The NAVC consists of annually laminated sediments that were deposited in several lakes adjacent to the margin of the retreating Laurentide Ice Sheet (LIS) in New York and New England between approximately 18 200 and 12 500 years ago (Figs. , ). These sediments occur in numerous stratigraphic sections throughout the region that were originally correlated and assembled into several floating varve chronologies by . These have subsequently been consolidated, corrected in a few places, and extended into a single 5659-year sequence by . In this section we briefly summarize the stratigraphy and sedimentology of NAVC sediments as they are relevant to this study; a complete review can be found in and .

The majority of the NAVC is composed of sediments deposited in proglacial lakes that occupied the north–south-trending Connecticut River Valley from central Connecticut to northern Vermont as the margin of the LIS receded northward. Although the extent of Connecticut Valley lakes varied with ice margin position, glacioisostatic rebound, and changes in outlet position and lake level, some portion of the lake system was continuously present and in contact with the ice margin until approximately 13 700 years ago, at which point changes in the sedimentological characteristics of the varves show that the lake was no longer receiving direct glacial meltwater. The complete chronology includes ∼ 4200 glacial varves overlain by ∼ 1500 paraglacial varves; the glacial–paraglacial transition is not isochronous across the entire lake system and is also gradational over ∼ 100–200 years at some sites.

Glacial varves in the NAVC are, in general, substantially thicker than paraglacial varves and are derived predominantly from direct glacial meltwater and sediment production, although paraglacial sources including surface runoff from the recently deglaciated landscape adjacent to the lake may contribute. At any one location in the lake, the contribution of paraglacial sediment to glacial varves increases upsection as the distance to the receding ice margin increases. Glacial varves, especially in areas proximal to the glacier, have melt season (summer) layers composed of a stack of micrograded beds that often fine upwards. Summer layers grade into a non-melt season (winter) layer composed of nearly pure clay, 60 % or more of which is typically less than 1 µm in size. Glacial varve sections also occasionally have extremely thick varve couplets (over 50 cm) with single thick graded beds produced by the sudden release of water from proglacial lakes impounded in tributary valleys (see, for example, ). Paraglacial varves are thinner, typically millimeter scale, and composed predominantly of glacial till, outwash, and other ice-marginal sediments that were deposited on the surrounding landscape and subsequently eroded and transported to the lake by surface runoff after deglaciation.

Paraglacial varves in the NAVC are considered to be varves formed with zero or negligible direct glacial input, although the transition between glacial and paraglacial varves is typically gradational. They are composed of silty and fine sandy summer layers, and may have occasional graded fine sand beds much thicker than a typical summer layer that represent unusual runoff or flood events that washed sandy sediment onto the lake floor. Winter layers in paraglacial varves have diffuse contacts with summer layers below and sometimes show single, internal silt to fine sand laminations that may represent fall overturning.

Although the NAVC is continuous for its entire length, the lakes in which varves were deposited drained ∼ 12 000 yr BP, so the varve chronology does not have an absolute connection to the calendar year timescale. The majority of the NAVC that lies near or below the glacial–paraglacial transition is replicated in multiple sections (Fig. ) and is therefore believed to have zero or negligible counting uncertainty; a number of spurious or missing varves at individual sections have been identified and removed from the chronology . The uppermost part of the NAVC consists of thin paraglacial varves that only occur at one section (Newbury; see Figs. , ), and estimated that counting uncertainty in the unreplicated part of the Newbury section above ∼ NAVC 7500 is (+35/-20) years at the top of the section. However, this counting uncertainty is not relevant for the present paper because we will not consider any ice core–NAVC correlations for varves above the glacial–paraglacial boundary. Therefore, if we assume that the NAVC is linear with respect to true calendar years, the calibration of the NAVC to the true calendar year timescale can be represented by a single value for the offset between NAVC years and calendar years. The offset throughout this paper is defined as the age in years BP of NAVC year zero, wherein “years BP” means “years before 1950”, as typically defined for purposes of radiocarbon age calibration. NAVC years are positive and increasing towards the present, and calendar years BP are positive and decreasing towards the present, so the offset is equal to the sum of the NAVC year of any varve and the calendar year BP in which that varve was deposited. Although previous publications (e.g., ) variously report estimates for (NAVC–calendar years BP) and (NAVC–calendar years before 2000) offsets, in this paper we use only the NAVC–calendar year BP offset to minimize confusion. Later in this paper, we will also correlate the NAVC with ice core records on the GICC05 timescale . Again, throughout this paper we apply the GICC05 timescale in years BP rather than years before 2000 as is sometimes used elsewhere. As the GICC05 timescale is not exactly linear with the true calendar year timescale because of imprecision in ice core layer counting and references therein, NAVC–cal yr BP and NAVC–GICC05 yr BP offsets may not be exactly the same, and we will use both of these terms as appropriate throughout this paper.

