Vol.3, No.5, 351-358 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.35047
Non-stationary drivers of polar sea ice area
Reginald R. Muskett
Geophysical Institute, University of Alaska Fairbanks, Fairbanks, USA;
Received 12 February 2011; revised 20 March 2011; accepted 18 April 2011.
ABSTRACT
From 2002 through 2008 the secular rate of de-
creasing sea ice area in the northern hemi-
sphere accelerated by a factor of 18, whereas
the secular rate of increasing sea ice area in the
southern hemisphere accelerated by a factor of
16, relative to the rates from 1978 through 2007.
These were derived from the daily sea ice area
retrieved from the Scanning Multi-channel Mi-
crowave Radiometer – Special Sensor Micro-
wave/Imager and the Advanced Microwave Scan-
ning Radiometer for the Earth Observation Sys-
tem. The “annual” cycle of northern and south-
ern sea ice areas, the number of days between
maxima and minima is 372.4, on average, a fre-
quency modulation, with a recurrence interval
of 61.7 years. Significant spectral power occurs
at the quasi-4-day through 120-day frequencies.
The frequency content and modulation of the
daily time series’ are consistent inter-monthly to
inter-seasonal frequencies of solar irradiance,
atmospheric-oceanic Rossby waves, length-of-
day, and polar motion. This suggests conserva-
tion of angular momentum of the atmosphere –
sea-ice – ocean system. The near 60-year modu-
lation and analysis of the detrended daily time
series of the Arctic and Antarctic sea ice areas
suggest the accelerations shown by the secular
trends are relatively short-lived and reversible
within an interval of one-quarter (15-years) to
one-half (30-years) of the modulation period.
Keywords: Hemispheric Sea-Ice Area Changes;
Trends; Frequency Modulations; Physical Drivers
1. INTRODUCTION
The sea ice areas at the polar oceans serve a vital
function through surface albedo in the energy balance
and climate system of Earth [1-5]. Forcing on sea ice
area (growth and decay) comes from solar radiation,
infrared radiation under cloudy-sky conditions, ocean
kinematics and heat transfer, and surface winds acting on
daily, seasonal, annual, inter-annual, decadal and longer
time scales. Satellite datasets of the daily sea ice area of
the northern and southern hemispheres can be assessed
for secular trends and variations [6-10]. Figure 1 shows
the northern (Arctic, left) and southern hemisphere (An-
tarctic, right) sea ice area, on 17 August 2008, seen in
colorized concentration per pixel from satellite observa-
tions.
The annual growth, decay and net changes in polar sea
ice areas and the hemispheric asymmetry derived by
satellite-borne passive microwave sensors were first de-
scribed by Cavalieri et al. [6]. These data are available
from the National Snow and Ice Data Canter, Univ. Col-
orado, as the NASA TEAM from late 1978 through end
of 2007 and the BOOTSTRAP from late 1978 through
end of 2006. The algorithms used in the retrieval of sea
ice area and area-extent use surface brightness tempera-
tures to derive grid cells with sea ice concentrations
above 15%. In this fashion, sea ice area-extent is defined
as the cumulative area of grid cells with concentration of
sea ice greater than 15% per gridcell, relative to water,
and sea ice area is defined as the cumulative area of sea
ice with 100% sea ice concentration per grid cell (a more
conservative estimator). The algorithmic measurement
and calibrations, for the scanning multi-channel micro-
wave radiometer (SMMR) which was flown on Nimbus
Figure 1. Northern (left) and southern hemisphere
(right) sea ice areas on 17 August 2008. Sea ice
concentration images were provided by the Polar
Research Group, Department of Atmospheric Sci-
ences, University of Illinois, Urbana-Champaign.

R. R. Muskett / Natural Science 3 (2011) 351-358 352
7 from late 1978 through late 1987, and the Defense
Meteorological Satellite Program special sensor micro-
wave/imager (SSM/I) which was flown on satellites F8,
F11, F13 and F15 (F13 is till operational and F15 re-
cently experienced anomalous behavior) began from
mid-1987 and current is described in Cavalieri et al. [7].
In this investigation we will use the daily sea ice area
(not extent) from the NASA TEAM algorithm, from the
northern (Arctic) and southern hemisphere (Antarctic)
since it covers the longer time interval from October
1978 through the end of December 2007. The daily
summation of the hemispheres gives the daily global sea
ice area. The SMMR portion of the dataset with missing
values and the early portion of the SSM/I record from 3
December through 12 January with missing values, were
filled by linear interpolation.
