For this study, a comprehensive effort was made to collect all published proxy precipitation and temperature records between 40∘ S and 40∘ N that cover the last 2000 years. The large majority of records were accessed from the NOAA Paleoclimatology and Pangaea Databases (https://www.ncdc.noaa.gov/data-access/paleoclimatology-data/datasets). In addition, over 200 tree ring records were taken from the dataset used by and hence were subject to their criteria, including length, intra-site signal coherence, and sample density (see Appendix  for details). A set of coral records was taken from the dataset made available by ; these were largely temperature proxies, although some were assigned as precipitation proxies or excluded altogether based on information in the original publications (see Appendix  for details).

After collection, all records were screened for a maximum dating error of 60 years. Although somewhat arbitrary, this cut-off was decided by taking double the averaging bin width of 30 years that was applied to the data prior to analysis (Appendix ). This is a step towards addressing the issue of dating uncertainty while allowing a wider range of proxies to be utilised. Proxies with larger dating errors generally have lower (multi-annual to multi-decadal) resolution but are also usually much longer and are arguably more useful for capturing long-term trends that may be less evident or reliable in annual resolution proxies cf.on low-frequency trends in tree rings. Other quality judgements regarding temporal resolution, record length, and proxy location are accounted for by the method set out in Sect.  and Appendix .

Instrumental climate data are the best available in terms of dating accuracy, calibration, and physical basis . However, their spatial coverage is not complete and sharply decreases back in time. The nature of the method used in this study calls for full spatial coverage over a long period; therefore, reanalysis products are more suitable. These are combinations of instrumental and satellite data interpolated using models. The 20th Century Reanalysis Version 2c (20CRv2c) is the longest global dataset of atmospheric circulation available, spanning AD 1851–2014. It is based on surface pressure, temperature, and sea ice distribution data, filled in with a deterministic ensemble Kalman filter (EKF). It has a spatial resolution of 2∘ latitude × 2∘ longitude × 24 vertical pressure levels and a temporal resolution of up to 6 h. It has been demonstrated that the 20CRv2c is competent at representing the global tropospheric circulation as well as the mean state and variability of the hydroclimate; for a detailed description and evaluation of the product see . Comparison with ENSO indices indicates that 20CRv2c accurately represents the temporal evolution of ENSO (Table ), and a recent comparison with other reanalyses (ERA-20C, JRA-55, and ERA-Interim) indicates that 20CRv2c shows similar variations in various climate indices, including NINO3.4 and SOI . The monthly mean surface air temperature and precipitation rate datasets were downloaded from the NOAA/ESRL/OAR-PSD website (http://www.esrl.noaa.gov/psd/). The 20CRv2c data were regridded to 2∘ × 3∘ to be comparable to the model data described below (Sect. ). The climatology (for the period 1851–2014) was removed to produce monthly anomalies, which were then averaged to annual resolution.

As noted in Sect. , the ENSO-like temperature pattern is similar to the IPO. Regardless of the directionality of influence between the two modes, the long-term ENSO-like state may thus be similar to the IPO/PDO phasing. The ENSO-like state (and the associated spatial pattern, here derived from 20CRv2c) is here referred to as ENSO-like.

There are several comprehensive modelling projects with the aim of improving comparability between GCMs produced by different teams. GCMs taking part in these projects perform a set of simulations with standardised forcings and boundary conditions. For this study, the pre-industrial control (piControl; pre-1850 parameters, no external forcings) and historical (AD 1850–2000) runs from the Coupled Model Intercomparison Project 5 CMIP5; were used, in addition to the last millennium (past1000; AD 850–1850) runs from the Paleoclimate Model Intercomparison Project 3 PMIP3;. Of the six GCMs that have all three runs available, two were chosen for their similarity to 20CRv2c in terms of spatial ENSO representation (see Appendix ) for precipitation (climate modelling groups in brackets):

CCSM4 (National Center for Atmospheric Research),

And two were chosen for temperature:

