Seasonal reconstructions coupling ice core data and an isotope enabled climate model – implications of seasonality, climate modes and selection of proxy data

enabled climate model – implications of seasonality, climate modes and selection of proxy data Jesper Sjolte1, Florian Adolphi1,3, Bo M. Vinther4, Raimund Muscheler1, Christophe Sturm2, Martin Werner5, and Gerrit Lohmann5 1Department of Geology – Quaternary Science, Lund University, Sölvegatan 12, 223 62, Lund, Sweden 2Swedish Meteorological and Hydrological Institute, 60176 Norrköping, Sweden 3Climate and Environmental Physics & Oeschger Centre for Climate Change Research, Physics Institute, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland 4Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Denmark 5Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Sciences, Bussestr. 24, 27515 Bremerhaven, Germany Correspondence: Jesper Sjolte (jesper.sjolte@geol.lu.se)

( Figure 1) for each year (t) using Eq. 1 ii) sort the model simulation by comparing the isotope patterns each year of the model simulation to the isotope patterns each year of the ice core data iii) define the best matching model years as ensemble member one, the second best matching years as ensemble member two, and-so-on, and test how many ensemble members to retain (p < 0.01) by calculating the Chi-square statistic between the modeled and the ice core PCs iv) extract the climate field variables from the selected model ensemble and calculate the ensemble mean, which comprises the climate reconstruction. (P C(k, t ′ ) model − P C(k, t) icecore ) 2 (1) The number of ensemble members (see Table 2) depends on the degrees of freedom, i.e., the length of the reconstruction, and how many closely matched model analogues that are found.
As outlined in the introduction the definition of the seasons or year is an important parameter for the reconstruction. This 135 applies both in terms of the seasonality of the proxy data and the target season of the reconstruction. Following the study of Vinther et al. (2010) we will use the definitions of summer as May-Oct (sum50), winter as Nov-Apr (win50), and winter centered annual mean Aug-Jul (win100) for the ice core data. These definitions will also be applied to the target seasons of the reconstructions, as well as the widely used definitions of summer (JJA) and winter (DJF). We investigate the seasonal and annual variability using these different definitions with two data sets for short 19 ice cores) and long 140 8 ice cores) reconstructions, resulting in a total of 12 reconstructions, where one for DJF covering 1241-1970 was published by Sjolte et al. (2018) (see Table 2).

Constraining summer reconstructions using tree-ring data
For the summer reconstructions also using tree-ring data we sort the 39 existing ensemble members based on the ice core 145 selection, using a similar Chi-square fit as for the ice core data. Then we evaluate the time series of normalized modeled temperature against the normalized tree-ring data. The fit is done using the JJA temperature from the model, which are the best months with respect to seasonal sensitivity for these 8 tree-ring records (Wilson et al., 2016). In a next step we test the ensemble mean temperature reconstruction against the time series of the tree-ring data at each site, by calculating the correlation to the tree-ring data while increasing the number of ensemble members from 1 to 39 (Supplementary Figure S2). Although a Chi-square test of the fit of the reconstructed temperature shows that including 24 ensemble members provides a good fit (p < 0.01), the correlation decreases quite rapidly when including more ensemble members and we choose to include only 20.
With this ensemble we capture the variability of the tree-ring data relatively well for the whole period of the reconstruction (Supplementary Figure S3).
In this study we follow the convention of using the term PCs for the time series of the main modes of variability, while using 155 the term EOFs for the spatial patterns of the modes. The method of Ebisuzaki (1997) is used to calculate the significance when correlating filtered time series in order to take auto-correlation into account.

The seasonal variability in observations and when combining proxy data and model output
In the introduction we mentioned seasonality, definition of seasons and shifts in circulation patterns as potential limiting factors 160 for the skill of climate field reconstructions. In general, seasonal dependency on climate variables, temporal resolution as well as the precision of the chronology of proxy records sets a limit on the temporal resolution of climate field reconstructions.
Seasonal resolution is likely the the highest possible resolution which can be attained due to these different factors. A key factor in how well seasonal climate reconstructions can represent climate itself, is the auto-correlation structure of atmospheric variability. This can be illustrated by investigating the monthly auto-correlation during the year of the 1st leading mode of 165 sea level pressure in the North Atlantic region, the NAO. We found that, for example, the 2nd and 3rd leading modes are too dissimilar between summer, autumn, winter and spring to allow a meaningful study of the monthly auto-correlation of these modes, as they simply represent different teleconnection patterns during each season. Figure 2 shows the monthly autocorrelation of each month of the PC-based NAO calculated from the 20CR. These figures show that during the cold season the NAO has the weakest auto-correlation with other months, as well as weaker year-to-year auto-correlation compared to summer.

