# FlowAccumulator: Component to do FlowAccumulation with the FlowDirectors¶

flow_accumulator.py: Component to accumulate flow and calculate drainage area.

Provides the FlowAccumulator component which accumulates flow and calculates drainage area. FlowAccumulator supports multiple methods for calculating flow direction. Optionally a depression finding component can be specified and flow directing, depression finding, and flow routing can all be accomplished together.

class FlowAccumulator(grid, surface='topographic__elevation', flow_director='FlowDirectorSteepest', runoff_rate=None, depression_finder=None, **kwargs)[source]

Component to accumulate flow and calculate drainage area.

This is accomplished by first finding flow directions by a user-specified method and then calculating the drainage area and discharge.

Optionally, spatially variable runoff can be set either by the model grid field ‘water__unit_flux_in’ or the input variable runoff_rate*.

Optionally a depression finding component can be specified and flow directing, depression finding, and flow routing can all be accomplished together.

NOTE: The perimeter nodes NEVER contribute to the accumulating flux, even if the gradients from them point inwards to the main body of the grid. This is because under Landlab definitions, perimeter nodes lack cells, so cannot accumulate any discharge.

FlowAccumulator stores as ModelGrid fields:

• Node array of drainage areas: ‘drainage_area’
• Node array of discharges: ‘surface_water__discharge’
• Node array containing downstream-to-upstream ordered list of node
IDs: ‘flow__upstream_node_order’
• Node array of all but the first element of the delta data structure:
flow__data_structure_delta. The first element is always zero.

The FlowDirector component will add additional ModelGrid fields. DirectToOne methods(Steepest/D4 and D8) and DirectToMany(DINF and MFD) use the same model grid field names. Some of these fields will be different shapes if a DirectToOne or a DirectToMany method is used.

The FlowDirectors store the following as ModelGrid fields:

• Node array of receivers (nodes that receive flow), or ITS OWN ID if
there is no receiver: ‘flow__receiver_node’. This array is 2D for RouteToMany methods and has the shape (n-nodes x max number of receivers).
• Node array of flow proportions: ‘flow__receiver_proportions’. This
array is 2D, for RouteToMany methods and has the shape (n-nodes x max number of receivers).
• Node array of links carrying flow: ‘flow__link_to_receiver_node’.
This array is 2D for RouteToMany methods and has the shape (n-nodes x max number of receivers).
• Node array of downhill slopes from each receiver:
‘topographic__steepest_slope’ This array is 2D for RouteToMany methods and has the shape (n-nodes x max number of receivers).
• Boolean node array of all local lows: ‘flow__sink_flag’
• Link array identifing if flow goes with (1) or against (-1) the link direction: ‘flow__link_direction’

The primary method of this class is run_one_step.

run_one_step takes the optional argument update_flow_director (default is True) that determines if the flow_director is re-run before flow is accumulated.

Parameters: grid (ModelGrid) – A Landlab grid. surface (field name at node or array of length node) – The surface to direct flow across. flow_director (string, class, instance of class.) – A string of method or class name (e.g. ‘D8’ or ‘FlowDirectorD8’), an uninstantiated FlowDirector class, or an instance of a FlowDirector class. This sets the method used to calculate flow directions. Default is ‘FlowDirectorSteepest’ runoff_rate (field name, array, or float, optional (m/time)) – If provided, sets the runoff rate and will be assigned to the grid field ‘water__unit_flux_in’. If a spatially and and temporally variable runoff rate is desired, pass this field name and update the field through model run time. If both the field and argument are present at the time of initialization, runoff_rate will overwrite the field. If neither are set, defaults to spatially constant unit input. Both a runoff_rate array and the ‘water__unit_flux_in’ field are permitted to contain negative values, in which case they mimic transmission losses rather than e.g. rain inputs. depression_finder (string, class, instance of class, optional) – A string of class name (e.g., ‘DepressionFinderAndRouter’), an uninstantiated DepressionFinder class, or an instance of a DepressionFinder class. This sets the method for depression finding. **kwargs (any additional parameters to pass to a FlowDirector or) – DepressionFinderAndRouter instance (e.g., partion_method for FlowDirectorMFD). This will have no effect if an instantiated component is passed using the flow_director or depression_finder keywords.

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator
>>> mg = RasterModelGrid((3,3))
>>> mg.set_closed_boundaries_at_grid_edges(True, True, True, False)
>>> _ = mg.add_field(
...     "topographic__elevation",
...     mg.node_x + mg.node_y,
...     at="node",
... )


The FlowAccumulator component accumulates flow and calculates drainage using all of the different methods for directing flow in Landlab. These include steepest descent (also known as D4 for the case of a raster grid) and D8 (on raster grids only). The method for flow director can be specified as a string (e.g., ‘D8’ or ‘FlowDirectorD8’), as an uninstantiated FlowDirector component or as an instantiated FlowDirector component.

The default method is to use FlowDirectorSteepest.

First let’s look at the three ways to instantiate a FlowAccumulator. The following four methods are all equivalent. First, we can pass the entire name of a flow director as a string to the argument flow_director:

>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director='FlowDirectorSteepest'
... )


Second, we can pass just the method name as a string to the argument flow_director:

>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director='Steepest'
... )


Third, we can import a FlowDirector component from Landlab and pass it to flow_director: >>> from landlab.components import FlowDirectorSteepest >>> fa = FlowAccumulator( … mg, … ‘topographic__elevation’, … flow_director=FlowDirectorSteepest … )

Finally, we can instantiate a FlowDirector component and pass this instantiated version to flow_director. You might want to do this if you used a FlowDirector in order to set up something before starting a time loop and then want to use the same flow director within the loop.

