| We use the length of the ice-free season (LIFS) and a quantity designated by inverse sea ice
index (ISII) to quantify the rapid decline of the Arctic sea ice that has been observed in the
past decades. The LIFS and ISII in each point for each year between 1979 and
2008 are derived from the daily sea ice concentrations C(y,d;i) for cell i on day
(y,d) = (year,day) which, in turn, are obtained from satellite passive microwave
imagery.
We define the LIFS L(y;i) at a certain point i in year y as the number of days between
the clearance of the ice and the formation (more exactly, the appearance) of the ice in that
point in that year. If the number of clearances and formations is larger than one the LIFS is
defined as the sum of the lengths of all periods between an ice clearance and the following ice
formation.
The criteria to identify dates of ice clearance and ice formation are as follows. We assume
that there is clearance on day d if the ice concentration is 0.15 or higher on days
d - 4,d - 3,d - 2 and d - 1 and below 0.15 on days d,d + 1,d + 2,d + 3 and d + 4. We
consider that there is formation on day d if the ice concentration is below 0.15 on days
d - 4,d - 3,d - 2 and d - 1 and 0.15 or higher on days d,d + 1,d + 2,d + 3 and
d + 4.
The ISII S(y;i) for point i in year y is given by S(y;i) = 1 - -
d=1NC(y,d;i)
N , where N is
the number of days in the year. This quantity, which varies between zero (when
there is a perennial ice cover) and one (when there is open water all year round),
measures the absence of sea ice throughout the year, hence the name inverse sea ice
index.
We argue that these variables are at least as suitable for the purpose of describing the
depletion of sea ice in the Arctic as those that are more often found in the literature, namely
the sea ice area and extent at the times of annual minimum.
Firstly, the sea ice extent and area are global variables while the length of the ice-free
season is a local one, and thus more appropriated to study locally the variation of the ice
cover in small regions such as narrow straits (which occupy one or only a few pixels in the
usual 12.5 or 25km grids). Secondly, while the ice extent or area must be calculated, say, for
each month of the year (for instance by averaging the daily ice extents or areas over one
month), the LIFS and ISII have one single value for each year for each point, thus being more
representative of the ice situation in a certain year than the usually quoted summer
minimum or winter maximum. Finally, minimum and maximum values can be
strongly affected by specific circumstances occurring in a comparatively short time
interval. It was noticed, for instance, that in the summer of 2007 there were unusually
clear skies over the Arctic Ocean which would have favoured a rapid melting, and
a particular wind pattern which would have led to a strong advection of the ice
out of the Arctic Ocean through Fram Strait (special conditions that may partly
explain the extraordinary depletion of sea ice in the Arctic Ocean in the summer of
2007).
We construct a time-series of the LIFS for the 1979-2008 period for each point of the
Arctic where sea ice was found at least one day in this period. We describe in detail the
melting seasons of 2007 (the longest on record) and 2008, and analyse the changes that took
place in the last 30 years in 85 disjoint regions of the Arctic Ocean and peripheral
seas.
We found that between 1979 and 2006 the spatially averaged ice-free season in the Arctic
increased at an approximately steady rate of 1.1 days/year and that the growth was
considerably faster (5.5 days/year), and monotonic, in the 2001-2007 period. In 2007 the
average LIFS in the Arctic was 168 days, dropping to 158 days in 2008, which
makes it the fourth longer since systematic satellite monitoring of the Arctic began. |