Testing the consistency of Holocene and Last Glacial Maximum spatial correlations in temperature proxy records

Holocene temperature proxy records are commonly used in quantitative synthesis and model‐data comparisons. However, comparing correlations between time series from records collected in proximity to one another with the expected correlations based on climate model simulations indicates either regional or noisy climate signals in Holocene temperature proxy records. In this study, we evaluate the consistency of spatial correlations present in Holocene proxy records with those found in data from the Last Glacial Maximum (LGM). Specifically, we predict correlations expected in LGM proxy records if the only difference to Holocene correlations would be due to more time uncertainty and more climate variability in the LGM. We compare this simple prediction to the actual correlation structure in the LGM proxy records. We found that time series data of ice‐core stable isotope records and planktonic foraminifera Mg/Ca ratios were consistent between the Holocene and LGM periods, while time series of Uk'37 proxy records were not as we found no correlation between nearby LGM records. Our results support the finding of highly regional or noisy marine proxy records in the compilation analysed here and suggest the need for further studies on the role of climate proxies and the processes of climate signal recording and preservation.

One way to characterize the proxy signal is to compare how records from the same site replicate (e.g. Fisher et al., 1985;DeLong et al., 2007) or to examine similarities between records collected in close spatial proximity to one another (e.g. Münch et al., 2016Münch et al., , 2017. These studies are often limited to the last millennium (e.g. Stephans et al., 2004;DeLong et al., 2013) and the Holocene (e.g. Reschke et al., 2019a). Reschke et al. (2019a) empirically estimated signal-to-noise ratios in compilations of temperature proxy data from the Holocene by comparing the correlations in time series from sites that are in close spatial proximity to one another to those obtained from climate model-derived time series from the same proxy sites and time period. They found an unexpectedly low correlation among neighbouring proxy sites in contrast to a strong correlation predicted by climate models, indicating either noisy proxy records or climate variations that vary on spatial scales that are too small to be captured by the relatively large-scale climate models.
As the Holocene is a climate state that is relatively stable, we extend previous investigations of the spatial correlation structure of proxy records (Reschke et al., 2019a), i.e. the similarity of proxy time series depending on the separation distance of sites, to a different climate state with a higher variability in the temperature proxy data: the Last Glacial Maximum (LGM). This provides a further test of the current understanding of the proxy signals. Specifically, we analyse for the first time the correlation structures between temperature proxy records in the LGM and test whether they are consistent with the spatial correlations found in Holocene temperature proxy records. First, we investigate the processes that may cause differences between the correlation structures of the Holocene and LGM such as the amount of climate variability relative to the noise component and the amount of time uncertainty. Then, we predict spatial correlations of surrogate time series for the LGM generated based on spatial correlations of Holocene temperature proxy data by accounting for these known processes and compare these expected LGM spatial correlations with estimates of the spatial correlation structure based on LGM temperature proxy records.

Data
The focus of this study is the comparison of the spatial correlation structure (i.e. the correlation of time series in dependence of the separation distance of proxy sites) of proxy records of two different climate states, i.e. the Holocene and the LGM, with a similar amount and quality of available highresolution temperature proxy records. Thus, we analyse the existing high-resolution globally distributed multi-archive and multi-proxy dataset of Holocene and LGM temperature proxy records of Rehfeld et al. (2018). Originally compiled to compare Glacial and Holocene temperature variability, this collection compiled available published records that have an established calibration to temperature, cover at least a 4-ka interval during an 8-ka period during the LGM (27-19 ka BP) and/or the Holocene (8-0 ka BP), and are available at a mean sampling frequency of at least 1/225 a −1 (Rehfeld et al., 2018). To have consistent Holocene and LGM datasets, we only used the three most common proxy types available for both time periods: (i) ice-core stable isotope records, (ii) marine sediment time series reconstructed from Uk'37 and (iii) planktonic foraminifera Mg/Ca ratios. This yielded 64 time series for the Holocene and 36 for the LGM ( Fig. 1; Table 1; Supporting  Information Table S1). For the marine records, we use the temperature calibrations of the original studies, while for the ice-core-based time series we use the recalibration of Rehfeld et al. (2018). As our study is based only on correlations, the results are largely independent of the calibration choice.

