Towards variance-conserving reconstructions of climate indices with Gaussian Process Regression in an embedding space

Abstract

We present a new framework for the reconstruction of climate indices based on proxy data such as tree rings. The framework is based on the supervised learning method Gaussian Process Regression (GPR) and aims at preserving the amplitude of past climate variability. It can adequately handle noise-contaminated proxies and variable proxy availability over time. To this end, the GPR is formulated in a modified input space, termed here embedding space. We test the new framework for the reconstruction of the Atlantic multi-decadal variability (AMV) in a controlled environment with pseudo-proxies derived from coupled climate-model simulations. In this test environment, the GPR outperforms benchmark reconstructions based on multi-linear principal component regression. On AMV-relevant timescales, i.e. multi-decadal, the GPR is able to reconstruct the true amplitude of variability even if the proxies contain a realistic non-climatic noise signal and become sparser back in time. Thus, we conclude that the embedded GPR framework is a highly promising tool for climate-index reconstructions.