Cross-correlation is used to measure the similarity between two signals.

Here is a method for you to consider.

Divide the whole area into grids and calculate the sample means in each grid. You then get a list as,

G(Grids)              V1(variable 1)                V2 (variable 2)

1                            value                          value

2                               ...                               ...

3                               ...                               ...

...

In this way, V1 and V2 are comparable as they represent values from the same location (grid). Then you can simply calculate the correlation (R) between V1 and V2 as what we normally do for time series. In fact, we can picture the Grids as Time (i.e. t1,t2,t3...). Values of R would represent how correlated v1 and v2 are in space.

This is a bit primitive but I hope it's easy to follow. You could go further by asking question like, if v1 and v2 are found to be highly correlated, from which direction in space they are more correlated? Then you might need consider more sophisticated methods (e.g. Variogram) to calculate the autocorrelation. I haven't figured out how it works for multiple variables.

You can use the Moran's spatial Cross-correlation.

You can use ArcGIS and matlab using Moran's I.

Check this documents:

http://pro.arcgis.com/en/pro-app/tool-reference/spatial-statistics/spatial-autocorrelation.htm

http://userwww.sfsu.edu/efc/classes/biol710/spatial/spat-auto.htm

http://www.mathworks.com/matlabcentral/fileexchange/13663-moran-s-i

For R spatial:

http://rspatial.org/analysis/rst/3-spauto.html

Well,

the attached article may be useful.

Sincerely

Article Hydrochemical model and probable pollution in the water of E...

I used Moran's index.

Best,

Claudio