In addition to the SMMR-SSM/I time series of sea ice
area we use daily sea ice area data from the Advanced
Microwave Scanning Radiometer for the Earth Observa-
tion System (AMSR-E), derived through an algorithm
developed by scientists Institute of Oceanography, Uni-
versity of Hamburg, Germany [11]. This sensor, flown
on the NASA-Aqua satellite, provides a dataset that
covers the period from mid-2002 through 2008, for
comparison with the SMMR-SSM/I data. The AMSR-E
sensor differs from the SSM/I passive-microwave sensor
in having more brightness temperature channels and a
greater spatial resolution, 6-by-4 km at the primary 89 GHz
channel. Comparisons of retrieved sea ice area by these
algorithms and ship-borne estimates showed good agree-
ment [11]. A few missing day-values of the AMSR-E
time series were filled by linear interpolation.
Figure 2 illustrates the daily sea ice area time series,
the polar sea ice area (sum of the same-day Arctic and
Antarctic sea ice areas), from SMMR-SSM/I from late-
1978 through 2007 (top) and from AMSR-E from late-
2002 through 2008 (bottom). The curious shape of the
sinusoidal is due to the day of the Arctic and Antarctic
minima and maxima which do not coincide. The calen-
dar-day occurrence of minimum and maximum varies
over the length of the time series. The green lines signify
the global area maxima and minima of the daily time
series for comparison. The global sea ice area attained an
upper-bound maximum in 1987 (top, solid green line).
Minima after 1997 (top, dashed green line) have been
variable, though decreasing since 2005 (bottom, dashed
green line).
Previous studies of trends and variations of Arctic and
Antarctic sea ice extents and areas utilized the same
SMMR-SSM/I daily satellite datasets although over dif-
ferent total-year lengths with monthly and annual aver-
aging and time-domain and frequency-domain smooth-
ing [6-8]. Uncorrelated inter-annual periodicities that
Figure 2. Daily time series of polar sea ice area from SMMR-
SSM/I NASA Team algorithm. Gaps in the records were filled
by linear interpolation.
remained were dominant at 5-year period in the Arctic,
and 3-year period in the Antarctic of sea ice extent. Net
decadal decrease in the Arctic sea ice extent – area and
the increase in Antarctic sea ice extent – area were at-
tributed to increasing atmospheric CO2 concentrations,
consistent with results of a global circulation model with
gradual CO2 forcing [6-12]. This has again been brought
to attention given the anomalous reduction of Arctic Sea
ice extent in the summer of 2007, while the Antarctic sea
ice extent continues to increase without any noted un-
usual seasonal changes [11,13,14].
We note the existence of calendar (day-month-year)
and averaging (aggregation) effects, which can lead to
spurious anomalies and trends; such as the leap-year
effect noted in daily/monthly temperature data and many
other calendar effects known to financial statistics [15,
16]. Smoothing of data whether in the time-domain or
the frequency-domain can be filled with problems asso-
ciated with introducing bias into the analysis [17]. The
SMMR-SSM/I daily sea ice extent and area time series
are both seasonal and non-stationary (i.e. the mean and
variance change over time, hence time dependent). This
has likely lent to reports of citing seemingly conflicting
derived trends, magnitudes and polarities [8,12,18]. Tem-
poral aggregating of discrete non-stationary time series
can lead to aliases, spurious correlations and false- eaks
in autoregressive moving average models [19,20]. For
these reasons, we will investigate the datasets without

R. R. Muskett / Natural Science 3 (2011) 351-358 353
calendar-based monthly and annual averaging, and with-
out time-domain and frequency domain smoothing or
autoregressive moving average techniques [21]. Our ap-
proach is to utilize linear regression to identify trends,
secular and higher-order, and the Discrete Fast Fourier
Transform with zero-padding [22,23]. We then use the
secular trends to detrend the daily Arctic, Antarctic and
Global time series to investigate their frequency content.
2. RESULTS
2.1. Sea Ice Areas: Means, Standard
Deviations and Seasonal Ranges
Table 1 summarizes sea ice areas, Arctic, Antarctic
and Polar, by their means (with uncertainty), standard
deviations and seasonal ranges from the daily sea ice
area estimates from SMMR-SSM/I from 29 Dec. 1978
through 29 Dec. 2007 and from AMSR-E from 31 Dec.
