# coding: utf8
# !/usr/env/python
"""terrainbento **BasicDdRt** model program.
Erosion model program using linear diffusion, stream power with stream power
with a smoothed threshold that increases with incision depth and spatially
varying erodibility based on two bedrock units, 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 TwoLithologyErosionModel
[docs]class BasicDdRt(TwoLithologyErosionModel):
r"""**BasicDdRt** model program.
This model program combines the :py:class:`BasicRt` and :py:class:`BasicDd`
programs by allowing for two lithologies, an "upper" layer and a "lower"
layer, and permitting the use of an smooth erosion threshold that increases
with erosion depth. Given a spatially varying contact zone elevation,
:math:`\eta_C(x,y))`, model **BasicDdRt** evolves a topographic surface
described by :math:`\eta` with the following governing equations:
.. math::
\frac{\partial \eta}{\partial t} = -\left[\omega
- \omega_{ct} (1 - e^{-\omega /\omega_{ct}}) \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_{ct}(x,y,t) = \max(\omega_c + b D_I(x,y,t)
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_{c}` is the in initial erosion threshold (for both
lithologies) and :math:`b` is the rate of change of threshold with
increasing cumulative incision :math:`D_I(x,y,t)`, 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",
]
[docs] def __init__(
self,
clock,
grid,
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_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.
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:`TwoLithologyErosionModel`.
Importantly these arguments specify the precipitator and the runoff
generator that control the generation of surface water discharge
(:math:`Q`).
Returns
-------
BasicDdRt : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicDdRt**. For more detailed examples, including steady-
state 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, BasicDdRt
>>> 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 = BasicDdRt(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)
if float(self.n) != 1.0:
raise ValueError("Model only supports n equals 1.")
self.threshold_value = water_erosion_rule__threshold
# Set up rock-till boundary and associated grid fields.
self._setup_rock_and_till()
# 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 StreamPowerSmoothThresholdEroder component
self.eroder = StreamPowerSmoothThresholdEroder(
self.grid,
K_sp=self.erody,
m_sp=self.m,
n_sp=self.n,
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=self.regolith_transport_parameter
)
def _update_erosion_threshold_values(self):
"""Update the depth dependent erosion threshold at each node."""
# 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 **BasicDdRt** 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. Updates the threshold value based on the cumulative amount of erosion
that has occured since model run onset.
6. Calculates detachment-limited erosion by water.
7. Calculates topographic change by linear diffusion.
8. 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 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(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)
thrt = BasicDdRt.from_file(infile)
thrt.run()
if __name__ == "__main__":
main()