>>> fd = FlowDirectorSteepest(mg, 'topographic__elevation')
>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest
... )


Now let’s look at what FlowAccumulator does. Even before we run FlowAccumulator it has the property surface_values that stores the values of the surface over which flow is directed and accumulated.

>>> fa.surface_values
array([ 0.,  1.,  2.,  1.,  2.,  3.,  2.,  3.,  4.])


Now let’s make a more complicated elevation grid for the next examples.

>>> mg = RasterModelGrid((5, 4))
>>> topographic__elevation = np.array([0.,  0.,  0., 0.,
...                                    0., 21., 10., 0.,
...                                    0., 31., 20., 0.,
...                                    0., 32., 30., 0.,
...                                    0.,  0.,  0., 0.])
>>> _ = mg.add_field("topographic__elevation", topographic__elevation, at="node")
>>> mg.set_closed_boundaries_at_grid_edges(True, True, True, False)
>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest
...      )
>>> fa.run_one_step()
>>> mg.at_node['flow__receiver_node'] # doctest: +NORMALIZE_WHITESPACE
array([ 0,  1,  2,  3,
4,  1,  2,  7,
8, 10,  6, 11,
12, 14, 10, 15,
16, 17, 18, 19])
>>> mg.at_node['drainage_area'] # doctest: +NORMALIZE_WHITESPACE
array([ 0.,  1.,  5.,  0.,
0.,  1.,  5.,  0.,
0.,  1.,  4.,  0.,
0.,  1.,  2.,  0.,
0.,  0.,  0.,  0.])


Now let’s change the cell area (100.) and the runoff rates:

>>> mg = RasterModelGrid((5, 4), xy_spacing=(10., 10))


Put the data back into the new grid.

>>> _ = mg.add_field("topographic__elevation", topographic__elevation, at="node")
>>> mg.set_closed_boundaries_at_grid_edges(True, True, True, False)
>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest
...      )
>>> runoff_rate = np.arange(mg.number_of_nodes, dtype=float)
>>> rnff = mg.add_field("water__unit_flux_in", runoff_rate, at="node", clobber=True)
>>> fa.run_one_step()
>>> mg.at_node['surface_water__discharge'] # doctest: +NORMALIZE_WHITESPACE
array([    0.,   500.,  5200.,     0.,
0.,   500.,  5200.,     0.,
0.,   900.,  4600.,     0.,
0.,  1300.,  2700.,     0.,
0.,     0.,     0.,     0.])


The flow accumulator will happily work with a negative runoff rate, which could be used to allow, e.g., transmission losses:

>>> runoff_rate.fill(1.)
>>> fa.run_one_step()
>>> mg.at_node['surface_water__discharge']
array([   0.,  100.,  500.,    0.,
0.,  100.,  500.,    0.,
0.,  100.,  400.,    0.,
0.,  100.,  200.,    0.,
0.,    0.,    0.,    0.])
>>> runoff_rate[:8] = -0.5
>>> fa.run_one_step()
>>> mg.at_node['surface_water__discharge']
array([   0.,    0.,  350.,    0.,
0.,    0.,  350.,    0.,
0.,  100.,  400.,    0.,
0.,  100.,  200.,    0.,
0.,    0.,    0.,    0.])


The drainage area array is unaffected, as you would expect:

>>> mg.at_node['drainage_area']
array([   0.,  100.,  500.,    0.,
0.,  100.,  500.,    0.,
0.,  100.,  400.,    0.,
0.,  100.,  200.,    0.,
0.,    0.,    0.,    0.])


The FlowAccumulator component will work for both raster grids and 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
>>> hmg = HexModelGrid((5, 3), xy_of_lower_left=(-1., 0.))
>>> _ = hmg.add_field(
...     "topographic__elevation",
...     hmg.node_x + np.round(hmg.node_y),
...     at="node",
... )
>>> fa = FlowAccumulator(
...      hmg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest
... )
>>> fa.surface_values
array([ 0. ,  1. ,  2. ,
0.5,  1.5,  2.5,  3.5,
1. ,  2. ,  3. ,  4. ,  5. ,
2.5,  3.5,  4.5,  5.5,
3. ,  4. ,  5. ])


If the FlowDirector you want to use takes keyword arguments and you want to specify it using a string or uninstantiated FlowDirector class, include those keyword arguments when you create FlowAccumulator.

For example, in the case of a raster grid, FlowDirectorMFD can use only orthogonal links, or it can use both orthogonal and diagonal links.