Approach and assumptions
We estimate the correlation of paired temperature-related proxy time series as a function of distance (spatial correlation) for the Holocene records (ρ Hol,Prx ) and the LGM proxy records (ρ LGM,Prx ). To test the current understanding of proxy signals by testing the consistency of the spatial correlation structure of temperature proxy records for different climate states, we then predict the spatial correlation expected for LGM proxy records based on the Holocene spatial correlations assuming that the correlation differences are caused only by a different amount of climate variability and time uncertainty between both climate states. Then, we compare these predicted correlations based on LGM surrogate time series (ρ LGM,tu ) with the observed correlations in LGM proxy records (Fig. 2).
Consistency between the observed and predicted correlations would indicate that we captured the main processes affecting the correlation structure and provide support for the low Holocene correlation estimates of Reschke et al. (2019a) although the level of consistency, and thus the degree of confirmation, hinges on the estimation uncertainty. If the results should turn out to be very different, this would challenge our current approaches to interpreting proxy records.
To predict the LGM spatial correlations, we assume that temperature proxy records consist of a climate signal and a noise component related to non-climate-related factors (e.g. different sampling protocols or a varying sedimentation rate). Furthermore, we make the following two assumptions and discuss their implications later: (i) the LGM climate system has the same or greater spatial correlations as the Holocene (based on our analyses of climate model simulations for both time periods), i.e. that paired temperature proxy records are more similar in the LGM than in the Holocene, e.g. due to a stronger variability in the LGM temperature signal; and (ii) the noise component related to non-climate-related factors is independent of the climate state: most error sources such as measurement uncertainties and aliasing due to a finite number of samples areto a first approximationindependent of the mean climate state and should therefore be similar in either time period (Laepple and Huybers, 2013;Dolman and Laepple, 2018;Laepple et al., 2018).
Compared to the Holocene we then expect differences in the proxy correlations due to a generally higher climate  variability (Rehfeld et al., 2018) and larger time uncertainty in the LGM. Changes in climate variability are estimated from the variance ratios σ σ / LGM 2 Hol 2 of LGM and Holocene proxy records (Rehfeld et al., 2018), while typical time uncertainties of LGM and Holocene proxy data are estimated using the datasets of Shakun et al. (2012) and Marcott et al. (2013).
Holocene and LGM spatial correlation structure from climate model simulation To gain an indication about possible differences in the spatial correlation structure between Holocene and LGM temperature proxy records we first rely on climate model simulations. We analysed the spatial correlation structure of (unfiltered) annual means of surface air temperatures extracted from ECHAM5/MPI-OM equilibrium model simulations of the Mid-Holocene (788 years; Wei and Lohmann, 2012) and the LGM (1000 years; Zhang et al., 2013). Data were extracted at grid cell level to estimate the correlations R as a function of site separation x. Then, the correlation decay length l d (i.e. the site separation at which the correlation of paired time series decayed to 1/e of the correlations of replicate cores) of the Mid-Holocene and LGM is estimated by fitting an exponential, = − / R e x l d , to the decay of correlations. The overall magnitude and structure of the correlation decay length is similar in both climate states (Fig. 3). During the LGM (2910 km), the mean interannual correlation decay length, l d , is higher compared to the Holocene (2080 km) with the strongest differences in the tropics and in the northern hemisphere. This Holocene result is consistent with findings (2240 km) by Reschke et al. (2019a) who used data from a 6-ka Holocene model simulation by Fischer and Jungclaus (2011).
We note that due to the unavailability of long LGM simulations, this analysis was performed on annual data, whereas the remaining study is based on centennial to millennial variations that are also affected by forcing factors (e.g. transient changes in insolation) not considered in the analysed simulations. Thus, we expect a higher spatial correlation with higher correlation decay lengths (5000 km) when considering climate variability on centennial to millennial time scales (Laepple and Huybers, 2014;Reschke et al., 2019a). Still, the similarity between the Holocene and LGM decay lengths of interannual data suggests that the general spatial correlation structures are a first-order property of the climate system that is only weakly affected by the mean climate state.

