AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-11-4725-2018Calculating uncertainty for the RICE ice core continuous flow analysis water
isotope recordRICE CFA water isotope record uncertaintyKellerElizabeth D.l.keller@gns.cri.nzBaisdenW. Troyhttps://orcid.org/0000-0003-1814-1306BertlerNancy A. N.EmanuelssonB. Danielhttps://orcid.org/0000-0002-9373-6951CanessaSilviaPhillipsAndyNational Isotope Centre, GNS Science, Lower Hutt, New ZealandAntarctic Research Centre, Victoria University of Wellington, Wellington, New Zealandnow at: Environmental Research Institute, University of Waikato, Hamilton, New ZealandElizabeth D. Keller (l.keller@gns.cri.nz)13August20181184725473627October20179January201821July201825July2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://amt.copernicus.org/articles/11/4725/2018/amt-11-4725-2018.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/11/4725/2018/amt-11-4725-2018.pdf
We describe a systematic approach to the calibration and uncertainty
estimation of a high-resolution continuous flow analysis (CFA) water isotope
(δ2H, δ18O) record from the Roosevelt Island
Climate Evolution (RICE) Antarctic ice core. Our method establishes robust
uncertainty estimates for CFA δ2H and δ18O
measurements, comparable to those reported for discrete sample
δ2H and δ18O analysis. Data were calibrated
using a time-weighted two-point linear calibration with two standards
measured both before and after continuously melting 3 or 4 m of ice core.
The error at each data point was calculated as the quadrature sum of three
factors: Allan variance error, scatter over our averaging interval (error of
the variance) and calibration error (error of the mean). Final mean total
uncertainty for the entire record is δ2H=0.74‰ and δ18O=0.21‰.
Uncertainties vary through the data set and were exacerbated by a range of
factors, which typically could not be isolated due to the requirements of the
multi-instrument CFA campaign. These factors likely occurred in combination
and included ice quality, ice breaks, upstream equipment failure,
contamination with drill fluid and leaks or valve degradation. We demonstrate
that our methodology for documenting uncertainty was effective across periods
of uneven system performance and delivered a significant achievement in the
precision of high-resolution CFA water isotope measurements.
Introduction
Stable water isotopes (δ2H, δ18O) are a
fundamental part of ice core studies. They are particularly important as a
temperature proxy (Dansgaard, 1964; Epstein et al., 1963) and are a key
component in establishing the age–depth scale and chronology of ice cores
(NGRIP Members, 2004; Vinther et al., 2006; Winstrup et al., 2017). They also
provide other information about climate, including accumulation rates,
precipitation source region, atmospheric circulation and air mass transport,
and sea ice extent (e.g. Küttel et al., 2012; Sinclair et al., 2013;
Steig et al., 2013; Bertler et al., 2018; Emanuelsson et al., 2018).
Historically, water isotopes from ice cores were analysed as a set of
discrete water samples using isotope ratio mass spectrometry (Dansgaard,
1964). Recent advances in laser absorption spectrometry have allowed
continuous flow analysis (CFA) to become common in ice core studies and are
an essential measurement technique for obtaining high-resolution climate
records (e.g. Kaufmann et al., 2008; Gkinis et al., 2011; Kurita et al.,
2012; Emanuelsson et al., 2015; Jones et al., 2017). However, the
simultaneous operation of seven measurement systems (Winstrup et al., 2017;
Pyne et al., 2018) and the continuous nature of CFA pose challenges for
calibration and uncertainty estimation. Because of the size and resolution of
CFA ice core data sets and the relatively new application of laser
spectroscopy to ice cores, few established methods exist for calculating
point-by-point uncertainty throughout measurements. Building on previous studies (e.g. Gkinis et al., 2011;
Kurita et al., 2012; Emanuelsson et al., 2015), we have developed a
systematic approach to calibration and error calculation that allows for
unique uncertainty estimates at each data point in a CFA water isotope
record. In this study, we report our methodology for the calibration and
calculation of uncertainty and demonstrate the application of the method on
the Roosevelt Island Climate Evolution (RICE) ice core δ2H and
δ18O data set.
The RICE collaboration retrieved a 760 m ice core from the north-eastern
edge of the Ross Ice Shelf over Roosevelt Island in Antarctica
(79.39∘ S, 161.46∘ W, 550 m a.s.l) during the austral
summer 2011–2012 and 2012–2013 field seasons (Bertler et al., 2018). The
RICE ice core provides a valuable record of a high snow accumulation site in
coastal West Antarctica with annual or sub-annual resolution at the upper
depths, representing the late Holocene. The climate reconstruction at the
RICE site for the last 2700 years using the CFA water isotope record is
available in a separate publication (Bertler et al., 2018). In addition to
the value in the methodology itself, this paper provides confidence in the
precision of the RICE data set and the climatic interpretation on annual and
sub-annual timescales. This method can be applied to other high-resolution
CFA ice core water isotope records in the future and may be suitable for
other continuous water isotope measurement applications.
