Continuous and complete vaporization is critical to reducing errors in all CRDS stable water isotope measurements, and it is especially important for attaining the per-meg precision necessary to detect meaningful variations in Δ17O. Previous studies have achieved continuous vaporization by heating sample water in the presence of dry air, either within an insulated stainless-steel tee (e.g., Gkinis et al., 2010, 2011) or within a concentric glass nebulizer with a vaporizing tube (e.g., Emanuelsson et al., 2015; Jones et al., 2017a). Gkinis et al. (2010, 2011) designed a flash vaporization process to instantaneously vaporize a continuous stream of sample water; the flash vaporization process involves a continuous stream of water that is combined with a continuous stream of dry air inside a 0.50 mm internal diameter stainless-steel tee that is maintained at near-ambient pressure. Steig et al. (2021) measured Δ17O by CFA–CRDS with the CFA configuration of Jones et al. (2017a): a continuous stream of water sample at 1030 kPa (150 psi) is aerosolized within a concentric glass nebulizer; the aerosolized sample droplets then evaporate completely within a 1.8 cm internal diameter, 20 cm long glass vaporizing tube that is heated to 200 ∘C. In this configuration, the CRDS analyzer draws vaporized sample from the vaporizing tube, and excess sample vapor is vented to the laboratory air (Jones et al., 2017a; Steig et al., 2021). Two critical differences between the Gkinis et al. (2010, 2011) and Jones et al. (2017a) methods are the volume of the vaporization chamber and the volume of vapor that is generated. The smaller volume of the flash vaporizer should limit signal smoothing between the vaporizer and the analyzer. However, the flash vaporization method described by Gkinis et al. (2010, 2011) generates vapor at approximately the rate that is required by the analyzer, whereas the nebulizer method of Jones et al. (2017a) produces an excess of vapor that is vented prior to reaching the analyzer. Producing excess vapor is another way to limit the signal smoothing upstream of the vapor vent because it increases the velocity of sample through the system.

For this study, we built a custom vaporizer unit that benefits from both the small volume of the flash vaporizer and also from the production of excess sample vapor; we also adopted additional monitoring techniques to ensure that there are stable flow conditions within the system during analysis. We use a 0.50 mm stainless-steel tee like Gkinis et al. (2010, 2011) but instead operate our vaporizer at a high mixing pressure (typically 200 kPa) ​​​​​​​to produce excess vapor. A small system volume combined with a high volumetric flow rate leads to a short retention time within the vaporizer that limits mixing of adjacent ice-core layers. An additional benefit of the small vaporizer volume is that flow inconsistencies (i.e., changes in sample flow rate caused by flow obstructions or bubble interruptions) that may occur within the vaporizer can be observed by the 1 Hz CRDS measurement values; patterns in water vapor concentration or instantaneous isotope readings provide information about vaporization conditions that is important for identifying and avoiding water isotope fractionation. We use CRDS observations of water concentration and uncalibrated water isotope values as well as electronic pressure sensors to infer vaporization conditions that may affect Δ17O. This information is used to tune the CFA–CRDS system prior to analysis, with the goal of reducing possible isotope fractionation that may cause errors in Δ17O; this process is described more fully in Sect. 3.1.

The CFA process from the ice-core melter to the vaporizer and vapor analyzer is described below and illustrated in Fig. 1. Glacial ice is melted on a 30 mm × 30 mm aluminum melt head that is fitted with four resistance heater cartridges and held at constant temperature by a PID controller (Bigler et al., 2011). Sample melt is drawn away from the melt head and through an automated selector valve (VICI, p/n C25Z-3186EMH) by a dedicated peristaltic pump, PUMP-1 (MasterFLex L/S 7535-04). The automated valve is configured to select a rotating sequence of calibration standards when ice cores are not being measured. Sample melt is carried by 0.5 mm internal diameter PFA conveyance tubing between all system components prior to the vaporizer; PFA tubing was chosen because its transparency is advantageous for identifying bubbles and investigating flow instability issues. From PUMP-1, water flows through a Darwin Microfluidics gas-permeable membrane bubble trap (44 µL internal volume, p/n LVF-3526) where bubbles are removed and vented into the laboratory air. Excess water pressure is relieved at a vent. Sample water is drawn away from the vent by PUMP-2 (same model as PUMP-1), whose flow rate is set to match the demand of the downstream vaporizer. The vent accommodates the difference between PUMP-1, which controls the melt rate, and PUMP-2, which controls the vaporization rate. Water flows through 2 and 1 µm in-line filters in series to restrict the flow of particulates into the vaporizer. PUMP-2 is also preceded and followed by electronic pressure sensors PI-1 (Elveflow PS3-Small) and PI-2 (Elveflow PS4-Small) to monitor injection pressure conditions and pump and filter performance. Typically, the pressurized dry air entering the vaporizer adds back pressure on the liquid sample injection line, which damps the cyclic pressure fluctuations of the peristaltic pump and stabilizes flow into the vaporizer. The system also includes a flow valve (FV-1) that can be used to adjust the back pressure on PUMP-2 before making a measurement.

