Polar ice sheets store deposited precipitation as stratified ice layers thousands of years back in time. This precipitation consists of stable water isotopes (δ18O, δD) that work as a direct proxy of the relative depletion of a water vapor mass in its transport from the evaporation source to the site where condensation takes place . This traceability manifests as a correlation between δ18O and the temperature in the cloud at the time of condensation . Thus, a relationship between δ18O and temperature is preserved in annual layers of precipitation on an ice cap. Hence, by drilling ice cores at polar sites such as Antarctica and Greenland, it is possible to access past temperatures imprinted on the δ18O signal. Several studies have examined the relation between temperature and ice core δ18O, and its linear or quadratic relationship has regularly been used as a transfer function to infer past temperature . While it is evident that δ18O and temperature covary, the δ18O signal is also affected by changes in sea ice and atmospheric circulation . Changes in regional quasi-stationary modes of climate variability such as the North Atlantic Oscillation can modulate global atmospheric circulation patterns (e.g., precipitation patterns) which affect the δ18O variability. Additionally, changes in sea ice extent affect the local moisture conditions, which particularly influence the coastal precipitated δ18O variability . Such variations have implications for a simple regression-based reconstruction of temperature from δ18O as the variability patterns between the ice core isotope signal and the oscillation modes and sea ice extent can have varied in strength back in time. Furthermore, in studies that analyze the relationship between polar precipitated δ18O and temperature, the temperature record is often substantially shorter than the δ18O series. While this is inevitable when performing temperature reconstructions, utilizing a short temperature record complicates the possibility of verifying whether the estimated δ18O–temperature relation is stable with time.

The aim of this study is to examine how much of the δ18O variability (1801–2014 CE) from a stack of ice cores drilled on the Renland peninsula, eastern Greenland, can be attributed to temperature variations (map in Fig. ). In the analysis, seasonally averaged δ18O time series have been compared with regional temperatures through instrumental temperature records from the coasts of east Greenland (1895–2014 CE) and Iceland (1830–2014 CE) and the regional atmospheric climate model HIRHAM5 2 m temperature output (1980–2014 CE). The δ18O signal is divided into its seasonal components as it potentially improves the reconstruction of variability in weather regimes and past temperatures . As Renland is located on the coast, its hydrological conditions are connected with the sea ice that is transported south annually along the coast of east Greenland. A relatively small loss in regional sea ice extent (≈10% or less) has previously been found to influence local Greenland moisture source water vapor, which is traceable in the corresponding ice core deuterium excess values . The deuterium excess signal (dxs=δD-8⋅δ18O; ) contains information about the kinetic fractionation occurring when moisture evaporates from the ocean surface and the ice core dxs has been found to correlate with relative humidity and sea surface temperature at the source region . Thus, besides investigating the regional δ18O–temperature relationship, this study examines if changes in the Arctic sea ice extent can be detected in the Renland stable water isotopes.

The Renland ice cap has an area of 1200 km2 with an average ice thickness of a few hundred meters. It is separated from the main Greenlandic ice sheet as a small peninsula on the east coast of Greenland (map in Fig. ). The ice cap experiences a high annual accumulation rate of around 0.47 m ice yr-1 with an annual surface temperature of -18 ∘C. Renland has probably never been overridden by the inland ice as it is surrounded by deep branches of the Scoresbysund Fjord which effectively drains the inland ice . Additionally, the small width of the ice cap, which is constrained by the surrounding mountains, prevents the ice elevation from significantly increasing from present-day height. As a result, the ice cap has not experienced any ice sheet elevation changes for the past 8000 years (except for slight uplift due to isostatic rebound) . This implies that lapse-rate-controlled temperature variations resulting from a varying ice sheet thickness will be negligible.

