# DetachmentLtdErosion: Solve stream power equations, but without stability checks¶

Simulate detachment limited sediment transport.

Landlab component that simulates detachment limited sediment transport is more general than the stream power component. Doesn’t require the upstream node order, links to flow receiver and flow receiver fields. Instead, takes in the discharge values on NODES calculated by the OverlandFlow class and erodes the landscape in response to the output discharge.

As of right now, this component relies on the OverlandFlow component for stability. There are no stability criteria implemented in this class. To ensure model stability, use StreamPowerEroder or FastscapeEroder components instead.

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import DetachmentLtdErosion


Create a grid on which to calculate detachment ltd sediment transport.

>>> grid = RasterModelGrid((4, 5))


The grid will need some data to provide the detachment limited sediment transport component. To check the names of the fields that provide input to the detachment ltd transport component, use the input_var_names class property.

Create fields of data for each of these input variables.

>>> grid.at_node['topographic__elevation'] = np.array([
...     0., 0., 0., 0., 0.,
...     1., 1., 1., 1., 1.,
...     2., 2., 2., 2., 2.,
...     3., 3., 3., 3., 3.])


Using the set topography, now we will calculate slopes on all nodes.

>>> grid.at_node['topographic__slope'] = np.array([
...     -0.        , -0.        , -0.        , -0.        , -0,
...      0.70710678,  1.        ,  1.        ,  1.        ,  0.70710678,
...      0.70710678,  1.        ,  1.        ,  1.        ,  0.70710678,
...      0.70710678,  1.        ,  1.        ,  1.        ,  0.70710678])


Now we will arbitrarily add water discharge to each node for simplicity. >>> grid.at_node[‘surface_water__discharge’] = np.array([ … 30., 30., 30., 30., 30., … 20., 20., 20., 20., 20., … 10., 10., 10., 10., 10., … 5., 5., 5., 5., 5.])

Instantiate the DetachmentLtdErosion component to work on this grid, and run it. In this simple case, we need to pass it a time step (‘dt’)

>>> dt = 10.0
>>> dle = DetachmentLtdErosion(grid)
>>> dle.erode(dt=dt)


After calculating the erosion rate, the elevation field is updated in the grid. Use the output_var_names property to see the names of the fields that have been changed.

>>> dle.output_var_names
('topographic__elevation',)


The topographic__elevation field is defined at nodes.

>>> dle.var_loc('topographic__elevation')
'node'


Now we test to see how the topography changed as a function of the erosion rate.

>>> grid.at_node['topographic__elevation']
array([ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
0.99936754,  0.99910557,  0.99910557,  0.99910557,  0.99936754,
1.99955279,  1.99936754,  1.99936754,  1.99936754,  1.99955279,
2.99968377,  2.99955279,  2.99955279,  2.99955279,  2.99968377])

class DetachmentLtdErosion(grid, K_sp=2e-05, m_sp=0.5, n_sp=1.0, uplift_rate=0.0, entrainment_threshold=0.0, **kwds)[source]

Landlab component that simulates detachment-limited river erosion.

This component calculates changes in elevation in response to vertical incision.

Calculate detachment limited erosion rate on nodes.

Landlab component that generalizes the detachment limited erosion equation, primarily to be coupled to the the Landlab OverlandFlow component.

This component adjusts topographic elevation and is contained in the landlab.components.detachment_ltd_sed_trp folder.

Parameters
• grid (RasterModelGrid) – A landlab grid.

• K_sp (float, optional) – K in the stream power equation (units vary with other parameters - if used with the de Almeida equation it is paramount to make sure the time component is set to seconds, not years!)

• m_sp (float, optional) – Stream power exponent, power on discharge

• n_sp (float, optional) – Stream power exponent, power on slope

• uplift_rate (float, optional) – changes in topographic elevation due to tectonic uplift

• entrainment_threshold (float, optional) – threshold for sediment movement

__init__(grid, K_sp=2e-05, m_sp=0.5, n_sp=1.0, uplift_rate=0.0, entrainment_threshold=0.0, **kwds)[source]

Calculate detachment limited erosion rate on nodes.

Landlab component that generalizes the detachment limited erosion equation, primarily to be coupled to the the Landlab OverlandFlow component.

This component adjusts topographic elevation and is contained in the landlab.components.detachment_ltd_sed_trp folder.

Parameters
• grid (RasterModelGrid) – A landlab grid.

• K_sp (float, optional) – K in the stream power equation (units vary with other parameters - if used with the de Almeida equation it is paramount to make sure the time component is set to seconds, not years!)

• m_sp (float, optional) – Stream power exponent, power on discharge

• n_sp (float, optional) – Stream power exponent, power on slope

• uplift_rate (float, optional) – changes in topographic elevation due to tectonic uplift

• entrainment_threshold (float, optional) – threshold for sediment movement

erode(dt, elevs='topographic__elevation', discharge_cms='surface_water__discharge', slope='topographic__slope')[source]

Erode into grid topography.

For one time step, this erodes into the grid topography using the water discharge and topographic slope.

The grid field ‘topographic__elevation’ is altered each time step.

Parameters
• dt (float) – Time step.

• discharge_cms (str, optional) – Name of the field that represents discharge on the nodes, if from the de Almeida solution have units of cubic meters per second.

• slope (str, optional) – Name of the field that represent topographic slope on each node.