Effect of changes in climate variability on the predicted correlations
Different palaeoclimate archives suggest a higher climate variability during the LGM (e.g. Ditlevsen et al., 1996;Rehfeld et al., 2018). Assuming the simplest possible model, we assume that our temperature proxy-based time series consist of two componentsa climate signal S and an independent random (white) noise ε. Thus, two proxy time series X and Y can be described as X = S + ε x and Y = S + ε y where the signal and noise components of both time series are uncorrelated, i.e. cor(S,ε x ) = cor(S,ε y ) = cor(ε x ,ε y ) = 0. We can then derive the expected correlation in the LGM, ρ LGM , from the correlation in the Holocene, ρ Hol , using LGM Hol where z is the assumed variance change between the Holocene and LGM climate signals (σ σ / LGM 2 Hol 2 ) (Appendix A). For a constant variance of the noise component, but a different variance of the signal component for the Holocene and LGM, changes in the variance ratio of the climate signal z of proxy records could indicate a reduction (for z < 1) or an increase (for z > 1) in the initial correlation, cor 0 , with the strongest changes occurring for cor 0 ≈ 0.5 (Fig. 4A).

Effect of changes in time uncertainty on the predicted correlations
We generally expect time uncertainty to increase as we go further back in time, i.e. the time uncertainty of age models based on radiocarbon dating should be higher for the LGM than for the Holocene records, e.g. due to reservoir effects (Ascough et al., 2005). The effect of time uncertainty on the correlation of time series depends on four factors: (i) the magnitude and temporal structure of time uncertainty, with higher time uncertainties leading to a stronger reduction in correlation; (ii) the initial correlation cor 0 of annually resolved time series without time uncertainty; (iii) the temporal structure (power spectrum) of the climate signal (rapidly varying signals are more susceptible to time uncertainty); and (iv) the timescale on which the correlation is estimated if the noise and the climate signal components have different temporal structures (Reschke et al., 2019b).
For simplicity, we assumed that the climate variability in point (iii) can be approximated as having a power-law scaling with a power spectral density = β − PSD f S , where f is the frequency and β S the slope of the climate signal. Such a scaling has been found to be a good description of Quaternary climate variability (e.g. Huybers and Curry, 2006;Laepple and Huybers, 2014).
As we are not aware of analytical expressions quantifying the effect of time uncertainty on the correlation structure, we rely on numerical simulations. To simulate time uncertainty, we defined control points at certain ages and shifted them by adding a random value from a normal distribution (with zero mean and a standard deviation equal to the time uncertainty). A new time axis is then created by linearly interpolating between the control points.
To illustrate the effect of time uncertainty on the correlation of time series, we apply different time uncertainties to 50-ka surrogate time series. As the applied procedure is also used for further analyses (described in next subsection) it is explained here in detail.
We performed a Monte Carlo procedure with 5000 repetitions. This yielded two 50-ka surrogate time series that each consisted of the superposition of an annual red noise (Huybers and Curry, 2006) power-law climate signal with a shallow (β S = 1; Laepple and Huybers, 2014) or steeper slope (β S = 1.5; if we also take the deglaciation into account) as well as annual non-climaterelated factors which were collectively included as an independent (white) noise component (β N = 0). The initial correlation of paired surrogate time series, cor 0 , was in the range 0.05-1. The time uncertainties of the surrogates were applied to control points every 10 ka and ranged from 100 to 1400 years. These values are similar to the age uncertainties obtained by Shakun et al. (2012) (127 to 1304 years) for the time window of 27-19 ka BP. As the application of time uncertainty generates an irregular sampling of the surrogate time series, we use the method described by Reschke et al. (2019b), which applies a linear interpolation of the irregular time series onto a regular grid (Δt = 10 years) subjected to a Gaussian filter with cut-off frequency f c , to determine the timescale-dependent correlations over a range of 2 to 1000 years, i.e. cut-off frequencies f c from 1/2 to 1/1000 a −1 .
The correlation of time series thus decreases with increasing time uncertainty and this effect is even more pronounced for higher initial correlations cor 0 (Fig. 4B,C). Furthermore, weaker trends in climate signals lead to a stronger decrease in cor 0 ( Fig. 4B vs Fig. 4C). Additionally, for climate signals with red noise spectra, correlations related to longer timescales (i.e. lower cut-off frequencies) are higher than for shorter ones (Supporting Information Fig. S1) which counteracts the decrease in correlation due to time uncertainty.
Estimating the surrogate-based LGM spatial correlation and accounting for parameter uncertainty Based on Holocene proxy records we use a four-step approach to predict the expected LGM spatial correlation ρ LGM,tu of surrogate time series (cf. Fig. 2). (i) We estimated the Holocene correlation structure of (time-uncertain) proxy data, ρ Hol,Prx . (ii) We corrected for the effect of time uncertainty to derive the underlying Holocene correlations of time-certain proxy data, ρ Hol . For this step, we rely on an empirical transfer function (for a time uncertainty of 220 years) mapping the time-certain and time-uncertain correlations based on surrogate data (similar to the subsection above). (iii) We accounted for the expected differences in climate variability of Holocene and LGM proxy records to estimate the LGM correlation structure without time uncertainty, ρ LGM (see 'Effect of changes in climate variability on the predicted correlations' above). (iv) We accounted for the time uncertainty and the uncertainty of a finite set of irregularly sampled finite time series by estimating the correlation ρ LGM,tu and its uncertainty on irregular time-uncertain surrogate time series.
In detail, we estimated the Pearson correlation between Holocene time series pairs for climate variability on millennial time scales (1000 years) using linear interpolation and Gaussian filtering (see Reschke et al., 2019a). Holocene spatial correlations, ρ Hol,Prx , were estimated using 2000-km bin sizes. As very distant sites will be essentially uncorrelated, we only considered spatial separations of up to 6000 km as previous studies suggest a correlation decay length of 5000 km for climate variability on centennial to millennial timescales (Laepple and Huybers, 2014;Reschke et al., 2019a). Then, we corrected the time uncertainty (a Holocene-typical value of 220 years; based on the dataset of Marcott et al., 2013) to derive the time-certain spatial correlation ρ Hol .
We use a Monte Carlo approach (5000 repetitions) similar to the one described in the subsection above to predict LGM spatial correlations: To test the consistency of the Holocene and LGM spatial correlations of proxy records we compared the expected results of spatial correlations from the surrogate LGM time series (ρ LGM,tu ) to those estimated from LGM proxy records (ρ LGM,Prx ). Following Reschke et al. (2019a), to determine the significance of proxy-based Holocene and LGM spatial correlations, we estimated confidence intervals of the null hypothesis of uncorrelated proxy data (90% quantiles) based on uncorrelated surrogate time series. This approach considers the total number of correlation pairs according to each bin.