The value of the NAVC–cal yr BP offset has been determined by fitting radiocarbon ages of plant macrofossils associated with individual varves to the INTCAL09 (in ) and subsequently INTCAL13 (in ) calibrated radiocarbon timescales. , using the INTCAL13 calibration, obtained a best estimate for the NAVC–cal yr BP offset of 20 820 years. The uncertainty in this estimate is not well quantified because residuals between the measured 14C ages and those predicted by the best-fitting offset to INTCAL13 scatter significantly more than expected from measurement uncertainty and are not normally distributed (see discussion in , and also in Sect. ). estimated the uncertainty in the calibrated value of the offset to be on the order of ∼ 200 years and also interpreted the distribution of the residuals to indicate that the most likely source of excess scatter was small amounts of sample contamination by postdepositional carbon. If true, this would imply that the true value of the offset is ∼ 100–200 years higher than the 20 820-year estimate.

Both and proposed that the estimate of the NAVC–cal yr BP offset could be further refined by aligning prominent climate variations evident in Greenland ice core records with changes in varve thickness and/or ice margin position recorded in the NAVC. For sections of the NAVC near 14 000 yr BP, this alignment yielded a NAVC–GICC05 offset of 20 820 years, which is the same as the best-fitting offset inferred from matching 14C data to INTCAL13. This result implies a zero offset between INTCAL13 calendar years and GICC05 years at 14 000 yr BP, which is within the range of existing estimates . For sections of the NAVC between 16 000 and 18 000 BP, their alignment of NAVC and ice core climate proxies yielded a NAVC–GICC05 offset of 20 750 years, which may be consistent with the observation that GICC05 likely undercounts ice layers in the 13 000–20 000 yr BP interval . However, as noted above, radiocarbon calibration of the NAVC still suggests that the NAVC–INTCAL13 offset may be ∼ 100–200 years larger than 20 820 years. In addition, it is important to note that matching variations in NAVC and ice core climate proxy records relies on the assumption that the responses of δ18O variations in Greenland ice cores and varve thickness records in New England to climate changes have similar lag and relative amplitude, which has not been independently established. Also, matches based on these correlations were derived by looking for possible correlations that were close to the NAVC–calendar year offset already estimated from the 14C data. Both ice core and varve records show periodic variability, so multiple matches could be possible in some time ranges.

Beryllium-10 fluxes to the Earth's surface in polar regions reconstructed from 10Be concentrations in ice cores have been widely used as a proxy for solar variability on interannual to centennial timescales (e.g., ), and 10Be fluxes to marine sediments have been used to infer paleomagnetic field strength changes on timescales from thousands to millions of years (e.g., , and references therein). By comparison, relatively few studies have attempted to identify solar variability on decadal to centennial timescales using 10Be measurements from lacustrine sediments. found that 10Be fluxes recorded in lacustrine sediments deposited between 900 and 1450 CE were similar to those recorded in Greenland ice cores for the same time period. More relevant to this study, and measured 10Be concentrations in annually laminated modern and late-glacial sediments, respectively, from European sites and concluded that variability in 10Be fluxes to the lake was attributable to both direct variations in fallout to the lake due to solar variability and variability in environmental factors affecting transport and scavenging of fallout 10Be in the lake. These authors suggested several approaches to accounting for these factors in reconstructing the 10Be fallout flux, mainly focused on multiproxy analysis of lake sediment and the use of multivariate correlation analysis to isolate variability in the 10Be flux that could not be explained by measured environmental proxies. In this work, we attempt to simplify approaches used in those studies by measuring both 9Be and 10Be in lake sediments and applying the following interpretive framework.

Our basic approach is to (i) use 9Be concentrations in sediment as a measure of both the delivery of background Be to the lake and any environmental factors affecting Be scavenging efficiency in the lake and then (ii) identify additional variation in the 10Be flux that cannot be accounted for by these effects and must therefore represent variability in the atmospheric fallout flux. We quantify this with a simple model for Be fluxes to glacial lake sediments. Because we are working with annually laminated sediments, we can directly measure Be fluxes to the sediment (throughout this paper represented in units of atomscm-2yr-1) as the product of the Be concentration in sediment (atomsg-1) and the mass accumulation rate (gcm-2yr-1) computed from annual layer thickness (cmyr-1) and density (gcm-3).

We assume that measured Be fluxes to lake sediments derive from one source of 9Be and two sources of 10Be. First, sediment delivered to the lake either from glacial discharge or landscape runoff contains “inherited” 9Be and 10Be. Inherited 9Be includes adsorbed 9Be resulting from subglacial and subaerial mineral weathering. Inherited 10Be could arise from a number of processes, presumably mainly including subglacial recycling of sediment with adsorbed 10Be from a past history of surface exposure and interaction between subglacial sediment and fallout 10Be already present in ice sheet ice. We refer to all Be arising from these sources collectively as “inherited” Be.