This study utilizes three ice cores drilled on Renland in the analyses (Table ). Two cores were drilled next to each other in the year 1988 (main (M) and shallow (S) cores), while the third was drilled approximately 2 km away in 2015 as part of the REnland ice CAP project (RECAP). The 1988 M and RECAP cores extend over the past 120 ka, while the 1988 S core only covers the time back to the year 1801. Despite two cores covering the past interglacial and glacial period, the study focuses on the period 1801–2014 CE where three overlapping ice core records and instrumental temperature recordings are available. Moreover, the separation of the summer and winter signals is better facilitated when the annual layers are not obliterated due to diffusion and ice thinning.

The records from 1988 were measured with an isotope ratio mass spectroscopy (IRMS) with a discrete resolution of 5.0 cm, while the RECAP core was measured using cavity ringdown spectroscopy (Picarro L2130) on a continuous flow analysis (CFA) system with a nominal resolution of 0.5 cm. For the RECAP core, the years 2011–2014 are covered by the snow pit core A6 drilled next to the drill site. The A6 core was measured discretely with a sample size of 5.0 cm on a Picarro L2130. This was done as the porous snow in the upper firn column easily inhibits a stable measurement flow in the CFA analysis, which complicates precise water isotope measurements.

Firn diffusion dampens the annual oscillations in the δ18O data. This takes place while firn (snow that survived a season) is transformed into ice in the top 60–80 m of the ice sheet. During this densification process, air in the open porous firn is interconnnected, which enables the stable water isotopes in the firn air to mix with the snow grains . This molecular diffusion process makes the δ18O signal become increasingly more smooth with depth until pore close-off. The firn diffusion of stable water isotopes imposes two challenges on the analysis presented in this study. First, the diffusion of the annual oscillations creates artificial trends in summer and winter season time series of δ18O . Secondly, it introduces a bias when comparing the ice cores drilled in 1988 with the ice core drilled in 2015. For instance, the δ18O signal representing the year 1987 has only experienced 1 year of firn diffusion in the 1988 ice cores, while it has experienced 28 years of firn diffusion in the 2015 core. The δ18O signal for overlapping years will therefore be more attenuated in the 2015 core.

As this study compares the seasonally averaged δ18O signals of three ice cores drilled in different years, it is necessary to ensure that each δ18O record has the same firn diffusive properties with depth. This is typically achieved by correcting each δ18O record such that the effect of increasing smoothing with depth is removed by deconvolving the measured δ18O signal to restore the originally deposited signal. However, Renland frequently experiences summer melting which causes steep isotopic gradients in the firn. Such high-frequency gradients complicate a deconvolution of the measured δ18O signal . Instead, this study forward-diffuses the three δ18O records with depth such that each δ18O series has been influenced by the same amount of firn diffusion. Diffusion of stable water isotopes is typically described by the diffusion length (σ), which is the average vertical displacement of a water molecule (units in meters). Thus, the δ18O series are forward-diffused (δ18Ofd) such that each record has the same σ with depth. Despite such a smoothing procedure slightly mixing the summer and winter signals, a distinction of the seasonal components is still possible due to Renland's thick annual layers greatly exceeding the diffusion length.

The procedure below outlines in three steps how this was done separately for the 2015, 1988 M and 1988 S cores.

Step 1. First, the amount of diffusion that the measured δ18O signal already has experienced with depth is computed through the diffusion length's density dependence (for origin, see ): 1σ2ρ=1ρ2∫ρoρ2ρ2dρdt-1Dρdρ, where D(ρ) is the firn diffusivity and dρ/dt is the densification rate. This study uses the firn diffusivity parameterization of (described in Appendix ) that employs the site-dependent parameters of temperature (-18∘C), accumulation rate (0.47 m ice yr-1), surface pressure (0.75 atm) and density. Density is here modeled with depth by fitting a densification model to density measurements from the drill sites. From Eq. (), it is possible to calculate the diffusion length that each layer has experienced (σ2(ρ)) (Fig. a).