This paper is structured as follows: in Sect. 2, we give an overview of our
data processing and data quality control procedure. We also detail our
methods for calibrating the isotope data and calculating the uncertainty for
each data point. Section 3 contains the resulting estimates for each
component of the total error of our data set and an analysis of the different
sources of error. We conclude in Sect. 4 with a summary and recommendations
for future CFA measurement campaigns.
Methods
The abundance of the rare isotope in a sample is conventionally reported in
delta notation, defined as
δ=RsampleRstandard-1,
where R is 18O/16O or 2H/1H for
water stable isotopes (Coplen, 2011). Results in this paper are reported as
δ values in parts per thousand (‰), normalized to the
international standard Vienna Standard Mean Ocean Water
and Standard Light Antarctic
Precipitation (VSMOW-SLAP) scale
(Gonfiantini, 1978).
Melting and data processing
Cores were melted and processed at the Ice Core Laboratory at the GNS
National Isotope Centre in Lower Hutt, New Zealand. There were two separate
melting campaigns, one in June–July 2013, in which the top 500 m were
melted, and the other in June–July 2014, in which the remaining 260 m
(500–760 m) were melted (Pyne et al., 2018). There were several important
differences between the 2 years in the CFA set-up (Emanuelsson et al., 2015;
Pyne et al., 2018), which necessitated that the data from each melting
campaign be processed separately. These differences are noted where they are
relevant to the calibration and uncertainty calculations; some factors were
calculated individually for each melting campaign and applied only to the
data from that campaign.
The ice was cut into 1 m segments and melted at a controlled rate of
approximately 3 cm min-1, producing a liquid flow rate of ∼16.8mLmin-1 (Pyne et al., 2018). The melting set-up is
based on Bigler et al. (2011) and is discussed in more detail in Emanuelsson
et al. (2015), Pyne et al. (2018) and Winstrup et al. (2017). Briefly, the
cores were placed vertically on a gold-coated copper melting plate and were
allowed to melt continuously under gravitational pull. The water from the
clean, inner part of the core was drawn from the centre of the
melt head and pumped to instruments
for CFA of stable isotopes, methane, black carbon, insoluble dust particles,
calcium, pH and conductivity and discrete samples for major ion and trace
element analyses. The water from the outer part of the core was saved in
vials for discrete stable and radioactive isotope analysis. Either three or
four 1 m core segments were stacked on top of each other and melted without
interruption (referred to here as a “stack”). At least one calibration
cycle of three water standards was run between each stack. An optical encoder
that rested on top of the core stack recorded the vertical distance
displacement as the core melted. This displacement was translated into depth
in millimetres and, along with the melting rate and other system information,
was written to a log file every 1 s using LabVIEW software (National
Instruments). These log files were used to align all CFA instrument data to
the depth scale. Breaks in the ice were measured and recorded to 1.0 mm
precision before melting. Any ice that was cut out and removed was recorded
as a gap in the depth scale. The raw data files were processed using a graphical user interface (GUI) and a
semi-automated script written in Matlab (Matlab Release 2012b, The MathWorks,
Inc., Natick, Massachusetts, United States). Occasionally, poor-quality ice
(i.e. ice containing fractures and slanted breaks) caused the upper part of
the stack to stick to the sides of the core holder; the depth encoder failed
to register any change in depth for a time, while the base of the stack
continued to melt. These intervals required linear interpolation (assuming a
constant melt rate) and introduced a small amount of uncertainty (Pyne et
al., 2018). This occurred more frequently deeper in the core in the brittle
ice zone (below 500 m). Given that the melt rate was fairly constant
throughout the campaign, the error introduced in the depth assignment was
negligible. More details of the data processing are available in Pyne et
al. (2018).
Water isotope values (δ2H, δ18O) were measured
using CFA with a water vapour isotope analyser (WVIA) using off-axis
integrated cavity output spectroscopy (OA-ICOS; Baer et al., 2002) and a
modified Water Vapour Isotopic Standard Source (WVISS) calibration unit
(manufactured by Los Gatos Research, LGR). This system is described in detail
in Emanuelsson et al. (2015). The 2013 and 2014 set-ups were largely the same
but differed in the construction of the vaporizer and the delivery of the
mixed vapour to the isotope analyser. In 2014, the heating element of the
vaporizer was modified, and a higher sample flow was delivered directly to
the IWA through an open split (Emanuelsson et al., 2015). Data were recorded
in an output file at a rate of 2 Hz (0.5 s) in 2013 and at 1 Hz (1.0 s)
for the remaining 260 m in 2014. The change in the recording rate of the
isotope data in 2014 was made to match the rate at which the depth was
recorded in both years (1 Hz). Note that this was not a change in the
instrument's internal data acquisition rate, only in the rate of output
aggregation.
The campaigns altogether required processing and alignment of over 5 million
raw data points. Depth alignment across multiple measurement systems is a key
issue for ice core campaigns and a fundamental requirement for producing an
age chronology (Winstrup et al., 2017). The interpretation and identification
of key events in the climate history thus depend on accurate depth alignment.