Because Be is insoluble and effectively adsorbed to sediment at neutral pH, we expect that sediment delivered to the lake by glacial meltwater discharge will include inherited 9Be and 10Be with a characteristic 10Be/9Be ratio. The factors controlling the 10Be/9Be ratio of glacial sediment are presumably complex and include the Be concentration of sediment source material, water–rock interactions in the subglacial environment, the concentration of 10Be in ice, and the rate and extent of basal and surface melting. However, we assume that whatever these processes, subglacial sediment mixing is effective across a significant area of the ice sheet and results in a characteristic 10Be/9Be ratio in subglacially discharged sediment that can be assumed to be constant, or at least slowly varying, over the 100- to 1000-year timescales represented by our sample sets.

Second, once glacial sediment with a characteristic 10Be/9Be ratio is delivered to a proglacial lake, additional 10Be can be supplied to the lake from atmospheric fallout and adsorbed to the sediment during transport or deposition, but 9Be cannot. Thus, Be in lake sediment includes inherited 9Be, inherited 10Be, and fallout 10Be.

With these assumptions, Be concentrations in lacustrine sediment (which we can measure) can be related to the flux of atmospheric fallout 10Be (which we seek to reconstruct) by 1Q10,T=Q9,TRS+Q10,Af, where Q10,T is the total 10Be flux (atomscm-2yr-1) to the sediment, which is the product of the measured 10Be concentration (atomsg-1) and the mass accumulation rate (gcm-2yr-1); Q9,T is the corresponding total 9Be flux (atomscm-2yr-1; calculated in the same way as Q10,T); Q10,A is the flux of atmospheric fallout 10Be to the surface (atomscm-2yr-1); RS (nondimensional) is the characteristic 10Be/9Be ratio of sediment supplied to the lake; and f (nondimensional) is a focusing factor. The two terms on the right-hand side of the equation represent the two possible sources of 10Be described above: inherited 10Be (Q9,TRS) and fallout 10Be (Q10,Af).

The focusing factor f reflects the fact that 10Be deposition occurs throughout the lake and perhaps an adjoining watershed on the ice sheet and/or the surrounding ice-free landscape, whereas sediment deposition only occurs in a fraction of the lake basin. Thus, in area-normalized units (atomscm-2yr-1), the deposition rate of fallout 10Be to lake sediment (Q10,Af) is greater than the fallout rate from the atmosphere (Q10,A) to the watershed. The focusing factor depends on the geometry of the lake and its watershed; for example, estimated f≃20 for a small lake, estimated f≃15 for the much larger Lake Lisan, and the results of implied f≃3 for the still larger Lake Baikal. Absent significant changes in the geometry of the lake and watershed, however, f is expected to be constant or changing slowly, so because we are interested in the short-term variability of the atmospheric fallout flux rather than its absolute value, it is sufficient for our purposes to estimate the quantity Q10,Af. Therefore, given the framework of Eq. () and measured total 9Be and 10Be fluxes to the sediment, the primary obstacle to reconstructing atmospheric fallout fluxes of 10Be is the need for an estimate of RS, which we discuss in detail later from the perspective of analyzing each of our data sets.

The purpose of the model described by Eq.  is to separate environmental effects influencing the delivery of Be to the lake from variations in 10Be fallout to the lake and watershed. If the assumptions of the model and the estimate of RS used in applying it are correct, variations in Q10,Af reconstructed by this method should correctly represent variations in fallout and not in Be transport processes. However, the model is very simple and several complications may be relevant for our data. One is that RS and f will likely change over time due to (i) retreat of the ice margin that results in an increase in the proportion of sediment supplied by the deglaciated portion of the watershed, (ii) changes in ice-marginal drainage, and eventually (iii) reduction in glacial meltwater and sediment supply in the transition from a glacial to a paraglacial lake. As noted above, however, it is likely that these changes will either be steady, gradual changes associated with ice margin retreat from the lake basin or large instantaneous changes associated with lake inlet or outlet switching or reconfiguration of ice-marginal drainage. It appears unlikely that these processes would be manifested as periodic decadal- to centennial-scale variations that might mimic the solar variability we seek to identify. A second complication is the possible role of watershed processes; if fallout 10Be were sourced from a significant ice-free watershed surrounding the lake, variations in 10Be fallout rates might be buffered by water–soil interactions in the watershed and reduce observed fallout variability in the lake (e.g., ). Finally, the potential importance of 10Be already present in ice sheet ice that could be released by surface melt is unknown. The expected contribution from typical 10Be concentrations in ice sheets (order 104 atomsg-1) at moderate melt rates averaged over the ablation zone (order 10 cmyr-1) would be small (order 105 atomscm-2yr-1) compared to the atmospheric fallout flux (order ∼ 1.5×106 atomscm-2yr-1; see ). On the other hand, if melt rates averaged over the contributing ablation area reached meters per year, which could be possible during periods of rapid retreat, this contribution might be significant.

