I do not understand this infatuation with linear trends. The relationship between two variables will be dictated by the science behind the effect. The relationship could be linear, exponential, logarithmic, some other, or none at all. A linear relationship should by no means be considered the default trend.
There are vastly more than two variables at play, and the chances of there being a linear rate of change in a complex system are very low. So there is no "infatuation" with linear trends - they are inherently extremely unlikely, particularly in the long run.
However, the chances of a complex system following binomial or logarithmic trends, let alone trinomial or higher factors, is even less likely than following a linear trend.
Complex systems do not follow mathematically neat trends. Trying to find them is futile. We are not seeing any linear trends in the Arctic today, but nor are we seeing any other trends that can be expressed in neat mathematical formulae.
The real-world data that we are dealing with seems to be following something close to a linear trend when it comes to statistical correlation. But what about physical causality? The ice is melting due to an increase in temperature, and during the 43 years that we are typically looking at, global temperatures have also followed a near-linear trend.
If we were to plot the two (e.g. global annual average temperatures v.s. annual average sea ice extent) we are very likely to see something very close to a linear correlation. This however does not imply causality. There is no reason to think that there is a linear causal relationship between the two, except contingently and temporarily under certain circumstances which may have governed the last 40 years, or perhaps we are not looking at a large enough timeframe.
But trying to find logarithmic or polynomial trends without a b****y good explanation of the physics that might be behind such a trend is never going to work. And when it comes to the Arctic we are very far away from being able to explain the physics behind a linear trend, let alone a polynomial one!