Quantitative reconstructions of past climates are an important resource for evaluating how well climate models reproduce climate changes. One widely used statistical approach for making such reconstructions from fossil biotic assemblages is weighted averaging partial least-squares regression (WA-PLS). There is however a known tendency for WA-PLS to yield reconstructions compressed towards the centre of the climate range used for calibration, potentially biasing the reconstructed past climates. We present an improvement of WA-PLS by assuming that: (i) the theoretical abundance of each taxon is unimodal with respect to the climate variable considered; (ii) observed taxon abundances follow a multinomial distribution in which the total abundance of a sample is climatically uninformative; and (iii) the estimate of the climate value at a given site and time makes the observation most probable, i.e. it maximizes the log-likelihood function. This climate estimate is approximated by weighting taxon abundances in WA-PLS by the inverse square of their climate tolerances. We further improve the approach by considering the frequency (  fx ) of the climate variable in the training dataset. Tolerance-weighted WA-PLS with fx correction greatly reduces the compression bias, compared with WA-PLS, and improves model performance in reconstructions based on an extensive modern pollen dataset.

There are large uncertainties in the estimation of greenhouse-gas climate feedback. Recent observations do not provide strong constraints because they are short and complicated by human interventions, while model-based estimates differ considerably. Rapid climate changes during the last glacial period (Dansgaard-Oeschger events), observed near-globally, were comparable in both rate and magnitude to current and projected 21st century climate warming and therefore provide a relevant constraint on feedback strength. Here we use these events to quantify the centennial-scale feedback strength of CO2, CH4 and N2O by relating global mean temperature changes, simulated by an appropriately forced low-resolution climate model, to the radiative forcing of these greenhouse gases derived from their concentration changes in ice-core records. We derive feedback estimates (expressed as dimensionless gain) of 0.14 ± 0.04 for CO2, 0.10 ± 0.02 for CH4, and 0.09 ± 0.03 for N2O. This indicates that much lower or higher estimates of gains, particularly some previously published values for CO2, are unrealistic.