class BasicStVs

Model BasicStVs

terrainbento Model BasicStVs program.

Erosion model program using linear diffusion and stream power. Precipitation is modeled as a stochastic process. Discharge is calculated from precipitation using a simple variable source-area formulation.

Landlab components used:

  1. FlowAccumulator

  2. DepressionFinderAndRouter (optional)

  3. FastscapeEroder

  4. LinearDiffuser

  5. PrecipitationDistribution

class BasicStVs(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility=0.0001, regolith_transport_parameter=0.1, hydraulic_conductivity=0.1, **kwargs)[source]

Bases: terrainbento.base_class.stochastic_erosion_model.StochasticErosionModel

BasicStVs model program.

This model program uses a stochastic treatment of runoff and discharge, using a variable source area runoff generation model. It combines BasicSt and BasicVs. The model evolves a topographic surface, \(\eta (x,y,t)\), with the following governing equation:

\[\frac{\partial \eta}{\partial t} = -K_{q}\hat{Q}^{m}S^{n} + D\nabla^2 \eta\]

where \(\hat{Q}\) is the local stream discharge (the hat symbol indicates that it is a random-in-time variable) and \(S\) is the local slope gradient. \(m\) and \(n\) are the discharge and slope exponent, respectively, \(K\) is the erodibility by water, and \(D\) is the regolith transport parameter.

This model iterates through a sequence of storm and interstorm periods. Given a storm precipitation intensity \(P\), the discharge \(Q\). is calculated using:

\[Q = PA - T\lambda S [1 - \exp (-PA/T\lambda S) ]\]

where \(T = K_sH\) is the soil transmissivity, \(H\) is soil thickness, \(K_s\) is hydraulic conductivity, and \(\lambda\) is cell width.

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, 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.

  • infiltration_capacity (float, optional) – Infiltration capacity (\(I_m\)). Default is 1.0.

  • hydraulic_conductivity (float, optional) – Hydraulic conductivity (\(K_{sat}\)). Default is 0.1.

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

Returns

BasicStVs

Return type

model object

Examples

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

Construct the model.

>>> model = BasicStVs(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
calc_runoff_and_discharge()[source]

Calculate runoff rate and discharge; return runoff.

run_one_step(step)[source]

Advance model BasicStVs 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.