Reconstructions of North Hemisphere summer temperature based on tree-ring proxies using linear and machine learning methods

In order to improve the climate reconstruction quality and better understand last millennium temperature variability, a reservoir computing (RC) method: Echo State Network (ESN) is applied for the reconstruction of the North Hemisphere summer seasonal temperature. ESN, a specialized type of recurrent neural network method, belongs to the family of machine learning methods, which is suitable for mapping complex systems with chaotic dynamics, for instance the hemisphere temperature variability. ESN is the widely implementation of RC and employs a structure with neuron-like nodes and recurrent connections, the internal reservoir, to handle the sequential data. It consists of three layers: input layer, reservoir layer and output layer; a randomly generated reservoir in ESN preserves a set of nonlinear transformations of the input data and a linear regression criterion is employed for its training process to optimize the parameters. ESN could provide an alternative nonlinear machine learning method that might improve the prediction or reconstruction skills of paleoclimate. In this context, we first conduct pseudoproxy experiments (PPEs) using three different Earth System Models (ESM), including Community Climate System Model CCSM4, the Max-Planck-Institute climate model MPI-ESM-P and the Community Earth System Model CESM1-CAM5. Two classical multivariable linear regression methods, Principal component regression and Canonical correlation analysis, are also employed as a benchmark. Among the three models providing climate simulations of the past millennium, both derived spatial and temporal reconstruction results based on PPEs demonstrate that ESN could capture more variance than other two classical methods, and could potentially achieve paleo-temperature reconstruction improvements. This suggests that the ESN machine learning method could be an alternative method for paleoclimate analysis.