HackCalculator: Calculate Hack’s law coefficients#
Calculate Hack parameters.
- class HackCalculator(*args, **kwds)[source]#
Bases:
Component
This component calculates Hack’s law parameters for drainage basins.
Hacks law is given as
- ..:math:
L = C * A**h
Where \(L\) is the distance to the drainage divide along the channel, \(A\) is the drainage area, and \(C`and :math:`h\) are parameters.
The HackCalculator uses a ChannelProfiler to determine the nodes on which to calculate the parameter fit.
Examples
>>> import pandas as pd >>> pd.set_option('display.max_columns', None) >>> import numpy as np >>> from landlab import RasterModelGrid >>> from landlab.components import ( ... FlowAccumulator, ... FastscapeEroder, ... HackCalculator) >>> np.random.seed(42) >>> mg = RasterModelGrid((50, 100), xy_spacing=100) >>> z = mg.add_zeros('node', 'topographic__elevation') >>> z[mg.core_nodes] += np.random.randn(mg.core_nodes.size) >>> fa = FlowAccumulator(mg) >>> fs = FastscapeEroder(mg, K_sp=0.001) >>> for i in range(100): ... fa.run_one_step() ... fs.run_one_step(1000) ... z[mg.core_nodes] += 0.01 * 1000 >>> hc = HackCalculator(mg) >>> hc.calculate_hack_parameters() >>> largest_outlet = mg.boundary_nodes[ ... np.argsort(mg.at_node['drainage_area'][mg.boundary_nodes])[-1:]][0] >>> largest_outlet 4978 >>> hc.hack_coefficient_dataframe.loc[largest_outlet, "A_max"] 2830000.0 >>> hc.hack_coefficient_dataframe.round(2) A_max C h basin_outlet_id 4978 2830000.0 0.31 0.62
>>> hc = HackCalculator( ... mg, ... number_of_watersheds=3, ... main_channel_only=False, ... save_full_df=True) >>> hc.calculate_hack_parameters() >>> hc.hack_coefficient_dataframe.round(2) A_max C h basin_outlet_id 39 2170000.0 0.13 0.69 4929 2350000.0 0.13 0.68 4978 2830000.0 0.23 0.64 >>> hc.full_hack_dataframe.head().round(2) basin_outlet_id A L_obs L_est node_id 39 39.0 2170000.0 3200.0 2903.43 139 39.0 2170000.0 3100.0 2903.43 238 39.0 10000.0 0.0 71.61 239 39.0 2160000.0 3000.0 2894.22 240 39.0 10000.0 0.0 71.61
References
Required Software Citation(s) Specific to this Component
None Listed
Additional References
Hack, J. T. Studies of longitudinal stream profiles in Virginia and Maryland (Vol. 294). U.S. Geological Survey Professional Paper 294-B (1957). https://doi.org/10.3133/pp294B
- Parameters:
grid (Landlab Model Grid instance, required) –
save_full_df (bool) – Flag indicating whether to create the
full_hack_dataframe
.**kwds – Values to pass to the ChannelProfiler.
- __init__(grid, save_full_df=False, **kwds)[source]#
- Parameters:
grid (Landlab Model Grid instance, required) –
save_full_df (bool) – Flag indicating whether to create the
full_hack_dataframe
.**kwds – Values to pass to the ChannelProfiler.
- property full_hack_dataframe#
Full Hack calculation dataframe.
This dataframe is optionally created and stored on the component when the keyword argument
full_hack_dataframe=True
is passed to the component init.It is pandas dataframe with a row for every model grid cell used to estimate the Hack parameters. It has the following index and columns.
- Index
node_id*: The node ID of the model grid cell.
- Columns
basin_outlet_id: The node IDs of watershed outlet
A: The drainage are of the model grid cell.
L_obs: The observed distance to the divide.
L_est: The predicted distance to divide based on the Hack coefficient fit.
- property hack_coefficient_dataframe#
Hack coefficient dataframe.
This dataframe is created and stored on the component.
It is a pandas dataframe with one row for each basin for which Hack parameters are calculated. Thus, there are as many rows as the number of watersheds identified by the ChannelProfiler.
The dataframe has the following index and columns.
- Index
basin_outlet_id: The node ID of the watershed outlet where each set of Hack parameters was estimated.
- Columns
A_max: The drainage area of the watershed outlet.
C: The Hack coefficient as defined in the equations above.
h: The Hack exponent as defined in the equations above.