The loss of Arctic sea ice is a conspicuous example of climate change. Climate models project ice-free conditions during summer this century under realistic emission scenarios, reflecting the increase in seasonality in ice cover. To quantify the increased seasonality in the Arctic-Subarctic sea ice system, we define a non-dimensional seasonality number for sea ice extent, area, and volume from satellite data and realistic coupled climate models. We show that the Arctic-Subarctic, i.e. The northern hemisphere, sea ice now exhibits similar levels of seasonality to the Antarctic, which is in a seasonal regime without significant change since satellite observations began in 1979. Realistic climate models suggest that this transition to the seasonal regime is being accompanied by a maximum in Arctic amplification, which is the faster warming of Arctic latitudes compared to the global mean, in the 2010s. The strong link points to a peak in sea-ice-related feedbacks that occurs long before the Arctic becomes ice-free in summer

Haine, Thomas W. N.

Martin, Torge

Scientific Reports

OceanRep

Supplementary Information for:The Arctic-Subarctic sea ice system is entering aseasonal regime: Implications for future ArcticamplificationThomas W. N. Haine1,* and Torge Martin21Earth & Planetary Sciences, The Johns Hopkins University, Baltimore, MD USA2GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany*Thomas.Haine@jhu.edu+These authors contributed equally to this work.ABSTRACTSupplementary information on the seasonality number and supporting figures.Discussion of Seasonality NumberDefinitionThe seasonality number, Se(T ), is defined by equation (1) of the main text. We consider a non-negative, time-dependentvariable x(t) which is (quasi-)periodic, for example with a period of 12 months. The seasonality number is the ratio of twoquantities, the seasonal range ∆x in the variable for a given year T ,∆x= x(t2)− x(t1), (SI1)and the average value over the season, x,x=1t2− t1∫ t2t1x(t ′) dt ′. (SI2)Namely,Se(T ) =|∆x|x. (SI3)In these formulae t1 and t2 are the times of consecutive extreme values of x, typically separated by about six months. Wetake the absolute value in the numerator of (SI3) to suppress the negative sign of Se for cases of seasonal decrease in x (whenx(t2)< x(t1), which we apply throughout). The seasonality number is a function of T because it can vary between successivepairs of extrema in x(t).Pedagogical ExamplesConsider the simple examples in Figure SI1 to make the seasonality number concept clear. The upper two panels show annualperiodic cycles with maxima and minima of x(t1) = 16 and x(t2) = 7, and hence ∆x=−9. They are inspired by the observed1980s–1990s winter Arctic sea ice extent (16×106 km2) being about twice the summer extent (7×106 km2). The upper panelshows sinusoidal and sawtooth periodic functions. Although the times of their maxima and minima differ, they have identicalranges and mean values (x= 11), so their seasonality numbers are the same and equal 0.78. These cases demonstrate the pointthat Se is independent of the shape of the periodic function x(t), so long as the range ∆x and the mean x are unaffected. Themiddle panel shows a clipped sinusoidal function, also with x(t1) = 16, x(t2) = 7, and ∆x=−9 (upper curve). This functionaccounts better for the different duration of the winter and summer seasons although still in a simplistic manner. The meanvalue x= 13 is larger than for the sinusoidal and sawtooth functions because the distribution of x values over the year for theclipped sinusoid is biased towards higher values. Therefore, the seasonality number Se= 0.71 is smaller than for the upperpanel. The middle panel also shows a clipped sinusoid function, but with x(t1) = 15,x(t2) = 4, hence ∆x=−11, and x= 11,crudely resembling the Arctic sea ice extent cycle in recent years that features a stronger decline in summer than in winter. Thiscase has Se= 1. The bottom panel shows a clipped sinusoid function that might resemble the Arctic sea ice extent cycle inthe coming decades. In this case, x(t1) = 10,x(t2) = 0, hence ∆x=−10, and x= 4.8, yielding Se= 2.1. The distribution of xvalues over the year is biased low