2D Water top surface profile

I am trying to create the effect of the water surface thickness with a vertex-fragment shader.

I am in a 3D game environment but It's a scroll view so a "2D" view. Here is a good tutorial of creating such effect in real 2D using fragment shader.

But this can't be used in my case I think. For the moment I have only a plane were I apply refraction.

And I want to apply the water thickness effect. But I don't know how to do it.

I am not trying to create some water deformation/displacement using vertex for the moment, this is not the point.

I don't know if it's possible with a simple quad maybe should I use an object like this.

Here are some examples.

I don't have any idea on how to create this effect.

Thanks a lot !

[EDIT] Added Rayman water effect to have a better reference of the effect.