You're familiar with this?

This is the graph that brought home the danger of arbitrary curve fitting for me. I believe the points on the graph are the average ice volume for the month of September from PIOMAS for each year through 2013, and the curve is an exponential fit to those points, so something like volume = a - k exp(c year) where a, k, and c are constants determined by the fit. Maybe Wipneus can chime in with the exact formula.

As a fit for the data, it's really good. But we want to use it to predict when the sea ice volume will go to zero, and it runs into problems for this purpose. The first thing to notice is that although most points fall inside the confidence interval, the data point for 2013 is above the confidence interval. The fact that the last actual value is off the curve should lead to doubt about the curve's ability to predict the future.

We don't have the 2014 value yet, but we can expect it to be close to the 2013 value based on the melt so far this year. So it looks like the 2014 value will be far outside the confidence interval for the predicted value. Looking ahead, the curve predicts that the 2015 value will be less than 2000 cubic kilometers. I could be wrong, but that seems very unlikely to me.

In addition, the 2012 version of the curve (without the 2013 data point) was an even better fit to all of the existing data, but the predicted value for 2013 was much too low. The prediction curve was even lower before the 2013 data point pulled it back up.

What this means is that the 2013 curve could not accurately predict the 2014 value, and the 2012 curve could not accurately predict the 2013 value. It does not have reliability for one year predictions, and yet people want to use it to predict when the ice volume will go to zero, 4 or 5 years in the future.

This curve's claim to fame is that the 2010 data predicted the 2011 and 2012 data points, but to me that just points up the danger of arbitrary curve fitting. Just because a particular curve works for some period in the future, that does not mean it will work for other periods.

At this moment a quadratic fit to this data gives a better fit than the exponential fit, but again there's no reason to assume that will continue to be true. A simple linear fit, while not great, is not unreasonable. The linear fit is also somewhat more stable than the other fits, with new data having a relatively small impact on the trend line.

On the basis of the data, the linear fit is likely to overestimate how long the ice will last. This is a personal preference, but I prefer this to the other alternative. There are two possible statements: This linear fit predicts the Arctic will be ice free by 2040, but there's a good chance it will be earlier than that. Or: This (exponential or quadratic) fit predicts the Arctic will be ice free by 2015, no 2017, no 2020, no, but real soon, I assure you.

I try to cautious in the predictions I make, so I try to be cautious with the regression functions I use.