class BasicHySa

Model BasicHySa

terrainbento model BasicHySa program.

Erosion model program using exponential weathering, soil-depth-dependent linear diffusion, stream-power-driven sediment erosion, mass conservation, and bedrock erosion, and discharge proportional to drainage area.

Landlab components used:

1. FlowAccumulator

2. DepressionFinderAndRouter (optional)

3. Space

4. DepthDependentDiffuser

5. ExponentialWeatherer

class BasicHySa(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility_sediment=0.001, water_erodibility_rock=0.0001, regolith_transport_parameter=0.1, settling_velocity=0.001, sediment_porosity=0.3, fraction_fines=0.5, roughness__length_scale=0.5, solver='basic', soil_production__maximum_rate=0.001, soil_production__decay_depth=0.5, soil_transport_decay_depth=0.5, sp_crit_br=0, sp_crit_sed=0, **kwargs)

Bases: terrainbento.base_class.erosion_model.ErosionModel

BasicHySa program.

This model program combines BasicHy and BasicSa to evolve a topographic surface described by \(\eta\) with the following governing equation:

\[ \begin{align}\begin{aligned}\eta = \eta_b + H\\\frac{\partial H}{\partial t} = P_0 \exp (-H/H_s) + \frac{V_s Q_s}{Q(A)\left(1 - \phi \right)} - K_s Q(A)^{m}S^{n} (1 - e^{-H/H_*}) -\nabla q_h\\\frac{\partial \eta_b}{\partial t} = -P_0 \exp (-H/H_s) - K_r Q(A)^{m}S^{n} e^{-H/H_*}\\Q_s = \int_0^A \left(K_s Q(A)^{m}S^{n} (1-e^{-H/H_*}) + K_r (1-F_f) Q(A)^{m}S^{n} e^{-H/H_*} - \frac{V_s Q_s}{Q(A)}\right) dA\end{aligned}\end{align} \]

where \(\eta_b\) is the bedrock elevation, \(H\) is the soil depth, \(P_0\) is the maximum soil production rate, \(H_s\) is the soil production decay depth, \(V_s\) is effective sediment settling velocity, \(Q_s\) is volumetric fluvial sediment flux, \(A\) is the local drainage area, \(Q\), is the local discharge, \(S\) is the local slope, \(\phi\) is sediment porosity, \(F_f\) is the fraction of fine sediment, \(K_r\) and \(K_s\) are rock and sediment erodibility respectively, \(m\) and \(n\) are the discharge and slope exponent parameters, \(H_*\) is the bedrock roughness length scale, and \(r\) is a runoff rate. Hillslope sediment flux per unit width \(q_h\) is given by:

\[q_h = -D H^* \left[1-\exp \left( -\frac{H}{H_0} \right) \right] \nabla \eta.\]

where \(D\) is soil diffusivity and \(H_0\) is the soil transport depth scale.

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_sediment=0.001, water_erodibility_rock=0.0001, regolith_transport_parameter=0.1, settling_velocity=0.001, sediment_porosity=0.3, fraction_fines=0.5, roughness__length_scale=0.5, solver='basic', soil_production__maximum_rate=0.001, soil_production__decay_depth=0.5, soil_transport_decay_depth=0.5, sp_crit_br=0, sp_crit_sed=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.

• settling_velocity (float, optional) – Normalized settling velocity of entrained sediment (\(V_s\)). Default is 0.001.

• sediment_porosity (float, optional) – Sediment porosity (\(\phi\)). Default is 0.3.

• fraction_fines (float, optional) – Fraction of fine sediment that is permanently detached (\(F_f\)). Default is 0.5.

• roughness__length_scale (float, optional) – Bedrock roughness length scale. Default is 0.5.

• solver (str, optional) –

  Solver option to pass to the Landlab Space component. Default is “basic”.

• 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

BasicHySa

Return type

model object

Examples

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

Construct the model.

>>> model = BasicHySa(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

check_stability()

Check model stability and exit if unstable.

run_one_step(step)

Advance model BasicHySa 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 erosion and deposition 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.

main()

Executes model.