At the vaporizer, filtered sample water is mixed and heated with dry air to produce a constant-humidity stream of vaporized sample. Immediately before entering the vaporizer, the liquid sample line is reduced to a 100 µm fused silica capillary tube. The 100 µm capillary provides sufficient flow restriction that is important for efficient vaporization while also performing well for periods of several days without clogging. The custom vaporizer includes a 0.50 mm internal diameter tee heated to 170 ∘C using a PID-controlled resistance heater cartridge, similar to Gkinis et al. (2010, 2011). The vaporizer combines pressurized dry air with liquid sample, and it is set within an aluminum enclosure that is lined with 3.175 cm of calcium silicate insulation. After the sample is vaporized, the vapor is drawn into the optical cavity where it is measured, and excess vapor is vented into the laboratory. Vapor is carried from the vaporizer to the optical cavity within insulated tubing to prevent condensation.

Design choices for the CFA system are intended to reduce and characterize the memory between measurements. Because our automated selector valve is positioned immediately after the ice-core melt head, reference waters pass through all components of the sample handling system except the melt head and its tubing; by design, the mixing length expected between measured ice-core layers with differing isotopic compositions can be approximated by the mixing length represented by transitions in reference waters if all other system conditions are identical. Mixing length within the system is reduced by increasing the flow velocity and therefore limiting the sample retention time in two ways: overall sample handling system volume and tubing diameters are minimized where possible, and excess sample volume is drawn through the entire system during ice-core analysis. Approximately 6 times more water is handled by PUMP-1 than is sent by PUMP-2 into the vaporizer; excess liquid volume is vented before PUMP-2. Similarly, approximately 30 times more vapor is generated than is analyzed; excess vapor is driven by the differential between PUMP-2 and the L2140-i inlet pump, and it is vented to laboratory air immediately before vapor enters the optical cavity. In this way, the liquid and vapor tubing is flushed with many times more sample volume than is required for analysis.

Because the vaporizer is sensitive to small fluctuations in sample flow rate, a careful balance of system pressures is required to control sample flow (Gkinis et al., 2010, 2011); specifically, the pressure of the sample at the vaporizer inlet must be slightly greater than the pressure of the dry air within the vaporizer. Maintaining a balance between the air pressure and sample pressure within the vaporizer requires knowledge of both pressure conditions. We monitor pressures at PI-1 and PI-2 so that it is possible to diagnose the source of system pressure changes when they occur; we also fix the pressure of the dry air line with the back pressure regulator (typically 200 kPa). Vacuum conditions at PI-1 indicate particulate loading across the filter screen at F-1; the filter screen will clog over time, and if the filter screen is not replaced, suction from the inlet of PUMP-1 can draw a vacuum at PI-1. Vacuum conditions at PI-1 can impact the downstream peristaltic pump (PUMP-2) performance, ultimately causing inconsistent flow into the vaporizer and analyzer. Under optimal analysis conditions, the pressure is near ambient at PI-1. A decrease in pressure at PI-2 indicates upstream vacuum conditions or worn peristaltic pump tubing at PUMP-2. An increase in pressure at PI-2 indicates clogging downstream, which can occur as particulate loading within F-2 or as mineral precipitation within the capillary or vaporizer. The pressure at PI-2 generally varied between 200 and 400 kPa, depending on the injection air pressure and the precipitate levels within the vaporizer or capillary tubing. High-pressure vaporizer conditions allow sample to flow despite the inevitable accumulation of precipitate within the vaporizer, which enables the system to operate in balance for days or even weeks. However, over time, precipitate accumulation within the vaporizer can restrict the flow of air, water, or both; this typically requires re-balancing of system flow conditions, but it can occasionally require removing and cleaning the vaporizer fittings with soap, water, and physical agitation.

