The deAlmeida Overland Flow Component¶
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This notebook illustrates running the deAlmeida overland flow component in an extremely simple-minded way on a real topography, then shows it creating a flood sequence along an inclined surface with an oscillating water surface at one end.
First, import what we'll need:
from landlab.components.overland_flow import OverlandFlow
from landlab.plot.imshow import imshow_grid
from landlab.plot.colors import water_colormap
from landlab import RasterModelGrid
from landlab.io.esri_ascii import read_esri_ascii
from matplotlib.pyplot import figure
import numpy as np
from time import time
%matplotlib inline
Pick the initial and run conditions
run_time = 100 # duration of run, (s)
h_init = 0.1 # initial thin layer of water (m)
n = 0.01 # roughness coefficient, (s/m^(1/3))
g = 9.8 # gravity (m/s^2)
alpha = 0.7 # time-step factor (nondimensional; from Bates et al., 2010)
u = 0.4 # constant velocity (m/s, de Almeida et al., 2012)
run_time_slices = (10,50,100)
Elapsed time starts at 1 second. This prevents errors when setting our boundary conditions.
elapsed_time = 1.0
Use Landlab methods to import an ARC ascii grid, and load the data into the field that the component needs to look at to get the data. This loads the elevation data, z, into a "field" in the grid itself, defined on the nodes.
rmg, z = read_esri_ascii('Square_TestBasin.asc')
rmg.add_field('node', 'topographic__elevation', z)
rmg.set_closed_boundaries_at_grid_edges(True, True, True, True)
We can get at this data with this syntax:
np.all(rmg.at_node['topographic__elevation'] == z)
True
Note that the boundary conditions for this grid mainly got handled with the final line of those three, but for the sake of completeness, we should probably manually "open" the outlet. We can find and set the outlet like this:
my_outlet_node = 100 # This DEM was generated using Landlab and the outlet node ID was known
rmg.status_at_node[my_outlet_node] = 1 # 1 is the code for fixed value
Now initialize a couple more grid fields that the component is going to need:
rmg.add_zeros('node', 'surface_water__depth') # water depth (m)
array([ 0., 0., 0., ..., 0., 0., 0.])
rmg.at_node['surface_water__depth'] += h_init
Let's look at our watershed topography
imshow_grid(rmg, 'topographic__elevation')
Now instantiate the component itself
of = OverlandFlow(rmg, steep_slopes=True) #for stability in steeper environments, we set the steep_slopes flag to True
Now we're going to run the loop that drives the component:
while elapsed_time < run_time:
# First, we calculate our time step.
dt = of.calc_time_step()
# Now, we can generate overland flow.
of.overland_flow()
# Increased elapsed time
print('Elapsed time: ', elapsed_time)
elapsed_time += dt
Elapsed time: 1.0 Elapsed time: 22.2013286086 Elapsed time: 39.94939454 Elapsed time: 55.0723820405 Elapsed time: 68.1011721277 Elapsed time: 79.6427396372 Elapsed time: 90.0483576541 Elapsed time: 99.5939522661
imshow_grid(rmg, 'surface_water__depth', cmap='Blues')
Now let's get clever, and run a set of time slices:
elapsed_time = 1.
for t in run_time_slices:
while elapsed_time < t:
# First, we calculate our time step.
dt = of.calc_time_step()
# Now, we can generate overland flow.
of.overland_flow()
# Increased elapsed time
elapsed_time += dt
figure(t)
imshow_grid(rmg, 'surface_water__depth', cmap='Blues')