This is particularly important deeper in the core, where a misalignment of a
few centimetres could equate to hundreds or even thousands of years (Lee et
al., 2018). Alignment of the isotope data to the depth scale is based on the
time lag between the depth log file and the WVIA instrument output. The time
lag was determined with an automated algorithm to detect the end of the
calibration cycle and the beginning of the ice core melt stream using the
abrupt increase in the change in numeric
derivatives of adjacent data points. The calculated time lags during each
measurement campaign averaged 418 s in 2013 and 156 s in 2014 but varied
slightly from day to day by 10–20 s. (The lag was shorter in 2014 due to
the reduction in length of tubing between the melter and WVIA. Variations
occurred from the periodic replacement of the tubing.) There were a few
occasions of equipment failure where manual depth alignment was necessary.
Poor ice quality also affected the accuracy of the depth log files, as
mentioned above (Pyne et al., 2018). The precise quantification of the
uncertainty introduced from the depth assignment is beyond the scope of this
paper; based on the variation in time lags, we estimate that, at most, it is
of the order of 1–10 mm.
Data quality control
We applied several basic selection criteria to identify and eliminate
poor-quality data from the raw δ2H and δ18O
data set. The two main reasons for data removal were (1) changes in the water
vapour concentration (H2O ppm) in the LGR analyser, and (2) the
finite response time of the analyser and the transitional period when
switching between water standards from the calibration cycle and RICE ice
core meltwater (which by design had very different isotopic values). In
addition, some gaps were introduced as a result of cutting the core into 1 m
segments and the fractures in the ice that occurred during the drilling,
recovery and handling process (Pyne et al., 2018).
The isotope ratio is dependent on water vapour concentration in the analyser
(Sturm and Knohl, 2010; Kurita et al., 2012). To minimize the need to correct
the data for this, the concentration in the analyser was kept as close to
20 000 ppm as possible. This value was monitored and recorded at the same
frequency as the isotope data. For the most part this concentration was
stable, but fluctuations and sudden changes did sometimes occur (for example,
when air bubbles passed through the line). We removed data when the
difference between the H2O ppm moving average over the short-term
system response time of ∼60s and over a longer-term, stable
time of ∼200s was greater than the standard deviation of the
short-term average (Emanuelsson et al., 2015): avgs-avgl>σs, where
σs is the standard deviation of the short-term average. In
addition, data were removed if the water vapour concentration fell below
15 000 ppm for an extended period. This filtering removed the need to
further correct for variations in water vapour concentration in the record
(Emanuelsson et al., 2015). Figure 1 shows a typical day of raw data,
including both RICE ice core stacks and calibration cycles. Data marked in
red were removed using these criteria. The majority of these points occur
during the switch from one water standard to another in the calibration cycle
and do not affect the data from the ice core itself. The percentage of data
removed using these criteria was 0.4 % of the total.
An example of the raw data from a full day of ice melting and
calibration cycles (2–3 July 2014): (a)δ2H,
(b)δ18O and (c) water vapour mixing ratio.
Isotope data that were removed because of water concentration anomalies are
marked in red in (a, b) panels.
It was also necessary to remove some data points at the beginning and end of
every stack during the transition period between the Milli Q
(18.2 MΩ) laboratory water standard and ice core. This transition is
illustrated in Fig. 2. The Milli Q standard is composed of local de-ionized
water and has an isotopic value much greater than the RICE ice core
(Table 1). Milli Q was run immediately before and after each stack, and there
is a period of instrumental adjustment and mixing when switching between them
due to memory effects and the finite response time of the spectrometer (see
Emanuelsson et al., 2015 for a full discussion). To ensure that the data are
not influenced by mixing at the beginning and end of the stack while
including as much data as possible, we calculated the numerical derivative
(or the rate of change) between consecutive δ2H data points
during the transition until the derivative falls below a threshold; all
points prior are then excluded. The same process is performed at the end of
the stack in reverse. The threshold was found empirically and is different in
2013 and 2014 because of the difference in the response times of the two
set-ups and the precision of the data. Data were inspected manually for cases
where the algorithm was inadequate. Approximately 2–5 cm at the beginning
and end of every stack was removed using this condition. These appear as
gaps in the depth of the final data set. There were also a few occasions when
melting was interrupted due to equipment failure, and Milli Q was run through
the system until melting could resume; these periods were removed using the
same procedure. A typical stack showing a portion of data removed is shown in
Fig. 2 (δ2H vs. depth). The fraction of total data removed was
5.4 %. This resulted in short data gaps of 2–5 cm every 3 or 4 m.
A selected example section of δ2H vs. depth. The data
marked in red represent the transitions between the Milli Q standard and ice
core at the boundaries of each 3 m stack. These data points (and other poor
quality data) were removed from the final data set.
Accepted values (VSMOW-SLAP scale) for water standards used for calibrations in per mil
(‰).