During operation of the CFA–CRDS, intermittent reductions in water vapor concentration can occur within the vaporizer, which can produce perturbations in the isotope data. Gkinis et al. (2010, 2011) described sample flow inconsistencies at their CFA flash vaporizer that caused extreme outliers in isotope data, though the cause of the fluctuations was unclear. We observe similar fluctuations, and the pressure sensor data provide insight into their cause. We find that the most common causes of such variations are microbubbles entering the vaporizer owing to particulate loading, which can cause poor debubbler performance and can also cause blockages to form within the small tubing fittings. Microbubbles that remain suspended in the fluid stream after the debubbler cause volumetric flow rate reductions at the vaporizer inlet. Blockages within fittings upstream of PUMP-2 can cause extreme vacuum conditions before the pump (i.e., pressure observations associated with blockages were as low as -140 kPa before PUMP-2 instead of the typical ambient conditions); this can lead to the contamination of system tubing with small bubbles that also cause temporary flow reductions. To avoid these inconsistencies, we find that it is important to periodically clean the debubbler unit and to maintain ambient pressure at the PUMP-2 inlet by replacing clogged filter screens or tubing fittings. Although data outliers could be systematically removed (as done in Gkinis et al., 2011), occasional bubbles do not substantially impact the isotopic mean value of our ice-core measurements and are retained here. We do exclude some reference-water calibration data, where bubble interruptions are most frequent due to limited operator oversight during the automated reference water measurements. Calibration measurement criteria are discussed in Sect. 3.4.

In addition to monitoring pressure evolution across the system, we can also observe the quality of vapor at the CRDS analyzer via characteristic patterns that arise in the CRDS data. Specific patterns in water vapor concentration and δ18O that emerge from unstable flow into the vaporizer are shown in Fig. 3. We observe that pulsating flow conditions can cause incomplete vaporization, identified by anticorrelated fluctuations in water vapor concentration and δ18O. When a pulse of water overwhelms the vaporizer, the isotopic composition becomes lighter as H216O preferentially evaporates into the vapor stream; as the vaporizer dries out between pulses, the isotopic composition becomes heavier, exhibiting an evaporation signal. Pulsating flow conditions are caused by pressure fluctuations from the peristaltic pump (> 70 kPa) when insufficient back pressure is applied on PUMP-2. The resulting patterns have a large amplitude (up to 10 000 ppm for water vapor and several ‰ for δ18O) and a frequency that mirrors that of the peristaltic pump (e.g., Fig. 3a). The observed fractionation that occurs during these vaporization conditions leads to large calibration bias for Δ17O, causing errors of tens to hundreds of per meg. If there is sufficient back pressure at PUMP-2, the pressure readings at PI-2 are typically < 40 kPa. We attribute small fluctuations in δ18O that are anticorrelated with water vapor concentration to the incomplete vaporization of individual droplets (e.g., Fig. 3b). Because inconsistent flow into the vaporizer can cause isotope fractionation and because it is important to measure calibration standards under the same conditions as the ice-core samples, we tune the system to maintain steady pressure readings at the vaporizer inlet prior to calibration standard and ice-core analysis, as discussed in Sect. 3.2; vapor concentration data that are typical of a well-maintained CFA system are shown in Fig. 3d.

Approximately 12 to 24 h before making an ice-core measurement, an operator maintained the CFA system to balance the flow rate into the vaporizer. For example, when indicated by anomalously high or low pressure sensor data, the filter screens, peristaltic pump tubing, or capillary tubing were replaced. When indicated by CRDS data trends as in Fig. 3, the vaporizer components were cleaned. Returning the CFA system to a balanced state before making measurements of all reference waters increases the likelihood of having usable, high-quality calibration data against which to calibrate the ice-core samples. At other times when ice-core measurements were not made, the system occasionally drifted out of balance and was not actively maintained such that some of the reference water measurements are of lower quality than those used to calibrate the ice-core measurements. This is discussed in more detail in Sect. 3.4.

