hypsometric_integral: calculate the hypsometric hypsometric_integral

hypsometric_integral(grid, outlet_id)[source]

Calculate the hypsometric integral for the model grid.

The hypsometric integral \(I\) is defined as

\[I = \frac{\frac{1}{N} \sum_{i=0}^{N} \left( z - \min \left( z\right) \right)} {\max \left(z\right) - \min \left( z \right)}\]

Where \(z\) is the set of elevation values, and \(N\) is the number of elevation values.

Parameters

  • grid (Landlab model grid) –

  • outlet_id (int) – Outlet id of the watershed.

Returns

I – The hypsometric integral.

Return type

float

Examples

First an example that only uses the hypsometric_integral function.

>>> from landlab import RasterModelGrid
>>> from landlab.components import FlowAccumulator
>>> from umami.calculations import hypsometric_integral
>>> grid = RasterModelGrid((10, 10))
>>> z = grid.add_zeros("node", "topographic__elevation")
>>> z += grid.x_of_node + grid.y_of_node
>>> fa = FlowAccumulator(grid)
>>> fa.run_one_step()
>>> hypsometric_integral(grid, 1)
0.5

Next, the same calculations are shown as part of an umami Metric.

>>> from io import StringIO
>>> from umami import Metric
>>> file_like=StringIO('''
... hi:
...     _func: hypsometric_integral
...     outlet_id: 1
... ''')
>>> metric = Metric(grid)
>>> metric.add_from_file(file_like)
>>> metric.names
['hi']
>>> metric.calculate()
>>> metric.values
[0.5]