# coding: utf8
# !/usr/env/python
"""terrainbento **BasicRtVs** model program.
Erosion model program using linear diffusion, stream power with spatiall
varying erodibility based on two bedrock units, and discharge proportional to
effective 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. `LinearDiffuser <https://landlab.readthedocs.io/en/master/reference/components/diffusion.html>`_
"""
import numpy as np
from landlab.components import FastscapeEroder, LinearDiffuser
from landlab.components.depression_finder.lake_mapper import _FLOODED
from terrainbento.base_class import TwoLithologyErosionModel
[docs]class BasicRtVs(TwoLithologyErosionModel):
r"""**BasicRtVs** model program.
This model program combines the :py:class:`BasicRt` and :py:class:`BasicVs`
programs by allowing for two lithologies, an "upper" layer and a "lower"
layer, and using discharge proportional to effective drainage area based on
variable source area hydrology. Given a spatially varying contact zone
elevation, :math:`\eta_C(x,y))`, model **BasicRtVs** evolves a topographic
surface described by :math:`\eta` with the following governing equations:
.. math::
\frac{\partial \eta}{\partial t} = - K(\eta,\eta_C) A_{eff}^{m}S^{n}
+ D\nabla^2 \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)}
A_{eff} = A \exp \left( -\frac{-\alpha S}{A}\right)
\alpha = \frac{K_{sat} 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:`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:`\alpha` is the
saturation area scale used for transforming area into effective area and 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`. :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.
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, 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_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.
hydraulic_conductivity : float, optional
Hydraulic conductivity (:math:`K_{sat}`). Default is 0.1.
**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
-------
BasicRtVs : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicRtVs**. 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, BasicRtVs
>>> 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 = BasicRtVs(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)
# ensure Precipitator and RunoffGenerator are vanilla
self._ensure_precip_runoff_are_vanilla()
# 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()
# Get the effective-area parameter
self._Kdx = hydraulic_conductivity * self.grid.dx
# 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,
)
# Instantiate a LinearDiffuser component
self.diffuser = LinearDiffuser(
self.grid, linear_diffusivity=self.regolith_transport_parameter
)
def _calc_effective_drainage_area(self):
r"""Calculate and store effective drainage area.
Effective drainage area is defined as:
.. math::
A_{eff} = A \exp ( \alpha S / A) = A R_r
where :math:`S` is downslope-positive steepest gradient, :math:`A` is
drainage area, :math:`R_r` is the runoff ratio, and :math:`\alpha` is
the saturation parameter.
"""
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
[docs] def run_one_step(self, step):
"""Advance model **BasicRtVs** 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. 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 effective runoff ratio
self._calc_effective_drainage_area()
# Zero out effective area in flooded nodes
if self._erode_flooded_nodes:
flooded_nodes = []
else:
flood_status = self.grid.at_node["flood_status_code"]
flooded_nodes = np.nonzero(flood_status == _FLOODED)[0]
self.grid.at_node["surface_water__discharge"][flooded_nodes] = 0.0
# Update the erodibility field
self._update_erodibility_field()
# 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)
vsrt = BasicRtVs.from_file(infile)
vsrt.run()
if __name__ == "__main__":
main()