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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_tutorials_example_variable_density.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_tutorials_example_variable_density.py:


================================================================================
Ocean water state law
================================================================================

In this tutorial ocean international equation of state (IES 1980) used in 
Freshkiss3D to compute density based on temperature and salinity tracers is plotted.

.. GENERATED FROM PYTHON SOURCE LINES 10-84

.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt
    import freshkiss3d.extra.plots as fk_plt
    from freshkiss3d.core.state_laws import *

    PLOT_DERIVATIVE = False

    fk_plt.set_rcParams()
    plt.rcParams["figure.figsize"]=[12,5]

    fig = plt.figure()
    ax1 = fig.add_subplot(121)

    P0 = 1.0
    T = [0, 5, 10, 15, 20]
    S = [0, 5, 10, 15, 20, 25, 30, 35]
    Rho = np.zeros( (len(S)) )

    #IES 1980: 
    for I in range(len(T)):
        for J in range(len(S)):
            Rho[J] = Rho_IES1980(P0, T[I], S[J])

        ax1.plot(S, Rho, label='T = {} °C'.format(T[I]))

    #Linear law: \rho = \rho_0 - \alpha*S
    for J in range(len(S)):
        Rho[J] = Rho_salinity(S[J])
    ax1.plot(S, Rho, color='k', ls=':', label='T = 10 °C (linear)')

    ax1.legend(loc=4, shadow=True, title="Temperature")
    ax1.set_xlabel('$S$ $(PSU)$')
    ax1.set_ylabel('$\\rho$ $(kg/m^3)$')
    ax1.set_xlim(0,35)
    ax1.set_ylim(995,1030)

    ax2 = fig.add_subplot(122)
    if PLOT_DERIVATIVE: ax2b = ax2.twinx()

    T = [-10, -5, 0, 5, 10, 15, 20, 25, 30]
    S = [0, 5, 10, 15, 20, 25, 30, 35]
    Rhob = np.zeros( (len(T)) )
    dRho_estimate = np.zeros( (len(T)) )
    P = 1
    eps = 0.0001

    #IES 1980:
    for I in range(len(S)):
        for J in range(len(T)):
            Rhob[J] = Rho_IES1980(P0, T[J], S[I])
            dRho_estimate[J] = (Rho_IES1980(P0, T[J]+eps, S[I])-Rho_IES1980(P0, T[J], S[I]))/eps

        ax2.plot(T, Rhob, label='S = {} PSU'.format(S[I]))

        if PLOT_DERIVATIVE:
            ax2b.plot(T, dRho_estimate, label='dRho_dT,S = {} PSU'.format(S[I]))

    #Quadratic law: \rho = \rho_0*(1 - \alpha*(T-4.0)**2)
    for J in range(len(T)):
        Rhob[J] = Rho_temperature(T[J])
    ax2.plot(T, Rhob, color='k', ls=':', label='S = 0 PSU (quadratic)')

    ax2.legend(loc=3, shadow=True, title="Salinity")
    ax2.set_xlabel('$T$ $(°C)$')
    ax2.set_ylabel('$\\rho$ $(kg/m^3)$')
    ax2.set_xlim(-5,25)
    ax2.set_ylim(980,1030)
    if PLOT_DERIVATIVE:
        ax2b.legend(loc=4, shadow=True, title="Salinity")
        ax2b.set_ylim(-0.2,0.2)

    plt.show()




.. image-sg:: /auto_examples_tutorials/images/sphx_glr_example_variable_density_001.png
   :alt: example variable density
   :srcset: /auto_examples_tutorials/images/sphx_glr_example_variable_density_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 85-90

.. note::

   * If only temperature is prescribed in Freshkiss3D, IES is used with a default salinity of 0 g/L. You can set the default value with ``the ies1980_default_S0`` key of the ``physical_parameters`` dictionary.
   * If only salinity is prescribed in Freshkiss3D, IES is used with a default temperature of 10 °C. You can set the default value with ``the ies1980_default_T0`` key of the ``physical_parameters`` dictionary.



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

   **Total running time of the script:** ( 0 minutes  0.267 seconds)


.. _sphx_glr_download_auto_examples_tutorials_example_variable_density.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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