<p>The box in the lower left of the bottom chart is key to understanding what is presented. Five attempts of a line of best fit have been presented. From the chart, the linear fit (yellow line) is the least best fit, so the loss of Arctic ice not a linear relationship. The other lines are different modeling scenarios the author has attempted. </p>

<p>When testing for lines of best fit, one is trying to find a mathematical equation that will neatly describe something - in this case Arctic ice loss over time.</p>

<p>The other four lines of best fit that were considered were: the exponential curve, Gompertz fit, logarithmic fit and a second order polynomial fit. Visual examination of these curves shows they are very close in describing the data and are close to each other.</p>

<p>The important thing to consider in such curve fits is the value of <em>R<sup>2</sup></em>, sometime denoted as <em>r<sup>2</sup></em>. A value of 1 means a perfect fit and a value of zero means absolutely not fit.</p>

<p>All four curved lines have a fit greater or equal to 0.902. That is a good result.</p>

<p>The Gompertz fit has an <em>R<sup>2</sup></em> of 0.917 which is the highest value of the options presented. It means that for the data analyzed and evaluated in this study the Gompertz fit is the one that best describes the data. However, given the closeness of <em>R<sup>2</sup></em> values, the other options also give good results, but not as good as the Gompertz fit.</p>

CC BY-SA 4.0
2020-02-16T14:01:36.730Z
Ideally, we penalize extra parameters to prevent overfitting, e.g. with [this](https://en.wikipedia.org/wiki/Bayesian_information_criterion#Gaussian_special_case).
J.G.
CC BY-SA 4.0
2020-02-17T15:45:16.443Z
Ah that's helpful because I didn't actually notice the fit values (never covered that bit in maths class).
BTW I try to understand this topic because I live right next to the North Sea and in a zone threatened by sea level rise and storm surge. The last storm surge put water yards from my house, so I want a handle on what the future holds, which isn't proving easy at all. My main concern about all that is whether the Arctic Sea Ice is melting faster than the IPCC tells governments that it will, as that drives flood defense policy.
Jimmy Widdle
CC BY-SA 4.0
2020-02-16T13:08:02.277Z
2020-02-16T13:08:02.277Z
Fred
<p>There are no "True" curves in the extent that there is no theory or physical laws that link the number of years with the disappearing of arctic ice. (These several curves are only interpolation models, they give a trend: only additional measure points would give us a more accurate fit.)</p>

<p>Based on other variables, we could imagine such a law depending on : CO<sub>2</sub> and CH<sub>4</sub> concentration in the air + surface with average albedo of ice sheets versus ice-free lands/ocean in arctic areas + average earth temperature. Time also would still have an influence, probably due to the accumulation of energy in matter over time.</p>

<p>Many parameters that could strongly suggest that the disappearing of arctic sea is non linear. </p>

CC BY-SA 4.0
2020-02-17T09:58:24.377Z
What do you mean by "the modern western system"?  Years have physical meaning.
gerrit
CC BY-SA 4.0
2020-02-17T10:29:37.590Z
@gerrit as you pointed out "years" have physical meaning. Instead of years, I talk about: "Time also would still have an influence, probably due to the accumulation of energy in matter over time" . I was trying to highlight some of underlying variables with which the disappearing of ice could have a linear behaviour.
Stephane Rolland
CC BY-SA 4.0
2020-02-17T15:47:47.740Z
Yes I have heard that there is as yet no theoretical explanation for the observations, that being rapid ice loss, although some recent work said that there is a natural variability to ice cover and we are on a down turn of that.
Jimmy Widdle
CC BY-SA 4.0
2020-02-17T17:17:40.227Z
I have edited and remove the mention "in modern western system" and let years alone if you think that is more correct. About the natural trend you are willing to see, I'm tempted to think that you should probably have to take a much larger sample set than only 40 years. Beware though that even with white noise one can make the interpolations one wants.
Stephane Rolland
CC BY-SA 4.0
2020-02-17T20:19:16.327Z
Yes I was looking for an appropriate long term graph, because I know the recent fast melt is anomalous, for whatever reason. The problem is, I think, that once open ocean arrives then we're in a new era due to low albedo and other issues. It would have to be an amazing recovery to make a difference to the trend to zero.
Jimmy Widdle
CC BY-SA 4.0
2020-02-16T06:02:48.377Z
2020-02-17T17:11:48.893Z
2020-02-17T17:11:48.893Z
Stephane Rolland
<p>I'd like help to understand these charts. They are charts of Sea Ice Volume. One is drawn with linear decline, the other has all sorts of curves fitted onto it.</p>

<p><a href="https://i.sstatic.net/XLM80.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/XLM80.png" alt="From PIOMAS site"></a></p>

<p><a href="https://i.sstatic.net/GnHfI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GnHfI.png" alt="From Wipneus Artische Penguin site"></a></p>

<p>Why do we have these different line fits and which is true ?</p>

CC BY-SA 4.0
2020-02-16T17:02:04.270Z
It's worth noting that ice volume is a combination of both extent and thickness and that there was a rather steep step-down in volume a few years back because almost all of the multi-year ice (ice that survived the summer thaw, and grew thicker over subsequent years) melted.
jeffronicus
<sea-ice><arctic>
Is the Arctic sea ice disappearing in a linear or non-linear way?
Jimmy Widdle
# Is the Arctic sea ice disappearing in a linear or non-linear way?