compared to a sinusoid with the same range. Therefore the mean value is smaller than x= 5,which is the case for a sinusoid with the same range. Hence, the seasonality number is larger than for a sinusoid with the samerange.Properties of the Seasonality NumberThese examples show that the seasonality number Se is mainly controlled by the range ∆x, and especially by the minimumvalue, not the mean value x. Specifically, the middle panel of Fig. SI1 shows an increase of 2 in ∆x (lower curve) and x¯ (uppercurve), compared to the upper panel. The ∆x change impacts Se three times more than the x¯ change (a 28% increase versus a9% decrease). The following arguments make this idea clear.In many cases, the periodic function is evenly distributed between maxima and minima, meaning that the distribution of x(t)between x(t1) and x(t2) is unbiased. Then, x= [x(t2)+ x(t1)]/2, and the seasonality number for this unbiased seasonal cycle isSe0(T ) = 2[ |x(t2)− x(t1)|x(t2)+ x(t1)]= 2( |ε−1|ε+1), (SI4)where ε = x(t2)/x(t1). For the examples in Figure SI1, ε = 7/16 = 0.438 (upper panel, upper curve on middle panel),4/15 = 0.267 (lower curve on middle panel), and 0/10 = 0 (lower panel). Therefore, an unbiased seasonal cycle givesSe0 = 0.783, as seen for the sinusoid and sawtooth functions in the upper panel. The upper clipped sinusoid in the middle panelexhibits a bias that drives x high and therefore Se= 0.71 is smaller than the value of Se0 = 0.783 for the unbiased cycle, butstill quite close. The lower clipped sinusoid in the middle panel is similar with Se0 = 1.16 but Se= 1. In the lower panel, theunbiased seasonal cycle gives Se0 = 2, somewhat less than the actual value of Se= 2.1 because of the low bias in x(t).This result shows that Se> 2 only occurs when there is a bias in the distribution of x(t) so that the mean value x is smallerthan [x(t2)+ x(t1)]/2. In other words Se0 ≤ 2, which is seen in (SI4) because |ε−1|/(ε+1)≤ 1. For this reason, we refer toseasonality numbers greater than two as being in the episodic regime (such as Fig. SI1 lower panel), meaning that x(t) onlyintermittently departs from near zero. There is no corresponding restriction on the smallness of Se in the perennial regimeSe< 1: as the range ∆x decreases for any minimum x(t) value greater than zero, Se also decreases towards zero without limit.Now consider that the mean value x must lie between the maximum and minimum values of x(t); x(t2)≤ x ≤ x(t1) (forε < 1, otherwise the inequalities are flipped). Therefore,|1− ε| ≤ Se(T )≤∣∣∣∣1ε −1∣∣∣∣ (SI5)(for ε < 1, otherwise the inequalities flip). For the examples in the upper panel and upper curve in the middle panel of FigureSI1, ε = 7/16 = 0.438 and therefore 0.563 ≤ Se ≤ 1.29, which is a moderately tight restriction on the seasonality number,regardless of the shape of the seasonal cycle x(t). For the lower panel, which shows an x(t) with a minimum value of zero, theseasonality number must satisfy Se≥ 1, meaning any x(t) with a minimum of zero cannot be in the perennial regime, regardlessof the shape of its seasonal cycle. This is a reasonable property of Se.Notice that other putative definitions of the seasonality number, for example with the minimum value of x in the denominator,not the average, have less desirable properties. In particular, if the denominator vanishes, as it does for Arctic sea ice in someof the CMIP5 models if the denominator is the minimum value, then the seasonality number diverges to infinity. That is lessuseful than the seasonality number defined by equation (1) of the main text, which naturally distinguishes between perennial,seasonal, and episodic regimes.Relation between Sea Ice Extent Se and Multi-Year Ice ExtentFigure SI2 plots multi-year sea ice extent MYI against seasonality number Se for the data shown in Fig. 1. Multi-year seaice extent is defined as the minimum extent for a given year. As expected from the discussion above, there is a compactrelationship between MYI and Se. The linear correlation coefficient for the northern hemisphere NSIDC data is -0.97, whichshows that over the observational record Se is strongly controlled by MYI (the line on Fig. SI2 is the best-fit to these data). Thesouthern hemisphere NSIDC data are offset to higher MYI values (above the line). The same is true for the southern hemisphereHadISST data, although the scatter to large MYI at Se≈ 1.25 is presumably due to data uncertainty before the satellite era. TheCMIP5 models depart from the linear correlation at Se& 1.3, MYI . 