| Summary: | The total Antarctic sea ice extent (SIE) experiences a distinct annual cycle, peaking in September and reaching its minimum in February. In this paper we propose a mathematical and statistical decomposition of this temporal variation in SIE. Each component is interpretable and, when combined, gives a complete picture of the variation in the sea ice. We consider timescales varying from the instantaneous and not previously defined to the multi-decadal curvilinear trend, the longest. Because our representation is daily, these timescales of variability give precise information about the timing and rates of advance and retreat of the ice and may be used to diagnose physical contributors to variability in the sea ice. We define a number of annual cycles each capturing different components of variation, especially the yearly amplitude and phase that are major contributors to SIE variation. Using daily sea ice concentration data, we show that our proposed invariant annual cycle explains 29% more of the variation in daily SIE than the traditional method. The proposed annual cycle that incorporates amplitude and phase variation explains 77% more variation than the traditional method. The variation in phase explains more of the variability in SIE than the amplitude. Using our methodology, we show that the anomalous decay of sea ice in 2016 was associated largely with a change of phase rather than amplitude. We show that the long term trend in Antarctic sea ice extent is strongly curvilinear and the reported positive linear trend is small and dependent strongly on a positive trend that began around 2011 and continued until 2016.
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