I've been brooding over PIOMAS volume data the last 3 days, following some discussion elsewhere about trends vs "weather" and the kind.
I'm staring here as I write at 4 graphs I derived from the PIOMAS data downloaded from the U.of Washington Polar Science center. I'm pondering what it implies about past changes in the Arctic and what import it has for the future.
Let me back up for a moment and describe what I've done first, and why.
There's been a lot of discussion on the Arctic forums recently around three dimensions we use to evaluate Arctic system health.
In our discussions and arguments we've wrestled with the reality that two of those measures - extent and area, particularly as they appear at the end of melt season - have become increasingly difficult to evaluate to make a skillful determination of how the Arctic will look in a few years. Our discussion has shifted and expanded now to where over the last two years there has been much more tracking and examination of the annual refreeze. This has given us some hints and generated quite a few more questions.
Roll back to what I'm doing now. I'm using PIOMAS daily volume data going back to 1979 (
http://psc.apl.uw.edu/data/)
My analysis is more empirical than theoretical. At this moment I'm less interested in prediction than I am the data set. I have a particular interest in volume as well. Unlike extent and area, it represents a far better proxy for key forces at work in the Arctic - heat exchange and total system enthalpy.
My second purpose is contrast volume changes with changes that have taken place during the time period in question and see if a pattern appears which follows or is affected by them.
Methods:
Simply digesting a raw and fairly substantial pile of data is unlikely to produce anything useful. However, I don't want to fall into the trap of over-analyzing the information - while it is good to reduce "noise", over-processing values can remove meaningful signals it contains. My approach to this is three fold.
1) Create a sample average from a meaningful but more controllable time frame.
Most analysis of this data has been around extreme endpoints in annual variation - the annual maximum extent/area/volume and corresponding minimum - which land on arbitrary dates and are very narrow samples. For my work here, I've picked to arbitrary but significant dates March 21 (Day 80/81 of each year) and September 21 (Day 260/262). I then averaged the daily volume for a time frame window which extends from two weeks before until two weeks after those dates to get what I call "Vernal" and "Autumnal" volume numbers for those dates.
My logic in doing this is this: Rather than use a metric which is volatile and fundamentally disconnected from other forces in play at the time they take place (annual minimum/maximum), I wanted to anchor the analysis to two specific points in them where we know predictable and measurable changes are taking place (the Spring and Fall equinoxes). Further, to make the new metric sensitive to conditions during the specific year and season, rather than simply pluck out one number, an average over a near-term time frame would better incorporate and smooth other signals from forces in play at the time.
In addition to these two numbers, I also created a baseline value for tracking behavior on a broader time scale. In this case, I created an annual average for each year, summarizing all volume measurements from January 1 to December 31 for each year in question.
2) Create a derivative average which further smooths the Vernal and Autumnal numbers over a wider time frame.
In this case, I created a second data set from my spring and fall averages, starting with 1983, which is a simple 5 year running average of those numbers. The goal here is to round off peaks and valleys without losing all of the signal they contain, and hopefully permit underlying trends to be more visible, and more importantly, better identify transitions in system behavior.
3) Create a third derivative/index to show system volatility.
At the start, these were actually the numbers I was most interested in. We've discussed this some on the forums, but the summary of my thought here is, this, and also may qualify as a hypothesis: As the Arctic as a system approaches behavioral limits, the volatility of the system - the relative change against base values - will increase.
Again keeping it simple, I created three values for each year in question. These were (a) The absolute difference between Vernal and Autumnal values (b) the Percent that value represented of the Vernal volume and (c) the Percent that value represented of the Annual volume as derived in (1) above. I did this for both the raw and 5 year running averages of Vernal, Autumnal and Annual values.
Note: all values I used were rounded up to three decimals. I figured the significance of fractional cubic KM of ice were meaningless based on the confidence of the measurements.
Findings:
From raw data and graphic analysis by Jim Pettit, Zach Labe and many others it's already clear that sea ice volume has been declining steadily over the time period in question. What isn't necessarily clear is the nuances of how those changes have taken place.
Both the smooth and averaged data clearly shows this trend. No surprises (nor were any expected).
However, annual seasonal loss has shown only a very modest increase - less than 10% over all - with an average of 14.242K KM3, median of 14.034K KM3 and deviation of 1.164K KM3. Breaking the loss dataset in half shows the 2nd half loss rate only increasing by about 1000KM3, and 2nd half loss volatility actually declined slightly. The 5 year running averages are correspondingly closer. This suggests strongly that large year to year variations in melt are not significant contributors to the reduction in volume over the period measured.
The first think that jumped out at me in particular in the averaged data, is I think I'm seeing two historical locations where I think there's a signal identifying a fundamental change in how the system behaves. The first is in the 1990-1994 time frame. There I think spring, fall and yearly average graphs start a break in slope, falling into the glide path that takes us down hill to where we are now. I'm not sure what the specific conditions were at the time, or, considering hysteresis, how far back we need to look for the trigger, but it strikes me that is a specific place in time and space we can point at where the system signals a change has taken place.
The second was the 2010-2013 time frame. in that range all three measures - Annual average, spring and fall - flatten out. As another interesting and possibly key item, annual loss intersects and then starts to follow the annual average curve. I'm not sure what this means yet, but it sure looks like a strong signal. Also, while the three major curves flatten, the *vernal* curve is still trending down. I think the running 5 year equinox graph shows this the best.
My general take away - I think the graphs support another of my thoughts - that as the total energy available to the system increases (reduced ice), the overall volatility of its metrics will increase - especially area and extent - which actually are more derivative of this than volume.
I'll be interested to hear what other folks think. If someone can point me in the right direction, I'll post the spreadsheet with my raw numbers someplace for people to tear apart.
(P.S. - the average volume will be off a bit for 2018 as we haven't finished the year. That said, we are far enough along it that the relative change is small enough to be negligible to my analysis.)