Water standardδ18O (‰)δ2H (‰)Milli Q-5.89±0.05-34.85±0.18WS1-13-10.84±0.10-74.15±0.94WS1-14-10.83±0.05-74.85±0.18RICE-13-22.54±0.05-175.02±0.19RICE-14-22.27±0.05-173.06±0.24ITASE-13-37.39±0.05-299.66±0.18ITASE-14-36.91±0.08-295.49±0.52
The entire data set was manually inspected for any other regions of poor
quality, and points that visibly fell outside the normal range or were
affected by known instrument problems were removed. This only applied to a
few isolated sections of data and was a very small portion
(< 0.1 %) of the total.
Calibration
It is necessary in laser spectroscopy to normalize the isotopic values to the
VSMOW-SLAP scale and to correct
for instrumental drift. To accomplish this, we used a two-point linear
calibration method (Paul et al., 2007; Kurita et al., 2012). Before and after
each ice core stack, we ran calibration sequences consisting of four
laboratory water standards: Milli Q, Working Standard 1 (WS1), RICE snow
(RICE) and US International Trans-Antarctic Scientific Expedition West
Antarctic snow (ITASE). An example of a
calibration cycle is shown in Fig. 3. Assigned or “true” values for these
standards measured against the VSMOW-2-SLAP-2 scale are listed in Table 1. Each batch of working
standards was calibrated to the International Atomic Energy Agency (IAEA)
primary standards, VSMOW-2 (δ18O=0.0‰;
δ2H=0.0‰), SLAP-2 (δ18O=-55.50‰; δ2H=-427.5‰) and
GISP (δ18O=-24.76‰; δ2H=-189.5‰), using three intermediate, secondary standards,
INS11 (δ18O=-0.37‰; δ2H=-4.2‰), CM1 (δ18O=-16.91‰;
δ2H=-129.51‰) and SM1 (δ18O=-28.79‰; δ2H=-225.4‰).
Time vs. raw δ18O (uncalibrated) for 1 day of melting
(3 July 2014). Values of standards drift noticeably over the course of the
day. An example of one calibration cycle of three water standards run between
ice core stacks is marked in colour: WS1 (red), RICE (green) and ITASE
(blue).
We note that there is a difference in the assigned values for RICE and ITASE
between 2013 and 2014. We have denoted them RICE-13, RICE-14, ITASE-13 and
ITASE-14 in Table 1 to indicate that these standards were prepared and stored
in different batches in each year, from water sources that had not been
treated as standards or homogenized, and thus are slightly different in
composition. We emphasize here that our standards are local working
standards, selected or mixed by our laboratory to match the isotope ratios of
the sample (melt stream). It is not unexpected that their isotopic value will
change between batches during long measurement campaigns, as it is not
practical to prepare and store all of the material in one batch.
Part of the difference in assigned values might be attributed to the
difference in measurement systems. The assigned values for the 2013
calibrations were determined using discrete laser absorption spectroscopy
measurements on an Isotope Water Analyzer (IWA) 35EP system. In 2014, our
instrument was upgraded with a second laser to IWA-45EP, and the 2014
calibrations utilize values from standards measured continuously with this
system. We were regrettably not able to calibrate our working standards
using the 2013 CFA set-up before the set-up was modified for the 2014
campaign, so we use the assigned values from the 2013 discrete measurements
in the 2013 calibrations. We thus consider the 2014 melting campaign to be
better calibrated than the 2013 campaign. This follows from the principle of
identical treatment (IT) of stable isotope analysis wherein samples and
reference materials should be subject to identical preparation, measurement
pathways and data processing to the greatest extent possible (Werner and Brand, 2001;
Carter and Fry, 2013; Meier-Augenstein, 2017).
The working standards used for the calibration, RICE and ITASE, have assigned
values which form an upper and a lower bound, respectively, for the majority of
the ice core isotopic values (the ice core samples from the younger, top
portion of the core occasionally fall slightly above the RICE standard). The
third water standard (WS1) served as a quality control to enable us to check
and quantify the accuracy of the calibration. Each standard was run
continuously for approximately 10 min (varying between 8 and 15 min over the
course of the melting campaigns), of which the first and last 100–200 s
were discarded to ensure only the middle, stable portion of the measurement
was used for calibrations. Around 300 s of data were averaged to arrive at
the mean value of the measurement.
Frequent measurements of calibration standards are necessary to correct
isotopic measurements for instrumental drift over time. At least one cycle of
all three standards was run between stacks, and in many cases, there were
several cycles. Melting a stack of three or four cores took around 2–2.5 h,
so the measurement at the midpoint of a stack (the points furthest from a
calibration) is about 1–1.25 h from the nearest calibration. While this is
longer than would be ideal for isotope laser spectroscopy, the stability of
other elements of the CFA system (in particular, continuous flow methane
measurements) required long uninterrupted periods of melting.
δ18O is typically more affected by drift than
δ2H. Drift can be worsened by experimental conditions such as
drill fluid contamination and leaks in the system as the analyte proceeds
toward the vacuum in the laser cavity. We have quantified the error
introduced by the amount of drift occurring between calibrations using the
Allan deviation, discussed in Sect. 2.4.1.
