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1) Photo mode's 'silhouette' option is just the depth buffer. Could use this to make your own effects out of screenshots.

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2) There's a bit of weird shadowing on non-flat surfaces beneath Mario. It's especially visible on particles from jumping off your hat. This implies that the game doesn't render a normal buffer, because with that you could clip the shadow on very uneven surfaces.

Gist is to sample what's been rendered so far with UVs adjusted based on the camera's view direction to emulate the high refractive index of water. Because the water is rendered after all the opaque pass, the buffer already has the frog and that gets shifted down along with what's under the water.