landlab.components.flow_accum.flow_accumulator

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[source]

Bases: Component

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 = [
...     [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.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"].reshape(mg.shape)
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"].reshape(mg.shape)
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=(10.0, 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"].reshape(mg.shape)
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(1.0)
>>> fa.run_one_step()
>>> mg.at_node["surface_water__discharge"].reshape(mg.shape)
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"].reshape(mg.shape)
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"].reshape(mg.shape)
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, 0.0))
>>> _ = 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"]
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).reshape(mg.shape)
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 = (2.0 / (3.0**0.5)) ** 0.5
>>> hmg = HexModelGrid((5, 3), spacing=dx, xy_of_lower_left=(-1.0745, 0.0))
>>> _ = 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, 0.0))

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)
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]])
>>> df_4.lake_map.reshape(mg.shape)
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)
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]])
>>> fa.depression_finder.lake_map.reshape(mg.shape)
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.

static __new__(cls, *args, **kwds)
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.

Returns:

  • 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”].

cite_as = ''
property coords

Return the coordinates of nodes on grid attached to the component.

property current_time

Current time.

Some components may keep track of the current time. In this case, the current_time attribute is incremented. Otherwise it is set to None.

Return type:

current_time

definitions = (('drainage_area', "Upstream accumulated surface area contributing to the node's discharge"), ('flow__data_structure_delta', "Node array containing the elements delta[1:] of the data structure 'delta' used for construction of the downstream-to-upstream node array"), ('flow__upstream_node_order', 'Node array containing downstream-to-upstream ordered list of node IDs'), ('surface_water__discharge', 'Volumetric discharge of surface water'), ('topographic__elevation', 'Land surface topographic elevation'), ('water__unit_flux_in', 'External volume water per area per time input to each node (e.g., rainfall rate)'))
property depression_finder

The DepressionFinder used internally.

depression_handler_raster_direction_method()[source]

Return ‘D8’ or ‘D4’ depending on the direction method used.

(Note: only call this function for a raster gird; does not handle multiple-flow directors)

flooded_nodes_present()[source]
property flow_director

The FlowDirector used internally.

flow_director_raster_method()[source]

Return ‘D8’ or ‘D4’ depending on the direction method used.

(Note: only call this function for a raster gird; does not handle multiple-flow directors)

classmethod from_path(grid, path)

Create a component from an input file.

Parameters:

  • grid (ModelGrid) – A landlab grid.

  • path (str or file_like) – Path to a parameter file, contents of a parameter file, or a file-like object.

Returns:

A newly-created component.

Return type:

Component

property grid

Return the grid attached to the component.

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]))
initialize_optional_output_fields()

Create fields for a component based on its optional field outputs, if declared in _optional_var_names.

This method will create new fields (without overwrite) for any fields output by the component as optional. New fields are initialized to zero. New fields are created as arrays of floats, unless the component also contains the specifying property _var_type.

initialize_output_fields(values_per_element=None)

Create fields for a component based on its input and output var names.

This method will create new fields (without overwrite) for any fields output by, but not supplied to, the component. New fields are initialized to zero. Ignores optional fields. New fields are created as arrays of floats, unless the component specifies the variable type.

Parameters:

values_per_element (int (optional)) – On occasion, it is necessary to create a field that is of size (n_grid_elements, values_per_element) instead of the default size (n_grid_elements,). Use this keyword argument to acomplish this task.

input_var_names = ()

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)
>>> np.flipud(
...     mg.add_field(
...         "topographic__elevation",
...         mg.node_x + mg.node_y,
...         at="node",
...     ).reshape(mg.shape)
... )
array([[4., 5., 6., 7., 8.],
       [3., 4., 5., 6., 7.],
       [2., 3., 4., 5., 6.],
       [1., 2., 3., 4., 5.],
       [0., 1., 2., 3., 4.]])
>>> fa = FlowAccumulator(mg, "topographic__elevation", flow_director="MFD")
>>> fa.run_one_step()
>>> link_order = fa.link_order_upstream()
>>> link_order  
array([ 5, 14, 10,  6, 11,  7, 23, 19, 15, 20, 16, 28, 24, 29, 25])
>>> link_order[0]
5
>>> sorted(link_order[1:4])
[6, 10, 14]
>>> sorted(link_order[4:9])
[7, 11, 15, 19, 23]
>>> sorted(link_order[9:13])
[16, 20, 24, 28]
>>> sorted(link_order[13:])
[25, 29]
>>> np.all(sorted(link_order) == mg.active_links)
True
name = 'FlowAccumulator'
property node_drainage_area

Return the drainage area.

property node_order_upstream

Return the upstream node order (drainage stack).

property node_water_discharge

Return the surface water discharge.

optional_var_names = ('topographic__elevation', 'water__unit_flux_in')
output_var_names = ('drainage_area', 'flow__data_structure_delta', 'flow__upstream_node_order', '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.

property shape

Return the grid shape attached to the component, if defined.

property surface_values

Values of the surface over which flow is accumulated.

unit_agnostic = True
units = (('drainage_area', 'm**2'), ('flow__data_structure_delta', '-'), ('flow__upstream_node_order', '-'), ('surface_water__discharge', 'm**3/s'), ('topographic__elevation', 'm'), ('water__unit_flux_in', 'm/s'))
classmethod var_definition(name)

Get a description of a particular field.

Parameters:

name (str) – A field name.

Returns:

A description of each field.

Return type:

tuple of (name, *description*)

classmethod var_help(name)

Print a help message for a particular field.

Parameters:

name (str) – A field name.

classmethod var_loc(name)

Location where a particular variable is defined.

Parameters:

name (str) – A field name.

Returns:

The location (‘node’, ‘link’, etc.) where a variable is defined.

Return type:

str

var_mapping = (('drainage_area', 'node'), ('flow__data_structure_delta', 'node'), ('flow__upstream_node_order', 'node'), ('surface_water__discharge', 'node'), ('topographic__elevation', 'node'), ('water__unit_flux_in', 'node'))
classmethod var_type(name)

Returns the dtype of a field (float, int, bool, str…).

Parameters:

name (str) – A field name.

Returns:

The dtype of the field.

Return type:

dtype

classmethod var_units(name)

Get the units of a particular field.

Parameters:

name (str) – A field name.

Returns:

Units for the given field.

Return type:

str