>>> mg = RasterModelGrid((5, 5))
>>> topographic__elevation = mg.node_y+mg.node_x
>>> _ = mg.add_field("topographic__elevation", topographic__elevation, at="node")
>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director='MFD',
...      diagonals = True
... )
>>> fa.run_one_step()
>>> mg.at_node['flow__receiver_node'] # doctest: +NORMALIZE_WHITESPACE
array([[ 0, -1, -1, -1, -1, -1, -1, -1],
[ 1, -1, -1, -1, -1, -1, -1, -1],
[ 2, -1, -1, -1, -1, -1, -1, -1],
[ 3, -1, -1, -1, -1, -1, -1, -1],
[ 4, -1, -1, -1, -1, -1, -1, -1],
[ 5, -1, -1, -1, -1, -1, -1, -1],
[-1, -1,  5,  1, -1, -1,  0, -1],
[-1, -1,  6,  2, -1, -1,  1, -1],
[-1, -1,  7,  3, -1, -1,  2, -1],
[ 9, -1, -1, -1, -1, -1, -1, -1],
[10, -1, -1, -1, -1, -1, -1, -1],
[-1, -1, 10,  6, -1, -1,  5, -1],
[-1, -1, 11,  7, -1, -1,  6, -1],
[-1, -1, 12,  8, -1, -1,  7, -1],
[14, -1, -1, -1, -1, -1, -1, -1],
[15, -1, -1, -1, -1, -1, -1, -1],
[-1, -1, 15, 11, -1, -1, 10, -1],
[-1, -1, 16, 12, -1, -1, 11, -1],
[-1, -1, 17, 13, -1, -1, 12, -1],
[19, -1, -1, -1, -1, -1, -1, -1],
[20, -1, -1, -1, -1, -1, -1, -1],
[21, -1, -1, -1, -1, -1, -1, -1],
[22, -1, -1, -1, -1, -1, -1, -1],
[23, -1, -1, -1, -1, -1, -1, -1],
[24, -1, -1, -1, -1, -1, -1, -1]])
>>> mg.at_node['drainage_area'].round(4) # doctest: +NORMALIZE_WHITESPACE
array([ 1.4117,  2.065 ,  1.3254,  0.4038,  0.    ,
2.065 ,  3.4081,  2.5754,  1.3787,  0.    ,
1.3254,  2.5754,  2.1716,  1.2929,  0.    ,
0.4038,  1.3787,  1.2929,  1.    ,  0.    ,
0.    ,  0.    ,  0.    ,  0.    ,  0.    ])


It may seem odd that there are no round numbers in the drainage area field. This is because flow is directed to all downhill boundary nodes and partitioned based on slope.

To check that flow is conserved, sum along all boundary nodes.

>>> round(sum(mg.at_node['drainage_area'][mg.boundary_nodes]), 4)
9.0


This should be the same as the number of core nodes — as boundary nodes in landlab do not have area.

>>> len(mg.core_nodes)
9


Next, let’s set the dx spacing such that each cell has an area of one.

>>> dx=(2./(3.**0.5))**0.5
>>> hmg = HexModelGrid((5, 3), spacing=dx, xy_of_lower_left=(-1.0745, 0.))
>>> _ = hmg.add_field(
...     "topographic__elevation",
...     hmg.node_x**2 + np.round(hmg.node_y)**2,
...     at="node",
... )
>>> fa = FlowAccumulator(
...      hmg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest
... )
>>> fa.run_one_step()
>>> hmg.at_node['flow__receiver_node']
array([ 0,  1,  2,
3,  0,  1,  6,
7,  3,  4,  5, 11,
12,  8,  9, 15,
16, 17, 18])
>>> np.round(hmg.at_node['drainage_area'])
array([ 3.,  2.,  0.,
2.,  3.,  2.,  0.,
0.,  2.,  2.,  1.,  0.,
0., 1.,  1.,  0.,
0.,  0.,  0.])


Now let’s change the cell area (100.) and the runoff rates:

>>> hmg = HexModelGrid((5, 3), spacing=dx * 10.0, xy_of_lower_left=(-10.745, 0.))


Put the data back into the new grid.

>>> _ = hmg.add_field(
...     "topographic__elevation",
...     hmg.node_x ** 2 + np.round(hmg.node_y) ** 2,
...     at="node",
... )
>>> fa = FlowAccumulator(
...      hmg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest
...      )
>>> fa.run_one_step()
>>> np.round(hmg.at_node['surface_water__discharge'])
array([ 500.,    0.,    0.,
200.,  500.,  200.,    0.,
0.,  200.,  200.,  100.,    0.,
0.,  100.,  100.,    0.,
0.,    0.,    0.])


Next, let’s see what happens to a raster grid when there is a depression.

>>> mg = RasterModelGrid((7, 7), xy_spacing=0.5)
>>> z = mg.add_field("topographic__elevation", mg.node_x.copy(), at="node")
>>> z += 0.01 * mg.node_y
>>> mg.at_node['topographic__elevation'].reshape(mg.shape)[2:5, 2:5] *= 0.1
>>> mg.set_closed_boundaries_at_grid_edges(True, True, False, True)


This model grid has a depression in the center.