2002 through 31 Dec. 2008. Comparison shows that the
mean Arctic sea ice area decreasing by about 3%, the
mean Antarctic sea ice area increasing by about 16%,
and the mean Polar sea ice area is increasing by about
7%. The seasonal range of Arctic sea ice area lowered its
minimum by about one million square kilometers and its
maximum remained unchanged, on average. The sea-
sonal range of the Antarctic sea ice area, in contrast,
raised its maximum by about two million square kilo-
meters and its minimum remained unchanged, on aver-
age. The seasonal range of the polar sea ice area raised-
both its minimum and maximum by about one million
square kilometers, on average. The standard deviations
of the areas show changes of 1% (Arctic), 14% (Antarc-
tic) and 30% (Global), on average, in the comparative
time periods.
2.2. Sea Ice Area Secular Trends and
Variations
The daily sea ice area time series were processed by
ordinary least-squares regression to derive secular and
quadratic trends. The daily time series were then de-
trended and processed by the Discrete Fast Fourier
Transform (DFFT) to derive the power spectral density.
The DFFT was applied on samples of 4096 in three
sub-ranges spanning the full-ranges of each SMMR-
SM/I time series, as well as the full-range (10593 sam-
ples) with zero-padding to 16384 samples (214). Fre-
quency components were the same in all the 4096 sub-
ranges, and over the full-range with zero-padding to a 2n
multiple. The AMSR-E time series (2192 samples) were
zero-padded to 4096 samples. Figures 3, 4 and 5 illus-
trate the trends (secular and quadratic) of the daily sea
ice area time series and the power spectral density (from
detrended time series) for the Arctic, Antarctic and Polar,
respectively. Table 2 summarizes the secular trends with
uncertainties.
Daily Arctic sea ice area has secular decreases of
17 998 ± 3 587 km2/yr (SMMR-SSM/I) from late-1978
through 2007 and 317 277 ± 37 212 km2/yr (AMSR-E)
from late-2002 through 2008 (Figure 3). Daily Antarctic
sea ice area has secular increases of 24 311 ± 5359 km2/yr
(SMMR-SSM/I) from late-1978 through 2007 and 371
680 ± 65 789 km2/yr (AMSR-E) from late-2002 through
2008 (Figure 4). Daily Polar sea ice area has secular
increases of 6 133 ± 2 332 km2/yr (SMMR-SSM/I) from
late-1978 through 2007 and 54 404 ± 33 391 km2/yr
(AMSR-E) from late-2002 through 2008 (Figure 5). The
rate of secular-decrease of the daily Arctic sea ice area
has increased by a factor of about 18, from late-2002
through 2008 relative to late-1978 through 2007 (Table 2).
Table 1. Arctic, antarctic and global sea ice area statistics, 1978 through 2008.
SMMR-SSM/I (29 Dec. 1978 through 29 Dec. 2007) Area (km2)
Arctic Antarctic Polar
Mean 9 431 838 ± 30 069 8 759 378 ± 44 911 18 191 215 ± 19 475
S.D. 3 094 748 4 622 378 2 004 386
Range ~4 to 14 (106) ~2 to 16 (106) ~13 to 23 (106)
AMSR-E (31 Dec. 2002 through 31 Dec. 2008) Area (km2)
Arctic Antarctic Polar
Mean 9 189 721 ± 65 515 10 458 208 ± 114 793 19 647 928 ± 57 870
S.D. 3 067 316 5 374 473 2 709 399
Range ~3 to 14 (106) ~2 to 18 (106) ~14 to 24 (106)

R. R. Muskett / Natural Science 3 (2011) 351-358 354
Figure 3. Trends and power density spectra (from detrended series) of the daily Arctic sea ice area. Trends are for secular
(dashed red line) and quadratic (solid red line). Numbers in the spectra indicate frequencies with power above the modeled χ2
red noise curve. The “annual” frequency is indicated by the capital letter.
Figure 4. Trends and power density spectra (from detrended series) of the daily Antarctic sea ice area. Trends are for secular
(dashed red line) and quadratic (solid red line). Numbers in the spectra indicate frequencies with power above the modeled χ2
red noise curve. The “annual” frequency is indicated by the capital letter.

R. R. Muskett / Natural Science 3 (2011) 351-358 355
Figure 5. Trends and power density spectra (from detrended series) of the daily Polar (sum of the northern and southern he-
mispheres) sea ice area. Trends are for secular (dashed red line) and quadratic (solid red line). Numbers in the spectra indicate
frequencies with power above the modeled χ2 red noise curve. The “annual” frequency is indicated by the capital letter.