Results
We estimated proxy-based Holocene spatial correlations, ρ Hol,Prx , for all combinations of Uk'37, Mg/Ca and ice-core stable isotopes time series independent of the proxy types as we assume that the difference between sea surface and air surface temperatures are negligible due to an indicated coupling of near surface air and sea surface temperatures (Morice et al., 2012). The correlation estimates are fairly constant at 0.2 for spatial separations up to 6000 km and statistically significant (Fig. 5A). This is slightly higher than the value of 0.18 found by Reschke et al. (2019a) and is probably the consequence of the use of a subset of their dataset and a time window of 8 ka instead of 6 ka in the present study. Correcting for the expected bias due to time uncertainty (assuming a climate signal with a spectral slope of β S = 1) slightly increased the correlations to a mean value of 0.23 (ρ Hol ). Accounting for a stronger expected climate variability in the LGM, ρ LGM resulted in an increase to 0.55, although this increase has a considerable uncertainty associated with it due to the uncertain increase in climate variability. Applying an LGM-typical time uncertainty reduced the predicted spatial correlation to ρ LGM,tu ≈ 0.4. In contrast to this expectation, the estimated proxy-based LGM spatial correlation, ρ LGM,Prx , is zero except for the spatial separations below 2000 km where it is 0.26.
As there are proxy-specific recordings of the climate component, e.g. a habitat-dependent seasonal and depthspecific recording of organism-based proxies (Leduc et al., 2010;Lohmann et al., 2013), we examined the effect that different organism-based proxy types (i.e. alkenone Uk'37, planktonic foraminifera Mg/Ca) can have on the results. Thus, we consider pairs of Uk'37, Mg/Ca and ice-core stable isotopes time series combining only the same proxy types (Fig. 5B). The estimated spatial correlations are generally slightly higher, although not too different from the mixed results (Fig. 5A) and still indicate an inconsistency between the predicted and observed LGM spatial correlations.
To further elucidate possible proxy type-specific effects, we separately analysed the Uk'37 proxy, which yielded higher Holocene correlations (0.47) than the combined proxy types (Fig. 5C). Correcting for the time uncertainty led to slight increases in ρ Hol (to 0.53), while accounting for the expected higher LGM climate variability led to an even stronger increase (to ρ LGM ≈ 0.81). Adding time uncertainty reduces the correlation (ρ LGM,tu ≈ 0.52). In contrast, the estimated LGM correlation of the Uk'37 proxy data ρ LGM,Prx is either close to zero or negative and thus indicates an even stronger inconsistency between the predicted and observed LGM correlations.
As the number of records is too low for Mg/Ca and ice-core stable isotopes to be analysed separately, we chose to analyse both proxy types together in all combinations of time series independent of the proxy type (Fig. 5D) to raise the statistical robustness of the correlation estimates. ρ Hol,Prx was 0.18 for separations below 2000 km and close to zero for greater separations. These values increased only slightly after removing time uncertainty (ρ Hol ). Accounting for a higher LGM climate variability increases the correlations yielding ρ LGM ≈ 0.52 for separations below 2000 km and 0.21 otherwise. Adding time uncertainty decreased ρ LGM,tu to 0.4 for separations below 2000 km and to 0.17 otherwise. For the combination of these two proxy types, the observed range of proxy-based LGM spatial correlations (0.05 < ρ LGM,Prx < 0.4) falls within the uncertainty range of ρ LGM,tu , thus indicating consistency between the predicted and observed LGM correlations.
We tested the effect of the use of different proxy types for paired time series on the results by using pairs of Mg/Ca and ice-core stable isotope time series combining only the same proxy types (Fig. 5E). As above, the spatial correlations are generally slightly higher for analysis of the same proxy types but remain similar to the mixed results (Fig. 5D). This also lends support to our previous finding that LGM spatial correlations and our predictions are consistent for these proxy types. These results are particularly sensitive to our assumption of the climate signal because a spectral slope of β S ≈ 1.5 leads to similar results (Supporting Information Fig. S2).