We cut an 87.5 cm ice-core sample from ∼ 92 m depth beneath the surface at Summit, Greenland, into nine 26 mm square slices to prepare them for continuous analysis. After preparing these nine CFA sticks, a 10th section of core was cut into 63 discrete depth intervals. Discrete ice samples were melted in sealed polyethylene sample bottles in a refrigerator at 4 ∘C. We measured the 87.5 cm section of ice 10 times: the nine replicate slices were measured by the CFA–CRDS configuration described above, and the 10th measurement was made by a discrete injection of 63 melt samples from the core using the commercially available vaporizer unit (Picarro p/n A0211) and automated injections as in Schauer et al. (2016). The depth resolution of the discretely measured ice is 1.39 cm.

For all CFA measurements, we made visual observations of the core height to monitor the melt rate during analysis, then later assigned a high-resolution depth equivalent for each analysis time that is based on the value of δ18O and the measured depth of discrete samples. Previous work has monitored core depth with electronic distance meters (e.g., Bigler et al., 2011; Jones et al., 2017a), and such measurements are critical for depth registration for routine CFA measurement campaigns. Here, we forego electronic depth registration and instead adjust initial depth estimates for each core section by aligning the seasonal cycle of δ18O for all core samples. Assigning depths by aligning the δ18O variations should largely eliminate depth-registration errors, since the strong seasonal δ18O variations must be essentially identical in each replicate sample, and the signal-to-noise ratio for δ18O is very high. Summit, Greenland, has a modern annual accumulation rate of 24 ± 5 cm (ice equivalent) per year (Meese et al., 1994; Dibb and Fahnestock, 2004; Hawley et al., 2008, 2020), and we expect to see 2 to 3 years represented by the core sample that we measured in replicate (Hastings et al., 2009). We compressed the timescale of each CFA time series to maximize the cross-correlation of δ18O (0.93 < r < 0.99) between the CFA measurements and the discrete measurements. We then assigned each CFA time a depth equivalent based on the depth of the corresponding discrete δ18O data. We note that the amplitude of the seasonal variations in δ18O is somewhat compressed in the lower ∼ 30 cm of this core sample, so the depth designations for this interval are likely a greater source of error than in the rest of the ice. Nevertheless, we are confident that our depth registration is precise to within 1 cm or better, determined by assessing the variance in depth assignments at inflection points.

Mitigating memory effects is important for both ice-core and reference water measurements; in addition to the design choices highlighted in Sect. 2.3, there are several operational choices that were made to reduce the memory between isotopically distinct waters. For example, increasing the pump rates at PUMP-1 during ice-core analysis should drive shorter retention times within the tubing upstream of the liquid vent, which should reduce system mixing. In this way, the transition times for reference waters (shown in Fig. 2) are a conservative estimate of mixing effects. The transition time between measurements of reference waters generally varied between 180 and 360 s. We therefore assume a conservative mixing time of 360 s during reference water transitions, and we ignore the 360 s that initiate and conclude each reference water measurement. Before measuring each section of ice (which is typically ∼ 1 m long), we also condition the system with at least 10 min of water with similar isotopic composition to prevent mixing between isotopically disparate reference waters and ice-core samples at the beginning of the analysis. Finally, the replicate CFA–CRDS measurements that are the focus of this study provide a practical evaluation of the effects of memory on measurement fidelity in this configuration.

To achieve an accurate calibration, similar treatment of reference waters and sample melt during vaporization is critical. For this study, we measured the calibration standards immediately before and after measuring an ice-core section; this ensures the most comparable treatment of reference waters and sample melt. Achieving similar treatment also requires that the system is stable during the entire measurement period, including reference water measurements and ice sample measurements. Because an individual ice-core measurement takes a few hours at the melt rates that we employ, we limit our reference water measurements to 3 h each to increase the likelihood that the complete sequence of reference waters and ice-core samples is measured under similar CFA and CRDS conditions.

