**Arctic Sea Ice September Minimum estimates by 1979-2019 trend extrapolations** The consensus definition of the first “ice free Arctic summer” is when the September minimum EXTENT goes below 1 million km2.

Volume = Extent x average Thickness

Extent = Volume / average Thickness

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Terminology key:

First value is midpoint estimate. (Low – High) = 95% confidence interval,

i.e. +/- 1.96 standard deviations.

Exponential trend = 2nd order polynomial regression model, i.e. simple curve model, for 1979-2019 observations.

Linear trend = 1st order linear regression, i.e. straight line model, for 1979-2019 observations.

Standard deviations used for confidence intervals based on annual errors of Linear model vs. 1979-2019 observed values.

M km2 and M km3 are Millions of squared or cubic kilometers.

**EXTENT** **a) Exponential Extent trend** *Rationale - Positive feedbacks from loss of MYI, thin ice physical and biological characteristics (e.g. algal darkening on the underside of thin floes), more open water causes decreased summer albedo, open water effects on wind fetch and ice mobility, increased Atlantification and Pacification of the Arctic, CAA becomes another export gateway, possible halocline breakdown (esp. in the Beaufort), more open water in winter causes more water vapor over the Arctic thus increasing the thermal blanket to moderate winter low temperatures, black carbon forest fires, permafrost thaw, oops, we never thought about that, continued GHG loading, increasing global average temperature. *

Opinion - Too aggressive for extrapolation because it ignores compensating negative feedback. **2020: 4.0 (3.0 – 5.0) km2 September average Extent.**First Year for <3M km2 = 2028 (2021 – 2034)

First Year for <2M km2 = 2034 (2028 – 2040)

First Year for <1M km2 = 2040 (2034 – 2045)

First Year for 0 km2 = 2045 (2040 – 2050)

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b) Gompertz Extent curve - no data

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**c) Linear Extent trend** *Rationale – The simplest model is the safest bet. Occam’s razor. The extra term in the exponential model was not statistically significant. Allows for both positive and negative feedbacks.***2020: 4.3M (3.3 – 5.3) km2 September average Extent ** *** The extrapolated linear September Volume and Extent linear trends are incompatible. If Volume reaches zero in 2033 (2024 – 2041), there would be no ice to create Extent.***

First Year for <3M km2 = 2037 (2024 – 2049)

First Year for <2M km2 = 2049 (2037 – 2061)

First Year for <1M km2 = 2061 (2049 – 2073)

First Year for 0 km2 = 2073 (2061 – 2085)

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**Improved EXTENT prediction accuracy as melt season observations become available.** R-square for reduction in variability of estimates derived from R values posted by Stephan at

https://forum.arctic-sea-ice.net/index.php/topic,2888.msg248300.html#msg248300 Confidence interval reduction for estimated September average Extent with MARCH, APRIL, or MAY observations as predictors: Not much.

---- See NSIDC “Maximum extent is not predictive of minimum extent”

https://nsidc.org/arcticseaicenews/2020/03/“Plotting the de-trended maximum versus minimum extent (Figure 2) shows a near-random distribution.”

“The seasonal maximum extent and the September minimum extent are not correlated” … “because summer weather conditions strongly shape the September minimum.”

Figure 2. This plot compares de-trended maximum extent (x-axis) with minimum extent (y-axis). The yearly values shown are calculated by subtracting the linear trend value for that year from the total extent. Credit: W. Meier, NSIDC

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Linear model estimate for 2020 September average Extent before any 2020 observations: 4.3M +/- 1.0 km2, (95% of outcomes expected to be within 3.3 – 5.3M km2,

i.e

**+/- 1.0M km2**)

With

**JUNE** Extent observation, confidence interval reduction:

**22%**Width of 95% CI with June observation:

**+/- 0.8M km2** With

**JULY** Extent observation, confidence interval reduction:

**56%**Width of 95% CI with July observation:

**+/- 0.5M km2** With

**AUGUST** Extent observation, conf. interval reduction:

**87%**Width of 95% CI with August observation:

**+/- 0.14M km2**