class BasicCh

# Model BasicCh¶

terrainbento BasicCh model program.

Erosion model program using cubic diffusion, basic stream power, and discharge proportional to drainage area.

Landlab components used:
class BasicCh(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility=0.0001, regolith_transport_parameter=0.1, critical_slope=0.3, number_of_taylor_terms=11, **kwargs)[source]

BasicCh model program.

This model program evolves a topographic surface, $$\eta$$, with the following governing equation:

\begin{align}\begin{aligned}\frac{\partial \eta}{\partial t} = -KQ^{m}S^{n} + \nabla^2 q_h\\q_h = -DS \left[ 1 + \left( \frac{S}{S_c} \right)^2 + \left( \frac{S}{S_c} \right)^4 + ... \left( \frac{S}{S_c} \right)^{2(N-1)} \right]\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, $$D$$ is the regolith transport efficiency, and $$S_c$$ is the critical slope. $$q_h$$ represents the hillslope sediment flux per unit width. $$N$$ is the number of terms in the Taylor Series expansion.

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, critical_slope=0.3, number_of_taylor_terms=11, **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.

• critical_slope (float, optional) – Critical slope ($$S_c$$, unitless). Default is 0.3.

• number_of_taylor_terms (int, optional) – Number of terms in the Taylor Series Expansion ($$N$$). Default is 11.

• **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

BasicCh

Return type

model object

Examples

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


Construct the model.

>>> model = BasicCh(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 BasicCh 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 erosion by water.

5. Calculates topographic change by nonlinear 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.