.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_13_horton_laws_of_stream_numbers.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_hydrology_plot_13_horton_laws_of_stream_numbers.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_hydrology_plot_13_horton_laws_of_stream_numbers.py:


Horton's laws of stream numbers (1945)
======================================

Robert Horton ordered the streams of a basin, from unbranched headwaters up to
the main river, and found that the number of streams of each order falls in a
geometric series while their mean length grows in another. Two ratios, the
bifurcation ratio and the length ratio, summarize the whole network. The
example fits both to a synthetic fifth-order basin (with Strahler's 1952
ordering) and compares the counts with Horton's law.

.. GENERATED FROM PYTHON SOURCE LINES 12-36



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_13_horton_laws_of_stream_numbers_001.png
   :alt: Horton: geometric laws of a drainage network
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_13_horton_laws_of_stream_numbers_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.hydrology import stream_length, stream_number

    order = np.arange(1, 6)
    counts = np.array([243, 58, 15, 4, 1])
    lengths = np.array([0.35, 0.82, 1.9, 4.6, 10.8]) * 1e3  # m
    bifurcation = 10 ** -np.polyfit(order, np.log10(counts), 1)[0]
    length_ratio = 10 ** np.polyfit(order, np.log10(lengths), 1)[0]
    predicted = stream_number(order, 5, bifurcation)
    assert 3.5 < bifurcation < 4.5 and 2 < length_ratio < 2.6
    assert np.all(np.abs(np.log(predicted / counts)) < 0.25)

    fig, ax = plt.subplots()
    ax.semilogy(order, counts, "o", label="stream count")
    ax.semilogy(order, predicted, "-", label=f"R_b = {bifurcation:.2f}")
    ax.semilogy(order, lengths, "s", label="mean length [m]")
    ax.semilogy(order, stream_length(order, stream_length(1, lengths[0], 1), length_ratio), "--", label=f"R_L = {length_ratio:.2f}")
    ax.set(xlabel="stream order", xticks=order, title="Horton: geometric laws of a drainage network")
    ax.legend()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.143 seconds)


.. _sphx_glr_download_api_gallery_hydrology_plot_13_horton_laws_of_stream_numbers.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/hydrology/plot_13_horton_laws_of_stream_numbers.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_13_horton_laws_of_stream_numbers.ipynb <plot_13_horton_laws_of_stream_numbers.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_13_horton_laws_of_stream_numbers.py <plot_13_horton_laws_of_stream_numbers.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_13_horton_laws_of_stream_numbers.zip <plot_13_horton_laws_of_stream_numbers.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_