaVs** model program.
This model program combines :py:class:`BasicSa` and :py:class:`BasicVs`.
Given a spatially varying soil thickness :math:`H` and a spatially varying
bedrock elevation :math:`\eta_b`, model **BasicSaVs** evolves a topographic
surface described by :math:`\eta` with the following governing equations:
.. math::
\eta = \eta_b + H
\frac{\partial H}{\partial t} = P_0 \exp (-H/H_s)
- \delta (H) K A_{eff}^{M} S^{N}
- \nabla q_h
\frac{\partial \eta_b}{\partial t} = -P_0 \exp (-H/H_s)
- (1 - \delta (H) ) K A_{eff}^{m} S^{N}
q_h = -D H^* \left[1-\exp \left( -\frac{H}{H_0} \right) \right] \nabla \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:`D` is the
regolith transport parameter, :math:`H_s` is the sediment production decay
depth, :math:`H_0` is the sediment transport decay depth, :math:`P_0` is
the maximum sediment production rate, and :math:`H_0` is the sediment
transport decay depth. :math:`q_h` is the hillslope sediment flux per unit
width.
: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,
soil_production__maximum_rate=0.001,
soil_production__decay_depth=0.5,
soil_transport_decay_depth=0.5,
hydraulic_conductivity=0.1,
**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.
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.
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
-------
BasicSaVs : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicSaVs**. 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, BasicSaVs
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicSaVs(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(BasicSaVs, self).__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)
# Get Parameters and convert units if necessary:
self.m = m_sp
self.n = n_sp
self.K = water_erodibility
soil_thickness = self.grid.at_node["soil__depth"]
bedrock_elev = self.grid.add_zeros("node", "bedrock__elevation")
bedrock_elev[:] = self.z - soil_thickness
# Get the effective-area parameter
self._Kdx = hydraulic_conductivity * self.grid.dx
# Instantiate a FastscapeEroder component
self.eroder = FastscapeEroder(
self.grid,
discharge_name="surface_water__discharge",
K_sp=self.K,
m_sp=self.m,
n_sp=self.n,
)
# Instantiate a DepthDependentDiffuser component
self.diffuser = DepthDependentDiffuser(
self.grid,
linear_diffusivity=regolith_transport_parameter,
soil_transport_decay_depth=soil_transport_decay_depth,
)
self.weatherer = ExponentialWeatherer(
self.grid,
soil_production__maximum_rate=soil_production__maximum_rate,
soil_production__decay_depth=soil_production__decay_depth,
)
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 **BasicVs** 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 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()
# 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]
# Zero out effective area in flooded nodes
self.grid.at_node["surface_water__discharge"][flooded] = 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)
# 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()
# Do some soil creep
self.diffuser.run_one_step(step)
# Finalize the run_one_step_method
self.finalize__run_one_step(step)
class BasicRtSa(TwoLithologyErosionModel):
r"""**BasicRtSa** model program.
This model program combines the :py:class:`BasicRt` and :py:class:`BasicSa`
programs by allowing for two lithologies, an "upper" layer and a "lower"
layer and explicitly resolving a soil layer. This soil layer is produced by
weathering that decays exponentially with soil thickness and hillslope
transport is soil-depth dependent. Given a spatially varying contact zone
elevation, :math:`\eta_C(x,y))`, a spatially varying soil thickness
:math:`H` and a spatially varying bedrock elevation :math:`\eta_b`,
model **BasicRtSa** evolves a topographic surface described by :math:`\eta`
with the following governing equations:
.. math::
\eta = \eta_b + H
\frac{\partial H}{\partial t} = P_0 \exp (-H/H_s)
- \delta (H) K Q^{m} S^{n}
- \nabla q_h
\frac{\partial \eta_b}{\partial t} = -P_0 \exp (-H/H_s)
- (1 - \delta (H) ) K Q^{m} S^{n}
q_h = -D H^* \left[1-\exp \left( -\frac{H}{H_0} \right) \right] \nabla \eta
K(\eta, \eta_C ) = w K_1 + (1 - w) K_2
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, 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:`H_s` is
the sediment production decay depth, :math:`H_0` is the sediment transport
decay depth, :math:`P_0` is the maximum sediment production rate, and
:math:`H_0` is the sediment transport decay depth. :math:`q_h` is the
hillslope sediment flux per unit width.
