The daily PIOMAS volume anomaly series shows the difference for each day's volume from the volume for an average period. In this post I've used the 20 year period 1979 to 1998 to calculate the daily average.
To melt a given volume of ice requires a certain amount of energy, this is the enthalpy of fusion, 334kj/kg. So the volume anomaly can be transformed into an energy anomaly, in this post I call this the implied energy anomaly: it's the energy anomaly implied by the volume anomaly.
To calculate the energy anomaly I've used density from Alexandrov et al 2010. The current PIOMAS series is based upon an analysis by Schweiger et al, they use a single density for ice of 928kg/m^3. However Alexandrov et al, which is a paper contributing to the Cryosat mission gives different densities for first-year and multi-year sea-ice. As I've posted previously, the evidence shows that the Arctic ice pack has transitioned from a mainly multi-year to a mainly first-year pack, so I consider it reasonable to account for this change.
Alexandrov et al give typical densities for first-year and multi-year ice as 916.7 kg/m^3 and 882 kg/m^3 respectively. Lacking a publicly available series, I've also used table 1 of Maslanik et al 2011 to make a timeseries of multi-year ice extent, first year ice extent is then calculated by subtracting multi-year extent from the average annual extent as calculated from the NISDC monthly sea-ice extent data.
Fig 1. Calculated density of sea-ice (kj/kg).
The changing regimes of the above graph merely reflect the 4 regimes outlined in Maslanik 2011 table 1, and associated text. Accounting for the changes in first-year and multi-year sea-ice may not be strictly necessary in view of the wider uncertainties in the data used, especially PIOMAS. However it does reveal that there has been an upward tendency in density due to the transition to a predominantly first-year sea-ice pack.
Fig 2. PIOMAS volume (1000km^3 - left) and calculated implied energy (joules - right).
Obviously the energy anomalies generally track the volume anomalies, as those are the greatest factor. But it can be seen that the two curves generally track until the 21st century, where the increase in density due to the transition to first-year predominance begins to increase the energy anomaly.
The following graph shows that the most recent (2010) annual energy anomaly is around half the annual range. The annual range has been calculated by taking the maximum from the minimum volume for each year and calculating the implied energy anomaly using the adjusted density, as outlined above.
Fig 3. Implied energy of volume anomaly and annual volume range (joules).
I've used extent not area because I have an extent series from 2003 courtesy of IARC-JAXA. Combining this with PIOMAS volume gives an indication of thickness since 2003.
Fig 4. Calculated thickness (metres), using PIOMAS volume and IARC-JAXA extent, calculated on a daily basis.
It should be borne in mind that as extent covers ice concentrations down to 15% and AMSRE shows a lot of low concentration ice in substantial peripheral areas at the minima; this is something of a clumsy tool. However as PIOMAS seems to be producing reasonable indication of volume trends it is possible to have some confidence in the qualitative message that this is providing. Furthermore, from what information is available, the calculated thicknesses seem reasonable, e.g. the Alfred Wegener Institute flights (i.e. Science Daily) & Polarstern.
The question now arises: There has been a marked drop in volume as reported by PIOMAS in 2010 and 2011, when is this loss of volume occurring? By calculating the average volume for each day using the baseline period 1979 to 1998 it's possible to calculate daily anomalies. Most recently it is clear that in 2010 and 2011 the greatest volume losses have been between April and June. 2009 and 2008 also have early season losses, but with significant losses in the latter part of the melt season.
Fig 5. PIOMAS Volume (1000km^3) anomaly series 2005 to 2011.
This suggests that the recent acceleration of volume loss shown by PIOMAS is not due to ice-ocean albedo feedback, as it's happening in the part of the season where there's less open water in the Arctic, as opposed to late summer when there is.
Note that if you follow the series along from one year to the next you find that in some years the end value of the preceding year does not tie in with the start value of the following year. This is because the 1979-1998 average for day 1 is 23.21885, whereas the average for day 365 is 22.835, this is the biggest change in the series of daily averages. I am unable to further explain this odd finding, but it does not substantially affect any of the results presented here.
Below is a graph of the IARC-JAXA extent anomaly years following 2007, I've not included the earlier years as it's hard enough to read as it is.
Fig 6. IARC-JAXA annual extent (km^2) anomaly 2007 to 2010.
It's apparent that there is a significant drop in extent anomaly in April to June 2010 and 2011 at the same time as PIOMAS shows the substantial volume loss. This suggests that the recent volume loss may be associated with the extent anomaly and whatever is causing that. Although 2007's extent loss over the same period, and afterwards, suggests the issue could be more complex, as the 2007 volume anomaly doesn't drop in line with extent.
I'd like to have a conclusion to this, but having sat on this work since early this month the matter is still unresolved. In particular I can't figure out why there is the issue with day 1 and day 365 averages. It's clear even from comparison of PIOMAS volume anomaly and annual cycle that the current energy anomaly is around half the annual cycle. This alone I find quite staggering. It suggests a substantial gain in energy since only the late 1990s. As for the finding that the recent (2010/2011) apparent acceleration of PIOMAS volume anomaly is due to loss during April to June, I don't know what to make of it. NSIDC Sea-Ice news mentions warm temperatures during those periods, but it does so at other times of the year without the same volume losses.
So without proper conclusions I can only claim to be 'playing around' with PIOMAS. Rather than mess around with this stuff further I've decided to post and leave it to readers to decide what it means. Opinions will be greatly appreciated.
Alexandrov et al, 2010, "The relation between sea ice thickness and freeboard in the Arctic."
NSIDC Monthly extent data: Fetterer, F., K. Knowles, W. Meier, and M. Savoie. 2002, updated 2009. Sea Ice Index. Boulder, CO: National Snow and Ice Data Center. Digital media.
Maslanik et al, 2011, "Distribution and trends in Arctic sea ice age through spring 2011."
Schweiger et al, 2011, "Uncertainty in Modeled Arctic Sea Ice Volume."