class BasicHySt

# Model BasicHySt¶

terrainbento Model BasicHySt program.

Erosion model program using linear diffusion for gravitational mass transport, and an entrainment-deposition law for water erosion and deposition. Discharge is calculated from drainage area, infiltration capacity (a parameter), and precipitation rate, which is a stochastic variable.

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

BasicHySt model program.

This model program that uses a stochastic treatment of runoff and discharge, and includes an erosion threshold in the water erosion law. It combines models BasicHy and BasicSt. The model evolves a topographic surface, $$\eta (x,y,t)$$, with the following governing equation:

\begin{align}\begin{aligned}\frac{\partial \eta}{\partial t} = \frac{V Q_s}{\hat{Q}} - K\hat{Q}^{m}S^{n} + D\nabla^2 \eta\\Q_s = \int_0^A \left(K(1-F_f)\hat{Q(A)}^{m}S^{n} - \frac{V Q_s}{\hat{Q}(A)}\right) dA\end{aligned}\end{align}

where $$\hat{Q}$$ is the local stream discharge (the hat symbol indicates that it is a random-in-time variable), $$S$$ is the local slope, $$A$$ is the local upstream drainage area, $$m$$ and $$n$$ are the discharge and slope exponent parameters, $$K$$ is the erodibility by water, $$V$$ is effective sediment settling velocity, $$Q_s$$ is volumetric sediment flux, $$r$$ is a runoff rate, and $$D$$ is the regolith transport efficiency.

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, settling_velocity=0.001, infiltration_capacity=1.0, fraction_fines=0.5, 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 ($$K_s$$). Default is 0.0001.

• nfiltration_capacity (float, optional) – Infiltration capacity ($$I_m$$). Default is 1.0.

• 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”.

• **kwargs – Keyword arguments to pass to StochasticErosionModel. These arguments control the discharge $$\hat{Q}$$.

Returns

BasicHySt

Return type

model object

Examples

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


Construct the model.

>>> model = BasicHySt(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 BasicHySt 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()[source]

Executes model.