In https://doi.org/10.1007/s00410-022-01925-6 we presented a new model for zircon saturation in silicate melts by fitting the results of 196 data from new experiments with 430 data from previous experimental studies. The new model covers temperatures from 750 to 1620 oC, pressures from 0.0001 to 4.0 GPa, and compositions with ASI values from 0.20 to 2.00 and water contents from 0 to 17 wt %. The model confirmed that temperature and melt composition are the dominant controls on zircon solubility, although pressure and water content also have resolvable effects. In this study we demonstrated that optical basicity (?) is the best descriptor of melt composition for zircon saturation compared to the parameters used in other models (M, G, B), as well as ASI and NBO/T. Our model (using ?) predicts zircon saturation temperatures within 10% of the experimental values for 92% of the collated dataset compared to < 80% for other models (Watson and Harrison, 1983; Boehnke et al. 2013; Gervasoni et al. 2016; Borisov and Aranovich 2019; Shao et al. 2019; 2020).

To demonstrate the improved accuracy of the new model, we compared the temperatures obtained to those estimated using the seven other zircon saturation models (note that two models are presented in Shao et al. 2020) for quartz-hosted melt inclusions from the Bishop Tuff (Fig. 11), for which temperature was independently constrained. However, two issues have emerged in our treatment of the Bishop Tuff data: (i) we included H2O wt % in our calculation of the mole fractions for M (while Watson and Harrison (1983) and Boehnke et al. (2013) do no state that H2O should be excluded from the calculation of mole fractions, this can be inferred from the values of M they report); and (ii) 13 of the 27 melt inclusions used have altered compositions with ASI < 0.90 and > 1.20.

Fig. 11
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a Temperature estimates for the Bishop Tuff from various geothermometers: (1) Fe-Ti oxides for the full eruptive suite (Hildreth and Wilson 2007); (2) and (3) Fe-Ti oxides for the early Bishop Tuff (Ghiorso and Evans 2008; Jolles and Lange 2019); (4) Fe-Ti oxides for the late Bishop Tuff (Jolles and Lange 2019); (5) δ18O for the full eruptive suite and (6) δ18O for the early Bishop Tuff (Bindeman and Valley 2002); (7) Ti-in-quartz for the early Bishop Tuff (Wark et al. 2007; Thomas and Watson 2012); (8) Ti-in-zircon for the early Bishop Tuff corrected for overestimates of aTiO2 (Schiller and Finger 2019); (9) MELTS (Ghiorso and Evans 2008; Gualda and Ghiorso 2013). b Predicted zircon saturation temperatures for quartz-hosted melt inclusions from the Bishop Tuff (Anderson et al. 2000; Schmitt and Simon 2004) using the models of Watson and Harrison (1983), Boehnke et al. (2013), Gervasoni et al. (2016), Borisov and Aranovich (2019), Shao et al. (2019), Shao et al. (2020) using G and M and Crisp and Berry (2022) abbreviated as WH83, B13 G16, BA19, S19, S20a, S20b and CB22, respectively. Data in Revised Supplementary Table ST4. In both a and b, the shaded area represents the eruption temperature from the early to late units (Bindeman and Valley 2002) and the dashed lines the approximate liquidus-solidus temperature range bounded by the wet granite solidus at 680°C (Schiller and Finger 2019). Modified from Schiller and Finger (2019)

