# coding: utf8
# !/usr/env/python
"""terrainbento **BasicRt** model program.
Erosion model program using depth-dependent linear diffusion, soil production
by exponential weathering, stream power with 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. `FastscapeEroder <https://landlab.readthedocs.io/en/master/reference/components/stream_power.html>`_
4. `DepthDependentDiffuser <https://landlab.readthedocs.io/en/master/reference/components/depth_dependent_diffusion.html>`_
5. `ExponentialWeatherer <https://landlab.readthedocs.io/en/master/reference/components/weathering.html>`_
"""
import numpy as np
from landlab.components import (
DepthDependentDiffuser,
ExponentialWeatherer,
FastscapeEroder,
)
from terrainbento.base_class import TwoLithologyErosionModel
[docs]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",
]
[docs] 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().__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_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=self.regolith_transport_parameter,
soil_transport_decay_depth=soil_transport_decay_depth,
)
[docs] 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)
# Update the erodibility field
self._update_erodibility_field()
# Do some erosion
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)
[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)
sart = BasicRtSa.from_file(infile)
sart.run()
if __name__ == "__main__":
main()
