class BasicThVs

Model BasicThVs

terrainbento model BasicThVs program.

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

Landlab components used:

  1. FlowAccumulator

  2. DepressionFinderAndRouter (optional)

  3. StreamPowerSmoothThresholdEroder

  4. LinearDiffuser

class BasicThVs(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility=0.0001, regolith_transport_parameter=0.1, hydraulic_conductivity=0.1, water_erosion_rule__threshold=0.01, **kwargs)[source]

Bases: terrainbento.base_class.erosion_model.ErosionModel

BasicThVs model program.

This model program combines models BasicTh and BasicVs. It evolves a topographic surface described by : math:eta with the following governing equations:

\[ \begin{align}\begin{aligned}\frac{\partial \eta}{\partial t} = -\left(K A_{eff}^{m}S^{n} - \omega_{c}\left(1-e^{-KA_{eff}^{m}S^{n}/\omega_{c}}\right)\right) + D\nabla^2 \eta\\A_{eff} = A \exp \left( -\frac{-\alpha S}{A}\right)\\\alpha = \frac{K_{sat} H dx}{R_m}\end{aligned}\end{align} \]

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 parameter.

\(\alpha\) is the saturation area scale used for transforming area into effective area \(A_{eff}\). It is given as a function of the saturated hydraulic conductivity \(K_{sat}\), the soil thickness \(H\), the grid spacing \(dx\), and the recharge rate, \(R_m\).

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

  • soil__depth

__init__(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility=0.0001, regolith_transport_parameter=0.1, hydraulic_conductivity=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.

  • hydraulic_conductivity (float, optional) – Hydraulic conductivity (\(K_{sat}\)). Default is 0.1.

  • **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

BasicThVs

Return type

model object

Examples

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

Construct the model.

>>> model = BasicThVs(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 BasicThVs 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 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 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.