Source code for terrainbento.derived_models.model_basicRtVs

# 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()