(Asked by: username_0 on 2020-02-16)

I'd like help to understand these charts. They are charts of Sea Ice Volume. One is drawn with linear decline, the other has all sorts of curves fitted onto it.

[![From PIOMAS site](https://i.sstatic.net/XLM80.png)](https://i.sstatic.net/XLM80.png)

[![From Wipneus Artische Penguin site](https://i.sstatic.net/GnHfI.png)](https://i.sstatic.net/GnHfI.png)

Why do we have these different line fits and which is true ?

**Tags:** sea-ice, arctic

> **Comments:**
> **username_1**: It's worth noting that ice volume is a combination of both extent and thickness and that there was a rather steep step-down in volume a few years back because almost all of the multi-year ice (ice that survived the summer thaw, and grew thicker over subsequent years) melted.  

---

## 2 answers

### Answer by username_2 on 2020-02-16. Score: 4

The box in the lower left of the bottom chart is key to understanding what is presented. Five attempts of a line of best fit have been presented. From the chart, the linear fit (yellow line) is the least best fit, so the loss of Arctic ice not a linear relationship. The other lines are different modeling scenarios the author has attempted.

When testing for lines of best fit, one is trying to find a mathematical equation that will neatly describe something - in this case Arctic ice loss over time.

The other four lines of best fit that were considered were: the exponential curve, Gompertz fit, logarithmic fit and a second order polynomial fit. Visual examination of these curves shows they are very close in describing the data and are close to each other.

The important thing to consider in such curve fits is the value of *R2*, sometime denoted as *r2*. A value of 1 means a perfect fit and a value of zero means absolutely not fit.

All four curved lines have a fit greater or equal to 0.902. That is a good result.

The Gompertz fit has an *R2* of 0.917 which is the highest value of the options presented. It means that for the data analyzed and evaluated in this study the Gompertz fit is the one that best describes the data. However, given the closeness of *R2* values, the other options also give good results, but not as good as the Gompertz fit.

> **Comments:**
> **username_3**: Ideally, we penalize extra parameters to prevent overfitting, e.g. with [this](https://en.wikipedia.org/wiki/Bayesian_information_criterion#Gaussian_special_case).  
> **username_0**: Ah that's helpful because I didn't actually notice the fit values (never covered that bit in maths class). BTW I try to understand this topic because I live right next to the North Sea and in a zone threatened by sea level rise and storm surge. The last storm surge put water yards from my house, so I want a handle on what the future holds, which isn't proving easy at all. My main concern about all that is whether the Arctic Sea Ice is melting faster than the IPCC tells governments that it will, as that drives flood defense policy.  

---

### Answer by username_4 on 2020-02-16. Score: 3

There are no "True" curves in the extent that there is no theory or physical laws that link the number of years with the disappearing of arctic ice. (These several curves are only interpolation models, they give a trend: only additional measure points would give us a more accurate fit.)

Based on other variables, we could imagine such a law depending on : CO2 and CH4 concentration in the air + surface with average albedo of ice sheets versus ice-free lands/ocean in arctic areas + average earth temperature. Time also would still have an influence, probably due to the accumulation of energy in matter over time.

Many parameters that could strongly suggest that the disappearing of arctic sea is non linear.

> **Comments:**
> **username_5**: What do you mean by "the modern western system"?  Years have physical meaning.  
> **username_4**: @username_5 as you pointed out "years" have physical meaning. Instead of years, I talk about: "Time also would still have an influence, probably due to the accumulation of energy in matter over time" . I was trying to highlight some of underlying variables with which the disappearing of ice could have a linear behaviour.  
> **username_0**: Yes I have heard that there is as yet no theoretical explanation for the observations, that being rapid ice loss, although some recent work said that there is a natural variability to ice cover and we are on a down turn of that.  
> **username_4**: I have edited and remove the mention "in modern western system" and let years alone if you think that is more correct. About the natural trend you are willing to see, I'm tempted to think that you should probably have to take a much larger sample set than only 40 years. Beware though that even with white noise one can make the interpolations one wants.  
> **username_0**: Yes I was looking for an appropriate long term graph, because I know the recent fast melt is anomalous, for whatever reason. The problem is, I think, that once open ocean arrives then we're in a new era due to low albedo and other issues. It would have to be an amazing recovery to make a difference to the trend to zero.  

---

