class BasicDd

Model BasicDd

terrainbento BasicDd model program.

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

Landlab components used:

1. FlowAccumulator

2. DepressionFinderAndRouter (optional)

3. StreamPowerSmoothThresholdEroder

4. LinearDiffuser

class BasicDd(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, water_erosion_rule__thresh_depth_derivative=0.0, **kwargs)

Bases: terrainbento.base_class.erosion_model.ErosionModel

BasicDd model program.

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

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

where \(Q\) is the local stream discharge and \(S\) 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 \(\omega_{ct}\) is the critical stream power needed for erosion to occur. \(\omega_{ct}\) changes through time as it increases with cumulative incision depth:

\[\omega_{ct}\left(x,y,t\right) = \mathrm{max}\left(\omega_c + b D_I\left(x, y, t\right), \omega_c \right)\]

where \(\omega_c\) is the threshold when no incision has taken place, \(b\) is the rate at which the threshold increases with incision depth, and \(D_I\) is the cumulative incision depth at location \(\left(x,y\right)\) and time \(t\).

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, water_erosion_rule__thresh_depth_derivative=0.0, **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 (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.

• water_erosion_rule__thresh_depth_derivative (float, optional) – Rate of increase of water erosion threshold as increased incision occurs (\(b\)). Default is 0.0.

• **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

BasicDd

Return type

model object

Examples

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

Construct the model.

>>> model = BasicDd(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 BasicDd 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.

update_erosion_threshold_values()

Update the erosion threshold at each node based on cumulative incision so far using:

\[\begin{split}\omega_{ct}\left(x,y,t\right) = \mathrm{max}\left(\omega_c + \\ b D_I\left(x, y, t\right), \omega_c \right)\end{split}\]

where \(\omega_c\) is the threshold when no incision has taken place, \(b\) is the rate at which the threshold increases with incision depth, and \(D_I\) is the cumulative incision depth at location \(\left(x,y\right)\) and time \(t\).

main()

Executes model.