# coding: utf8
# !/usr/env/python
"""terrainbento **BasicDd** model program.
Erosion model program using linear diffusion, stream power with a smoothed
threshold that varies with incision depth, and discharge proportional to
drainage area.
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 <https://landlab.readthedocs.io/en/master/reference/components/stream_power.html>`_
4. `LinearDiffuser <https://landlab.readthedocs.io/en/master/reference/components/diffusion.html>`_
"""
from landlab.components import LinearDiffuser, StreamPowerSmoothThresholdEroder
from terrainbento.base_class import ErosionModel
[docs]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"]
[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,
**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
)
[docs] 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
[docs] 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)
[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)
ldsp = BasicDd.from_file(infile)
ldsp.run()
if __name__ == "__main__":
main()