2×106 km2. At large seasonality number (Se& 1.7 ,MYI . 1×106 km2), the multi-year ice extent no longer varies with Se because it then depends mainly on the average extent(the denominator in equation SI3). Therefore, MYI is a good proxy for Se for the Arctic over the observational record, and untilthe summer minimum sea ice extent drops below about 2×106 km2.2/9Practical ConsiderationsA few practical issues should be considered when computing the seasonality number from a periodic time series. First, a clearidea of the period of interest t2− t1 is required in order to avoid spurious extrema in x at shorter periods. For annually-repeatingvariables, we expect t2− t1 to be close to six months, for example. Second, using the extreme values to define the range ∆x ofx(t) can be problematic when the time series contains significant random noise. Then, the extrema may be sensitive to the noisein undesirable ways. Although, this problem is unlikely to severely impact the computation of the seasonality number, it maybe preferable to define ∆x as the difference between (for example) the 95th and 5th percentiles of the distribution of x(t) valuesbetween successive extrema. Third, for an annually-repeating variable one has the choice of defining the seasonality numbereach year based on the increase in x(t) (ε > 1) or on the decrease in x(t) (ε < 1). These two seasonality numbers may differsomewhat if x(t) is biased differently for the increasing phase of its cycle compared to the decreasing phase.Application to other VariablesThe seasonality number is particularly useful for sea ice and can be applied to other Earth system quantities, such as insolation,ice mass, or heat content of the upper ocean. These are extensive (additive) quantities, which are non-negative by definition.The seasonality number can be applied to intensive quantities too, but care is required. Specifically, it is not applicable tovariables with an arbitrary offset. Temperature is a good example: it makes sense to talk of the seasonality number of absolutetemperature measured in Kelvin (which is non-negative with a non-arbitrary zero), but not of temperature measured using anempirical scale such as Celsius or Fahrenheit.3/90 3 6 9 12 15 18 21 24 27 30 33 36Month051015QuantityRange = 9Mean = 11Se = 0.780 3 6 9 12 15 18 21 24 27 30 33 36Month051015QuantityRange = 9Mean = 13Se = 0.71Range = 11Mean = 11Se = 10 3 6 9 12 15 18 21 24 27 30 33 36Month051015Quantity Range = 10Mean = 4.8Se = 2.1Figure SI1. Example annual periodic functions x(t) and their seasonality numbers Se to illustrate the seasonality of Arctic seaice extent. The range and mean are defined by equations (SI1) and (SI2), respectively, and Se is computed using (SI3).4/90 0.5 1 1.5 2 2.5Seasonality number,  Se0246810Multi-year sea ice extent (x106  km2 )NSIDCWalsh et al.HadISSTPIOMASCMIP5Figure SI2. Multi-year sea ice extent plotted against seasonality number for the datasets shown in Fig. 1. The large black dotsare the pedagogical examples from Fig. SI1. The line is the best fit to the northern hemisphere NSIDC data.5 10 15 20 25 30Average sea ice volume (x103  km3 )51015202530Sea ice volume range (x103 km3 )5 10 15 20 25 30Average sea ice extent (x106  km2 )51015202530Sea ice extent range (x106  km2 )0.30.61.01.41.82.23.04.0EpisodicSeasonalP e r e n n i a lextentvolumeNSIDCPIOMASFigure SI3. Northern hemisphere seasonal sea ice extent (from NSIDC and PIOMAS) and volume (from PIOMAS) rangesplotted against the corresponding seasonal averages. The seasonality numbers are shown with contours. The sea ice extent andvolume seasonality numbers increase with time (Figs. 1b and 2b), mainly because the ranges increase and the averagesdecrease, respectively.5/91900 1950 2000 2050 2100Year01020ExtentACCESS1-01900 1950 2000 2050 2100Year01020ExtentACCESS1-31900 1950 2000 2050 2100Year01020ExtentBNU-ESM1900 1950 2000 2050 