OK, so we're moving on...
"delayed ice reformation (with accompanying under ice mass loss effects)."
But I have argued that the delayed ice reformation may not produce as much a thinning in winter as some seem to think. Using Semptner's simple model (which seems to me to be at the heart of sea ice growth, and the modelling thereof), I have used a simple example to demonstrate the effect.
An objection has been raised that taking it to May is unrealistic, this is not the case, in the Central Arctic thickening continues to May, and as the peripheral seas are mainly seasonal now (even in the last two years), the Central Arctic region is the one that matters.
What is unrealistic is the constant -15degC. However -15degC is not as cold as in mid winter over the Central Arctic, and I wanted to keep things simple to pull out the effect I outline.
Heat flux through the ice is proportional to 1/thickness (of sea ice). To generate various freeze start dates the temperature of the surface is kept at the same temperature of the ice/ocean interface (i.e. -1.8degC), until I want freezing to start, at which time it is set to -15degC.
Looking at the end thickness on 15 May and the proportion of the freeze season, the impact of delayed freeze can be seen. For 1 October being 100% of the freeze season, and for the 1 October case thickness on 15 May being 100% thickness:
For 87% of the freeze season growth is 93%.
For 74% of the freeze season growth is 87%.
For 61% of the freeze season growth is 79%.
So there is a diminishing return on delaying the freeze season, although at some point you will get substantially thinner ice, the point is the large growth rates as the freeze starts and the rate reduces as the ice thickens, so the effect of delaying the freeze season is not as much as expected by many.
In reality of course the late start will happen as the ocean vents heat warming the atmosphere, and the thinner ice later in the season will also allow heat through, leading to further winter warming of the atmosphere. How to treat this in a simple way as we don't have a public copy of PIOMAS on which to perform experiments.
Here I turn to Freezing Degree Days (FDD), where monthly avg temperature is negative, I've used the sum of monthly average temperature multiplied by days in month for September through to the following April, temperature being NCEP/NCAR 2m temperature for the ESS.
Take 2007 and 2012 they had FDDs of 3972, and 3869 respectively. The average FDD for the 2000s was 3953. So even those extreme lows were unable to severely reduce FDD, the ice thickness resulting were of the order of 2m thick.
The problem is this: Winter is damned cold. Every way I look at it I have found that winter will remain damned cold, cold enough to make sure much of the pack is near 2m thick minimum within the Arctic Ocean, such thicknesses are not melting out totally.
To get to a July loss regime, virtually ice free (or at least substantil open water in July), PIOMAS April thickness needs to drop by around 1m in April from thicknesses typical of recent years, as shown by experiment. Now I am prepared to be loose on this, we don't know at what point between 2m and 1m early June loss is feasible, So I'll give down to 1.5m as the sort of April thickness needed to give massive open water by July, that's at least 2 months at the end of summer with near as damn it virtually ice free conditions.
I'm struggling to see anything but words supporting your June 1st loss scenario, no papers, no math, in other words nothing convincing. I'll meet you 'halfway' with a July loss scenario at an April thickness of around 1.5m. But to get that FDDs need to drop by around half.
Now maybe we're talking at cross purposes, maybe you envisage this happening after 2025, OK I reckon mid 2020s to mid 2030s. But I get the feeling you're talking about something more imminent than that (this decade?).
what is also not considered is regional land-heating effects and surface water runoff effects. Once the ice is gone we will see a 20C regional temperature spike and convective heating becoming a major factor as well as down/shortwave absorption.
Once again, where is the evidence for your stated 20degC spike?
Lawrence et al "Accelerated Arctic land warming and permafrost degradation during rapid sea ice loss." finds a warming of 3degC/decade in Oct Nov Dec during periods of rapid ice loss on land immediately adjacent to the Arctic Ocean in CCSM 3. However post 2007 the average temperature for OND is -17degC, which implies many decades to get the region to zero degC. Lets say that's biassed low, let's double the warming rate (not happening right now 1979 to 1986 avg OND temperature was -22.7degC, 1999 to 2006 was -19.0degC).... Let's double it to 6degC per decade, and assume it applies from now onwards, that is still three decades until OND temperatures are around 0 degC.
River discharges will affect that peripheral seas, and may be a significant factor in them already being seasonal. But remember, to get the pack to virtually zero in the late summer we're looking at the Central Arctic, where the effect of river discharge will be less.