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.. "examples/12_sum_model/00_simple_sum_model.py"
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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_12_sum_model_00_simple_sum_model.py>`
        to download the full example code.

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

.. _sphx_glr_examples_12_sum_model_00_simple_sum_model.py:


Creating a Sum Model
--------------------

This tutorial demonstrates how to create and use sum models in GSTools.
We'll combine a Spherical and a Gaussian covariance model to construct
a sum model, visualize its variogram, and generate spatial random fields.

Let's start with importing GSTools and setting up the domain size.

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.. code-block:: Python


    import gstools as gs

    x = y = range(100)








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First, we create two individual covariance models: a :any:`Spherical` model and a
:any:`Gaussian` model. The Spherical model with its short length scale
will emphasize small-scale variability, while the Gaussian model with a larger length scale
captures larger-scale patterns.

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.. code-block:: Python


    m0 = gs.Spherical(dim=2, var=2.0, len_scale=5.0)
    m1 = gs.Gaussian(dim=2, var=1.0, len_scale=10.0)








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Next, we create a sum model by adding these two models together.
Let's visualize the resulting variogram alongside the individual models.

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.. code-block:: Python


    model = m0 + m1
    ax = model.plot(x_max=20)
    m0.plot(x_max=20, ax=ax)
    m1.plot(x_max=20, ax=ax)




.. image-sg:: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_001.png
   :alt: 00 simple sum model
   :srcset: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_001.png
   :class: sphx-glr-single-img





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As shown, the Spherical model controls the behavior at shorter distances,
while the Gaussian model dominates at longer distances. The ratio of influence
is thereby controlled by the provided variances of the individual models.

Using the sum model, we can generate a spatial random field. Let's visualize
the field created by the sum model.

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.. code-block:: Python


    srf = gs.SRF(model, seed=20250107)
    srf.structured((x, y))
    srf.plot()




.. image-sg:: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_002.png
   :alt: Field 2D structured: (100, 100)
   :srcset: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_002.png
   :class: sphx-glr-single-img





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For comparison, we generate random fields using the individual models
to observe their contributions more clearly.

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.. code-block:: Python


    srf0 = gs.SRF(m0, seed=20250107)
    srf0.structured((x, y))
    srf0.plot()

    srf1 = gs.SRF(m1, seed=20250107)
    srf1.structured((x, y))
    srf1.plot()




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_003.png
         :alt: Field 2D structured: (100, 100)
         :srcset: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_004.png
         :alt: Field 2D structured: (100, 100)
         :srcset: /examples/12_sum_model/images/sphx_glr_00_simple_sum_model_004.png
         :class: sphx-glr-multi-img





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As seen, the Gaussian model introduces large-scale structures, while the
Spherical model influences the field's roughness. The sum model combines
these effects, resulting in a field that reflects multi-scale variability.


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

   **Total running time of the script:** (0 minutes 2.023 seconds)


.. _sphx_glr_download_examples_12_sum_model_00_simple_sum_model.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 00_simple_sum_model.ipynb <00_simple_sum_model.ipynb>`

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

      :download:`Download Python source code: 00_simple_sum_model.py <00_simple_sum_model.py>`

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

      :download:`Download zipped: 00_simple_sum_model.zip <00_simple_sum_model.zip>`


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