# coding: utf8
# !/usr/env/python
"""terrainbento **BasicDdSt** model program.
Erosion model program using linear diffusion, smoothly thresholded stream
power, and stochastic discharge with a smoothed infiltration capacity
threshold. The program differs from BasicStTh in that the threshold value
depends on cumulative incision depth, and so can vary in space and time.
Landlab components used:
1. `FlowAccumulator <https://landlab.readthedocs.io/en/master/reference/components/flow_accum.html>`_
2. `DepressionFinderAndRouter <https://landlab.readthedocs.io/en/master/reference/components/flow_routing.html>`_ (optional)
3. `StreamPowerSmoothThresholdEroder`
4. `LinearDiffuser <https://landlab.readthedocs.io/en/master/reference/components/diffusion.html>`_
5. `PrecipitationDistribution <https://landlab.readthedocs.io/en/master/reference/components/uniform_precip.html>`_
"""
from landlab.components import LinearDiffuser, StreamPowerSmoothThresholdEroder
from terrainbento.base_class import StochasticErosionModel
[docs]class BasicDdSt(StochasticErosionModel):
r"""**BasicDdSt** model program.
This model program uses a stochastic treatment of runoff and discharge, and
includes an erosion threshold in the water erosion law. The threshold
depends on cumulative incision depth, and therefore can vary in space and
time. It combines models :py:class:`BasicDd` and :py:class:`BasicSt`.
The model evolves a topographic surface, :math:`\eta (x,y,t)`,
with the following governing equation:
.. math::
\frac{\partial \eta}{\partial t} = -\left[K_{q}\hat{Q}^{m}S^{n}
- \omega_{ct} \left(1-e^{-K_{q}\hat{Q}^{m}S^{n}
/ \omega_{ct}}\right)\right)]
+ D \nabla^2 \eta
where :math:`\hat{Q}` is the local stream discharge (the hat symbol
indicates that it is a random-in-time variable) and :math:`S` is the local
slope gradient. :math:`m` and :math:`n` are the discharge and slope
exponent, respectively, :math:`\omega_c` is the critical stream power
required for erosion to occur, :math:`K` is the erodibility by water, and
:math:`D` is the regolith transport parameter.
:math:`\omega_{ct}` may change 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"]
[docs] 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,
infiltration_capacity=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 : 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.
infiltration_capacity: float, optional
Infiltration capacity (:math:`I_m`). Default is 1.0.
**kwargs :
Keyword arguments to pass to :py:class:`StochasticErosionModel`.
These arguments control the discharge :math:`\hat{Q}`.
Returns
-------
BasicDdSt : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicDdSt**. 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, BasicDdSt
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
Construct the model.
>>> model = BasicDdSt(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:
self.m = m_sp
self.n = n_sp
self.K = water_erodibility
self.threshold_value = water_erosion_rule__threshold
self.thresh_change_per_depth = (
water_erosion_rule__thresh_depth_derivative
)
self.infilt = infiltration_capacity
if float(self.n) != 1.0:
raise ValueError("Model only supports n equals 1.")
# instantiate rain generator
self.instantiate_rain_generator()
# Run flow routing and lake filler
self.flow_accumulator.run_one_step()
# 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,
discharge_field="surface_water__discharge",
erode_flooded_nodes=self._erode_flooded_nodes,
threshold_sp=self.threshold,
)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(
self.grid, linear_diffusivity=regolith_transport_parameter
)
[docs] def update_threshold_field(self):
"""Update the threshold based on cumulative erosion depth."""
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 _pre_water_erosion_steps(self):
self.update_threshold_field()
[docs] def run_one_step(self, step):
"""Advance model **BasicDdSt** 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)
# Handle water erosion
self.handle_water_erosion(step)
# Do some soil creep
self.diffuser.run_one_step(step)
# Finalize the run_one_step_method
self.finalize__run_one_step(step)
[docs]def main(): # pragma: no cover
"""Executes model."""
import sys
try:
infile = sys.argv[1]
except IndexError:
print("Must include input file name on command line")
sys.exit(1)
em = BasicDdSt.from_file(infile)
em.run()
if __name__ == "__main__":
main()
