"""Landlab component that simulates detachment-limited river erosion.
This component calculates changes in elevation in response to
vertical incision.
"""
import numpy as np
from landlab import Component
[docs]
class DetachmentLtdErosion(Component):
"""Simulate detachment limited sediment transport.
Landlab component that simulates detachment limited sediment transport is more
general than the stream power component. Doesn't require the upstream node
order, links to flow receiver and flow receiver fields. Instead, takes in
the discharge values on NODES calculated by the OverlandFlow class and
erodes the landscape in response to the output discharge.
As of right now, this component relies on the OverlandFlow component
for stability. There are no stability criteria implemented in this class.
To ensure model stability, use StreamPowerEroder or FastscapeEroder
components instead.
.. codeauthor:: Jordan Adams
Examples
--------
>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import DetachmentLtdErosion
Create a grid on which to calculate detachment ltd sediment transport.
>>> grid = RasterModelGrid((4, 5))
The grid will need some data to provide the detachment limited sediment
transport component. To check the names of the fields that provide input to
the detachment ltd transport component, use the *input_var_names* class
property.
Create fields of data for each of these input variables.
>>> grid.at_node["topographic__elevation"] = [
... [0.0, 0.0, 0.0, 0.0, 0.0],
... [1.0, 1.0, 1.0, 1.0, 1.0],
... [2.0, 2.0, 2.0, 2.0, 2.0],
... [3.0, 3.0, 3.0, 3.0, 3.0],
... ]
Using the set topography, now we will calculate slopes on all nodes.
>>> grid.at_node["topographic__slope"] = [
... [0.0, 0.0, 0.0, 0.0, 0.0],
... [0.70710678, 1.0, 1.0, 1.0, 0.70710678],
... [0.70710678, 1.0, 1.0, 1.0, 0.70710678],
... [0.70710678, 1.0, 1.0, 1.0, 0.70710678],
... ]
Now we will arbitrarily add water discharge to each node for simplicity.
>>> grid.at_node["surface_water__discharge"] = [
... [30.0, 30.0, 30.0, 30.0, 30.0],
... [20.0, 20.0, 20.0, 20.0, 20.0],
... [10.0, 10.0, 10.0, 10.0, 10.0],
... [5.0, 5.0, 5.0, 5.0, 5.0],
... ]
Instantiate the `DetachmentLtdErosion` component to work on this grid, and
run it. In this simple case, we need to pass it a time step ('dt')
>>> dt = 10.0
>>> dle = DetachmentLtdErosion(grid)
>>> dle.run_one_step(dt=dt)
After calculating the erosion rate, the elevation field is updated in the
grid. Use the *output_var_names* property to see the names of the fields that
have been changed.
>>> dle.output_var_names
('topographic__elevation',)
The `topographic__elevation` field is defined at nodes.
>>> dle.var_loc("topographic__elevation")
'node'
Now we test to see how the topography changed as a function of the erosion
rate.
>>> grid.at_node["topographic__elevation"].reshape(grid.shape)
array([[ 0. , 0. , 0. , 0. , 0. ],
[ 0.99936754, 0.99910557, 0.99910557, 0.99910557, 0.99936754],
[ 1.99955279, 1.99936754, 1.99936754, 1.99936754, 1.99955279],
[ 2.99968377, 2.99955279, 2.99955279, 2.99955279, 2.99968377]])
References
----------
**Required Software Citation(s) Specific to this Component**
None Listed
**Additional References**
Howard, A. (1994). A detachment-limited model of drainage basin evolution. Water
Resources Research 30(7), 2261-2285. https://dx.doi.org/10.1029/94wr00757
"""
_name = "DetachmentLtdErosion"
_unit_agnostic = True
_info = {
"surface_water__discharge": {
"dtype": float,
"intent": "in",
"optional": False,
"units": "m**3/s",
"mapping": "node",
"doc": "Volumetric discharge of surface water",
},
"topographic__elevation": {
"dtype": float,
"intent": "inout",
"optional": False,
"units": "m",
"mapping": "node",
"doc": "Land surface topographic elevation",
},
"topographic__slope": {
"dtype": float,
"intent": "in",
"optional": True,
"units": "-",
"mapping": "node",
"doc": "gradient of the ground surface",
},
}
[docs]
def __init__(
self,
grid,
K_sp=0.00002,
m_sp=0.5,
n_sp=1.0,
uplift_rate=0.0,
entrainment_threshold=0.0,
slope="topographic__slope",
):
"""Calculate detachment limited erosion rate on nodes.
Landlab component that generalizes the detachment limited erosion
equation, primarily to be coupled to the the Landlab OverlandFlow
component.
This component adjusts topographic elevation.
Parameters
----------
grid : RasterModelGrid
A landlab grid.
K_sp : float, optional
K in the stream power equation (units vary with other parameters -
if used with the de Almeida equation it is paramount to make sure
the time component is set to *seconds*, not *years*!)
m_sp : float, optional
Stream power exponent, power on discharge
n_sp : float, optional
Stream power exponent, power on slope
uplift_rate : float, optional
changes in topographic elevation due to tectonic uplift
entrainment_threshold : float, optional
threshold for sediment movement
slope : str
Field name of an at-node field that contains the slope.
"""
super().__init__(grid)
assert slope in grid.at_node
self._K = K_sp
self._m = m_sp
self._n = n_sp
self._I = self._grid.zeros(at="node") # noqa: E741
self._uplift_rate = uplift_rate
self._entrainment_threshold = entrainment_threshold
self._dzdt = self._grid.zeros(at="node")
[docs]
def run_one_step(self, dt):
"""Erode into grid topography.
For one time step, this erodes into the grid topography using
the water discharge and topographic slope.
The grid field 'topographic__elevation' is altered each time step.
Parameters
----------
dt : float
Time step.
"""
S = self._grid.at_node["topographic__slope"]
Q = self._grid.at_node["surface_water__discharge"]
Q_to_m = np.power(Q, self._m)
S_to_n = np.power(S, self._n)
self._I = (
self._K * Q_to_m * S_to_n
) - self._entrainment_threshold # noqa: E741
self._I[self._I < 0.0] = 0.0
self._dz = (self._uplift_rate - self._I) * dt
self._grid["node"]["topographic__elevation"] += self._dz