IPSL-CM5A-LR (Institute Pierre Simon Laplace),

Pseudo-proxies are simulated proxies that attempt to mimic various sources of uncertainty inherent in the real proxy records. This ranges from adding white Gaussian noise with a prescribed signal-to-noise (SNR) ratio approximating non-climatic random noise to more sophisticated process-based additions that take into account effects such as dating error, nonlinear and multivariate responses of the proxy sensor to the climate variable, and sampling biases . The utility of any pseudo-proxy exercise lies in the fact that the answer to the question is known as it can be derived directly from the original model dataset. By putting the “signal plus noise” pseudo-proxies through a method to make a reconstruction of the signal, it allows for inferences about the stability and limitations of the method, estimates of uncertainties due to noise and other proxy record characteristics, and, as highlighted by the method used here, it provides a way of objectively and systematically selecting the most appropriate data seefor an introduction to pseudoproxy experiments.

Ideally, all pseudo-proxies in this study would be created from proxy system models PSMs; e.g.. Unfortunately, many proxies (e.g. δ18O from corals or speleothems) would require isotope-enabled GCMs, which are not available for the model runs used in this study. Tree ring widths (TRWs), however, can easily be simulated using the VS-Lite Model, which is a freely available PSM designed to estimate TRW based on minimal climatic input . It is a simplified version of the full Vaganov–Shashkin model and only requires temperature, precipitation, and latitude information. All TRW records in the proxy dataset used in this study were thus represented using VS-Lite-derived pseudo-TRW series. For the rest of the proxies, the GCM raw temperature or precipitation series were used.

Coral δ18O is known to be particularly vulnerable to showing multivariate responses, depending on both the δ18O of the seawater (which can be altered through changes in sea surface salinity (SSS) linked to ocean circulation or precipitation amount) and SST, which is usually the desired variable . Since there is no simple method of determining the extent of this contamination of the SST signal without an isotope-enabled GCM and coral PSM, the decision has been made here to exclude all coral δ18O records. Other coral proxies such as Mg / Ca or Sr / Ca have been retained as they are more directly associated with SST variations. Exclusion of these coral records equates to the loss of 12 potential proxies that meet the minimum length criterion. Testing showed that the exclusion of these proxies did not alter the conclusions of this paper (not shown).

White Gaussian noise was added to all model temperature, precipitation, and TRW series. Where the original publications or in the case of the coral records, provided an indication of the strength of the proxy–climate relationship (e.g. R value), the SNR was calculated. For all other records, a prescribed SNR of 0.4 (which corresponds to an R value of ∼± 0.38) was used as this has been shown to be a realistic average . The median calculated SNR was 0.63 overall, 0.62 for precipitation, and 0.58 for temperature proxies, suggesting that the prescribed SNR of 0.4 is a conservative estimate. The pseudo-proxies were also degraded to reflect the length, time span, and resolution of the real proxies.

The creation of a network ensemble was done using a calibration–validation scheme to assess the ability of various pseudo-proxy combinations to reconstruct multi-decadal ENSO-like precipitation or temperature variations over the past millennium. As 20CRv2c only covers ∼ 160 years, it is not suitable for testing over these time spans and the past1000 runs from the GCMs were used instead. To account for the fact that the ENSO patterns in the GCMs are different from the pattern in 20CRv2c (and the real ENSO pattern is likely to be different again), two different GCMs are used for the calibration and validation stages. This means that the sensitivity of the networks to the shape of the ENSO-like pattern is tested. GCM selection is described in Appendix . The precipitation and temperature calibration GCMs (GCMcal) were CCSM4 and ISPL-CM5A-LR respectively; the corresponding validation GCMs (GCMval) were GISS-E2-R and BCC-CSM1-1.

