#### Data

The NOAA has a handy page with historical information. Since sea ice extent is at a minimum in September, that would be the month we expect the first ice-free Arctic Ocean.

#### Algorithm

To predict this, I'm using an incredibly simple algorithm to get a general idea:

- find the recent loss per year
- find the spread in losses from year to year
- simulate with that loss per year and spread (assuming normally distributed variations) a bunch of times

Since the last full year of real data is 2017, I used the data up until then.

#### Calculating simulation terms

Since the spread from year to year is high, I worked with 10-year averages. The average sea ice extent in September was:

- 7.2 million km^2 in the period centered at 1982
- 6.8 million km^2 in the period centered at 1992
- 5.9 million km^2 in the period centered at 2002
- 4.7 million km^2 in the period centered at 2012

Clearly, the value is dropping, and the rate at which it drops is accelerating. In the last 20 years, that rate is 0.12 million km^2 per year. From the numbers above, the rate at which the loss accelerates is 0.004 million km^2/year^2. Finally, I get that the standard deviation of the variations from year to year is 0.69 million km^2./year

These are the terms I'm using in the simulations.

#### Results

First, I just assumed the loss is steady (linear). 0.12 million km^2/year of loss with a spread of 0.69 million km^2/year. Running that 1000 times, I get the following results:

To read that graph...the middle 80% of all simulations fall within the wider, colored region (10th percentile to 90th percentile). The middle 50% of all simulations fall within the narrower, colored region (25th percentile to 75th percentile). The median simulation is the dotted line.

This tells us that with the linear loss assumption, the first ice-free September occurred:

- by 2030 in 10% of the simulations
- by 2037 in 25% of the simulations
- by 2050 in 50% of the simulations
- by 2072 in 75% of the simulations
- after 2100 in 10% of the simulations

Based on the historic data, the rate of loss looks to be increasing each year. Factoring that in, the is the same simulation with the only difference being that the loss increases by 0.004 million km^2/year each year:

The graph can be read the same way. This tells us that with the increasing loss assumption, the first ice-free September occurred:

- by 2030 in 10% of the simulations
- by 2035 in 25% of the simulations
- by 2042 in 50% of the simulations
- by 2052 in 75% of the simulations
- by 2066 in 90% of the simulations

This is all when defining 'blue ocean event' as a sea ice extent of 0 million km^2. A more reasonable number to use is 1 million km^2 as that would represent a mostly ice-free Arctic Ocean. Using that, I get the following for the linear assumption:

- by 2027 in 10% of the simulations
- by 2032 in 25% of the simulations
- by 2041 in 50% of the simulations
- by 2062 in 75% of the simulations
- after 2100 in 10% of the simulations

For the assumption that ice loss increases each year, I get:

- by 2026 in 10% of the simulations
- by 2031 in 25% of the simulations
- by 2037 in 50% of the simulations
- by 2049 in 75% of the simulations
- by 2060 in 90% of the simulations

#### Conclusions

This is a very simple model, but it hopefully gives an idea of how the spread in the data compare with the actual trend. The takeaway is that with the more accurate but still incredibly simple model here, the first blue ocean event would be expected by 2037, and it wouldn't be shocking to see one by 2026.

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