Discussion
We estimated the correlation of Holocene and LGM proxy time series for different spatial separations of the sites and used the Holocene spatial correlations to predict the expected LGM spatial correlations using surrogate power-law time series. Both the proxy-based and the predicted spatial LGM correlations were largely consistent for time series reconstructed from planktonic foraminifera Mg/Ca and ice-core stable isotopes. In contrast, data compilations containing time series based on Uk'37 resulted in inconsistent proxy-based and predicted correlations as the spatial correlations in LGM Uk'37 datasets were surprisingly low. In the following, we discuss possible reasons for the different behaviour of the proxy types.

Proxy-specific recording and finite number of records
In our study, we assumed that all proxy types were recording the same climate component. However, the processes of climate recording and preservation are known to be proxy-specific, which limits the validity of our assumption. For example, marine organism-based proxies show a habitat-dependent seasonal and depth-specific recording (Leduc et al., 2010;Lohmann et al., 2013) and preferred dissolution of shells (Lea, 2003). While parts of this proxy-specific recording are accounted for in the proxy-specific temperature calibrations, other parts will persist and lead to systematic errors. This could lead to a potential underestimation of the Holocene and LGM spatial correlations depending on the chosen proxy type. Thus, our finding that spatial correlations using different proxy types (Fig. 5A,D) showed slightly lower (difference not statistically significant) correlations than the same correlations using the same proxy types (Fig. 5B,E) is consistent with the expectation that correlations of mixed-proxy-type analyses are less similar than those of single-proxy-type analyses due to the comparison of, for example, summer atmospheric temperature vs. mixedlayer winter temperature. This suggests that one should use proxy-specific and expert-driven knowledge for analyses and interpretations of individual sites.
Nevertheless, these effects should act in both climate states and thus do not explain the inconsistency we observed between the strong Holocene correlations and missing LGM spatial correlations (Fig. 5C) in the Uk'37 proxy records.