>>> mg.at_node['topographic__elevation'].reshape(mg.shape)
array([[ 0.    ,  0.5   ,  1.    ,  1.5   ,  2.    ,  2.5   ,  3.    ],
[ 0.005 ,  0.505 ,  1.005 ,  1.505 ,  2.005 ,  2.505 ,  3.005 ],
[ 0.01  ,  0.51  ,  0.101 ,  0.151 ,  0.201 ,  2.51  ,  3.01  ],
[ 0.015 ,  0.515 ,  0.1015,  0.1515,  0.2015,  2.515 ,  3.015 ],
[ 0.02  ,  0.52  ,  0.102 ,  0.152 ,  0.202 ,  2.52  ,  3.02  ],
[ 0.025 ,  0.525 ,  1.025 ,  1.525 ,  2.025 ,  2.525 ,  3.025 ],
[ 0.03  ,  0.53  ,  1.03  ,  1.53  ,  2.03  ,  2.53  ,  3.03  ]])
>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest
...      )
>>> fa.run_one_step()  # the flow "gets stuck" in the hole
>>> mg.at_node['flow__receiver_node'].reshape(mg.shape)
array([[ 0,  1,  2,  3,  4,  5,  6],
[ 7,  7, 16, 17, 18, 11, 13],
[14, 14, 16, 16, 17, 18, 20],
[21, 21, 16, 23, 24, 25, 27],
[28, 28, 23, 30, 31, 32, 34],
[35, 35, 30, 31, 32, 39, 41],
[42, 43, 44, 45, 46, 47, 48]])
>>> mg.at_node['drainage_area'].reshape(mg.shape)
array([[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
[ 0.25,  0.25,  0.25,  0.25,  0.5 ,  0.25,  0.  ],
[ 0.25,  0.25,  5.  ,  1.5 ,  1.  ,  0.25,  0.  ],
[ 0.25,  0.25,  3.  ,  0.75,  0.5 ,  0.25,  0.  ],
[ 0.25,  0.25,  2.  ,  1.5 ,  1.  ,  0.25,  0.  ],
[ 0.25,  0.25,  0.25,  0.25,  0.5 ,  0.25,  0.  ],
[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ]])


Because of the depression, the flow ‘got stuck’ in the hole in the center of the grid. We can fix this by using a depression finder, such as DepressionFinderAndRouter.

>>> from landlab.components import DepressionFinderAndRouter


We can either run the depression finder separately from the flow accumulator or we can specify the depression finder and router when we instantiate the accumulator and it will run automatically. Similar to specifying the FlowDirector we can provide a depression finder in multiple three ways.

First let’s try running them separately.

>>> df_4 = DepressionFinderAndRouter(mg)
>>> df_4.map_depressions()
>>> mg.at_node['flow__receiver_node'].reshape(mg.shape)
array([[ 0,  1,  2,  3,  4,  5,  6],
[ 7,  7, 16, 17, 18, 11, 13],
[14, 14,  8, 16, 17, 18, 20],
[21, 21, 16, 16, 24, 25, 27],
[28, 28, 23, 24, 24, 32, 34],
[35, 35, 30, 31, 32, 39, 41],
[42, 43, 44, 45, 46, 47, 48]])
>>> mg.at_node['drainage_area'].reshape(mg.shape)
array([[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
[ 5.25,  5.25,  0.25,  0.25,  0.5 ,  0.25,  0.  ],
[ 0.25,  0.25,  5.  ,  1.5 ,  1.  ,  0.25,  0.  ],
[ 0.25,  0.25,  0.75,  2.25,  0.5 ,  0.25,  0.  ],
[ 0.25,  0.25,  0.5 ,  0.5 ,  1.  ,  0.25,  0.  ],
[ 0.25,  0.25,  0.25,  0.25,  0.5 ,  0.25,  0.  ],
[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ]])


Now the flow is routed correctly. The depression finder has properties that including whether there is a lake at the node, which lake is at each node, the outlet node of each lake, and the area of each lake.

>>> df_4.lake_at_node.reshape(mg.shape)  # doctest: +NORMALIZE_WHITESPACE
array([[False, False, False, False, False, False, False],
[False, False, False, False, False, False, False],
[False, False,  True,  True,  True, False, False],
[False, False,  True,  True,  True, False, False],
[False, False,  True,  True,  True, False, False],
[False, False, False, False, False, False, False],
[False, False, False, False, False, False, False]], dtype=bool)
>>> df_4.lake_map.reshape(mg.shape)  # doctest: +NORMALIZE_WHITESPACE
array([[-1, -1, -1, -1, -1, -1, -1],
[-1, -1, -1, -1, -1, -1, -1],
[-1, -1, 16, 16, 16, -1, -1],
[-1, -1, 16, 16, 16, -1, -1],
[-1, -1, 16, 16, 16, -1, -1],
[-1, -1, -1, -1, -1, -1, -1],
[-1, -1, -1, -1, -1, -1, -1]])
>>> df_4.lake_codes  # a unique code for each lake present on the grid
array([16])
>>> df_4.lake_outlets  # the outlet node of each lake in lake_codes
array([8])
>>> df_4.lake_areas  # the area of each lake in lake_codes
array([ 2.25])


Alternatively, we can initialize a flow accumulator with a depression finder specified. Calling run_one_step() will run both the accumulator and the depression finder with one call. For this example, we will pass the class DepressionFinderAndRouter to the parameter depression_finder.

>>> mg = RasterModelGrid((7, 7), xy_spacing=0.5)
>>> z = mg.add_field("topographic__elevation", mg.node_x.copy(), at="node")
>>> z += 0.01 * mg.node_y
>>> mg.at_node['topographic__elevation'].reshape(mg.shape)[2:5, 2:5] *= 0.1
>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director='FlowDirectorD8',
...      depression_finder=DepressionFinderAndRouter
... )
>>> fa.run_one_step()


This has the same effect of first calling the accumulator and then calling the depression finder.

