This is a largely false statement. The correct part is the East Antarctic ice sheet is close to mass balance (e.g. Shepherd et al., 2012; Gardner et al., 2017 (just published today)) and that the recent changes in Antarctic sea ice cover are explained by natural variability (Turner et al., 2016; Meehl et al, 2016).
The statement is definitely false for Arctic sea ice, which is decreasing dramatically since the 1990's as a response to human greenhouse gas emissions. In fact, there is a direct and linear relation between CO2 emitted and sea ice decline: each metric ton CO2 emitted leads to a 3 m2 loss of Arctic sea ice (Notz and Stroeve, 2016). The current loss of sea ice falls outside of natural variability and has been unprecedented in at least the last 1,450 years (Kinnard et al., 2011).
West Antarctic mass loss is rapidly increasing since the 1990's (e.g. Gardner et al., 2017). Glacial retreat in the Amundsen Sea region, the main driver of this mass loss, appears to have started already in the earlier 20th century (Smith et al., 2016). The rate of retreat is rapid and widespread (Rignot et al., 2014), with no mechanism for future stabilisation (Joughin et al., 2014).
Current ice sheet mass loss contributes significantly (almost 40%, Rietbroek et al., 2016) to observed 21st century sea level rise. Until 2016, Arctic sea ice loss has dominated over slight Antarctic sea ice gain. In 2016 and 2017, Antarctic sea ice has been in decline as well, and reasons for this are currently under study.
References
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Joughin, I., Smith, B.E., Medley, B., 2014. Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica. Science. 344, 735–738.
Kinnard, C., Zdanowicz, C.M., Fisher, D.A., Isaksson, E., de Vernal, A., Thompson, L.G., 2011. Reconstructed changes in Arctic sea ice over the past 1,450 years. Nature 479, 509–512.
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