.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/04_krige_geometric.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_04_krige_geometric.py>`
        to download the full example code.

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

.. _sphx_glr_examples_04_krige_geometric.py:


Geometric example
=================

A small example script showing the usage of the 'geographic' coordinates type
for ordinary kriging on a sphere.

.. GENERATED FROM PYTHON SOURCE LINES 9-52

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    from pykrige.ok import OrdinaryKriging

    # Make this example reproducible:
    np.random.seed(89239413)

    # Generate random data following a uniform spatial distribution
    # of nodes and a uniform distribution of values in the interval
    # [2.0, 5.5]:
    N = 7
    lon = 360.0 * np.random.random(N)
    lat = 180.0 / np.pi * np.arcsin(2 * np.random.random(N) - 1)
    z = 3.5 * np.random.rand(N) + 2.0

    # Generate a regular grid with 60° longitude and 30° latitude steps:
    grid_lon = np.linspace(0.0, 360.0, 7)
    grid_lat = np.linspace(-90.0, 90.0, 7)

    # Create ordinary kriging object:
    OK = OrdinaryKriging(
        lon,
        lat,
        z,
        variogram_model="linear",
        verbose=False,
        enable_plotting=False,
        coordinates_type="geographic",
    )

    # Execute on grid:
    z1, ss1 = OK.execute("grid", grid_lon, grid_lat)

    # Create ordinary kriging object ignoring curvature:
    OK = OrdinaryKriging(
        lon, lat, z, variogram_model="linear", verbose=False, enable_plotting=False
    )

    # Execute on grid:
    z2, ss2 = OK.execute("grid", grid_lon, grid_lat)








.. GENERATED FROM PYTHON SOURCE LINES 53-54

Print data at equator (last longitude index will show periodicity):

.. GENERATED FROM PYTHON SOURCE LINES 54-67

.. code-block:: Python


    print("Original data:")
    print("Longitude:", lon.astype(int))
    print("Latitude: ", lat.astype(int))
    print("z:        ", np.array_str(z, precision=2))
    print("\nKrige at 60° latitude:\n======================")
    print("Longitude:", grid_lon)
    print("Value:    ", np.array_str(z1[5, :], precision=2))
    print("Sigma²:   ", np.array_str(ss1[5, :], precision=2))
    print("\nIgnoring curvature:\n=====================")
    print("Value:    ", np.array_str(z2[5, :], precision=2))
    print("Sigma²:   ", np.array_str(ss2[5, :], precision=2))





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Original data:
    Longitude: [122 166  92 138  86 122 136]
    Latitude:  [-46 -36 -25 -73 -25  50 -29]
    z:         [2.75 3.36 2.24 3.07 3.37 5.25 2.82]

    Krige at 60° latitude:
    ======================
    Longitude: [  0.  60. 120. 180. 240. 300. 360.]
    Value:     [5.29 5.11 5.27 5.17 5.35 5.63 5.29]
    Sigma²:    [2.22 1.32 0.42 1.21 2.07 2.48 2.22]

    Ignoring curvature:
    =====================
    Value:     [4.55 4.72 5.25 4.82 4.61 4.53 4.48]
    Sigma²:    [3.79 2.   0.39 1.85 3.54 5.46 7.53]




.. GENERATED FROM PYTHON SOURCE LINES 68-74

We can see that the data point at longitude 122, latitude 50 correctly
dominates the kriged results, since it is the closest node in spherical
distance metric, as longitude differences scale with cos(latitude).
When kriging using longitude / latitude linearly, the value for grid points
with longitude values further away as longitude is now incorrectly
weighted equally as latitude.

.. GENERATED FROM PYTHON SOURCE LINES 74-81

.. code-block:: Python


    fig, (ax1, ax2) = plt.subplots(1, 2)
    ax1.imshow(z1, extent=[0, 360, -90, 90], origin="lower")
    ax1.set_title("geo-coordinates")
    ax2.imshow(z2, extent=[0, 360, -90, 90], origin="lower")
    ax2.set_title("non geo-coordinates")
    plt.show()



.. image-sg:: /examples/images/sphx_glr_04_krige_geometric_001.png
   :alt: geo-coordinates, non geo-coordinates
   :srcset: /examples/images/sphx_glr_04_krige_geometric_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.053 seconds)


.. _sphx_glr_download_examples_04_krige_geometric.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 04_krige_geometric.ipynb <04_krige_geometric.ipynb>`

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

      :download:`Download Python source code: 04_krige_geometric.py <04_krige_geometric.py>`

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

      :download:`Download zipped: 04_krige_geometric.zip <04_krige_geometric.zip>`


.. only:: html

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

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