Comparing Bivariate Binned Frequency Histograms

I am modeling emissions at work zones for different principal components,
level of congestion and work zone configuration. Emission modeling relies on
second-by-second vehicle kinematics. I binned the speed (x-axis) and
acceleration (y-axis) then computed the percent of time vehicles spend within
each of the grouped bins. The binned groups are not equal in size. I have multiple distributions based on the
classified work zones and my objective is to compare these distributions and
determine if they are the same or different.

I came across a paper when I was trying to look at ways to compare bivariate
frequency histograms “Implementing a 3D histogram version of the energy test
in ROOT”. This paper discusses an approach which was developed by two
researchers Cohen and Piatsezky and implemented in ROOT. Cohen shared the package on his personal web page but I need more help understanding whether I can apply it to my data since it is bivariate.

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