xr.corr, receiving different values depending on if dim applied on 2D arrays

[ZZMitch]

Hello,

I have two xarray.DataArray and was interested in the overall correlation between them. They are both of 2D arrays of shape 6001 x 6001 that align spatially with the same CRS and contain NaNs i.e.,:

arr1:

arr2:

When quantifying their correlation, I receive very different results depending on if I set the dim parameter in xr.corr().

Without setting dim, i.e., xr.corr(arr1, arr2) I receive a correlation of array(0.08744669).
When setting dim, i.e., xr.corr(arr1, arr2, dim = ['x', 'y']) I receive a correlation of array(0.4891213, dtype=float32).

I checked pearsonr from scipy.stats...

from scipy.stats import pearsonr  

# If null in either arr, set to null in both
arr1 = xr.where((arr1 .isnull() | arr2.isnull()), np.nan, arr1)
arr2 = xr.where((arr1 .isnull() | arr2.isnull()), np.nan, arr2)

# Flatten
arr1 = arr1.to_numpy().flatten()
arr2 = arr2.to_numpy().flatten()

# Drop null
arr1 = arr1[~np.isnan(arr1)]
arr2 = arr2[~np.isnan(arr2)]

# Calculate pearson r
pearsonr(arr1 , arr2) # PearsonRResult(statistic=np.float64(0.4891210562797157), pvalue=np.float32(0.0))

This indicates that setting the dim explicitly achieves the correct result (within rounding error of pearsonr result).

I am not sure if this is a bug in xr.corr or me misunderstanding the function. From limited testing, I found differences (although much smaller) if I subset to tiny portions of each array and portions without an NaNs.

Any comments appreciated!