We have used a two-point linear normalization procedure, which is routinely
used to adjust measured δ values to an isotopic reference scale (Paul
et al., 2007). The correction takes the form of linear regression:
δcorrected=m⋅δmeasured+b, where m is
the slope of the line and b is the y intercept. The measured δ values of two laboratory standards are regressed against their assigned
δ values. The slope m can be calculated by plotting the measured
values of the standards on the x axis and their assigned values on the
y axis and then using trigonometric formulas to relate them to the true
value of the sample (Paul et al., 2007). The result is the ratio of the
difference between the true RICE and ITASE δ values and the actual
difference measured:
mi=δRICET-δITASETδRICEi-δITASEi,
where δRICET and
δITASET are the assigned true values and
δRICEi and δITASEi are the ith
measured values of the standards RICE and ITASE, respectively. The correction
then takes the following form:
δcorrected=δRICET-δITASETδRICEi-δITASEi⋅δraw-δRICEi+δRICET.
By design, the y intercept or offset b is equal to the difference between
δRICET and δRICEi when the slope
m is 1. We applied this correction to each data point by weighting the
factors calculated from the RICE and ITASE calibration measurements both
before and after the stack with the time difference between the data point
and the calibration:
δcorrectedt=δraw-δRICE1⋅m1+δRICET⋅1-f+δraw-δRICE2⋅m2+δRICET⋅f,
where δraw is the uncalibrated, raw δ2H or
δ18O value of the ice core sample, δRICE1 and
δRICE2 are the measured values of the RICE standard before
and after the stack, respectively, t is the time of the
δraw measurement, and f is a dimensionless weighting
factor, f=(t-t1)/t2-t1, t1 is the starting time
of the δRICE1 measurement before the stack, and t2 is the ending
time of the δRICE2 measurement after the stack. We note that
this method assumes that drift is approximately linear over the measurement
period. Our calibration procedure was validated by comparison with discrete
measurements in Emanuelsson et al. (2015). The values of the slope
corrections and the RICE and ITASE raw measurements used to calibrate the
data in each year are shown in Figs. S2–S4 in the Supplement; mean values
and standard deviations are in Table S1 in the Supplement.
Uncertainty calculation
We identified three main sources of uncertainty in our measurements: (i) the
Allan variance error (a measure of our ability to correct for drift, a
systematic source of uncertainty due to instrumental instability), (ii) the
scatter or noise in the data over our chosen averaging interval, and (iii) a
general calibration error relating to the overall accuracy of our
calibration. Our three error factors can be formally categorized as follows:
Allan variance error is the
systematic error or bias due to our imperfect ability to correct for drift;
scatter error is the error of the
variance, precision or random variation of replicate
measurements;
calibration error is the error of
the mean or trueness.
The last two can be quantified with general analytical expressions (Kirchner,
2001). Systematic error does
not have a general analytical form; isotopic drift is fortunately amenable to
correction, but the method is imperfect.
We assume that the three error factors are uncorrelated to a large degree.
This is supported by the general framework that we have used (Kirchner, 2001;
Analytical Methods Committee, 2003) and the actual errors calculated at each
data point (R2 < 0.05 in each year for both isotopes). In
practice it is impossible for all error factors to be completely
uncorrelated, as some underlying sources of error will affect all aspects of
the system. However, our data suggest that these interactions are small
and/or short-lived and negligible to the total uncertainty. With this
assumption, we calculate each error factor separately and add them in
quadrature to arrive at the total uncertainty estimate:
σtotal=σAVE2+σscatter2+σcalib2.
Each data point in the final record is assigned a unique error value. A
detailed explanation of the calculation of each source of uncertainty
follows.
Allan variance error
The Allan variance σallan2, or two-sample frequency
variance (Allan, 1966), is often used as a measure of signal stability and
instrumental precision in laser spectroscopy (Werle, 2011; Aemisegger et al.,
2012). In the context of CFA isotope measurements, it is also used as an
estimate of how much instrumental drift accumulates over a specified period.
It is defined by
σallan2τ=12n∑j=1nδ(τ)j+1-δ(τ)j2,
where τ is the averaging time, n is the number of time intervals, and
δ(τ)j and δ(τ)j+1 are the mean values of adjacent
time intervals j and j+1 with length τ. The Allan deviation is
the square root of the variance, σallan.
We calculated the Allan deviation of our system using measurements of the
Milli Q standard, run continuously for 24–48 h. We conducted these tests
periodically during both measurement campaigns (usually over the weekend when
the instruments were otherwise idle; see Emanuelsson et al., 2015, for
details). On a log–log plot of the Allan deviation vs. averaging time
(τ), there is a minimum at the averaging time where the precision is
highest; before this point, at very short averaging times, instrumental noise
affects the signal, and after, at longer averaging times, the effects of
instrumental drift can be seen. Thus, the Allan deviation provides an
estimate of the optimal averaging time, before and after which precision
decreases.
