I'll go out on a limb and make a prediction. The Autumn melt spike on Greenland that we saw this year (End of September 2022) will become the normal situation as the years go by. So what is the reasoning behind this prediction.
First let's look at the normal (usual up till now) situation with the Hadley Cells. The equatorial Hadley cell is powered by the heating of land and sea around the equator. Let's keep it simple and ignore various finer grained effects involving, for instance latent heat. The air is heated from below by the warm surface of the earth, rises and flows North and South at altitude.
The Polar Hadley cell is powered by the air radiating heat into space, becoming dense and sinking. It is not heated from below because the snow and ice over the Arctic Ocean reflects most of the radiation falling on it back into space. Besides, much of the year, in winter, there is virtually no radiation falling on the land, and ice covered sea.
Consider for a moment what would happen if these two cells met at 45 degrees North (Let's ignore the Southern Hemisphere for now). Air at 45 degrees north is trying to both rise and fall with the Arctic Hadly cell air warming as it flows southward and 'wanting' to rise. Air from the Equatorial Hadley cell, flowing northward at altitude cools by radiation and wants to descend, Instead what happens is a third cell, the Ferrel cell is induced.
This third cell, the Ferrel Cell acts like an idler wheel in an engine (the one that keeps your fan belt tight, for instance) ((if you are still driving an ICE dinosaur))
Incidentally, jet streams occur, at altitude, where Hadley cells meet
Now we throw a spanner in the works.
We add greenhouse gasses to the atmosphere and this results in the melting of more and more floating ice on the Arctic Ocean. Radiation that falls on this open water over the summer penetrates the water and is absorbed, heating the water. This results in more melting ice and more heat absorption. The sensible heat of water is high (one Calorie* per kg of water) and the heating is over a considerable depth so a lot of heat is absorbed with a modest increase in temperature.
*A large Calorie as opposed to a small calorie (which will heat one gram of water one degree C).
In the mean time, the land is heating up. The land only heats up at the surface; say a foot in depth or so and the sensible heat of land is less than water so the same amount of heat will raise the temperature of land more than water. It can become quite hot on land, in the Arctic, in summer. This induces an onshore wind. The air over the ice-covered ocean is cold and flows toward the land which is warm. (Air rising, over land, sucking air from the ocean) With Coriolis, you have the polar Nor-Easterlies (Air flowing toward the South West). So now we get to what is likely to happen in the fall.
The land has warmed much more than the ocean, but not absorbed much heat and it cools off quickly as solar radiation decreases. Not so the sea and the open water that increases year by year. It cools more slowly. In addition, when it cools enough to freeze, it gives off latent heat of crystallization which slows the cooling. The effect I'm talking about, namely autumn melting spikes, will occur more and more as we see increased open water during the summer.
With the land around the Arctic cold and the ocean still relatively (to the land) warm, you should have off-shore winds. In fact you may even induce a 4 Hadley cell system for a while*. And when the Arctic really gains power due to much more open ocean, holding much more heat, eventually, you should actually suck the whole system northward and have a two Hadley cell system. A good indication that we have reached this situation will be when the Polar Jet Stream disappears. Jet streams occur where Hadley cells meet. So now, how about Green land melting.
* Since jet streams occur where Hadley cells meet, you might even observe an extra jet stream for a short time.
Air flowing off the land will be warming and becoming humid as it flows across an ever more open ocean and will tend to form counter-clockwise systems due to Coriolis. This warm moist air will impinge on Greenland where not only will there be rain but a kg of moisture condensing out of the air onto the ice, releases enough heat to melt 5 or 6 kg of ice*. (For water the latent heat of evaporation/condensing is 6 times as much as the latent heat of melting/crystallization). Another couple of effects may come into play here.
* Heat of crystallization/melting is 80Cal per kg. Heat of evaporation/condensation is 540Cal per kg.
If one of these low pressure area sidles up to the West coast of Greenland, on its northern side it will be sucking air down the slope and on the southern side pushing air up the slope. Lets look at the North side. When air flows down a slope, it heats up by 9.8 degrees C per km fall. This warming air will melt ice if it reaches and exceeds 0 degrees C.
On the Southern side it is pushing humid air up the slope and, depending on exact conditions, may be causing rain which melts the ice. And if the humidity in the air flow is condensing on the ice, it will be melting ice due to the latent heat effect described above.
There is another possibility. If the air is simply flowing toward Greenland, (atmospheric river?) it will come into contact with the ice and condense, causing melting as described above. This will make the air dense and it may be full of droplets of water (fog) making it effectively even more dense and it will flow down slope to the sea. We have the adiabatic melting effect described above, and may form sort of a miniature Walker cell between the ice and the sea. Convective processes are much more effective at transferring heat than conductive or radiative effects and this could melt the ice at a shocking rate. Essentially, heat is being transferred to the ocean from the huge store accumulated all summer in the ocean .
(Read Plains of Passage, by Jean Auel - chapter 41 or so. The book is a novel but Jean did her homework and described what happens when Foen winds occur over ice), The resulting Peteraqs are intense. Classic Peteraqs are typically well below 0 degrees but the atmosphere is warming. Imagine one of these density winds that is above the freezing point, blasting across the ice.
Then, if all that wasn't enough, there are storms that come up the East coast of North America. If the water they flow over is cold, they loose their umph but as the water becomes ever warmer, they can travel further North. We have another mechanism for putting a storm up against Greenland with the same results as above.
Even a high pressure area sitting beside Greenland can do the same as long as the winds it creates are blowing across a warm ocean.
If these storms sidle up to the East coast, the same as above applies except the rain will be induced at the northern edge and the adiabatic melting at the southern edge of the storm.
So in conclusion, I think it is quite likely that we will see melting spikes in the fall just like the one this year. They will occur in years in which the sea has accumulated a lot of heat and will happen as the land cools off, resulting in a strong pressure gradient from the land to the sea. The strength of off-shore winds around the Arctic Ocean will signal the start of this process and how strong the melting is likely to be in any year. As the sea freezes over, and especially if it acquires an insulating layer of snow, the process will stop. Initially we may see a short-lived, extra jet stream but eventually as the Arctic ocean gains power, the northern-most jet stream will likely disappear in the fall.
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