>>> mg.at_node['flow__receiver_node'].reshape(mg.shape)
array([[ 0,  1,  2,  3,  4,  5,  6],
[ 7,  7, 16, 17, 18, 18, 13],
[14, 14,  8, 16, 17, 18, 20],
[21, 21, 16, 16, 24, 25, 27],
[28, 28, 23, 24, 24, 32, 34],
[35, 35, 30, 31, 32, 32, 41],
[42, 43, 44, 45, 46, 47, 48]])
>>> mg.at_node['drainage_area'].reshape(mg.shape)
array([[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
[ 5.25,  5.25,  0.25,  0.25,  0.25,  0.25,  0.  ],
[ 0.25,  0.25,  5.  ,  1.5 ,  1.  ,  0.25,  0.  ],
[ 0.25,  0.25,  0.75,  2.25,  0.5 ,  0.25,  0.  ],
[ 0.25,  0.25,  0.5 ,  0.5 ,  1.  ,  0.25,  0.  ],
[ 0.25,  0.25,  0.25,  0.25,  0.25,  0.25,  0.  ],
[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ]])


The depression finder is stored as part of the flow accumulator, so its properties can be accessed through the depression finder.

>>> fa.depression_finder.lake_at_node.reshape(mg.shape)  # doctest: +NORMALIZE_WHITESPACE
array([[False, False, False, False, False, False, False],
[False, False, False, False, False, False, False],
[False, False,  True,  True,  True, False, False],
[False, False,  True,  True,  True, False, False],
[False, False,  True,  True,  True, False, False],
[False, False, False, False, False, False, False],
[False, False, False, False, False, False, False]], dtype=bool)
>>> fa.depression_finder.lake_map.reshape(mg.shape)  # doctest: +NORMALIZE_WHITESPACE
array([[-1, -1, -1, -1, -1, -1, -1],
[-1, -1, -1, -1, -1, -1, -1],
[-1, -1, 16, 16, 16, -1, -1],
[-1, -1, 16, 16, 16, -1, -1],
[-1, -1, 16, 16, 16, -1, -1],
[-1, -1, -1, -1, -1, -1, -1],
[-1, -1, -1, -1, -1, -1, -1]])
>>> fa.depression_finder.lake_codes  # a unique code for each lake present on the grid
array([16])
>>> fa.depression_finder.lake_outlets  # the outlet node of each lake in lake_codes
array([8])
>>> fa.depression_finder.lake_areas  # the area of each lake in lake_codes
array([ 2.25])


Finally, note that the DepressionFinderAndRouter takes a keyword argument routing (‘D8’, default; ‘D4’) that sets how connectivity is set between nodes. Similar to our ability to pass keyword arguments to the FlowDirector through FlowAccumulator, we can pass this keyword argument to the DepressionFinderAndRouter component.

>>> fa = FlowAccumulator(
...      mg,
...      'topographic__elevation',
...      flow_director=FlowDirectorSteepest,
...      depression_finder=DepressionFinderAndRouter,
...      routing='D4'
... )


FlowAccumulator was designed to work with all types of grids. However, NetworkModelGrid’s have no cell area. Thus, in order for FlowAccumulator to this type of grid, an at-node array called cell_area_at_node must be present.

>>> from landlab.grid.network import NetworkModelGrid
>>> y_of_node = (0, 1, 2, 2)
>>> x_of_node = (0, 0, -1, 1)
>>> nodes_at_link = ((1, 0), (2, 1), (3, 1))
>>> nmg = NetworkModelGrid((y_of_node, x_of_node), nodes_at_link)
>>> area = nmg.add_ones("cell_area_at_node", at="node")
>>> z = nmg.add_field(
...     "topographic__elevation",
...     nmg.x_of_node + nmg.y_of_node,
...     at="node",
... )
>>> fa = FlowAccumulator(nmg)
>>> fa.run_one_step()
>>> nmg.at_node['flow__receiver_node']
array([0, 0, 2, 1])


References

Required Software Citation(s) Specific to this Component

None Listed

Additional References

Braun, J., Willett, S. (2013). A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution. Geomorphology 180-181(C), 170-179. https://dx.doi.org/10.1016/j.geomorph.2012.10.008

Initialize the FlowAccumulator component.

Saves the grid, tests grid type, tests imput types and compatability for the flow_director and depression_finder keyword arguments, tests the argument of runoff_rate, and initializes new fields.

__init__(grid, surface='topographic__elevation', flow_director='FlowDirectorSteepest', runoff_rate=None, depression_finder=None, **kwargs)[source]

Initialize the FlowAccumulator component.

Saves the grid, tests grid type, tests imput types and compatability for the flow_director and depression_finder keyword arguments, tests the argument of runoff_rate, and initializes new fields.

accumulate_flow(update_flow_director=True, update_depression_finder=True)[source]

Function to make FlowAccumulator calculate drainage area and discharge.

Running accumulate_flow() results in the following to occur:

1. Flow directions are updated (unless update_flow_director is set as False). This incluldes checking for updated boundary conditions.
2. The depression finder, if present is updated (unless update_depression_finder is set as False).
3. Intermediate steps that analyse the drainage network topology and create datastructures for efficient drainage area and discharge calculations.
4. Calculation of drainage area and discharge.
5. Return of drainage area and discharge.
Parameters: update_flow_director (optional, bool) – Whether to update the flow director. Default is True. update_depression_finder (optional, bool) – Whether to update the depression finder, if present. Default is True. drainage_area (array) – At node array which points to the field grid.at_node[“drainage_area”]. surface_water__discharge – At node array which points to the field grid.at_node[“surface_water__discharge”].
depression_finder

The DepressionFinder used internally.

flow_director

The FlowDirector used internally.

headwater_nodes()[source]

Return the headwater nodes.

These are nodes that contribute flow and have no upstream nodes.