The Allan deviation can also provide an indication of the uncertainty due to
instrumental drift as a function of the time difference between the
measurement and the nearest calibration. For our system to stay under the
precision limit of 1.0 ‰ and 0.1 ‰ for δ2H
and δ18O, respectively (and to permit analysis with deuterium
excess, d=δ2H-8⋅δ18O), a
calibration cycle to correct for drift should occur at least every ∼1h during ice core measurements (Emanuelsson et al., 2015).
However, as noted above, system limitations prevented us from running
calibrations as frequently as would have been optimal. We use the Allan
deviation here to estimate how quickly instrumental drift increased and thus
how well we were able to correct for drift using our calibrations.
We plot the mean σallan for all tests performed against
averaging time τ on a log–log scale (done separately for 2013 and
2014) and perform a linear regression
on the curve for averaging times greater than the minimum
σallan. The equation of the linear fit gives what we refer
to as the Allan variance error (denoted by σAVE to
distinguish our error from the official definition of the Allan deviation):
logeσAVE=a⋅loget+bσAVE=ta⋅eb,
where t is the time difference between the data point and the calibration
(as measured from the start of the measurement of the RICE standard), and a
and b are constants determined from the linear regression. This error
factor is calculated for each data point as a function of t. Because we
calibrated using standards measured both before and after each stack, there
are two factors at each point that are combined with a time-weighted average,
using the same weighting used for the calibration (Eq. 4):
σAVEt=t-t1a⋅eb⋅1-f+t-t2a⋅eb⋅f,
where f is defined as before in Sect. 2.3. Allan variance error vs. depth
over the whole data set is shown in Fig. 4. The local maximum for each stack
occurs in the middle, at the point furthest away in time from the two
calibrations bracketing the stack, reflecting that it is at this point that
we are most uncertain of the amount of instrumental drift.
Allan variance error vs. depth in per mil. δ2H is in
blue and δ18O is in red. The low points of the dips are the
start and end of a stack, between which calibrations were carried out.
Scatter error
A second error derives from the scatter or noise in the signal over our
averaging interval (15 s). This averaging interval was chosen by the RICE
project team as a suitable scale over which to smooth measurement noise
without obscuring important features in the data. This equates to
approximately 7–8 mm on the depth scale. Due to this deliberate choice, the
error calculation that follows applies over this interval. To quantify this
analytical uncertainty, we calculate the standard deviation for every 15 s
time interval contained in each measurement of the RICE standard using a
moving window (so that each adjacent, overlapping interval is advanced by
1 s) and average over the
duration of the measurement:
σscatter=1N∑1Nσini=meanσini,i=[1…N],
where σi is the standard deviation, N is the total number of
intervals, and ni is the number of data points in the ith
interval (n=∼30 in 2013 and ∼15 in 2014). We note that
the number of points that are contained in the interval is different in 2013
and 2014, resulting from the difference in output aggregation (not the
instrument's internal data acquisition rate). This could affect the amount of
noise in the data. However, we have not attempted to analyse this in detail,
as we are only concerned here with quantifying the uncertainty associated
with our averaging interval, regardless of the number of data points
averaged.
Again, because the RICE standard was measured both before and after each
stack, we calculate σscatter for both measurements and linearly
combine them using a time-weighted average. Note this error is linear with
time within a stack but is discontinuous at the points at which a stack begins
and ends. This linearity is rooted in the fact that the noise in a set of
measurements from the same sample can in general be modelled as a Gaussian
process, with a normal distribution of independent random variables. The
mean-squared displacement is linear with time. Scatter error vs. depth for
the length of the core is shown in Fig. 5.
Scatter error vs. depth in per mil. δ2H is in blue
and δ18O is in red.
Calibration error
Finally, we calculate the error of the mean after applying our calibration
procedure to quantify the trueness
of the measurement with respect to our reference scale, denoted by
σcalib. This captures both random, unsystematic components
of uncertainty and systematic biases in the calibration stemming from a
variety of (unspecified) sources. This quantity is often calculated as a
check on the overall quality of the
calibration procedure. Because it encompasses multiple sources of error, we
expect it to be a relatively large error. Here, we make use of the large set
of WS1 measurements that were taken during the calibration cycles. To
calculate this factor, we apply the calibration formula using the RICE and
ITASE standards (Eqs. 2 and 3) to the third quality-control standard, WS1,
measured in the same cycle. The error is defined as the difference between
the corrected, measured value and the assigned value of the WS1 standard. An
example is shown in Fig. 6. We calculated this difference for all calibration
cycles containing measurements of all three standards (RICE, ITASE and WS1)
of sufficient quality (there were 221 such calibration cycles in 2013 and 318
in 2014) and then took the mean of the differences. Separate error estimates
for the 2013 and 2014 melting campaigns were calculated and applied only to
the data points from the respective year. The calibrated values obtained for
all of the WS1 measurements throughout both campaigns are shown in Fig. S1 in
the Supplement.
Representative δ18O calibration of ice core stack and
WS1, using RICE and ITASE standards from the same cycle, 15 s moving average
vs. time (measured on 2 July 2014). The difference between the true value of
WS1 (blue) and the calibrated measured value of WS1 (red) is the calibration
error. The error that was applied to the CFA data set is the average
difference of all WS1 calibration measurements during the melting campaign.
