How to compute the Wasserstein Distance between two random 2-D possibility distribution functions?

I have two 2-D possibility distribution functions, now I need to compute the Wasserstein Distance between them. However, I cannot find any code or functions that can treat 2D PDF, all existing code can only deal with the 1-D curves.

[Torsten]

Never heard of the Wasserstein Distance for 2d probability density functions. Can you give the definition ?