Reconstructing the NH Mean Temperature: Can Underestimation of Trends and Variability Be Avoided?

Abstract

Abstract There are indications that hemispheric-mean climate reconstructions seriously underestimate the amplitude of low-frequency variability and trends. Some of the theory of linear regression and error-in-variables models is reviewed to identify the sources of this problem. On the basis of the insight gained, a reconstruction method that is supposed to minimize the underestimation is formulated. The method consists of reconstructing the local temperatures at the geographical locations of the proxies, followed by calculating the hemispheric average. The method is tested by applying it to an ensemble of surrogate temperature fields based on two climate simulations covering the last 500 and 1000 yr. Compared to the regularized expectation maximization (RegEM) truncated total least squares (TTLS) method and a composite-plus-scale method—two methods recently used in the literature—the new method strongly improves the behavior regarding low-frequency variability and trends. The potential importance in real-world situations is demonstrated by applying the methods to a set of 14 decadally smoothed proxies. Here the new method shows much larger low-frequency variability and a much colder preindustrial temperature level than the other reconstruction methods. However, this should mainly be seen as a demonstration of the potential losses and gains of variability, as the reconstructions based on the 14 decadally smoothed proxies are not very robust.