We collected several sample sets from a total of seven varve sections, with various sampling strategies designed to address different aspects of the study (Table  and discussion below). Samples were extracted from (i) short cores collected from surface outcrops by cleaning outcrops and driving in short (typically 0.6 m) sections of PVC pipe with a steel cap and sledge hammer as well as from (ii) deep (up to 50 m), continuously sampled hollow-stem auger cores collected in 2007–2009. Cores are archived at Tufts University. All cores were split after collection and partially dried to improve visual identification of layers and facilitate sampling of individual varves. Only cores with minimal coring deformation were sampled. We sampled winter and summer layers of single varves, complete single varves, and continuous sets of contiguous varves by scraping core surfaces and cutting interior sections of the cores to remove any possible surface contamination, then separating varves along partings between layers and scraping top and bottom surfaces to isolate the varve(s) of interest. Each sample was a column or wedge cut such that the cross-sectional area was constant for all varves incorporated in the sample. As in previous work relating to the NAVC , we consider a single varve to extend from the bottom of the coarse-grained summer layer to the top of the fine-grained winter layer.

We measured grain size distributions for all samples using a combination of mechanical sieving (for grain sizes larger than 4 Φ) and pipette analysis for smaller grain sizes (e.g., ). Throughout this paper we represent grain size using the logarithmic phi scale of , which is commonly used in sedimentology: Φ is the negative base-2 logarithm of the grain diameter in millimeters, so larger values of Φ represent smaller grain sizes. We halted the pipette analysis at 11 Φ (∼ 0.5 µm), but significant fractions (up to 60 %) of all samples were finer than this (Fig. ). Thus, to calculate mean grain size and sorting parameters (see, e.g., ) that require the complete distribution, we fit a lognormal distribution to the observed data for each sample and used the fitted lognormal distribution to compute mean grain size and sorting (Fig. ).

Measurements of sediment density are required to interpret a Be concentration by weight (atomsg-1) as a Be flux to the sediment (atomscm-2yr-1). We measured the dry density of representative samples of glacial varves at the Kelsey–Ferguson (KF) site, paraglacial varves from the North Haverhill (NHV) site, and separate summer and winter layers from North Hatfield (NHT) by pressing a cylinder of known volume into wet sediment and drying and weighing the resulting sample (Fig. ; Table S2 in the Supplement). This procedure has several potential sources of inaccuracy, primarily due to the stiff and friable nature of the sediment, which causes difficulty in completely filling the standard volume without deforming or compressing the sediment or introducing voids. It is important to note that the purpose of this study is to identify variations in Be flux to the sediment, not to make an accurate estimate of the absolute flux, so from this perspective inaccuracies in density measurements are not necessarily significant. On the other hand, if we assumed a constant density when, in fact, periodic variations in density were present, we could infer spurious Be flux variations. Density variations, in turn, are most likely to be the result of variations in grain size and therefore in porosity and the relative proportion of silt and clay, and our measurements show this effect (Fig. ). Thus, for subsequent Be flux calculations we compute the density of all samples from mean grain size measurements using the linear relationship shown in Fig. , with an uncertainty derived from the standard deviation of the residuals (±0.05 gcm-3).

We measured concentrations of adsorbed 9Be using the procedure described in , which involves drying and powdering sediment samples, leaching in 6M HCl for 24 h, then diluting to a suitable concentration for analysis and measuring the Be concentration with a JY Horiba Optima inductively coupled plasma optical emission spectrometer (ICP-OES). discusses step-leaching experiments and other data used for quality control by assessing the reliability of the procedure. This procedure extracts only adsorbed Be and not structural Be contained in Be-bearing minerals (e.g., beryl). Although the nominal internal precision of the ICP-OES measurement inferred from replicate analysis of liquid standards was typically 1 %–2 %, replicate analyses of splits of the powdered sediment samples showed a total uncertainty of 3.5 %. Thus, we assume that all 9Be measurements have 3.5 % uncertainty.

