landlab.components.lateral_erosion.lateral_erosion

Grid-based simulation of lateral erosion by channels in a drainage network.

ALangston

class LateralEroder[source]

Bases: Component

Laterally erode neighbor node through fluvial erosion.

Landlab component that finds a neighbor node to laterally erode and calculates lateral erosion. See the publication:

Langston, A.L., Tucker, G.T.: Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models. Earth Surface Dynamics, 6, 1-27, https://doi.org/10.5194/esurf-6-1-2018

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator, LateralEroder
>>> np.random.seed(2010)

Define grid and initial topography

  • 5x4 grid with baselevel in the lower left corner

  • All other boundary nodes closed

  • Initial topography is plane tilted up to the upper right with noise

>>> mg = RasterModelGrid((5, 4), xy_spacing=10.0)
>>> mg.set_status_at_node_on_edges(
...     right=mg.BC_NODE_IS_CLOSED,
...     top=mg.BC_NODE_IS_CLOSED,
...     left=mg.BC_NODE_IS_CLOSED,
...     bottom=mg.BC_NODE_IS_CLOSED,
... )
>>> mg.status_at_node[1] = mg.BC_NODE_IS_FIXED_VALUE
>>> rand_noise = np.array(
...     [
...         [0.00436992, 0.03225985, 0.03107455, 0.00461312],
...         [0.03771756, 0.02491226, 0.09613959, 0.07792969],
...         [0.08707156, 0.03080568, 0.01242658, 0.08827382],
...         [0.04475065, 0.07391732, 0.08221057, 0.02909259],
...         [0.03499337, 0.09423741, 0.01883171, 0.09967794],
...     ]
... ).flatten()
>>> mg.at_node["topographic__elevation"] = (
...     mg.node_y / 10.0 + mg.node_x / 10.0 + rand_noise
... )
>>> U = 0.001
>>> dt = 100

Instantiate flow accumulation and lateral eroder and run each for one step

>>> fa = FlowAccumulator(
...     mg,
...     surface="topographic__elevation",
...     flow_director="FlowDirectorD8",
...     runoff_rate=None,
...     depression_finder=None,
... )
>>> latero = LateralEroder(mg, latero_mech="UC", Kv=0.001, Kl_ratio=1.5)

Run one step of flow accumulation and lateral erosion to get the dzlat array needed for the next part of the test.

>>> fa.run_one_step()
>>> mg, dzlat = latero.run_one_step(dt)

Evolve the landscape until the first occurence of lateral erosion. Save arrays volume of lateral erosion and topographic elevation before and after the first occurence of lateral erosion

>>> while min(dzlat) == 0.0:
...     oldlatvol = mg.at_node["volume__lateral_erosion"].copy()
...     oldelev = mg.at_node["topographic__elevation"].copy()
...     fa.run_one_step()
...     mg, dzlat = latero.run_one_step(dt)
...     newlatvol = mg.at_node["volume__lateral_erosion"]
...     newelev = mg.at_node["topographic__elevation"]
...     mg.at_node["topographic__elevation"][mg.core_nodes] += U * dt
...

Before lateral erosion occurs, volume__lateral_erosion has values at nodes 6 and 10.

>>> np.around(oldlatvol, decimals=0)
array([ 0.,  0., 0., 0.,
        0.,  0., 79., 0.,
        0.,  0., 24., 0.,
        0.,  0., 0., 0.,
        0.,  0., 0., 0.])

After lateral erosion occurs at node 6, volume__lateral_erosion is reset to 0

>>> np.around(newlatvol, decimals=0)
array([ 0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,
        0.,  0., 24.,  0.,
        0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.])

After lateral erosion at node 6, elevation at node 6 is reduced by -1.41 (the elevation change stored in dzlat[6]). It is also provided as the at-node grid field lateral_erosion__depth_increment.