2100Year01020ExtentCCSM41900 1950 2000 2050 2100Year01020ExtentCESM1-BGC1900 1950 2000 2050 2100Year01020ExtentCESM1-CAM51900 1950 2000 2050 2100Year01020ExtentEC-EARTH1900 1950 2000 2050 2100Year01020ExtentHadGEM2-AO1900 1950 2000 2050 2100Year01020ExtentHadGEM2-CC1900 1950 2000 2050 2100Year01020ExtentHadGEM2-ES1900 1950 2000 2050 2100Year01020ExtentMIROC-ESM-CHEM1900 1950 2000 2050 2100Year01020ExtentMIROC51900 1950 2000 2050 2100Year01020ExtentMIROC-ESM1900 1950 2000 2050 2100Year01020ExtentMPI-ESM-LR1900 1950 2000 2050 2100Year01020ExtentMPI-ESM-MRFigure SI4. Annual maxima and minima of sea ice extent for the CMIP5 models. The historical and RCP8.5 projections areshown. Black lines indicate the multi-model means.6/91900 1950 2000 2050 2100Year024Volume104ACCESS1-01900 1950 2000 2050 2100Year024Volume104ACCESS1-31900 1950 2000 2050 2100Year024Volume104BNU-ESM1900 1950 2000 2050 2100Year024Volume104CCSM41900 1950 2000 2050 2100Year024Volume104CESM1-BGC1900 1950 2000 2050 2100Year024Volume104CESM1-CAM51900 1950 2000 2050 2100Year024Volume104EC-EARTH1900 1950 2000 2050 2100Year024Volume104HadGEM2-AO1900 1950 2000 2050 2100Year024Volume104HadGEM2-CC1900 1950 2000 2050 2100Year024Volume104HadGEM2-ES1900 1950 2000 2050 2100Year024Volume104MIROC-ESM-CHEM1900 1950 2000 2050 2100Year024Volume104MIROC51900 1950 2000 2050 2100Year024Volume104MIROC-ESM1900 1950 2000 2050 2100Year024Volume104MPI-ESM-LR1900 1950 2000 2050 2100Year024Volume104MPI-ESM-MRFigure SI5. As Fig. SI4 except for sea ice volume.7/91900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100Year0.511.522.53Seasonality number,  Se(a) Sea ice extent1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100Year0.511.522.53Seasonality number,  Se(b) Sea ice volumeACCESS1-0 ACCESS1-3 BNU-ESM CCSM4 CESM1-BGC CESM1-CAM5EC-EARTH HadGEM2-AO HadGEM2-CC HadGEM2-ES MIROC-ESM-CHEM MIROC5MIROC-ESM MPI-ESM-LR MPI-ESM-MR multi-model meanFigure SI6. Seasonality of Arctic sea ice extent (upper) and volume (lower) for the CMIP5 models. The black line marks themulti-model mean.8/9-0.05 0 0.05 0.1 0.15Arctic SAT (°C yr -1)-0.1-0.0500.05Arctic SIA (106km2  yr-1 )(a)-0.025 0 0.025 0.05Global SAT (°C yr -1)-0.1-0.0500.05year(b)190019251950197520002025205020752100Figure SI7. Calculation of the peak in coincident sea-ice retreat and surface air temperature (SAT) warming. (a) Annual rateof change in Arctic (> 70oN) sea ice area (SIA) minimum as a function of the Arctic autumn (September to November) meanSAT annual rate of change (see Fig. 4c). The black × marks the year with the largest normalized distance from the origin,namely, the largest change in both SIA and SAT, which we define as the peak in the sea ice feedback (see equation (2)). TheSIA and SAT data are from the multi-model mean of the CMIP5 models. (b) Same as (a) but for global autumn mean SAT(notice the different abscissa scale).9/9

The Arctic-Subarctic sea ice system is entering a seasonal regime: Implications for future Arctic amplification

AbstractThe loss of Arctic sea ice is a conspicuous example of climate change. Climate models project ice-free conditions during summer this century under realistic emission scenarios, reflecting the increase in seasonality in ice cover. To quantify the increased seasonality in the Arctic-Subarctic sea ice system, we define a non-dimensional seasonality number for sea ice extent, area, and volume from satellite data and realistic coupled climate models. We show that the Arctic-Subarctic, i.e. the northern hemisphere, sea ice now exhibits similar levels of seasonality to the Antarctic, which is in a seasonal regime without significant change since satellite observations began in 1979. Realistic climate models suggest that this transition to the seasonal regime is being accompanied by a maximum in Arctic amplification, which is the faster warming of Arctic latitudes compared to the global mean, in the 2010s. The strong link points to a peak in sea-ice-related feedbacks that occurs long before the Arctic becomes ice-free in summer.</jats:p

The Arctic-Subarctic sea ice system is entering a seasonal regime: Implications for future Arctic amplification

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