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Using paleoclimate proxy-data to select optimal realisations in an ensemble of simulations of the climate of the past millennium

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Abstract

We present and describe in detail the advantages and limitations of a technique that combines in an optimal way model results and proxy-data time series in order to obtain states of the climate system consistent with model physics, reconstruction of past radiative forcing and proxy records. To achieve this goal, we select among an ensemble of simulations covering the last millennium performed with a low-resolution 3-D climate model the ones that minimise a cost function. This cost function measures the misfit between model results and proxy records. In the framework of the tests performed here, an ensemble of 30 to 40 simulations appears sufficient to reach reasonable correlations between model results and reconstructions, in configurations for which a small amount of data is available as well as in data-rich areas. Preliminary applications of the technique show that it can be used to provide reconstructions of past large-scale temperature changes, complementary to the ones obtained by statistical methods. Furthermore, as model results include a representation of atmospheric and oceanic circulations, it can be used to provide insights into some amplification mechanisms responsible for past temperature changes. On the other hand, if the number of proxy records is too low, it could not be used to provide reconstructions of past changes at a regional scale.

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Acknowledgements

We would like to thank J. Luterbacher for sending us his reconstruction of European temperatures. M. Collins and two anonymous referees made very useful comments on an earlier version of this manuscript. H. Goosse is Research Associate with the Fonds National de la Recherche Scientifique (Belgium). H. Renssen is sponsored by the Netherlands Organization for Scientific Research (N.W.O). A. Timmermann is supported by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) through its sponsorship of the International Pacific Research Center. M.E. Mann was supported by the NOAA- AND NSF-supported “Earth Systems History” program. This study was carried out as part of the Second Multiannual Scientific Support Plan for a Sustainable Development Policy (Belgian Federal Science Policy Office, contracts EV/10/7D and EV/10/9A) and the Action Concertée Incitative Changement Climatique (project Changement Climatique et Cryosphère) from the French Ministry of Research. This is IPRC Publication # 370 SOEST publication # 6726.

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Correspondence to Hugues Goosse.

Appendices

Appendix 1: Influence of the choice of the cost function

In the main text, in the computation of the cost function (hereafter referred to as CF1), all the weights w i have the same value (see Sect. 4). Here, we study the influence of the choice of the cost function by selecting different w i . In the first additional CF (CF2), w i is proportional to the correlation between the proxy-based reconstruction and instrumental temperature data (Table 2). The goal is to give more weight in the evaluation of the cost function to the proxy record that provides a better reconstruction of the temperature. Finally, in the second additional CF (CF3), the data density is taken into account in a simple way: the weight of a record is proportional to its correlation with instrumental data as for CF2 but, in addition, is divided by the number of records in the same region. As WUM, WUB, JTL (Table 2) all provide information on the Western United states and Canada, their weight is divided by three while the weight of WGF and WGV (Western Greenland) is divided by two.

As expected, the correlations using CF2 are generally lower than with CF1 for the records that exhibit a low correlation with instrumental data (e.g. CSC), while they are greater for the records that exhibit a high correlation with instrumental data (e.g. PUB and LCV) (Table 4). For CF3, the correlations tend to be lower for the records located in data-rich regions than with CF2 (e.g. WUM, JTL) while the other correlations do not change significantly.

Table 4 Correlation between model simulations and proxy-reconstruction for a 25 year averaging period

The convergence of the method is similar for the three cost function tested. Nevertheless, Fig. 10 shows that using CF2, the value of the cost function is lower than using CF1. This means that the model is generally in closer agreement with proxy records at locations where the proxy has itself a good correlation with instrumental data and shows less good agreement at locations where this correlation is lower (e.g. CSC or MOD, see Table 3). Nevertheless, this is not universally true. For example, the agreement between model results and proxy records is good for record CHY though the correlation with instrumental data is low. On the other hand, CF3 yields nearly the same correlation as CF2. As a consequence, taking into account the density of the proxies for the different regions does not seem to have an important influence on the value of the cost function in the present framework.

Fig. 10
figure 10

Evolution of the cost function using 12 proxy records averaged over the last 1,000 years as a function of the number of experiments for different cost functions

Appendix 2: Testing the technique using synthetic time series

A lack of consistency between the proxy records and the best pseudo-simulation selected by the technique proposed here could be due to different factors. First, this could be due to a too small number of simulations that does not allow finding a good analogue to the real evolution of the climate system. Second, this could be related to model deficiencies, the model not being able to simulate correctly some processes at large-scale or at the scale recorded by the proxy. Third, the uncertainties on the forcing evolution are quite large with a potential impact on the simulated results. Fourth, proxies do not only record changes in climatic conditions, they are also affected by non-climatic factors. The interpretation of proxy-record is also sometimes very difficult (e.g. Bradley 1999; Briffa 2000; Jones and Mann 2004). Among all those possible sources of discrepancy between model and observations, only the first one is related to the technique itself.