The function :math:`\delta (H)` is used to indicate that water erosion will
act on soil where it exists, and on the underlying lithology where soil is
absent. To achieve this, :math:`\delta (H)` is defined to equal 1 when
:math:`H > 0` (meaning soil is present), and 0 if :math:`H = 0` (meaning
the underlying parent material is exposed).
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``
- ``soil__depth``
"""
_required_fields = [
"topographic__elevation",
"lithology_contact__elevation",
"soil__depth",
]
def __init__(
self,
clock,
grid,
soil_production__maximum_rate=0.001,
soil_production__decay_depth=0.5,
soil_transport_decay_depth=0.5,
**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.
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.
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:`TwoLithologyErosionModel`.
Importantly these arguments specify the precipitator and the runoff
generator that control the generation of surface water discharge
(:math:`Q`).
Returns
-------
BasicRtSa : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicRtSa**. 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, BasicRtSa
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
>>> _ = constant(grid, "lithology_contact__elevation", value=-10.)
Construct the model.
>>> model = BasicRtSa(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(BasicRtSa, self).__init__(clock, grid, **kwargs)
# verify correct fields are present.
self._verify_fields(self._required_fields)
# Set up rock-till boundary and associated grid fields.
self._setup_rock_and_till()
# Instantiate a FastscapeEroder component
self.eroder = FastscapeEroder(
self.grid,
K_sp=self.erody,
m_sp=self.m,
n_sp=self.n,
discharge_name="surface_water__discharge",
)
soil_thickness = self.grid.at_node["soil__depth"]
bedrock_elev = self.grid.add_zeros("node", "bedrock__elevation")
bedrock_elev[:] = self.z - soil_thickness
# Instantiate diffusion and weathering components
self.diffuser = DepthDependentDiffuser(
self.grid,
linear_diffusivity=self.regolith_transport_parameter,
soil_transport_decay_depth=soil_transport_decay_depth,
)
self.weatherer = ExponentialWeatherer(
self.grid,
soil_production__maximum_rate=soil_production__maximum_rate,
soil_production__decay_depth=soil_production__decay_depth,
)
def run_one_step(self, step):
"""Advance model **BasicRtSa** 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 value 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 field
self._update_erodibility_field()
# Do some erosion (but not on the flooded nodes)
self.eroder.run_one_step(
step, flooded_nodes=flooded, K_if_used=self.erody
)
# 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)
#Call the erosion routines.
fr.run_one_step()
lm.map_depressions()
floodedNodes = np.where(lm.flood_status == 3)[0]
sp.run_one_step(dt=dt, flooded_nodes=floodedNodes)
#fetch the nodes where space eroded the bedrock__elevation over topographic__elevation
#after conversation with charlie shobe:
b = mg.at_node['bedrock__elevation']
b[:] = np.minimum(b, mg.at_node['topographic__elevation'])
#calculate regolith-production rate
expWeath.calc_soil_prod_rate()
#Generate and move the soil around.
DDdiff.run_one_step(dt=dt)
#run the landform classifier
lc.run_one_step(elevationStepBin, 300, classtype=classificationType)
#run lpjguess once at the beginning and then each timestep after the spinup.
if elapsed_time < spin_up:
outInt = outIntSpinUp
if elapsed_time == 0:
#create all possible landform__ID's in here ONCE before lpjguess is called
create_all_landforms(upliftRate, totalT, elevationStepBin, mg)
write_netcdf('./temp_output/current_output.nc',
mg,
format='NETCDF4',
attrs={