To calibrate our measurements, we create a two-point linear calibration from the nearest measurements of our internal reference waters, SW2 and SPS2; a third reference water (CW) is used as an independent verification of the calibration. The values of SW2, CW, and SPS2 have been measured independently and are normalized to the VSMOW-SLAP scale as in Schoenemann et al. (2013). An alternating sequence of the three reference waters was measured between ice core analyses; the selector valve was programmed to automatically switch between the reference water containers every 3 h. Automated reference water measurements were typically unsupervised. Reference water measurements were automated and typically unsupervised. Because measurement conditions evolve over time due to particulate loading and mineral precipitation within the CFA components and because there were periods of time during the analysis window when no operator was available to monitor system conditions, there were periods of time during which the water vapor concentration was outside the ideal range, during which large bubbles or other flow inconsistencies degraded the quality of reference water data, or during which the CFA system was not operating; consequently, only about 50 % of the data within the study period is included in this analysis, as described below and in Table 2. We automatically reject calibration data and measurements of CW that were generated from water vapor concentrations beyond the targeted range (i.e., < 20 000 or > 50 000 ppm) or data with insufficient vaporizer operations, indicated by σδ18O > 0.5 ‰ across the measurement window. Typical variability of water vapor concentration within a single 3 h period is 0.5 % to 5 %. We identify transitions from one reference water to the next in the data by the second derivative of δD and assign known standard values based on the uncalibrated measurement values of δD. We include measurements of SW2 and SPS2 that contain at least 6000 s of analysis time, and we trim 360 s of data from the beginning and end of each measurement interval to avoid memory effects. The mean and standard deviation of the analysis time for calibration standard data are 9350 ± 660 s. To calibrate all ice-core and CW measurements made during this study, we use 47 continuous 3 h measurements of SW2 and 40 continuous 3 h measurements of SPS2. All analyses include measurements for δ17O, δ18O, and δD. Calculations of d and Δ17O were obtained from the calibrated δ values as given in Eqs. (1) and (2), respectively. Calibration for Δ17O is more completely described below.

The calibration data used for all measurements are generated from adjacent measurements of SW2 and SPS2 that meet the screening criteria above; calibration data and the sequence of CFA–CRDS measurements are provided in Table 2. For each calibration of CW or ice-core data, we employ the nearest measurements of SW2 and SPS2 for the calibration. The calibration is performed separately for δ17O and δ18O: using a least-squares approach, we fit a linear equation to the uncalibrated average measurements so that the calibrated SW2 and SPS2 measurements match their known values. The calibration equation therefore becomes 3δcalibrated=m×δuncalibrated+b, where δ represents either δ17O or δ18O. An account of m and b for both δ17O and δ18O is shown for all measurements in Table 2. Finally, Δ17O is calculated from the calibrated values of δ17O and δ18O: 4Δ17Ocalibrated=ln⁡δ17Ocalibrated+1-0.528ln⁡δ18Ocalibrated+1. The mean and standard deviation of all CW measurements of Δ17O during the analysis period are 25 ± 12 per meg (n = 53). The subset of CW measurements with the most consistent CFA operations – and therefore the lowest variability for δ18O (σ < 0.06 ‰) – had corresponding Δ17O values of 25 ± 6 per meg (n = 36). Low variability among reference water measurements gives confidence in the use of this system for this study of replicate ice-core measurements.

After assigning approximate depth values and calibrating the ∼ 1 Hz data, we discretize the CFA–CRDS data by binning the calibrated data into prescribed depth intervals and averaging across the entire interval. This enables a direct comparison between the continuous CFA–CRDS time series and the discrete CRDS measurements. Small differences in the instantaneous melt rate cause some variability in the data-averaging duration for each reported measurement; the typical instantaneous melt rate was ∼ 0.3 cm min-1, but rates ranged from ∼ 0.1 to ∼ 0.4 cm min-1 during analysis. We report our CFA–CRDS measurements with 1.39 cm resolution to match the resolution of our discrete CRDS measurements. We also explore the effects of depth resolutions that range from 0.5 to ∼ 40 cm, given that increasing the averaging window of the ∼ 1 Hz spectroscopic measurements reduces instrumental noise (e.g., Werle et al., 1993; Gkinis et al., 2010, 2011; Steig et al., 2014, 2021; Schauer et al., 2016; Jones et al., 2017a).

We compare our CFA–CRDS data for Δ17O with discrete CRDS measurements to evaluate the CFA–CRDS method. We present the mean value and standard error of all replicate measurements in Fig. 4 with 1.39 cm averaging (representing approximately 270 s of data per interval for each individual CFA–CRDS replicate); Fig. 4 also shows the discrete CRDS measurements with the root mean square error of the corresponding discrete reference water measurements. The mean of all CFA–CRDS measurements (representing more than 2000 s of data per interval) is well correlated with the discrete measurements (r = 0.52, where 0.28 ≤ r ≤ 0.69 with 95 % confidence), especially in the upper 50 cm of the core (r = 0.74, where 0.54 ≤ r ≤ 0.88 with 95 % confidence). Both the CFA–CRDS data and the discrete CRDS data show clear seasonal Δ17O variations at this measurement resolution that are matched in magnitude and timing.

