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What causes ice to melt in these patterns?

Melting Ice

And why does this always happen when the ice is covered in snow?

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up vote 2 down vote accepted

Those are drainage dendrites around the central clear area, much like what you see with rivers as they branch into smaller tributaries upstream. So, at least part of the answer is that the water melting from the snow is joining together into a generally downhill flow towards the central region.

Furthermore, it's quite likely the central region is a lot warmer because there is no longer any snow there to reflect sunlight. Once such a spot forms -- and it has to eventually if there's too much energy coming in -- it will become both a radiating heat source that encourages further melting around it, and also a lower level (no snow) that encourages melt water to drain into it, drainage-style.

So, some predictions: (1) This should happen mostly on dark, flat surfaces with little or no slope, such as asphalt parking lots, and (2) It should happen only when the sun is out.

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This totally makes sense! – user17615 Mar 13 '13 at 10:30

The pattern shown is an ice star. It is formed in the fall just as ice starts to form on a pond. After a snow a slushy layer forms. Slightly warmer water convects up and melts a hole. Probably at the intersection of three convection cells. Two competing effects are at work to form the dentratic pattern. The warm water welling up from below wants to spread out radially when it gets to the surface. This tends to make the channels branch. On the other hand, wider channels through the slush are more efficient at carrying heat away from the center and tend to widen and lengthen channels along a specific radial. The balance between these competing "forces" creates the star like pattern.

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