Inferring climate variability from nonlinear proxies: application to palaeo-ENSO studies

Abstract. Inferring climate from palaeodata frequently assumes a direct, linear relationship between the two, which is seldom met in practice. Here we simulate an idealized proxy characterized by a nonlinear, thresholded relationship with surface temperature, and we demonstrate the pitfalls of ignoring nonlinearities in the proxy–climate relationship. We explore three approaches to using this idealized proxy to infer past climate: (i) methods commonly used in the palaeoclimate literature, without consideration of nonlinearities; (ii) the same methods, after empirically transforming the data to normality to account for nonlinearities; and (iii) using a Bayesian model to invert the mechanistic relationship between the climate and the proxy. We find that neglecting nonlinearity often exaggerates changes in climate variability between different time intervals and leads to reconstructions with poorly quantified uncertainties. In contrast, explicit recognition of the nonlinear relationship, using either a mechanistic model or an empirical transform, yields significantly better estimates of past climate variations, with more accurate uncertainty quantification. We apply these insights to two palaeoclimate settings. Accounting for nonlinearities in the classical sedimentary record from Laguna Pallcacocha leads to quantitative departures from the results of the original study, and it markedly affects the detection of variance changes over time. A comparison with the Lake Challa record, also a nonlinear proxy for El Niño–Southern Oscillation, illustrates how inter-proxy comparisons may be altered when accounting for nonlinearity. The results hold implications for how univariate, nonlinear recorders of normally distributed climate variables are interpreted, compared to other proxy records, and incorporated into multiproxy reconstructions.