class BasicHyVs

# Model BasicHyVs¶

terrainbento model BasicThVs program.

Erosion model program using linear diffusion, stream-power-driven sediment erosion and mass conservation, and discharge proportional to effective drainage area.

Landlab components used:
class BasicHyVs(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility=0.0001, regolith_transport_parameter=0.1, settling_velocity=0.001, fraction_fines=0.5, hydraulic_conductivity=0.1, solver='basic', **kwargs)[source]

BasicHyVs model program.

This model program combines BasicHy and BasicVs to evolves a topographic surface described by $$\eta$$ with the following governing equations:

\begin{align}\begin{aligned}\frac{\partial \eta}{\partial t} = -\left(KQ(A)^{m}S^{n} - \omega_c\left(1-e^{-KQ(A)^{m}S^{n}/\omega_c}\right)\right) + V\frac{Q_s}{Q(A)} + D\nabla^2 \eta\\Q_s = \int_0^A \left(KQ(A)^{m}S^{n} - \frac{V Q_s}{Q(A)} \right) dA\\Q = 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, $$\omega_c$$ is the critical stream power needed for erosion to occur, $$V$$ is effective sediment settling velocity, $$Q_s$$ is volumetric sediment flux, and $$D$$ is the regolith transport efficiency.

$$\alpha$$ is the saturation area scale used for transforming area into effective area $$A_{eff}$$ (used as discharge). 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, settling_velocity=0.001, fraction_fines=0.5, hydraulic_conductivity=0.1, solver='basic', **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.

• settling_velocity (float, optional) – Settling velocity of entrained sediment ($$V$$). Default is 0.001.

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

• solver (str, optional) – Solver option to pass to the Landlab ErosionDeposition component. Default is “basic”.

• 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

BasicHyVs

Return type

model object

Examples

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


Construct the model.

>>> model = BasicHyVs(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 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.