landlab.grid.gradients

Calculate gradients of quantities over links.

Gradient calculation functions

calc_grad_at_link(node_values[, out])	Calculate gradients of node values at links.
calc_diff_at_link(node_values[, out])	Calculate differences of node values over links.

calc_aspect_at_node(grid, slope_component_tuple=None, elevs='topographic__elevation', unit='degrees', ignore_closed_nodes=True)

Get array of aspect of a surface.

Calculates at returns the aspect of a surface. Aspect is returned as radians clockwise of north, unless input parameter units is set to ‘degrees’.

If slope_component_tuple is provided, i.e., (slope_x, slope_y), the aspect will be calculated from these data.

If it is not, it will be derived from elevation data at the nodes, which can either be a string referring to a grid field (default: ‘topographic__elevation’), or an nnodes-long numpy array of the values themselves.

If ignore_closed_nodes is False, all proximal elevation values will be used in the calculation. If True, only unclosed nodes are used.

Parameters:

• slope_component_tuple ((slope_x_array, slope_y_array) (optional)) – Tuple of components of slope in the x and y directions, defined on nodes, if already known. If not, provide elevs.

• elevs (str or array (optional)) – Node field name or node array of elevations. If slope_component_tuple is not provided, must be set, but unused otherwise.

• unit ({'degrees', 'radians'}) – Controls the unit that the aspect is returned as.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calc.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 4))
>>> z = mg.node_x**2 + mg.node_y**2
>>> mg.calc_aspect_at_node(elevs=z)
array([225.        ,  240.16585039,  255.2796318 ,  258.69006753,
       209.83414961,  225.        ,  243.54632481,  248.77808974,
       194.7203682 ,  206.45367519,  225.        ,  231.94498651,
       191.30993247,  201.22191026,  218.05501349,  225.        ])
>>> z = z.max() - z
>>> mg.calc_aspect_at_node(elevs=z)
array([45.        ,  60.16585039,  75.2796318 ,  78.69006753,
       29.83414961,  45.        ,  63.54632481,  68.77808974,
       14.7203682 ,  26.45367519,  45.        ,  51.94498651,
       11.30993247,  21.22191026,  38.05501349,  45.        ])

>>> mg = RasterModelGrid((4, 4), xy_spacing=(3.0, 2.0))
>>> z = mg.node_x**2 + mg.node_y**2
>>> mg.calc_aspect_at_node(elevs=z)
array([236.30993247,  247.52001262,  259.97326008,  262.40535663,
       220.75264634,  234.41577266,  251.13402374,  255.29210302,
       201.54258265,  215.47930877,  235.73541937,  242.24162456,
       196.69924423,  209.43534223,  229.19345757,  236.30993247])

Note that a small amount of asymmetry arises at the grid edges due to the “missing” nodes beyond the edge of the grid.

calc_diff_at_link(node_values, out=None)

Calculate differences of node values over links.

Calculates the difference in quantity node_values at each link in the grid.

Parameters:

• node_values (ndarray or field name) – Values at grid nodes.

• out (ndarray, optional) – Buffer to hold the result.

Returns:

Differences across links.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> rmg = RasterModelGrid((3, 3))
>>> z = np.zeros(9)
>>> z[4] = 1.0
>>> rmg.calc_diff_at_link(z)
array([ 0.,  0.,  0.,  1.,  0.,  1., -1.,  0., -1.,  0.,  0.,  0.])

calc_grad_at_link(node_values, out=None)

Calculate gradients of node values at links.

Calculates the gradient in node_values at each link in the grid, returning an array of length number_of_links.

Parameters:

• node_values (ndarray or field name (x number of nodes)) – Values at grid nodes.

• out (ndarray, optional (x number of links)) – Buffer to hold the result.

Returns:

Gradients across active links.

Return type:

ndarray

Examples

>>> from landlab import RasterModelGrid
>>> rg = RasterModelGrid((3, 4), xy_spacing=10.0)
>>> z = rg.add_zeros("topographic__elevation", at="node")
>>> z[5] = 50.0
>>> z[6] = 36.0
>>> calc_grad_at_link(rg, z)  # there are 17 links
array([ 0. ,  0. ,  0. ,  0. ,  5. ,  3.6,  0. ,  5. , -1.4, -3.6,  0. ,
       -5. , -3.6,  0. ,  0. ,  0. ,  0. ])

>>> from landlab import HexModelGrid
>>> hg = HexModelGrid((3, 3), spacing=10.0)
>>> z = hg.add_zeros("topographic__elevation", at="node", clobber=True)
>>> z[4] = 50.0
>>> z[5] = 36.0
>>> calc_grad_at_link(hg, z)  # there are 11 faces
array([ 0. ,  0. ,  0. ,  5. ,  5. ,  3.6,  3.6,  0. ,  5. , -1.4, -3.6,
        0. , -5. , -5. , -3.6, -3.6,  0. ,  0. ,  0. ])

calc_grad_at_patch(grid, elevs='topographic__elevation', ignore_closed_nodes=True, unit_normal=None, slope_magnitude=None)

Calculate the components of the gradient at each patch.

