# coding: utf8
# !/usr/env/python
"""terrainbento model **BasicHySa** program.
Erosion model program using exponential weathering, soil-depth-dependent linear
diffusion, stream-power-driven sediment erosion, mass conservation, and bedrock
erosion, 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. `Space <https://landlab.readthedocs.io/en/master/reference/components/space.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,
Space,
)
from terrainbento.base_class import ErosionModel
[docs]class BasicHySa(ErosionModel):
r"""**BasicHySa** program.
This model program combines :py:class:`BasicHy` and :py:class:`BasicSa` to
evolve a topographic surface described by :math:`\eta` with the following
governing equation:
.. math::
\eta = \eta_b + H
\frac{\partial H}{\partial t} = P_0 \exp (-H/H_s)
+ \frac{V_s Q_s}{Q(A)\left(1 - \phi \right)}
- K_s Q(A)^{m}S^{n} (1 - e^{-H/H_*})
-\nabla q_h
\frac{\partial \eta_b}{\partial t} = -P_0 \exp (-H/H_s)
- K_r Q(A)^{m}S^{n} e^{-H/H_*}
Q_s = \int_0^A \left(K_s Q(A)^{m}S^{n} (1-e^{-H/H_*})
+ K_r (1-F_f) Q(A)^{m}S^{n} e^{-H/H_*}
- \frac{V_s Q_s}{Q(A)}\right) dA
where :math:`\eta_b` is the bedrock elevation, :math:`H` is the soil depth,
:math:`P_0` is the maximum soil production rate, :math:`H_s` is the soil
production decay depth, :math:`V_s` is effective sediment settling
velocity, :math:`Q_s` is volumetric fluvial sediment flux, :math:`A` is the
local drainage area, :math:`Q`, is the local discharge, :math:`S` is the
local slope, :math:`\phi` is sediment porosity, :math:`F_f` is the fraction
of fine sediment, :math:`K_r` and :math:`K_s` are rock and sediment
erodibility respectively, :math:`m` and :math:`n` are the discharge and
slope exponent parameters, :math:`H_*` is the bedrock roughness length
scale, and :math:`r` is a runoff rate. Hillslope sediment flux per unit
width :math:`q_h` is given by:
.. math::
q_h = -D H^* \left[1-\exp \left( -\frac{H}{H_0} \right) \right]
\nabla \eta.
where :math:`D` is soil diffusivity and :math:`H_0` is the soil transport
depth scale.
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_sediment=0.001,
water_erodibility_rock=0.0001,
regolith_transport_parameter=0.1,
settling_velocity=0.001,
sediment_porosity=0.3,
fraction_fines=0.5,
roughness__length_scale=0.5,
solver="basic",
soil_production__maximum_rate=0.001,
soil_production__decay_depth=0.5,
soil_transport_decay_depth=0.5,
sp_crit_br=0,
sp_crit_sed=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.
settling_velocity : float, optional
Normalized settling velocity of entrained sediment (:math:`V_s`).
Default is 0.001.
sediment_porosity : float, optional
Sediment porosity (:math:`\phi`). Default is 0.3.
fraction_fines : float, optional
Fraction of fine sediment that is permanently detached
(:math:`F_f`). Default is 0.5.
roughness__length_scale : float, optional
Bedrock roughness length scale. Default is 0.5.
solver : str, optional
Solver option to pass to the Landlab
`Space <https://landlab.readthedocs.io/en/master/reference/components/space.html>`_
component. Default is "basic".
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:`ErosionModel`. Importantly
these arguments specify the precipitator and the runoff generator
that control the generation of surface water discharge (:math:`Q`).
Returns
-------
BasicHySa : model object
Examples
--------
This is a minimal example to demonstrate how to construct an instance
of model **BasicHySa**. 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, BasicHySa
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicHySa(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)
soil_thickness = self.grid.at_node["soil__depth"]
bedrock_elev = self.grid.add_zeros("node", "bedrock__elevation")
bedrock_elev[:] = self.z - soil_thickness
self.m = m_sp
self.n = n_sp
self.K_br = water_erodibility_rock
self.K_sed = water_erodibility_sediment
# Instantiate a SPACE component
self.eroder = Space(
self.grid,
K_sed=self.K_sed,
K_br=self.K_br,
sp_crit_br=sp_crit_br,
sp_crit_sed=sp_crit_sed,
F_f=fraction_fines,
phi=sediment_porosity,
H_star=roughness__length_scale,
v_s=settling_velocity,
m_sp=self.m,
n_sp=self.n,
discharge_field="surface_water__discharge",
solver=solver,
)
# 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=regolith_transport_parameter,
soil_transport_decay_depth=soil_transport_decay_depth,
)
self.grid.at_node["soil__depth"][:] = (
self.grid.at_node["topographic__elevation"]
- self.grid.at_node["bedrock__elevation"]
)
[docs] def run_one_step(self, step):
"""Advance model **BasicHySa** 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 erosion and deposition 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)
# 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:
erode_factor = self.boundary_handlers[
"PrecipChanger"
].get_erodibility_adjustment_factor()
self.eroder.K_sed = self.K_sed * erode_factor
self.eroder.K_br = self.K_br * erode_factor
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)
# Check stability
self.check_stability()
[docs] def check_stability(self):
"""Check model stability and exit if unstable."""
fields = self.grid.at_node.keys()
for f in fields:
if np.any(np.isnan(self.grid.at_node[f])) or np.any(
np.isinf(self.grid.at_node[f])
):
raise SystemExit(
"terrainbento ModelHySa: Model became unstable"
)
[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)
hysa = BasicHySa.from_file(infile)
hysa.run()
if __name__ == "__main__":
main()
