class BasicSaVs

Model BasicSaVs

terrainbento model BasicSaVs program.

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

Landlab components used:

  1. FlowAccumulator

  2. DepressionFinderAndRouter (optional)

  3. FastscapeEroder

  4. DepthDependentDiffuser

  5. ExponentialWeatherer

class BasicSaVs(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, hydraulic_conductivity=0.1, **kwargs)[source]

Bases: terrainbento.base_class.erosion_model.ErosionModel

BasicSaVs model program.

This model program combines BasicSa and BasicVs. Given a spatially varying soil thickness \(H\) and a spatially varying bedrock elevation \(\eta_b\), model BasicSaVs evolves a topographic surface described by \(\eta\) with the following governing equations:

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

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

\(\alpha\) 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, soil_production__maximum_rate=0.001, soil_production__decay_depth=0.5, soil_transport_decay_depth=0.5, hydraulic_conductivity=0.1, **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.

  • 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

BasicSaVs

Return type

model object

Examples

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

Construct the model.

>>> model = BasicSaVs(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 BasicVs 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 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.