Step 2. Eq. () can be used to calculate the auxiliary diffusion needed to transform a δ18O record into having a uniform diffusion length independent of depth. An auxiliary diffusion (σ2(ρ)aux) is calculated as the difference between the final diffusion length at the pore close-off density (σ2(ρpc=804.3 kg m-3)) and the diffusion length at a given layer in meters of ice-equivalent depth: 2σ2(ρ)aux=ρpcρi2σ2(ρpc)-ρ(z)ρi2σ2(ρ)⋅ρiρ(z)2, where the fraction ρi/ρ(z) ultimately is multiplied onto the auxiliary diffusion length in order to transform the σ2(ρ)aux from representing ice-equivalent depth to density-equivalent depth (as the annual oscillations are squeezed during firn compaction). Using Eq. (), an auxiliary diffusion profile with respect to density (and thus depth) is calculated for an ice core (Fig. a).

Step 3. Forward diffusion is then simulated through a convolution of the measured data (δ18Omeas) with a Gaussian filter (G) with a standard deviation equal the auxiliary diffusion length as this is mathematically equivalent to firn diffusion : 3δ18Ofdz=δ18Omeas∗G, where 4Gz=1σaux2πe-z2/2σaux2. As the auxiliary diffusion length decreases with depth, the width of the Gaussian filter changes accordingly. Thus, the convolution (using the σaux for the corresponding depth) is applied to a moving 2 m section which is shifted in small steps equal to the sampling interval. For each convolved data section, only the midpoint of the sliding window is retained as the new forward-diffused δ18Ofd value. In order to avoid tail problems when diffusing the top 2 m measurements, the δ18Omeas data were extended by using its prediction filter coefficients estimated from a maximum entropy method algorithm by . This assumes that the extended series has the same spectral properties as the original series. After applying this smoothing routine to the entire record, a δ18Ofd series with constant σ is obtained. A comparison between δ18Ofd and δ18Omeas is shown in Fig. .

It is important to ensure that the chronologies of the three ice cores are synchronous before comparing the δ18O variability. The two cores drilled in 1988 were manually dated by counting the summer maxima and winter minima in the δ18O series and verified by identifying signals of volcanic eruptions in the electrical conductivity measurements . For the 2015 RECAP core, the period 1801–2007 was dated with the annual layer algorithm (StratiCounter) presented in and the years 2007–2014 were manually counted similar to the 1988 cores (the RECAP chronology is presented in ). The annual layer algorithm uses signals in the ice core that all have annual oscillations or peaks such as the chemical impurities (Na+, Ca, SO42- and NH4+), electrical conductivity and stable water isotopes. Even though the model automatically counts years, the chronology is still restricted by the same volcanic eruptions as in the 1988 cores. The model marks a year when Na+ has a peak, which indicates winter. Na+ is a result of the transport of salt from the ocean, and it peaks during winter due to the strong winds during the fall. As the timing of this winter peak might not be similar to the timing of the δ18O series' winter minima (used for the 1988 cores), this study has tuned the RECAP dating presented slightly. For each year, this is done by tuning the timing of the summer and winter in the dated RECAP record to match the maximum and minimum of the δ18O series. The chronology is only shifted a maximum of a few months, and it is only changed within a given year. This ensures that the modified dating profile remains consistent with the original chronology, while it facilitates an optimal comparison between the manually dated and the automatically dated stable water isotopes profiles.

In order to analyze the seasonal signals of the δ18O series, we need to distinguish between snow deposited during summer and winter. Under the assumption that δ18O and temperature extremes in the Greenland region occur simultaneously, found it best to define the summer and winter seasons such that they each contain 50 % of the annual accumulation. Besides maximizing the amount of utilized data, this definition ensures that the winter and summer signals contain no overlapping data. This study has therefore defined the summer and winter seasons similarly to . The summer, winter and annually averaged δ18O data used in this study are thus seasonal or annual averages of the forward-diffused δ18O series.