Using the GCMcal past1000 dataset, 1000 proxy networks were created via an “add-one-in” pseudo-proxy algorithm that automatically builds a network based on how much each proxy improves the reconstructive power of the network (Fig. ). Similar to a forward stepwise regression procedure, GCMcal-derived pseudo-proxies are gradually added to a base network of zero proxies, testing the quality of the network with each addition, until all proxies have been incorporated (Fig. a, b). The final optimal network is the one that performed best over all steps (Fig. c). By repeating the process 1000 times, adding different random noise series to the pseudo-proxies each iteration, it addresses the influence of stochastic processes on the ability of a proxy network to optimally reconstruct the large-scale ENSO pattern.

The reconstruction process itself is a weighted average approach, where the proxy weights are based on the ENSO-like empirical orthogonal function (EOF) pattern of the GCMcal past1000 run (for the add-one-in network building) or 20CRv2c (for the final reconstruction). First, all (pseudo)-proxies in the network were normalised to a common period of at least 100 years (see Sect. ) and transformed using an inverse transform sampling ITS; to approach a normal distribution. The EOF values w at the proxy locations i were scaled such that their absolute sum at each time step t is 1 (Eq. ). This EOF scaling deals with the fact that the number of proxies available changes over time, preventing more proxy-dense periods from being amplified. Each proxy series pi was then weighted by its corresponding (scaled, time variable) EOF value wi, and the n-weighted proxy series were summed to create a single reconstruction series ENSOr (Eq. ). This is essentially a sparse reconstruction of the PC, which is the dot product of the full raw dataset and EOF. The quality of a network was assessed by comparing ENSOr with the principal component (PC) using the Pearson rank correlation R (see Appendix ).

Validation was performed in two steps. First, the 1000 networks produced with the GCMcal were used to make reconstructions using GCMval past1000 data and the GCMcal EOF. Using data from a different GCM ensures complete separation between the calibration and validation periods and tests the sensitivity of the networks to the spatial stability of the EOF pattern as the ENSO-like EOFs from each model and from 20CRv2c are different. The switch from GCMcal to GCMval thus mirrors the switch between the GCMs and 20CRv2c. Each network was reconstructed 1000 times using GCMval pseudo-proxies, again adding different noise realisations for each iteration. Validation test scores were calculated to check the quality of these validation reconstructions compared to the validation PC (calculated using EOFcal and GCMval past1000 data). Second, critical values for the validation test scores were calculated by repeating the first validation step but using the GCMval piControl run. If the validation R value of a network failed to exceed Rcrit, its reconstruction was deemed to be no better than random noise and was consequently discarded.

The remaining networks were used to create an ensemble of ENSOrs using the real proxy data. The proxy records were first normalised to account for the different units (Eq. ) and were subjected to an ITS transform before undergoing the same reconstruction process used in the network creation. All ensemble members (ENSOr) were then re-normalised to the reference period 0–650 yr BP to ensure comparability. The final ENSO reconstruction was taken as the ensemble mean, while the ensemble range represents part of its uncertainty envelope.

The last step in creating the reconstruction was calculating the final error range. RMSEs were calculated for each network during validation, providing 1000 error estimates for each ensemble member. The 95th percentile for each member was calculated from this and added and subtracted from the ENSOr series to find the maximum and minimum error limits. The uncertainty envelope around the final ENSO reconstruction (i.e. the ensemble mean) is thus a combination of the reconstruction ensemble range and the error ranges for individual ensemble members.

The absence of a known reference period to which the reconstructions can be calibrated precludes any absolute comparison of the result with recent trends. However, it is possible to ascertain whether the MCA and the LIA differ significantly in how El Niño-like they are. Evaluating the LIA–MCA difference also directly removes the bias introduced by taking any reference period . To do this, the means over the two periods were taken and the MCA mean was subtracted from the LIA mean. If the difference is significantly greater than zero, the LIA is more El Niño-like than the MCA; if the difference is significantly less than zero, the MCA is more El Niño-like than the LIA.

