# coding: utf8
# !/usr/env/python
"""terrainbento model **BasicDdVs** program.
Erosion model program using linear diffusion, stream power with a smoothed
threshold that varies with incision depth, 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. `StreamPowerSmoothThresholdEroder <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 LinearDiffuser, StreamPowerSmoothThresholdEroder
from landlab.components.depression_finder.lake_mapper import _FLOODED
from terrainbento.base_class import ErosionModel
[docs]class BasicDdVs(ErosionModel):
r"""**BasicDdVs** model program.
This model program combines :py:class:`BasicDd` and :py:class:`BasicVs`.
It evolves a topographic surface described by :math:`\eta` with the
following governing equations:
.. math::
\frac{\partial \eta}{\partial t} = -\left(KA_{eff}^{m}S^{n}
- \omega_{ct}\left(1-e^{-KA_{eff}^{m}S^{n}/\omega_{ct}}\right)\right)
+ D\nabla^2 \eta
A_{eff} = A \exp \left( -\frac{-\alpha S}{A}\right)
\alpha = \frac{K_{sat} H 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:`K` is the erodibility by water, :math:`D` is the
regolith transport parameter, 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`.
:math:`\alpha` is the saturation area scale used for transforming area into
effective area. 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`.
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``
- ``soil__depth``
"""
_required_fields = ["topographic__elevation", "soil__depth"]
[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,
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 : 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.
hydraulic_conductivity : float, optional
Hydraulic conductivity (:math:`K_{sat}`). Default is 0.1.
**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
-------
BasicDdVs : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicVs**. 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, BasicDdVs
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicDdVs(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(vsa_precip=True)
# verify correct fields are present.
self._verify_fields(self._required_fields)
if float(n_sp) != 1.0:
raise ValueError("Model BasicDdVs only supports n = 1.")
self.m = m_sp
self.n = n_sp
self.K = water_erodibility
self.threshold_value = water_erosion_rule__threshold
# Get the effective-area parameter
self._Kdx = hydraulic_conductivity * self.grid.dx
# 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,
discharge_field="surface_water__discharge",
erode_flooded_nodes=self._erode_flooded_nodes,
K_sp=self.K,
m_sp=self.m,
n_sp=self.n,
threshold_sp=self.threshold,
)
# 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
)
def _calc_effective_drainage_area(self):
"""Calculate and store effective drainage area."""
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 **BasicVs** 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. Calculates detachment-limited 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)
# 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
# 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
# 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)
my_model = BasicDdVs.from_file(infile)
my_model.run()
if __name__ == "__main__":
main()
