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This is a map of my alternate Earth with a focus on ocean currents, courtesy of Mikael Asikainen:
As you can see here, Greenland looks smooshed, but that is because it is arranged to the extent that Mont Forel, its highest peak, is the North Geographic Pole. Incidentally, this creates and Arctic Ocean with more room for ocean currents to pass through.
Based on this map, how frozen would the Arctic Ocean on this alternate Earth be during the summer months?
Under roughly present climate conditions (well, ignoring anthropogenic global warming), Greenland (um, "Arctica" would be more fitting) is going to be like Antarctica. Ice sheets are likely to be continuous from there into northern Siberia, Alaska and the Canadian Arctic islands, and quite likely much more extensive and extending further south. Odds are that the Beaufort Sea has permanent ice cover.
Without being as nearly surrounded, you can't really talk about an "Arctic Ocean" any more, it's the Atlantic proceeding nearly to the pole. That's going to cause some interesting climatic effects; without the narrowing of the GIUK Gap that restricts some currents a bit and locks cold water into the present Arctic Ocean, the high ocean latitudes there are unlikely to experience a permanent polar cap, so you might get a bizarre situation where you could sail almost to the North Pole while ice sheets extend significant distances south on land.
ADDENDUM: One thing I forgot: the highest peak in Greenland isn't Mount Forel, it's Gunnbjørn Fjeld (about 300 meters taller). It's further north but on the same side of the island, so the map won't change that dramatically.
Also, thinking about it some more, I'm not even sure the preceding example is necessarily true. While I assume Arctica might look like Antarctica, that's not a given: Antarctica only became permanently covered in ice beginning 34 million years ago, and required not just a global drop in temperature but the presence of the Southern Current to isolate it from warmer waters. That isn't going to be the case in this scenario because there's nothing preventing warmer water from getting to very high latitudes.
There are thousands of variables needed to create a precise prediction
But why do you need precise, or even accurate? What you need is believable.
So, start with the current world's map including the ice pack. As you shift Greenland (etc.), shift the pack above it along with it (the ground is acting like an anchor for the ice, so it would move). As it moves, it's opening up space that the current would whittle into. Not a ton, because currents are only one of the proverbial thousands of variables, but some.
Bear in mind that ice grows and shrinks over the year (and decade, and century, there are many cycles). So you might consider asking what time of year you want to base your ice pack on.
Result? A completely believable map.
I think that sometimes we authors get too caught up in the pursuit of technical perfection when, realistically, that level of perfection won't benefit a story, or a game, or anything else at all. If you need a better answer than this, please explain why it's that important. Cheers.