Figure  shows the correlation between 1000 randomly chosen combinations of temperature and precipitation ensemble members as an indication of the agreement between the two climate variables. There is no correlation – positive or negative – apparent between the temperature and the precipitation reconstructions, neither over the entire 1500 years nor over the MCA or LIA individually. Whether this is a true physical phenomenon or simply a reflection of the high uncertainty in the reconstructions is difficult to separate. Therefore, it is not possible to categorically determine a systematic difference between the ENSO signals in temperature and precipitation proxies.

The definitions of the MCA and the LIA used here are based on those given by ; there are many alternative definitions, however . To test the sensitivity of the results to the definition of these periods, we recalculated the LIA–MCA difference using two widely used alternative definitions: from (MCA = AD 950–1250, LIA = 1400–1700) and the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report MCA = AD 950–1250, LIA = 1450–1850;. Figure  shows the range of LIA–MCA differences for the individual members within the precipitation and temperature ensembles, using the three definitions. Using the definition, the precipitation interquartile range indicates that the LIA is more El Niño-like than the MCA, though the difference is statistically insignificant (p=0.22). For temperature, there is no evidence of any difference between the ENSO-like state of the MCA and the LIA, with a median value very close to 0 (p=0.48). There are also many more outliers (i.e. values outside the 95 % confidence interval) compared to precipitation, again reflecting the high uncertainty in the temperature reconstruction. Applying the definitions used by or only makes minor, and largely statistically insignificant, differences. For precipitation, the difference between the two periods is more pronounced for the alternative definitions, with a weakly significantly more El Niño-like LIA (p<0.1). For temperature there is very little change; although the median is negative for the alternative definitions, the interquartile range still encompasses zero. The precipitation reconstruction thus qualitatively suggests that the LIA was more El Niño-like than the MCA, but our conclusion that there is no evidence for any precipitation–temperature correlation stands.

There may be alternative interpretations of the reconstructions presented here due to the fact that ENSO interacts with various other climatic phenomena. The ITCZ is a zone of low-level atmospheric convergence that lies over the warmest water and creates substantial positive precipitation anomalies. It follows a seasonal migratory pattern, moving southwards towards the Equator during the boreal winter and retreating northwards during the summer months. As mentioned in the Introduction (Sect. ), there is a significant link between the movement of the ITCZ and ENSO state of the climate. This is thought to be true on interannual to millennial timescales . On decadal to centennial timescales, proxy and modelling evidence points to a potential NH temperature forcing on the ITCZ, causing it to shift southwards in response to cooler NH temperatures. This hypothesis has been invoked to explain an apparent southward shift of the ITCZ during the LIA . Similarly, there is evidence for a northward shift of the ITCZ during the MCA . A southward shift is analogous to an El Niño-like state , suggesting that the MCA was characterised by a La Niña-like climate state and the LIA by an El Niño-like state. However, recent studies hint at an expansion and contraction of the ITCZ in the West Pacific during the MCA and LIA respectively , accompanied by a respective weakening and strengthening of the Pacific Walker Circulation (PWC). El Niño is characterised by a weakening in the PWC, which would imply a La Niña-like state during the LIA.

The most frequently used precipitation proxies (Fig. ) are located in the West Pacific, which is an important region for ENSO, partly due to the relatively large latitudinal migration of the ITCZ. The precipitation reconstruction presented here suggests a slightly El Niño-like LIA (Fig. ), which appears congruous with a southward shift of the ITCZ (and a weakening of the PWC), but not with a contraction of the ITCZ. However, inspection of the West Pacific proxy records indicates that all but two records are assigned negative EOF weights (i.e. their locations experience drought during El Niño), including the most frequently used and most heavily weighted proxies (Fig. ). If the ITCZ did contract during the LIA, this could show up in the ensemble as an El Niño-like shift as these heavily weighted proxies would have experienced drought. Nevertheless, the ensemble is not solely based on these Western Pacific proxies, instead incorporating information from across the Pacific Basin. Thus, while it is possible that a contraction of the ITCZ influenced the results, this is (at least partially) mitigated by proxies in other locations. Further examination would be needed to conclusively determine the extent to which the ITCZ plays a role in driving the precipitation reconstruction here.

