.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/1single/plot_weighted-eof.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_1single_plot_weighted-eof.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_1single_plot_weighted-eof.py:


Weighted EOF analysis
========================

Weighted EOF analysis (in S-mode) maximises the temporal variance
considering each gridpoint with a different weight. We compare the
results for an EOF analysis based on (1) the covariance matrix, (2) area
weighting based on latitude (coslat weighting), (3) the correlation matrix
and finally (4) correlation matrix + coslat weighting.

Load packages and data:

.. GENERATED FROM PYTHON SOURCE LINES 13-26

.. code-block:: Python


    import xarray as xr
    import matplotlib.pyplot as plt
    import seaborn as sns
    from matplotlib.gridspec import GridSpec
    from cartopy.crs import Orthographic, PlateCarree

    from xeofs.models import EOF

    sns.set_context("paper")

    t2m = xr.tutorial.load_dataset("air_temperature")["air"]








.. GENERATED FROM PYTHON SOURCE LINES 27-28

Perform the actual analysis

.. GENERATED FROM PYTHON SOURCE LINES 28-53

.. code-block:: Python


    components = []
    scores = []
    # (1) Based on covariance matrix
    model_cov = EOF(n_modes=5, standardize=False, use_coslat=False)
    model_cov.fit(t2m, "time")
    components.append(model_cov.components())
    scores.append(model_cov.scores())
    # (2) Based on coslat weighted covariance matrix
    model_lat = EOF(n_modes=5, standardize=False, use_coslat=True)
    model_lat.fit(t2m, "time")
    components.append(model_lat.components())
    scores.append(model_lat.scores())
    # (3) Based on correlation matrix
    model_cor = EOF(n_modes=5, standardize=True, use_coslat=False)
    model_cor.fit(t2m, "time")
    components.append(model_cor.components())
    scores.append(model_cor.scores())
    # (4) Based on coslat weighted correlation matrix
    model_cor_lat = EOF(n_modes=5, standardize=True, use_coslat=True)
    model_cor_lat.fit(t2m, "time")
    components.append(model_cor_lat.components())
    scores.append(model_cor_lat.scores())









.. GENERATED FROM PYTHON SOURCE LINES 54-55

Create figure showing the first mode for all 4 cases

.. GENERATED FROM PYTHON SOURCE LINES 55-89

.. code-block:: Python


    proj = Orthographic(central_latitude=30, central_longitude=-80)
    kwargs = {
        "cmap": "mako",
        "transform": PlateCarree(),
        "vmin": 0,
    }
    titles = [
        "(1) Covariances",
        "(2) Covariances + coslat",
        "(3) Correlation",
        "(4) Correlation + coslat",
    ]
    fig = plt.figure(figsize=(10, 12))
    gs = GridSpec(4, 2)
    ax_pcs = [fig.add_subplot(gs[i, 0]) for i in range(4)]
    ax_eofs = [fig.add_subplot(gs[i, 1], projection=proj) for i in range(4)]

    for i, (a1, a2) in enumerate(zip(ax_eofs, ax_pcs)):
        a1.coastlines(color=".5")
        components[i].sel(mode=1).plot(ax=a1, **kwargs)
        scores[i].sel(mode=1).plot(ax=a2, color="darkred")
        a2.set_xlabel("")
        a1.set_title("", loc="center")
        a2.set_title("", loc="center")
        a2.set_title(titles[i], loc="left", weight="bold")
        if i < 3:
            a2.set_xticks([], [])
            sns.despine(ax=a2, trim=True, bottom=True)
        else:
            sns.despine(ax=a2, trim=True, bottom=False)

    plt.tight_layout()
    plt.savefig("weighted_eof.jpg", dpi=200)



.. image-sg:: /auto_examples/1single/images/sphx_glr_plot_weighted-eof_001.png
   :alt: (1) Covariances, (2) Covariances + coslat, (3) Correlation, (4) Correlation + coslat
   :srcset: /auto_examples/1single/images/sphx_glr_plot_weighted-eof_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.928 seconds)


.. _sphx_glr_download_auto_examples_1single_plot_weighted-eof.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_weighted-eof.ipynb <plot_weighted-eof.ipynb>`

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

      :download:`Download Python source code: plot_weighted-eof.py <plot_weighted-eof.py>`


.. only:: html

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

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