User guide and example for the Landlab threshold_eroder component¶

This notebook provides a brief introduction and user’s guide for the threshold eroder component for landscape evolution modeling.

Threshold eroder that cuts off slopes at a given threshold slope (\(Sc\)) and assumes material to dissolve away with

\[S(S>Sc) \rightarrow Sc\]

where S is the topographic slope and \(Sc\) represents a set threshold slope

Threshold eroder with regular grid¶

[ ]:

import numpy as np

from landlab import RasterModelGrid
from landlab.components import PriorityFloodFlowRouter, ThresholdEroder

mg = RasterModelGrid((5, 5))
mg.set_closed_boundaries_at_grid_edges(False, False, False, False)
z = np.array(
    [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0]
    + [0.0, 1.0, 10.0, 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 Threshold Eroder
fdir = PriorityFloodFlowRouter(mg)
th_ero = ThresholdEroder(mg, slope_crit=0.6)

# Run the components for ten short timepsteps
for t in range(2):
    fdir.run_one_step()
    th_ero.run_one_step()

# Check final topography

np.allclose(
    mg.at_node["topographic__elevation"],
    np.array(
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.6, 0.6, 0.6, 0.0]
        + [0.0, 0.6, 1.2, 0.6, 0.0, 0.0, 0.6, 0.6, 0.6, 0.0]
        + [0.0, 0.0, 0.0, 0.0, 0.0]
    ),
)

Threshold eroder with regular grid using a bedrock and soil field¶

[ ]:

mg = RasterModelGrid((5, 5))
mg.set_closed_boundaries_at_grid_edges(False, False, False, False)
z = np.array(
    [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0]
    + [0.0, 1.0, 10.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0]
    + [0.0, 0.0, 0.0, 0.0, 0.0]
)
topo = mg.add_zeros("topographic__elevation", at="node")
bed = mg.add_field("bedrock__elevation", z, at="node")
soil = mg.add_ones("soil__depth", at="node")
soil[mg.boundary_nodes] = 0
topo[:] = soil + bed

# Instantiate Flow director (steepest slope type) and Threshold Eroder
fdir = PriorityFloodFlowRouter(mg)
th_ero = ThresholdEroder(mg, slope_crit=0.6)

# Run the components for ten short timepsteps

for t in range(2):
    fdir.run_one_step()
    th_ero.run_one_step()

# Check final topography

np.allclose(
    mg.at_node["topographic__elevation"],
    np.array(
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.6, 0.6, 0.6, 0.0]
        + [0.0, 0.6, 1.2, 0.6, 0.0, 0.0, 0.6, 0.6, 0.6, 0.0]
        + [0.0, 0.0, 0.0, 0.0, 0.0]
    ),
)

Threshold eroder with hexagonal grid¶

[ ]:

import numpy as np

from landlab import HexModelGrid
from landlab.components import FlowAccumulator, FlowDirectorSteepest, ThresholdEroder
from landlab.plot.imshow import imshow_grid

hmg = HexModelGrid((8, 8))

topo = hmg.add_zeros("topographic__elevation", at="node")
topo[hmg.core_nodes] += 100

# Instantiate Flow director (steepest slope type) and Threshold Eroder
fdir = FlowDirectorSteepest(hmg)
fa = FlowAccumulator(hmg)
th_ero = ThresholdEroder(hmg, slope_crit=0.6)

# Run the components for ten short timepsteps
for t in range(5):
    fdir.run_one_step()
    fa.run_one_step()
    th_ero.run_one_step()
imshow_grid(hmg, "topographic__elevation")

np.allclose(
    hmg.at_node["topographic__elevation"],
    np.array(
        [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.6, 0.6, 0.6, 0.6, 0.6]
        + [0.6, 0.6, 0.0, 0.0, 0.6, 1.2, 1.2, 1.2, 1.2, 1.2, 1.2, 0.6, 0.0, 0.0]
        + [0.6, 1.2, 1.8, 1.8, 1.8, 1.8, 1.8, 1.2, 0.6, 0.0, 0.0, 0.6, 1.2, 1.8]
        + [1.8, 1.8, 1.8, 1.8, 1.8, 1.2, 0.6, 0.0, 0.0, 0.6, 1.2, 1.2, 1.2, 1.2]
        + [1.2, 1.2, 1.2, 0.6, 0.0, 0.0, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6, 0.6]
        + [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
    ),
)

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