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While the lower auto-correlation during winter shows stochastic nature of the variability, it is also during winter that the NAO variability is the most vigorous. Thus, the portion of a given climate signal that can be reconstructed is a balance of what is recorded in the proxy at a certain resolution, as well as the strength and auto-correlation of the signal sampled at this resolution.
It is noteworthy that Figure 2 also illustrates that targeting the calendar year in a reconstruction (or any sort of analysis) splits up the variability mid winter and mixes the variability of two consecutive winters that have little variability in common. This 175 is the motivation for using the definition of winter centered annual mean for the annual data in this study. Vinther et al. (2010) tested the ice core data used in this study using correlation with observed temperature, leading to the division of the in seasons using the definition of sum50, win50 and win100 as outlined in Section 3. Due to the changes in the patterns and variability of the circulation modes from summer to winter we furthermore test the seasonality in terms of circulation modes. We do this by performing monthly reconstructions for pressure and evaluating the resulting main modes 180 of circulation against the modes of the 20CR. This is done using the same method as for the seasonal reconstructions, but only picking individual months from the matching year of the model simulation. We do not suggest that it is feasible to reconstruct climate on monthly timescales using seasonal ice core data. This exercise is purely for testing purposes. The combinations of these influences. The difference in the reconstructions using 8 ice cores and 19 ice cores, respectively, is mainly seen for win100, where more months across the year show significant skill when using more ice cores in the reconstruction.
Furthermore, the monthly skill for the win100 data set indicate that it is feasible to reconstruct the winter circulation (e.g. DJF).
This test suggests that in order to get the highest average skill possible for all modes during winter the reconstruction should target DJF, while for summer the full span of the season (May-Oct) is likely better, also taking into account the higher monthly 195 auto-correlation during the warm season. The EOF patterns of surface pressure will be discussed further in Section 4.2.2.

Evaluation of reconstructions
In the following sections we evaluate and compare the reconstructions using different methods. We start with point-by-point correlation maps for the North Atlantic sector of the reconstructions to 20CR SLP and T2m as well as the COBE SSTs. This is a general evaluation in terms of spatial coverage and skill of the reconstructions. We also include a comparison to the longest 200 instrumental records of temperature from Greenland and Iceland. Next we evaluate the skill of the reconstructions in terms of atmospheric circulation modes. In the final part of the evaluation we investigate if the main patterns of North Atlantic SSTs and their variability can be reconstructed using the method of this study. We would like to emphasize that none of these reconstructions have been calibrated to observations, but that the model provides us directly with the physical variables of SLP and T2m for the years where modeled and measured δ 18 O patterns match. The evaluation of these reconstructions are thus 205 done using completely independent data sets.

Reconstructed temperature and sea level pressure
Investigating the results for correlations and the spatial patterns of skill for SLP, T2m and SSTs reveals a complex interplay of factors influencing the reconstructions for different seasons, as well as how different definition of seasons influence the skill.
Reconstructions for the summer season show the least skill, but perform better using the extended definition of the target season 210 (May-Oct) ( Figure 4) rather than JJA ( Figure 3). The summer reconstruction also appears to benefit the most from including 19 ice cores rather than 8 (Table 3). Including more cores and using the extended season likely reduces noise in the reconstruction.
Using the extended season also smooths out the variability of the 20CR data, which can partly account for the higher skill of the short sum50 reconstruction for summer. The reconstructions for winter shows the highest skill of the reconstructions, in-line with the findings of Vinther et al. (2010), that δ 18 O is found to be a more efficient climate proxy during winter (Sjolte et al., large signal-to-noise ratio in δ 18 O records with respect to their ability to record circulation changes. All of the these factors contribute to better reconstructions for winter compared to summer both in terms of spatial skill and strength of correlation with 20CR. As opposed to summer, the winter reconstructions for DJF performs better, rather than the extended season Nov-Apr. This is probably due to the migration of circulation patters and low auto-correlation of atmospheric circulation during winter 220 as discussed in Section 4.1.
One of the questions of this study is about the use of annual data for reconstructions of climate and atmospheric circulation.
For the reconstructions targeting the winter centered annual mean (win100) the skill and patterns of correlation are reminiscent to that of the winter reconstructions, although clearly with less areal coverage of significant correlation for SLP. We interpret this as being due the migration of the circulation patterns with the seasons, as discussed above. However, for SSTs the win100 225 reconstruction shows the highest spatial skill of all the reconstructions, including better capturing low latitude variability, with the correlation pattern being reminiscent of the spatial pattern of Atlantic Multi-decadal Oscillation (AMO) -type variability.
As with the extended summer season, part of the increase in skill for the win100 SST reconstruction could also originate from a smoother signal for annual data -in both observations and reconstruction, where some of the noise is reduced compared to seasonal data, but some of the signal is also lost. Targeting the winter season (DJF) using the winter centered annual data results 230 in a clear gain in skill for SLP, while the skill for SST is somewhat reduced, although retaining the overall correlation pattern of the winter centered annual mean reconstruction. This indicates that it is feasible to reconstruct winter variability from annual data, if the definition of the winter centered annual mean is used for the proxy data. Seasonal δ 18 O data are increasingly sparse going back in time, and using winter centered annual mean data could be an alternative for reconstructing winter variability beyond the reach of seasonal δ 18 O data when seasonality in the ice can still be defined from e.g., aerosol records.

