Evaluation of statistical climate reconstruction methods based on pseudoproxy experiments using linear and machine-learning methods

Abstract

Abstract. Three different climate field reconstruction (CFR) methods are employed to reconstruct spatially resolved North Atlantic–European (NAE) and Northern Hemisphere (NH) summer temperatures over the past millennium from proxy records. These are tested in the framework of pseudoproxy experiments derived from two climate simulations with comprehensive Earth system models. Two of these methods are traditional multivariate linear methods (principal component regression, PCR, and canonical correlation analysis, CCA), whereas the third method (bidirectional long short-term memory neural network, Bi-LSTM) belongs to the category of machine-learning methods. In contrast to PCR and CCA, Bi-LSTM does not need to assume a linear and temporally stable relationship between the underlying proxy network and the target climate field. In addition, Bi-LSTM naturally incorporates information about the serial correlation of the time series. Our working hypothesis is that the Bi-LSTM method will achieve a better reconstruction of the amplitude of past temperature variability. In all tests, the calibration period was set to the observational period, while the validation period was set to the pre-industrial centuries. All three methods tested herein achieve reasonable reconstruction performance on both spatial and temporal scales, with the exception of an overestimation of the interannual variance by PCR, which may be due to overfitting resulting from the rather short length of the calibration period and the large number of predictors. Generally, the reconstruction skill is higher in regions with denser proxy coverage, but it is also reasonably high in proxy-free areas due to climate teleconnections. All three CFR methodologies generally tend to more strongly underestimate the variability of spatially averaged temperature indices as more noise is introduced into the pseudoproxies. The Bi-LSTM method tested in our experiments using a limited calibration dataset shows relatively worse reconstruction skills compared to PCR and CCA, and therefore our working hypothesis that a more complex machine-learning method would provide better reconstructions for temperature fields was not confirmed. In this particular application with pseudoproxies, the implied link between proxies and climate fields is probably close to linear. However, a certain degree of reconstruction performance achieved by the nonlinear LSTM method shows that skill can be achieved even when using small samples with limited datasets, which indicates that Bi-LSTM can be a tool for exploring the suitability of nonlinear CFRs, especially in small data regimes.