如何计算两个 N 维 xarray 的 Pearson 相关性？

Question

I have two.netcdf files, imported as xarrays (please see summary images below), containing seasonal precipitation data (lat, lon, season, precip) over Africa (regridded to the same grid). I would like to compare each season by calculating a Pearson's correlation coefficient (a pattern correlation) to be used in a Taylor diagram (for each season). I have tried numpy's corrcoef , but this returns a matrix and I need a single value. I have also tried scipy's pearsonsr but it raises an error (The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()). I am new to python and.netcdf files and so would appreciate any guidance.

File1:

<xarray.DataArray 'pre' (season: 4, lat: 162, lon: 162)>
array([[[       nan,        nan,        nan, ...,        nan,
                nan,        nan],
        [       nan,        nan,        nan, ...,        nan,
                nan,        nan],
        [       nan,        nan,        nan, ...,        nan,
                nan,        nan],
        ...,
        [       nan,        nan,        nan, ..., 21.462164 ,
         21.921623 , 20.583786 ],
        [       nan,        nan,        nan, ..., 22.240545 ,
         21.24054  , 21.135136 ],
        [       nan,        nan,        nan, ..., 20.78919  ,
         20.45946  , 18.62973  ]]], dtype=float32)
Coordinates:
  * lon   (lon) float64 -20.25 -19.75 -19.25 -18.75 ... 59.25 59.75 60.25
  * lat   (lat) float64 -40.25 -39.75 -39.25 -38.75 ... 39.25 39.75 40.25
  * season(season) object 'DJF' 'JJA' 'MAM' 'SON'

File2:

<xarray.DataArray 'tp' (season: 4, lat: 162, lon: 162)>
array([[[        nan,         nan,         nan, ...,         nan,
                 nan,         nan],
        [        nan,         nan,         nan, ...,         nan,
                 nan,         nan],
        [        nan,         nan,         nan, ...,         nan,
                 nan,         nan],
        ...,
        [        nan,         nan,         nan, ..., 21.7096725 ,
         21.09724263, 19.69123712],
        [        nan,         nan,         nan, ..., 21.2375123 ,
         20.71120389, 20.73519617],
        [        nan,         nan,         nan, ..., 20.80748653,
         19.70237051, 18.9941896 ]]])
Coordinates:
  * lon   (lon) float64 -20.25 -19.75 -19.25 -18.75 ... 59.25 59.75 60.25
  * lat   (lat) float64 -40.25 -39.75 -39.25 -38.75 ... 39.25 39.75 40.25
  * season(season) object 'DJF' 'JJA' 'MAM' 'SON'

Answer 1

If you're just looking for a single correlation coefficient across all the values, between one array and the other, try flattening the arrays and then get one of the values off the diagonal (eg [0, 1] ).:

>>> res = np. corrcoef(arr1.values.flat, arr2.values.flat)
>>> res
array([[1.       , 0.9985713],
       [0.9985713, 1.       ]])

>>> res[0, 1]
0.9985713

corrcoef always returns an array giving the correlation with respect to each slice of the arrays, but if you're looking for the correlation across all elements in the two then you need to reshape them to be vectors.

Answer 2

You can do this:

    pearson = xr.corr(file1,file2)
pearson = np.array(pearson)  #like this you can see the value