landlab.components.depth_dependent_diffusion.hillslope_depth_dependent_linear_flux¶

Created on Fri Apr 8 08:32:48 2016.

@author: RCGlade

class DepthDependentDiffuser[source]¶

Bases: Component

This component implements a depth and slope dependent linear diffusion rule in the style of Johnstone and Hilley (2014).

Hillslope sediment flux uses depth dependent component inspired by Johnstone and Hilley (2014). The flux \(q_s\) is given as:

\[q_s = - D S H^* (1.0 - exp( - H / H^*)\]

where \(D\) is is the diffusivity, \(S\) is the slope (defined as negative downward), \(H\) is the soil depth on links, and \(H^*\) is the soil transport decay depth.

This component will ignore soil thickness located at non-core nodes.

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import ExponentialWeatherer
>>> from landlab.components import DepthDependentDiffuser
>>> mg = RasterModelGrid((5, 5))
>>> soilTh = mg.add_zeros("soil__depth", at="node")
>>> z = mg.add_zeros("topographic__elevation", at="node")
>>> BRz = mg.add_zeros("bedrock__elevation", at="node")
>>> expweath = ExponentialWeatherer(mg)
>>> DDdiff = DepthDependentDiffuser(mg)
>>> expweath.calc_soil_prod_rate()
>>> np.allclose(mg.at_node["soil_production__rate"][mg.core_nodes], 1.0)
True
>>> DDdiff.run_one_step(2.0)
>>> np.allclose(mg.at_node["topographic__elevation"][mg.core_nodes], 0.0)
True
>>> np.allclose(mg.at_node["bedrock__elevation"][mg.core_nodes], -2.0)
True
>>> np.allclose(mg.at_node["soil__depth"][mg.core_nodes], 2.0)
True

Now with a slope:

>>> mg = RasterModelGrid((3, 5))
>>> soilTh = mg.add_zeros("soil__depth", at="node")
>>> z = mg.add_zeros("topographic__elevation", at="node")
>>> BRz = mg.add_zeros("bedrock__elevation", at="node")
>>> z += mg.node_x.copy()
>>> BRz += mg.node_x / 2.0
>>> soilTh[:] = z - BRz
>>> expweath = ExponentialWeatherer(mg)
>>> DDdiff = DepthDependentDiffuser(mg)
>>> expweath.calc_soil_prod_rate()
>>> np.allclose(
...     mg.at_node["soil_production__rate"][mg.core_nodes],
...     np.array([0.60653066, 0.36787944, 0.22313016]),
... )
True
>>> DDdiff.run_one_step(2.0)
>>> np.allclose(
...     mg.at_node["topographic__elevation"][mg.core_nodes],
...     np.array([1.47730244, 2.28949856, 3.17558975]),
... )
True
>>> np.allclose(
...     mg.at_node["bedrock__elevation"][mg.core_nodes],
...     np.array([-0.71306132, 0.26424112, 1.05373968]),
... )
True
>>> np.allclose(mg.at_node["soil__depth"], z - BRz)
True

Now, we’ll test that changing the transport decay depth behaves as expected.

>>> mg = RasterModelGrid((3, 5))
>>> soilTh = mg.add_zeros("soil__depth", at="node")
>>> z = mg.add_zeros("topographic__elevation", at="node")
>>> BRz = mg.add_zeros("bedrock__elevation", at="node")
>>> z += mg.node_x.copy() ** 0.5
>>> BRz = z.copy() - 1.0
>>> soilTh[:] = z - BRz
>>> expweath = ExponentialWeatherer(mg)
>>> DDdiff = DepthDependentDiffuser(mg, soil_transport_decay_depth=0.1)
>>> DDdiff.run_one_step(1)
>>> soil_decay_depth_point1 = mg.at_node["topographic__elevation"][mg.core_nodes]
>>> z[:] = 0
>>> z += mg.node_x.copy() ** 0.5
>>> BRz = z.copy() - 1.0
>>> soilTh[:] = z - BRz
>>> DDdiff = DepthDependentDiffuser(mg, soil_transport_decay_depth=1.0)
>>> DDdiff.run_one_step(1)
>>> soil_decay_depth_1 = mg.at_node["topographic__elevation"][mg.core_nodes]
>>> np.greater(soil_decay_depth_1[1], soil_decay_depth_point1[1])
False

References

Required Software Citation(s) Specific to this Component

Barnhart, K., Glade, R., Shobe, C., Tucker, G. (2019). Terrainbento 1.0: a Python package for multi-model analysis in long-term drainage basin evolution. Geoscientific Model Development 12(4), 1267–1297. https://dx.doi.org/10.5194/gmd-12-1267-2019

Additional References

Johnstone, S., Hilley, G. (2015). Lithologic control on the form of soil-mantled hillslopes Geology 43(1), 83-86. https://doi.org/10.1130/G36052.1

Parameters:

grid (ModelGrid) – Landlab ModelGrid object
linear_diffusivity (float) – Hillslope diffusivity, m**2/yr
soil_transport_decay_depth (float) – Characteristic transport soil depth, m

__init__(grid, linear_diffusivity=1.0, soil_transport_decay_depth=1.0)[source]¶

Parameters:

grid (ModelGrid) – Landlab ModelGrid object
linear_diffusivity (float) – Hillslope diffusivity, m**2/yr
soil_transport_decay_depth (float) – Characteristic transport soil depth, m

static __new__(cls, *args, **kwds)¶

cite_as = '\n @article{barnhart2019terrain,\n author = {Barnhart, Katherine R and Glade, Rachel C and Shobe, Charles M\n and Tucker, Gregory E},\n title = {{Terrainbento 1.0: a Python package for multi-model analysis in\n long-term drainage basin evolution}},\n doi = {10.5194/gmd-12-1267-2019},\n pages = {1267---1297},\n number = {4},\n volume = {12},\n journal = {Geoscientific Model Development},\n year = {2019},\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 = (('bedrock__elevation', 'elevation of the bedrock surface'), ('soil__depth', 'Depth of soil or weathered bedrock'), ('soil__flux', 'flux of soil in direction of link'), ('soil_production__rate', 'rate of soil production at nodes'), ('topographic__elevation', 'Land surface topographic elevation'), ('topographic__slope', 'gradient of the ground surface'))¶

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 = ('soil__depth', 'soil_production__rate', 'topographic__elevation')¶

name = 'DepthDependentDiffuser'¶

optional_var_names = ()¶

output_var_names = ('bedrock__elevation', 'soil__depth', 'soil__flux', 'topographic__elevation', 'topographic__slope')¶

run_one_step(dt)[source]¶

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

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

soilflux(dt)[source]¶

Calculate soil flux for a time period ‘dt’.

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

unit_agnostic = True¶

units = (('bedrock__elevation', 'm'), ('soil__depth', 'm'), ('soil__flux', 'm^2/yr'), ('soil_production__rate', 'm/yr'), ('topographic__elevation', 'm'), ('topographic__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 = (('bedrock__elevation', 'node'), ('soil__depth', 'node'), ('soil__flux', 'link'), ('soil_production__rate', 'node'), ('topographic__elevation', 'node'), ('topographic__slope', 'link'))¶

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