2.4. Mass fraction of snow in snow-origin ice
To determine the mass fraction of snow in snow-origin ice (hereafter, ‘snow fraction’), we used a mass balance equation (Jeffries et al., 1994, 2001):
f snow + f sea = 1, (1)
f snow δsnow +f sea δsea = δobs, (2)
where f represents the mass fraction of snow or seawater, δ represents their δ18O values, and the subscripts ‘snow’, ‘sea’, and ‘obs’ indicate snow, under-ice seawater, and observed bulk ice, respectively. For δsea, we used the parent water δ18O values collected during JARE60 (−0.7‰) rather than the value that includes the fractionation factor during seawater freezing (see Jeffries et al., 1994, 2001) because we assumed that all granular ice with a δ18O value below that of the under-ice water was snow ice (Granskog et al., 2004; Jeffries et al., 1994). In addition, we assumed that granular ice with a δ18O value below that of under-ice water was snow-origin ice. Based on the result obtained from the JARE60 samples, we used δsea = −0.7‰. δsnow was taken as the mean δ18O value of snow samples (−20.3‰) collected during JARE56–60. We estimated the errors on the snow fractions to be less than 12.2% by calculating the effect of changing the snow δ18O values by their standard deviation (±2.1‰).