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I believe open water acts later in the season as bottom melt as Rob explained before; some mixing is needed for that too. I imagine it also permits warm air to get humidity and transport it on top of the ice, but warm air is needed too.
Melt ponds OTOH have the potential to extend over a much greater surface, helping amplify albedo further even when its albedo is reduced only a half.
I guess it is the complex dynamics of the Arctic.
Quite complex it is, indeed. Add to the mix the fact that open water allows much of sunlight entering it to go rather deep - meters and dozens meters down into the water column, where it gradually gets absorbed, while melt ponds do not do that; yes, they reflect much more than open water, but the part melt ponds end up absorbing is all concentranted within rather thin water layer of centimeters to dozens centimeters thick.
Then also add soot on top of it all. Soot falling onto open water, or happening to be added onto it after melt - makes it way down the water column, eventually sinking deep enough to stop being significant factor in terms of surface albedo. Smaller soot particles are
measured to have significantly higher density than water. The snow/ice surface soot, as well as soot within melt ponds, - obviously does not sink, "working" continusouly to reduce albedo. And while the difference at any given single spot (i mean extra amounts of soot due to increasing amount and size of forest fires next to Arctic) - may be very small, when integrated over whole Arctic or CAB in particular, it adds up to serious extra energy absorbed. Of course, once melt ponds start to drain into the ocean, this "soot factor" diminishes, but not completely - some soot is taken into ocean water when ponds start to drain, but not all of it. And, of course, sunlight is needed to make this factor change some things, too - not always present, patterns and amount vary.
And then there are all sorts of combinations of water currents, surface air temps and winds, ice states, and even waves if it's storm and ice is broken into small enough pieces (we've seen that during 2012 GAC on a huge scale alright). For example, if you have thick clouds, warm open water but cold air, then you'll have lots of evaporation, and that takes heat away from surface water, - that heat is not melting ice. But if you got same situation but it's some ice, then obviously there wouldn't be much evaporation (cold air would even freeze shallow melt ponds, if those were present initially - near-zero water in melt ponds is most easy to form tiny layer of ice on top of it), and so all the warm water under the ice would end up giving its heat not to warm up the air, but to melt ice. So, the mere fact of ice presense - melt ponds or not, - changes lots of things in terms of how much melt we end up seeing total - either descreasing or increasing melt amount depends on the specific circumstances, and to keep every possible combination and consider every possible state of ice (Melt ponds? How big? Concentration? Thickness? Mechanical properties? etc) and how exactly it affects its own melting "regime" - is one too complex task indeed.