chi_intercept and chi_gradient: \(\chi-z\) fit metrics

chi_gradient(chi_finder)

Return the slope to a linear fit through a \(\chi\)-z plot.

This is a loose wrapper around the Landlab function ChiFinder.best_fit_chi_elevation_gradient_and_intercept.

Parameters

chi_finder (an instance of a ChiFinder) –

Returns

out – The slope value.

Return type

float

Examples

First an example that only uses the chi_gradient function.

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator, ChiFinder
>>> from umami.calculations import chi_intercept
>>> grid = RasterModelGrid((10, 10))
>>> z = grid.add_zeros("node", "topographic__elevation")
>>> z += grid.x_of_node**2 + grid.y_of_node**2
>>> fa = FlowAccumulator(grid)
>>> fa.run_one_step()
>>> cf = ChiFinder(grid, min_drainage_area=1.0)
>>> cf.calculate_chi()
>>> np.round(chi_gradient(cf), decimals=0)
23.0

Next, the same calculations are shown as part of an umami Metric.

>>> from io import StringIO
>>> from umami import Metric
>>> grid = RasterModelGrid((10, 10))
>>> z = grid.add_zeros("node", "topographic__elevation")
>>> z += grid.x_of_node**2 + grid.y_of_node**2
>>> file_like=StringIO('''
... cg:
...     _func: chi_gradient
... ''')
>>> metric = Metric(grid, chi_finder_kwds={"min_drainage_area": 1.0})
>>> metric.add_from_file(file_like)
>>> metric.names
['cg']
>>> metric.calculate()
>>> np.round(metric.values, decimals=0)
array([ 23.])

chi_intercept(chi_finder)

Return the intercept to a linear fit through a \(\chi\)-z plot.

This is a loose wrapper around the Landlab function ChiFinder.best_fit_chi_elevation_gradient_and_intercept.

Parameters

chi_finder (an instance of a ChiFinder) –

Returns

out – The intercept value.

Return type

float

Examples

First an example that only uses the chi_intercept function.

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator, ChiFinder
>>> from umami.calculations import chi_intercept
>>> grid = RasterModelGrid((10, 10))
>>> z = grid.add_zeros("node", "topographic__elevation")
>>> z += grid.x_of_node**2 + grid.y_of_node**2
>>> fa = FlowAccumulator(grid)
>>> fa.run_one_step()
>>> cf = ChiFinder(grid, min_drainage_area=1.0)
>>> cf.calculate_chi()
>>> np.round(chi_intercept(cf), decimals=0)
-4.0

Next, the same calculations are shown as part of an umami Metric.

>>> from io import StringIO
>>> from umami import Metric
>>> grid = RasterModelGrid((10, 10))
>>> z = grid.add_zeros("node", "topographic__elevation")
>>> z += grid.x_of_node**2 + grid.y_of_node**2
>>> file_like=StringIO('''
... ci:
...     _func: chi_intercept
... ''')
>>> metric = Metric(grid, chi_finder_kwds={"min_drainage_area": 1.0})
>>> metric.add_from_file(file_like)
>>> metric.names
['ci']
>>> metric.calculate()
>>> np.round(metric.values, decimals=0)
array([-4.])