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The error in M affected temperatures calculated using the Watson and Harrison (1983), Boehnke et al. (2013) and Shao et al. (2020) models. The melt inclusions from the Bishop Tuff contain ~ 4.50 wt % H2O, which when included in the mole fraction calculations results in M values that are ~ 0.35 greater than when H2O wt % is excluded. Therefore, our zircon saturation temperatures using the Watson and Harrison (1983), Boehnke et al. (2013) and Shao et al. (2020) models are ~ 24, 37 and 31 oC lower, respectively, than they should have been. The corrected predicted average zircon saturation temperatures for the Bishop Tuff melt inclusions are 731 ± 8, 678 ± 9 and 717 ± 9 oC for the Watson and Harrison (1983), Boehnke et al. (2013) and Shao et al. (2020) models, respectively. The Watson and Harrison (1983) temperature is within the estimated eruption and liquidus-solidus temperature intervals but is ~ 20 oC lower than the average inferred temperature of 750 oC. In contrast, the average zircon saturation temperature predicted by our model is 748 ± 10 oC. The temperatures predicted by the Boehnke et al. (2013) and Shao et al. (2020) models underestimate the actual temperature by 75 and 35 oC, respectively. Temperature underestimates using the Boehnke et al. (2013) model were also noted by Siégel et al. (2018) and Schiller and Finger (2019) when applied to other examples. Removing the 13 data with ASI values < 0.90 and > 1.20 has a negligible effect on the average zircon saturation temperatures predicted using the eight models. The correct values of M and zircon saturation temperatures for the Bishop Tuff melt inclusions using the Watson and Harrison (1983), Boehnke et al. (2013) and Shao et al. (2020) models are provided in a revised version of Supplementary Table 4. The revised data are also shown in a new version of Fig. 11, which also excludes data with anomalous ASI values.

This error in M applies only to our calculations for the Bishop Tuff. All other M values (those used in the collated dataset) are those reported in the studies from which they were sourced, or where not reported were calculated on an anhydrous basis. We note that the definitions of M in Watson and Harrison (1983) and Boehnke et al. (2013) may lead to confusion in its calculation i.e., “M is the cation ratio of (Na + K + 2Ca)/(Al . Si)” – Watson and Harrison (1983) and “M is calculated by obtaining the molar amounts of each component, renormalising, and then obtaining the ratio” – Boehnke et al. (2013). A calculation of the mole fraction should include all the melt components. In Watson and Harrison (1983) and Boehnke et al. (2013) this was SiO2, TiO2, Al2O3, MgO, FeO, CaO, Na2O and K2O wt %. MnO and P2O5 are common components that are routinely determined and should also be included in the mole fraction calculations. Of course, if the concentration of a component is low, then ignoring it will have little effect. Calculating M on an anhydrous basis may be advantageous because H2O contents are not routinely determined.

In reviewing M we have identified several studies in our collated dataset that included Zr and F in the calculation of mole fractions (Shao et al. 2019, 2020). We suggest that these components should be excluded, particularly Zr as this is the element of interest, and so we re-calculated the M values for these experimental data using the “M_calculator” detailed below. The re-calculated M values are ~ 0.3 higher.

We have included a spreadsheet (M_calculator) for calculating M with the components that we suggest should be included in the mole fraction calculation (SiO2, TiO2, Al2O3, MgO, MnO, FeOT, CaO, Na2O, K2O, P2O5). To ensure consistency in the calculation of M between studies, M was re-calculated using the “M_calculator”. This resulted in a change in 75 out of 626 (24 due to Zr, 8 due to F, 43 source of error undetermined) M values by between 0.04 and 0.80 with an average of 0.33. For these data, the average difference in zircon saturation temperature from that calculated using M including H2O was 59, 106 and 84 oC using the Watson and Harrison (1983), Boehnke et al. (2013) and Shao et al. (2020) models. The differences between the actual and predicted temperatures (Tres; actual – predicted) for the corrected and original M for the full dataset (626 data) using the three models are negligible, and the results of statistical comparisons are unchanged. Therefore, the discrepancies between literature M values and those calculated here due to the components included in the mole fraction calculation do not lead to any changes in the conclusions that we made in the paper, and have no effect on the zircon saturation model that we present. All M values are provided in a revised version of Supplementary Table 3. All other melt parameters (G, B, NBO/T, ?) are unchanged.

While predicted temperatures for the example of the Bishop Tuff using the Crisp and Berry (2022) model are now in closer agreement to those predicted using Watson and Harrison (1983), our statistical comparison of the zircon saturation models demonstrates that a melt parameter that includes all melt components, and discriminates between different non-bridging oxygen components (such as CaO, MgO, and the alkalis), provides more accurate estimates of zircon saturation.

We thank Blake Wallrich and Calvin Miller for bringing to our attention the discrepancy between our estimates of temperature using the Watson and Harrison (1983) model for the Bishop Tuff and those determined when evaluating M on an anhydrous basis, and for constructive discussions of the calculation of M and Bishop Tuff compositions.