In order to make tests focussed only on the technique, we have made one additional simulation with ECBILT–CLIO–VECODE driven by both natural and anthropogenic forcings as in the ensemble of 105 simulation analysed here. From this simulation, we have extracted 12 time series at the same locations as the ones used in Sect. 4. Using, those 12 time series as pseudo-proxies, we have then tried to find the simulations among the ensemble of 105 which were the closest to the additional experiment. In this case, all the differences between the pseudo-proxies and the best pseudo-simulation will be related to the technique itself. Model errors would have no impact, as the same model is applied in all the simulations, the same forcing is used in the ensemble and in the additional simulation and the pseudo-proxies are perfect indicators of model temperature.

Table 5 provides results that are very similar to Table 3 when real proxies were used. The correlation is better for pseudo-proxies as expected but the difference is not very large. When using the pseudo-proxies, the cost function for 12 data using a 25-year averaging period, has a value of 0.60, while it was 0.65 for real proxies. When the number of proxies used to constrain the choice of the best simulation is reduced, the correlation between pseudo-proxies and the best pseudo-simulation is lower at locations not used in the computation of CF. For some locations, the decrease is small. For instance, the correlation between the pseudo-proxy record for WUB and the best pseudo-simulation using eight data (two in North America) is 0.70. This contrasts with the real proxy for which the correlation drops to 0.33 in the same type of experiment. Apparently, the constraint in the model results is still high enough for the Northern America when using two pseudo-proxies. In particular, the area corresponding to WUM and WUB are partly overlapping (Jones and Mann 2004). On the other hand, when using real proxies, we must take into account that the correlation between the proxy records WUB and WUM is quite weak. In such a case, constraining model results using WUM is thus of little help in obtaining a good correlation between WUB and the best pseudo-simulation. For some other locations, like WGV, the constraint in nearly the same area but for a different season (WGF) is not sufficient to give a good correlation between the pseudo-proxy records and the best pseudo-simulation (Table 5). For TOB, when using four proxies, the correlation is even smaller than 0.20. On average, the correlations using four proxies are not very high at locations not used in the computation of CF, but still higher than using the real proxies.

Table 5 Correlation between the 105 model simulations and an additional independent simulation performed with the model for a 25 year averaging period

We have also performed the same type of test, but this time using a higher density of proxies in a particular region (Table 6). To do so, in addition to the pseudo-proxy records used above, we have selected 8 additional pseudo-proxies: low countries in summer (LCS) and in winter (LCW) (in order to avoid duplicate information LCV is not used anymore), Western Russia in summer (RUS) and Winter (RUW), Switzerland in summer (SSB) and in winter (SWM), Eastern France in summer (BSC), Czech lands in summer (CLS) and winter (CLW).

Table 6 Correlation between the 105 model simulations and an additional independent simulation performed with the model for a 25 year averaging period

Again, in some case, the correlation between the pseudo-proxy and the best simulation can be very good for some pseudo-proxies that are not used in the computation of CF. For instance, the correlation for Eastern France (BSC) is very high, the information form Switzerland (SSB, SWM), an adjacent grid box compare to the one corresponding to eastern France in the model, providing a strong constraint on the choice of the best simulation. On the other hand, for TOB, the correlation is very low as soon as this record is not used in the computation of CF, the pseudo proxies in the nearby Western Russia being of little help.

Those experiments using pseudo-proxies show thus results similar to the ones obtained using real proxies. Extrapolating toward regions where no proxy is available should thus be performed with great care. In some cases, the information contained in nearby location could be sufficient but it is not a general rule. It is necessary to test in each case if this extrapolation is reasonable, providing robust results in the model world, as for instance done in Sect. 6 (Fig. 8). The potential inadequacies in the forcing, model formulation or in the interpretation of the proxies provide additional source of trouble in this extrapolation.

On the other hand, for annual mean hemispheric temperature, the correlation between the best pseudo-simulation and the one of the additional simulation is higher than 0.9, if more than eight pseudo-proxy records are used. For an average over Europe, the correlation between the best pseudo-simulation and the additional simulation is higher than 0.80 for annual, summer and winter mean temperatures, except in the cases where only four pseudo-proxy records are used in Europe. This shows that using the best pseudo-simulation to make an average over a relatively large region is a much safer procedure than the extrapolation to region where no data is available.

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Goosse, H., Renssen, H., Timmermann, A. et al. Using paleoclimate proxy-data to select optimal realisations in an ensemble of simulations of the climate of the past millennium. Clim Dyn 27, 165–184 (2006). https://doi.org/10.1007/s00382-006-0128-6

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