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To further assess the skill of the reconstructed temperature we compare to data from three stations on the Greenland coast and one Icelandic station. Vinther et al. (2010) showed that the first Principal Component (PC1) of Greenland isotope data (20 cores) has strong correlation (r = 0.71) to the stacked Greenland coastal data (South West Greenland temperature, SWG index) during winter (Nov-Apr), while PC1 of the isotope data for summer is most strongly correlated to data from Iceland (r = 0.55) (May-Oct). Here we compare the reconstructed site temperature both to data from each of the stations and to the SWG 240 index. The highest correlations are found for the 8 core Win50 reconstruction at Nuuk and Qaqortoq with a correlation of 0.6 at both sites (Table 4). It is also for this reconstruction we find the highest correlation of 0.63 with the SWG index. The 19 core reconstructions have slightly lower correlations to the Greenland temperature data. This could be due to a weighting of the variability more to the east, as most of the additional cores in the shorter reconstructions are to the east of the ice divide. For the summer reconstructions the correlations to the Greenland station data are below 0.3. However, the 8 core Sum50 reconstruction 245 captures a substantial part of the longer term variability with a correlation of 0.44 to the decadally filtered SWG index. With respect to the definition of the winter season, the DJF reconstructions appear to better capture the long term variability with slightly higher correlation for the filtered data compared to the Win50 reconstructions. The Win100 and the Win100 DJF reconstructions both show only slightly lower correlations than the Win50 and DJF reconstructions, indicating that for temperature alone the seasonal data is less crucial than for reconstruction SLP, at least when comparing locally to the Greenland coastal indicates a similar behavior as for the ice core PC1 correlation with respect to the winter data responding more to the Western Greenland temperature and the summer data having better coherency with Icelandic data. The predominance of the summer 255 signal east of Greenland also results in the reconstructions based on the winter centered annual mean not having very high skill for Icelandic temperatures, at least for the long term variability.
Comparing the summer reconstructions including tree-ring data with the 20CR we find that the skill for SLP, T2m and SST has increased considerably compared to the summer reconstructions only using 8 ice cores (Table 3 and Supplementary Figure   S8). The skill is improved in particularly for temperature in the eastern sector of the domain, while the skill for SLP is still low 260 near Greenland, although the skill has clearly increased over Northern Europe for JJA.  From the time series of EOFs (PCs) it is evident that the reconstructions have realistic amplitudes of the year-to-year variability ( Figure 6). In other words, the spectrum of the reconstructions are similar to actual weather variability as also found for the DJF reconstruction by Sjolte et al. (2018). Correlating the reconstructed PCs to that of the 20CR (see Figure 7) shows that i) the variability of PC1 is well captured by the winter and annual data ii) only the Win50 DJF reconstruction has skill for PC2

Main modes of atmospheric variability
iii) the summer reconstructions have some skill for PC3 iv) in some instances the decadally filtered data capture a significant 290 part of the 20CR variability, even with no correlation for annual data (e.g. PC2 and PC3 of DJF Win100 (8 cores)). The very low values 1851-1860 in the 20CR PC1 is possibly a bias in the reanalysis and is not seen in the HadCRU NAO time series (not shown). Comparing the reconstructions for winter and annual data to the HadCRU NAO results in higher correlations than for 20CR, also for the filtered data. For summer it is not meaningful to use the station-based NAO due to the shifted centers of action during summer compared to winter. As discussed in Section 4.2.1 the skill for SLP improves locally when 295 including tree-ring data to constrain the summer reconstructions. However, the skill for the circulation patterns is not improved by including the tree-ring data.

