A Methodology for Robust Multiproxy Paleoclimate Reconstructions and Modeling of Temperature Conditional Quantiles

Abstract

Great strides have been made in the field of reconstructing past temperatures based on models relating temperature to temperature-sensitive paleoclimate proxies. One of the goals of such reconstructions is to assess if current climate is anomalous in a millennial context. These regression-based approaches model the conditional mean of the temperature distribution as a function of paleoclimate proxies (or vice versa). Some of the recent focus in the area has considered methods that help reduce the uncertainty inherent in such statistical paleoclimate reconstructions, with the ultimate goal of improving the confidence that can be attached to such endeavors. A second important scientific focus in the subject area is the area of forward models for proxies, the goal of which is to understand the way paleoclimate proxies are driven by temperature and other environmental variables. One of the primary contributions of this article is novel statistical methodology for (i) quantile regression (QR) with autoregressive residual structure, (ii) estimation of corresponding model parameters, (iii) development of a rigorous framework for specifying uncertainty estimates of quantities of interest, yielding (iv) statistical byproducts that address the two scientific foci discussed above. We show that by using the above statistical methodology, we can demonstrably produce a more robust reconstruction than is possible by using conditional-mean-fitting methods. Our reconstruction shares some of the common features of past reconstructions, but we also gain useful insights. More importantly, we are able to demonstrate a significantly smaller uncertainty than that from previous regression methods. In addition, the QR component allows us to model, in a more complete and flexible way than least squares, the conditional distribution of temperature given proxies. This relationship can be used to inform forward models relating how proxies are driven by temperature.

KEY WORDS:

• Principal components
• Quantile regression with time series errors
• Statistical paleoclimate reconstructions
• Uncertainty quantification