Next, we characterize the variability observed among our nine CFA–CRDS measurements. In addition to the depth alignment errors discussed above, sources of variability introduced by the CFA–CRDS method may include high-frequency instrumental noise, calibration errors, and smoothing or bias generated by mixing within the CFA system. High-frequency, high-amplitude noise (∼ 1 ‰) in the uncalibrated CRDS data is inherent to the instrument and can cause large aberrations from the true value of Δ17O, especially over short averaging times; long averaging times (> 1000 s) are typically used when measuring Δ17O by CFA–CRDS to minimize instrumental noise. Calibration errors in Δ17O occur when measurement treatment differs between calibration standards and samples or between calibration standards; this can cause fractionation to occur in the uncalibrated δ17O and δ18O measurements, leading to biased calibration slope and intercept information. Despite efforts to stabilize vaporizer system conditions prior to ice-core sample analysis and to measure ice-core samples with the same treatment, it is likely that some calibration errors persist in our ice-core data because it is not possible to measure the standards and the sample at the same time. Finally, CFA measurement error for Δ17O may result from mixing isotopically distinct waters during CFA processing or from other processing issues that affect the internal variability (i.e., perceived seasonality) of the continuous ice-core measurement.

Typical CRDS characterization studies have used repeated measurements of reference waters to identify measurement error; for this study, we instead use repeated measurements of an ice core to characterize the sources of the measurement error. By measuring reference waters, it is possible to approximate the precision of the uncalibrated measurements by determining the effect of averaging time on the intrinsic noise of the measurement; it is also possible to quantify the variance of the calibrated, averaged data. Our best data for CW were measured at 25 ± 6 per meg, but without additional information, it is not straightforward to identify whether the error associated with this measurement is caused by instrumental limitations, calibration bias, or other CFA processing effects. Our replicate CFA–CRDS measurements provide an opportunity to identify the source of CFA–CRDS errors because we can separately analyze the variability internal to each time series (e.g., due to the seasonal cycle of Δ17O or due to CFA errors) and the variability between the mean values for each ice-core replicate (e.g., due to calibration offsets); further, we can compare this variability with instrument expectations at different averaging times

To isolate the error imparted by the calibration strategy, we processed the data in two ways: first, we calibrated the data as described in Sect. 3.4, and second, we set the mean values of all calibrated CFA measurements equal to the mean value of the discrete CFA measurements in order to consider only the variability internal to each measurement. Steig et al. (2021) demonstrated that making a linear adjustment to the calibration intercept for δ17O and δ18O could reduce the noise of their CFA–CRDS measurements for Δ17O in the SPC14 core. They exploited additional reference water information taken before or after the CFA measurement to define an adjusted calibration intercept value. Here, we can instead use the mean value of the CFA–CRDS measurements themselves, further eliminating uncertainty around this correction by setting the mean of each calibrated CFA–CRDS time series equal to the mean value of our discrete ice-core measurements; in this way, we are able to eliminate offsets in calibration and examine the variability within each continuous measurement. We define the calibration-adjusted Δ17O data as below: 5Δ17OadjustedCFA=Δ17OcalibratedCFA+1n×∑i=1nΔ17Ocalibrateddiscrete(i)-1n×∑i=1nΔ17OcalibratedCFA(i), where the value of n, which represents the number of data points per meter, varies as a function of the depth resolution.

The calibration offset error is therefore Δ17OadjustedCFA-Δ17OcalibratedCFA. Equivalently, Δ17OadjustedCFA can be expressed in terms of δ17O and δ18O using calibration correction information that is based on the differences between average δ17O and δ18O values for the discrete and continuous datasets. That is, 6Δ17OadjustedCFA=ln⁡m17×δ17OuncalibratedCFA+b17+b17_corr+1-0.528ln⁡m18×δ18Ouncalibrated+b18+b18_corr+1, where the correction values b17_corr and b18_corr are defined by the difference in mean δ for CFA and discrete measurements. This calibration adjustment method is analogous to that used in Steig et al. (2021).

