
class
BasicDdVs
¶
Model BasicDdVs¶
terrainbento model BasicDdVs program.
Erosion model program using linear diffusion, stream power with a smoothed threshold that varies with incision depth, and discharge proportional to effective drainage area.
 Landlab components used:

class
BasicDdVs
(clock, grid, m_sp=0.5, n_sp=1.0, water_erodibility=0.0001, regolith_transport_parameter=0.1, water_erosion_rule__threshold=0.01, water_erosion_rule__thresh_depth_derivative=0.0, hydraulic_conductivity=0.1, **kwargs)[source]¶ Bases:
terrainbento.base_class.erosion_model.ErosionModel
BasicDdVs model program.
This model program combines
BasicDd
andBasicVs
. It evolves a topographic surface described by \(\eta\) with the following governing equations:\[ \begin{align}\begin{aligned}\frac{\partial \eta}{\partial t} = \left(KA_{eff}^{m}S^{n}  \omega_{ct}\left(1e^{KA_{eff}^{m}S^{n}/\omega_{ct}}\right)\right) + D\nabla^2 \eta\\A_{eff} = A \exp \left( \frac{\alpha S}{A}\right)\\\alpha = \frac{K_{sat} H dx}{R_m}\end{aligned}\end{align} \]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, and \(\omega_{ct}\) is the critical stream power needed for erosion to occur. \(\omega_{ct}\) changes through time as it increases with cumulative incision depth:
\[\omega_{ct}\left(x,y,t\right) = \mathrm{max}\left(\omega_c + b D_I\left(x, y, t\right), \omega_c \right)\]where \(\omega_c\) is the threshold when no incision has taken place, \(b\) is the rate at which the threshold increases with incision depth, and \(D_I\) is the cumulative incision depth at location \(\left(x,y\right)\) and time \(t\).
\(\alpha\) is the saturation area scale used for transforming area into effective area. 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 atnode 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, water_erosion_rule__threshold=0.01, water_erosion_rule__thresh_depth_derivative=0.0, 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.
water_erosion_rule__threshold (float, optional) – Erosion rule threshold when no erosion has occured (\(\omega_c\)). Default is 0.01.
water_erosion_rule__thresh_depth_derivative (float, optional) – Rate of increase of water erosion threshold as increased incision occurs (\(b\)). Default is 0.0.
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
BasicDdVs
 Return type
model object
Examples
This is a minimal example to demonstrate how to construct an instance of model BasicVs. For more detailed examples, including steadystate 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, BasicDdVs >>> clock = Clock(start=0, stop=100, step=1) >>> grid = RasterModelGrid((5,5)) >>> _ = random(grid, "topographic__elevation") >>> _ = random(grid, "soil__depth")
Construct the model.
>>> model = BasicDdVs(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 timestep of duration step.
The run_one_step method does the following:
Directs flow, accumulates drainage area, and calculates effective drainage area.
Assesses the location, if any, of flooded nodes where erosion should not occur.
Assesses if a
PrecipChanger
is an active boundary handler and if so, uses it to modify the erodibility by water.Calculates detachmentlimited erosion by water.
Calculates topographic change by linear diffusion.
Finalizes the step using the
ErosionModel
base class function finalize__run_one_step. This function updates all boundary handlers handlers bystep
and increments model time bystep
.
 Parameters
step (float) – Increment of time for which the model is run.