Time uncertainty of proxy records
While our analysis accounted for uncertainties in radiocarbon dating of sediment cores, this did not include uncertainties resulting from assumptions about reservoir age or the spatial and temporal variation of reservoir ages (Ascough et al., 2005) which depend on the (local) climate and oceanic circulation patterns. In particular, polar waters and sea ice can exhibit higher reservoir ages. Studies of the Younger Dryas and Early Holocene reservoir ages have shown an increase by 300-400 years in glacial conditions (Haflidason et al., 2000) compared to the current reservoir ages of 200-400 years for the mixed layer of the oceans (Stuiver et al., 1986). The true time uncertainty, especially for the LGM, might therefore be higher due to these time-variable reservoir effects. Our estimates of the Holocene spatial correlation ρ Hol (without time uncertainty) might therefore be too low, causing an underestimation

Contrary behaviour of Uk'37 records
For Uk'37 LGM proxy records, the correlation of the proxy time series (ρ LGM,Prx ) was indistinguishable from zero and fell outside the range of the predicted ρ LGM,tu values (Fig. 5C). This either indicates that the Uk'37 proxy recorded a climate signal that is spatially more coherent in the Holocene or that the Uk'37 time series are more corrupted by non-climate effects in the LGM compared to the Holocene. It is conceivable that the stronger climate variations in the LGM are also accompanied by more complex signals such as changes in water masses (and thus nutrients) or a stronger seasonality that would increase the level of non-temperature effects on the LGM records. One other possibility is that the high correlations in the Holocene records may be the result of spatially coherent non-climatic effects in the Holocene Uk'37 proxy signal. The results for the Uk'37 record stand out, as those for other proxy types (planktonic foraminiferal Mg/Ca, ice-core stable isotopes) were consistent in both ρ LGM,Prx and ρ LGM,tu . A different behaviour in Uk'37-and Mg/Ca-based temperature reconstructions has already been described in previous studies (e.g. Lohmann et al., 2013;Liu et al., 2014;Marsicek et al., 2018) where these discrepancies are attributed to different ecological (e.g. habitat depth) and seasonal (e.g. production season) biases of the proxy carrier, whereas others attributed these discrepancies to regional differences in the distribution of different proxy records (e.g. Mix et al., 2000;Mix, 2006;Leduc et al., 2010), or to re-deposition and post-depositional effects (e.g. Hoefs et al., 1998;Gong and Hollander, 1999;Ohkouchi et al., 2002;Regenberg et al., 2006). Furthermore, the number and distribution of Uk'37 time series differ between the Holocene and LGM, with a particular scarcity of LGM time series in the North Atlantic (Fig. 1). The strong linear cooling trend present in most Holocene Uk'37 time series favours an overestimation of the spatial correlation at distances between 2000 and 6000 km. Due to the lack of LGM data from the North Atlantic, we cannot currently test the hypothesis of higher spatial correlations due to stronger trends recorded by Uk'37 in Holocene time series. As this study requires the use of high-resolution time series, which are common in the coastal and continental shelf regions, the analysis of sets of time series for the area of the deeper ocean (e.g. the central North Atlantic) covering the Holocene and LGM is not possible as there is generally a lower resolution of the proxy records due to lower sedimentation rates of the deeper ocean.

Spatial correlation structure and orbital trends
Model simulations suggested a higher spatial correlation during the LGM (Fig. 3) which seems to contradict our proxy-based results (Fig. 5). While our model-based estimates of the correlation structure are based on an equilibrium model simulation that is not orbitally forced, the proxy records contain orbitally forced temperature trends and seasonal temperatures which can create large-scale patterns and thus affect the correlation structure (e.g. Lohmann et al., 2013). It has been suggested that such patterns and also differences between proxy types could be explained by seasonal recordings of orbitally driven trends in the Holocene (Leduc et al., 2010). However, by evaluating insolation and seasonal temperature trends in the Holocene and LGM, we did not find any systematic differences in the amplitude of the orbital trends between either time period (Supporting Information Fig. S3).

Expanding the time window of proxy time series
It is possible to increase the number of proxy records and thus the robustness of the analyses presented in this study by extending the time window covered by the time series, e.g. by considering Marine Isotope Stage (MIS) 2 (29-14 ka BP) instead of the LGM (27-19 ka BP) or analysing MIS 1 (14-0 ka BP) instead of the Holocene (8-0 ka BP). On the one hand, a longer time window is required to analyse spatial correlations related to, for example, climate variability on timescales >2 ka and thus to allow the use of a higher number of low-resolution time series from the central oceans.
Furthermore, we expect higher correlations for MIS 2 compared to the LGM as there should be stronger temperature signals due to the deglaciation and Heinrich event 1, and the analysis of MIS 1 should also cause higher correlations of paired proxy time series due to the cooling during the Younger Dryas. This can help to test the plausibility of the observed low spatial correlations of Uk'37 LGM proxy records (Fig. 5C).