The three ice cores' δ18O data as representative of the isotope hydrology on Renland are first evaluated by calculating Pearson correlation coefficients and signal-to-noise variance ratios (SNRs) on the forward-diffused δ18O records in the overlapping period 1801–1987. The correlation coefficient is a metric that describes the linear relation between two signals and it has been calculated for different combinations of the presented ice cores (Table ). For all correlation coefficient calculations throughout this study, the level of significance is estimated based on a Monte Carlo routine described in Appendix . From the results displayed in Table , it is evident that the lowest correlation coefficients are found for the winter-averaged data with values ranging from 0.60 to 0.78, while the summer- and annually averaged signals have higher values ranging from approximately 0.64 to 0.84. The high correlation coefficients indicate that there is a strong linear relationship between the δ18O records. This is further illustrated by the visual covariation of the annually averaged δ18O records in Fig. . In all instances, the highest correlations are found when correlating the two ice cores drilled in 1988. This might be attributed to the use of a similar dating method and their close proximity. Nonetheless, all the presented ice cores correlated significantly during the 1801–1987 period.

The δ18O variability can be further analyzed by examining the mean single series SNR which provides an insight into the amount of signal and noise in the δ18O series . Noise can originate from depositional effects such as wind shuffling of snow and melt layers and from dating uncertainties (±1 year) in between the three cores. By averaging n (3) overlapping ice core data records, the mean single series SNR is calculated by comparing the variance of an averaged record (VARs) with the mean of the variances (VAR‾) for the n individual records : 5SNR=VARs-VAR‾nVAR‾-VARs. Alternatively, a recent study by introduced a new way of calculating timescale-dependent SNR values, which provides a basis for interpreting noise across timescales. The SNR results are shown in Table . Similar to the high correlation, it is evident that merging the two 1988 records results in the highest SNR values. Moreover, the summer-averaged signal has a higher SNR compared to the winter-averaged signal, which probably is a consequence of winters having more windy conditions that generate the redeposition of snow. A similar pattern has previously been found for the seasonal isotopes of GRIP ice core (n=5; SNR summer: 0.70; winter: 0.51), Dye-3 ice core (n=2; SNR summer: 1.73; winter: 1.56) and NEEM ice core (n=4; SNR summer: 1.28; winter: 0.64) (map in Fig. ) . This comparison also shows that the SNR values of the three Renland ice cores are high compared to GRIP, Dye-3 and NEEM which likely can be attributed to a combination of a high accumulation rate and a good cross-dating between the compared cores.

From this analysis, the study can comment on two things. First, the two 1988 cores have the most robust common signal of all the tested combinations. As this was for two adjacently drilled ice cores, utilizing all three records still results in a larger spatial atmospheric representativeness of the region. Secondly, the high SNR and correlation coefficients imply that the chronologies from the annual layer detection algorithm and the manual counting are consistent. This has implications for future ice core science as manual layer counting can be a slow and inefficient procedure. Thus, manual counting can effectively be replaced with the StratiCounter software by for ice cores, where several datasets that contain observable annual peaks or oscillations are available.

The high combined SNR values and correlation coefficients indicate that it is beneficial to combine the time series into a stacked δ18O record. We choose to employ all three ice cores as that increases the spatial representativeness of δ18O, while it provides water isotopic variability for the years 1988–2014. A stacked record is typically created by averaging the time series but the time span 1801–2014 consists of an inhomogeneous amount of data records as only the RECAP core contains data in the 1988–2014 period, while it also has a gap between 1954 and 1961 due to missing ice samples. Thus, it is important to implement a variance correction in order to avoid bias issues when averaging time series with nonuniform length . This variance correction (c) can be expressed directly through the SNR values in Table  and the number of records (m) used in the averaging for the given year (derivation can be found in ): 6c=SNRSNR+1m. Before stacking, the three time series are standardized based on the period of overlap (1801–1987) (δ18OSD has mean = 0 and standard deviation = 1). An average δ18Oavr value is then calculated by multiplying c onto the mean δ18OSD for each year: 7δ18Oavr=c⋅1m∑i=1mδ18OSDi. The amplitude and variability of the original δ18O series are then restored by using the average variance (VAR‾) and the average (δ18O‾) of the three time series (from the period where the time series were standardized): 8δ18Ostack=δ18Oavr⋅VAR‾+δ18O‾.