We measured 10Be concentrations in sediment samples at the University of Vermont (UVM) using an adaptation of the potassium bifluoride fusion method of . We dried sediment samples, homogenized them by powdering in a Spex shatterbox mill, and subsampled 0.5 g of the homogenized sediment. We mixed the sample with KHF2 and Na2SO4 and spiked the mixture with 0.4 mg of one of several Be carriers prepared from deep-mined beryl and having 10Be/9Be in the range 2–8×10-16. We then extracted Be by fusion of the sample, leaching of the fused sample in water, precipitation of excess K as KClO4, and precipitation of Be hydroxide. We modified the published method by adding an ion exchange step in which we redissolved Be hydroxide in dilute HCl, loaded it onto cation exchange resin (Bio-Rad AG50W X8), eluted B and other cations in dilute HCl, recovered Be in 6M HCl, evaporated to dryness, redissolved in dilute HCl, and precipitated Be hydroxide. Finally, we converted Be hydroxide to BeO for Be isotope ratio measurement by accelerator mass spectrometry (AMS) at the Scottish Universities Environmental Research Centre (SUERC) in East Kilbride, Scotland . For these analyses, we sputtered samples and isotope ratio standards in the ion source for the same amount of time in order to suppress any effect of variations in emittance during sputtering. All 10Be measurements are normalized to the NIST SRM4325 standard material with an assumed 10Be/9Be ratio of 2.79×10-11, which is equivalent to the 07KNSTD standardization of . We processed samples in batches of 16, each containing one process blank and at least one replicate of a sample that was also analyzed in a different batch (see below). The process blank for Be fusion extraction at UVM utilizes a sample of fine-grained fluvial sediment chosen because of its naturally low bulk 10Be concentration and subsequently powdered, homogenized, and etched in dilute HNO3 in a heated sonic bath for an extended period to remove adsorbed Be. We processed 0.5 g aliquots of this material in the same way as the samples. Complete carrier and process blanks contained between 120 000 and 310 000 atoms 10Be, representing 0.1 %–0.7 % of total atoms measured in samples.

In contrast to the leaching procedure used to measure 9Be concentrations, the total fusion method extracts both adsorbed 10Be and mineral-bound 10Be that could result from in situ production of cosmogenic 10Be in any fraction of the sediment that previously experienced surface exposure. However, concentrations of in-situ-produced cosmogenic 10Be are expected to be negligible for the purposes of this study because in situ cosmogenic production rates at moderate elevations (order 10 atomsg-1yr-1) are insignificant compared to deposition rates of atmospherically produced 10Be (order 106 atomscm-2yr-1) and because NAVC sediments are mostly subglacially derived and therefore not previously exposed to the surface cosmic-ray flux. In-situ-produced cosmogenic 10Be concentrations in glacial sediments associated with the Laurentide Ice Sheet, where measured (e.g., ), are on the order of 10 000 atomsg-1, which is negligible compared to total 10Be concentrations of order 108 atomsg-1 measured in this study. We therefore assume that the technical inconsistency between our measurements of leachable 9Be and total 10Be is insignificant and disregard it.

To quantify total measurement uncertainty and as a general quality control measure, we prepared large quantities of two representative samples to be analyzed repeatedly throughout the project. The first of these consisted of varves NAVC 3569-3570 from the Kelsey–Ferguson site, collected as part of the 80-year biennial record described above, which we refer to here by the internal UVM sample name BD3. When the BD3 sample was exhausted after 15 measurements, we prepared a second sample for replicate analysis (BD-STAN) by mixing and homogenizing aliquots of several other glaciolacustrine sediment samples from this study. The BD-STAN sample was subsequently analyzed six times.

The purpose of chemical purification of Be for AMS analysis is to produce a sample of BeO that is sufficiently pure to produce a Be ion beam of the same intensity as produced by pure reagent BeO used as an isotope ratio standard. Poor or inconsistent Be yield from chemical purification, or failure to consistently remove contaminants from the BeO target, can result in Be ion beam currents that are low and/or inconsistent compared to those from standards (see ). This is undesirable because (i) low beam currents reduce measurement precision by reducing 10Be count rates, and (ii) inconsistent beam currents can introduce systematic errors in isotope ratio measurements due to current-dependent variations in beam emittance, ion beam transport, or detector efficiency. Although the goal of AMS beamline and detector setup and adjustment is to remove or minimize any beam current dependence of ratio measurements, it is difficult to verify whether this has been achieved for an arbitrarily large range in beam current, so instrument tuning is not a complete substitute for consistent sample preparation.

AMS analysis of Be samples prepared in the first eight chemistry batches showed low and inconsistent beam currents (Fig. ; mean and standard deviation of sample beam currents relative to standards for these batches were 0.63 ± 0.25). We found that this effect was related to trace Cl remaining in samples after hydroxide precipitation, so we further modified the Be extraction procedure by redissolving Be hydroxide in dilute HNO3 and reprecipitating. Be beam currents from samples in 17 chemistry batches after this modification were higher and less variable (Fig. ; mean and standard deviation of relative sample beam currents after the modification were 0.87 ± 0.16).

Although this change to the sample preparation method significantly improved beam current performance, the complete data set displays high variability in Be currents. Thus, we used the results of replicate analyses, which spanned a range of Be currents, to look for and quantify any beam current dependence in the AMS results. In both replicate analyses and in analyses of groups of samples with similar 10Be concentrations, we observed a relationship between Be beam current and apparent 10Be concentrations derived from AMS-measured 10Be/9Be ratios (Fig. ). Although apparent concentrations do not display a significant correlation with beam current for samples with beam currents similar to standards (between ca. 80 % and 110 % of standard currents), our data include a much wider range of beam currents, and when all data are considered, significant correlations are present (Fig. ). We observed this effect to be persistent through many AMS measurement periods during a 3-year period and similar to the current dependence observed for many replicate measurements of in-situ-produced 10Be in the CRONUS-N quartz standard measured at the SUERC accelerator by as well as for analysis of the CoQtz-N quartz standard at an anonymous AMS facility described by their Fig. 3.

