Abstract
Abstract. An important goal of climate research is to determine the causal contribution of human activity to observed changes in the climate system. Methodologically speaking, most climatic causal studies to date have been formulating attribution as a linear regression inference problem. Under this formulation, the inference is often obtained by using the generalized least squares (GLS) estimator after projecting the data on the r leading eigenvectors of the covariance associated with internal variability, which are evaluated from numerical climate models. In this paper, we revisit the problem of obtaining a GLS estimator adapted to this particular situation, in which only the leading eigenvectors of the noise's covariance are assumed to be known. After noting that the eigenvectors associated with the lowest eigenvalues are in general more valuable for inference purposes, we introduce an alternative estimator. Our proposed estimator is shown to outperform the conventional estimator, when using a simulation test bed that represents the 20th century temperature evolution.
Highlights
An important goal of climate research is to determine the causes of past global warming in general and the responsibility of human activity in particular (Hegerl et al, 2007); this question has emerged as a research topic known as detection and attribution (D&A)
D&A studies are usually based on linear regression methods, often referred to in this particular context as optimal fingerprinting, whereby an observed climate change is regarded as a linear combination of several externally forced signals added to internal climate variability (Hasselmann, 1979; Bell, 1986; North et al, 1982; Allen and Tett, 1999; Hegerl and Zwiers, 2011)
We evaluate the performance of the estimators described above, by applying it to simulated values of y obtained from the linear regression equation y = xβ + ν assumed by the model of Eq (1), where the noise ν is simulated from a multivariate Gaussian distribution with covariance and where β = (1, 1) is used
Summary
An important goal of climate research is to determine the causes of past global warming in general and the responsibility of human activity in particular (Hegerl et al, 2007); this question has emerged as a research topic known as detection and attribution (D&A). D&A studies are usually based on linear regression methods, often referred to in this particular context as optimal fingerprinting, whereby an observed climate change is regarded as a linear combination of several externally forced signals added to internal climate variability (Hasselmann, 1979; Bell, 1986; North et al, 1982; Allen and Tett, 1999; Hegerl and Zwiers, 2011). . ., xp) the n×p matrix concatenating the p externally forced signals and ν the internal climate variability noise, the regression equation is as follows:. The results of the inference on the vector of regression coefficients β, and the magnitude of its confidence intervals, determine whether the external signals “are present in the observations” (Hegerl and Zwiers, 2011) and whether or not the observed change is attributable to each forcing.
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