As mentioned in Sect. , the interpretation of the reconstructions is potentially confounded by interactions between ENSO and the PDO/IPO. The two (pseudo)-oscillations are known to share many similarities in their spatial pattern , and the temperature EOF used in this study (Fig. ) is indeed very similar to the IPO pattern as reported in . Many proxy records used here have decadal or lower resolution (Appendix ), and the 30-year averaging applied here brings the reconstructions into the realm of IPO/PDO variability. Moreover, many records, for example the North American tree rings, lie in PDO-sensitive North America . This again raises the issue of how individual proxies are interpreted, potentially changing proxy–climate relationships at different timescales. Many proxy records of low resolution have been interpreted as ENSO reconstructions see based on modern-day climate–proxy interactions, just as the reconstructions presented in this paper are based on modern-day (interannual) spatial ENSO patterns.

Comparison of the precipitation reconstruction in this study with a reconstruction of the PDO based on North American tree rings over AD 993–1996 shows a slight tendency for the precipitation and PDO series to have the same sign over the MCA and LIA separately, but the relationships are not statistically significant. There is no indication of any relationship between the PDO and the temperature reconstructions, despite the fact that many of the temperature proxies are located in potentially PDO-sensitive areas (most notably North America). find a strongly negative PDO during the MCA (roughly equivalent to a La Niña-like spatial pattern), which corresponds to the qualitatively La Niña-like tendency of the precipitation reconstruction presented here. find no significant correlation between Boreal winter NINO3 SST and a 9-year smoothed reconstruction of the Asian expression of the PDO based on East Asian tree rings as opposed to the North American tree rings used by, for example,, suggesting that the ENSO–PDO link may be spatially variable. There is also no statistically significant correlation between the temperature or precipitation reconstructions and this Asian PDO reconstruction. The lack of co-variability between the reconstructions presented here and these PDO reconstructions may be due to the fact that this study relies on a wider proxy network that takes into account non-Pacific locations. Another possibility is that the IPO/PDO oscillation and spatial pattern is not robust further back in time, as suggested by and . The resolution of proxy data employed in this study prevents a robust separation of variability on ENSO and IPO/PDO timescales, leaving open the question of how these oscillations influence each other.

Not addressed in this study is the role of different “flavours” of ENSO patterns. A different type of ENSO pattern, first defined by and dubbed ENSO Modoki, differs from the traditional (canonical) ENSO pattern in the shift of positive SST anomalies from the West Pacific (mainly in NINO3 and NINO3.4) to the central Pacific (NINO4; 170–120∘ W and 5∘ S–5∘ N) and its mid-latitude teleconnections. It is sometimes defined as the EOF2 of detrended SST data note that the data in this study were not detrended; hence, here it would be EOF3; or a combination of EOF1 and EOF2 . Some modelling studies suggest that ENSO Modoki will increase in frequency compared to canonical ENSO as a result of anthropogenic climate change , and there is some model evidence that ENSO Modoki was also more common in the mid-Holocene . The difference in equatorial spatial pattern and teleconnections has implications for the interpretation of the proxy reconstructions in this study as ENSO-Modoki-like climate change may appear here as a reduction in ENSO-like activity.

The poor quality of the temperature reconstruction, which limits the statistical robustness of the precipitation–temperature comparison, is likely due to the low number and unequal distribution of available data locations. Most temperature proxies are located in teleconnected regions outside the ENSO source region, which have been shown to be subject to more temporal variability in precipitation–temperature relationships . A multi-region tree ring reconstruction of ENSO variability displays substantial variability in the strength of ENSO teleconnections over time and space . The authors find that the Pacific Northwest and Texas–Mexico regions show highly unstable teleconnections (although there is no discussion on whether this is related to the different ENSO flavours). This may explain the lack of signal in the temperature reconstruction presented here as many of the temperature proxies are located in these teleconnected regions (Fig. ). If the strength of the teleconnection has indeed changed over time, the weightings based on modern-day ENSO patterns would not reflect this; thus, this reconstruction should be regarded as an indication of change of the modern-day ENSO-like climate pattern only. Without proxies located in the centre of action or more robustly teleconnected areas, the loss of signal due to unstable teleconnections can be expected to be substantial, as suggested by the results presented here.