North Atlantic sea surface temperature
The correlation maps with the COBE SSTs (Figures 3 and 4)  explain more than 50% of the COBE North Atlantic SST variability (r = 0.72 and r = 0.74, respectively) ( Figure 9). While the long term SST changes for summer are underestimated, the reconstructions of winter SST match the COBE amplitudes of the 305 decadal-multidecadal SST variability very well. As mentioned in Section 4.2.1 the skill for temperature and SST is markedly improved when in including the tree-ring data in the summer reconstructions. This is also see in the higher correlations and stronger significance for the North Atlantic SST index for these reconstructions (Figure 9).
To further investigate how much information of the North Atlantic SST variability is obtainable using this type of reconstruction, we also compared the patterns and variability of the main modes of reconstructed SSTs to that of the COBE SSTs (Figures The inherent properties of climate variability with respect to auto-correlation and changes in governing weather patterns as il-330 lustrated in Section 4.1 are probably the reason for the differences in skill seen for the reconstructions using different definitions of the target season. One consequence is that the skill for secondary circulation modes is better for the reconstructions targeting DJF rather than Nov-Apr, and a secondly that using the wider definition of summer (May-Oct) may reduce some noise in the temperature reconstruction, an effect which likely also can be seen for the temperature reconstructions of the winter centered annual mean. Additionally, reconstruction of the DJF atmospheric circulation using winter centered annual mean ice core data 335 is attainable, which opens up the possibility of extending the winter reconstructions further back than with seasonal data. This could be done by using high resolution chemistry data (e.g., Rasmussen et al., 2006) to define the seasons in the ice core data, even though the annual cycle in the ice core isotope data cannot be recovered.
The evaluation of correlation to the North Atlantic SSTs shows a particular strong sensitivity to SSTs variability north of 50 o N. This is in principle true for all seasons, but in particularly in winter, where the amplitude of the decadal changes in SSTs 340 are captured by the reconstruction. This is achieved without tuning the reconstruction to observations. This indicates a clear potential for reconstructing AMO-like variability. Furthermore, the reconstructions yield qualitatively similar main patterns of variability as those based on observations (EOF1, 2 and 3). These SST patterns are connected to the main atmospheric modes of variability.
The reconstructions in this study only based on ice core data are using what one might call a minimal proxy data set. The 345 thought behind is to select few -but high quality well dated, and well studied proxy data, rather than a large collection of data where the link between climate parameters and all proxy data has not been tested in details. Furthermore, the use of isotope records have the property discussed in the introduction of not only recording local information, while the assimilation using an isotope enabled climate model allows coupling the model and proxy data without calibration. However, it is clear that the skill of the summer reconstructions is generally lower than the the winter reconstructions. For this reason we also include European

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To attain the best possible reconstruction of climate variability, taking into account the the nature of the target for the reconstruction is important. This is illustrated by the dependency of the skill of the climate reconstructions on the definition of seasonality, due to the seasonal changes of the patterns or variability. For winter a narrow definition of the season (DJF) yields better performance for circulation patterns. Furthermore, in some cases a wider definition of the season, e.g. for summer and annual data, can provide better performance for temperature due to better capturing the signal during months of higher 375 auto-correlation and less variability.
Further development of seasonal climate field reconstructions requires a larger data set of well studies proxy records. Isotope records of tree-ring cellulose from regions with sustained winter snow are potential sources for expanding the spatial coverage for winter (Seftigen et al., 2011;Edwards et al., 2017). In more temperate climates such records could be used for reconstructing summer variability (Labuhn et al., 2016). Speleothem data could potentially also be used, however is a challenge to find 380 high resolution continuous data sets due to growth hiatuses (e.g., de Jong et al., 2013). Newly updated isotope enabled climate models (e.g., Cauquoin et al., 2019) shows the continual development of this field. This makes running new millennium length model simulations attractive for the purpose of providing better sampling pools for finding model analogues to match the proxy data. Although not shown in this study, reconstruction of precipitation is also possible using the analogue method. However, in particularly for precipitation better model resolution is important to capture storm tracks and orographic effects. Finally, the 385 indication found in this study of that is possible to capture the main SST patterns of the North Atlantic, makes this approach a good supplement to marine records due to better precision of the dating of terrestrial records.