Conclusions
In this study, we have analysed the correlation structure of temperature proxy records from the LGM that have been collected in close proximity to one another. Spatial correlations were low and only statistically significant for spatial separations <2000 km. For Uk'37, we found no correlation between sites regardless of the distance considered.
To test the consistency between the spatial correlations in the Holocene and LGM, we predicted the expected LGM correlations by accounting for changes in climate variability and time uncertainty. When focusing on planktonic foraminifera Mg/Ca and ice-core stable isotope records, we found consistency between the observed and predicted correlations. In contrast, the observed Uk'37 LGM correlations unexpectedly fell outside the range of the predicted LGM correlations. This suggests that for Uk'37 other effects not accounted for in this study may have caused the inconsistency.
The different behaviour of Uk'37 vs. other proxy types agrees with previous findings (e.g. Lohmann et al., 2013;Liu et al., 2014;Marsicek et al., 2018) and suggests that different proxy types are affected by proxy-specific non-climatic components and uncertainties that may not be fully understood yet. This suggests that analyses using multi-core and multi-proxy datasets (e.g. Reschke et al., 2019a) may be biased by the choice of the proxy type, as some of the underlying assumptions may be oversimplifications of complex climatic and proxy recording processes. Furthermore, the consistency between Holocene and LGM records for planktonic foraminifera Mg/Ca and ice-core stable isotopes after accounting for time uncertainty and changes in climate variability provide some confirmation for the Holocene-based result of low spatial correlations (Reschke et al., 2019a), indicating that current proxy records either record very regional climate signals or have a low signal to noise ratio.
Author contributions-M.R. and T.L. designed the research. M.R. performed the analysis with the aid of I.K. and wrote the first draft of the manuscript. M.R., I.K. and T.L. contributed to the interpretation and to the preparation of the final manuscript.

Data availability statement
All data that support the findings of this study are related to the dataset of Rehfeld et al. (2018), which is available at https://www. nature.com/articles/nature25454#supplementary-information.
Conflict of Interest-The authors declare that they have no conflicts of interest.
Figur S1. Effect of time uncertainty depending on the related timescale of the correlation for a spectral slope of (A) = β S = 1 and (B) = β S = 1.5. Due to low-pass filtering, climate variability is removed on short timescales, whereas it is still present on long timescales (i.e. all frequencies up to the cut-off frequency f c ). This raises the correlation among time series, assuming the time series contains a superposition of a red noise climate signal and an independent white noise component. The higher the spectral slope β S of the climate signal (i.e. the 'redder' the climate), the higher is the timescale-dependent correlation after filtering. Figure S2. Spatial correlation (upper panel) and number of proxy record pairs (lower panel) for the Holocene and LGM. Correlations over distance are summarized in 2000-km-wide bins. The expected spatial correlation for the LGM is based on the reconstructed Holocene spatial correlations without time uncertainty and assumes a higher variance of the signal component (μ = 4.4, σ = 1.15). The expected correlation of time-uncertain LGM records and its confidence interval (i.e. 90% quantiles) is based on a Monte Carlo procedure with 5000 repetitions applying a time uncertainty of 450 years on time series with a spectral slope of the climate signal of β S = 1.5. 90% quantiles of the spatial correlations of uncorrelated Holocene and LGM surrogate data are used as a significance test for the proxy-based spatial correlations. Note that in D and E the correlation estimates between 4000 and 6000 km are based only on Mg/Ca and/or Mg/ Ca vs. ice-cores as no ice-core pair at this distance is available. Figure S3. Orbital trends in seasonal temperatures for (a) the Holocene and (b) LGM, and (c) the latitudinal mean. The temperature differences are based on model simulations of the Holocene (6-0 ka BP; Fischer and Jungclaus, 2011) and the LGM (27-19 ka BP; Zhang et al., 2013). Both time periods exhibit stronger temperature differences in the polar regions than in the tropics. Table S1. List of records used in this study. This subset is part of the dataset used by Rehfeld et al. (2018).