Results and discussion
Total error vs. depth for the whole record is shown in Fig. 7 and summarized
in Table 2. The mean total errors for all data points
are 0.74 ‰ (δ2H) and 0.21 ‰
(δ18O). Separated by melting campaign, mean total errors in
2013 are 0.85 ‰ (δ2H) and 0.22 ‰
(δ18O) and in 2014 they are 0.44 ‰
(δ2H) and 0.19 ‰ (δ18O). The total
error reduces sharply at a depth of 500 m due to the switch between 2013 and
2014 campaigns and the greatly reduced calibration error in 2014. However, we
observe a larger variability in the error in the 2014 data. This is mainly a
result of the highly variable amount of noise in the measurements, which is
discussed below.
The mean Allan errors for all data
are 0.12 ‰ for
δ2H and 0.14 ‰ for δ18O. Calculated
separately by melting campaign, the mean errors are 0.13 ‰
(δ2H) and 0.16 ‰ (δ18O) in 2013 and
0.083 ‰ (δ2H) and 0.11 ‰
(δ18O) in 2014. As expected, the Allan error peaks at the
points in the middle of the stack, furthest from a calibration (Fig. 4). It
is both absolutely and proportionally larger for δ18O, as
δ18O is typically more affected by drift.
The amount of scatter in the data varies considerably over the length of the
record, particularly in 2014. The mean scatter errors over the whole record are 0.29 ‰ (δ2H) and 0.10 ‰
(δ18O). Separated by melting campaign, the mean errors are
0.26 ‰ (δ2H) and 0.093 ‰
(δ18O) in 2013, and 0.37 ‰ (δ2H) and
0.13 ‰ (δ18O) in 2014. On average, the scatter error
is larger in 2014, although during the periods of best instrumental
performance, σscatter is lower than at any point in 2013.
The instrument performance was highly variable in 2014, much more so than
2013. The standard deviations of σscatter are
0.11 ‰ (δ2H) and 0.045 ‰
(δ18O) in 2014, as opposed to 0.026 ‰
(δ2H) and 0.012 ‰ (δ18O) in 2013.
Total uncertainty vs. depth, along with each individual error factor
in per mil. (a): δ2H.
(b): δ18O. There is a noticeable discontinuity at
500 m; the melting campaign was paused at 500 m in 2013, and melting was
resumed in 2014 with a modified set-up. The reduced calibration error in 2014
is responsible for the large step down in total error.
Among the three error factors, the general calibration error is the largest
contributor to the total error in 2013: σcalib(δ2H)=0.80‰ and σcalib(δ18O)=0.12‰. However, this error is
greatly reduced for 2014: σcalib(δ2H)=0.22‰ and σcalib(δ18O)=0.078‰, reflecting the improved measurement of the assigned
values of the standards. We were not able to measure the
standards against VSMOW-SLAP using the 2013 CFA set-up (time constraints did
not permit us to conduct additional measurements after the 2013 campaign
concluded, as our instrument was sent to the manufacturer for modification),
which would provide a better comparison between measured and assigned values,
following from the principle of
identical treatment (Werner and
Brand, 2001). The 2013 σcalib is thus likely to be a very
conservative estimate of the error. In addition, the assigned value of WS1 is
well outside the range of the RICE ice core and is much greater than the RICE
and ITASE standards, and thus RICE and ITASE could be considered poor choices
for calibrating WS1. The two calibration standards, RICE and ITASE, were
chosen to be similar in isotopic value to the ice core samples being measured
(Werner and Brand, 2001), with the quality-control standard being of
secondary concern. Ideally, we would use a quality-control standard that
falls within the range of the values of our two calibration standards. While
we could have used WS1 and ITASE as our calibration standards and RICE as a
quality-control, WS1 is less appropriate than RICE for calibrating the range
of isotopic values found in the ice core. Testing the sensitivity of the
calibration error to our selection of quality-control standards,
however, is outside the scope of
this paper.
The scatter error dominates the total error in 2014. The magnitude of this
error was highly variable from day to day, and thus the total error also
varied considerably. There were some periods in which the instrument
performed exceptionally well. During these periods, total errors
were as low as 0.3 ‰
(δ2H) and 0.1 ‰ (δ18O). These
represent the high end of system capability. However, for much of the 2014
melting campaign the total errors were closer to the average of
0.44 ‰ (δ2H) and 0.19 ‰
(δ18O).
There are three main possible reasons for the large variations in performance
in 2014. They are (1) response to breaks in the ice and associated bubbles;
(2) performance degradation due to unexpected levels of drill fluid in the
melt stream (a mixture of Estisol-240 and Coasol was used to keep the drill
hole open; although all pieces of ice were thoroughly cleaned before melting,
some contamination occurred through existing microfractures in the ice);
and (3) leaks or valve degradation in the laser spectrometer, which operates
under vacuum. There were significantly more performance issues in 2014. In
addition to the different set-up and gradual build-up of drill fluid in the
instruments over time, the ice itself was of poorer quality at lower depths
(especially in the brittle ice zone at depths below 500 m; Pyne et al.,
2018), containing more breaks that caused interruptions in the CFA
measurements and possible drill fluid contamination. Although we have only
anecdotal evidence, the more frequent stopping and restarting of the system
in 2014 seemed to introduce more noise into the measurements.