Examples

>>> from numpy.testing import assert_array_equal
>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator
>>> mg = RasterModelGrid((5, 5))
>>> mg.set_closed_boundaries_at_grid_edges(True, True, True, False)
>>> _ = mg.add_field(
...     "topographic__elevation",
...     mg.node_x + mg.node_y,
...     at="node",
... )
>>> fa = FlowAccumulator(mg, 'topographic__elevation')
>>> fa.run_one_step()
>>> assert_array_equal(fa.headwater_nodes(), np.array([16, 17, 18]))


Return the upstream order of active links.

Examples

>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator
>>> mg = RasterModelGrid((5, 5))
>>> mg.set_closed_boundaries_at_grid_edges(True, True, True, False)
>>> _ = mg.add_field(
...     "topographic__elevation",
...     mg.node_x + mg.node_y,
...     at="node",
... )
>>> fa = FlowAccumulator(mg, 'topographic__elevation')
>>> fa.run_one_step()
>>> fa.link_order_upstream()
array([ 5, 14, 23,  6, 15, 24,  7, 16, 25])


This also works for route-to-many methods

>>> mg = RasterModelGrid((5, 5))
>>> mg.set_closed_boundaries_at_grid_edges(True, True, True, False)
>>> _ = mg.add_field(
...     "topographic__elevation",
...     mg.node_x + mg.node_y,
...     at="node",
... )
>>> fa = FlowAccumulator(mg,
...      'topographic__elevation',
...      flow_director='MFD')
>>> fa.run_one_step()
>>> fa.link_order_upstream()
array([ 5, 14, 10,  6, 11,  7, 23, 19, 15, 20, 16, 28, 24, 29, 25])

node_drainage_area

Return the drainage area.

node_order_upstream

Return the upstream node order (drainage stack).

node_water_discharge

Return the surface water discharge.

pits_present()[source]
run_one_step()[source]

Accumulate flow and save to the model grid.

1. Flow directions are updated. This incluldes checking for updated boundary conditions.
2. The depression finder, if present is updated.
3. Intermediate steps that analyse the drainage network topology and create datastructures for efficient drainage area and discharge calculations.
4. Calculation of drainage area and discharge.
5. Return of drainage area and discharge.

An alternative to run_one_step() is accumulate_flow() which does the same things but also returns the drainage area and discharge. accumulate_flow() additionally provides the ability to turn off updating the flow director or the depression finder.

surface_values

Values of the surface over which flow is accumulated.

# LossyFlowAccumulator: Component to accumulate flow with the FlowDirectors, while water is lost or gained downstream¶

lossy_flow_accumulator.py: Component to accumulate flow and calc drainage area, while permitting gain or loss of discharge during flow.

DEJH, late 2018

class LossyFlowAccumulator(grid, surface='topographic__elevation', flow_director='FlowDirectorSteepest', runoff_rate=None, depression_finder=None, loss_function=None, **kwargs)[source]

Component to calculate drainage area and accumulate flow, while permitting dynamic loss or gain of flow downstream.

This component is closely related to the FlowAccumulator, in that this is accomplished by first finding flow directions by a user-specified method and then calculating the drainage area and discharge. However, this component additionally requires the passing of a function that describes how discharge is lost or gained downstream, f(Qw, nodeID, linkID, grid). See the Examples below to see how this works in practice.

Optionally, spatially variable runoff can be set either by the model grid field ‘water__unit_flux_in’ or the input variable runoff_rate*.

Optionally a depression finding component can be specified and flow directing, depression finding, and flow routing can all be accomplished together. Note that the DepressionFinderAndRouter is not particularly intelligent when running on lossy streams, and in particular, it will reroute flow around pits even when they are in fact not filled due to loss.

NOTE: The perimeter nodes NEVER contribute to the accumulating flux, even if the gradients from them point inwards to the main body of the grid. This is because under Landlab definitions, perimeter nodes lack cells, so cannot accumulate any discharge.

LossyFlowAccumulator stores as ModelGrid fields:

• Node array of drainage areas: ‘drainage_area’
• Node array of discharges: ‘surface_water__discharge’
• Node array of discharge loss in transit (vol/sec). This is the
total loss across all of the downstream links: ‘surface_water__discharge_loss’
• Node array containing downstream-to-upstream ordered list of node IDs: ‘flow__upstream_node_order’
• Node array of all but the first element of the delta data structure:
flow__data_structure_delta. The first element is always zero.

The FlowDirector component will add additional ModelGrid fields; see the FlowAccumulator component for full details. These are:

• Node array of receivers (nodes that receive flow), or ITS OWN ID if
there is no receiver: ‘flow__receiver_node’
• Node array of flow proportions: ‘flow__receiver_proportions’
• Node array of links carrying flow: ‘flow__link_to_receiver_node’
• Node array of downhill slopes from each receiver:
‘topographic__steepest_slope’
• Boolean node array of all local lows: ‘flow__sink_flag’

The primary method of this class is run_one_step.

Examples

These examples pertain only to the LossyFlowAccumulator. See the main FlowAccumulator documentation for more generic and comprehensive examples.

