landlab.components.lateral_erosion package#
Submodules#
landlab.components.lateral_erosion.lateral_erosion module#
Grid-based simulation of lateral erosion by channels in a drainage network.
ALangston
- class LateralEroder(*args, **kwds)[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 >>> mg.add_zeros("topographic__elevation", at="node") array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) >>> 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, ... ] ... ) >>> mg.at_node["topographic__elevation"] += ( ... mg.node_y / 10. + mg.node_x / 10. + 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:
’basic’ (default): explicit forward-time extrapolation. Simple but will become unstable if time step is too large or if bedrock erodibility is vry high.
’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:
’basic’ (default): explicit forward-time extrapolation. Simple but will become unstable if time step is too large or if bedrock erodibility is vry high.
’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.
landlab.components.lateral_erosion.node_finder module#
- angle_finder(grid, dn, cn, rn)[source]#
Find the interior angle between two vectors on a grid.
- Parameters:
- Returns:
Angle between vectors (in radians).
- Return type:
Examples
>>> import numpy as np >>> from landlab import RasterModelGrid >>> from landlab.components.lateral_erosion.node_finder import angle_finder
>>> grid = RasterModelGrid((3, 4)) >>> np.rad2deg(angle_finder(grid, 8, 5, 0)) 90.0 >>> np.rad2deg(angle_finder(grid, (8, 9, 10, 6), 5, 6)) array([ 135., 90., 45., 0.])
Module contents#
- class LateralEroder(*args, **kwds)[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 >>> mg.add_zeros("topographic__elevation", at="node") array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) >>> 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, ... ] ... ) >>> mg.at_node["topographic__elevation"] += ( ... mg.node_y / 10. + mg.node_x / 10. + 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:
’basic’ (default): explicit forward-time extrapolation. Simple but will become unstable if time step is too large or if bedrock erodibility is vry high.
’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:
’basic’ (default): explicit forward-time extrapolation. Simple but will become unstable if time step is too large or if bedrock erodibility is vry high.
’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.