We conclude from these observations that apparent measured 10Be concentrations for our samples that had anomalously low or high AMS beam currents are inaccurate due to beam current dependence of the measured isotope ratios. Lacking a physical model for the observed beam current dependence, we devised the following procedure to correct for this bias. If (C/CS) is the beam current for a sample relative to the average current for standards measured simultaneously, RM is the apparent 10Be/9Be ratio observed for the sample, and RC is a nominally correct 10Be/9Be ratio that would be observed for (C/CS)=0.9, then we can define an empirical linear correction factor S such that RM/RC=1-S(0.9-C/CS). In the case in which blank corrections are small to negligible (as is the case for these data; see above) the ratio of apparent and corrected nuclide concentrations NM/NC, where NM and NC are nuclide concentrations in atomsg-1, is equal to RM/RC. Thus, to account for small variations in sample and 9Be carrier masses among replicate samples, we correct apparent concentrations instead of ratios using NM/NC=1-S(0.9-C/CS). 0.9 is chosen as the normalizing value because it is the modal value of (C/CS) for our complete data set, so it minimizes required corrections. Choosing a normalizing value not equal to 1 might introduce a small systematic bias in measured 10Be concentrations relative to the primary measurement standards, but that would not affect any of the results in this study because we are concerned with variability in the 10Be flux and not with a precise measurement of the absolute flux.

We estimate S by choosing the value that minimizes scatter among replicate analyses of the same sample. The sample with the largest number of replicates (BD3; see discussion above) yields S=0.164. The CRONUS-N data of yield S=0.185, which highlights the apparent consistency of this effect across multiple samples, chemical preparation methods, and AMS measurement periods. Figure  shows the effect of applying this correction procedure with S=0.174 (the average of the above two values) for the data in Fig. . Corrected data are uncorrelated with relative beam currents. Note that this correction scheme has the property that corrections for measurements with beam currents comparable to standards (C/CS between ca. 0.8 and 1.1, within which range no significant correlation between the current and ratio is observed) are minimal and comparable to individual measurement uncertainties; corrections only become significant for samples with extreme relative currents. Figure  further highlights this point for the 80-year biennial record from North Haverhill (NHV), which was entirely measured in duplicate. The correction procedure improves agreement between the two sets of measurements primarily by correcting a minority of data that were biased low due to anomalously low beam currents without having a significant effect on the majority of the measurements. For the remainder of this paper, we correct all 10Be concentrations for beam current bias using S=0.174. Although presumably this estimate of S has some uncertainty, a formal estimate of the uncertainty is not necessary because, as discussed below, we derive total measurement uncertainties for 10Be concentrations from the statistics of replicate analyses after correction for beam current bias rather than by propagation of errors through the correction process.

Nominal measurement uncertainties on corrected 10Be concentrations include: (i) AMS measurement uncertainties derived from machine stability and counting statistics (∼ 1 %) and replicate analyses of secondary isotope ratio standards during AMS measurement periods (∼ 1 %); (ii) uncertainty in 9Be carrier concentrations (<1 %); (iii) blank uncertainty (<0.2 %); and (iv) uncertainty in S as discussed above (unknown). Combined, these indicate measurement uncertainties no less than 1.5 %–2 % for most samples. Scatter in measured 10Be concentrations in replicate aliquots of homogenized sediment samples, however, is significantly higher, which indicates that propagation of known uncertainties would underestimate the true measurement uncertainty. Figure 8 shows the reproducibility of replicate analyses of a total of 84 samples. The mean relative standard deviation of all sets of replicate analyses is 4 %, that for BD3 is 3.5 % (for 15 measurements), and that for BD-STAN is 4.1 % (for 6 measurements). We conclude that the true uncertainty in a typical measurement from our sample set is near 4 %, which likely reflects the known measurement uncertainties enumerated above, errors introduced by the correction for current dependence, and imperfect homogenization of sediment samples during preparation. Thus, we compute total uncertainties for all 10Be concentration measurements as follows. First, we assume that each individual measurement has 4 % precision. Second, to incorporate the principle that repeated measurements of the same sample should improve total measurement precision, for samples analyzed more than once, we calculate a weighted mean and standard error (although, as all individual measurements are assigned 4 % uncertainty, they are weighted equally). Summary concentrations and uncertainties calculated via this approach appear in the Supplement and are used henceforth throughout the paper.

The purpose of sampling two 80-year varve sequences at 2-year resolution is to determine whether or not the 11-year Schwabe solar cycle is present in 10Be flux records. This cycle is evident in ice cores e.g., and some lake sediments e.g.,. Recognizing this cycle in the 10Be flux to NAVC sediments would be strong evidence that the NAVC does, in fact, contain a record of global variations in 10Be production and fallout.

