A total of 45 aliquots (4,500 grains) from five samples were measured by the SAR procedure, and we rejected grains with poor DRCs based on criteria 1)‒5) before building rSGCs (Li et al., 2016; Fu et al., 2020). Within SGC determination, 1) we fitted the measured L_x/T_x data for individual grains using a general-order kinetic (GOK) function, i.e., ( x ) = a [ 1 − ( 1 + b c x ) ( − 1 c ) ] + d , where x represents the radiation dose and a, b, c, and d are constants (Guralnik et al., 2015; Li et al., 2016). We chose this function here because it has proved to be flexible and robust for fitting DRCs with different shapes (see Peng and Li, 2017),and then, the ‘signal growth ratio’ (SGR), defined as the ratio between the L_x/T_x values at 200 and 50 Gy based on the best-fit DRCs for individual grains, is calculated. 2) The SGRs of all investigated grains were divided into k groups using the finite mixture model (FMM) (Roberts et al., 2000), with a zero overdispersion value (σ _b = 0) for each group (i.e., assuming that the sources of error associated with the signal intensity have been adequately taken into account, see details in Hu et al., 2019). To determine the optimal number of rSGC groups, k was increased from 2 to 10. The optimal number of groups was then estimated as the one associated with the lowest Bayesian information criterion (BIC). 3) The LS-normalization procedure was applied separately to each group to determine their group-specific SGCs.

The SGRs for all the investigated grains are shown in Figure 1A. A large range of SGRs from ∼1 to ∼3 was observed, indicating that grains have a wide range of saturation doses. For example, the grains with SGRs close to 1.08 (marked by black circle in Figure 1A) correspond to early saturated grains (i.e., there was a negligible increase in the OSL signal beyond 50 Gy). In contrast, grains with L_x/T_x ratios close to 2.85 (marked by yellow triangle in Figure 1A) have a large saturation dose level (keep growing even after 400 Gy). Figure 1C displays the LS-normalized L_x/T_x ratios and common SGCs for all eight groups as a function of the dose. To test the validity of the groupings and establishment of the SGCs, we calculated the ratio between the individual LS-normalized L_x/T_x values and their expected values (based on the best-fit curve) for all the regenerative doses greater than zero. The ratios are plotted in radial plots in Supplementary Figure S2. Around 89–95% of the measured-to-SGC ratios for each group are consistent with unity at 2σ. We propose, therefore, that the DRCs of the Lake Woods quartz grains mentioned here can be represented by eight common SGCs; the best-fit GOK parameters for each SGC are summarized in Supplementary Table S3. Comparing with cSGC (k =6, Supplementary Table S3), our rSGCs have more group numbers and thus have different GOK parameters. When building cSGCs, Fu et al., (2020) assumed all groups have the same σ _b value (0.06). As a 6% overdispersion accounts for the between-grain differences in the DRCs, it may lead to a smaller group number for cSGCs. For a better comparison with the cSGCs, we repeated the building of the rSGC steps but with a fixed σ _b value (σ _b = 0.06), and the calculated optimal k is 5 (Figures 1D–F). As samples for rSGCs were from the same region (i.e., Lake Woods), the fewer groups (with σ _b value of 0.06) than cSGC may contribute to relatively similar OSL properties (e.g., inherent brightness or the shape of the OSL decay curve) of the individual quartz grains. About 90–93% of the measured-to-SGC ratios for each group from five group SGCs (σ _b = 0.06) are consistent with unity at 2σ (Supplementary Figure S3). The validation of these two sets of rSGCs is tested in Section 3.2.

To validate D_e estimates generated by rSGCs, a practical test must demonstrate that the rSGC method can adequately generate the same results as a full SAR protocol. During building of the rSGCs, each grain was assigned to one of the eight groups (σ _b = 0) or to one of the five groups (σ _b = 0.06) (step 2), and the natural signal has been normalized when applying the LS-normalization procedure to each group to determine their group-specific SGCs (step 3). Thus, the normalized natural signal can directly project onto the corresponding SGC to estimate the D_e value for that grain. The obtained SGC D_e values for all non-rejected grains are compared to the SAR D_e values obtained from individual DRCs (Figure 2A and Supplementary Figure S4A). For the SGCs, D_e values were obtained by eight group SGCs (σ _b = 0), and the two sets of D_e values are in good agreement, with 96.4% of the ratios (rSGC D_e/SAR D_e) consistent with unity at 2σ (Figure 2B). Similarly, the ratios are with 94.4% consistency with unity at 2σ for rSGC D_e values obtained by five group SGCs (σ _b = 0.06) (Supplementary Figure S4B).