Figure  shows the summer, winter and annual δ18Ostack series for the period 1801–2014. In the figure, a 5-year moving average has been applied to the stacked records in order to filter out any remaining high-frequency noise variability. From the figure, it is evident that the summer-averaged signal is less depleted than the annual and winter-averaged signals. Moreover, the summer signal has the largest trend in δ18O with an increase of 0.54 ‰ per century, while the winter and annually averaged data show lower increases of, respectively, 0.24 ‰ per century and 0.37 ‰ per century. The amount of variability that correlates with temperature will be examined in Sect. .

A strengthening and weakening of, respectively, the low-pressure system over Iceland and high-pressure system over the Azores control both the direction and strength of westerly winds and storm tracks over the North Atlantic. Fluctuations in the difference in atmospheric pressure at sea level between Iceland and the Azores is described by the North Atlantic Oscillation (NAO). Changes in the NAO has previously been found to have an imprint on precipitation in western Greenland . Correspondingly, the winter isotope signal of west and south Greenland ice cores have previously been found to anticorrelate with the atmospheric circulation changes from the NAO . Despite showing that ice cores drilled on the Greenland east coast revealed no connection with the NAO, this study examines potential correlation in order to determine if changes in the NAO can be linked to the varying δ18O–temperature relationship.

While the NAO is best described through a principal component analysis of multiple sea level pressure records or gridded datasets of sea level pressure in the North Atlantic region, this study uses an approximation where the NAO index is based on pressure observations only near the two centers of action of the surface pressure field (the Azores and Iberian Peninsula and Iceland). Such an approximation was carried out by , who reconstructed the NAO variation back to 1821 (and have since extended it up to present time). This study uses a slightly modified version of this NAO index by , who improved the NAO record in the period 1821–1856 by using extra pressure series.

The connection between the NAO index and seasonally (and annually) averaged δ18O stacks is examined by estimating their correlation. Correlation coefficients have been calculated on 5-year moving averages of the NAO and δ18O stacks and shown in Table  (the annual NAO record is plotted in Fig. ). The level of significance is estimated based on a Monte Carlo routine described in Appendix . In the complete 1821–2014 period, the summer, winter and annually averaged NAO and δ18O data are uncorrelated with coefficients of 0.01, -0.05 and 0.02, respectively. If we instead examine the time before and after the δ18O–temperature correlation terminated (the year 1909), the summer and annually averaged data yield positive correlations of 0.29 and 0.30 between 1821 and 1909, while the winter and annually averaged data yield negative correlations of -0.25 and -0.22 between 1910 and 2014. Thus, there is a varying relation between the NAO and the δ18O data, and the weak δ18O–NAO anticorrelation coincides with a covarying δ18O–temperature relation. However, the weak correlations during 1821–1909 imply that the NAO only can account for around 8 %–9 % of the corresponding δ18O variability. It therefore seems unlikely that strengthening and weakening of the NAO causes changes in the δ18O–temperature relation.

