#! /usr/bin/env python
"""Functions to calculate flow distance."""
import numpy as np
from landlab import FieldError
from landlab import RasterModelGrid
[docs]
def calculate_flow__distance(grid, add_to_grid=False, clobber=False):
"""Calculate the along flow distance from node to outlet.
This utility calculates the along flow distance based on the results of
running flow accumulation on the grid. It will use the connectivity
used by the FlowAccumulator (e.g. D4, D8, Dinf).
Parameters
----------
grid : ModelGrid
add_to_grid : boolean, optional
Flag to indicate if the stream length field should be added to the
grid. Default is False. The field name used is ``flow__distance``.
clobber : boolean, optional
Flag to indicate if adding the field to the grid should not clobber an
existing field with the same name. Default is False.
Returns
-------
flow__distance : float ndarray
The distance that has to be covered from an imaginary flow, located in
each node of the grid, to reach the watershed's outlet.
Examples
--------
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator
>>> from landlab.utils.flow__distance import calculate_flow__distance
>>> mg = RasterModelGrid((5, 4), xy_spacing=(1, 1))
>>> mg.at_node["topographic__elevation"] = [
... [0.0, 0.0, 0.0, 0.0],
... [0.0, 21.0, 10.0, 0.0],
... [0.0, 31.0, 20.0, 0.0],
... [0.0, 32.0, 30.0, 0.0],
... [0.0, 0.0, 0.0, 0.0],
... ]
>>> mg.set_closed_boundaries_at_grid_edges(
... bottom_is_closed=True,
... left_is_closed=True,
... right_is_closed=True,
... top_is_closed=True,
... )
>>> fr = FlowAccumulator(mg, flow_director="D8")
>>> fr.run_one_step()
>>> flow__distance = calculate_flow__distance(mg, add_to_grid=True, clobber=True)
>>> mg.at_node["flow__distance"]
array([0. , 0. , 0. , 0. ,
0. , 1. , 0. , 0. ,
0. , 1.41421356, 1. , 0. ,
0. , 2.41421356, 2. , 0. ,
0. , 0. , 0. , 0. ])
Now, let's change to D4 the flow_director method, which does not
consider diagonal links bewtween nodes.
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator
>>> from landlab.utils.flow__distance import calculate_flow__distance
>>> mg = RasterModelGrid((5, 4), xy_spacing=(1, 1))
>>> mg.at_node["topographic__elevation"] = [
... [0.0, 0.0, 0.0, 0.0],
... [0.0, 21.0, 10.0, 0.0],
... [0.0, 31.0, 20.0, 0.0],
... [0.0, 32.0, 30.0, 0.0],
... [0.0, 0.0, 0.0, 0.0],
... ]
>>> mg.set_closed_boundaries_at_grid_edges(
... bottom_is_closed=True,
... left_is_closed=True,
... right_is_closed=True,
... top_is_closed=True,
... )
>>> fr = FlowAccumulator(mg, flow_director="D4")
>>> fr.run_one_step()
>>> flow__distance = calculate_flow__distance(mg, add_to_grid=True, clobber=True)
>>> mg.at_node["flow__distance"]
array([0., 0., 0., 0.,
0., 1., 0., 0.,
0., 2., 1., 0.,
0., 3., 2., 0.,
0., 0., 0., 0.])
The flow__distance utility can also work on irregular grids. For the example we
will use a Hexagonal Model Grid, a special type of Voroni Grid that has
regularly spaced hexagonal cells.
>>> from landlab import HexModelGrid
>>> from landlab.components import FlowAccumulator
>>> from landlab.utils.flow__distance import calculate_flow__distance
>>> dx = 1
>>> hmg = HexModelGrid((5, 3), spacing=dx)
>>> _ = hmg.add_field(
... "topographic__elevation",
... hmg.node_x + np.round(hmg.node_y),
... at="node",
... )
>>> hmg.status_at_node[hmg.boundary_nodes] = hmg.BC_NODE_IS_CLOSED
>>> hmg.status_at_node[0] = hmg.BC_NODE_IS_FIXED_VALUE
>>> fr = FlowAccumulator(hmg, flow_director="D4")
>>> fr.run_one_step()
>>> flow__distance = calculate_flow__distance(hmg, add_to_grid=True, clobber=True)
>>> hmg.at_node["flow__distance"]
array([0., 0., 0.,
0., 1., 2., 0.,
0., 2., 2., 3., 0.,
0., 3., 3., 0.,
0., 0., 0.])
"""
# check that flow__receiver nodes exists
if "flow__receiver_node" not in grid.at_node:
raise FieldError(
"A 'flow__receiver_node' field is required at the "
"nodes of the input grid."
)
if "flow__upstream_node_order" not in grid.at_node:
raise FieldError(
"A 'flow__upstream_node_order' field is required at the "
"nodes of the input grid."
)
# get the reciever nodes, depending on if this is to-one, or to-multiple,
# we'll need to get a different at-node field.
if grid.at_node["flow__receiver_node"].size != grid.size("node"):
to_one = False
else:
to_one = True
flow__receiver_node = grid.at_node["flow__receiver_node"]
# get the upstream node order
flow__upstream_node_order = grid.at_node["flow__upstream_node_order"]
# get downstream flow link lengths, result depends on type of grid.
if isinstance(grid, RasterModelGrid):
flow_link_lengths = grid.length_of_d8[
grid.at_node["flow__link_to_receiver_node"]
]
else:
flow_link_lengths = grid.length_of_link[
grid.at_node["flow__link_to_receiver_node"]
]
# create an array that representes the outlet lengths.
flow__distance = np.zeros(grid.nodes.size)
# iterate through the flow__upstream_node_order, this will already have
# identified the locations of the outlet nodes and have
for node in flow__upstream_node_order:
# get flow recievers
reciever = flow__receiver_node[node]
# assess if this is a to one (D8/D4) or to multiple (Dinf, MFD)
# flow directing method.
if to_one:
potential_outlet = reciever
else:
# if this is an outlet, the first element of the recievers will be
# the nodes ID.
potential_outlet = reciever[0]
# assess if this is an outlet or not.
if potential_outlet == node:
not_outlet = False
else:
not_outlet = True
# if not an outlet
if not_outlet:
# deal with the two cases of route to one and route to multiple.
if to_one:
# get the stream length of the downstream node
downstream_stream_length = flow__distance[reciever]
# get the stream segment length from this node to its downstream
# neigbor
stream_increment_length = flow_link_lengths[node]
else:
# non-existant links are coded with -1
useable_receivers = np.where(reciever != grid.BAD_INDEX)[0]
# we will have the stream flow to the downstream node with the
# shortest distance to the outlet.
# in the event of a tie, we will choose the shorter link length.
# get the flow distances of the downstream nodes
potential_downstream_stream_lengths = flow__distance[
flow__receiver_node[node]
][useable_receivers]
# get the stream segment lengths from this node to its downstream
# neighbor
potential_stream_increment_lengths = flow_link_lengths[node][
useable_receivers
]
# get the lowest downstream stream length.
downstream_stream_length = np.min(potential_downstream_stream_lengths)
# determine which of the stream increments flowed to this
# downstream neighbor.
which_link = np.where(
potential_downstream_stream_lengths == downstream_stream_length
)[0]
# and choose the smallest of these links.
stream_increment_length = np.min(
potential_stream_increment_lengths[which_link]
)
# set the total stream length of this node
flow__distance[node] = downstream_stream_length + stream_increment_length
# store on the grid
if add_to_grid:
grid.add_field("flow__distance", flow__distance, at="node", clobber=clobber)
return flow__distance