>>> np.around(oldelev, decimals=2)
array([0.  , 1.03, 2.03, 3.  ,
       1.04, 1.77, 2.45, 4.08,
       2.09, 2.65, 3.18, 5.09,
       3.04, 3.65, 4.07, 6.03,
       4.03, 5.09, 6.02, 7.1 ])

>>> np.around(newelev, decimals=2)
array([0.  , 1.03, 2.03, 3.  ,
       1.04, 1.77, 1.03, 4.08,
       2.09, 2.65, 3.18, 5.09,
       3.04, 3.65, 4.07, 6.03,
       4.03, 5.09, 6.02, 7.1 ])

>>> np.around(dzlat, decimals=2)
array([ 0.  ,  0.  ,  0.  ,  0.  ,
        0.  ,  0.  , -1.41,  0.  ,
        0.  ,  0.  ,  0.  ,  0.  ,
        0.  ,  0.  ,  0.  ,  0.  ,
        0.  ,  0.  ,  0.  ,  0. ])

References

Required Software Citation(s) Specific to this Component

Langston, A., Tucker, G. (2018). Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models. Earth Surface Dynamics 6(1), 1–27. https://dx.doi.org/10.5194/esurf-6-1-2018

Additional References

None Listed

Parameters:

  • grid (ModelGrid) – A Landlab square cell raster grid object

  • latero_mech (string, optional (defaults to UC)) – Lateral erosion algorithm, choices are “UC” for undercutting-slump model and “TB” for total block erosion

  • alph (float, optional (defaults to 0.8)) – Parameter describing potential for deposition, dimensionless

  • Kv (float, node array, or field name) – Bedrock erodibility in vertical direction, 1/years

  • Kl_ratio (float, optional (defaults to 1.0)) – Ratio of lateral to vertical bedrock erodibility, dimensionless

  • solver (string) –

    Solver options:

    1. ’basic’ (default): explicit forward-time extrapolation. Simple but will become unstable if time step is too large or if bedrock erodibility is vry high.

    2. ’adaptive’: subdivides global time step as needed to prevent slopes from reversing.

  • inlet_node (integer, optional) – Node location of inlet (source of water and sediment)

  • inlet_area (float, optional) – Drainage area at inlet node, must be specified if inlet node is “on”, m^2

  • qsinlet (float, optional) – Sediment flux supplied at inlet, optional. m3/year

  • flow_accumulator (Instantiated Landlab FlowAccumulator, optional) – When solver is set to “adaptive”, then a valid Landlab FlowAccumulator must be passed. It will be run within sub-timesteps in order to update the flow directions and drainage area.

__init__(grid, latero_mech='UC', alph=0.8, Kv=0.001, Kl_ratio=1.0, solver='basic', inlet_on=False, inlet_node=None, inlet_area=None, qsinlet=0.0, flow_accumulator=None)[source]
Parameters:

  • grid (ModelGrid) – A Landlab square cell raster grid object

  • latero_mech (string, optional (defaults to UC)) – Lateral erosion algorithm, choices are “UC” for undercutting-slump model and “TB” for total block erosion

  • alph (float, optional (defaults to 0.8)) – Parameter describing potential for deposition, dimensionless

  • Kv (float, node array, or field name) – Bedrock erodibility in vertical direction, 1/years

  • Kl_ratio (float, optional (defaults to 1.0)) – Ratio of lateral to vertical bedrock erodibility, dimensionless

  • solver (string) –

    Solver options:

    1. ’basic’ (default): explicit forward-time extrapolation. Simple but will become unstable if time step is too large or if bedrock erodibility is vry high.

    2. ’adaptive’: subdivides global time step as needed to prevent slopes from reversing.

  • inlet_node (integer, optional) – Node location of inlet (source of water and sediment)

  • inlet_area (float, optional) – Drainage area at inlet node, must be specified if inlet node is “on”, m^2

  • qsinlet (float, optional) – Sediment flux supplied at inlet, optional. m3/year

  • flow_accumulator (Instantiated Landlab FlowAccumulator, optional) – When solver is set to “adaptive”, then a valid Landlab FlowAccumulator must be passed. It will be run within sub-timesteps in order to update the flow directions and drainage area.

static __new__(cls, *args, **kwds)
cite_as = '\n    @article{langston2018developing,\n      author = {Langston, A. L. and Tucker, G. E.},\n      title = {{Developing and exploring a theory for the lateral erosion of\n      bedrock channels for use in landscape evolution models}},\n      doi = {10.5194/esurf-6-1-2018},\n      pages = {1---27},\n      number = {1},\n      volume = {6},\n      journal = {Earth Surface Dynamics},\n      year = {2018}\n    }\n    '
property coords

Return the coordinates of nodes on grid attached to the component.

property current_time

Current time.