Table 2. Secular trends of Arctic, Antarctic and Polar sea ice
area.
SMMR-SSM/I (29 Dec. 1978 through 29 Dec. 2007) Rates (km2/yr)
Arctic Antarctic Polar
−17 998 ± 3 587 +24 311 ± 5 359 +6 133 ± 2 332
AMSR-E (31 Dec. 2002 through 31 Dec. 2008)
Arctic Antarctic Polar
−317 277 ± 37 212 +371 680 ± 65 789 +54 404 ± 33 391
By comparison (Table 2), the rate of secular-increase in
the daily Antarctic sea ice area has increased by a factor
of about 16, comparing the same periods. However in
the same comparative periods, the rate of secular-in-
crease in the daily Polar sea ice area has increased by a
factor of about 9 (Table 2).
Power spectral density of the detrended series indi-
cated significant, above the modeled χ2 99% confidence
level, frequency components. The detrended SMMR-
SM/I daily Arctic sea ice area series has significant
power located at 4, 11, 16, 24, 61, and 120-day frequen-
cies. The detrended SMMR-SMM/I daily Antarctic sea
ice area series has significant power located at 4, 5, 10,
16, 27, 51, 61, and 120-day frequencies. The detrended
AMSR-E daily Arctic sea ice area series has significant
power located at 4, 5, 10, 26, 46, 61, and 120-day fre-
quencies. The detrended AMSR-E Antarctic sea ice area
series has significant power located at 4, 5, 10, 13, 16,
56, 72, and 120-day frequencies. The detrended SMMR-
SSM/I and AMSR-E daily Polar sea ice area series con-
tained significant power at the same frequencies as the
Arctic and Antarctic sea ice area series. In all the de-
trended daily time series, SMMR-SSM/I and AMSR-E,
the annual cycle for the Arctic, Antarctic and Polar areas
was 372.4 days, on average (Figures 3, 4 and 5).
3. DISCUSSIONS
Power spectra (Figures 3, 4 and 5) of the detrended
daily sea ice area time series show significant power at 4,
5, 10, 13, 16, 27, 51, 61 and 120-day frequencies in the
Arctic, Antarctic and Polar sea ice areas. These short-
term variations in sea ice area are consistent with the
same variations of solar irradiance (total and ultraviolet),
Rossby waves in the atmosphere and ocean, length-of-
day and polar motion [24-36].
The annual cycle of the SMMR-SSM/I and AMSR-E
daily sea ice area time series has a period of 372.4-days,
on average. Close inspection of time series by day-count
of sea ice area maximum-to-maximum and minimum-to-
minimum show that the annual cycle varied from 305-

R. R. Muskett / Natural Science 3 (2011) 351-358 356
days (minima) in 1995-96 to 394-days (maxima) in
1989-90, SMMR-SSM/I Arctic sea ice area time series
and 333-days (minima) in 2005-06 to 389-days (minima)
in 2006-07, AMSR-E Arctic sea ice time series. The An-
tarctic and Polar sea ice time series show similar varia-
tions in the annual cycle day-count ranges spanning mi-
nima-to-minima and maxima-to-maxima. This indicates
a frequency modulation on the timing of minima and
maxima from year to year of the sea ice area, with a re-
currence period of 61.7 years; i.e. a sinusoidal forcing
with a period on the order of 60 years. The 60-year
modulation of the annual cycle of both hemispheres sea
ice areas is consistent with the 60-year modulation of
global air temperature and circulation by the coupled
solar irradiance – length-of-day variations [37,38]. The
physical basis for coupling this modulation to Polar sea
ice area variations would be through conservation of
atmospheric-ocean angular momentum [39,40]. This is a
natural consequence given that sea ice acts as a bound-
ary layer between the atmospheric and ocean momentum
fields [4,41,42].
The long-term quadratic trend in the daily SMMR-
SSM/I Arctic and Polar sea ice area time series and the
short-term quadratic trends in the daily AMSR-E Arctic,
Antarctic and Polar sea ice area time series suggest pe-
riodic forcing acting on the growth and decay of sea ice
area. The long-term quadratic trend suggests a forcing
on the Arctic sea ice area with a period of 60-years, con-
sistent with solar irradiation – length-of-day modulation
of surface temperatures and atmospheric-ocean circula-
tion. The short-term quadratic trends may themselves
be linked to Rossby waves to conserve angular momen-
tum in the coupled atmosphere-sea ice-ocean system of
the northern and southern hemispheres.
