Pattern matching


Imagine two similar patterns as shown below which are drawn on same time scale. From eyeballing we can say both are similar pattern but scale is different . My issue is how to prove this hypothesis with statistics (or any other analytical tools).

There are two issues I want to handle for comparisons
1- Can we scale both axis on same scale without losing information. I read that edges do not lose information in scaling. Pointer to any standard method would be helpful
2- Even if we do not scale , can we compare these two distributions for similarity. Again is there any standard non parametric test for same ?