The northern sea ice melt season is well underway and PIOMAS has updated, so it’s time to review status. I follow the PIOMAS series because it tracks ice *volume*, and it seems to me that total ice mass (or volume) should be the most meaningful and coherent indicator.

The graph shows two traces:

- The light-blue-filled total ice volume curve, plotted on the left axis. That varies through a huge range with the annual freeze-thaw cycle, currently between about 22,000 and 3,000 cubic kilometres (yes, cubic kilometres – or, if you like, billion tonnes … near enough).
- The dark blue line, plotted on the right axis, which shows the same results expressed as anomalies from the annual average curve. For the average curve I use the mean daily volumes for 30 year interval 1979 — 2008, a fixed interval from the start of the PIOMAS series, which is slightly different from the interval used in the Polar Science Centre graph (source below).

Note that the scale is the same on both vertical axes, and the right (anomaly) axis is positioned so that the horizontal axis crosses it at -12.6, the anomaly at which there will be zero ice at the date of the annual average minimum (12 September). So if the dark blue trace reaches the bottom axis around mid September some year soon, that’s it, there is no ice left (according to PIOMAS).

The graph also shows two fitted and extrapolated curves, which is a matter of some contention (see below).

So far this year the anomaly trace suggests that melt has been a little less severe than in recent years, though there is no meaningful departure from trend. The slow motion train wreck continues. More below…

**The “data”**

PIOMAS is the Pan-Arctic Ice Ocean Modeling and Assimilation System (version ~~2~~ 2.1) by the Polar Science Centre at the University of Washington. That’s a data assimilation model tracking the total volume of ice floating on the Arctic Ocean and surrounding seas and tidal waterways. That is ice *volume* as opposed to ice *area* (actual frozen surface) or ice *extent* (sea surface with at least some ice). A model is needed because, while area and extent can be readily measured by satellite remote sensing, until recently ice thickness (and hence volume) could not be. PIOMAS uses a numerical model representing the physics of ice generation, movement and melting, constrained by observations such as ice extent, sea surface temperature in ice free areas, and polar weather effects such as wind (affecting ice movement and structure) and cloud (affecting incident solar radiation). It’s also calibrated against historical thickness observations like those from nuclear submarines.

This model has been showing severe decreases in ice volume for many years. Until recently the polar science community appeared to treat it with a kind of quiet scepticism, but that changed last year when early data from the new CryoSat 2 high precision radar altimeter satellite began to indicate comparable ice thicknesses and hence volumes. (CryoSat 2 estimates thickness by accurately measuring the height of the top of the floating ice above sea level, a somewhat challenging task from 700 km up.) As a result, many now appear to grant PIOMAS considerable veracity.

**Choosing the fitting function**

There’s been criticism of fitting parabolas (second order polynomials) to these results: “over-fitting”, “no basis”; that sort of thing. To me a second order fit is the logical and defensible choice.

What is the most commonly fitted function? That would be the straight line, also called a *first order polynomial*. Why? Often it’s because there’s an underlying understanding — a justifiable expectation of a linear process, or of a linear trend for a time series. In other cases the choice seems more prosaic. It’s *what you do* (rather, what everyone else does), or, more generously, it’s seen to be the parsimonious choice. There can be no justification for excess complexity (William of Ockham), and a straight line is the simplest choice.

That is plainly correct. We have:

*y = mx + c*

Or, as a function of time:

*f(t) = mt + f(0)*

The extreme simplicity is obvious in the differential form, where the equation is just:

*f'(t) = m*

The rate of change with time is a constant. There is no simpler time-varying function.

The problem with that for the PIOMAS output is twofold:

- Except over some narrow time window, there is no reasonable expectation of a linear trend. The basic expectation is of an accelerating process via the likes of albedo feedback and decreasing ice structural strength.
- It doesn’t fit.

So parsimony is good, but if the function is inadequately complex to fit the expectation and the data, then it is unsuitable. We need adequate, preferably justifiable, complexity.

In the polynomials, the next most complex option is the second order:

*y = ax² + bx + c*

Or, as a time function:

*f(t) = at² + f'(0).t + f(0)*

That is also a very simple function, again most obviously in its differential form. It’s just the function for which the acceleration in the rate of change is a constant:

*f”(t) = 2a*

That is the simplest of all functions with a time-varying rate of change, which is the same as saying that it is the parsimonious choice in a case where there is a sound basis to expect acceleration. My view is that PIOMAS is such a case.

Others have been fitting more complex things to PIOMAS, including exponential functions and various S-curves. While there is a suggestion of S-shaped behavior in some global climate model simulations, in my view the evidence is insufficient at present for any particular S-function choice to be considered parsimonious.

**Extrapolation**

The next common objection to plots like this lies with the extrapolation to zero ice volume. It is argued that is done without justification or validity. Extrapolation of a fitted function amounts to statistical prediction, a process that is often misapplied. A key point is that correlation by itself is never reliably predictive. The risk of death by car crash has been steadily decreasing at the same time as mobile phone use has been exploding, so does that mean that if I use my mobile phone while driving, I’ll be safer? There are countless absurd examples.

What’s needed for statistical prediction to be reasonable is *causation*: some quite fundamental understanding leads us to expect that *a* is causally related to *b* in a certain way; we observe that *a* and *b* are correlated in line with the expectation; then given *b* we can predict *a* and estimate the statistical uncertainty. (If the causal relationship is incomplete or incompletely established, there may also be extra systematic uncertainly.)

So what of PIOMAS? Ice loss is not caused by the elapse of time, but we know that global warming processes have been inexorably increasing over recent decades, that those processes are continuing, and that they should cause sea ice loss — accelerating sea ice loss. I think the case for “secondary” causation is unusually clear here, and therefore statistical prediction is strongly justified. It follows that *so is extrapolation* (although obviously not without limit).

**The future**

How soon will the ice be gone? On the model results the summer ice will all be gone sometime between about ~~2015 and 2022~~ 2017 and 2023 (PIOMAS v2.1 update). At the resolution of the PIOMAS model, “gone” might not mean every last bit, but it surely means “gone for practical purposes”. More interestingly perhaps — and on a much longer extrapolation — the results suggest that we should expect zero northern sea ice for about half the year sometime around 2030.

When the northern ice cap on the only planet you’ve got suddenly vanishes, it could be time to sit up and take notice. Ever considered the possibility that you’ve been lied to?

Humans beings are not wired to care long term or be sustainable creatures

Very nicely explained, Gerg!

Tks.

I suspect zero Arctic sea ice timing is a bit of a red herring.

If, say, half the Arctic Ocean is ice-free and half still has a few floes, then the ice-free half may still suffer the same effects now that the other half will also suffer when its ice is all gone. In other words, major temperature variation won’t wait for zero sea ice everywhere, rather it may occur earlier at an ice-free local level – provided “local” is big enough and early enough in the summer.

Of course, there is still plenty of ice in the northern ice cap. Once heat influx cannot be absorbed by melting sea ice, it will likely increase water evaporation to condense on or above the Greenland ice sheet which will speed the calving bergs to provide negative feedback to hide the underlying heat flux.

2030: See, still ice in the Arctic Ocean. Told you so – there’s no problem, it’s all hype. Nice to see Greenland looking so … green.