First, a very simple example. Here’s a 50% loss of discharge every time flow moves along a node:

>>> import numpy as np
>>> from landlab import RasterModelGrid, HexModelGrid
>>> from landlab.components import FlowDirectorSteepest
>>> from landlab.components import DepressionFinderAndRouter

>>> mg = RasterModelGrid((3, 5), xy_spacing=(2, 1))
>>> mg.set_closed_boundaries_at_grid_edges(True, True, False, True)
>>> z = mg.add_field("topographic__elevation", mg.node_x + mg.node_y, at="node")

>>> def mylossfunction(qw):
...     return 0.5 * qw

>>> fa = LossyFlowAccumulator(mg, 'topographic__elevation',
...                           flow_director=FlowDirectorSteepest,
...                           loss_function=mylossfunction)
>>> fa.run_one_step()

>>> mg.at_node['drainage_area'].reshape(mg.shape)
array([[ 0.,  0.,  0.,  0.,  0.],
[ 6.,  6.,  4.,  2.,  0.],
[ 0.,  0.,  0.,  0.,  0.]])
>>> mg.at_node['surface_water__discharge'].reshape(mg.shape)
array([[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
[ 1.75,  3.5 ,  3.  ,  2.  ,  0.  ],
[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ]])
>>> mg.at_node['surface_water__discharge_loss'].reshape(mg.shape)
array([[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
[ 0.  ,  1.75,  1.5 ,  1.  ,  0.  ],
[ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ]])


Here we use a spatially distributed field to derive loss terms, and also use a filled, non-raster grid.

>>> dx=(2./(3.**0.5))**0.5  # area to be 100.
>>> hmg = HexModelGrid((5, 3), spacing=dx, xy_of_lower_left=(-1.0745, 0.))
>>> z = hmg.add_field(
...     "topographic__elevation",
...     hmg.node_x**2 + np.round(hmg.node_y)**2,
...     at="node",
... )
>>> z[9] = -10.  # poke a hole
>>> lossy = hmg.add_zeros('node', 'mylossterm', dtype=float)
>>> lossy[14] = 1.  # suppress all flow from node 14


Without loss looks like this:

>>> fa = LossyFlowAccumulator(hmg, 'topographic__elevation',
...                           flow_director=FlowDirectorSteepest,
...                           depression_finder=DepressionFinderAndRouter)
>>> fa.run_one_step()
>>> hmg.at_node['flow__receiver_node']
array([ 0,  1,  2,
3,  0,  9,  6,
7,  9,  4,  9, 11,
12,  9,  9, 15,
16, 17, 18])
>>> np.round(hmg.at_node['drainage_area'])
array([ 7.,  0.,  0.,
0.,  7.,  1.,  0.,
0.,  1.,  6.,  1.,  0.,
0., 1.,  1.,  0.,
0.,  0.,  0.])
>>> np.round(hmg.at_node['surface_water__discharge'])
array([ 7.,  0.,  0.,
0.,  7.,  1.,  0.,
0.,  1.,  6.,  1.,  0.,
0., 1.,  1.,  0.,
0.,  0.,  0.])


With loss looks like this:

>>> def mylossfunction2(Qw, nodeID, linkID, grid):
...     return (1. - grid.at_node['mylossterm'][nodeID]) * Qw
>>> fa = LossyFlowAccumulator(hmg, 'topographic__elevation',
...                           flow_director=FlowDirectorSteepest,
...                           depression_finder=DepressionFinderAndRouter,
...                           loss_function=mylossfunction2)
>>> fa.run_one_step()
>>> np.round(hmg.at_node['drainage_area'])
array([ 7.,  0.,  0.,
0.,  7.,  1.,  0.,
0.,  1.,  6.,  1.,  0.,
0., 1.,  1.,  0.,
0.,  0.,  0.])
>>> np.round(hmg.at_node['surface_water__discharge'])
array([ 6.,  0.,  0.,
0.,  6.,  1.,  0.,
0.,  1.,  5.,  1.,  0.,
0., 1.,  1.,  0.,
0.,  0.,  0.])
>>> np.allclose(
...     hmg.at_node["surface_water__discharge_loss"],
...     lossy * hmg.at_node["surface_water__discharge"],
... )
True


(Loss is only happening from the node, 14, that we set it to happen at.)

Finally, note we can use the linkIDs to create flow-length-dependent effects:

>>> from landlab.components import FlowDirectorMFD
>>> mg = RasterModelGrid((4, 6), xy_spacing=(1, 2))
>>> mg.set_closed_boundaries_at_grid_edges(True, True, False, True)
>>> z = mg.add_field("topographic__elevation", 2.0 * mg.node_x, at="node")
>>> z[9] = 8.
>>> z[16] = 6.5  # force the first node sideways

>>> L = mg.add_zeros('node', 'spatialloss')
>>> mg.at_node['spatialloss'][9] = 1.
>>> mg.at_node['spatialloss'][13] = 1.
>>> def fancyloss(Qw, nodeID, linkID, grid):
...     # now a true transmission loss:
...     Lt = (1.0 - 1.0 / grid.length_of_link[linkID] ** 2)
...     Lsp = grid.at_node["spatialloss"][nodeID]
...     return Qw * (1.0 - Lt) * (1.0 - Lsp)

>>> fa = LossyFlowAccumulator(
...     mg,
...     "topographic__elevation",
...     flow_director=FlowDirectorMFD,
...     loss_function=fancyloss,
... )
>>> fa.run_one_step()

>>> mg.at_node['drainage_area'].reshape(mg.shape)
array([[  0. ,   0. ,   0. ,   0. ,   0. ,   0. ],
[  5.6,   5.6,   3.6,   2. ,   2. ,   0. ],
[ 10.4,  10.4,   8.4,   6.4,   4. ,   0. ],
[  0. ,   0. ,   0. ,   0. ,   0. ,   0. ]])
>>> mg.at_node['surface_water__discharge'].reshape(mg.shape)
array([[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ],
[ 4. ,  4. ,  2. ,  2. ,  2. ,  0. ],
[ 0. ,  8.5,  6.5,  4.5,  2.5,  0. ],
[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ]])


References

Required Software Citation(s) Specific to this Component

None Listed

Additional References

Braun, J., Willett, S. (2013). A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution. Geomorphology 180-181(C), 170-179. https://dx.doi.org/10.1016/j.geomorph.2012.10.008

Initialize the FlowAccumulator component.