The analysis showed no constant linear coupling between the Renland δ18O signal and the advance and retreat of the Greenland Sea's SIL. However, the SIL record documented a great sea ice extent in the Greenland Sea prior to the 1910s. Hence, despite the two datasets not being linearly connected, a large sea ice extent still coincides with the weakened δ18O–temperature correlation. Furthermore, the analysis showed that fluctuations in Fram Strait SIE could be connected with the regional δ18O–temperature relationship. Despite the apparent connection, this study has not proved any causality between the δ18O–temperature relation and the SIE. Still, a proposed hypothesis for this connection is that the fluctuating SIE conditions during cold years impose changes in the location of the local moisture sources, which suppress the imprint of Iceland temperature variability in Renland δ18O. It is likely that this connection has its strongest impact on ice cores drilled in the coastal regions near sea ice as found that the δ18O records of Greenlandic ice cores drilled in south and central Greenland correlated well with a southwest Greenland instrumental temperature series in the period 1785–1980 . With reference to this temperature series, Fig.  shows that these temperatures do not have a stable linear covariation with the Renland δ18O stack (winter averages are here chosen as they constitute the longest and most homogeneous record). Besides Renland obviously being located far away from the southwest Greenland instrumental temperature stations, this contrariety might result from the isotope distillation process being more manifest as a temperature variability in the δ18O signal when the precipitation has had a longer distillation path and has risen in more altitude than that of the coastal region, further depleting the δ18O signal. In order to evaluate this hypothesis, more studies using isotope-enabled modeling are needed. The impact of changes in sea ice on the Arctic δ18O precipitation has previously been investigated by , who found that the δ18O precipitation on Greenland only responded to perturbations of the Baffin Bay sea ice coverage. However, they used a horizontal resolution of ∼1.4∘×1.4∘ which barely resolved the Renland Ice Cap of ∼1200 km2. Thus, a further examination of how changes in sea ice extent is connected with the coastal Greenlandic precipitation on a higher spatial resolution grid is essential in order to evaluate this hypothesis.

Alternatively, if the seasonal distribution of precipitation on Renland changed significantly prior to the 1910s, it could lead to a change in the relationship between the δ18O signals and temperature. While the dating resolution does not permit a direct assessment of such changes, we do observe that the difference between the summer and winter δ18O have in fact changed over the 1801–2014 period (Fig. ).

Moreover, while this study found that the Renland δ18O signal anticorrelated with variations in the sea ice extent outside west Greenland (Sect. ), a similar pattern was found with the HIRHAM5 temperature correlations presented in Sect. . It is therefore likely that the connection represents a reduced sea ice coverage due to increasing temperatures rather than an actual interconnection between Renland δ18O and Baffin Bay sea ice.

This study found that by quantifying the mean signal-to-noise variance ratios, a robust seasonal δ18O signal (1801–2014) could be extracted by stacking three ice cores from Renland. This δ18O stack was correlated with instrumental temperature records from east Greenland and Iceland and with the HIRHAM5 2 m temperature output. Results showed that there were high correlations between δ18O and regional temperatures on both a seasonal and annual scale between 1910 and 2014. A similar anticorrelation was found between the δ18O stack and the amount of sea ice exported through Fram Strait. However, both correlations diminished in the 1830–1909 period. The results indicated that the varying regional temperature variability in the δ18O signal could not be explained by the North Atlantic Oscillation. Instead, the linear δ18O–temperature relation depended on whether the temperatures were warmer or colder than the temperature anomaly. Warm years were associated with a high correlation and accompanied by less sea ice transported south along the coast, while cold years were associated with zero correlation that accompanied a fluctuating amount of sea ice along the coast. These results implied that changes in the extent of open water outside Renland might affect the local moisture conditions. Hence, greater sea ice flux along the coast of Greenland may suppress the Iceland temperature signature in the δ18O signal; however, this was not confirmed by correlations between dxs and sea surface temperature in the Arctic region. Thus, more high-resolution isotope-enabled modeling focused on the effect of Arctic sea ice on coastal precipitation are needed in order to quantify this process.

These results have implications for ice core temperature reconstructions based on the linear relationship between δ18O variability and local temperature records. For Renland, the linear δ18O–temperature relationship was unstable with time which implied that the annual-to-decadal variability of δ18O measured in an ice core could not be directly attributed to temperature variability. Similar conditions might apply for other ice cores drilled in the vicinity of a fluctuating sea ice cover. This reinforces the interpretation that δ18O is an integrated signal of all the hydrological activity that a vapor mass experiences en route from the evaporation at the source to its condensation at the drill site.