Evaluating both Δ17OcalibratedCFA and Δ17OadjustedCFA allows us to disentangle the calibration offset error from other sources of measurement error. We discretized the CFA–CRDS data to a series of depth-resolution schemes that ranged from 1.39 to 43.75 cm; the data are provided for three different depth resolutions in Fig. 5. We calculated the standard error for all depth intervals across all measurement resolutions. The total error for the Δ17OcalibratedCFA and the error for the Δ17OadjustedCFA are approximated by the blue and red lines in Fig. 6, respectively. The region between the two solid lines is the fraction of the total error that can be attributed to the calibration offset. Figures 5 and 6 indicate that the calibration offset noise is essentially indistinguishable from the instrumental noise at short averaging times, so the calibration offset adjustment does little to improve the measurement for the best-resolved data. The results show that the total error is < 10 per meg for all data. The total error is ∼ 5 per meg at averaging times longer than ∼ 3000 s, which corresponds to depth averages of ∼ 15 cm at the melt rates we used. Figure 6 also shows that the error that arises from differences in internal variability (i.e., the CFA error) for the CFA–CRDS data is < 2 per meg by ∼ 3000 s and that the total error is dominated by calibration offset error at long averaging times.

Finally, we directly compare the variability of our CFA–CRDS data with the variability of reference waters measured by CFA–CRDS, which is determined by an Allan variance analysis. An Allan variance analysis quantifies the relationship between signal noise and integration time (Allan, 1966; Werle et al., 1993); for CRDS data, this analysis of reference water measurements is commonly used to approximate the measurement precision of the system for any given measurement duration (Gkinis et al., 2010; Steig et al., 2014). We determine the Allan deviation (square root of the Allan variance) from a long continuous analysis (∼ 8.5 h) of the SW2 reference water made during our analysis window (see Table 2); the result is shown in Fig. 7. Differences between the Allan deviation and the standard deviation of our measurements should confirm whether the magnitude and timing of the variability are as precise as during reference water measurements, or if there are other changes imparted by the CFA system or calibration that may degrade CFA–CRDS data quality. We find the standard deviation σcalibrated_CFA-Δ17O among all nine Δ17OcalibratedCFA datasets averaged over integration windows that vary from 5 mm to 43.75 cm. This analysis compares the variability of the final, calibrated measurements along the depth of the core sample with the variability of the reference water measurement, and ultimately quantifies the reproducibility of our CFA–CRDS measurements. We track the analysis time associated with each averaging interval and overlay the measured σcalibrated_CFA-Δ17O with the corresponding mean integration time for each depth interval on Fig. 7a.

Figure 7a shows generally good agreement between σcalibrated_CFA-Δ17O and σAllan-Δ17O at integration times less than 400 s, but the σcalibrated_CFAΔ17O data asymptotically approach a limit of 10 per meg at longer averaging times instead of following the stability trend expected by the Allan variance analysis. To evaluate to what extent this mismatch between expected and observed σ can be attributed to errors arising from the calibration offset (as shown in Fig. 6), we repeat this analysis for the Δ17OadjustedCFA data. Figure 7b shows excellent agreement between σadusted_CFA-Δ17O and σAllan-Δ17Oat all integration times; this demonstrates that the drift in σcalibrated_CFA-Δ17O shown in Fig. 7a can be entirely attributed to calibration effects and not to the CFA process directly. Figure 7 suggests that reducing the error of calibrated CFA–CRDS measurements is not limited by the CFA process – nor by the CRDS instrument – but rather by the quality of the calibration information, which depends on the treatment and frequency of reference water measurements.

Our work complements previous studies that have examined the seasonal cycle of Δ17O in the polar regions, and good agreement with earlier work validates our measurements. Consistent with previous measurements from Greenland, the Δ17O signal in our data is anticorrelated with d and anticorrelated with the seasonal cycle in δ18O (Landais et al., 2008). The measurements presented here were made from a core that represents approximately 2 years of ice accumulation from the 1760s (Hastings et al., 2009). The measured magnitude (peak to trough) of the seasonal cycle in Δ17O is ∼ 45 per meg at 1.39 cm resolution in our data (Fig. 4), which is in excellent agreement with the magnitude of the seasonal cycle reported previously for Greenland. Specifically, Landais et al. (2012b) reported seasonal magnitudes of ∼ 25 per meg from a shallow firn core at NEEM (in northwestern Greenland) that represented accumulation periods between 1962–1963 and between 2003–2005; when we coarsen our measurement resolution to 3.6 cm – which approximates the ∼ monthly (5 cm) measurement resolution in the NEEM core (detailed in Steen-Larsen et al., 2011) – the magnitude of the seasonal cycle in our data is ∼ 30 per meg. Low errors between replicate values and the good agreement with previous studies strengthen confidence in the CFA–CRDS approach for high-resolution Δ17O.