Saves the grid, tests grid type, tests imput types and compatability for the flow_director and depression_finder keyword arguments, tests the argument of runoff_rate, and initializes new fields.

Parameters: grid (ModelGrid) – A Landlab grid. surface (field name at node or array of length node) – The surface to direct flow across. flow_director (string, class, instance of class.) – A string of method or class name (e.g. ‘D8’ or ‘FlowDirectorD8’), an uninstantiated FlowDirector class, or an instance of a FlowDirector class. This sets the method used to calculate flow directions. Default is ‘FlowDirectorSteepest’ runoff_rate (field name, array, or float, optional (m/time)) – If provided, sets the runoff rate and will be assigned to the grid field ‘water__unit_flux_in’. If a spatially and and temporally variable runoff rate is desired, pass this field name and update the field through model run time. If both the field and argument are present at the time of initialization, runoff_rate will overwrite the field. If neither are set, defaults to spatially constant unit input. depression_finder (string, class, instance of class, optional) – A string of class name (e.g., ‘DepressionFinderAndRouter’), an uninstantiated DepressionFinder class, or an instance of a DepressionFinder class. This sets the method for depression finding. loss_function (Python function, optional) – A function of the form f(Qw, [node_ID, [linkID, [grid]]]), where Qw is the discharge at a node, node_ID the ID of the node at which the loss is to be calculated, linkID is the ID of the link down which the outflow drains (or a d8 ID if the routing is d8), and grid is a Landlab ModelGrid. The function then returns the new discharge at the node after the function is applied. Note that if a linkID is needed, a nodeID must also be specified, even if only as a dummy parameter; similarly, if a grid is to be passed, all of the preceding parameters must be specified. Both nodeID and linkID are required to permit spatially variable losses, and also losses dependent on flow path geometry (e.g., flow length). The grid is passed to allow fields or grid properties describing values across the grid to be accessed for the loss calculation (see examples). This function expects (float, [int, [int, [ModelGrid]]]), and return a single float, the new discharge value. This behavior is verified during component instantiation. **kwargs (optional) – Any additional parameters to pass to a FlowDirector or DepressionFinderAndRouter instance (e.g., partion_method for FlowDirectorMFD). This will have no effect if an instantiated component is passed using the flow_director or depression_finder keywords.
__init__(grid, surface='topographic__elevation', flow_director='FlowDirectorSteepest', runoff_rate=None, depression_finder=None, loss_function=None, **kwargs)[source]

Initialize the FlowAccumulator component.

Saves the grid, tests grid type, tests imput types and compatability for the flow_director and depression_finder keyword arguments, tests the argument of runoff_rate, and initializes new fields.

Parameters: grid (ModelGrid) – A Landlab grid. surface (field name at node or array of length node) – The surface to direct flow across. flow_director (string, class, instance of class.) – A string of method or class name (e.g. ‘D8’ or ‘FlowDirectorD8’), an uninstantiated FlowDirector class, or an instance of a FlowDirector class. This sets the method used to calculate flow directions. Default is ‘FlowDirectorSteepest’ runoff_rate (field name, array, or float, optional (m/time)) – If provided, sets the runoff rate and will be assigned to the grid field ‘water__unit_flux_in’. If a spatially and and temporally variable runoff rate is desired, pass this field name and update the field through model run time. If both the field and argument are present at the time of initialization, runoff_rate will overwrite the field. If neither are set, defaults to spatially constant unit input. depression_finder (string, class, instance of class, optional) – A string of class name (e.g., ‘DepressionFinderAndRouter’), an uninstantiated DepressionFinder class, or an instance of a DepressionFinder class. This sets the method for depression finding. loss_function (Python function, optional) – A function of the form f(Qw, [node_ID, [linkID, [grid]]]), where Qw is the discharge at a node, node_ID the ID of the node at which the loss is to be calculated, linkID is the ID of the link down which the outflow drains (or a d8 ID if the routing is d8), and grid is a Landlab ModelGrid. The function then returns the new discharge at the node after the function is applied. Note that if a linkID is needed, a nodeID must also be specified, even if only as a dummy parameter; similarly, if a grid is to be passed, all of the preceding parameters must be specified. Both nodeID and linkID are required to permit spatially variable losses, and also losses dependent on flow path geometry (e.g., flow length). The grid is passed to allow fields or grid properties describing values across the grid to be accessed for the loss calculation (see examples). This function expects (float, [int, [int, [ModelGrid]]]), and return a single float, the new discharge value. This behavior is verified during component instantiation. **kwargs (optional) – Any additional parameters to pass to a FlowDirector or DepressionFinderAndRouter instance (e.g., partion_method for FlowDirectorMFD). This will have no effect if an instantiated component is passed using the flow_director or depression_finder keywords.