landlab.components.transport_length_diffusion.transport_length_hillslope_diffusion¶

Created on Tue Apr 11 10:13:38 2017.

@author: margauxmouchene

class TransportLengthHillslopeDiffuser[source]¶

Bases: Component

Transport length hillslope diffusion.

Hillslope diffusion component in the style of Carretier et al. (2016, ESurf), and Davy and Lague (2009)

\[ \begin{align}\begin{aligned}\frac{dz}{dt} = -E + D (+ U)\\D = \frac{q_s}{L}\\E = k S\\L = \frac{dx}{(1 - (S / S_c)^2}\end{aligned}\end{align} \]

Works on regular raster-type grid (RasterModelGrid, dx=dy). To be coupled with FlowDirectorSteepest for the calculation of steepest slope at each timestep.

Component written by Margaux Mouchene, 2017

Parameters:

grid (ModelGrid) – Landlab ModelGrid object
erodibility (float) – Erodibility coefficient [L/T]
slope_crit (float (default=1.)) – Critical slope [L/L]

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowDirectorSteepest
>>> from landlab.components import TransportLengthHillslopeDiffuser

Define grid and initial topography:

3x5 grid

east and west boundaries are open, north and south are closed

Initial topography is plane at base level on the boundaries and 1m of elevation elsewhere (core)

>>> mg = RasterModelGrid((5, 5))
>>> mg.set_closed_boundaries_at_grid_edges(False, True, False, True)
>>> z = [
...     [0.0, 0.0, 0.0, 0.0, 0.0],
...     [0.0, 1.0, 1.0, 1.0, 0.0],
...     [0.0, 1.0, 1.0, 1.0, 0.0],
...     [0.0, 1.0, 1.0, 1.0, 0.0],
...     [0.0, 0.0, 0.0, 0.0, 0.0],
... ]
>>> _ = mg.add_field("topographic__elevation", z, at="node")

Instantiate Flow director (steepest slope type) and TL hillslope diffuser

>>> fdir = FlowDirectorSteepest(mg)
>>> tl_diff = TransportLengthHillslopeDiffuser(
...     mg, erodibility=0.001, slope_crit=0.6
... )

Run the components for ten short timepsteps

>>> for t in range(10):
...     fdir.run_one_step()
...     tl_diff.run_one_step(1.0)
...

Check final topography

>>> np.allclose(
...     mg.at_node["topographic__elevation"].reshape(mg.shape),
...     [
...         [0.0, 0.0, 0.0, 0.0, 0.0],
...         [0.0, 0.96175283, 0.99982519, 0.96175283, 0.0],
...         [0.0, 0.96175283, 0.99982519, 0.96175283, 0.0],
...         [0.0, 0.96175283, 0.99982519, 0.96175283, 0.0],
...         [0.0, 0.0, 0.0, 0.0, 0.0],
...     ],
... )
True

References

Required Software Citation(s) Specific to this Component

None Listed

Additional References

Carretier, S., Martinod, P., Reich, M., Godderis, Y. (2016). Modelling sediment clasts transport during landscape evolution. Earth Surface Dynamics 4(1), 237-251. https://dx.doi.org/10.5194/esurf-4-237-2016

Davy, P., Lague, D. (2009). Fluvial erosion/transport equation of landscape evolution models revisited. Journal of Geophysical Research 114(F3), F03007. https://dx.doi.org/10.1029/2008jf001146

Initialize Diffuser.

Parameters:

grid (ModelGrid) – Landlab ModelGrid object
erodibility (float) – Erodibility coefficient [L/T]
slope_crit (float (default=1.)) – Critical slope [L/L]

__init__(grid, erodibility=0.001, slope_crit=1.0)[source]¶

Initialize Diffuser.

Parameters:

grid (ModelGrid) – Landlab ModelGrid object
erodibility (float) – Erodibility coefficient [L/T]
slope_crit (float (default=1.)) – Critical slope [L/L]

static __new__(cls, *args, **kwds)¶

cite_as = ''¶

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 = (('flow__receiver_node', 'Node array of receivers (node that receives flow from current node)'), ('sediment__deposition_coeff', 'Fraction of incoming sediment that is deposited on the node'), ('sediment__deposition_rate', 'Deposition rate on node'), ('sediment__erosion_rate', 'Erosion rate on node'), ('sediment__flux_in', 'Incoming sediment rate on node (=qs/dx)'), ('sediment__flux_out', 'Outgoing sediment rate on node = sediment eroded on node + sediment transported across node from upstream'), ('sediment__transfer_rate', 'Rate of transferred sediment across a node (incoming sediment - deposited sediment on node)'), ('topographic__elevation', 'Land surface topographic elevation'), ('topographic__steepest_slope', 'The steepest *downhill* slope'))¶

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 = ('flow__receiver_node', 'topographic__elevation', 'topographic__steepest_slope')¶

name = 'TransportLengthHillslopeDiffuser'¶

optional_var_names = ()¶

output_var_names = ('sediment__deposition_coeff', 'sediment__deposition_rate', 'sediment__erosion_rate', 'sediment__flux_in', 'sediment__flux_out', 'sediment__transfer_rate', 'topographic__elevation')¶

run_one_step(dt)[source]¶

Advance one timestep.

Advance transport length-model hillslope diffusion component by one time step of size dt and tests for timestep stability.

Parameters:: dt (float (time)) – The imposed timestep.

property shape¶: Return the grid shape attached to the component, if defined.

tldiffusion(dt)[source]¶

Calculate hillslope diffusion for a time period ‘dt’.

Parameters:

grid (ModelGrid) – Landlab ModelGrid object
dt (float (time)) – The imposed timestep.

unit_agnostic = True¶

units = (('flow__receiver_node', '-'), ('sediment__deposition_coeff', '-'), ('sediment__deposition_rate', 'm/yr'), ('sediment__erosion_rate', 'm/yr'), ('sediment__flux_in', 'm/yr'), ('sediment__flux_out', 'm/yr'), ('sediment__transfer_rate', 'm/yr'), ('topographic__elevation', 'm'), ('topographic__steepest_slope', 'm/m'))¶

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 = (('flow__receiver_node', 'node'), ('sediment__deposition_coeff', 'node'), ('sediment__deposition_rate', 'node'), ('sediment__erosion_rate', 'node'), ('sediment__flux_in', 'node'), ('sediment__flux_out', 'node'), ('sediment__transfer_rate', 'node'), ('topographic__elevation', 'node'), ('topographic__steepest_slope', '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