One idea is to make a sprite of a ring and spawn that where the player is. Then you have the rings increase in size and fade in opacity. You could play around with how you draw the ring. Maybe have feathered edges, and maybe shade it. You can also play around with using the additive blend on the rings. There may even be a shader to distort the texture underneath.
To limit this effect on water tiles you'll need to mask it somehow. Put the rings on a layer with force only texture and a tilemap on top with the destination-out blend. There may be cleaner ways to mask it with sub-layers or other blend modes.
You could also do it as a simulation. Basically each point of water has a spring to make it return to a normal level and there are also springs connecting the 4 adjacent point of water. This could be done with an array. Then to draw it you could draw it with drawingcanvas if you want to simulate per pixel, or maybe utilize a distort mesh for a simpler sim. You could it with a color gradient based on depth. For mesh that would mean you'd use a gradient texture and mess with the uvs to have a color per vertex. Alternately you could color it like a normal map. The latter could be more useful when used with effects but you'll have to look into what's available for distortion effects. There are other ideas to explore here.
Limiting all that to just the water still requires making. Or just make the ground drawn higher.