We now describe results from sampling two ∼ 1000-year varve sequences at decadal resolution. The purpose of these sample sets is to determine whether or not the centennial-scale variability in 10Be fallout fluxes evident in ice core records can be identified in NAVC sediments and, if identified, matched to ice core 10Be records. During some of the time periods represented by these sequences, in particular near 14 000 years ago, ice core 10Be records show centennial-period variations in 10Be deposition with a relative magnitude exceeding 50 %, substantially greater than expected from the 11-year solar cycle. Thus, it is more likely that these longer-period, larger-amplitude variations could be distinguished from measurement noise in NAVC sediments.

We found that the majority of 10Be in glacial and paraglacial varves in the NAVC is inherited and already adsorbed to sediment when supplied to the lake. This means that variation in the total 10Be flux to the lake predominantly reflects variations in the supply of inherited 10Be, which are mostly the result of grain size variations, and not variations in fallout 10Be. By using 9Be as a normalizing isotope, we were able to identify variations in the 10Be flux that are not explained by variations in the inherited Be supply to the lake and which we therefore attribute to variations in atmospheric 10Be fallout. In most cases, this yielded reconstructed 10Be fallout fluxes that were weakly correlated or uncorrelated with total Be fluxes, which supports the argument that this procedure is effective at separating environmental processes from fallout variations. This is an important element of this study: if we had not measured 9Be concentrations, it might be difficult or impossible to separate variations in inherited and fallout 10Be fluxes. Having quantified the relationship between grain size and Be concentrations in this study, however, it might be possible in future studies of the NAVC to extract variability in 10Be fallout without 9Be measurements by instead identifying variations in the total 10Be flux not explained by grain size, which would be similar to the approach of multivariate correlation with various sedimentological proxies applied in other studies e.g., . Regardless, using 9Be as a normalizing isotope appears simpler.

Our initial strategy in this study was to test the hypothesis that 10Be fallout variations are recorded in NAVC sediments by trying to identify the characteristic 11-year solar variability period in 10Be fallout variations. This strategy was not successful because of the high ratio of inherited 10Be to fallout 10Be in NAVC sediments. Expected fallout variability of 15 %–20 % around the mean associated with the 11-year solar cycle translates into variability in the total 10Be flux that has a similar magnitude as the measurement uncertainty. Thus, we were not able to distinguish short-period solar forcing of 10Be fallout variations, if present, from measurement noise.

On the other hand, in 1000-year varve sequences sampled with biennial resolution at two sites, we did observe centennial-scale variability in the reconstructed 10Be fallout flux resembling 10Be fallout variations observed in ice cores. This leads us to believe that 10Be concentrations in NAVC sediments do, in fact, record at least some prominent high-amplitude variations in 10Be fallout that can potentially be used to correlate NAVC and ice core records.

An unexpected result of this study is that glacial varves are likely better suited to reconstructing 10Be fallout than paraglacial varves. Initially, we supposed that paraglacial varves would be more likely to yield a record of 10Be fallout simply because they are typically an order of magnitude thinner than glacial varves, so 10Be fallout would be less diluted by higher sedimentation rates and associated larger inherited Be fluxes. This supposition was incorrect, and we found that variability in 10Be fallout was evident in glacial varve sequences but nearly entirely suppressed in paraglacial varves.

This result is most likely explained by the different roles of the watersheds that contribute to glacial and paraglacial lakes. In a paraglacial environment in which the lake is not receiving direct glacial meltwater, the lake watershed predominantly consists of a deglaciated landscape mantled by fresh glacial sediment. A significant fraction of 10Be fallout to the watershed is therefore adsorbed to sediment in developing soils, which limits the delivery of fallout 10Be to the lake and buffers variations in fallout rates.

In contrast, the contributing watershed of a proglacial lake in direct contact with the ice margin most likely includes large areas of the ablation zone of the ice sheet. Fallout 10Be cannot be stored on the ice in the ablation zone, so each year's fallout must be flushed into the lake by supraglacial or englacial discharge during the summer melt season. We hypothesize that this phenomenon can result in substantial focusing of fallout 10Be in glacial lake sediment and a minimal lag time between fallout variations and recording of those variations in glaciolacustrine sediment records. If true, this implies that varved glacial lake sediments, if deposited in a lake with a large supraglacial watershed, may be very effective recorders of atmospheric 10Be fallout. This hypothesis could easily be tested in modern proglacial lakes with large contributing areas on the ice surface, perhaps in west Greenland.

We found values of the NAVC–GICC05 yr offset that resulted in acceptable correlations between reconstructed variations in 10Be fallout flux in NAVC sediments and an ice core 10Be flux stack for two varve sequences: a sequence at Newbury deposited near 14 000 yr BP and overlapping sequences at Kelsey–Ferguson (KF) and Glastonbury (GL) deposited ca. 16 000–17 000 yr BP. The NAVC–GICC05 yr BP offsets derived from these matches are not the same for both sections and also differ by 50–200 years from previously proposed values of the NAVC–calendar year offset inferred from radiocarbon dating of NAVC sediments and event matching between NAVC varve thickness records and Greenland ice core climate records.