Because the campaign was conducted to operate many measurement systems
simultaneously, as is characteristic of ice core CFA campaigns, it was
typically not possible to conduct comprehensive performance tests and
systematic evaluations during the 1 day of downtime in each week-long,
7-day cycle. As a result, the precise sources of performance
deterioration were difficult to isolate. Our method for calculating
uncertainty is designed to capture the changing day-to-day conditions
resulting from a range of system variations and performance issues, even if
it is not possible to pinpoint the exact cause.
Summary and conclusions
We have described a systematic approach to the data processing and
calibration for the RICE CFA stable water isotope data set and presented a
novel methodology to calculate uncertainty estimates for each data point
derived from three factors: Allan deviation, scatter, and calibration
accuracy. The mean total errors for
all data points are 0.74 ‰
(δ2H) and 0.21 ‰ (δ18O). Mean total
errors in 2013
are 0.85 ‰
(δ2H) and 0.22 ‰ (δ18O) and in 2014
they are 0.44 ‰
(δ2H) and 0.19 ‰ (δ18O). This represents a significant achievement in the
precision of high-resolution CFA water isotope measurements, and
documentation of uncertainty calculations for isotope analyses in a
continuous measurement campaign comprising multiple complex measurement
systems.
The isotope analyser system performed exceptionally well during some time
intervals in 2014, demonstrating high capability, even though this was not
sustained. The variability in quality could be due to poor ice quality,
interruptions in the CFA measurements, the build-up of residual drill fluid
in the instrument, and/or leaks and valve degradation. Most likely, it was a
combination of all of these factors.
The more accurate measurement of our laboratory water standards for the 2014
melting campaign enabled us to reduce the uncertainty considerably for the
data at depths greater than 500 m. More generally, a reduction in the
uncertainty in the system could be achieved through more rapid calibration
cycles, enabling both the insertion of calibration during stacks and more
rapid troubleshooting to isolate causes of degraded performance.
Our uncertainty estimates do not take into account the additional
uncertainty introduced from the smoothing of the data during the melting
procedure and the measurement response time. This is an important issue,
particularly for deep, older ice, where annual layers are greatly compressed
and measurement resolution is crucial to the ability to date the core
accurately. The degree of mixing in the melting procedure itself can be
controlled through the melting rate and the diameter of tubing leading from
the melter to the CFA instruments. Our system was designed primarily for
high throughput and multiple, simultaneous measurements. However, these
parameters can be adjusted to increase resolution for older ice (the very
bottom of the RICE core has yet to be measured).
The volume of the evaporation chamber is usually a limiting factor in the
temporal resolution and response time of the IWA and can introduce a
significant amount of uncertainty. While we reduced the volume of the chamber
from the manufacturer's default of 1.1 L to 40 mL (Emanuelsson et al.,
2015), there is still a finite amount of time required to fill and replace the chamber
with new sample. We estimate that our depth resolution was between
1.0 and 3.0 cm (Pyne et al., 2018). A more comprehensive evaluation of the
effect of the mixing inherent in the melting and measurement procedure on the
overall uncertainty is beyond the scope of this paper but is an important
consideration for future work.
The RICE CFA stable isotope data are currently embargoed
but will be made available in a forthcoming publication. Data for the past
2700 years are available as a supplement to Bertler et al. (2018)
(10.15.94/PANGAEA.880396) and at
http://www.rice.aq/data-collection.html (last access: 8 August 2018).
The supplement related to this article is available online at: https://doi.org/10.5194/amt-11-4725-2018-supplement.
EK and TB designed and calculated the
CFA stable isotope uncertainty estimates. NB, TB and DE designed the CFA
set-up and took the measurements. EK and SC processed the CFA data. AP
took the laboratory water standard measurements. All authors contributed
to the writing of this paper.
The authors declare that they have no conflict of
interest.
Acknowledgements
Funding for this project was provided by the New Zealand Ministry of
Business, Innovation, and Employment grants through Victoria University of
Wellington (RDF-VUW-1103, 15-VUW-131), GNS Science (540GCT32, 540GCT12),
and Antarctica New Zealand (K049). We are indebted to everyone from the 2013
and 2014 RICE core processing teams. We would like to thank the Mechanical
and Electronic Workshops of GNS Science for technical support during the RICE
core progressing campaigns. This work is a contribution to the Roosevelt
Island Climate Evolution (RICE) programme, funded by national contributions
from New Zealand, Australia, Denmark, Germany, Italy, China, Sweden, UK and
USA. The main logistic support was provided by Antarctica New Zealand and the
US Antarctic Program. Edited by: Frank
Keppler
Reviewed by: three anonymous referees
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