It should be noted that the comparisons between the SAR and rSGC D_e values shown in Figure 2A and Supplementary Figure S4A are only available for those grains that produce reliable results using both approaches. As shapes for DRCs and for rSGCs are different, the number of grains that pass criteria 6)–8) is also different (Supplementary Table S4). To further test the reliability of the rSGCs, we compared the D_e distributions of three representative Lake Woods samples (Pit5_1.5, Pit5_2.6, and Pit6_1.13) in Figure 3 and Supplementary Figure S5. For a well-bleached beach sample (Pit6_1.13), the SAR and rSGC D_e (σ _b = 0) distributions have overdispersion values of 20.0 ± 4.8 and 29.8 ± 2.9%, respectively, with most individual D_e values spread randomly about a weighted mean D_e of ∼0.98 Gy (Figure 3A). As the CAM D_es are consistent at 2σ (Table 1), we suggest that this increased spread for rSGC D_es does not affect the weighted mean D_e to a significant extent, and similar observations were previously stated by Fu et al. (2020). For lacustrine samples (Pit5_1.5 and Pit5_2.6), both of them showed broad and continuous distribution of D_e values (Figures 3B,C); the corresponding OD values are 94.9 and 106.0% for SAR D_es and 93.3 and 113.1% for rSGC D_es (σ _b = 0). The large spread in D_e may be due to heterogeneous bleaching prior to deposition and/or reworking by bioturbation. In addition to CAM D_e, the Minimum Age Model (MAM) was also applied to these samples to partly identify well-bleached grains. Except the CAM D_e value for Pit5_2.6, the weighted mean D_e values by different measurement methods (i.e., SAR and rSGC) for these samples are consistent at 2σ (Table 1). Sample Pit5_2.6 includes grains with large D_e values, and around 124 grains (account for 20% of accepted grains) were rejected for criteria 6) and 7) (Supplementary Table S4), which lead to truncation of the full D_e distribution. As the shape for DRCs is different from that of rSGCs, few grains (i.e., 66 grains, account for 10% of accepted grains) were rejected because of extrapolation or saturation. With reduced impact by truncation, the obtained CAM D_e increased from 17.2 ± 0.7 Gy (by SAR data) to 19.0 ± 0.8 Gy (by rSGC data) (Table 1). Regardless of the saturated grains, the general consistency between SAR and rSGC D_es (σ _b = 0) supports that rSGCs perform well for Lake Woods samples. In addition, the OD and the D_e estimates by the CAM and MAM obtained by eight group SGCs are in agreement with those for D_es obtained by five group SGCs (Table 1), and we suggest both rSGC sets are reliable for D_e estimation in Lake Woods.

In an ideal situation (i.e., the cSGC is reliable for samples from Lake Woods), only three SAR cycles are necessary for cSGC D_e estimation, which involves one cycle for the natural signal and two for regenerative doses, and rejection criteria 1), 4), 6), 7), and 8) can be applied to them. Thus, for each grain, we selected the natural signal, the signal for the second lowest regenerative dose (the lowest being 0 Gy), which lies in the linear portion of the DRC, and the signal for the largest or second largest regenerative dose (which lies beyond the linear region) for cSGC D_e calculation. Using this approach, more grains are accepted than that for SAR or rSGC analysis (Supplementary Table S4). The two selected regenerative doses were referred as D_r1 and D_r2, respectively. The ratio between the L_x/T_x values of D_r1 and D_r2 for each accepted grain is calculated, and the obtained ratio is compared with the corresponding ratio for each of the six cSGCs; the latter ratios were calculated by dividing the SGC values at D_r2 by those at D_r1. As the L_x/T_x ratio can quantify the saturation characteristics (e.g., shape of DRC or SGC) of different grains or different group SGCs (Li et al., 2016), this comparison can help us select the specific SGC with similar saturation characteristics to the studied grain. Based on this step, each grain was assigned to one of the six groups from Fu et al., (2020). To normalize the natural signal, the L_r1/T_r1 and L_r2/T_r2 for each grain are multiplied by a scaling factor, such that the sum of squared residuals is minimized. With the scaling factor, the normalized L_n/T_n value can be projected onto the relevant cSGCs to get cSGC D_e, and the obtained cSGC D_e show excellent statistical consistency with the SAR D_e (Figure 2C) and with the rSGC D_e estimates (Supplementary Figure S6A). Around 92.5% of the cSGC-to-SAR D_e ratios (Figure 2D) and 93.9% of the cSGC-to-rSGC D_e ratios (Supplementary Figure S6B) are within 2σ, which validate the use of cSGCs for rapid and robust D_e estimation for quartz grains from Lake Woods.

D_e distributions for the three representative samples (discussed in Section 3.2) are visualized using probability density plots in Figure 4, and the patterns of D_e distributions are generally consistent between the cSGC and rSGC datasets. The OD and the D_e estimates by the CAM and MAM for D_es obtained by cSGC are in agreement with those for D_es obtained by rSGC (Table 1), which further prove the reliability of cSGCs.