Altimetry diagnostics
*********************

This section show comparisons on geostrophic velocities computed from Sea Level Anomaly (SLA)

#. From Croco model, the SLA is computed from the difference between SSH and SSH integrated over the year.

   .. math:: 
       SLA(t)=zeta(t)-zeta_{mean}
   
   Then the EKE is computed from geostrophic velocities 
   
   .. math:: 
       EKE=\frac{1}{2}*(u^{'2}+v^{'2}) \\
          =\frac{g^2}{2f^2}*((\frac{-\partial{SLA}}{\partial{y}})^2+(\frac{\partial{SLA}}{\partial{x}})^2)


#. The Altimetry products used here are AVISO products which provide directly the components of geostrophic velocities *ugosa* and *vgosa*

   https://www.aviso.altimetry.fr/en/data/product-information/aviso-user-handbooks.html

#. Filtering of Data

   Once the EKE is computed for both Data and model, a temporal filter is applied to separate the low and high components.
   The filter used is the butterworth filter with a cut-off frequency of 100 days.

#. What plots ?

   * Maps of low and high passed EKE comparisons
   * Spatial mean over the differents basins in mediterranea and plot of the time series
  
    .. image:: images/ALTI/eke_low_pass.png

    .. image:: images/ALTI/eke_time_serie_low_pass.png
    
    .. image:: images/ALTI/eke_high_pass.png
    
    .. image:: images/ALTI/eke_time_serie_high_pass.png
    
    .. image:: images/ALTI/eke_all_pass.png
    
    .. image:: images/ALTI/eke_time_serie_all_pass.png
    


#. What scripts ?
   
   **diags_alti.ipynb** is the notebook to use to compute and do the plots