An interesting observation of the EOF maps presented here (Figs.  and ) is the low to no correlation between EOF weighting (bubble shading) and how often proxies are used (bubble size). Correlations of temperature proxy frequency of occurrence versus GCM-derived and 20CRv2c-derived EOF weighting are 0.23 and 0.20 respectively (p<0.05); there is no significant correlation for temperature proxies (p>0.54). Two possible explanations for this are (i) that the climatic noise in the high-occurrence but low-weighted areas is less spatially correlated with the noise elsewhere than in the low-occurrence but higher-weighted areas or (ii) that the length and resolution of the proxy records have a more important effect on a proxy's utility than its weighting. For instance, the proxies off the Australian coast and in the western Pacific Islands are mostly short (<500 years) coral records; while several of them have high weighting, their frequency of occurrence is very low. The proxy at the southern tip of Australia, in contrast, is a ∼3600-year-long tree ring record and is the most frequently used temperature proxy. Overall, however, temperature proxy length is only very weakly correlated to occurrence frequency (R=0.17,p<0.05). The SNR assigned to the temperature pseudo-proxies is similarly only very weakly correlated to frequency (R=0.13,p<0.05). In the precipitation case, neither length nor SNR are significantly correlated to how often the proxies occur in the ensemble. The selection process is likely driven by a combination of these factors rather than any single factor and is modulated by the number of proxies available. More detailed analysis will be needed to elucidate this.

The method set out in this study is one of few that attempt to take into account the effect of real spatial and temporal patterns of proxy records, thus increasing our confidence in their ability to accurately evaluate the effectiveness of the networks. To our knowledge, this is the only study in which realistic temporal proxy resolution in addition to their length has been taken into account by the pseudo-proxies. This is an improvement of the pseudo-proxy design used by, for example, , who take into consideration the declining proxy availability back in time but not their resolution. The authors find that this already significantly impacts the quality of multi-proxy reconstructions; thus, the inclusion of proxy resolution as done here is likely to have further impacts. More extensive research is needed to quantify this however.

The optimal network creation still has scope for improvement. Although we have screened for maximum dating errors, its effect on the included proxies is not explicitly assessed. This issue is often neglected in (multi)-proxy reconstructions but seefor a recent effort to address it systematically. Moreover, the noise simulation used here is relatively simplistic; the use of a wider noise spectrum (including red, and possibly even blue, noise) may alter the composition of the networks and references therein. However, the issue remains that there is no easy way to determine the real noise spectrum of the proxies. With the advent of more isotope-enabled GCM simulations, further improvement could come from the use of more proxy system models to more accurately estimate the proxy–climate relationships for all types of proxies see.

The choice of dataset from which to derive an EOF is also a source of uncertainty see as differences in the EOF pattern will affect the weighting of the proxies. This is particularly pertinent for the precipitation reconstruction as the modern-day ENSO precipitation signature is much less well-established than for temperature due to less and lower-quality instrumental data. This is partially tested by using different GCMs to calibrate and validate the proxy networks. However, the true ENSO-like pattern has been non-stationary over time, as has been shown to be true in 20CRv2 for the North Atlantic Oscillation (NAO) and Pacific North American pattern (PNA), for example . We tested the stability of the 20CRv2c temperature EOF used in this study by recalculating it for a running 30-year window and found substantial variability in the spatial pattern and amount of variance captured by the EOF. Further investigation is necessary to explore whether this result is an artefact of internal variability, is due to uncertainties in the reanalysis dataset, or reflects real changes in the nature of ENSO. Nevertheless, it highlights the vulnerability of the majority of ENSO reconstructions (including ours) to the assumption that the modern-day ENSO is a good analogue for the past.