class BasicSa

Model BasicSa

terrainbento BasicSa model program.

Erosion model using depth-dependent linear diffusion with a soil layer, basic stream power, and discharge proportional to drainage area.

Landlab components used:

  1. FlowAccumulator

  2. DepressionFinderAndRouter (optional)

  3. FastscapeEroder

  4. DepthDependentDiffuser

  5. ExponentialWeatherer

class BasicSa(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility=0.0001, regolith_transport_parameter=0.1, soil_production__maximum_rate=0.001, soil_production__decay_depth=0.5, soil_transport_decay_depth=0.5, **kwargs)[source]

Bases: terrainbento.base_class.erosion_model.ErosionModel

BasicSa model program.

This model program explicitly resolves a soil layer. This soil layer is produced by weathering that decays exponentially with soil thickness and hillslope transport is soil-depth dependent. Given a spatially varying soil thickness \(H\) and a spatially varying bedrock elevation \(\eta_b\), model BasicSa evolves a topographic surface described by \(\eta\) with the following governing equations:

\[ \begin{align}\begin{aligned}\eta = \eta_b + H\\\frac{\partial H}{\partial t} = P_0 \exp (-H/H_s) - \delta (H) K A^{M} S^{N} - \nabla q_h\\\frac{\partial \eta_b}{\partial t} = -P_0 \exp (-H/H_s) - (1 - \delta (H) ) K Q^{m} S^{N}\\q_h = -D H^* \left[1-\exp \left( -\frac{H}{H_0} \right) \right] \nabla \eta\end{aligned}\end{align} \]

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 parameter, \(H\) is the regolith thickness, \(H_s\) is the sediment production decay depth, \(P_0\) is the maximum sediment production rate, and \(H_0\) is the sediment transport decay depth. \(q_s\) represents the hillslope sediment flux per unit width.

The function \(\delta (H)\) is used to indicate that water erosion will act on soil where it exists, and on the underlying lithology where soil is absent. To achieve this, \(\delta (H)\) is defined to equal 1 when \(H > 0\) (meaning soil is present), and 0 if \(H = 0\) (meaning the underlying parent material is exposed).

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, soil_production__maximum_rate=0.001, soil_production__decay_depth=0.5, soil_transport_decay_depth=0.5, **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.

  • soil_production__maximum_rate (float, optional) – Maximum rate of soil production (\(P_{0}\)). Default is 0.001.

  • soil_production__decay_depth (float, optional) – Decay depth for soil production (\(H_{s}\)). Default is 0.5.

  • soil_transport_decay_depth (float, optional) – Decay depth for soil transport (\(H_{0}\)). Default is 0.5.

  • **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

BasicSa

Return type

model object

Examples

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

Construct the model.

>>> model = BasicSa(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 BasicSa 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. Produces soil and calculates soil depth with exponential weathering.

  6. Calculates topographic change by depth-dependent 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()[source]

Executes model.