Secular trends show apparent increases in the rates of
Arctic sea ice area decrease, Antarctic sea ice area in-
crease, and Polar sea ice area increase from 2002 through
2008 relative to those from 1978 through 2007 (Table 2).
The detrended daily AMSR-E Arctic and Antarctic sea
ice area showed steady changes in the magnitudes of the
seasonal minima and maxima from late-2002 through
2008 (Figure 6). The Arctic seasonal maxima showed
steady increase while the seasonal minima showed de-
creases. Interestingly the Antarctic seasonal maxima
showed decreases and its seasonal minima showed some
decreases (Figure 6, bottom). These findings suggest
processes operating to moderate the long- term secular
trends (Table 2). If these processes continue as linked to
the 60-year solar – atmosphere – length-of- day modula-
tion, then the secular trends of decreasing Arctic seas ice
area and increasing Antarctic sea ice area could be re-
versed within as little as 15 to 30-years, a quarter to
one-half period.
Figure 6. Detrended daily time series of Arctic (top) and Ant-
arctic (bottom) sea ice area. Arrows indicate changes in the
seasonal minima and maxima. Green lines are for visual refer-
ence of contrasting minima to maxima.
4. CONCLUSIONS
The satellite instrument retrievals of daily northern
and southern hemisphere sea ice areas were investigated
for secular trends and periodic variations. The daily re-
trievals derived from the SMMR-SSM/I NASA Team
algorithm from 1979 through 2007 and the AMSR-E
Institute of Oceanography – University of Hamburg al-
gorithm from 2003 through 2008. Secular trends show a
decrease in Arctic sea ice area and an increase Antarctic
sea ice area over their respective time periods. Since
2003 the AMSR-E secular trends indicated accelerations
of decreasing Arctic sea ice area, by a factor 18, and
increasing Antarctic sea ice area, by a factor of 16 rela-
tive the SMMR-SSM/I secular trends, respectively. The
Polar sea ice area, the daily sum of the northern and
southern sea ice regions, showed an acceleration of in-
creasing sea ice area, due to the increase in Antarctic sea
ice area, since 2003 (AMSR-E) as well.
Spectral analysis of the daily sea ice areas showed the
annual cycle to be 372.14 days, on average, for the
SMMR-SSM/I and AMSR-E time series. The annual
cycle varied from 305 days to 394 days. The recurrence
interval of the annual cycle is about 61.7 years, on aver-
age. Significant spectral power occurred at from 4-day
through 120-day frequencies, which were consistent with

R. R. Muskett / Natural Science 3 (2011) 351-358 357
those of solar irradiation, Rossby waves, length-of- day
and polar motion. These results suggest a linkage of the
daily sea ice area variations in the northern and southern
hemispheres with the 60-year solar – atmosphere –
length-of-day modulation. We hypothesize the spectral
content of the daily Polar sea ice variations is a conse-
quence of conservation of angular momentum, solar ir-
radiation and ocean heat content variations.
The detrended daily AMSR-E Arctic sea ice area
shows the Arctic seasonal maxima to be increasing,
while the seasonal minima decreasing. The detrended
daily AMSR-E Antarctic seasonal maxima show the
seasonal minima decreasing, and the seasonal maxima
decreasing. These findings suggest processes operating
to moderate the long-term secular trends. If these pro-
cesses continue as linked to the 60-year solar – atmos-
phere – length-of-day modulation, then the long- and
short-term secular trends, decreasing Arctic seas ice area
and increasing Antarctic sea ice area, are reversible
within a range of 15 to 30-years.
5. ACKNOWLEDGEMENTS
We thank the Arctic Region Supercomputing Center, University of
Alaska Fairbanks for computing facilities support and the Japan Aero-
space Exploration Agency for computing facilities support at the In-
ternational Arctic Research Center. The National Snow and Ice Data
Center, University of Colorado, The Polar Research Group, University
of Illinois, Urbana-Champlain, USA, and the Institute of Oceanogra-
phy, University of Hamburg, Germany are thanked. Prof. Syun-Ichi
Akasofu is thanked for encouraging this work. This work was per-
formed by R.R. Muskett at the International Arctic Research Center,
University of Alaska Fairbanks, Alaska, USA.
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