Spatial Distances¶

Calculate grid cell distances for use in calculating spatial covariances.

The calculation of the matrix Q in equation 2 depends on the spatial covariance matrix E. This matrix E is defined as $e^{(-X_s/l_s)}$ where $X_s$ 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 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¶

Equation 2 uses a parameter l_s for specifying the spatial covariance E. In the inversion code, a constant value of l_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