by Greg Goodman
This year, as every year, there has been much excitement in the media about ‘catastrophic’ melting of Arctic sea-ice, run-away melting, tipping points, death spirals and “ice-free” summers.
There has been the usual guessing game about when exactly the minimum will / has occurred and what the ice area or extent will be on that day.
Claims of ‘ice-free’ conditions at some time in the summer have been bandied about for years in various forms but as the reality sinks in that it’s not as bad as some had claimed, the dates when this is expected happen have often been pushed out beyond the life expectancy of those making the claims.
The meaning of “ice-free” has also been the subject of some serious goal-post relocation efforts, we are now told that ‘ice-free’ does not actually mean free of ice, it means there will be less than one million square km of ice left.
This special branch of mathematics is apparently based on the axiom that zero = 10 6
The problem with this obsessive focusing on one single data point out of 365, is that there is a lot of short term, weather driven variability that can affect the exact timing and size of the minimum in ice coverage. Since the main interest ( outside maritime navigational requirements ) is the hope to find some indications of long term changes in climate, this is not a very instructive way to use the detailed data available.
There have been three notably low summer minima in recent years: 2007, 2012 and 2016. The 2012 event was the lowest in the satellite record going back to 1979. The other two years tie for second place, meaning the current minimum is indistinguishable from the one which occurred nine years previously and the lowest one lies between the two. This incompatible with claims of run-away melting. This was a reasonable hypothesis and cause for concern in 2007 when the relatively short record could be characterised as an increasing rate of change but this interpretation is not compatible with what has happened since.
In the golden days of “run-away” melting, leading up to the ‘catastrophic’ 2007 Arctic sea-ice minimum, this was often presented as the ‘canary in the coal-mine’ for global warming and climate change. It is still referred to as such.
The aim here is to try to separate the changes in the annual cycle from the weather-driven and other short-term variability and to see if we can learn something about the life expectancy of our canary.
Method and Results
In order to determine an objective timing for the sea-ice minimum, it is necessary to filter out short-term variability. Visual inspection of the northern hemisphere sea-ice data  shows that there are periods of about a week in length having alternating greater and lesser rates of change throughout most of the year. Spectral analysis also reveals notable cyclic components at around 4, 10, 16 days. This means that the date of the minimum tends to fluctuate rather erratically over the first three weeks of September.
The criterion adopted here for having sufficiently removed the short term variability in order to get a stable estimation of the turning point ( minimum sea-ice extent ) of the annual cycle, was that there shall be only one change of direction. Since the annual cycle only has one minimum, anything producing multiple localised minima is noise in this context.
To detect this condition, the rate of change of the NSIDC NH sea-ice extent was taken and a 3-sigma gaussian low-pass filter applied. The length of the filter was increased progressively until all years in the data had a unique turning point (ie. a change of sign in the time derivative ).
This was achieved in practice by a single operation: convolution of the daily data with a diff-of-gaussian kernel [*] of the chosen length. The data point at the change of sign was taken as the date of the minimum in the annual cycle for each year.
As is typically the case for satellite records, the data processed by NDISC comes from a number of different satellites as instruments and spacecraft fail. They are cross-calibrated as well as possible to provide one continuous time series. One notable change in the data is that the earlier orbits only provided full surface coverage every six days  and were originally processed to give a data point every three days. These have apparently been interpolated to give a homogeneous time series. Obviously data with only a three day time resolution will be less accurate at determining the exact date of the turn-around. To mark the different nature of the early data this section is plotted in a different colour.
Comparison to the minima of 5 day trailing average presented by NSIDC shows the expected reduction in the variability that was the aim of this study. This manifests primarily as the reduced occurrence of later minimum dates. The pre-1998 data change little. This is probably due to the blurring effect of the extended 6 day orbital coverage being similar to the gaussian smoothing applied in this analysis. It can thus be inferred that the short-term, weather driven variations introduce an asymmetric shift to a later restart to freezing.
There is a clear non linear nature to the variation in the timing of the annual minimum in Arctic sea-ice extent from NSIDC. It reached its latest recent date for the turning point in 2007 and has been getting progressively earlier ever since.
That is to say, that the freezing season has been beginning steadily earlier for about a decade, having drifted in the opposite sense for the previous two decades.
There is much talk about naive assumptions of the effects of reduced ice area on the energy budget of the region. The simplistic argument being that less solar energy will be reflected by water compared to an ice or snow surface leading to further warming and thus ever more melting. However, there are several other effects which need to be measured and taken into account to determine whether this extra energy input will cause an overall positive feedback ( and accelerated melting ) or whether it will be counted by other effects. Open water emits more infra-red energy to space and evaporation of surface water in the windy Arctic region will remove substantial amounts of heat from the surface. Both of these effects will continue during 12 months of the year, not just the short summer. It is far from obvious how these factors and others will balance out. Climate models are notoriously poor at reproducing both Arctic temperatures and sea ice coverage. (They tend to under-estimate both temperature and ice loss). Clearly the ‘basic physics’ for this region is poorly understood.
The observational data can help shed some light on the how the region is responding to the reduced ice cover since the 2007 minimum.
The decadal rate of melting has also reduced since 2007 as measured by ice area data retrieved by the University of Illinois .
The derivation of that graph is detailed here:
There are two ways to interpret the observational data:
1) the net feedback from open water is negative , not positive and run-away melting was an erroneous interpretation. It is not happening.
2) the feedbacks are not the key driver of Arctic sea ice melting, there is another external force, such as N. Atlantic sea surface temperature and ocean currents, which is dominant and run-away melting was an erroneous interpretation. It is not happening.
The death spiral is dead.
Update: Since the rate of change at the beginning of refreezing tends to be faster than end of melting, removing higher frequencies with a filter introduces a general drift to a earlier date of minimum ice extent. This simply reflects the asymmetry of the annual cycle. This underlines the caution needed in merging the two sections of the dataset : the earlier Nimbus and the later military satellites which had different orbit resolution. The data are not fully compatible and comparing dates of ice minimum without suitable filtering will lead to an exaggerated impression of later melting.
 The NH sea-ice extent data are provided by NSIDC as daily anomalies form an average cycle plus the annual cycle which has been subtracted. The “near real time” data for the current, incomplete year is provided as a separate file in the same format. Documentation for the NSIDC data : http://nsidc.org/data/docs/noaa/g02135_seaice_index
 DMSP Satellite F8 was the first of a series a spacecraft and flew from 7 September 1987, it was flown by US department of defence. Data from this family is combined with that from earlier NASA provided Nimbus-7 spacecraft which flew similar but somewhat different polar orbits. https://nsidc.org/data/docs/daac/nimbus-7_platform.gd.html “The Nimbus-7 observatory provides global coverage every six days, or every 83 orbits.” This section of the combined record is less reliable for estimating the turning point due to lack of time resolution. The data has to be in-filled to produce daily data series and contributions to one ice extent figure are actually spread over 6 days of flight time.
 An implementation of the diff-of-gaussian filter is presented here: https://climategrog.wordpress.com/2016/09/18/diff-of-gaussian-filter/
 The sea-ice area data used in the decadal trend analysis are provided by Cryosphere Today team at U. Illinois. http://arctic.atmos.uiuc.edu/cryosphere/timeseries.anom.1979-2008
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