class BasicRt

Model BasicRt

terrainbento BasicRt model program.

Erosion model program using linear diffusion, stream power with spatially varying erodibility based on two bedrock units, and discharge proportional to drainage area.

Landlab components used:

1. FlowAccumulator

2. DepressionFinderAndRouter (optional)

3. FastscapeEroder

4. LinearDiffuser

class BasicRt(clock, grid, **kwargs)

Bases: terrainbento.base_class.two_lithology_erosion_model.TwoLithologyErosionModel

BasicRt model program.

This model program improves upon the Basic program by allowing for two lithologies, an “upper” layer and a “lower” layer. Given a spatially varying contact zone elevation, \(\eta_C(x,y))\), model BasicRt evolves a topographic surface described by \(\eta\) with the following governing equations:

\[ \begin{align}\begin{aligned}\frac{\partial \eta}{\partial t} = - K(\eta,\eta_C) Q^{m}S^{n} + D\nabla^2 \eta\\K(\eta, \eta_C ) = w K_1 + (1 - w) K_2\\w = \frac{1}{1+\exp \left( -\frac{(\eta -\eta_C )}{W_c}\right)}\end{aligned}\end{align} \]

where \(Q\) is the local stream discharge, \(S\) is the local slope, \(W_c\) is the contact-zone width, \(K_1\) and \(K_2\) are the erodabilities of the upper and lower lithologies, and \(D\) is the regolith transport parameter. \(m\) and \(n\) are the discharge and slope exponent parameters. \(w\) is a weight used to calculate the effective erodibility \(K(\eta, \eta_C)\) based on the depth to the contact zone and the width of the contact zone.

The weight \(w\) 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 \(K_1\) and \(K_2\); above and below the contact, the erodibility approaches the value of \(K_1\) and \(K_2\) 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) 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

__init__(clock, grid, **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 (\(m\)). Default is 0.5.

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

• water_erodibility_upper (float, optional) – Water erodibility of the upper layer (\(K_{1}\)). Default is 0.001.

• water_erodibility_lower (float, optional) – Water erodibility of the upper layer (\(K_{2}\)). Default is 0.0001.

• contact_zone__width (float, optional) – Thickness of the contact zone (\(W_c\)). Default is 1.

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

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

Returns

BasicRt

Return type

model object

Examples

This is a minimal example to demonstrate how to construct an instance of model BasicRt. 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, BasicRt
>>> clock = Clock(start=0, stop=100, step=1)
>>> grid = RasterModelGrid((5,5))
>>> _ = random(grid, "topographic__elevation")
>>> _ = constant(grid, "lithology_contact__elevation", value=-10.)

Construct the model.

>>> model = BasicRt(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)

Advance model BasicRt 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. 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 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()

Executes model.