Matching ice core 10Be records with 10Be fallout flux variations inferred from the older KF and GL varve sequences implies a NAVC–GICC05 yr BP offset in the range 20 965–21 165 years, with the best correlation at 21 110 years. However, the match between the two records mainly relies on aligning millennial-scale trends in the two records rather than distinct peaks associated with centennial-scale variations. As the KF–GL record is only 1000 years long, this could lead to spurious results. In addition, centennial-scale variations in the 10Be fallout flux in ice core records during this time period are relatively subtle. This match is not consistent with the NAVC–cal yr BP offset inferred from fitting NAVC 14C data to the INTCAL13 calibration curve, even when likely differences between the GICC05 ice core timescale and the true calendar year timescale are taken into account. Although offsets in the range implied by this match yield an acceptable correlation between ice core climate records and NAVC varve thickness records for events near NAVC 4800 and 16 000 GICC05 yr BP (Fig. ), they are not consistent with the expected relationship between NAVC and ice core climate proxy records for younger or older periods (Figs. , ). Overall, the apparent match between the KF–GL 10Be fallout flux and ice core 10Be does not appear consistent with most independent evidence and is unlikely to be valid.

Matching the 10Be fallout record from the glacial section at Newbury with ice core 10Be records, in contrast, relies on correlation of prominent large-magnitude, centennial-scale variations in both records and implies a NAVC–GICC05 offset in the range 20 900–20 940 (Fig. 22), with the best correlation at 20 925 years. This value of the offset is consistent with the 14C data set and, if the likely undercounting of ice core years in the GICC05 timescale between ∼ 13 000 and 17 000 yr BP is considered, also consistent with correlations between NAVC and Greenland ice core climate proxy records for periods surrounding the Hatfield event near NAVC 4800 and 16 000 GICC05 yr BP (Fig. ) and the Chicopee Readvance near NAVC 3400 and 17 400 GICC05 yr BP (Fig. ). This value of the offset yields an acceptable correlation between the stratigraphic boundaries of the Littleton–Bethlehem Readvance and the GI-1d stadial (Fig. ) but does not clearly align the associated period of decreased varve thicknesses, which is interpreted to reflect decreased meltwater production during a cold period, with stadial boundaries. Thus, the 20 925-year NAVC–GICC05 yr BP offset inferred from 10Be fallout matching at Newbury is consistent with the majority of independent evidence and may be valid, but a reassessment of the climate significance of varve thickness variations associated with the Littleton–Bethlehem Readvance would be required to resolve all conflicts with independent data.

The weakest part of our argument that the correlation between the 10Be fallout flux in NAVC sediments at Newbury and the ice core stack is valid is that the correlation is based on a short record comprising only 600 glacial varves that display two prominent peaks in reconstructed 10Be fallout flux. The ice core stack, on the other hand, includes three major fallout peaks between 14 000 and 15 000 GICC05 yr BP and a number of relatively high-amplitude secondary features. In addition, we only observed these 10Be fallout peaks at one section, so we cannot prove by replication between sections that they represent true fallout variations. Finally, the 25-year sampling resolution at Newbury is long relative to the size of the expected fallout peaks. For example, one of the most prominent apparent peaks is only represented by a single sample, and this effect alone could potentially explain much of the apparent ∼ 100-year difference between our proposed correlation based on the 10Be flux and that based on correlation of climate records in previous work. Another significant weakness derives from the property of our linear model for reconstructing the 10Be fallout flux that the apparent amplitude of reconstructed fallout variations displays a strong dependence on the value chosen for the inherited 10Be/9Be ratio RS, so the amplitude of reconstructed fallout variations cannot be used as a point of comparison with ice core records. These weaknesses could in part be addressed by (i) higher-resolution sampling at the Newbury section to better resolve apparent fallout peaks and (ii) replication of the 10Be fallout record from additional varve sequences that overlap with Newbury in the range NAVC 6000–7000. Several overlapping sections exist, including the Perry Hill Basin site shown in Fig. , that could be used for this purpose. Higher-resolution 10Be measurements from older parts of the NAVC might be helpful in resolving whether or not the NAVC–ice core 10Be match at KF–GL is or is not valid, but they are less likely to be successful because 10Be fallout variability in the ice core stack between 15 000 and 18 000 GICC05 yr BP has a lower amplitude than that in the 13 000–15 000 GICC05 yr BP range. Overall, collecting higher-resolution 10Be data on replicate sections of glacial varves from the portion of the NAVC between approximately NAVC 5800 and the glacial–paraglacial transition near NAVC 7000 is likely the best strategy for resolving the remaining ambiguous results of this study.