Technical note: Considerations on using uncertain proxies in the analogue method for spatiotemporal reconstructions of millennial-scale climate

Abstract

Inferences about climate states and climate variability of the Holocene and the deglaciation rely on sparse paleo-observational proxy data. Combining these proxies with output from climate simulations is a means for increasing the understanding of the climate throughout the last tens of thousands of years. The analogue method is one approach to do this. The method takes a number of sparse proxy records and then searches within a pool of more complete information (e.g., model simulations) for analogues according to a similarity criterion. The analogue method is non-linear and allows considering the spatial covariance among proxy records. Beyond the last two millennia, we have to rely on proxies that are not only sparse in space but also irregular in time and with considerably uncertain dating. This poses additional challenges for the analogue method, which have seldom been addressed previously. The method has to address the uncertainty of the proxy-inferred variables as well as the uncertain dating. It has to cope with the irregular and non-synchronous sampling of different proxies. Here, we describe an implementation of the analogue method including a specific way of addressing these obstacles. We include the uncertainty in our proxy estimates by using “ellipses of tolerance” for tuples of individual proxy values and dates. These ellipses are central to our approach. They describe a region in the plane spanned by proxy dimension and time dimension for which a model analogue is considered to be acceptable. They allow us to consider the dating as well as the data uncertainty. They therefore form the basic criterion for selecting valid analogues. We discuss the benefits and limitations of this approach. The results highlight the potential of the analogue method to reconstruct the climate from the deglaciation up to the late Holocene. However, in the present case, the reconstructions show little variability of their central estimates but large uncertainty ranges. The reconstruction by analogue provides not only a regional average record but also allows assessing the spatial climate field compliant with the used proxy predictors. These fields reveal that uncertainties are also locally large. Our results emphasize the ambiguity of reconstructions from spatially sparse and temporally uncertain, irregularly sampled proxies.