Our results reinforce the use of the CFA–CRDS method for high-precision, high-resolution measurements of Δ17O in ice cores. CFA–CRDS methods are valuable for detecting detail in Δ17O variations in deep ice layers, for measuring Δ17O in ice from sites with low accumulation rates, or for measuring Δ17O in any glacial ice where high depth resolution is desired.

Because the error of all Δ17O measurements by CRDS depends on the calibration, the importance of establishing a robust calibration strategy for CFA–CRDS cannot be understated. We iteratively revised our CFA–CRDS system and designed our calibration strategy as recommended below.

First, the CFA–CRDS configuration must be capable of stable operations that span the total duration of the ice-core and reference water measurements. System stability for a given CFA system should be characterized with an Allan variance analysis. We have chosen to measure calibration standards immediately before and after ice-core measurements to improve the likelihood of measuring the calibration standard under the same system conditions as the ice-core sample. Additionally, limiting system memory and reducing the transition time between reference waters maximize the useful fraction of reference water data, allowing measurements of longer duration or measurements of more reference waters to be made within a period of consistent CFA operations.

Next, quantifying the drift in calibration information over time can allow an operator to determine the physical controls on fractionation within a CFA–CRDS system. The change in calibration information can be used to inform system maintenance schedules or operational sequences. For example, we have observed that after operating our CFA–CRDS system for several weeks, the fractionation responses for δ17O and δ18O diverge, degrading the quality of calibration data for Δ17O. Cleaning the vaporizer fittings appears to “reset” the calibration response, suggesting that the fractionation that occurs over long timescales is a result of physical effects within the vaporizer itself, likely owing to visible precipitate formation.

Though our system is capable of high-precision measurements for Δ17O, our analysis suggests that calibration bias persists in our data, which is unsurprising when considering previously published work on similar methods. The largest offsets (shown in Table 2) were associated with poor CFA stability due to a dirty vaporizer chamber. Large errors in Δ17O were occasionally observed during the analysis of the South Pole ice core (SPC14); Steig et al. (2021) attributed these errors to calibration differences and performed a correction by shifting the mean value of their measurements based on the offset identified by a calibrated reference water measurement, similarly to Eq. (6). Our work supports the attribution of these errors to the calibration, and it also supports the calibration adjustment method. We recommend the use of additional reference water measurements to account for calibration offsets in Δ17O, and we also recommend that CFA systems are designed to ensure complete vaporization with flow conditions that are stable over long timescales. In our vaporizer, we observe that precipitate coatings can change the geometry of the vaporizer chamber and lead to incomplete vaporization over time, which degrades the quality of the calibration over time. When there is clear evidence of inconsistent vaporization (as in Fig. 3), we observe large calibration errors in Δ17O by this method (tens to hundreds of per meg). Such issues likely also influence the vaporization process in other CFA systems, though they will not be readily detected in measurements of δ18O or δD if the water vapor has homogenized before reaching the analyzer.

Finally, though it is perhaps impractical to measure replicate ice-core samples as we have done here, the average of our nine CFA–CRDS measurements shows that, like dual-inlet IRMS operations, stacking the CFA–CRDS data effectively averages over calibration inconsistencies. The results are comparable to highly resolved discrete CRDS or IRMS measurements. While CFA–CRDS measurements resolved to the centimeter scale still require long measurement times to achieve precise Δ17O data (> 1000 s for 10 per meg precision), stacking CFA–CRDS measurements is an effective way to increase analysis time. Typically, achieving long measurement times while maintaining high depth resolution necessitates a reduction of melt rates. In practice, reduced melt rates may be incompatible with other measurement goals (such as trace gases) during an ice-core measurement campaign; reduced melt rates may also prevent the measurement of both ice-core samples and calibration standards within a period of stable system operations. We show that stacking multiple CFA–CRDS measurements provides a viable alternative strategy; stacking replicate CFA–CRDS measurements improves the accuracy of the measurement by averaging over the calibration offset noise, and it improves the measurement precision or measurement resolution by increasing the total analysis time for a given depth interval.