class BasicTh

Model BasicTh

terrainbento BasicTh model program.

Erosion model program using linear diffusion, stream power with a smoothed threshold, and discharge proportional to drainage area.

Landlab components used:

  1. FlowAccumulator

  2. DepressionFinderAndRouter (optional)

  3. StreamPowerSmoothThresholdEroder

  4. LinearDiffuser

class BasicTh(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, **kwargs)[source]

Bases: terrainbento.base_class.erosion_model.ErosionModel

BasicTh model program.

This model program evolves a topographic surface described by \(\eta\) with the following governing equation:

\[\frac{\partial \eta}{\partial t} = -\left(K Q^{m}S^{n} - \omega_c\left(1-e^{-KQ^{m}S^{n}/\omega_c}\right)\right) + D\nabla^2 \eta\]

where \(Q\) is the local stream discharge, \(S\) is the local slope, \(m\) and \(n\) are the discharge and slope exponent parameters, \(K\) is the erodibility by water, \(\omega_c\) is the critical stream power needed for erosion to occur and \(D\) is the regolith transport efficiency.

Refer to Barnhart et al. (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

__init__(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, **kwargs)[source]
Parameters

  • clock (terrainbento Clock instance) –

  • grid (landlab model grid instance) – The grid must have all required fields.

  • m_sp (float, optional) – Drainage area exponent (\(m\)). Default is 0.5.

  • n_sp (float, optional) – Slope exponent (\(n\)). Default is 1.0.

  • water_erodibility (float, optional) – Water erodibility (\(K\)). Default is 0.0001.

  • regolith_transport_parameter (float, optional) – Regolith transport efficiency (\(D\)). Default is 0.1.

  • water_erosion_rule__threshold (float, optional) – Erosion rule threshold when no erosion has occured (\(\omega_c\)). Default is 0.01.

  • **kwargs – Keyword arguments to pass to ErosionModel. Importantly these arguments specify the precipitator and the runoff generator that control the generation of surface water discharge (\(Q\)).

Returns

BasicTh

Return type

model object

Examples

This is a minimal example to demonstrate how to construct an instance of model BasicTh. 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, BasicTh
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")

Construct the model.

>>> model = BasicTh(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
run_one_step(step)[source]

Advance model BasicTh 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 PrecipChanger is an active boundary handler and if so, uses it to modify the erodibility by water.

  4. Calculates detachment-limited, threshold-modified erosion by water.

  5. Calculates topographic change by linear diffusion.

  6. Finalizes the step using the 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.

main()[source]

Executes model.