Some components may keep track of the current time. In this case, the current_time attribute is incremented. Otherwise it is set to None.

Return type:

current_time

definitions = (('drainage_area', "Upstream accumulated surface area contributing to the node's discharge"), ('flow__receiver_node', 'Node array of receivers (node that receives flow from current node)'), ('flow__upstream_node_order', 'Node array containing downstream-to-upstream ordered list of node IDs'), ('lateral_erosion__depth_increment', 'Change in elevation at each node from lateral erosion during time step'), ('sediment__influx', 'Sediment flux (volume per unit time of sediment entering each node)'), ('topographic__elevation', 'Land surface topographic elevation'), ('topographic__steepest_slope', 'The steepest *downhill* slope'), ('volume__lateral_erosion', 'Array tracking volume eroded at each node from lateral erosion'))
classmethod from_path(grid, path)

Create a component from an input file.

Parameters:

  • grid (ModelGrid) – A landlab grid.

  • path (str or file_like) – Path to a parameter file, contents of a parameter file, or a file-like object.

Returns:

A newly-created component.

Return type:

Component

property grid

Return the grid attached to the component.

initialize_optional_output_fields()

Create fields for a component based on its optional field outputs, if declared in _optional_var_names.

This method will create new fields (without overwrite) for any fields output by the component as optional. New fields are initialized to zero. New fields are created as arrays of floats, unless the component also contains the specifying property _var_type.

initialize_output_fields(values_per_element=None)

Create fields for a component based on its input and output var names.

This method will create new fields (without overwrite) for any fields output by, but not supplied to, the component. New fields are initialized to zero. Ignores optional fields. New fields are created as arrays of floats, unless the component specifies the variable type.

Parameters:

values_per_element (int (optional)) – On occasion, it is necessary to create a field that is of size (n_grid_elements, values_per_element) instead of the default size (n_grid_elements,). Use this keyword argument to acomplish this task.

input_var_names = ('drainage_area', 'flow__receiver_node', 'flow__upstream_node_order', 'topographic__elevation', 'topographic__steepest_slope')
name = 'LateralEroder'
optional_var_names = ()
output_var_names = ('lateral_erosion__depth_increment', 'sediment__influx', 'topographic__elevation', 'volume__lateral_erosion')
run_one_step_adaptive(dt=1.0)[source]

Run time step with adaptive time stepping to prevent slope flattening.

run_one_step_basic(dt=1.0)[source]

Calculate vertical and lateral erosion for a time period ‘dt’.

Parameters:

dt (float) – Model timestep [T]

property shape

Return the grid shape attached to the component, if defined.

unit_agnostic = False
units = (('drainage_area', 'm**2'), ('flow__receiver_node', '-'), ('flow__upstream_node_order', '-'), ('lateral_erosion__depth_increment', 'm'), ('sediment__influx', 'm3/y'), ('topographic__elevation', 'm'), ('topographic__steepest_slope', '-'), ('volume__lateral_erosion', 'm3'))
classmethod var_definition(name)

Get a description of a particular field.

Parameters:

name (str) – A field name.

Returns:

A description of each field.

Return type:

tuple of (name, *description*)

classmethod var_help(name)

Print a help message for a particular field.

Parameters:

name (str) – A field name.

classmethod var_loc(name)

Location where a particular variable is defined.

Parameters:

name (str) – A field name.

Returns:

The location (‘node’, ‘link’, etc.) where a variable is defined.

Return type:

str

var_mapping = (('drainage_area', 'node'), ('flow__receiver_node', 'node'), ('flow__upstream_node_order', 'node'), ('lateral_erosion__depth_increment', 'node'), ('sediment__influx', 'node'), ('topographic__elevation', 'node'), ('topographic__steepest_slope', 'node'), ('volume__lateral_erosion', 'node'))
classmethod var_type(name)

Returns the dtype of a field (float, int, bool, str…).

Parameters:

name (str) – A field name.

Returns:

The dtype of the field.

Return type:

dtype

classmethod var_units(name)

Get the units of a particular field.

Parameters:

name (str) – A field name.

Returns:

Units for the given field.

Return type:

str