.. highlight:: rest

.. _distance:

Spatial Distances
=================

Calculate grid cell distances for use in calculating spatial covariances.

The calculation of the matrix Q in :ref:`equation 2 <equation2>` depends on the spatial covariance matrix E.  This matrix E is defined as :math:`e^{(-X_s/l_s)}`
where :math:`X_s` are the spatial distances between grid cells.  These spatial distances need to be calculated only one time for a spatial domain.  These distances are 
calculated using the script :program:`make_sc.py`::

        Usage: python make_sc.py [-c configfile] 

        where
                configfile - configuration file. If not specified, use 'config.ini'.

        Output:
                A numpy save file with dimensions nlandcells x nlandcells, with distance in kilometers between each cell. 
                The name of this file is set in the configuration file with key 'sp_cov_file', e.g. sp_cov_file = "spcov.npy"

Example::

        >>> import numpy
        >>> a = numpy.load("spcov.npy")
        >>> a
        array([[    0.        ,   109.46755851,   218.93484013, ...,
                 7671.1452984 ,  7672.82817131,  7686.81558107],
               [  109.46755851,     0.        ,   109.46755851, ...,
                 7669.83574638,  7671.1452984 ,  7683.27826395],
               [  218.93484013,   109.46755851,     0.        , ...,
                 7668.90000321,  7669.83574638,  7680.10975617],
               ..., 
               [ 7671.1452984 ,  7669.83574638,  7668.90000321, ...,
                    0.        ,    20.35208384,   122.06006263],
               [ 7672.82817131,  7671.1452984 ,  7669.83574638, ...,
                   20.35208384,     0.        ,   101.73045238],
               [ 7686.81558107,  7683.27826395,  7680.10975617, ...,
                  122.06006263,   101.73045238,     0.        ]])
        >>> a.shape
        (3470, 3470)
        >>> 

Spatial Correlation Length
--------------------------

:ref:`Equation 2 <equation2>` uses a parameter l\ :sub:`s` for specifying the spatial covariance E.  In the inversion code, a constant value of l\ :sub:`s` is used, and is defined in the configuration file with key name 'spatial_corr_length'.  The units for this value are in kilometers.

Example::

        spatial_corr_length = 500.0