Identification of linear relationships from noisy data using errors-in-variables models-relevance for reconstruction of past climate from tree-ring and other proxy information

Reliable paleoclimate reconstructions are needed to assess if the recent climatic changes are unusual compared to pre-industrial climate variability. Here, we focus on one important problem in climate reconstructions: Transfer functions relating proxies (predictors) and target climatic quantities (predictands) can be seriously biased when predictand and predictor noise is not adequately accounted for, resulting in biased amplitudes of reconstructed climatic time series. We argue for errors-in-variables models (EVM) for unbiased identification of linear structural relationships between noisy proxies and target climatic quantities by (1) introducing underlying statistical concepts and (2) demonstrating the potential biases of using the EVM approach, the most commonly used direct ordinary least squares (OLS) regression, inverse OLS regression, or the reduced major axis method ('variance matching') with a simulation example of artificial noise-disturbed sinusoidal time series. We then develop an alternative strategy for paleoclimate reconstruction from tree-ring and other proxy data, explicitly accounting for the identified problem.