If ignore_closed_nodes is True, closed nodes do not affect gradient calculations. If a closed node is present in a patch, the patch gradient is set to zero in both x and y directions.

Parameters:

• elevs (str or ndarray, optional) – Field name or array of node values.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calc.

• unit_normal (array with shape (num_patches, 3) (optional)) – The unit normal vector to each patch, if already known.

• slope_magnitude (array with size num_patches (optional)) – The slope of each patch, if already known.

Returns:

gradient_tuple – Len-2 tuple of arrays giving components of gradient in the x and y directions, in the units of units.

Return type:

(x_component_at_patch, y_component_at_patch)

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_y
>>> (x_grad, y_grad) = mg.calc_grad_at_patch(elevs=z)
>>> np.allclose(y_grad, np.pi / 4.0)
True
>>> np.allclose(x_grad, 0.0)
True

calc_slope_at_node(grid, elevs='topographic__elevation', method='patch_mean', ignore_closed_nodes=True, return_components=False, **kwds)

Array of slopes at nodes, averaged over neighboring patches.

Produces a value for node slope (i.e., mean gradient magnitude) at each node in a manner analogous to a GIS-style slope map. It averages the gradient on each of the patches surrounding the node, creating a value for node slope that better incorporates nonlocal elevation information. Directional information can still be returned through use of the return_components keyword.

Note that under these definitions, it is not always true that:

mag, cmp = mg.calc_slope_at_node(z)
mag**2 == cmp[0] ** 2 + cmp[1] ** 2  # not always true

If ignore_closed_nodes is False, all proximal elevation values will be used in the calculation. If True, only unclosed nodes are used.

Parameters:

• elevs (str or ndarray, optional) – Field name or array of node values.

• method ({'patch_mean', 'Horn'}) – By equivalence to the raster version, 'patch_mean' returns a scalar mean on the patches; 'Horn' returns a vector mean on the patches.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calculation.

• return_components (bool) – If True, return a tuple, (array_of_magnitude, (array_of_slope_x_radians, array_of_slope_y_radians)). If False, return an array of floats of the slope magnitude.

Returns:

If return_components, returns (array_of_magnitude, (array_of_slope_x_radians, array_of_slope_y_radians)). If not return_components, returns an array of slope magnitudes.

Return type:

float array or length-2 tuple of float arrays

Examples

>>> import numpy as np
>>> from landlab import RadialModelGrid, RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_x
>>> slopes = mg.calc_slope_at_node(elevs=z)
>>> np.allclose(slopes, 45.0 / 180.0 * np.pi)
True

>>> mg = RasterModelGrid((4, 5))
>>> z = -mg.node_y
>>> slope_mag, cmp = mg.calc_slope_at_node(elevs=z, return_components=True)
>>> np.allclose(slope_mag, np.pi / 4.0)
True
>>> np.allclose(cmp[0], 0.0)
True
>>> np.allclose(cmp[1], -np.pi / 4.0)
True

>>> mg = RadialModelGrid(n_rings=3)
>>> z = mg.radius_at_node
>>> slope_at_node = np.round(mg.calc_slope_at_node(elevs=z), decimals=5)

>>> nodes_at_ring = [
...     np.where(np.isclose(mg.radius_at_node, radius)) for radius in range(3)
... ]
>>> slope_at_node[nodes_at_ring[0]]
array([0.85707])
>>> slope_at_node[nodes_at_ring[1]]
array([0.79417,  0.79417,  0.79417,  0.79417,  0.79417,  0.79417])
>>> slope_at_node[nodes_at_ring[2]]
array([0.77542,  0.78453,  0.78453,  0.77542,  0.77542,  0.78453,
       0.78453,  0.77542,  0.77542,  0.78453,  0.78453,  0.77542])

calc_slope_at_patch(grid, elevs='topographic__elevation', ignore_closed_nodes=True, unit_normal=None)

Calculate the slope (positive magnitude of gradient) at patches.

If ignore_closed_nodes is True, closed nodes do not affect slope calculations. If a closed node is present in a patch, the patch slope is set to zero.

Parameters:

• elevs (str or ndarray, optional) – Field name or array of node values.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calc.

• unit_normal (array with shape (num_patches, 3) (optional)) – The unit normal vector to each patch, if already known.

Returns:

slopes_at_patch – The slope (positive gradient magnitude) of each patch.

Return type:

n_patches-long array

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_x
>>> S = mg.calc_slope_at_patch(elevs=z)
>>> S.size == mg.number_of_patches
True
>>> np.allclose(S, np.pi / 4.0)
True

calc_unit_normal_at_patch(grid, elevs='topographic__elevation')

Calculate and return the unit normal vector <a, b, c> to a patch.

Parameters:

elevs (str or ndarray, optional) – Field name or array of node values.

Returns:

nhat – The unit normal vector <a, b, c> to each patch.

Return type:

num-patches x length-3 array

Examples

>>> from landlab import HexModelGrid
>>> mg = HexModelGrid((3, 3))
>>> z = mg.node_x * 3.0 / 4.0
>>> mg.calc_unit_normal_at_patch(z)
array([[-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8],
       [-0.6,  0. ,  0.8]])